LULEA UNIVERSITY OF TECHNOLOGY - Poac.com

LULEA UNIVERSITY OF TECHNOLOGY

@ POAC 89The 10th International Conferenceon Port and Ocean Engineeringunder Arctic Conditions.June 12-16 1989, LuleA, SwedenVOLUME 1Edited byK.B.E AxelssonL.A. FranssonDepartment of Civil EngineeringLuleA University of TechnologyLulei, SwedenTEKNKKA~ O U U I I W ~ Research Report TULEA 1989:08LULEA UNIVERSITY OF TECHNGiOGY

SponsorsMinistry of IndustryLuleA University ofTechnologyThe town of LuleALuleA Harbour AuthorityThe COLDTECH programmeSwedish Building ResearchCouncil (BFR)The National SwedishAdministration ofShipping and NavigationScandinavian Airlines (SAS)Co-sponsorsLe Comite Arctique InternationalNational Science Foundation, USAThe Swedish Ass. of EngineeringIndustries(Sveriges Mekanforbund)Swedish National IndustrialBoard (SIND)SSPA Maritime Consulting ABVBB-SWECOGotaverken Arendal (GVA)Swedish Polar ResearchSecretariatRoyal Swedish Academy ofEngineering Sciences, (IVA)Organizing CommitteeProf K B.E. Axelsson (Chairman)Mr. R. Lindmark (Secretary General)Prof. L.C. ElfgrenDr. S. KnutssonDr. LA FranssonMs C. NilssonMs. L. KarbinPOAC International CommitteeMr. A. Engelbrektsson (President), VBB-SWECO, SwedenProf. G.R Peters (Vice President), Memorial Univ., CanadaProf. P Bruun (Secretary General), NTH, NorwayDr. W Aung, National Science Foundation, USAMr K R Croasdale, Esso Resources, CanadaDr A. Kovacs, CRREL, USADr M Oshima, Mitsui, JapanDr-Ing J.J. Schwarz, HSVA, F R GermanyMr. T. Setchfield, Exxon Production Research Co, USAMr. H. Soininen, WartsilA Marine Ind Inc., FinlandProf P Vartsta, Helsinki Univ of Technology, FinlandDr. W F Weeks, Univ of Alaska, USAHonorary membersProf. T. Carstens, NHL, NorwayProf. P Jumppanen, Wartsila, FinlandProf B. Michel, Laval Univ., CanadaProf. W.M Sackinger, Univ. of Alaska, USAProf. P. Tryde, Technical Univ of Denmark, DenmarkMr. G Viggoson, Icelandic Harbour Authority, IcelandIll

List of reviewers at POAC'89 conferenceAndersson, AnnikaAndersson, Lars-OlovAung, WinAxelsson, KennetBengtsson, LarsBergdahl, LarsBillfalk, LennartBruun, PerCarstens, TorkildCederwall, KlasCederwall, KristerChristensen, FlemmingCox, GordonCroasdale, K RDomaschuk, LenElfgren, LennartEngelbrektsson, AlfForsman, BjornFransson, LennartFrederking, RobertHorrigmoe, GeirHAkansson, BertilHdglund, ErikHogbom, ThomasJansson, Jan-ErikJohansson, BerndtJordaan, I JJumppanen, PauliKovacs, AustinKnutsson, SvenKarna, TuomiLepparanta, MattiLiljestrom, GoranLmet, SveinungMichel, BernardMcKenna, RichardMattaanen, MauriNixon, WilfredOmstedt, AndersOshima, MasanaoPersson, SturePeters, RossRichter-Menge, JacquelineSackinger, WilliamSchwarz, JoachimSandkvist, JimSellgren, AndersSetchfield, TSjolind, Stig-GoranSodhi, DevinderSoininen, HarriStehn, LarsThompson, ThomasTimco, GarryTryde, PerTunik, AlfredUlriksen, PeterVarsta, PetriViggoson, GWeeks, Willy

CONTENTSPAGEPrefacePOAC in the global perspectiveJubilee LecturesPOAC Before - Now - and in the FutureP. Bruun(USA)The Link Across "StoreBaeltf'- Ice Forces on thePiers of the Western BridgeP. Tryde(Norway )Keynote LecturesR. Colony(USAL. Gold( Canada )B. Johansson(Canada)D. Kheisin(USSR)M. Oshima(Japan )J. Sandkvist( Sweden )P. Varsta(Finland)Nansen's LuckHabbakukA State-of-the-Art IcebreakerIce Forces on HydraulicStructuresRecent Ice Sea FieldEngineering Activitiesin the Okhotsk Sea Coastin JapanOil Spills in Arctic Regions -Environmental Hazards andRecovery TechniquesResearch on IcebreakingProcessThe Internal StructureComposition and Propertiesof Brackish Ice from theBay of Bothnia during theBepers-88 ExperimentV0l. 3V0l. 3Vol. 3V0l. 3V0l. 3Vol. 3V0l. 3V0l. 3

PREFACEThese proceedings comprise the papers to be presented at the10th International Conference on Port and Ocean Engineeringunder Arctic Conditions in Lulea, 12-16 June 1989. About 140papers have been submitted and accepted, all of a highscientific standard.The POAC-conferences have been organized biennially since1971, when Professor Per Bruun at the Norwegian Institute ofTechnology in Trondheim took the initiative of organizing aconference within the growing area of arctic technology.This vast field embraces topics from Ice Morphology and IceMechanics over Ice/Structure Interaction, Ice Breaking Technologyand Ice Navigation-Management to Offshore Platforms,Productions Systems and Operation Experiences in the Arctic aswell as Climate and Ice Forecasting. Since 1971, arctictechnology has developed tremendously and the POAC Conferenceshave contributed greatly to the scientific and industrialexchange of ideas. After Trondheim 1971, POAC has been held inReykjavik, Iceland 1973, Fairbanks, Alaska 1975, St John's,Newfoundland 1977, Trondheim 1979, Quebec, Canada 1981,Helsinki, Finland 1983, Narssarssuaq, Greenland 1985 andFairbanks, Alaska 1987.Since the Conference is taking place in northern Sweden, theGulf of Bothnia and the Baltic is, of course, dealt with tosome extent. Here the Remote Sensing Project BEPERS and the newSwedish Ice Breaker Oden could be mentioned.Most of the papers presented at POAC-89 are printed in Vol. 1and 2 of the Proceedings available at the Conference. However,Keynote Lectures and some papers will appear in a postconference volume, Vol. 3, also containing discussions etc.It is an honour for the town of Lulea and for Luleti Universityof Technology to host this 10th POAC. The town of LuleAwas founded in 1621 as a commercial centre and harbour for theimportant trade with the inland of northern Sweden. Lulea issituated close to the Arctic Circle but its harbour has yeararound-trafficeven though the Gulf of Bothnia is ice-coveredfrom December to May. LuleA University is young, it was opened

in 1971, and has, among other areas, focused on Cold RegionTechnology.This conference was organized with financial support from theMinistry of Technology, Lulei University of Technology, thetown of Lulei, the COLDTECH-program, the Swedish BuildingResearch Council, the National Swedish Administration ofShipping and Navigation and Scandinavian Airlines. We areindebted to the POAC International Committee for theirguidance. A special thank goes to the President of POAC, Mr AlfEngelbrektsson and to Prof. Per Bruun for their encouragingsupport.The local planning of the conference has been carried out bya small Organizing Committee at Lulei University which,however, has been supported by an Advisory Committee withrepresentatives from Universities, Research Centres, Industriesand Authorities. The Advisory Committee is gratefully acknowledged.We are also indebted to the many reviewers for theirsuccessful work of improving the papers for the conference.A special acknowledgement is given to Ms Christina Nilssonwho has administrated all questions concerning papers,reviewers and all the work with these proceedings.Finally, we wish to thank all the keynote lecturers and allthe authors of papers for their important scientific contributionas well as all participants for their interest in theconference and their contribution.Kennet B.E. AxelssonLennart A. Fransson

POAC in the global perspectivePretentious though it might appear, I believe that FQBC deserves tobe regarded in the global perspective for a while, before going intoits near-field and the specific agenda for this conference and for thenearest future. Obviously, when entering into the near-field, we willstill be dealing with matters of global concern: Arctic explorationand exploitation, the large-scale energy situation and associatedpollution risk, the coupling between the oil market and the econony ofinvolved nations.We may have different opinions about if or where and when the Arcticresources should be taken advantage of. Whatever the views might be, Ibelieve that the problems have to be discussed cr> a global level andassessed on the basis of increased scientific understanding and technologicalknow-how.Hopefully, I am not mistaken when characterizing the large-scalepolitical situation as fairly premising: increasing international canmunicationsand subsequent understanding of the advantages of ccninomsolutions.As regards the energy situation, the increasing concerns regardingthe envirccmental impacts are also, basically, premising, though thereare sane-times overreactions which are not based on scientific groundsbut on a general suspicion or distrust of natural science and tech-nology, at least the latter. We engineers and scientists, being respcnsiblefor one part or another of the rapid technological developmentof means and methods for energy production, must be prepared forsuch criticism, however. Maybe we have to swallow the unfair parts asa punishnent for our mistakes, when hurrying too eagerly into technicallylimia'ture operations, exposing nature and human beings to unnecessaryrisks. Unfortunately, the exploitation of resources and newtechnology is often a step before the development of the necessarysafety devices and criteria.New, why shouldn't we take the opportunity, offered by the presentoil-market situation, to avoid this phase lag. Let us intensify Arcticresearch and development Instead of cutting the budgets, based onshort-sighted investment plans. Most likely, we will sooner or laterneed the Arctic oil resources, and I believe that it is possible toIncrease our knowledge of the Arctic and to develcpe technical meansand methods sufficiently in the meantime, to fully control even themost unlikely events, let it be extreme ice forces, malfunctions ofequipment or human beings, oil-spill or whatsoever.

The role of PQAC in these preparatory operations is evident:basically to provide a forum for international exchange of informationconcerning research and engineering for activities in Arc-tic marineenvironments and to initiate and encourage international cooperationand coordination of research and development within the Arctic field.In order to emphasize the particular fitness of PQAC for this role,we may refer to acme key points ancng PQAC ' s objectives and charac-teristics:- its efforts to cover the entire field of Arctic Marine Science andTechnology and to concentrate on that field- its continuity and traditions, manifested basically at the biennialconferences since 1971 and relating proceedings- its independence of any particular organization and commercialinterest.Therefore, let us benefit by the 10th conference, not only to canetogether and share today's know-how but also to discuss commoninternational efforts, technical and administrative, to resolve themost important Arctic issues and to provide a reliable and convincingbasis for future operations in the sensitive Arctic environment.The PQAC Internaticmal Committee is responsible for preserving thecontinuity by supporting the national organizers of each conferenceand by promoting international cooperation and coordination thrcughPQAC, activities that must be kept going between the conferences.The potential of the International Committee for overviewiqresearch and development in the member countries and for initiatingcoordinated internationl efforts has not yet been taken full advantageof. Per Bruun has drawn our attention to this fact and suggestedconcrete action plans that he will present at this conference. Ttvameans for implementation will be a topic of high priority on theagenda of the International Committee during the 10th conference. Wehope that all the delegates will participate in the discussions con-earning the future activities of PQAC and I saiggest that you don'thesitate to transfer your ideas to the members of the InternationalCommi-ttee.LuleA, June 1989Alf Engelbrektsson

PAGE1. SEA ICE PROPERTIES1 .I Ice Mor~~loav. I ce -lft etcT. CarstensS. VefsnmoS.M. Lov&s(Norway)R. Colony(USA)M.D. CoonP.A. LauS.H. BaileyB.J. Taylor(USA)D. Dickins( Canada )B. Erlingsson(Norway)L. FranssonL. StehnL. ktr6mB. HakanssonA 0mStedt( Sweden )B. H6kanssonA Omstedt( Sweden)0. JohansenJ.P. MathisenK. Skoqnes(Norway)A.s. Johnsen(Norway)P. KankanpaS(Finland)The Generation of theFoundation for the SkagenSpit, North Jutland,Denmark, by the Actionof Ice, Glacial Eustacyand Rise of Sea Level,Erosion and AccretionDevelopment of Ice DriftModels for the BarentsSeaWanted: A New Metric forSea Ice StrainObservations of Ice FloeStress in the EasternArcticMulti-Year Ice Thicknessin the Beaufort SeaShear-Zones and CoastalSea Ice DeformationsVariation of IceProperties in an Area of1 x 2 km in the Gulf ofBothnia, March 1988Sea Ice Concentrationin the Bothnian SeaObtained from VisualSatellite DataIce Drift and underIce Currents in theBarents SeaRelations between Topand Bottom IceTopography using aScanning SonarStructure of FirstYear Pressure Ridgesin the Baltic Sea17

J.E. LewisM. LepparantaH.B. Granberq(Canada )M.W. MilesR.G. Barry(USA 1D. Myrhauq(Norway)A.C. PalmerI. KonukJ. LoveK. BeenG. Comfort(U.K. )Airborne LaserProfiling of IceRidges in theBaltic SeaLarge-ScaleCharacteristics ofFractures in Multi-Year Arctic Pack IceWater Drag on SeaIce - A RevisitIce Scour MechanismsF Pwrwshasb Small Scale ModellingJ. I. Clark of Iceberg Scouring ofC.M.T. Woodworth- the SeabedLynas(Canada )R. RomagnoliR. Varvelli(ItalyStudy of the Behaviourof Ice Masses in MarineEnvironmentsR.W. Schreiber Multiyear Ridge ForceT.D. RalstonVariabilityD. E. Egging(USA)T. Vinje(Norway)Analysis of Sea Ice Driftin a Coastal Ice ZoneAn Upward Looking SonarIce Draft SeriesVol. 3S.J. Bolsenga(USA)J.P. DempseyY. WeiS. DeFrancoR. RubenR. Frachetti(USA )Certain Properties ofSpectrally Integrated andSpectral Transmittancesof Freshwater Ice From400-700 nmFracture Toughness ofS2 Columnar FreshwaterIce: Crack Length andSpecimen Size Effects -Part 11

M. A. LanqeH. HellmannJ.A. Richter-MengeS.F. Ackley(West Germany)Z. LiJ. SuiD. YanG. Menq(China)J. MeyssonnierP. Lhival( France)B. MichelF. Picard( Canada )B. Nordell( Sweden )P. Palathingal(West Germany)J.A. Richter-MengeS.F. AckleyM. A. Lange(USA)P.R. SammondsS.A.F. Murrell(U.K. )S.S. Shanaa( India)L. StehnL. Fransson( Sweden )S.L. WangC.R. Hazel1C.C. Hsiung( Canada )s. WuG-W. LiC-H. Liu(China)Elastic Properties ofFrazil Ice from theWeddell Sea, AntarcticaTemperature, Salinity, andDensity Profiles in a FastIce Sheet in Liao Dong BayCreep Behaviour of DamagedIce under UniaxialCompression: A PreliminaryStudyMajor Differences in theFailure Modes of an IceSheet on an Inclined Plane:Laboratory TestsPressure-Melting of Ice 249Some Laboratory Test Results 259on the Creep Behaviour ofFresh Water IceComparison of the Compressive 269Strength of Antarctic FrazilIce and Columnar Saline IceGrown in the LaboratoryA Laboratory Investigation of 279the Fracture of Multi-Year SeaIce under Triaxial Stresses at-20 OC and -40 OCStrength Profiles of Dakshin 289Gangotri Ice Shelf in EasternAntarcticaA Field Instrument for Fracture 300Toughness Testing of IceDynamic Response of an Icebeam 311with Flooding Water EffectThe Measurement of "Elastic 321Coefficients u of Bohai SeaIce under Uniaxial Compression

M. ZhanqG. MenqD. YanY. YU(China)Plane Strain Fracture ToughnessKiC of Sea IceK. AxelssonD-C. ShenqB. NystrOmS. Knutsson( Sweden )M. Lensu(Finland)Q-M. LuE.B. Rasmussen0. Jensen( Denmark)M.P. MontemurroJ.F. Sykes( Canada )M. NystrOmG. Horrigme( Sweden )A. Omstedt( Sweden)L.H. ShapiroT. Takeuchi(USAM. StoneI.J. JordaanS . J . JonesR.F. McKenna(Canada )G.W. TimcoR.M. FrederkingS.K. Sinqh(Canada )M.S. MuS.S. Sunder(USA)J. xuX. Chen(China)On A Finite Element Model forFreezing and Thawing SoilsIce Floe DistributionsSensitivity Test of Couplinga Sea Ice Model with anOcean ModelEvaluation of ConstitutiveLaws for Sea Ice withApplication to Adam's IslandCreep Analysis of an AnisotropicIce SheetDynamic and ThermodynamicModelling of Sea Ice inCoastal SeasThe Deformation of FloatingIce Sheets of VariableThickness under In-planeCompressive LoadingDamage of Isotropic PolycrystallineIce underModerate ConfiningPressuresThe Transfer FunctionApproach for a StructureSubjected to Ice CrushingConstitutive Modeling ofPolycrystalline IceA Visco-Plastic Creep Modelfor Static Ice Loads Analysis

2. ICE/STRUCTURE INTERACTION2.1 Ice Forces on StructuresF.T. ChristensenN-E. Ottesen HansenS. SpangenbergL.J. Vincentsen( Denmark)J.F. DorrisM.M. Kinkier(USA)D. Duthinh( Canada )A Enqelbrektsson( Sweden)M.G. Gladkov(USSR)K. Holthe(Norway)X-H. JiW. Shen(China)R.C. JohnsonA Prodanovic(USA)M.J. Kaldjian(USAB. Lfifquist( Sweden)A.R. MarshallR.M. FrederkingM. SayedJ.P. NadreauK.R. CroasdaleI.J. Jordaan( Canada )Dynamic Ice Loads on theGreat Belt Western BridgeThe Use of Residual Strengthin the Calculation of GlobalCrushing Forces on WideStructuresOn the Relationship betweenGlobal and Local IceCrushing LoadsParametric Study of Iceberg 492Impact LoadsAn Ice-Structure Interaction 504Model Based on Observationsin the Gulf of BothniaDetermination of the Ice Load 518on Piles of Fixed OffshoreStructuresA Numerical Model forPredicting the Responseof Concrete GravityPlatforms to Iceberg ImpactThe Primary Study of IceForce on the Structure inBohai SeaCalculation of IcebergImpact ForcesIce Loads on OffshoreStructures of VariousWaterline GeometryTransverse Static IcePressure on Bridge PiersMeasurements of LoadTransmission ThroughGrounded Ice Rubble

D.A. PinturJ.F. Sykes( Canada )M. SayedR.M. Frederkinq( Canada )D.S. SodhiJ.J. Gaqnon(USAQ.J. WangJ.X. Zhu(China)E. WesselsP . Jochmann(West Germany)2.2 Imoact on iceU. BjOrkenstamM. Lindqren( Sweden )S.N. ChinF.11. Williams(Canada )L. DomaschukD.H. ShieldsR. Kenyon( Canada )A.L. Tunik(USA)2.3 Sorav Ice and IcingThe Sensitivity and UncertaintyAnalysis of anIceberg Structure CollisionModelAn Ice Failure ModelIncorporating Size EffectsIce Force Measurements on aBridge Pier in a Small RiverThe Characteristics of BohaiIce Load Analysing MethodFull-scale Ice ForceMeasurements with Tip-PanelSystem at NorstromsgrundLighthouseWave Interaction between TwoFloating BodiesMeasurement of Impact Forceson Sea IcePenetration of Spheres andRods into IceImpact Crushing Strengthof Ice596V0l. 3606Vol. 3A. Andersson A Numerical Model of Water 671U. Svensson Droplet Trajectories( Sweden )R. Z . Blackmore Ice Growth on a Ship's Mast Vol. 3W.P. ZakrzewskiE.P. Lozowski( Canada )A.C.T. Chen Strength and Deformation 681K.G. Gramof Spray Ice(USA)I HorjenT. Carsten(Norway )Numerical Modelling of Sea 694Spray Icing on Vessels

M. HagqstrOmL. StehnI. Thiger( Sweden)Atmospheric Icing of MastsJ.E. OverlandC.H. Pease(USA)Prediction of Vessel Icing:A 1989 UpdateW.P. Zakrzewski The Use of Ship IcingE.P. Lozowski Models for the ForecastingI. Horjen Icing Rates on Sea-Going(Canada )Ships2.4 Ice Breaking TechnologyK. Lindberg The Hull Structure of Oden I1 Vol. 3B. JohanssonL. HammarstrOm( Sweden)G. Lindqvist( Finland)A Straightforward Method 722for Calculations of IceResistance of ShipsS. Liukkonen About Physical Modelling of 736(Finland)Kinetic Friction betweenIce and ShipK. Riska(Finland)H. Soininen(Finland)J.C. Tatinclaux(USA)L.G. Tsoy(USSR)An Analysis of Factors 750Influencing Ship Responsein Collision with Multi-YearIce FloesMission-Based Approach inModern Icebreaker DesignModel Tests on an Icebreakerat Two Friction FactorsInvestigations of the Effectof the Principal DimensionsRatio and Hull Shapes on theShip's Passability in Ice3. MATERIALS AND COMPONENTS IN THE ARCTIC3.1 Material Behaviour under Low TemeraturesL-0. Andersson Adhesion of Ice to( Sweden ) Polymer MaterialsK. CederwallL mansson( Sweden)P-A. DaerqaU. OhlssonL. Elfgren( Sweden)Cracking of Roof Feltcaused by an Ice-CoverBehaviour of Concrete atLow Temperatures

V. LarionovI. Chersky(USSR)Problems of Design andService of Machinery andStructures for PolarRegionsSome Experimental Observa- 831tions on Concrete Behaviourat Low TemperatureR. Nord6n( Sweden )Extra High Strength Structural 839Steels for Ice BreakersC.V.~. Veen The Behaviour of Reinforced 852H.W. Reinhardt Concrete at Low Temperature(The Netherlands)3.2 Structures and Coai~onents under Arctic ConditionsM. Jussila Ice Loads on Propeller BladeP. Koskinen of Small Car Ferry(Finland)M.J. Stephens Effects of Cyclic Loading onP. Hassinen the Lateral Load Capacity ofT.J.E. Zimmerman a Composite Ice-Resisting3. Kouhi Wall System(Canada)4 OPERATIONS IN THE ARCTICL. BerqdahlI. P&lsson( Sweden )K. EriksenH. VaboB. Ronninq(Norway)R.E. FultonK-N. ChianqD. Goehlich(USA)Marine Operations of aDetachable ProductionPlatformAn Investigation ofEnvironmental Conditionsand an Evaluation ofSuitable Platform forthe Southern Barents SeaAdvances in NonlinearAnalysis Methods forOcean Structures UsingParallel ComputersK.B. OlsenThe Technical and EconomicJ . WaeqterFeasibility of PlatformK.A. Sorensen Systems in Iceberg Infested( Denmark ) Areas4.2 Cold Reaion PortsC.A. WortleyL.T. Nelson(USA)Underwater Observationsof Ice/Structure Interactionsin Small-CraftHarbours

4.3 Cold Region Geotechnical EnaineeringK.D. Eigenbrod Measurements of PoreJ.P. BurakPressures in Freezing( Canada ) and Thawing SoilsZ.A. Zhaqparovich(USSR)Bearing Capacity ofSeason-Freezing andThawing Soils byHorizontal Stress Change4.4 Overation Ex~eriences under Arctic ConditionsA ArikaynenB. Levit(USSR)Estimation of Ship and 962Convoy Speed in ArcticWaters in Evaluating FleetDevelopment EffectivenessM.E. Haapanen Antarctica, as seen by a 975(Finland)ShipbuilderD. HaugumL. ElfqrenP. GjOrup( Sweden )Building Technology in an 983Arctic Climate. A PreliminaryReport from the Buildingof a Swedish Research Stationon the Antarctic in 1988-89J. Lindahl Maintenance Aspects ofL.R. SchmidtFloating Moorings in( Denmark) GreenlandS. O'Connell Scientific Ocean DrillingP. Rabinowitz in the Polar RegionsJ. BaldaufB. ClementA. JulsonA MeyerE. Taylor(USA)J. SandkvistL BjelmR. Gartner( Sweden )Polargas Operations atHaketangen, Svalbard4.5 Climate. Ice Forecastina and Remote SensinqP.M. HauganIce Forecasting in the0. Skaqseth Barents Sea Using RemoteO.M. Johannessen Sensing AssimilationT. Olaussen Techniques(Norway)M.J. HensleyJ.T. Bales(USA)Data Collection forDesign - the AlaskanExperienceVol. 3Vol. 3

M.O. JeffriesW.M. Sackinger(USAA. KovacsJ.S. Holladay(USA)T.L. KozoL.D. FarmerJ.P. Welsh( USA )F-C. LiW.M. SackingerM.O. JeffriesM-c. Lu(USA)S. SandvenO.M. Johannessen(Norway)Y. SunZ.X. GuH.T. JinL.K. Zhang(China)T. Thompson( Sweden )Analysis and Interpretationof an Airborne SyntheticAperture Radar Image ofoHobson's Choice w Ice IslandAirborne Sea Ice ThicknessSoundingWind-Generated Polynyi offthe Coasts of Bering SeaIslandsComputer Simulations of theProbability of Ice IslandMovements in the ArcticOceanStudies of Sea Ice ForcingDuring MIZEX887Radar Observation on theSort of Sea IceBepers-88, A Sea Ice RemoteSensing Experiment in theGulf of Bothnia4.6 Ice Navigation - Ice HanaaeaeffltA Backman( Sweden )Experiences with the NewSwedish Icebreaker ODENV. Beletskiy Arctic Operations in the(USSR)Western Part of SovietH . JensenS. Loset(NorwayP. Kujala( Finland)Numerical Simulation ofIce Formation in FrequentlyTransited Navigation ChannelsIce Management in theBarents SeaResults of Long-Term Ice LoadMeasurements Onboard M/S Kemiraduring the Winters 1985-1988

5. COLD REGION ENVIRONMENTAL TECHNOLOGY 11300. Johansen(Norway )L. Lyck( Denmark)S. Marklund( Sweden)6. GENERAL - OVERVIEWSG. HuardM. Huther(France)Oil Spill in Ice SimulationModel DevelopmentStrategies ConcerningEnvironmental Aspects ofIndustrial Activities inthe ArcticWater Conservation at theSwedish Antarctic Wasa Base -Implementation and Results1988/89Pollution-Free PetroleumProduction and TransportationSystems in the Arctic RegionDip01 Actions in the FrenchPolar TechnologyA. Lobanov The MCEI Laboratory as a1.Sh. Khalfin Centre of Offshore Oil and(USSR)Gas Producing StructuresResearchAUTHOR INDEX WILL BE IN THE END OF EACH VOLUME

SEA ICE PROPERTIES

THE GENERATION OF THE FOUNDATION FOR THE SKAGENSPIT, NORTH JUTLAND, DENMARK, BY THE ACTION OFICE, GLACIAL EUSTACY AND RISE OF SEA LEVEL,EROSION AND ACCRETIONPer BruunSouth Carolina, USASecretary General, POACSkaqen, DenmarkABSTRACTIce-ages have occurred in various geological periods. During thelast half million years, their largest magnitudes were in the northerncountries: Canada, Greenland, Iceland, Scandinavia, the Balticum, theUSA and the USSR. The latest glaciation took place 16,000 -24,000years BP with a rapid advance in Scandinavia 20,000 BP. The ice movedhuge quanitites of materials from Norway and Sweden south andwestward. Denmark was mostly covered with ice, but the westernmostpart of the peninsula Jutland was not. In the final withdrawal phase,commencing about 16,000 BP, the glaciers left enormous bottom andmarginal moraines in Denmark.Following the withdrawal of the ice (13,000 BP in Jutland), strongglacial rebounds started. Simultaneously, sea level rose due toincreasing temperatures, gradually encroaching upon the rebound.Today, the two movements are almost equal in the northernmost Jutlandwhile sea level rise has taken over south of here. Glacial reboundsstill are strong on the Scandinavian peninsula.With the ocean free of ice the newly born shores were subjected towave action of increasing magnitude as ice vanished and sea level rosecausing erosion and longshore drifts. The result of the battlebetween nature's forces ultimately became a spectacular coastalgeomorphological development generating one of the largest marineforelands in the world, the Skagen Odde (spit) extending out in ortowards the deep Norwegian Trench on softer marine deposits (Fig. 4).

THE LATE GLACIAL STAGEFigs. 1 and 2 (Strand Petersen, 1985,b) show the land-seaconfiguration in the late middle Weichselian, 22,000 - 16,000 BP andin the late Weichselian, 16,000 - 13,000 BP, respectively. When theice withdrew from Fig. 1 to Fig. 2, large areas of the northeast werecovered by an Arctic Younger Yoldia Sea. The maximum marinetransgression was reached in the northern province of Jutland,Vendsyssel, north of the Lime Fiord between 14,000 and 13,000 BP whendeposits of arctic clays including the remains of an arctic faunaoccurred in the sea between Sweden and Denmark (Fig. 3).Fig. 3 (Strand Petersen, 1985,b) shows the land/sea configuration inthe late Weichselian around 11,000 BP. The late glacial environmentwas very rich over and above the presence of mammoths, including polarbears and brown bears. Some of the first traces of human post-glacialoccupation in Denmark are from that period. By about 11,000 BP, thereare no further traces on dry land of the marine arctic Yoldia Sea(Strand Petersen, 1985.b).We know little about the thickness and movements of the ice whichcame from Norway and Sweden. All we see is the results of its actionsin the form of huge deposits of moraine materials ranging from claysto rocks up to 10-20 tons. The ice cap exerted high pressures on theground. Following the melting of the ice, large isostatic rebounds(uplifts) took place. They have continued since then on theScandinavian peninsula. In Denmark and in Southern Sweden uplifts arenow being overtaken by sea level rise. The zeroline seems to belocated in the Hirtshals-Frederikshavn area (Fig. 4). From here andnorth, the isostatic lifts have the upper hand and are up to about10mm per year in the northern part of Sweden and in Finland. In thesouthernmost Swedish province, Skaane, sea level rise is thestrongest.In the northern parts of Denmark, older arctic Marine Yoldia clays(from earlier glacial periods) and interglacial (before latest glacialperiod) Eemian clays have a thickness up to 150 meters (StrandPetersen, 1985.b).The highest part is found in elevation - 25 meterswhile the younger Yoldia shorelines are found up to 60 meters abovepresent sea level (14,000 - 15,000 BP). This indicates a much highersea level relative to land about 11,000 BP when glacial pressures wereless relieved and rebounds were still relatively small in magnitudes -but not in rates.

Using the equation:PAWT (Past Water Table Elevation + GR (GlacialRebound) = PRW (Present Elevation) (1)with a recorded shoreline elevation of 60m above MSL today one arrivesat a water table of minus 70 meters (11,000 BP) and a 130 glacialrebound. If rebound is less rise of water table is also less. Eq.(1) has two unknowns.HOW THICK WAS THE GLACIAL ICE COVER?The thickness of the ice during the melting period is unknown, butover the Norwegian mountains the ice cap was probably a dome on thetop of the mountain rocks. Comparing to Iceland glaciers, (Bjornsson,1986), Svalbard glaciers (Dowdeswill, et al, 1986) and to conditionsin the Antarctic (Crabtree and Doake, 1986). one arrives at athickness of

periods it has probably been much larger. Yoldia Sea shorelines arefound at Frederikshavn (Fig. 4) at elevation 60m above present sealevel.As mentioned above Eq. (1) with sea level 70m below present gives aglacial rebound of 130m which corresponds to an average rise of 1cm =10mm over 13,000 years. This matches with present records for northand northeast Scandinavia. Shorelines at Frederikshavn 7,000 BP arenow located 15m above MSL. With a rebound of about 40m (4,000 x 5mmt 3,000 x 3mm) one arrives at a MSL 25 meters below present. Thiscorresponds to the Atlantic Period when dry areas of the north Seaduring the Boreal (land) period were being flooded. Strand Petersen(1985b) states that "it has been possible to establish an earlyAtlantic transgression to a height of -25 meters around 7,800 BP inthe northern Denmark".The special conditions at the Skagen Spit are dealt with in afollowing section. It does not seem likely that glacial ice has beengrounded in the deep finger of the Norwegian trench extending fromnorth to south towards Skagen (Fig. 4). The Skagen Spit has, from aperiod at least 1,000 years or more back, extended out in the trenchwhere depths may have been >200 meters (Fig. 4). We know that theSkagen Spit is founded upon marine deposits without limestone at about200111 depth (as it is normally south of Skagen). The lack of propersoil mechanics investigations based on deep core-borings makes itdifficult to determine whether the ice has rested on the bottom or -in case - if it was there long enough to leave a still lastinginfluence on the depth versus pressure relation to prove that itcertainly was there1 If it actually was - for a while - we shouldfind a "bump" in the (pressure versus depth) diagram proving that thesubsoil has a "memory". This was revealed in many cores in the NorthSea during drillings for oil and gas. The soil still has notforgotten the ice! Some seismic movements may, however, also beassociated with the Norwegian Trench.ICE PUSH-UPS OF MORAINESThe ice in it's final movements pushed up or deposited the largemarginal moraines which we now find as shore cliffs elevated on thetop of Yoldia Sea deposits on the west, north and east side ofVendsyssel. These cliffs are very distinct lines which in part foundtheir final slopes during the Atlantic Period occurring 7,500 -3,000

BP when the world sea level was up to 3 -5 meters above present. Atthat time the isostatic uplift had not ~rogressed up to today's level.The old shorelines in northern Vendsyssel are now by glacial reboundelevated 10 - 20 meters above present MSL.The following is an attempt to explain the directional configurationof the old marginal moraines.Fig. 4 was reprinted from Hydrographic Map of the Skagerrack (DanishHydrographic Service). Fig. 5 is a schematics extracted from Fig. 4showing the direction of the old moraine shore cliffs, at some placesislands, and various depth contours in the Skagerrack.The 50m, 100m. and 200m depth contours have been rectified in Fig.5. The moraine cliffs shown in the schematics are very distinct lineswhich were finally formed during the Littorina (Atlantic) Period whensea level in the oceans was above present. Elevations of thesemoraines are 40 to 90 meters above MSL at present. The line Blokhus-Lpkken - Rubjerg - Hirtshals continues north in the offshore SkawBank.Comparing Figs. 4 and 5 it may be observed that:(1) Depth contours 50m, 100m and 200m in the western section arelargely parallel to the line Hirtshals - Hanstholm and only deviateabout 20 degrees from the line Blokhus to Hirthsals.(2) the about 90 degrees corner at Hirtshals - Rubjaerg, 120 degreesfor Hirtshals - Hanstholm, corresponds to the 120 degrees cornerfor the 100m depth contour or the 200m contour. Following thecorner, the multi-cliffline Hirtshals - Frederikshavn is largelyparallel to the 100m and 200m depth contours running about 50 kmtowards the east-northeast followed by a 100 degree turn making the100m contour run northeast 40 km towards Sweden.The moraine cliffs demonstrate a late phase in the glaciation stage16,000 - 14,000 years ago. The similarity of the configuration anddirection of these marginal moraines and the depth contours lendsitself to a physical explanation relating forces to configuration.The ice movement may have refracted, its propagation being dictated bythe depth contours and by what was land at that time.The Norwegian Trench which also existed during the glacial periodwhen it was covered with ice of unknown thickness. Geophysically andmechanically it is unlikely that the ice has been in a moving contactwith the bottom across the deepest part of the trench. No forces wereavailable to lift the ice up several 100 meters following a dip into

the open-ended ocean trench. The ice probably floated across the deeptrench. Experimentally it may be assumed that the ice during the lateglacial period was in contact with the bottom at the break in slope at300111 depth at present on the Norwegian side (200 to 230111 during theglacial stage) and at 100 to 150m on the Danish side. The ice moveddown the Norwegian mountains under high pressure after which it waslifted by water across the 50km wide section of the Skagerrack (70-100m to be added to obtain sea level today).The ice movementrefracted and tended to become perpendicular to the depth contours, acommon experience (Bruun, 1983).The ice movement had two maindirections from north, as shown in Fig. 2, perhaps separated by somehundreds or a few thousands of years. Finally the ice propagated froma more easterly or even southeasterly direction generating the morainesouth of Frederikshavn. In Denmark the ice ran aground on glacial andinterglacial deposits of earlier date and pushed up moraines andfinally the large marginal moraines which we today observe as the verydistinct shore cliffs now elevated above sea level on the northern andeastern frontier of Vendsyssel. This is due to the glacial reboundoverpowering the sea level rise until recently. On the western, lessdistinct frontier, erosion due to high exposure has eaten in on themoraine cliffs. These movements, of course, have been irregular.What we see today is the ultimate result as of 1988.MECHANICAL EXPERIMENTFig. 6 is a schematic showing a cross section of Skagerrack with anice cover 200m thick on the Norwegian side and only 50m thick on theDanish side. The 200m is an arbitrary figure based on Antarctic RossSea, Svalbard and Greenland experiences. The ice is assumed to be incontact with the bottom at 200m depth (270111 today) on the north sideand at 50m depth (about 120m today) on the DK-side. If this shall betrue, the ice must have melted down in thickness by 150 meters acrossthe Skagerrack. An arbitrary figure for glacial movement of 1m perday is now chosen. It is high compared to Alpine glaciers (which arein a trough with high friction) and low compared to some glaciers inGreenland. To move across 50,000 meters will take 50,000 days.during that time the ice is assumed to melt 150 meters or 3mm per day.This figure does not sound unrealistic. Assuming during the lateglacial stages that evaporation equalled snowfall all melting wouldhave to be from the bottom. But melting or evaporation may also

have been from the top, preserving glacial materials1Ice at the bottom of the glacier would melt at 0-plus degrees (it isunder high pressure) while water temperature might have been e.g. 1(one) plus in water of salinity about 3% decreasing going east untilfinally the ice (possibly including saline bottom ice) was in contactwith the bottom in the easternmost section (Figs. 1 and 2). This, ofcourse, is speculative.At 50m depth (late glacial age now about 120m) on the DK sidetheglacier may start pushing. This pushing may have taken place atvarious "floors", where only the upper floor moved relativelyfast.Assuming a 50m high front generated by soils resistance under icepressure up to 50 tons per m 2 such front would meet a passive earthpressure of approximately in submerged condition:Force/m = l/2(xh tan 2(45 +V) or with (friction angle)about 20 degrees (lose masses) and h = 50m, F = 2,500 tonsequal 50 times 50m from the ice(50 = crush F/M~)This is an ideal case, probably not fully realistic, but it gives animpression of the kind of forces which were at work and finally formedthe moraine border areas, later re-configurated in details by soilerosion and by wave erosion during a higher sea level during theAtlantic period.The ice in the uppermost floors may have continued pushing longafter the lower floors had stopped their movements and had become"dead ice". This built up moraines on the top of other moraines, aswe find them today.There is perhaps a chance that "the finger" of the Norwegian Trenchextending south towards Skagen (Fig. 4) might have functioned as akind of "tunnel valley" carrying discharge water from the ice-meltingout in the North Sea. It is hydrodynamically acceptable that theSkagen Spit extended out following the current main trend of flowingwhere resistance was least, that means in a (deep) channel. Theerosive or sediment carrying effects of such flow may have beenrelatively large due to the confined cross section in a low ceilingtunnel.THE LATE GLACIAL PERIODThe ice withdrew gradually in melting. The withdrawal wasirregular, the ice pushing forward and back several times building nota single but a few rows of marginal moraines as e.g. found between

Hirtshals and Frederikshavn (Fig. 4). Introductorily deposits weremoraine materials, later Yoldia Clay in layers - several meters thickand thinner layers of Saxicava Sands. These deposits took place inice-filled waters where severe wave action could not occur due to thedamping effect of the ice. Deposits are many meters thick.The melting of the ice generated rivers which carried materials tothe sea where coarser particles were deposited in the nearshore whilefiner were carried further offshore for deposition.With the vanishing of the ice, large free fetches for wave actiondeveloped causing erosion and littoral drifts. The ultimate result wasthe formation of the Skagen Spit as a high Marine Foreland growingnorth out in or towards the Norwegian Trench and Norway.DID ICE INFLUENCE THE DEVELOPMENT AFTER THE GLACIAL STAGE?No doubt the influence of the ice was considerable during the lateglacial period. Ice continued carrying materials to the area as e.g.witnessed by submerged reefs like the Herthas Flak and the Skaw Bank(Fig. 4). The ice's damping effect on the waves caused relativelylittle erosion by sea forces as know from arctic areas today (Bruun,1987). During the following periods ice probably always occurredduring the winter time - perhaps not during the Atlantic Period. Icepiled up on beaches and moved some material around, but with little orno effect on the coastal geomorphological development. Ice, however,may have contributed to the erosion of barren cliffs by towing andfreezing and ice "gauging" has undoubtedly occurred offshore as knownfrom Beaufort Sea Shores in Alaska.

FIR 2 ~~nd-~ea-~c~ cont~gur.,t~on In thcs Lot? M~ddlc W~~h5el1an FltIl FIR 3 Land-s~a cont~guratfon the Late We~chxl~dn 51x1h Tcenarloscm~?r~o,1 b,OUO - I %,UOO BP (8) around 11,000 BP (8)

Fig .4THE SKAGERRACK

Fig. 6CROSS SECTIOR OF THX SKAGERRACK DURING LATE GLACIAL STAGESCHEMATICS (not to .wale).

DEVELOPMENT OF ICE DRIFT MODELS FOR THE BARENTS SEATorkild CarstensHead of ResearchSylvi VefsnmoResearch EngineerStig M. LavAsResearch EngineerNorwegian Hydrotechnical LaboratoryNorwegian Hydrotechnical LaboratoryNorwegian Hydrotechnical LaboratoryNorwayNorwayNorwayABSTRACTIn order to cover initial needs for ice drift modelling in the BarentsSea, NHL is implementing several models under the ESSO/SINTEF ArcticResearch Program (ESARC). The different terms in a dynamic ice drift formulaare discussed. A short description of the implemented ice driftmodels (both statistical and dynamic) is given as well as some case simulations.A characteristic feature of any flow in the Barents Sea is inertialoscillations as a result of the coincidence of the M2 tidal period and theinertial period. Accordingly a vectorial model is needed to allow inertialoscillations of the order of 1 - 10 km to be forecast.1. INTRODUCTIONExtensive ice surveys are required when ice is a design concern. Thetechniques used include satellite and aircraft imagery of many kinds.Wherever ice is a threat to operations, ice monitoring is routinely carriedout by dedicated aircraft.Ice forecasting models are implemented to provide an estimate of how iceconditions may change. Several North-American consulting companies nowoffer short-term ice forecasts. These forecasts are based on either a simplifieddynamic model, and autoregressive (AR) model using observed trajectoriesas input or an ARX type hybrid model with forecast excitation(X) by the wind and current. ESARC has focused on these categories ofmodels.The justification for our interest in ice drift forecasting rests with

the present need for this type of forecasting tool for the Barents Sea.Since these models tend to be developed for site spesific conditions, theice drift model is tailored to conditions typical for the Barents Sea.2. EXCITATION FORCESThe starting point for any truly dynamic ice drift formula, and for themore pragmatic formulas with excitation "force" variables as well, is themomentum balance equationma = Fg c i rm - mass of icea = Du/dt = du/dt + u(du/dx) acceleration of the ice+Fa - air drag on the projected area exposed to the wind+F - water drag on the projected area exposed to the currentSg - gravity force due to surface tiltSc - Coriolis force due to the rotation of the earth-.F, - contact force between adjacent ice masses-.Fr - radiation stress due to the reflection of surface gravity wavesEquilibrium drift (a=O) is obtained quickly (White et al., 1981) by anice floe (within 10 - 15 minutes) after a sudden change in forcing by windor current. Icebergs with their larger mass naturally require more time toadjust, and should not as a rule be considered in equilibrium beforeseveral hours to half a day after a sudden change in forcing.Free ice drift (;=0) is commonly assumed, perhaps too much so. The iceto ice force is negligible when the ice concentration (c) is low but doesbecome important for c > 0.7 (Sverdrup, 1928). Free drift models are successfullyused for ice edge drift (El-Tahan, 1987). in particular for anadvancing ice edge.Drag terms for ice floes and icebergsThe fluid drag on a projected surface area exposed to wind or current isgiven by the surface stress T~ times the projected area A. For ice floesthe projected area is the horizontal one, while for icebergs the projectedarea is the vertical area (Figure 1). The fluid drag per unit area is:

whereThek =1.0 for ice floes0.5 for icebergsCf = drag coefficientof = fluid densityqf = fluid velocity-3Vi= ice velocitydrag coefficient, Cf, is a function of the surface shape, the fluidflow profile, Vf(z), and the ice velocity, V,.The wind drag is given by the surface wind, usually at 10 m. In theliterature one can find considerable information on the drag coefficient.For example,- for open water (Pond and Pickard, 1981)Caw = 1.5 10-3

The Coriolis force FcThe deflecting Coriolis force directed 90Â to the right of the ice velocityvector, is a function of ice velocity V,, the circular frequency ofthe earth Q. latitude and ice mass mwhere f is the Coriolis parameter (of order 10'~s")Wave radiation stress F_The characteristic bands of ice near open water reveal the existence ofa wave-related force F . When waves encounter an ice edge, they are partiallyreflected. This produces a reaction force per unit length normal tothe exposed floe edge (Longuet Higgins, 1977).where a_ is the incident, a_ the reflected and a, the transmitted wave amplitude,respectively, and L is the projected length of the ice floe alongthe wave crest. Carstens and Rosdal (1987) found the reflection coefficientR = a_/a,, to be less than 10% except for thick ice. Icebergs havemuch higher reflection coefficients, and regular tabular bergs are perfectwave reflectors with R = 1.The ice-ice interaction forceThe first formulation of a specific force to account for ice-ice interactionwas Sverdrup's (1928) linear ice resistance k:As shown in Figure 2 even small k's of the order of the Coriolis parameterf affect the drift significantly.Later many authors (Glen. 1970; Kheisin, 1972; Hibler, 1974, 1979, 1984;Rothrock, 1975) have derived ice-ice interaction from constitutive laws ofall kinds: The ice is seen as a viscous or turbulent fluid, as an elasticand/or plastic solid etc. No matter which rheology is proposed for theice, the ice resistance is given by the stress gradientswhere aJk is the two-dimensional stress tensor set up by wind and currents.An Eulerian grid model is convenient for deriving F once the forcingis known and an ice rheology chosen. However, at present there is atendency to revert to simpler models again (Erlingsson, 1988; Hibler,1988, personal communication).

Figure 2. Relative ice drift vectors with variable ice resistanceSea surface tiltThe GEOSAT observations of the geoide by radar altimeter since itslaunch two years ago have revealed a sea surface topography with slopes asthe rule rather than the exception. This information is bound to add newdetails to the picture of surface currents.The force due to a sloping water surface S,, = dq/dx is the gravity componentin the downslope directionThe most important tilts are listed in Table 1.Table 1. Order of magnitude of surface tilts.Cause of surface tilt-log SmaxCommentsGeostrophic boundary currentGeostrophic gyresTideAir pressure (inverted barometer)Wind pile upfdrawdownFriction5 - 666554Current 0.1 - 1 m /sCurrent 0.1 m/sNorthern Barents SeaNear storm centreShallow coastal waterStrong currents inshallow watersThetable shows that the topographically determined friction slope may3 5

override other surface slopes, as is well known from, say, the Strait ofBelle Isles.Storm events produce slopes of order 10-5 due to the inverted barometermechanism. In the open ocean the associated slope forces can be assumed tohave a random orientation. Pile-ups/drawdowns along shallow coasts tend tocounteract drift normal to the shore, with S "" 10-5. When the tilt forcesfrom geostrophic and tidal currents are of the same magnitude, as onSpitsbergenbanken, regular intertial oscillations prevail in the absenceof storms.Iceberg responseIcebergs in free drift in the area of interest may be expected to behaveas follows:While moving with the mean current in calm weather, the icebergs performinertial oscillations. The sea surface rises slightly in a belt surroundingshoals such as Spitsbergenbanken. When an iceberg on the sloping seahas a velocity lower than the mean current, it will slide downslope anddrift into deeper water. Conversely, icebergs with velocity higher thanthe current will climb upslope and ground when their draft exceeds thewater depth. Normally the iceberg velocity will be close to the velocityof the mean current, but wind drag will speed up or slow down the berg.Assuming a mean flow in anticyclonic circulation around Spitsbergenbanken,northerly and easterly winds will tend to ground icebergs along the easternslope. Southerly and westerly winds tend to ground icebergs along thewestern slope.3. AUTOREGRESSIVE MODELSTrends,seasonal patterns and cycles might be regarded as deterministiccomponents following fixed mathematical equations, and the quasi-cyclesandother statistical fluctuations as stochastic and describable by shortterm correlation structure. For a finite data set it is not always easy todiscriminate betweenthese two types, and a common description using theclass of AutoRegressive Integrated Moving-Average (ARIMA) models is nowwidelyused. The form of these models is that of difference equations (orrecurrence relations) relating present and past values of the series.Thecorrelation structure in stationary time series may often be repre-sented by a model with a small number of parameters belonging to the ARIMAclass. If the stationary series w has been derived from the originalseries xt by differencing, then xt is said to follow an ARIMA model. Firstorder differencing will remove a linear trend.3 6

Taking wt = Vdxt, the autoregressive (AR) model with p autoregressiveparameters @, , @, , ----- . @ represents the structure of wt by thewhereat is an uncorrelated series with mean 0 and constant variance oa2.A series generated by this model will only be stationary provided restrictionsare placed on S,, ---- , S to avoid unstable growth of wt .An ARIMA model is particularly suited to extrapolation of time series.Forecast error limits are easily deduced. This process requires knowledgeonly of the model orders and parameters together with a limited set of thetime series. If new observations come to hand, then the model equationscaneasily be used to update the state before constructing forecasts fromthe end of the new observations. This is particularly useful when fore-casts are constructed on a regular basis.'4.MODEL CONCEPTSThe development of a drift model package called BASEMOD has been startedduring the ESARC program. BASEMOD is a master program which calls onseveral subprograms. The subprograms are divided into 4 main modules whichcontain disjoint simulation models respectively for ice floe drift, icebergdrift, ice pack drift and oil drift (Figure 3). The master programconsists of individual drift simulation models which are organized to beused either as a part of the total system or on a stand alone basis. Themodels are especially tailored to fit the Barents Sea. The final BASEMODpackage will be based on extensive testing of each submodel. Thus the presentset of models may not be the final one. A brief description of themodels is given below:ICEPRED: This model deals with the motion of both the ice edge andidentifiable ice floes. The model is particularly well-suitedfor operations as it does not depend on pre-processing ofsatellite data. Input to the model is extracted directly fromAVHRR quick-looks (Shapiro, 1987) at irregular intervalsdepending on satellite passes and cloud cover. The programdetermines the longitude and latitude for any point on thequick-look one wishes to digitize. The program also performs astatistical forecast (AR model) of the ice edge position in thenear future.FLOEDRIFT: A dynamic model for the drift of a single ice floe based on airdrag, water drag and Coriolis forces. An ice-ice interactionforce based on Sverdrup (1928) is also included. Space and timedependent wind from a hindcast wind model is implemented in themodel. Space dependent current (tidal current, Ekman drift,Stokes drift, residual current) are also included. Other inputsare dimensions of the ice floe and water drag/ air drag coeffi-

cients.ARFLOE:Autoregressive model for ice floe drift. The model predicts icefloe trajectories based on the track data.BERGDRIFT: A very simplified dynamic model for iceberg drift based on airdrag, water drag and Coriolis forces. The model does notaccount for the transient three-dimensional wind and currentfield. In addition, mechanical and thermal deterioration oficebergs are not included in the model.ARBERG :MCRIM:OILINICE:Autoregressive (AR) model for iceberg drift. The model predictsiceberg trajectories based on the track data.An operational version of the Hibler-NORDA multi-categoryregional ice model (MCRIM). The model has been implemented forthe Barents Sea, see Lavas (1987). MCRIM is a comprehensivemodel providing forecasts of ice conditions on a regionalscale. The model predicts ice velocity, changes in ice characteristics,and the large scale internal ice stress resultingfrom convergence of the pack ice. The thermal calculations ofthe model consider formation and melting of ice.Oil drift in ice model concept. The model approach is based ona particle in fluid concept, where the oil spill is representedin terms of a cloud of particles advected by ocean currents orice drift, see Johansen (1989).fsS?,BARENTSp&SEADRIFT MODELSICEBERG OIL DRIFTFigure 3. The Barents Sea Ice Models package.3 8

5. CASE HISTORIESAtthe beginning of January 1988 five Argos buoys were deployed on icefloes in the marginal ice zone North of Bjornoya. The drift of one ofthese ice floes has been simulated by means of the numerical modelFLOEDRIFT which is an independent dynamic model for ice floe drift in theBASEMOD package. The simulated drift period is from day 055/1200 to day065/1200.Spatialand temporal variations of the tidal current, residual current,wind induced current and wave induced current are implemented into themodel for the area of interest. The tidal current data are from Gjevik'smodel (Gjevik, 1989). The current information is given for the area with agrid size of50 km. The residual current data are based on the currentmaps of the Norwegian Meteorological Institute (DNMI) and current measure-ments. Hindcast wind data from the numerical model at DNMI are used asinput to the model. The spatial variations of the wind speedat the be-ginning of the simulations (055/1200) are shown in Fig 4 with a grid sizeof 50 km. The wind data are for every 6 hours. Near gale from southwestwasregistered on day 056 in the drift area. The remaining input data forthe model is presented in Table 2.The simulated and recorded ice floe drift from day 055/1200 to day065/1200 are shown in Figure 5. The simulated track (dashed line) deviatesfromthe satellite tracked ice floe (solid line). With so many parametersit is always possible to obtain a better fit. For instance, a physicallyacceptable adjustment of the poorly known mean current can remove the dis-crepancy.Severalicebergs have been satellite tracked during 1988 in the BarentsSea. One of these icebergs drifted south of 74O~ late April 1988 (Carstenset al., 1988). The statistical model ARBERG for iceberg drift has beenused to simulate the drift pattern. Since ARBERG is an autoregressivemodel we have used tracked data from day 111/0240 to day 116/2022 as inputto the model. The time interval used in the forecast model is 6 hours. Thesimulated drift from day 116/2022 to day 117/2022 is shown in Figure 6(dashed line) as well as the satellite tracked drift (solid line).The simulated drift may deviate substantially from the observed onesince the forecast depends much on the time step used in its derivation.This modelrequires only information from past track history and w i l l begreatly improved if forcing variables such as wind and current areincluded.

Table 2. Input data to the model.1 ICE FLOE DIMENSIONSThickness of ice floeINITIAL POSIITON OF ICE FLOE--Latitude - - - - - - : 76.082Longitude - - - - - - : 26.8751 INITIAL VELOCITY OF ICE FLOEAmplitude - - - - - - :0.04 m/sDirection - - - - - - : 90Â1 DRAG COEFFICIENTSAir drag coefficient : 1.2 10- 3Water drag coefficient : 5 10-3Figure 4. Spatial variations of thewind speed on day 055/1200(24 February 1988)Figure 5. Simulated (---)and recorded (-)ice floe drift.4 0

3IE 18IE20ISINTEF GROUPFigure 6.Model based on track history (A-B).Simulated drift (B-C). Recorded iceberg drift (B-C').6. CONCLUDING REMARKSThe order of magnitude analysis of forces has revealed that a largenumber of independent variables enters the balance of forces. Accordingly.a full simulation of the force balance is ruled out by the lack of properinput. Based on the discussion of the different terms in Section 2. wearrive at the following conclusions for short-term ice modelling:1. For any but very weak winds, wind drag is the most important excitation.2. In the absence of wind. current drag and sea surface tilt due totide are the dominating excitations.

3. A free drift dynamic model can be expected to work well only inopen pack. Even a weak ice resistance has significant effects onthe drift trajectory.4. Tilt forces associated with moving wind fields are likely togenerate most of the noise in the simulations.To model the trajectories of a drifting iceberg, one needs to accountfor the transient three-dimensional wind and current fields and to solvefor iceberg position in the two horizontal coordinates, including Coriolisand geostrophic effects. Mechanical and thermal deterioration of icebergsshould also be included.7. ACKNOWLEDGEMENTThe authors gratefully acknowledge Esso Norge a.s for the permission torelease information from the ESARC project "Ice drift - Preliminary modeldevelopment" and to publish this paper.8. REFERENCESBanke and Smith (1973): "Wind stress on Arctic sea ice". Journal ofGeophysical Research, Vol 78, No. 35, pp 7871-7883. Box, C.E.P.,Carstens, T. and Rasdal, A. (1987): "Wave reflection from an ice edge".POAC-87, Fairbanks.Carstens. T., Laset, S.. LavAs, S.M. (1988): "Ice Drift Modelling in theBarents Sea", Polartech'88, Trondheim.El-Tahan, M. (1987): "Ice and Iceberg Drift Forecast off Canada's EastCoast". Ice Management 87 Symposium, St. John's, Newfoundland, Canada.Erlingsson, B. (1988): "Two dimensional deformation patterns in sea Ice".Journal of Glaciology. Vol. 34, No. 118, pp 301-308, 1988.Gjevik, B.N. and Straume, T. (1989): "Model simulation of the M, and theK, tides in the nordic seas and the Arctic Ocean", Tellus (1989),4lA,pp.73-96.Glen (1970): Thoughts on a viscous model for sea ice. AIDJEX Bulletin 2,18-27.Hibler W.D. (1974): "Differential sea ice drift". Journal of Glaciology13, 457-471Hibler, W.D. (1979): "A dynamic thermodynamic sea ice model". J. Phys.Ocean. 9 (4), 1979, PP. 815-846.Hibler, W.D. (1984): Ice dynamic. CRREL Monograph 84-3, 52 p.

Johansen, 0. (1989): "Oil spill in ice simulation model development". The10th International Conference on port and ocean engineering under arcticconditions (POAC189), Lule5 (In press).Kheisin, D.E. (1972): "Excitation of compressive stresses in ice duringthe hydrodynamic stage of compact ice drift". AIDJEX Bulletin 16,97-107.Longuet Higgins, M. (1977): "The Mean Forces Exerted by Waves on Floatingor Submerged' Bodies with Applications to Sand Bars and Wave PowerMachines". Proc. Royal Society A352, 463-480.L@v5s, S.M. (1987) Tailoring theory and a computer model for computing icetransport in the Barents Sea. Thesis, Div. of Port and Ocean Engineering,NTH. (In Norwegian).Pond, S. and Pickard, D.L. (1979): Introductory dynamic oceanography.Pergamon Press.Rothrock, D.A. (1975): "The mechanical bihavior of pack ice". Ana. Reviewsof Earth and Planetary Science 3, 317-342.Sverdrup, H.U. (1928): "The hind-drift of the ice on the North-SiberianShelf. The Norwegian North Polar Expedition with the "Maud" 1918-1925,Vol. IV, No. 1, Bergen.White, P.M., Spaulding, M.L. and Gominho, L. (1980): "Theoretical estimatesof the various mechanisms involved in iceberg deterioration in theopen ocean environment". U.S. Coast Guard R & D Center Rep. C6-D62-80,126 p.

OBSERVATIONS OF ICE FLOE STRESSIN THE EASTERN ARCTICM. D. Coon, PhD, Manager The BDM CorporationP. A. Lau, Sr. Staff Member 16300 Christensen Road, Suite 315S. H. Bailey, Sr. Staff Member Seattle, Washington USA 98188B. J. Taylor, Associate Staff MemberABSTRACTDuring the early fall of 1988, three fluid-filled, 20-cm-diameter uniaxial stress sensorswere implanted in a rosette pattern in a multi-year ice floe in the Eastern Arctic. Theimplantation site was selected by surveying the ice surface and depth to locate a region ofnear constant ice thickness. On-site laboratory tests were conducted to measure thebending strength and Young's modulus of lead ice and compressive strength and Young'smodulus of multi-year ice. A pressure ridge was formed from the lead ice at the edge of amulti-year floe in which the stress sensors were implanted.In this paper, ridging forces are derived from the stress sensor data and compared againstpredicted force levels from several models. Observations of ridge sail height are comparedwith the limit heights of a ridge calculated from ridge building models. Stress data indicatethat the forces occurring prior to ridge building may be larger than those forces whichoccurred during the ridging event.1. INTRODUCTIONMeasurements of ridge building forces associated with the ridging process are importantto verify large scale modeling of sea ice dynamics as well as the prediction of ice forces onman-made structures. Analytical models such as that of Pannerter and Coon (1972),have been developed to understand the forces associated with ridge building events.Croasdale, et.al. (1988) summarized several sources of ridging force predictions.Unfortunately, there has been a lack of field data available for comparison with modelpredictions.

Coon (1988) described the measurements to be made during the Coordinated EasternArctic Experiment (CEAREX). Geotech flatjack pressure sensors were implanted in amulti-year floe with the intent of obtaining a long time series of in-plane stressmeasurements. On October 7, 1988 the pressure ridge shown in Figure 1 was formed atthe boundary of the instrumented multi-year floe and a re-frozen lead. Figure 2 shows theposition of the Geotech stress sensors relative to the pressure ridge. Stresses wererecorded before, during and after this event. Ice mechanical properties measured at an on-site laboratory allow interpretation of the stress data in terms of ridge initiation and ridgebuilding forces.In the following sections, the ridge model of Parmerter and Coon (1972) is used inconjunction with CEAREX data and observations to offer an interpretation of the pressureridge formation.Figure 1 - Pressure Ridge Building

I0--36'fromSlorientation of a1Stma Ro~ttc: 231 m from Shipon 1 bearing of 359" TrueS3True North83'TrueFigure 2 - Stress Sensor Locations2. BACKGROUNDThe mechanisms of pressure ridge formation have been studied since the work ofParmerter and Coon (1972). The basic mechanism is that the ice blocks which form theridge are broken from the parent ice sheet by bending. Observations indicate that ridgingstarts from refrozen leads. The modeling of Parmerter and Coon shows that for ice of agiven thickness, strength, and modulus, there is a limit height to which a ridge can build.Further compression of the ice results in a rubble field stabilizing at the limit height.Because of the lack of field data, open questions remain about ridge building:1. Is the force to start a ridge larger or smaller than the force to build the ridge ?2. What are the limiting forces?3. What are the actual ridge limit heights?The data presented herein may help answer these questions.Figure 3 shows a force vs. time plot from the model of ridge formation. Before buildingstarts, the force could be larger or smaller than the force during ridge formation. Theparabolic curve shown represents a limiting average force. However, actual ridge buildingis dynamic, and therefore the force varies in time with peaks about twice the magnitude ofthe average force.

DynamicRidge~ ~ ~ ~ e ' t ~start ridgeTIMEFigure 3 - Ridge Force PredictionsMany ridges form as a result of flexural failure at the interface of lead ice and multi-yearice. Figure 4a also shows the force balance (Fl, F2) between the multi-year and lead ice.The lead ice also has a bending moment (M) required to maintain static equilibrium. Asridge initiation starts, the force balance and bending moment will change. If the bendingmoment generates stresses which exceed the flexural strength of the ice, the ice will fail inbending. As the ridge is building, the force balance continues to change. The sail and keelof the ridge are formed at the junction of the lead and multi-year ice as shown in Figure 4b.The limit sail height (He) and limiting force are now in question in that they may beassociated with either the lead ice or the multi-year ice.MLeadIce ThMulti-year IceFi = F2=FH-h) M=-2Figure 4 - Ridge Building Process4 7

3. CEAREX STRESS MEASUREMENTSAs shown in Figure 2 the site chosen was 231 m from the Polarbjom on a bearing of 354'true. Site selection for stress measurements was based on a preliminary survey andinspection of interior regions of the main floe within a few hundred meters of the ship. Theice thickness averaged 160 cm at the site with thickness variations of not more than 20 cmwithin a 15 m diameter zone. Three 20-cm-diameter Geotech stress sensors wereimplanted in a rosette at a depth of 55 cm for the detection of in-plane stress (see Figure 2).See the Geotech Instruction Manual (Geotech. 1988) for a detailed description of the stresssensors.Sensor implantation followed the method described by Duckworth and Westerman(1988) modified to suit the Geotech sensors. For each sensor, a 35 cm square by 20 cmdeep pit was cut with a chain saw. Blocks of ice from the pits were retained for tests ofsalinity, crystal orientation, and mechanical properties. By inserting the chain saw motorbody into the excavated cavity, the 50-cm bar reached the desired implantation depth. Avertical slot was cut with the chain saw at the bottom of the pit. After removing loose icefrom the bottom of the pit, cold fresh water was poured into the slot until it was full, atwhich time the sensor was quickly plunged to the bottom. This process ensured that thefresh water froze around the sensor face without any air voids, thereby allowing the sensorto become well coupled to the surrounding ice. As the fresh water froze, large stresssignals developed which gradually relaxed by creep of the surrounding ice within a 24 hourperiod.Coupling of the stress sensors to the ice is critical to ensure reliable stress data. Eachsensor was shown to be well coupled to the ice by applying an impulsive hydraulic signalto the sensor face by means of a hand-operated plunger integral to the sensor design andobserving its subsequent time history. When well coupled, a large (45 kPa or greater)offset was observed 15 seconds after the application of the impulse. The offset was causedby hydraulic deflection of the sensor diaphragm as it encountered the surrounding ice.Each sensor displayed impulsive offsets of 70 to 80 kPa. Poorly coupled sensorsdisplayed an offset of 5 kPa or less.A Campbell Scientific CR10 Datalogger was programmed to sample each stress sensoronce every second. These measurements were averaged over two minute intervals, theresults were stored in a SM107 storage module. The stress gauge data was processed on aMacintosh SE computer to calculate and display the principal stresses and angle in thehorizontal plane. The principal stress and angle time histories of the ridging event observedOctober 7, 1988 are displayed in Figure 5. The principal stress, 01, reached a peak valueof 19.8 kPa at 0950Z and thereafter declined (Figure 5a). The principal stress, 02, reached

a minimum value of -41.9 kPa also at 09502 Figure 5b). During this period of activity theorientation angle, 6 was about 36O with respect to GI (Figure 5c).(Degress measuredrelative lo n o d of Sl)Time (2 min between points)-36.6"(b) 09502Figure 5 - Ridging Event Principal Stresses and Angle(04. SEA ICE MECHANICAL PROPERTIES MEASUREDDURING CEAREXTo interpret the stress data in terms of ridging forces, the mechanical properties offlexural strength (of) and Young's modulus (E) of the lead ice are required. Force anddeformation measurements were recorded during 3-point bending tests of 5 cm x 5 cm x 30cm beams cut from the center of a 13 cm thick lead ice block. The samples were tested at astrain rate of approximately 4x10'5 sec -I. Figure 6 shows a typical force-deformation plotalong with strength and modulus data for each test. Average values for of and E were 860kPa and 1.4 x 106 kPa respectively. By applying the relationships discussed below,flexural strength (of) and Young's modulus (E) for the 38 cm lead ice observed at the timeof the ridging event may be extrapolated from laboratory bending tests of 13 cm thick icesamples taken earlier from the same lead.I0 50 100 150 200Deformation (cm)Figure 6 - Lead Ice Mechanical Property Data4 9

It is known from the work of Cox and Weeks (1973) that salinity varies through thethickness of the ice sheet. Applying the relationships of Cox and Weeks (1973), theaverage salinity, S, for 13 cm ice was calculated at 11.78  1.5 ¡lo S for 38 cm ice is9.85 1.5 0100. From Frankenstein and Garner (1967), the corresponding ranges of thesquare root of brine volumes for these average salinities are:11.5 5 5 13.1 ppt for 13 cm iceband10.3 56s. 12.1 ppt for 38 cm ice.bVaudrey (1977) shows the relationship between of and fvh'; using the above values andscaling on the average measured flexural strength for 13 cm ice gives a flexural strengthrange for 38 cm ice of:820

At 0510Z, compressive stress begins to build and increases until the compressive stresslevel reaches an average value of 35 kPa for approximately one (1) hour. Calculating thebending stress per unit width of the ice sheet, ~ b for , the flexural failure mechanismindicated in Figure 4a yields:Ob= My11 = 1770 kPa at 0950ZWhere:M = moment per ice sheet unit widthI = moment of inertia per unit widthy = half of ice sheet thicknessAs discussed in the previous section, the flexural strength of the 38 cm ice was calculatedto be 820 < ~f< 1020 kPa based on mechanical property field data. Thus, by 0950Z, thebending stress, oh, has exceeded the flexural strength of the 38 cm ice and failure has beeninitiated. The maximum force per unit width, Fmax, was determined assuming a uniform35 kPa stress through the 160 cm ice sheet:Fmax = 6.6 x 104 Nlm.From observations, the ridge continued to build for approximately 40 minutes. A ridgebuilding force, Fb = 3.7 x 104 N/m may be determined from the average stress level duringthe observed ridge building event. These values are shown in Figure 8 plotted againstseveral ridge building force estimates summarized by Croasdale, et.al. (1988).RANGE REVIEWEDBY VIWRAT ANDKREIDER (2m ICE)-HIGH-RANGE USEDIN THIS PAPER(AU THICKNESSES)0 1 2ICE THICKNESFigure 8 - Ridging Force Compared with Predictions(Croasdale, et. al., 1988)5 1

From the stress data time series shown in Figure 7, it is clear that the maximum stress(thus maximum force level) occurred prior to the observed ridge building event. Thismaximum force was approximately twice the ridge building force. The CEAREX stressmeasurements provided the first direct field observations of these forces.From 1140Z to 1220Z, the ridge built to an estimated average height of 180 cm withheight variations observed between 90 cm to 270 cm. Using the ranges of flexural strengthand Young's modulus previously discussed, limit sail heights between 75 and 95 cm forthe 38-cm lead ice were calculated using the relationships developed by Parmerter andCoon (1972). A limit sail height of approximately 250 cm for the 160 cm multi-year icewas calculated using an average value of Young's modulus of 7.6 x 105 kPa determined byhorizontal compression tests of the multi-year ice and a flexural strength of 958 kPa basedon Vaudrey (1977) for ice with zero brine volume. The average sail height observed(180 cm) lies between these two calculated values. The range of observed sail heightscorrelates well with the lead and multi-year sail heights.".Average ridge building forces, F, may be predicted from Parmerter and Coon (1972)utilizing:where: HS = sail height pr = rubble densityt = lead ice thickness {, =thickness parameterPi = ice density p = friction coefficientg = gravitational acceleration (1) = keel angleThe first term in the above equation is the component of the force due to the potentialenergy in the sail and keel assuming isostatic equilibrium at the center of the ridge. Thesecond term is the component of the force due to friction of the keel on the ice sheet (theforce due to the sail is small and considered negligible by comparison). Using the averageobserved ridge sail height of 180 cm in conjunction with the above equation, ridge-buildingforce predictions were calculated. A coefficient of friction of 0.3 was used in the aboveequation to watch the calculated value with the observed value. The coefficient of frictionis a means of accounting for energy consumed during ridge formation.

6. CONCLUSIONSRidge building forces can be measured using stress sensors in multi-year ice. For theridging event documented in this paper, the forces prior to---~ridge formation-were larger than- ~-the forces observed during-ridge building Using measured material properties, ridgebuildingforces were calculated from models. For a simple model in which energy isconsumed as potential energy and friction, a friction coefficient of 0.3 was required toachieve agreement between measured and calculated force levels.7. ACKNOWLEDGMENTThe authors wish to thank the science staff of the CEAREX drift and the crew of thePolarbjom for their support during the collection of the data reported in this paper. Thiswork was supported by ONR contract N00014-88-C-0222 with The BDM Corporation.8. REFERENCESCoon, M. D. (1988). Ice Monitoring During CEAREX Instrumentation andMeasurements in the Polar Regions, Proceedings of a workshop by LEEEIOceanicEngineering Society, pp. 405-413.Cox, G., and Weeks, W. (1973). Salinity Variation of Sea Ice, AIDJEX Bulletin No. 19,University of Washington, Seattle, WA, USA, pp. 1-17.Croasdale, K.R., Graham, B.W., and Comfort, G. (1988). Limit Force Leads andMeasurements of Pack Ice Driving Forces in the Beaufort Sea, Alaska OCS Region SeaIce Forces and Mechanics, Conference Proceedings, pp. 5-11.Duckworth, R. and Westerman, P.H. (1988). Stress and Stain Measurements in Ice,Instrumentation and Measurements in the Polar Region. Proceedings of a workshopIEEIOceanic Engineering Society, pp. 357-37 1.Frankenstein, G. and Gamer, R. (1967). Equations for Determining the Brine Volume ofSea Ice from -OSO to -22.90C, Journal of Glaciology, Vol. 6, No. 48, pp. 943-944.Geotech (1988), Instrumentation Manual for Geotech Stress Sensor. GeotechnicalResources,Calgary, Canada.Parmerter, R.R. and Coon, M.D. (1972). A Model of Pressure Ridge Formationin Sea Ice, Journal of Geophysical Research, Vol. 77, pp. 6565-6575.Vaudrey, K.D. (1977). Ice Engineering - Study of Related Properties of Floating Sea IceSheets and Summary of Elastic and Viscoelastic Analyses, Civil Engineering Laboratory,TR860, Port Huenene, CA, USA, pp. 18-23.

David DickinsPresidentDF DickinsAssociates Ltd.CanadaABSTRACTThe use of large marine structures in dynamic ice zones of theBeaufort Sea is now commonplace.Gulf's Conical Drilling UnitKulluk and Mobile Arctic Caisson Moliqpaq are two such designsrequiring a reliable estimation of ice forces.Multi-year floes are the most probable massive ice featureslikely to impact moored or bottom founded structures.present data base covering multi-year ice thicknessdistributions is based mainly on remote sensing techniques andtheoretical analysis supported by limited field measurements.This study was initiated to provide basic design criteria fortypical multi-year floe thickness in the Beaufort Sea.TheFourteen floes ranging in size from 220 m to 2.2 km wereprofiled in April 1982, in 200 m of water offshore of BanksIsland, using both manual drilling and sonar profiling.The data was analyzed to provide overall thicknessdistributions, and to evaluate the localized edge geometry offloes. Results showed a median multi-year ice --- thickness of 4.2m with an upper decile value of 6.5 m. There wasa- - - -~statistically significant trend to thinner ice within 5 m of the-. -- - . - -floe edge.- - - --The data set described in this paper constitutes the mostcomprehensive set of field measurements of multi-year icethickness in the public domain.

1. INTRODUCTION AND OBJECTIVESA critical design condition affecting the engineering designand safe operation of Arctic bottom founded structures such asTarsiut, the SSDC, or Moliqpaq, involves multi-year floe impact.Gulf Canada Resources initiated the study described here in aneffort to improve the quality of engineering design informationwith regard to the distribution of multi-year floe thickness.Study objectives were to: (1) provide a representative set ofmulti-year ice thickness measurements, and (2), to search forevidence of any trend toward thinning or thickening of near thefloe edge (an important factor in considering the forces duringpenetration of the floe by an structure).Floes were chosen as "typical" in terms of size, shape andsurface roughness. Severely deformed multi-year hummock fieldsor ridge features were not considered within the scope of thisstudy.2. SITE SELECTION AND METHODOLOGYSachs Harbour on Banks Island, Northwest Territories wasselected as the logistics support base for the multi-yearprofiling study.The study area in the vicinity of 73'08' N x 128'24' W isshown in Figure 1. All floes were within 20 km of the polarpack edge, delineated by a sharp increase in local multi-yearice concentration from 2/10 to >7/10.A total of 14 floes were documented over a 12 day period, fiveby manually drilling, seven with both sonar and drilling, andtwo with sonar only. Vertical 35 nun photography was obtainedfor nine floes. In all 172 drill-holes were completed togetherwith 13356 surface elevations.The following characteristics were sought in selectingspecific floes for study: (1) smoothly undulating surfacewithout major ridge sails within 150 m of the floe edge, (2)peak elevations along surveyed lines of less than 2.0 m, (3)well defined floe edge without significant pile-ups or evidenceof recent fracture, and (4) overall rounded shape indicatingsome maturity in terms of time elapsed since last major floesplitting.

y Area 7AMUNDSEN GULF \Beaufort SeaNORTHWESTFigure 1. Site location mapTypical measurement techniques applied to each floe included thefollowing items: (1) level elevation surveys (snow and icesurface) at 2 m spacing along profile lines run 100 m in fromthe floe edge, (2) drill-hole measurements along the same linesat a 5 to 10 m spacing, (3) sonar profiling, and (4) aerial nearvertical photography (floes 8 to 14 only).Drilling used continuous stainless steel augers (1.0 m x 0.05m) driven by electric drills powered from a portable generator.Ice thickness was measured to the point on the auger wherepenetration occurred (considered accurate to within 10 cm)In the event that the augers failed to penetrate by the 10 mdepth, drilling was halted because of the increasing risk ofjamming (and losing) the augur string. This depth limitationproved to be a detriment on only one profile where thicknessalong the entire line was greater than 10 m.The primary sonar system was a Mesotech Model 952 profiling

system. The head was usually positioned 23 m below the icethrough a 30 cm hole drilled in first year ice within 15 m ofthe floe edge. The sonar automatically scanned through 180' inlo steps. In profiles where sonar was the primary tool,drilling was limited to several check holes along the line.This paper deals principally with results from the drill-holedata. The sonar result compared favourably with the directmeasurements (typically within 10% in mean thickness).3. STATISTICAL ANALYSIS3.1 General Floe ThicknessAs an initial confirmation of drilling results, Floes 1 through11 were checked for hydrostatic balance by calculating the icespecific gravity implied by the ratio of mean freeboard to icethickness.Results given in Table 1 show that in order to float inbalance, Floes 1 to 11 would have to have a mean ice specificgravity of 0.903. This value agrees with published sea icedensity values at typical multi-year ice salinities. The smallstandard deviation of 0.01 proves that the floes are wellconsolidated, and that drilling on a relatively course spacing(5 to 10 m) provides an adequate measure of floe volume.Table 2. Calculated ice specific gravityFloe No. Mean Freeboard* (m)Mean Thickness (m)Specific GravityMean Specific Gravity = 0.903 Â 0.010* Snow depths converted to ice equivalent andadded to actual ice freeboard

Notes : Specific Gravity of cold seawater taken as 1.03Specific Gravity of snow taken as 0.32Calculations assume no voids and hydrostatic equilibriumTable 1 shows that the floes surveyed in this study fall intotwo groupings depending on surface roughness. Floes 1 through 6appeared quite smooth both from the air and on the ice. Peakelevations for floes in this group fall in the range 1 to 2 mwith an average elevation of 0.5 m. In contrast, Floes 7through 14 tended to appear much rougher with peak elevations inthe 2 to 6 m range and an average mean elevation of 0.7 m. Meanice thickness values for these two groups were: 4.2 m  1.4 m (#1 to 6) and 5.3 m k 1.7 m (# 7 to 14).The initial treatment of data involved plotting andsummarizing all available ice thickness measurements alongsurveyed lines perpendicular to the floe edge. Figure 2 is anexample of one of the rougher floes with the sonar profilecompared to drill-holes. Figure 3 shows the ice thicknessfrequency and % exceedance based on all available drill-holereadings.Thickness results are summarized as follows in terms of the-surface roughness categories described earlier:50thUpperPercentile DecileElSELWX ess (m) ss (mlDrilling A1 1DrillingSmoothSonarRoughInterestingly, the ratio of median ice thickness for smooth andrough floes is 1.29, very close to the ratio of mean elevationsfor those floe groups (1.32). There is a significant differencein extreme (10%) ice thickness values depending on the surfaceroughness of the floe; rougher floes are 2.5 m thicker at the10% exceedance level vs. 1.1 m at the median. Values fromFigure 3 which combine both floe types (slight dominance ofsmoother floedata) effectively fall mid way between the individualrough/smooth data sets.

'tHorizontal Distance (m)nt80Snow DepthIce ElevationDrillHolesSonar Under Ice Profile14Figure 2. Example floe profile.Ice Thickness (m)Figure 3. Ice thickness frequency and % exceedance(all data combined)

Table 2 compares the results obtained in this study with otherpublic sources.Table 2.Comparison of results with previous studiesThickness fml(method) Mean k Upper DecileAckley (1976) AIDJEX 3.6 1.5 --(Drill-hole)Wetzel (1971-75) Sverdrup Basin 2.9 -- 4.5(Drill-hole)Makyut (1977) Theoretical 3.2 - - 7.0Wadhams (1980) Beaufort Sea 3.9 2.1 --(Sonar)C-CORE (1980)5 Beaufort Sea 3.7 1.5 --(Airborne Radar)Vaudrey (1981) U. S. Beaufort 6.5 2.3(drill-holes)Dickins (1982) Beaufort sea7 4.2 1.4This study(Drill-holes)Beaufort sea8 5.4 1.7(Sonar/Drilling)Notes :one floe, 31 holes6300 data pointsThermodynamic and mass balance1,400 line km by submarine (USS Gurnard)27 line km99 drill-holes in 9 multi-year floes offshore Prudhoe Bay6 smooth floes/116 holes7 rough floes/56 holes and sonar

Direct comparison of the different data sources shown in Table2 is not possible for a number of reasons. Different datacollection techniques may lead to unavoidable bias in the samplepopulation, e.g., a dependence on tracked vehicles couldprohibit rough ice sapling; submarine sonar profiles include acomplete ice cross section requiring selective filtering ofleads, first year ice and ridge keels to derive level multi-yearice thickness.3.2 Floe Edge GeometryThe purpose of this form of data analysis was to search forsignificant trends in multi-year thickness as a function ofdistance from the floe edge.The under ice profiles for selected floe edges are plotted andsuperimposed in Figure 4 as a visual presentation of the rangeof edge geometries measured in this study (surface profiles areblended to show a single envelope of elevations).The data shows considerable spread, but the mean resultsindicate a trend to a relatively shallow angle of entry at theedge (23Ok 14').Any appreciable thinning of the floe was onlyapparent within the first few meters of penetration. The meanice thickness for measurements within 3 m of the floe edge was3.51 m compared to an overall mean for all distances of 4.45 m.Beyond the initial penetration distance into the floe, thereappears to be a tendency towards a shoulder or crest in theunder ice profile. The maximum draft in the first 20 m ofhorizontal penetration along a line perpendicular to the floeedge, averages 5.6 m,which is significantly greater than themean of 4.2 m for all drill-hole thickness data (0 to 100 m fromthe edge) .Derived profiles from sonar data showed similar trends in floeedge geometry with evidence of a deep shoulder within 25 m ofthe edge and localized thinning within the first 10 m.

Figure 4.Example floe edge profiles.4. CONCLUSIONSThe ice thickness distributions derived in this study comprisethe most extensive set of multi-year field measurementsavailable for the Beaufort Sea.Floes were separated into two categories according to surfaceroughness.SmoothRough

- -Median Thickness 3.7 m 4.8 mCorresponding ice thickness values from drilling and sonar are:Upper Decile Thickness 5.4 m 7.9 mMaximum Thickness 7.5 m 14.0 mProfiles were deliberately selected so as to avoid ridges andmajor hummock features (some influence from these features isunavoidable in documenting the rougher floes).Floe sizes were not of primary concern in the study, butqualitative impressions gained from two weeks of aerialobservations indicated that multi-year floes within 20 km of thepolar pack edge are predominantly less than onekilometer in- - --diameter.. --A statistical treatment of all thickness measurements as afunction of distance from the floe edge showed a trend tothinner ice within five metres of the edge (0.8 m averagereduction) and possible evidence of an underwater shoulderwithin the first 20 m of the edge.REFERENCESC-CORE (1980). Multi-Year ice thickness distribution in theBeaufort Sea determined by airborne impulse radar, for EssoResources and Canadian Marine Drilling, Calgary.Maykut, G.A. (1977). Estimates of the regional heat mass balanceo the ice cover in the central Arctic, AIDJEX Symposium,Seattle.Vaudrey, K.D. (1981). Beaufort Sea multi-year ice featuressurvey Volume 1: Field Survey, AOGA Project 139.Wadhams, P. and R.J. Horne (1980). An analysis of ice profilesobtained by submarine sonar in the Beaufort Sea, Journal ofGlaciology Vol. 25 No. 93, pp. 401-424, Cambridge.Wetzel, V.F. (1971 to 1975). Statistical study of late winterice thickness distribution in the Arctic Islands, A.P.O.A.Projects 96-1 to 96-1 by Sun Oil Company, Calgary.

ACKNOWLEDGEMENTSThe author wishes to acknowledge the contributions ofindividuals who worked long hours making this field program asuccess: David McGonigal, Ken Anderson, Yos Lussenberg, BrianWright and Harry Iyer of Gulf Canada, Helmut Lanziner ofOffshore Survey, and Pat Kudlak of Sachs Harbour. The people ofSachs Harbour provided community services, bear monitors andfield assistants. DF Dickins Associates Ltd. was responsiblefor the drill-hole program, elevation surveys, overall datainterpretation and final report. The sonar profiling andassociated analysis was contracted to Offshore Survey andPositioning Services Ltd.

ICE DRIFT AND UNDER ICE CURRENTSIN THE BARENTS SEA0istein Johansen,Jan Fetter Mathisen,Kjell SkognesOceanographic Company of Norway, WSPic-senteret, N-7005 TrondheimNorwayABSTRACTAs part of an environmental data measurement programme in the BarentsSea, conducted by Oceanor on behalf of the Norwegian PetroleumDirectorate, a dedicated experiment was carried out during winter 1987-88,incorporating measurements of ocean currents under ice and ARGOS satellitetracking of ice floes. The analysis of the data from this experiment haveup to date concentrated on ice drift trajectories, but features of generalinterest have also been found from the current measurements. The mainconclusions to be drawn from the data at the present stage of analysis are1)A strong correlation is found between ice drift and local wind, 2)Ice: floe drift is closely coupled to the tidal current regime of the region,3)Current measurements at 10m depth and below reveal no evidentcorrelation with ice drift at frequencies away from tidal frequencies, and4)The current response at 10m and below are dominated by topographiceffects and mesoscale oceanographic processes.1. INTRODUCTIONOCEANOR has been engaged in a comprehensive environmental datameasurement programme for the Barents Sea since 1978 on behalf of theNorwegian Petroleum Directorate (NPD). The programme has includedmeasurements of wave, current, hydrographical and meteorologicalparameters, with emphasis on the Tromsaflaket, Bjarneiya and Sentralbankenregions. However, in the period from November 1987 to July 1988, currentmeasurements were also made along a section across the ice border West ofSentralbanken. In addition an ice floe tracking experiment was initiatedin the same region in January 1988. In this paper, results from this partof the programme will be presented and discussed.

6 1 1 1I , ICE (2~4 ml-, -Figure 1 (Above). Location of current meter stations.The average monthly extensions of the ice edgeshown in the map are based on DNMI's ice charts.Figure 2 (Left). Example of current meter mooring design(Station S3, water depth 157111).

Length:Diameter instrument/cylinder:Diameter battery/svitch cylinder:Veight1350 mm125 mm115 mm20 kgFigure 3 (Above). Deployment positions of ice drifters.The average monthly ice borders shown on themap are based on DNMI1s ice charts.Figure 4 (Left). Design of the ARGOS positioned icedrifters used in the experiment.

2. DESCRIPTICN OF THE EXPEXIMENT2.1 Current measurementsThe locations of the different moorings are shown on the map in figure1, on which the monthly average extension of the ice edge (ice coverageexceeding 6/10) is also shown for reference. As indicated, stations Sl,S2 and S3 were under the ice cover for most of the experimental pericd,while stations S4 and S5 were located in open water south of the iceborder.Three different types of current meters were used in the experiment,i.e. Aanderaals RCM-4, Simradls UCM-30 and !3G+Grs VMCM. The meters weremounted at different depths in an 1-type mooring as shown in figure 2.The number of current meters mounted on each mooring varied from 3 to 6,depending on the water depth at each site, but the general design was asshown in figure 2, i.e. one mete1 at 10 m below the free water surface,one 5 meters above the bottom, and the remaining spaced at varyingdistances within the water column.Despite the short distance between the upper current meter and the underice surface, only one of the moorings was disturbed by ice floes driftingby in the experimental pericd (station Sl). This mooring was redeployedin a new position in January 1988. Fxcept for this accident, the datarecovery was in general very good, with 75 to 100% data return for mst ofthe current meters, with a few exceptions due to battery failure orelectronic problems.2.2 Ice driftersThe initial locations of the ice floes tracked in the experiment areshown in figure 3. Each location is designated by the ARGOS transmitterID number, while the different symbols are used to indicate approximatetimes of deployment. The ice floe drift was recorded by speciallydesigned ARGOS positioned buoys, made up of glass fibre and divinycell(ref. figure 4). The buoys were fixed to the ice floes by inserting theleg of the buoy in predrilled holes in the ice. When the ice floe brokeup or melted, the divinycell float kept the buoys in surface position.The switches mounted on the leg of the buoys were intended to provideindications on melting or break up of the floes. The on or off status ofthe swithes were transmitted as signals over the ARGOS system. However,this system proved to give too early warnings, probably due to local

melting around the leg of the buoys. Thus, retrieval of the buoys hadinstead to be guided by inspection of weekly ice charts issued by theNorwegian Meteorological Institute (ENMI).In this section, results from the experiment will be given in terms ofselected examples of current recordings and ice drift trajectories. Thetotal set of recordings is presented in detail in a data report preparedfor NPD (Johansen et. al. 1988).3.1 Current masurementsAll current measurements show mrked oscillations at diurnal andsemidiurnal periods, most probably related to astronomical tides.However, at these Northern latitudes, inertial oscillations will have aperiod close to the principal lunar tide (m), and may thus not be easilydistinguishable from the tidal fluctuations. Harmonic analysis of timeseries extending over several months will however in general exclude themore or less sporadically occurring inertial oscillations. Results fromthis analysis are given for each station in figure 5, in terms of thetidal ellipse for the two dominating tidal constituents.In order to obtain a picture of the mean flow, tidal oscillations wereremoved by a 24 hour low pass filter. In figure 6, smoothed currents arecompared for a pericd of 30 days with wind data obtained from griddedhindcast wind delivered by ENMI. The wind data is also smoothed by a 24hour low pass filter. The results show no obvious correlation eitherbetween the recordings at each station, or with wind data.The lack of any evident correlation in the currents observed at eachstation reveal the presence of a significant current shear in this zone,where warm Atlantic Water from the South West strikes cold Polar Waterfrom the North East. This situation is reflected in the more or lesspersistent mean flow towards North East observed at station S4, comparedto the dominating southward mean flow at station S2 (cfr. progressivevector diagrams drawn from the smoothed time series in figure 7). Thereadings are however far from featureless, while all stations show largevariations in current speed and direction at periods corresponding to 5 to10 days, probably related to mesoscale oceancqraphic processes (e.g.eddies).

Figure 5. The dominating tidal constituents derived from harmonicanalysis of the current measurements at lorn depth. Thescale is indicated by the reference ellipse drawn at theupper right.a)-semidiurnal tidal current ellipsis (MZ).b) Diurnal tidal current ellipsis (Kl).

Time. Jul~on dayFigure 6. Smoothed (24 hour low pass filtered) currentdata measured at 10m depth. Wind vectors (alsosmoothed) from DNMI's hindcast data adjacentto station S5 are shown for comparison.Figure 7. Progressive vector diagram for a 30 day periodbased on the data presented in figure 6. Therelative locations between stations are givenin scale.

3.2 ice drift velocitiesFigure 8 shows an example of observed drift trajectories from the firstdrift period. The number of position fixes pr. day may be as high as 18to 20 on the best days, while data may be missing for shorter periods,probably due to adverse conditions for radio transmission (cfr. graphinserted in figure 8). Due to this rather high positioning frequency,oscillations at tidal periods are easily detected in the trajectories,particularily in the first part of the drift period.Smoothed drift trajectories, where the tidal fluctuations are removed bya 24 hour low pass filter, are shown in figure 9 for the five ice floestracked in the first experiment. The ice border at the end of week 2,which is shown in the same map, indicates that the buoys may have enteredopen water a few days prior to the end of each drift period.Tidal analysis of the drift was made on the residual drift obtained bysubtracting the smoothed trajectory from the original position data. Inorder to account for spatial variations in the tidal fluctuations alongeach trajectory, the analysis of these oscillations are made with a movingtime window of 7 days, centred at time intervals of 1 day. The analysismade at two tidal frequencies, i.e. M2 and Kl, revealed drift velocityamplitudes comparable to the results obtained from the moored currentmeters.However, due to the rather short time period covered by each window, anacceptable separation of oscillations near the semidiurnal frequencies cannot be expected (i.e. M2, $2 and sporadic inertial oscillations are notdistinguishable). The most reliable results in terms of tidal ellipsisare thus expected to come from the analysis of at the diurnal frequencies.Figure 10 shows results obtained for the diurnal constituent (Kl)plotted at intervals of five days for all drift periods during theexperiment. At locations adjacent to the current meter stations, theresults are found to compare favourably with the tidal ellipses obtainedfrom the current meters (ref. figure 5). This indicates that thedrifting ice floes are closely coupled to the tidal currents in the watermasses.Such a close coupling between the oscillatory motions of the ice floesand tidal ocean currents is also reported by other investigators (Reynoldset.al.1985, Morison et.al. 1987). On the other hand, no strongcorrelation seems to exist between the mean (i.e. smoothed) drift and themean water flow. This is seen from the following graphs, where ice driftvelocities are found to reflect variations in local wind, while no such

76 1. =:;. :::,;::;:....-:~..-. ..- .- ..- -'.... . ~ .-.O]''.'''.'' ' " ' - '20 25 50 35 aJULIAN DAYFigure 8. Trajectory from ARGOS buoy 4414 in the first drift period.The inserted graph shows the number of position fixes pr.day obtained from the ARGOS system.Figure 9. Smoothed trajectories from the first drift period. The iceborder drawn at the map are based on weekly ice chartsdelivered by DNMI.7 3

correlation could be detected in the current meter readings.3.3 Wind induced driftIn order to check the degree of correlation between ice drift and wind,a least mean square vector regression analysis has been performed,presuming that ice drift is proportional to the local wind, superimposedon a quasi-permanent background current. The factor of proportionality isexpressed as a vectorial quantity, combining the ratio between ice driftand wind velocity and the deflection angle between drift and winddirection. The analysis is made using a 5 day moving time window on thebasis of 24 hour low pass filtered drift trajectories, resampled at 6 hourintervals. The corresponding wind is extracted from DNMI's griddedhindcast wind, using values from grid points closest to the trajectory atany time.Figure 11 shows an example from the second drift period for buoy 4115.The drift velocities are obtained from the 24 hour low pass filtered drifttrajectories, resampled at 6 hour intervals. Smoothed wind vectors basedon gridded hindcast data adjacent to the trajectories are shown on thesame graph. The bottom graph shows the wind drift factor presented as avector of length corresponding to the factor of proportionality betweendrift velocity and wind speed, while the orientation, measured clockwiserefers to the deviation angle between drift and wind direction.The results were in general found to reveal surprisingly consistentcorrelations, with wind drift factors most frequently in the range from 1to 3% of the wind, and deflection angles predominantly in the range from 0to 30' to the right of the wind. In most cases, large deviations fromthis range are found to be related to periods when buoys are drifting inopen water. Moreover, a close inspection of the data indicates that driftfactors near the lower range (1.5%) in general coincide with locationsdistant from the ice border, while larger drift factors (2.5%) areobserved in locations closer to the border.The background current pattern obtained from the analysis is in generalfound to be quite irregular and relatively week, but the trend indicates astronger south-westerely flow adjacent to the southern ice border,consistent with the established flow pattern in the region.

Figure 10. Diurnal tidal ellipsis (Kl) obtained by analysis oftrajectory data for all drift periods. The ellipsisare drawn at five days spacing along each trajectory.00 ^^ 0o'\!a00,,,, ,,,, , , , , 1 , , , , I ,,,, ,,,, I ,,,,,,,,, ,,,, ,,,, F40 45 50 55 60 65 70 75 80 85 90Time. &Lion dayFigure 11. Smoothed drift velocities derived from the trajectoryof buoy 4115 in the second drift period (b), comparedwith hindcast wind data along the trajectory (a). Winddrift factors obtained by the complex correlation analysisare shown as vectors in (c).

4. CONCLUSIONSThe results of the analysis so far have revealed several interestingfeatures with general implications. The close coupling between the tidalLcurrent regime and the drift-of-iczfl3es reported by other investigatorshave also been found in this study. A close correlation has also beendetermined between surface winds and ice drift, expressed in terms of awind drift factor ranging from 1 to 3%, with the variation seeming toreflect the distance of the ice floe from the ice edge. On the otherhand, no evident correlation has been found between surface wind and--- --current measurements, which were made at a depth of 10m and below. This-seems to indicate that the variations in the current meter data atfrequencies below the tidal range were dominated by mesoscaleoceanographic processes rather than direct wind forcing. The largedirectional deviations in the currents observed at adjacent stations seemsto strengthen this assumption.A more detailed study of the data obtained in this experiment isexpected to give additional results of importance for short term ice driftpredictions in the marginal ice zone. Such a study should be focused onthe observed variations in the wind response of the ice floes, and themesocale variability in current measurements.5. REFERENCES0. Johansen, J.P. Mathisen and P. Steinbakke, 1988. Environmental DataCollection in the Barents Sea. OCEANOR Report 88059 prepared for NPDand ODAP. Oceanor a/s, Trondheim, Norway, 457 pp.J.H. Morison, M.G. McPee and G.A. Mayku, 1987. Boundary Layer, UpperOcean, and Ice Observations in the Greenland Sea Marginal Ice Zone.Journal of Geophysical Research, Vol. 92, No C7, pp. 6987-7011.M. Reynolds, C.H. Pease and J.E. Overland, 1985. Ice Drift and RegionalMeteorology in the Southern Bering Sea: Results from MIZEX West.Journal of Geophysical Research, Vol. 90, No C6, pp. 11967-11981.

RELATIONS BETWEEN TOP AND BOTTOM ICE TOPOGRAPHYUSING A SCANNING SONARAnund Sigurd JohnsenSea ice researcherNorwegian Polar Research InstituteP.O.box 158N-1330 OSLO LUFTHAVNNORWAYABSTRACTTen ice floes in the Barent Sea has been mapped on the top and bottomsurface with a theodolite, stereo photoes and a high accuracy,profiling sonar system. The mapping area varied from 500m2 to 4000m2,and all the sites were in the marginal ice zone less than 90km fromthe ice edge. The correlation between the freeboard and the icethickness was studied.Previous observations of level ice yielded correlation coefficientsof 0.8. Our measurements revealed correlation coefficients of 0.7 formulti-yearice.partly deformed ice and 0.5 for first-year very deformedApart from measurement errors, it is believed that this differences-- . --.-are due to the effects of thermodynamic processes, isostaticrelaxation and deformation processes. Thermodynamic processes and-isostatic relaxation seem to increase the correlation while- --deformation processes tend to reduce the correlation.-1. INTRODUCTIONThis work is an attempt to describe the typical ice floes of an icefield with ridges and level ice. An imaging system similar to theIMAPS system described on POAC-87 (Harrington & Kreider, 1987) hasbeen used at the Norwegian Polar Research Institute since 1986. Themain goal was to study the size of the domes under the ice were oilcould be trapped after an oil catastrophe. Therefore we tried to mapfloes that were representative for the area. When time allowed, wealso mapped the ice surface.

Many previous studies have concentrated on large multi-year ridges(Wright et al. (1978) and (1979). Dickens & Wetzel (1981). Kovacks(1983), Harrington & Kreider (1987)). This is very specializedstudies, because only 2-3 ridges per km is normally observed(Wadhams. 1983). Other authors have avoided the deformed ice andmeasured level ice (Hibler et al. (1972). Vinje & Finnekgsa (1986)).SONSON73N73N7 EN76N741174NFigure 1. Map showing the locations of the measurement sites.Crosses show sites with first-year ice, circles show siteswith multi-year ice in summer situation and triangels showsites with multi-year ice in winter situation.2. FIELD AREATen ice floes in the Barent Sea have been surveyed , 7 first-yearfloes (March), 1 multi-year floe in summer situation (late August)and 2 multi-year floes in winter situation (March). Multi-year floesand first-year floes where distinguished by their surface shape andsalinity-profiles. All the sites were in the marginal ice zone, less

than 90 km from the ice edge (fig.1). The size of the measurementarea varied between 500m2 and 4000m23. MEASUREMENTSTO DATA UNITkOCEAN L- ANGLE OF VIEW;' 1.7OFigure 2.Sketch of the sonar arrangement on an ice floe.A Mesotech 971 scanning sonar was used to map the ice bottomtopography. The sonar had 1.7 angle of view, and was mounted at theend of a 15m long metal bar and lowered through a hole in the ice.The sonar was pulled to a horizontal position and a 80m long profileof the ice bottom, 4Om to each side, was measured every 5 degrees ina star shaped pattern. A step motor turned the sonar head in steps of0.225' , while the turning of the metal bar was done by hand.Autocorrelation of ice thicknesses separated by a distance X, wascalculated (Johnsen & Vinje, 1987). The data were interpolated into agrid with 2m grid spacing, and recorded in a data base. Objectiveanalysis was used as interpolation technique, and the autocorrelationfunction was the weighting function.The top surface was usually surveyed with a theodolite. We measuredpoints on the surface that were "special", like a top or adepression, or points that were representative for a larger area. Thedata were corrected for snow at the surface and plotted. Contourlines were drawn manually while taking into account the comments fromthe field and pictures taken from the ship. A grid was placed on themap and the grid points were recorded in a data base.

At one site, the snow cover was negligible, and the surface gridwas constructed from stereo photos taken froma heliocopter.4. MEASUREMENT ERRORSThe Mesotech 971 sonar has a time resolution of 15.kus giving 1cmerror in distance measurements. There are four other principalsources of error; The sonar is sending the signal in a conical beamof 1.7. density differences in the water can change the direction ofthe sound signals, the sound speed may be different from the oneassumed by the sonar and the metal bar may be tilting or twisting.These are all errors that increases with distance from the sonarhole.Density changes is small in the upper 15m (Rudels, pers. comm.),and the sound velocity can be calibrated, so these two sources oferror can be compensated or neglected.The sonar is transmitting in a conical beam of 1.7'. It is mostlikely that we get a return signal from the top part of the conicalbeam when the transmission direction is nearly parallell to thehorizon (ice bottom). The sonar will act as if it was a center beamreturn. This will give errors both in the vertical and in thehorizontal. 4Om from the sonar hole can vertical errors be up to 50cmwhile horizontal errors are negligible. At the sonar hole, however,vertical errors are negligible while horizontal errors can be up to20cm. The data is corrected for such errors assuming that it alwaysget a top return from the conical beam.The metal bar may be tilted by the current relative to the icefloe. It consists of five bars connected together. Both theconnections and the bar itself, give room for tilting.Each measurement of a floe takes one hour. The relative current tothe ice floe is often varying during such a time span. It istherefore difficult to extract the error from the data. Severe1techniques is used, where the main point is to compare profiles withneighbouring profiles and assume that the mean surface should tiltapproximately the same way.Only six connections in the metal bars give very little room fortwisting, so this error is small compared with the others.Altogether we believe that the errors of the grid values of the icebottom is approximately 10cm close to the sonar hole, and increaseswith the distance from the center to 50cm in 40m distance. The error

is less in flat areas and larger in rough areas.The theodolite is a high precision instrument, but it is sensibelto wave action on the floe. The errors of the theodolite measurementsvaried from lcm-5cm in height and 0.2m-lm in the horizontal plane,increasing with distance from the theodolite and increasing withswell height. This means that the vertical error in each surface gridpoint could vary from lcm-50cm depending on the topography. Thelargest error could occur in steep slopes on the surface.DISTANCE(m)Figure 3. The autocorrelation of freeboards separated by a distanceX, as a function of X. The autocorrelation is calculatedfrom the surface grids.The freeboard autocorrelation function (fig.3) calculated from thesurface grids, clearly shows that measurements less than 1m apart arewell correlated (correlation coefficient larger than 0.90). Meanerror in the surface grid is therefore assumed to be 2cm in flatareas and 5cm in ridged and rafted areas.5. CORRELATION BETWEEN FREEBOARD AND ICE THICKNESSThe essential results of the correlations between the freeboard andthe total ice thickness are presented in table 1.The three multi-year floes were reasonably well correlated with acorrelation coefficient (CC) between 0.64 and 0.73. The seven firstyearfloes had generally less correlation (0.18

, .75 53 E26 If- NOR36 PCLARI NSTI TU7'X-DlRECTI ON (rn)24/3/1988 13 48 GRI D SPACI NG 2. OmN75 58 E26 18 NORSK POLARI NSTI TUTTFigure 4.Map of a first-year floe. Upper map is the top surface andthe lower is the bottom. Heigths is distance from sealevel (m). The cross shows the sonar hole.

Table 1. Results of the correlation between the freeboard (F) andthe ice thickness (T).I= Ice categoryNW = First-Year ice in WinterMYSMYWCC= Multi-Year ice in Summer= Multi-Year ice in Winter= Correlation CoefficientT = Mean ice Thickness (meter)F = Mean Freeboard (meter)T/FoTF= Ice Thickness to Freeboard from regression= Standard deviation of T on F in regression (meter)oTF/T = oTF divided by TN = Number of grid points correlatedPOSITIONN7518 E2325N7637 E3010N7605 E2341N7558 E2618N7542 E2541N7523 E2249N7521E2247N8024 E3108N7812 E3144N7503E2107IFYWFYWFYWFYWFYWFYWFYWMYSMYWMYWCC T F T/F oTF oTF/T N0.36 1.29 0.23 5.67 0.91 0.71 10200.75 1.39 0.17 7.92 0.81 0.58 10210.41 1.58 0.15 8.91 1.16 0.73 9450.52 1.77 0.19 8.15 0.79 0.45 1210.64 2.91 0.40 6.04 1.63 0.56 1570.18 1.66 0.29 5.79 0.59 0.36 1570.59 1.85 0.24 6.59 0.99 0.54 1340.67 3.98 0.68 5.37 1.43 0.36 7210.64 2.78 0.32 8.01 1.26 0.45 4590.73 4.13 0.61 5.98 1.72 0.42 405MeanMeanMeanNWMYSMYW7120.49 1.78 0.24 7.01 0.98 0.56 35550.67 3.98 0.68 5.37 1.43 0.36 7210.69 3.46 0.47 7.00 1.49 0.44 864correlation coefficient of 0.52, which is close to the mean.The mean ice thickness was 3.7m for the multi-year floes and 1.8mfor the first-year floes. The standard deviation was 1.2m and 0.810respectively.The regression lines were forced through origo (Vinje & Finnekhsa,1986) with both T and F as independent variables. T/F was taken asthe mean of the two regression lines. The overall observed value ofT/F was 6.8 with a standard deviation of 1.3, implying a mean ice

density of only 0.88t0.02 g/cm 3 . I am not aware of any publishedmeasurements of the ice density in this area, but it is most probablytoo low. We should expect 0.91-0.92 g/cm 3 (Nakawo, 1983 and ownmeasurements from surrounding areas). This deviation is supposed tobe caused by overestimation of the freeboard, which is mainly due tothe difficulty in distinguishing between snow and ice on the surface.It is equivalent with a freeboard error of 5cm for first-year ice andl6cm for multi-year ice. The state of the snow/ice interface changesfrom floe to floe. but is consistent at the individual floe. Thismeans that the freeboard overestimation is almost a constant at onefloe, and will not affect the correlation results.However, there is an error of the freeboard with standard deviation3cm and an error of the ice thickness with standard deviation 20cm(chap. 4). that weakens the correlation. First-year ice is moreinfluenced by the measurement errors than multi-year ice due to thesmaller standard deviations of T and of T on F. Correcting for theassumed errors, the average correlation coefficient is increased from0.49 to 0.57 for first-year ice and from 0.68 to 0.71 for multi-yearice.6. CONCLUSIONS AND DISCUSSIONEarlier observations have consentrated on the flat part of the icefloes, the so called level ice. It has reached its present thicknessby natural thermodynamic growth alone, and is supposed to be inisostatic equilibrium. From 31 drillings in multi-year ice, Hibler etal. (1972) obtained the ratio T/F=8.58 with a correlation coefficient(CC) of 0.79 and a standard error of estimate of T on F (oTF) of0.60m. Vinje & FinnekAsa (1986) calculated T/F=8.35 from 362drillings in mainly multi-year ice. CC was 0.80 and oTF was 0.68~1.When we extend our area of interest to include deformed ice, wenote that the correlation coefficient is lower than for level ice. CCfor multi-year ice is found to be 0.7 while it is 0.8 for themulti-year level ice. The deformed ice also increases oTF to 1.5~1.The observations of the first-year ice were made in the marginalice zone in the Barent Sea, a higly dynamic area with wave action andfrequent passages of low pressures. Floes are constantly breaking upand refreezing. Most larger floes prooved to consist of smaller floes(10-50m diameter) frozen together. It was almost impossible toseparate first year level ice from deformed ice. Floes that seemed to

e flat, often prooved to have blocks of ice pressed underneath.The field areas with first-year ice consisted therefore mainly ofdeformed ice, and the correlation coefficient was as low as 0.5 onthe mean. However, some floes had high correlations (COO.75). whileothers had almost none (C00.18). oTF was only 1.0~1, but that wascaused by the lower mean ice thickness. The relative standarddeviation (oTF/T) was 0.40 for multi-year ice while it was 0.56 forfirst-year ice. This value can be taken as an index of deformation.The young winter ice is sensitive to deformation processes.Thermodynamic processes and isostatic relaxiation need long time toaffect the shape of ridged and rafted ice floes, at least one meltingseason. The shape of winter ice in the marginal ice zone is thereforemainly imposed by the deformation processes.A multi-year floe is thicker and more consolidated than a firstyearfloe, and it is therefore more resistant to deformationprocesses. The thermodynamic processes and isostatic relaxation haveworked long enough to also be important factors in shaping the floe.Level ice is defined as undeformed ice, and thermodynamic effectsand isostatic relaxation control the shaping of the floe.Previous measurements of level ice yielded correlation coefficientsof 0.8 (Hibler et al. (1972), Vinje & Finnekhsa (1986)). We obtainedcorrelation coefficients of 0.7 for multi-year partly deformed iceand 0.5-0.6 for first-year very deformed ice. The main reason forthis difference is supposed to be due to the fact that ourmeasurements also include ridges where there often is a skew verticalmass distribution.Although the data are limited, these differences are supposed to bedue to the effects of thermodynamic forces, isostatic relaxation anddeformation processes. Thus, thermodynamic forces and isostaticrelaxation seem to increase the correlation between the freeboard andthe ice thickness, while deformation processes tend to reduce thecorrelation. This is illustrated by the summarized results :Level ice : CC = 0.8 (other authors)Partly deformed ice : CC = 0.7 (present measurements)Very deformed ice : CC = 0.5 - 0.6 (present measurements)

7. REFERENCESDickens, D.F. & Wetzel, V.F. (1981). Multi-year pressure ridge study,Queen Elisabeth Island. Proceedings of 6th International POACConference, Quebec City, Canada, 765-775.Harrington, M.G. & Kreider, J.R. (1987). Profiling multi-year icefeatures. Proceedings of 9th International POAC Conference,Fairbanks, Alaska.Hibler 111, W.D., Ackley, S.F., Weeks, W.F. & Kovacs, A. (1972). Topand bottom roughness of a multi-year ice floe. AIDJEX Bull. 13.Div. of Marine Res., University of Washington, US.Johnsen, A.s. & Vinje, T. (1987). Havisundersakelser i Barentshavet(Sea ice research in the Barent Sea). Utkast ti1 sluttrapport,AKUP-prosjekt 1.3, Norsk Polarinstitutt, Oslo, Norway. (InNorwegian).Kovacs, A: (1983). Characteristics of multi-year pressure ridges.Proceedings of 7th International POAC Conference, Helsinki,Finland, Volume 3.Nakawo, M. (1983). Measurements on air porosity of sea ice. Annals ofGlaciology 4, 204-208.Vinje, T. & Finnekasa, 0. (1986). The ice transport through the FramStrait. Skrifter Nr. 186, Norsk Polarinstitutt, Oslo, Norway.Wadhams. P. (1983). Sea ice thickness distribution in Fram Strait.Nature 305,5930.Wrigth, B.D., et al. (1978). Sea ice pressure ridges in the BeaufortSea. IAHR Symposium on ice problems, Lulea, Sweden, 249-271.Wrigth, B.D., et al. (1979). Multi-year pressure ridges in theCanadian Beaufort Sea. Proceedings of 5th International POACConference, Trondheim, Norway, 107-126.

STRUCTURE OF FIRST YEAR PRESSURE RIDGESIN THE BALTIC SEAMs Paula KankaanpaaResearch assistantFinnish Institute of Marine ResearchBox 3300931 HelsinkiFinlandABSTRACTThis work presents the results of field measurements of themorphology of ice pressure ridges. Transverse and longitudinalprofiles across ridges were made. The surface profile of 62ridge sail profiles was determined by levelling. The size andshape of the keel and the porosity of 8 entire ridges weremeasured by a motor drill.The average height of all the studied ridges is 0.65 m. Theaverage height of the sails whose keel was also measured was1.0 m and the mean depth 6.3 m. The mean porosity of theentire ridges is 29 %. The porosity in the sails is about 8 %lower than in the keels. The ratio of sail height to keeldepth is 1/5.8 on average. Apparent isostatic imbalance iscommonly present in the measurements.There is a positive correlation between the maximum blockthickness and the ridge size../ -.--1. INTRODUCTIONSea ice ridges occur every winter in the Baltic Sea and theyconstitute a severe problem to winter navigation and offshorestructures. Better knowledge of ice ridges is important forengineering and also for various areas in sea ice geophysics

and for interpretation of remote sensing images. Ridges resultfrom compressional and shearing motion between ice floes indrifting ice.An intensive study of sail height distributions in the Gulfof Bothnia of the Baltic Sea was made by Lepparanta (1980). Hemade observations with a laser profilometer from a icebreakerdeck. The mean sail height was 38-67 cm and ridge density 2.1-22.1 ridges/km. The cutoff height for sails was 30 cm.Measurements of several ridge profiles in the Baltic Sea aregiven in Palosuo's studies (1975). He studied the size andgeometry of ridges by means of diving. The height of most ofthe sails was between 0.5-2 m and keel depth 6-14 m. Sailinclination was between 1O0 and 50' and the average was 30'.Keel inclination was between 15Â and 60' and the average was3g0.There is only very little information about the effects ofice thickness, ice block size and orientations on the ridge inthe Baltic Sea. And there is only one experimental study ofthe porosity of an entire ridge in the Baltic Sea (Kankaanpaa1989). Also, only a few measurements of ice ridge porosityexist for Arctic Sea areas.This work is concerned with a study of geometry and internalstructure of 8 pressure ridges based on field measurements inthe Baltic Sea. Also the sail geometry and snow thickness of54 sails is determined. The size, thickness and orientationsof ice blocks incorporated 10 ridge sails were measured.2. METHODSAll measurements were made during March and April 1988.Ridges were studied at the five sites shown in Figure 1.Studied ridges include both single ridges and a rubble fieldarea. The profiles of the sails and snow thickness on themwere obtained by taking surface elevations using standardlevelling techniques. The inside structure of the ridge andthe shape and size of the keel were defined by a motor driven55 mm diameter drill designed by Kovacs (see References). Thedrill holes were made along the levelled profiles in 0.5 - 5 m

intervals. To insure that the bottom of thekeel was penetrated a plumb-linewas lowered in every drillinghole at least 10 m below thekeel.The surface dimensions andthicknesses were recorded fromabout 10 ice blocks of 10 sails.The surface dimensions of iceblocks are the length (longestaxis of the top surface of theblock), and width (the axis atthe half way of the length perpendicularto it).The width determination of asingle ridge sail is difficultbecause it is not self-evidentfrom where it should be measuredi.e. from where the sail begins.Subjectively it is often relativelyeasy to say, but notFig. 1. The locations ofthe studied ridgesalways. When handling the data statistically there is a needfor some clear way to determine it. One simple way, which isused here is to measure the width from the point from wherethe level ice starts to bend continuously up towards the sail.At rubble field areas or at places where the ridges have growntogether the Rayleigh-criterion has been used to distinguishseparate sails from each other. According to this criterion,two ridges are resolved to be separate, if the trough betweenthem has a minimum relief which is less than half of theshallower of the two ridges (Wadhams 1986).The criterion fits quite well with our imagination of what isa separate sail but tells only little about the keeldistribution. One keel may have several sails according toRayleigh-criterion.The slope inclination was calculated as follows. First theapparent area of the cross-section of half of the sail profilewas determined (Fig. 2). Then a right-angled triangle, whoseheight is the same as the relative height (the height abovethe surrounding ice surface) of the sail, was determined in a

way that its area is the same as the area of the half crosssectionof the sail. The slope anlge a and width w of the sailare then taken from this triangle (see Fig. 2).La=arctan(h/w)-w-watersurfaceFig. 2. Determination of an average slope angle of a sail.The determination of keels and their slope angles are made inthe same way.The apparent porosity was determined from the number andthickness of the interblock voids encountered during thedrilling. This is naturally an estimate because the actualgeometry of the internal voids was impossible to determine.3. RESULTS3.1 Ridge profilesRidges Rl, R2, R3 and T (Fig. 3) were formed in a driftingice field. The diameters of the ice floes in which the ridgeswere found were roughly 40-100 m, and their thicknesses wereabout 40 cm. The thickness of the ice blocks in the sailswere 15-30 cm. Consequently the ridges were formed from ice ofa thinner refrozen lead or earlier in the winter when thefloes themselves were thinner. The latter assumption is morelikely, because the ridges were supposed to be old. The mainresults of entirely measured ridges are expressed in Table 1.and ice block results are given in Table 2.

profile Iprofile Tw1Ñ\ ----snow surfaceice'slush'voidmoving ice blockprofile RR3Fig.3. Cross-sections of ridges I, T and R.

Ridge profiles A and I (Fig. 3 and 4) were obtained at theedge of a large rubble field area located at the edge of thefast ice. The rubble field was roughly 6-10 km long by 1-3 kmwide and had been formed from ice drifting against the fast iceedge. For ridge A the height was 1.65 m and depth extended 12.3m below the water surface. The mean height of the ridges inrubble area near A was 0.43 m. The keels were grown together asa wide keel. Their depth was about 3.72 m.An interesting feature of the longitudinal profile of theridge A is the abrupt cutoff of the north edge of the profile(Fig. 4 , longitudinal profile of A).A 180 m long surface profile (profile I. Fig. 3) of therubble field was levelled about 300 m south from profile A. Theshape of the sails in the rubble were very variable. Theaverage angle of the west side of the sails were 22.4' and eastside 14.8".Profiles R1-R3, T, A and I were measured at the beginning ofMarch. Ridges Sl, S2 and S3 were measured more than one monthlater when the sea ice had begun to melt. The profiles areshown in figure 5.

surtwv proNw d A1 and A2Elongitudinal profile of A A, A A2iceslush'----snow surfaceridge A.

, profile S121 NE S W- profile S2longitudinal profile of S221 NWs2profile S32FÑÑÑÑÑÑÑÑ----snow surfaceiceslush'voidmoving ice blockFig.5. Cross-sections of ridges Sl, S2 and S3

Table 1. The main results of studied ridges. (The lettersbefore the angle results express the wind direction of the sideof the ridge, see figures 3-5.)ridge Rl R2 R3 T A Sl S2 S3height (m)depth (m)sail width (TO)keel width (m)angles ( ¡ :sailkeelporosity (%) :sailkeeltotalTable 2. The main results of ice block measurements.The big ridge of profile: I sail East I1 sail Eastridge A Al A2 fromA fromA R2 R3 T Sl S2height (m) 1.6 1.65 1.03 0.23 0.58 1.74 0.97 0.85 1.23 0.6depth (m) 12.29 12.51 12.40 - 3.72 8.41 7.48 3.46 4.64 5.13rnax. thick.(cm)31 33 21 18 12 34 32 22 23 16max. length 140 250 148 125 140 213 240 195 125 110thickness oflevel ice (cm) 35 35 35 35 35 44 44 44 35 30

3.2 Ridge height versus ice block thicknessThe mean height of all the studied sails is 0.65 m. If onlysails higher than 0.3 m are taken into account the averageheight is 0.78 m. Because the winter 1988 was temperate and thefield studies were made late in the winter the ice blocks inthe ridge sails had undergone melting. Therefore, calculationsof the mean block thickness are useless. The thickest ice blockmeasured from the sails was taken to represent the thickness ofthe ice from which the ridge was formed. These ice blocks weresheltered from melting by other blocks and snow.There is a positive correlation between the maximum blockthickness and sail height (Fig. 6a) (r = 0.84, n = 10, p

where h is sail height and t is ice block thickness. Theconstant is smaller than the constants of 3.69 and 3.71determined by Tucker and Govoni (1981, 1984a). In addition tothe fact the ridge height is related more or less to thethickness of the ice, it is also related to the magnitude andduration of the forcing. In the Baltic Sea the distances are soshort that strong winds can not generate as much force in theice field as in the Arctic. The growth of ridges is thereforemore limited in the Baltic and this is believed the reason forsmaller constant of 2.22 in eq. 1.There was no correlationbetween the block thickness , ( ,and its lengthaccordingto 3, . . . . . . . ,the whole ice block data. 2.5One reason for this is thatthe blocks were melted re- 2markably. However, the maximumice block thickness and 1the maximum length of the Osl Jice blocks found in the sail0 0correlated with each other 0 005 0.1 0.15 0.2 0.25 0.3 0.35 CK.t(Fig. 7) (linear correlation(mlcoefficient r=0.74, n=10, p

criterion, by local minimum-height points, mean width andsubjectively, there was not found any kind of correlationbetween height and width.The mean slope angle of the 62 sails is 14.4' with standarddeviation of 14.2'; if only sails higher than 30 cm were takeninto account the average slope angle is 17.3' (std = 14.5') andfurther the sails higher than 50 cm have an average angle of21'. The angles varied between lo-51.9'. The average angles arelower than the angles reported in earlier studies. For examplein the Baltic Sea Palosuo (1975) reports mean angle of 30' andfor Arctic ridges Kovacs and Mellor (1974) 24" and Tucker &Govoni (1984a) 25'.The lower angle can be explained partly by the method'for the angle determination used here: 11 sail slopes of crosssectionfigures of ridges of Wright's et al. report (1979) weredetermined by this calculating method, and it resulted 3' (std2) lower angles than the angles determined by Wright et al.Consequently these angle results agree well with earlierstudies (ridges higher than 0.5 m; angle 21' + 3' = 24¡) butit also seems that the other reason for lower angles is thatthe earlier studies are made from ridges considerably higher(mostly 2-6 m high) than the ridges studied here. It isinteresting that there is found positive correlationbetween sail heights and their slope angles (r = 0.51, n = 124and p

The sail height to keeldepth ratio varied between1/3.8 to 1/8.6. The averagewas 1/5.8 (Fig. 8). Palosuo's(1975) data collectedfrom the Baltic Sea andmeasurements of multi-yearridges in the Arctic byWright et al. (1979) areadded to the figure. Theregressions were calculatedseparately for both areas.The measurement series madein the Baltic fit togethervery well and the linearcorrelation coefficient is0.93 (n=22, p

3.5 PorosityThe porosity of a whole ridge is 29 % on average (std=6). Themean porosity of a carefully studied ridge in the Gulf ofBothnia one year earlier was 27 % (Kankaanpaa 1989). Theaverage sail porosity was 19 % (std=10) and in the keel it was30 % (std=6). The sail porosity values vary more because oflimited amount of drill hole results and limited sail volumestudied. One reason for that the porosity of sails weremeasured to be lower than in keels is believed that because thewater is denser intermediate substance than the air, itprevents the blocks to press against each other so thightly.There is not found a relationship between the porosity andthe size of a ridge or between the porosity and the icethickness or size of the blocks.There are no other corresponding studies of the porosity. ButKovacs and Mellor (1974) estimated it to be 10-40 % in theArctic. In mechanistic models void ratios of 10 to 30 % havebeen assumed and in a laboratory study it was calculated to befrom 19 to 50 % (Weiss 1980, cit. Tucker et al. 1984b).Tucker et al. (1984b) have experienced a specialporosimeter for the sail of three grounded ridges. Theymeasured the sail porosity to be 21 %. Keinonen (1977) measuredthe porosity of two sails in the Baltic Sea by making a crosssectionin two ridge sails by a motor saw and determining theporosities from both sides of the cross-section. He got thesail porosity to be 36 % and 43 %.During the drilling it was noticed that in the keel therewere places which were not ice but also not actually voids.These parts were assumed to be slush or very worn ice. Thesewere found also by the diver. There is this "slush" 6.4 % on anaverage and it ranged between 1 to 16 %.

4. CONCLUSIONSIn this study the geometry and internal structure of 8 about1 m height and 6 m deep freely floating pressure ridges in theGulf of Bothnia and the Gulf of Finland were studied. Also thegeometry of about 54 sails were determined.The mean slope angle of sails higher than 50 cm is 21'. Thekeel angle was 11- steeper on an average. Ridge heights andslope angles of sails correlated with each other. The porosityis 29 % on an average. The mean porosity of sails (21 %) isabout 8 % lower than the average porosity of keels (29 %).According to the measurements isostatic imbalance was commonat the ridge areas.The ratio of sail height to keel depth is 1/5.8 on anaverage. It ranged between 1/3.8 to 1/8.6.There was a positive correlation between the sail height (h)and the maximum thickness (t) of the ice blocks in the sail.The regression estimate for the data is 2.2 t1j2.ACKNOWLEDGEMENTSThis work was carried out by the support of the Academy of Finland.I wish to thank Dr. Matti Lepparanta for valuable guidance.5. REFERENCESHibler, W.D. I11 (1980). Modeling on variable thickness sea icecover. Mon. Wea. Rev., 108(12) 1943-1973.Kankaanpaa, P. (1988). Structure of an ice ridge in the BalticSea. Geophysica, (in press).Keinonen, A. (1977). Measurements of physical characteristicsof ridges on April 14 and 15, 1977. Styrelsen for vintersjofartsforskninq,22. 9 pp.

Kovacs, A. (1970). On the structure of pressured sea ice.USACRREL. 57 pp.Kovacs, A. and Mellor, M. (1974). Sea ice morphology and ice asa geologic agent in the southern Beaufort Sea. Reprint fromCoast and shelf of the Beaufort Sea. The Arctic Institute ofNorth America, 1974. CRREL. 164 pp.Lepparanta, M. (1980). Statistical features of sea ice ridgingin the Gulf of Bothnia. Styrelsen for vintersjofartsforskning,23. 42 pp.Palosuo, E. (1975). Formation and structure of ice ridges inthe Baltic. Styrelsen for vintersjofartsforskning, 12. 54 pp.Tucker 111, W.B. and Govoni, J.W. (1981). Morphologicalinvestigations of first-year sea ice pressure ridge sails.Cold Regions Science and Technology, 5. 1-12.Tucker 111, W.B. and Govoni, J.W. (1984a). The structure offirst year pressure ridge sails in the Brudhoe Bay region. InBarnes, P.W., Schell, D.M. and Reimnitz (eds.). The AlaskanBeaufort Sea: Ecosystems and Environments. pp. 115-136.Tucker 111, W.B., Rand, J.H. and Govoni, J.W. (1984b). A methodof detecting voids in rubbled ice. Cold Regions Science andTechnology, 9 (1984), 183-188.Wadhams, P. (1986). On the spacing and draft distribution forpressure ridge keels. J. of Geophys. Res., 91, C9. 10697-10708.Weiss, R.T., Prodanovic, A. and Wood, K.N. (1980).Determination of ice rubble shear properties. In: Proc. ofInternational Ass. for Hydraulic Research InternationalSymposium on Ice. Quebec, Canada, July 27-31, 1981. Proc.available from: Prof. Bernard Michel, Departement de geniecivil, Universite Laval, Cite Universitaire, Quebec, Canada,pp. 860-870.Wright, B., Hnatiuk, J. and Kovacs, A. (1979). Multiyearpressure ridges in the Canadian Beaufort Sea. The 5th Int.Conf. of Port and Ocean Engineering under Arctic Conditions(P0AC179) . 1. 107-126.

LARGE-SCALE CHARACTERISTICS OF FRACTURESIN MULTI-YEAR ARCTIC PACK ICEM .W. MilesResearch AssistantR.G. BarryProfessorCooperative Institute for Researchin the Environmental Sciencesand Department of GeographyUniversity of ColoradoBoulder, CO 80309-0449ABSTRACTFractures (leads) in sea ice occur in a large range ofscales, from widths of meters to kilometers. Multi-sensorremote sensing methods allow for the determination of fracturecharacteristics throughout the full range of scales. Thermaland visible wavelength data from operational satellites allowfor detection of features greater than 250 meters wide, withcoverage several times per day. Higher resolution imagery canbe used to determine smaller-scale lead characteristics.Defense Meteorological Satellite Program (DMSP) imagery isused to determine the distribution of large fractures. Casestudies were conducted for the Canada Basin using satelliteobservations from the period 1980-85. Wind fields, derivedfrom Arctic Ocean Buoy Program pressure data, are correlatedwith the observed fracture fields, providing a quantitativerelationship between fracture orientation and geostrophicwinds. Increased understanding of fracture fields and theirrelationship to atmospheric and other forcings furthers ourknowledge of ice dynamics, and can be useful for engineeringand transportation in the Arctic.1. INTRODUCTIONThe characteristics and occurrence of fractures (open or103

efrozen leads) in the ice are significant for understandingsea ice mechanics and the associated atmospheric forcings.(Here, the term "lead" is used interchangeably with"fracture".) Sea ice fracture patterns induced by icedivergence have been shown to be strongly related to persistentatmospheric driving forces (Ackley and Hibler, 1974). Leadsform as a result of tensile-failure in the ice in response tothe shear stresses created by the differential motions of bothair and water. In an ideal situation, leads "form in a band ofuniform width, running at right angles to the direction of themajor principal stress in the ice" (Mellor, 1986, p. 264).There exists a scarcity of information about the spatial andtemporal distribution of leads on a basin-wide scale, thoughsome geometric aspects have been researched (Marko and Thomson,1977). This research aims to provide some of this informationfrom remotely sensed data. The results of meso-scale analysisfrom satellite imagery are discussed.2. REMOTE SENSING OF FRACTURESIt is necessary first to determine the actual, rather thanthe nominal, resolution of satellite sensors, with regard tomapping sea ice fractures. Based on comparisons of nearconcurrent DMSP (nominally 600x11 resolution) and Landsatmultispectral scanner (80x11 resolution) imagery, it wasdetermined that under optimal conditions, fractures as narrowas 250m can be detected on DMSP imagery (which, unlike Landsatimagery, is available on a daily basis including the Arcticwinter night). While fractures of this size may represent only1-2% of the size frequency distribution in this region(McLaren, 1987) they account for approximately 20% of the totalopen water/young ice (0-30 cm thick) area, and are of majorsignificance in terms of large-scale ice dynamics and heattransfer.Neither the thermal nor visible band imagery allowed for thediscernment of open vs. refrozen leads, a capability which doesexist to some degree with low-altitude aerial panchromaticphotography.104

3. FRACTURE PATTERNS FROM SATELLITE IMAGERYThe determination of fracture patterns per se can provideuseful information for research and operation (Ackley andHibler, 1974). Of specific interest here is the recurrence ornonrecurrence of typical fracture patterns at certain times ofthe year, for comparison with lead statistics obtained fromsubmarine sonar transects of under-ice draft from previousyears (see McLaren, 1987). The assemblage of lead orientationswhich comprises a lead pattern may influence the width andspacing statistics derived from such methods; i.e., a nonperpendicularintersection between transect and lead affectsthe statistics on lead width and spacing.3.1 Data and MethodsFracture patterns for the Canada Basin and adjacent areas(Figure 1) have been derived from visible (0.4-1.1 fim) andthermal infrared (8-13 fim) DMSP (600 m resolution) imagery,available in the National Snow and Ice Data Center (NSIDC),Boulder, Colorado.Figure 1. Arctic Ocean and surrounding coastlines.Study area(outlined) includes area from 70Â - 8S0 N and 130Â W - 160Â E.105

Individual cases were studied for various months from 1980-1985, and selected daily series. Lead patterns were taken fromimages and overlain by a lo latitude x 5" longitude grid. Thelead orientation in each grid cell was determinedtrigonometrically as a vector showing the preferred direction(Curray, 1956) .3.2 ResultsFigure 2 shows a series of lead patterns from May observationin three consecutive years. Each pattern exhibits markedlydifferent characteristics. It is readily apparent that a highdegree of interannual variability exists. Moreover, fracturepatterns can change substantially on short time scales inresponse to wind forcings, and also through the course of theseasons. Considering the seasonal variability in iceconcentration, extent, motion, and synoptic pressure fields,this result could be expected (Serreze and Barry, 1988). Fromthese and other cases, it is concluded that a typical,consistent lead pattern does not exist, for areas away from thecoast.Near the coast, however, there tend to be more regularfracture patterns. There is a contrasting stress regimeinvolved here between the landfast ice and the mobile pack ice.Ice motion in these areas is less controlled by synoptic-scalepressure systems and more by stress gradients within the ice.4. CORRELATION WITH ATMOSPHERIC PRESSURE FIELDSThe effect of geostrophic winds on sea ice motion away fromcoasts has been quantified by Thorndike and Colony (1982). Forthe central Arctic Ocean, more than 70% of the variance of theice velocity is accounted for by the geostrophic wind.Associated with these ice velocities are periods of icedivergence and convergence, which in turn are largelyresponsible for distribution of openings in the ice cover. Itfollows then, that there ought to be a quantifiablerelationship between lead patterns and geostrophic wind fields.10 6

Figure 2. Imagery-derived leadpatterns in the Canada Basinin May of 3 successive years:(a) 1983, (b) 1984, and (c)1985.4.1 Data and MethodsGeostrophic wind fields were derived from daily pressurefield data provided by the Arctic Ocean Buoy Program (Thorndikeand Colony, 1981 and succeeding annual reports through Colonyand Munoz, 1986).The wind fields have been referenced to thelo x 5O grid used in determining the lead orientations. Forall grid cells containing observable leads, the wind directionsare assigned values in the same 15' increments as thecorresponding lead orientations.This procedure was done foreach of the four days preceding the lead orientationobservation.In this manner, each grid cell has a pair ofangular values: 1) lead orientation (+), and 2) wind direction(6) , and the difference 6 = 4> - 0 .There is no generally agreed upon measure of two-dimensionaldirectional/vector correlation; several different correlationstatistics have been recently proposed, both non-parametric andparametric (Klink, 1986). An appropriate correlation statisticwas selected for its ability to include: 1) a bounded range, 2)rotational dependencies, and 3) ease of interpretation, assuggested by Klink (1986).That the lead "direction" has two107

values, (t> and i(> + ISO", is also important.The correlation statistic used is essentially that prescribedby Batschelet (1981), where r0 is the correlation coefficient:A large rB value indicates that 6 is strongly dependent on 6,whereas if r,, approaches zero, the two variables areuncorrelated. This statistic can be modified to give thedirection of the rotation (angular covariation) and directionof a mean resultant correlation vector (Klink and Willmott,1985). These correlation procedures provide an indicator ofthe variability of lead patterns which may be attributable toatmospheric forcings.The lead orientations and wind directions for the individualcases were correlated in the above manner. The resultingrelationships were then assessed with regard to iceconcentrations, convergence/divergence, and pressure regime.4.2 ResultsOf the 18 cases for which lead statistics were obtained(Table I), 4 show a high correlation (rO > 0.82) between leadorientation and wind direction, 12 are moderately correlated(0.57 < rB < 0.82), and 2 are weakly correlated (rB < 0.57) .These classes correspond to >66, 33-66, and

Table 1. Correlation of geostrophic wind and lead orientationfrom case studies. Correlation coefficient (r,) and rotationangle (0.) are shown for the wind directions during the 3 dayspreceding the lead observation. QÃ > 0 indicates that the leadis rotated clockwise from the wind direction.WINTER/ 2-d before 1-d before same day meanSPRINGPressureDate r2 0 OBI r. 0.0 r, regime23 Jan 8018 Mar 8014 Apr 8012 May 821 Feb 8312 May 8322 Nov 8323 Jan 8415 May 848 Jan 8512 Dec 85MEAN 71 +12 .77 t11 .74 -13 .74 -SUMMER/ 2-d before 1-d before same day meanFALLPressureDate 2 Gal ~ B O ffao re regime28 Sep 838 Jun 8413 Aug 8430 Sep 8426 Oct 8418 Jun 8518 Oct 85MEANspring. Even strong pressure systems may be countered byhighly resistant ice; for example, ice velocities in theBeaufort Gyre reach a minimum in April, despite the fact thatthe intensity of the Arctic anticyclone reaches a maximum then(McLaren et al., 1987). Generally, winter correlations aresimilar to summer correlations; i.e., the seasonal contrast issmall or nonexistent.Another factor in low correlation cases is simply that thisscheme is insufficient to account for some wind-induced largescalefracturing. Figures 3 and 4 provide an illustration ofsuch a case. Figure 3 shows the remote sensing-derived spatialdistribution of large fractures which did not exist 21 January109

3. Distribution of large fractures which developed between21 -25 January 1983.4. Mean sea-level pressure field from 22 January 1983.1983, but appear on the next available imagery (25 January1983) . These new fractures evident on the 25 January imageryappear to form in response to strong ice motion (about 10-15km/day) induced by an intense anticyclone (PWx = 1050 mb) overthe area. Figure 4 shows the sea-level pressure field on 22January 1983. The directional correlation between these newfractures and the geostrophic wind is nearly perfect (rB = .90)and the angle of rotation (0,) is 5@, indicating that thefractures are oriented along essentially the same direction as110

the geostrophic wind. Due to the continued presence of theantecedent fractures (not shown), this relationship would beobscured using the previous methodology.In general, large fracturing events occur throughout anygiven time series of observations. While new fractures becomeevident, some previous leads may remain evident for days, evenweeks. Thus, the overall lead pattern for a given observationmay be the product of numerous different fracturing events,each event the resultt of ice divergence largely induced byatmospheric forcings. As such, perhaps the optimal approach isan image "differencing" method (as in Figure 3) carried outrepeatedly through a long time-series of observations. Theresults of these differences, could then be correlated withsynoptic-scale systems.5. CONCLUDING REMARKSThe effective spatial resolution of satellite images forfracture detection and mapping has been shown to beapproximately 2 - 2.5X the nominal resolution of the sensor.The study has provided new information on the occurence of suchfeatures in the Canada Basin. The relationships betweensynoptic-scale atmospheric events and fracture fields have beenexplored. The orientations of major fractures in the CanadaBasin are shown to be broadly correlated with geostrophic winddirection and have similar synoptic (time and space) scalepatterns. However, persistence of antecedent patterns has animportant effect which needs to be further investigated. Thisresearch represents a first-order estimation of theserelationships. Further research may ultimately lead to thedevelopment of predictive statistical models of fracturepatterns based primarily on pressure systems.6. ACKNOWLEDGEMENTSThis study was supported by the Office of Naval ResearchUniversity Research Initiative Program Contract N00014-86-K-0695.Ill

7. REFERENCESAckley, S.F. and Hibler, W.D. (1974) .Measurements of ArcticOcean ice deformation and fracture patterns from satelliteimagery. AIDJEX Bulletin, 26, 33-47.Batschelet, E. (1981). Circular statistics in biology, AcademicPress, London.Colony, R. and Munoz, E.A. (1986) . Arctic Ocean Buoy Programdata report, 1 January 1984 - 31 December 1985, Polar ScienceCenter, University of Washington, Seattle.Curray, J.R. (1956).The analysis of two-dimensionalorientation data. Journal of Geology, 64, 117-131.Klink, K. (1986).Space-time analysis of the surface windfield using vector-based principal components analysis.Master's Thesis, University of Delaware.Klink, K., and Willmott, C. J. (1985) . Comments on "Evaluatingthe similarity of geographic flows". Professional Geographer,37, 56-58.Marko, J.R., and Thomson, R.E. (1977) .Rectilinear leads andinternal motions in the ice pack of the western Arctic Ocean.Journal of Geophysical Research, 82, 979-987.McLaren, A.S, Serreze, M.C. and Barry, R.G. (1987).Seasonalvariations in sea ice motion in the Canada Basin and theirimplications. Geophysical Research Letters, 114, 1123-1126.Mellor, M. (1986).Mechanical behavior of sea ice. InUntersteiner, N. (ed.) The geophysics of sea ice, 165-282,Plenum Press, New York.Serreze, M.C., and Barry, R.G. (1988).Synoptic activity inthe Arctic Basin, 1979-1985. Journal of Climate, 1, 1276-1295.Thorndike, A. S., and Colony, R. (1981) .Arctic Ocean BuoyProgram data report, 1 January 1980 - 31 December 1980. PolarScience Center, University of Washington, Seattle.Thorndike, A.S., and Colony, R. (1982).Sea ice motion inresponse to geostrophic winds, Journal of GeophysicalResearch, 87, 5845-5852.

WATER DRAG ON SEA ICE - A REVISITDag MyrhaugDivision of Marine HydrodynamicsNorwegian Institute of TechnologyN-7034 Trondheim - NTH,NorwayABSTRACTGeostrophic and surface water drag on sea ice are presented forrough turbulent flow in a neutrally stable boundary layer. Thegeostrophic drag coefficient (Cg) and the direction of the surfaceshear stress (a) are obtained by using similarity theory and by determiningthe constants, as required by similarity theory, from availabledata. An approximation for Cg by disregarding the rotation of thevelocity in the boundary layer is also presented. Some representativewater drag data for rough turbulent flow from different investigationsare also presented by utilizing the semi-empirical results obtained bydisregarding the rotation of the velocity in the boundary layer, andthe data show consistency. Theoretical model predictions according toa simple eddy viscosity approach are also presented showing goodagreement with both the semi-empirical approaches and the data. Thesurface drag coefficient (C,) referenced to an elevation z, based onthe logarithmic boundary layer flow model, is also given togetherwith data.1. INTRODUCTIONKnowledge of the water drag is important for accurate determinationof the dynamics of sea ice. Although the wind is the primary forcethat drives the ice, a numerical model of ice motion must also includethe influence of water drag against the ice. Other contributions tothe forces exerted on the ice are from waves, sea surface tilt and

internal ice stress. The vertical structure of the current boundarylayer near the ice surface is in the most general and complex casedominated by several interacting physical effects. Among tnese effectsare the earth's rotation, stratification due to temperature and salinitygradients, internal friction in the fluid and topographicaleffects.One important feature of the vertical structure of the boundarylayer is determined by the influence of the planetary rotation onsteady, horizontally uniform, unbounded and unstratified flow. In thiscase there is a balance between the driving pressure gradient, themomentum flux gradient and the Coriolis force. Outside the boundarylayer the flow is geostrophic, in which the friction is negligible andthe pressure gradient is balanced by the Coriolis force. Thisidealized boundary layer flow may occur in the ocean away from anycoasts. Further the flow is steady over times comparable with theinertial period, 2n/f, where f = 2QsinI) is the Coriolis parameter.Here Q is the earth's angular frequency of rotation and I) the latitude.Water drag data on sea ice are available from several investigationsover the last years. Shirasawa (1986) gives results of his owninvestigations, together with reviews of earlier investigations.The purpose of the present paper is to emphasize that water dragdata for sea ice, which represent different ice conditions fromvarious investigations, can be presented in a consistent way by utilizingresults from similarity theory. Further, the semi-empiricalwater drag formula presented here represents a rational working formulawhich should be useful for engineering applications.2. THEORETICAL BACKGROUND2.1 Geostrophic drag coefficientThe geostrophic drag coefficient associated with the friction velo-city at the surface is defined aswhere G = ug + ivg is the geostrophic velocity in complex form withthe magnitude 1 G 1 . ug and vg are the geostrophic velocity components

along horizontal orthogonal x- and y-axis, respectively. The x-axis istaken along the shear stress at the surface, TO, which has an angle arelative to the geostrophic velocity direction, i.e. in counterclock-wise rotation relative to the geostrophic velocity direction in thenorthern hemisphere. Further, u* = (T~/P)% is the friction velocity, pis the density of the fluid and i = (-l)%.Following G i l l (1982) the geostrophic velocity for steady homoge-neous (neutrally stable) flow can be written asu* "*u + iv = à [In (-)- A - iB]g 9 z0according to similarity theory. Here K is von Karman's constant(= 0.4), 20 is the roughness parameter of the surface, A and B areconstants as required by similarity theory. By using Eq. (1) the magnitudeof Eq. (2) can be written aswhere c = e'^ is a constant. Since ug = 1 G 1 cosa, vg = -1 G 1 sina andby using Eq.(I), A and B are given from Eq. (2) asA = n(Gl~sina./Ñà - cosa and B = -fzO 9(4)Thus (4) determines A and B for a given data set. Then Cg can befound from Eq. (3), and a is determined from the last expression in(4). i.e.sina = 5An approximation to Eq. (3) is given bywhich equivalently can be written as

u* c'u*1 G 1 = - I n (-1fzOIn this approximation the rotation of the velocity in the boundarylayer as the surface is approached is disregarded, and the logarithmicboundary layer flow model (Eq. (7)) is extended beyond its range ofvalidity. The logarithmic boundary layer flow model is valid only in aregion where the shear stress is constant. Here it is extended to aheight c'u*/f where the velocity is equal to the magnitude of thegeostrophic velocity. Thus, for a given data set c' can be determinedfrom Eq. (7).According to Schlichting (1979) the rough turbulent flow regime isgiven by z0u/v > 2.3 where v is the kinematic viscosity of the fluid.The given quantities are 1 G 1 , f and zo which is combined to the non-dimensional Rossby number Ro = \ G \ /fzo. By making use of this in Eq.(3), the geostrophic drag coefficient for rough turbulent flow isgiven by2.2 Surface drag coefficientBy assuming a logarithmic boundary layer flow model the velocity isgiven bywhere uz is the velocity referenced to an elevation z below the surface.Eq. (9) is considered to be valid when the fluid is in neutralstability and the mean flow is steady. By making use of the definitionof the surface drag coefficient (Cz) and Eq. (9), Cz can be expressedas

3. RESULTS AND DISCUSSIONIn Myrhaug (1989) the constants A and B in Eq. (2) were determinedaccording to (4) by using two data sets from measurements of the turbulentflow structure under multiyear drifting Arctic pack ice in theBeaufort Sea reported by McPhee and Smith (1976). The main parametersand results from the experiment are summarized in Table 1. The datarepresent neutrally stable conditions. More details about the experimentand analysis of the data are given in McPhee and Smith (1976).u* was determined by the eddy correlation method, that is, by using therelationship u* = ( 1 u'w' 1 )" where u' and w' are the downstream andvertical components, respectively, of the turbulent eddy fluctuatingvelocity, and the overbar represents a time average which is long comparedto the periods of the turbulent eddy fluctuations. zo was calculatedfrom Eq. (9) by using u* and the measured velocity at the 2 melevation (u2). It appears that both data sets are in the rough turbulentflow regime.Myrhaug (1989) used the mean values of A and B as determined from thetwo data sets and the corresponding value of c in Eq. (3), i.e.c' values were also determined from Eq. (7) by using these two datasets and the mean value was used in Eqs. (6) and (7), i.e. c' = 0.12.Thus, the approximation in Eq. (6) corresponds to the use of Eq. (3)withFigs. 1 and 2 show Cg and a, respectively, versus Ro. It appearsthat Eq. (3) using (12) is a good approximation to Eq. (3) using (11)(see Fig. 1).Table 1 also gives water drag data and main parameters from currentmeasurements under sea ice, taken from some relevant investigations.It appears that all the data are in the rough turbulent flow regime.The magnitude of the geostrophic velocity ( 1 G 1 ) is here calculatedaccording to Eq. (7).In Shirasawa (1986), Johannessen (1970), Pease et a1. (1983),Untersteiner and Badgley (1965) and Hunkins (1972) u* and zo are

Table 1. Water drag data and current measurements under sea ice.InvestigatorsType of ice/locationMcPhee andSmith (1976)Shirasawa (1986Multiyear/Beaufort SeaFirst-year/LandcasterSound, N.W.TJohannessen(1970)Pease et a1(1983)Untersteinerand Badgley(1965)Hunkins (1972)Langleben (1983Shirasawa andLangleben (1976Multiyear/Gulf ofSt. LawrenceMultiyear/North PoleFirst-year1Bering SeaMultiyear/Greenland SeMultiyear/Beaufort SeaMultiyear/North PoleFirst-year/Robeson ChanN.W.T

lo4 lo5 lo6 10' lo8Rossby number, Ro = I G I /fzoFigure 1. Geostrophic drag coefficient versus Rossby number: - Eq.(8) using (11); - - - Eq. (8) using (12); - -- -Myrhaug's (1988) predictions. Data legend: x McPhee andSmith (1976); Shirasawa (1986); + Johannessen (1970);WPease et a1. (1983): X Untersteiner and Badgley (1972); xHunkins (1972); Langleben (1983); A Shirasawa and Langleben(1976), see Table 1.10 lo6 10'Rossby number, Ro= IG l /fzoFigure 2. Direction of surface shear stress versus Rossby number: -Eqs. (5) and (8) using (11); - - - - Myrhaug's (1988)predictions; x McPhee and Smith's (1976) data, see Table 1.

determined by the profile method, that is, by fitting the logarithmicboundary layer flow model (Eq. (9)) to the measurements. The data setin Table 1 which is selected from Untersteiner and Badgley (1965), istaken from their Fig. 2 and corresponds to the water velocity 20 cm/s(at 4 m).In Shirasawa and Langleben (1976) and Langleben (1983) ZQ wasdetermined from Eq. (9) when uz is known at an elevation z. The dataset in Table 1 which is selected from Langleben (1983) is taken fromhis Fig. 1 and corresponds to the largest velocity (ul = 16.8 cm/s).The data given in Table 1 are presented in Fig. 1 together withtheoretical model predictions according to Myrhaug (1988), which isbased on a simple eddy viscosity approach. McPhee and Smith's (1976)data are presented in Fig. 2 together with Myrhaug's (1988) predictions.It appears to be a reasonably good agreement between thetheoretical model predictions and both the semi-empirical approachesand the data.Myrhaug (1988) presents an analytical theory which describes thefluid motion in a turbulent boundary layer near a rough sea bed. Aninverted boundary layer similar to that at the sea bed is applicableunder the sea ice and is used to predict the vertical structure of thecurrent motion under drifting pack ice. The flow is determined by abalance between the driving pressure gradient, the shear stress gradientsand the Coriolis force. A two-layer eddy viscosity is used torepresent the shear stress. The eddy viscosity in the inner layerincreases quadratically with the height above the sea bed. In theouter layer the eddy viscosity is taken as a constant. This eddyviscosity representation is a reasonable compromise between accuracyand simplicity and has the benefit over the linear profile of havingone disposable constant which determines the magnitude of the eddyviscosity in the outer layer, as well as the height of the overlappoint. This admits for some adjustment of the model to data.The surface drag coefficient referenced to the 1 m elevation, isalso given in Table 1. These data will of course follow the graphexpressed by Eq. (lo), i.e. C l versus the ratio z(= lm)/zo.Some final remarks should be given to the approach presented here.It should be noted that Eqs. (3) and (6) can be applied with othervalues of 8, c and c' if in the future other very precise experimentsshould give other values. Since the present formula is based on verylimited data, sensitivity analyses on the results may be useful.

However, for engineering purposes, it is useful to have working formulasas long as possible limitations are kept in mind.In most cases the boundary layer flow is in the rough turbulent flowregime, but it also appears in practice that the flow conditions mightbe in the smooth and transitional smooth-to-rough turbulent flowregimes. Data reported by Untersteiner and Badgley (1965) demonstratethat this can occur. Obviously, most of the data were in the rough andthe transitional smooth-to-rough turbulent flow regimes. The presentapproach can also be extended to cover smooth and transitional smoothto-roughturbulent flow as well as to give similar formulas for airdrag on sea ice. This is made in Myrhaug (1989).4. CONCLUSIONSGeostrophic and surface water drag on sea ice are presented forrough turbulent flow in a neutrally stable boundary layer. Thegeostrophic drag coefficient (Cg) and the direction of the surfaceshear stress (a) are obtained by using similarity theory and by determiningthe constants, as required by similarity theory, fromavailable data. Cg and a versus the nondimensional Rossby number interms of the independent variables geostrophic velocity, Coriolisparameter and surface roughness parameter are presented. An approximationfor Cg by disregarding the rotation of the velocity in the boundarylayer is also presented. In this case the logarithmic boundarylayer flow model is extended to a height where the velocity is equalto the magnitude of the geostrophic velocity. Some representativewater drag data for rough turbulent flow from different investigationsare also presented in terms of the Rossby number by utilizing thesemi-empirical results obtained by disregarding the rotation of thevelocity in the boundary layer. By this presentation the data fromdifferent investigations show consistency. Theoretical model predictionsaccording to a simple eddy viscosity approach are also presentedshowing good agreement with both the semi-empirical approaches and thedata. Further, the surface drag coefficient (C,) referenced to an elevationz versus the elevation to roughness ratio, based on thelogarithmic boundary layer flow model, is given together with data.The semi-empirical water drag formula presented here represents asimple working formula which should be useful for engineering purposes.

5. REFERENCESGill, A.E. (1982). Atmosphere - Ocean Dynamics, Academic Press, NewYork.Hunkins, K. (1972). Water stress and ocean current measurements atcamp 200, Arctic Ice Dyn. Joint Exp. Bull., 12, 35-60.Johannessen, O.M. (1970). Note on some vertical profiles below icefloes in the Gulf of St.Lawrence and near the North Pole, J.Geophys. Res., 75 (15), 2857-2861.Langleben, M.P. (1983). Water stress on pack ice in the vicinity ofthe North Pole, 7th Int. Conf. on Port and Ocean Engineering underArctic Conditions (POAC '83), Helsinki, Proc., 1, 128-137.McPhee, M.G. and Smith, J.D. (1976). Measurements of the turbulentboundary layer under pack ice, J. Phys. Oceanography, 6,696 - 711.Myrhaug, D. (1988). Prediction of the current structure under driftingpack ice, J. Offshore Mech. and Arctic Engineering, ASME, 110(4),395-402.Myrhaug, D. (1989). Simple approach to air and water drag on sea ice,J. Waterway, Port, Coastal and Ocean Engineering, ASCE, to appear.Pease, C.H., Salo, S.A. and Overland, J.E. (1983). Drag measurementsfor first-year sea ice over a shallow sea, J. Geophys. Res., 88(C5), 2853-2862.Schlichting, H.(1979). Boundary-Layer Theory, 7th Edition, McGraw-Hill,New York.Shirasawa, K.(1986). Water stress and ocean current measurements underfirst-year sea ice in the Canadian Arctic, J. Geophys. Res., 91,14305 - 14316.Shirasawa, K. and Langleben, M.P. (1976). Water drag on Arctic sea ice,J. Geophys. Res., 81(36), 6451-6454.Untersteiner, N. and Badgley, F.I. (1965). The roughness parameters ofsea ice, J. Geophys. Res., 70 (9), 4573-4577.

ICE SCOUR MECHANISMSAndrew PalmerIbrahim KonukJeremy LoveKen PeenGeorqe ComfortAndrew Palmer and Associates, LondonCanada Oil and Gas Lands Administration, OttawaGeotechnical Consulting Group, LondonGolder Associates, CalgaryFleet Technology, KanataABSTRACTSeabed soil deformation by grounded ice determines the forces requiredfor scour to occur, and has important implications for pipelines. If largedeformations extend deep into the ground, a pipeline might still be damagedeven if it were buried below the maximum gouge depth. This paper describesan approach to the problem of determining how far below the ice the gougingdeformations extend. It applies soil cutting theory, and derivesdeformation modes from discontinuous velocity field theory developed inother areas of soil mechanics.INTRODUCTIONIce gouging (ice scour) occurs over wide areas of the seabed of theBeaufort Sea, and in many other parts of the Arctic. There is a large database of descriptive statistics of gouge depth, geometry, frequency and rateof formation in different regions. Many gouges are several metres deep.The motivation for the research described here is the need to protectpipelines. Oil and gas from the Beaufort Sea will probably be transportedto shor~ by pipeline, which almost invariably offers the most economicalmode of year-round transportation. An ice mass that cuts a gouge severalmetres deep must be large and heavy, and there has to he a very largecutting force, generated by wind and current forces on the other ice massesthat push the gouging mass forward. If the cutting force were applieddirectly to a pipeline on or within the seabed, the line might be damaged.A tacit assumption of most early research on pipelines and ice gougingwas that the pipeline would only be endangered if -it were to project abovethe lowest point in the gouge cross-section, so that the ice could contactit directly. The ice must however exert very large forces on the seabed inorder to cut a deep qouqe. These forces must be transmitted downwards intothe soil, possibly causing large deformations and certainly inducing highstresses. It follows that a pipeline trenched below the maximum gougedepth might still be crushed or ruptured by the surrounding soil, eventhough the pipe did not come into contact with it.What happens to a trenched pipeline close to a gouge depends on thedeformation of the seabed soil. A first step towards rational design of apipeline is therefore an understanding of gouging mechanisms.

GOUGE MECHANICSSeabed gouging is a soil cutting process, but a process of a distinctkind to soil cutting in other contexts such agricultural implements,earthmoving machinery, tracked vehicles, tunneling machines and anchors.As a cuttinq device, the ice is very blunt , and the cutting face has alarge backwards rake, so that it tends to press the soil down rather thanto lift it up. It cuts very inefficiently, and there is a large upwardforce. The ice surface is far from smooth. Since the ice is close tothermodynamic equilibrium with the sea, it is only lust below its meltingpoint, and is "warm" and quite weak, so that small fragments of the ice canbreak away and alter the cutting surface.There has been some research on soil cuttinq (see, for example, Zelenin,Hettiarachi, Palmer) in the context of earth-moving machinery and ploughs.In principle, the deformations and stresses in the soil could be foundanalytically from soil mechanics. In practice, this cannot yet be done,because knowledge of the stress-strain behaviour of soils undergoing largedeformations is still incomplete, and because of the daunting computationalproblem of following the large deformations involved. Most understandinoof soil cutting has been gained through experimental studies, supported bydimensional analysis.In the simplest form of gouging, an ice mass moves horizontally through auniform level seabed at a uniform speed. The driving force is large enoughfor the movement to continue, and the ice is strong enough to carry thegouge forces imposed by the soil.This simple condition forms a starting point for quantitative analysis.It is clearly not the only condition possible. The bottom may have asignificant slope, so that the depth of the gouge increases as the ice massadvances, the driving force may fall so that it is no longer large enoughfor movement to continue, the soil properties may be irregular, the icemass may break up under the soil forces, the ice mass may lift or rotate asit moves, and so on. All these factors sometimes play a role in the field,but progress towards these more complicated unsteady conditions must followunderstanding of the simpler steady-state. Analysis of Beaufort Sea gougedata indicates that gouges are surprisingly uniform over long distances,often 10 km or more, and that the seabed is often almost horizontal, with abottom slope of the order of 0.001 (perhaps because repeated gouging has itselfcreated a level bottom).Figure 1 is a schematic section through the centreline of an ice mass insteady-state gouging.direction of motion< gouge deadmoundwedge zone 1zone 2Figure 1.Longitudinal section of ice gouging.zone 3

The cutting face of the ice is at a relatively low angle to thehorizontal, less than 30Â (and often much less). This corresponds to theobserved sections of deep multi-year keels. Some of the soil is carriedalong with the ice, forming a soil wedge which has essentially the samevelocity as the ice. Dead zones of this kind are seen in experiments onsoil cutting by blunt backward-raked blades, and during the operation ofcutting equipment such as trenching ploughs, and are well known in metalcutting with poorly-lubricated tools. In practice, dead zones are oftenintermittent and slightly unstable, so that soil enters the dead zone atits leading face, is for a time carried along with the blade, and laterbreaks away. In a sense, the presence of the dead zone modifies theeffective shape of a cutting surface, so that a surface with a largebackward rake is transformed into a new surface with less rake.In front of the dead zone, in zone 1 in Figure 1, the soil is liftedupwards into a mound in front of the ice. Mounds are seen at the ends ofgouges, where the ice has come to a halt. Similar mounds are seen inexperiments in which indentors are dragged across metal surfaces.In a steady-state gouging, there has to be a clearing mechanism whichprogressively removes the mound, since the mound would otherwise growcontinuously in size. The clearing mechanism appears to be that the soilin the mound is pushed sideways, transverse to the gouge direction. A bermis formed on either side of the gouge. The soil may be pushed sidewaysunder transverse forces in the mound, a process loosely analogous tolateral movement in front of an angled bulldozer blade. Alternatively -and perhaps at the same time - blocks of soil may roll or slide down thesteep forward face of the advancing mound. The details are unclear, andneed further experimental investigation. Field observations do not seem tohave investigated berm formation.A puzzling feature of profiles across gouges is that the berms areunexpectedly small. The cross-section of the berm, above the general levelof the bottom, is smaller than the cross-sectional area of the gouge,whereas it would be expected to be the same size or larger, because mostsoils dilate rather than contract during deformation. This may be alimitation of the method of measurement: if soil is pushed downwards andsideways over the whole breadth of the gouge, upward displacement at thesides will occur over a similar breadth, and may not be distinguishableabove the general level of the bottom. A second explanation may be thatraised berms are rapidly eroded by sediment transport under waves, or thatother ice masses rapidly push them back into the gouge.In zone 2, at a lower level, the soil is dragged forward by the ice, butnot lifted in front of it. It does not enter the mound, and is not movedsideways into the berm. Instead, it ultimately moves downwards beneath theice (possibly after some initial lifting), and the ice passes over it.This soil does not move laterally to any significant extent.At a still lower level, zone 3 in Figure 1, the deformation of the soilis much smaller. Its horizontal movement is in response to the stresses inthe soil created by the ice above, but it is not dragged, and does not movevertically.The boundary between zone 1 and zone 2 is well-defined. Above it, soilis lifted upwards and sideways into the mound, and ultimately forms part ofthe berm. Below it, the ice moves over the soil, possibly after some smallvertical movements. In soil cutting experiments, the boundary is distinct,

as it is in earthmovinq. The boundary between zone 2 and zone 3 is lessdefinite, and partly a matter of degree, but it sems likely that there is adistinction between soil which is draaged horizontally and that which onlyexperiences elastic deformation.DEFORMATIONS IN STEADY-STATE GOUGING: VELOCITY FIELDSImagine a stationary observer watching a vertical section through thesoil, and able to see its movements as an ice mass approaches and passes.He sues the soil begin to move, at first very slowly and then more rapidly,to lift and move sideways, and then to come to rest. The motion isirregular, unsteady and discontinuous.An observer moving with the ice, on the other hand, sees a much simplerpicture. He sees the soil move towards the ice, lift, divide, and flowunder and past the ice. From his viewpoint, the flow is steady andcontinuous, and does not change with time. For this reason, it is mucheasier to think of deformations as they would be seen by an observed movingwith the ice, and to relate them to a moving frame of reference stationaryin relation to the ice. Equivalently, one can think of the ice as fixedand the soil as flowing past it.In relation to a moving frame of reference, the deformation of the soilis completely described by a steady velocity field. Figure 2 depicts asimple field. It shows velocity magnitudes and streamlines coincident withthe local velocity vector. The division between zone 1 and zone 2corresponds to a dividing streamline.Fignrc 3 is the same field, but shows velocities relative to the soil ata large distance from the ice. It therefore corresponds to theinstantaneous velocities seen by a fixed observer.Figure 2.Instantaneous velocity field seen by stationary observer.Figure 3.Steady velocity field seen by observer moving with ice.126

Soil particle displacements can be calculated by integrating the particlevelocity field along a streamline. A particle displacement is the timeintegral of the difference between the velocity field in Figure 3 and theuniform velocity at a large distance from the ice.Though the idea of a steady-state velocity field helps to clarifydeformation mechanisms, this simple picture is itself an idealisation.Most observations of soil cutting mechanisms show that the detaileddeformation is partly irregular and discontinuous. In particular,large-scale deformation is characterised by the repeated formation ofdiscrete shear zones, across which large relative movements occur over adistance of a few nun, separated by regions where the deformation iscontinuous and relative movements are less abrupt. A shear zone isinitiated at a stress concentration, extends in length, and becomes activeand develops larger relative deformations, but the resulting changes ingeometry and stress later cause it to become inactive, and relativemovements across it come to a stop. A new shear zone is initiated, and theprocess repeats. This phenomenon is particularly noticeable in brittlesoils such as hard clay and dense sand. It does not invalidate theusefulness of the continuous-flow steady state velocity field, but ought tobe incorporated in a more refined theoretical approach.Conventional soil mechanics has been primarily concerned with stress inthe soil, rather than with deformations. Recent research has moved towardsa greater emphasis on deformations, first through studies of movementsclose to retaining walls and latterly through research on cutting and onbulk flow in hoppers.A soil will generally tend to change volume when it is deformed in shear,but its freedom to change volume depends on the ability of water to movebetween the soil particles. A saturated soil will can only increase itsvolume by drawing water into the spaces between the particles, if theparticles are to move apart, or by driving water out from between theparticles, if they are to move closer together. If the deformation is toorapid for the water to move, or if the soil is too impermeable, thedeformation of the soil is undrained. During an undrained dcformation,the pore pressure changes. Its changes alter the effective stress, andthence the details of the deformation. If the deformation is rapid, andthe soil has a strong tendency to dilate, the pore pressure can fall to alevel at which cavitation occurs. Experience with the interpretation ofspeed effects on the behaviour marine pipeline ploughs in dilatantmaterials shows that the water depths in which gouging is important do notproduce enough hydrostatic pressure to suppress cavitation.Gouge deformations in clay and fine silt will always be undrained. Insands and coarser silts, completely undrained deformations probably onlyoccur if the gouging velocity is greater than about 1 m/s, which isunlikely. This conclusion is reached by analogy with the observedbehaviour of seabed ploughs (Grinsted). The critical speed at whichpartial drainage begins to occur depends on both the permeability of thesoil and its tendency to dilate.In sand and gravel, the soil dilates during the deformation. The extentto which it dilates depends on its initial condition. If it has been inplace undisturbed under large vertical loads (perhaps applied by overlyingstrata in earlier ideological times), it may dilate strongly. If it is in avery loose state (as a result of slow deposition in water, or recentdisturbance), then it may not dilate at all.

If the soil has been repeatedly deformed, and there have been longintervals in which the water could move within the soil and reequilibrate,the soil will have reached a critical state. It can then be continuouslydeformed without tending to dilate or to develop changes in pore pressure.It is suspected - but not certain - that seabed soils in active gouge areasmay have reached this condition, as a result of repeated gouging eventsover geological intervals short by comparison with the time needed forsedimentation to add new strata.If the soil does dilate, the relation between the shear strain rate andthe volumetric strain rate is governed by the angle of dilation V. Intwo-dimensional deformationsv can be treated as a material property, provided that this is consistentwith the underlying stress-strain behaviour of the soil. At the criticalstate, volume changes do not occur, and v is zero. If density changes canoccur without shear strain, V is 90". In general, V is a function of astate parameter which is the difference between the current voids ratio andthe voids ratio at which the soil would be in the critical state under thesame mean principal effective stress (Been).The general problem of soil deformation mechanics is to find akinematically-admissible velocity field consistent with the boundaryconditions, and at the same time to find a statically-admissible stressfield which is consistent with the velocity field and the soilstress-strain relation. In the present primitive state oflarge-deformation soil mechanics, almost no non-trivial problems have beensolved. However, some progress can been made by searching for consistentvelocity fields and then using statics to find boundary forces (but notusually complete stress fields).VELOCITY FIELDS IN GOUGING OF DILATANT SOILSIn other studies of large two-dimensional deformations of soils(Drescher), it has proved helpful to consider a restricted class ofvelocity fields. The deformation plane is divided into a number discreteregions separated by strong discontinuities. Within each region, thevelocity is uniform in magnitude and direction, so that there is no shearstrain or volume change. All dilation and shear occurs in thediscontinuities.In steady flow, the relative velocities across a discontinuity must obeytwo discontinuity conditions, loosely analogous to the Rankine-Huqoniotconditions in fluid mechanics. The two conditions are:1 The product of the density and the velocity component normal to thediscontinuity must have the same value on either side of thediscontinuity;2 The relative velocity across the discontinuity is at an angle V to thediscontinuity.

The first condition expresses mass conservation across a discontinuity.The second condition expresses the relationship between the shear andvolume strain rates, and can be derived by integrating the relativevelocity through a finite zone in which velocity changes. Infinitely-thindiscontinuities in steady flow do not necessarily imply large strains: thiscontrasts to shear band discontinuities in incremental deformationproblems.A velocity field made up of regions of uniform velocity separated bydiscontinuities is kinematically admissible if it obeys the aboveconditions. It does not necessarily correspond to the velocity field whichwill occur in practice, because the implied strain rates are notnecessarily consistent with a stress field which obeys equilibrium and thest.ress-strain relationship for the soil.The discontinuity conditions can be combined to give a relation betweenthe angles between a normal to a discontinuity and the streamlines upsteamand downstream of the discontinuity. If a is the upstream angle ofincidence, B the downstream angle of incidence (measured from the normal),and p, and p2 the upstream and downstream densities, thentan =tan Cttan V + (p,/p2-1)Figure 4 shows a velocity field for two-dimensional steady-state icegouge by an ice mass whose leading face is inclined at 30" to thehorizontal.1.5,0.05 indicates V is 5' and volumetric strain 0.05Fiqure 4Velocity field: gouging in strongly-dilatant soilIt has to satisfy additional geometric conditions besides the generalconditions listed earlier. In particular:1 the velocity in regions 2, 3, and 5 must be parallel to the adlacentboundaries of the dead wedge and the ice mass;2 the velocity in region 6, in material which has passed throughdiscontinuities d e and f, must be horizontal and equal to thevelocity I) in region 0, since otherwise there is an additionalvelocity discontinuity extending infinitely far to the left of pointB. In the actual problem, brought to rest by the superposition of ahorizontal velocity U, this would imply that the some of the soil isleft in motion after the ice has passed, which is not possible;

3 the ratio of the vertical distance between points C and B to thevertical distance between points A and B is the same as the ratiobetween the initial soil density and the soil density after the soilhas passed through discontinuities d e and f.The dilation angles and volume changes are noted on the Figure, andcorrespond to intense shears in a strongly dilatant material.The heights of point A and B relative to the base of the ice areimportant for pipeline applications. Point A marks the boundary betweenzone 2 and zone 1. Point B marks the boundary between zone 3 and zone 2.In this velocity field, point A is 10 per cent of the qouqe depth below thebottom of the qouqe. Point B is 70 per cent of the gouge depth below thebottom of the gouge. It must be emphasised that this velocity field is not.unique, and that other possible velocity fie]-ds have different ratios.Although the soil in zone 6 is moving at the same velocity as the soil inzone 0, it has been displaced relative to it. In other words, two adjacentparticles on either side of a horizontal line throuqh point A and to theleft of it would no longer be adjacent after the soil above the line hadpassed throuqh discontinuities d e and f. This is because the soil abovethe line is "diverted" through regions 4 and 5, where velocities are lower.In the original problem, with stationary soil and moving ice, this offsetis the distance by which soil below the gouge bottom is dragged forward bythe passage of the ice over it. It can be calculated from the velocities,and is found to be approximately 4 times the gouge depth.The above numbers are thought to be overestimates of actual displacementsand depths, since they apply to a dilatant material with strong volumechanges. In a nondilatant material in the critical state, the velocitydisturbances do not reach so far into the soil.Together, these results suggest that the state of the soil has a strongeffect on the extent of subgouge disturbance. If the soil is stronqlydilatant, subgouge disturbance extends to an additional depth which is asubstantial fraction of the gouge depth. If the soil is nondilatant,deformations below the qouqe depth are minimal.Hettiarachi and Reece report experiments in which an inclined blade ispushed horizontally into a mass of sand, through a displacement severaltimes the blade height. They found that the movements of the soil did notextend below the blade. A shear zone extended horizontally from the tip ofthe blade, in the way shown in Figure 5.shear zoneFigure 5Displacement field observed by Hettiarachi and ReeceIn contrast, experiments on small horizontal translation movements ofretaining walls towards the soil generally find that there are movementsbelow level the foot of the wall. The difference may be that smallmovements do occur on a succession of shear surfaces, and that movements oneach surface briefly becomes active and the stops. Continued large movement

only occurs above the level of the blade tip.A tentative conclusion is that small gouge deformations in dilatant soilssometimes extend a little way below the bottom of the ice, but that largemovements do not. There is conflicting evidence from experiments, and moreinvestigation is needed. Deep-seated movements are more likely to occur ifthe soil is strongly dilatant. A difficulty in the interpretation ofreported experiments is that the initial state of the soil is notaccurately characterised, because the significance of dilation was notrecognised. More experiments - and ideally field measurements - are neededto test this.VELOCITY FIELDS IN GOUGING OF NON-DILATANT SOILSVelocity fields for gouging in non-dilatant materials are relativelysimple. Figure 6 shows one simple field, which has a dead wedge in frontof the ice and three shear discontinuities. The field does not extendbelow the ice, and it seems likely that this is generally true of gougingin non-dilatant materials, though this conclusion too needs to be testedmore rigourously.Figure 6.Velocity field: gouging in non-dilatant soilIf a non-dilatant soil is treated as an ideally-plastic material with anassociated flow rule, the techniques of plasticity theory can be brought tobear, and the limit theorems can be applied. A straightforward calculationbased on any velocity field gives an upper bound on the gouging force. Theupper bound method can he used to derive an outer bound on the interactionsurface describing the combinations of horizontal and vertical gougingforce that can occur. This will be examined in a subsequent paper.Analysis of velocity fields in non-dilatant materials indicates that theroughness of the surface of the advancing ice keel has a significantinfluence on the pattern of deformation. It is found that if the surfaceis perfectly rough (so that the interface with the soil can transmit ashear traction equal to the shear that the soil can carry), the deformationdoes not extend below the ice, but that if the interface cannot transmitshear the deformation reaches much deeper.LIMITS IMPOSED BY ICE STRENGTH AND MOVEMENTThe stresses induced by gouging are large by comparison with thosegenerally observed in soil mechanics. Typical values for deep gouges areof the order of 400 kPa in sand, and 6 tines the undrained shear strengthfor clay. The corresponding stresses in the ice are significantly smallerthan the stress that can be carried by the ice of a multi-year ridge or aniceberg, in a highly-constrained situation with compressive principal

stresses. In those cases, qouginq will not be limited by the strength ofthe ice. Fracture of the ice under gouging forces may however occur whenthe ice is a unconsolidated first-year ridge, or initially when the ice hassharp corners.Vertical ice movements are highly significant, both for icebergs and forsmaller floating masses. A typical horizontal gouging for a medium-sizedgouqe force is 10 PIN (the force required to cut a gouge 3 m deep and 15 mwide in 50 kPa clay). Analysis shows that the vertical force is largerthan the horizontal force, by a factor of between 1 and 2, and sometimesnore, depending on the shape of the ice surface. If the waterplane area ofthe gouging mass is 50 m square, a vertical force of 20 MN is enough toreduce the mean draft by 0.8 m. Lifting of the ice is therefore important,and is often accompanied by significant pitch and roll rotations.CONCLUSIONA rational approach to selection of pipeline trenching depths in relationto observed gouging depths demands a knowledge of soil deformation beneatha qouginq ice mass. The extent of deformation will depend on the soilproperties, and particularly on the extent to which the soil is dilatant.Strongly-dilatant soils are much more like to induce deep-seateddeformations below the ice.ACKNOWLEDGEMENTMost of the research described in this paper was carried out under acontract with COGLA (Canada Oil and Gas Lands Administration), whosesupport is gratefully acknowledged.REFERENCESBeen, K. and Jefferies, M.G. (1985) A state parameter for sand.Geotechnique, 35, 99-112.Drescher, A. and Michalowski, R.L. (1984) Density variation inpsuedo-steady plastic fl.ow in granular media. Geotechnique, 34, 1-10.Grinsted, T.W. (1985) Earthmoving in submerged sands. Unpublished PhDdissertation, University of Newcastle-upon-Tyne.Hettiarachi, D.R.P. and Reece, A.R. (1975). Boundary wedges intwo-dimensional passive soil failure. Geotechnique, 25, 197-220.Palmer, A.C., Kenny, J.P., Perera, M.R. and Reece, A.R. (1979) Design andoperation of an underwater pipeline trenching plough. Geotechnique, 29,305-322.Zelenin, A.N. (1968) Osnovy razrusheniya gruntov mekhanicheskimisposobani. Izdatel'stvo Mashinostroenie, Moscow.

SMALL SCALE MODELLING OF ICEBKUGSCOURING OF THE SEABEDF. PoorooshasbResearch EngineerJ.I. ClarkDirectorC-COREMemorial Universitv of Newt ound I ,indSt. John's, NF, Canada A1B 3x5C.M.T.Woodworth-LynasSenior ResearcherABSTRACTThis paper out1 nips the results of small scale phvsical model 1 un?,undertaken at 1 gravity to investigate the processes involved in icehetftscouring of the seabed. The modell~rig was undei taken in a tank rout:\imn~:clay-encrusted gravity consolidated aged saturated sill ovei1.1111 bywater. The iceberg was represented by an aluminum mod~i n1 hO011mi bv 7OOntmin plan. A series of springs and bearings allowed the model iceberg toheave and pitch. with spring stiffnesses chos~n so as to modi-1 theprototype (real) iceberg. Two tests at ditfering scour depths were r~iiie11out in this silt bed. During the tests, the model icebrr;: was displ.ict:d ata constant velocity along the silt tank, and allowed to pitch and heaveaccording to the spring response. Pore pressure response lot the bhal lowerof the two tests was measured and recorded, and the surface and subburfaredisplacements resulting from the scour were deternnned. The rubults f iomthese experiments are compared against existing morpholo~ic.il evid~uc~,and are also briefly compared with theoretical modpls.1. INTRODUCTIONScour of the seabed by a moving ice mass is a common problem in theCanadian offshore. Areas of particular relevance are those currentlybeing exploited for their mineral resources, which include I he UrdndBanks of Newfoundland and the Beaufort Sea (dark & Guignc5l19881 I . Seabedscour may be caused by icebergs or bv deep keels of pressure ridges inmotion. Scours are stretches of uniform, relatively straight fiiriow cind

may be many kilometres in length, traversing both up and down slopes(Woodworth-Lynas et all19861). On the Grand Banks, for example, themajority of scours display a centreline depression under a metre andwidth between 20 and 40 metres (Lewis & Barriel19811). This geometry makesit possible that a seabed scouring event may interact with a man-madelinear feature placed on or just under the seabed, such as a gas or oilpipeline or a submarine communications link (dark et ali19881). Hence, anunderstanding of soil behaviour during a scouring event is necessary toallow the safe and economic development of designs for subseabedconstructions.Experimental evidence of the type of deformation accompanying ascouring event is relatively scanty. Submarine and sonar mapping of seabedfeatures has occurred (eg Hodgson et all19881) yielding information aboutthe surface morphology (figure 1) but no information as to the extent ofdamage beneath the seabed. However, the excavation of relict scours fromglacial Lake Aggassiz in Manitoba (Woodworth-Lynas & Guignef19891) hasdetected deep faults which appear to be related to the scouring event(figure 2). These faults are orientated in such a manner as to beanalogous to a shallow foundation failure (figure 3;. To the authors'knowledge. this represents the only full-scale evidence of the type andextent of damage to be expected underneath a submarine scour.Theoretical and experimental studies of related problems have beenundertaken. Prominent among these studies is that of Harrisonf19721. inwhich he considered the problem of the grouser plate under inclined loads(a grouser plate is a horizontal plate with a vertical plate attached toone end. typically used for anchoring objects such as artillery pieces).He assumed a Coulomb soil model, and showed that in the two dimensionalcase, the depth of damage was restricted to the toe of the vertical platewhen the grouser plate was displaced horizontally. He was also able toperform 2-dimensional experiments 111 sand which bore out his conclusions.Due to the experimental verification which was obtained for this analysis,this model has gained some acceptance in the offshore industry. However.the results from the Manitoba scour investigation have led to thequestioning of the Harrison model as being applicable to ice scour, rindalso prompted this series of experiments.2. EXPERIMENTAL PROCEDURES2.1 Equipment and Test PreparationsThe justification for the modelling in this experiment was presented by

.^cottIl"JBBl 111 which tip presented a series of scale factors for 1-fiavitv reduced scale r~iodelling of soil related phenomena.tin- modplHe argued thathull should be at the same state relative to the critical state(Schofield and Wioth[196Sl) under model stress levels as it would be atthe fullscalp. Thi5 implies .a numbel of scdle factors, the most relevantbt'iii:; he-ale factois of n for linear dimension and for soil strength, andii"Â¥ foivflor~ tv. Atthe inception of the experiment. the only propertywhich w.is fixed was that of soil stiengtli, which therefole constrained thei,ii~,",+~ ot v.i1~1rs ot n.The pirst-nt r\ppri~nrnts wrie conductrd 111 a concrete tank filled withgi.ivitv consolid.Urd silt. The silt bed wd.s ini in length by 3m in width by0. 1711; inilr3pt h. 'I'hr s i 1 t's strrn~th varied across the bed: in most areas.it v,i< f-5kPii, but in one region it rose to l0kP.f. Overlying the entiretit~il ot 51 It w:is ction at l ine D-D. it could beused to i'iod1*1 d scorn event with d sm,*l1 dt~ught-to-width ratlo, 01 onewl t 11 .1 :~lllc'ti I1 l~til'l- 1 ,It 10.A sinti\ WJ?. loc.ittvi on r:ill.s which dllowrd it to travel along thelni~th nt the tank. and the icetwig wa+ attached to this gantry. A:~~Iii~ii!,~t ic ntthe dl t.ichn#t~iit is shown in tiguie 5: it m:ivbe se~ii that thf,t~~nflt'l uct~t'i?. ifr tire to he-ave and to pitch igoverned bv the hpiii~gr~ii\t.iiit s 1 1 t 1s movtvl alorif. t h ~ tdrikbv the g.iiit rv. Provisions hadbf'c~~ rn/ifJ~ to ineiisiite the vei tical and horizont.11 forces on the' iceberg,but ,tcomb~n.it Kin ol :,riiaI 1 toict's anrl f I icti011,il t~lfeel.Â¥- niddt* the qud1 itvot these inp.i-.ui ei.ient > problemat I(:. Howcvet . d certant df~gi'~e of pitchinc,wd-- ol~si't vt'il. which rut i espondt'd to the achievement of tlif ir~!beig'spqm lib1 iinn position, both due to the change in si l t strength as, desoib~din ~ I I P p.irrif.i.tphb abov~. .ind dur to ch.tng~s in surt.ice topoaraphy.Six DnickI'DCRSI nini~.ttuif pore pi cssui-e tt.tiisducers were but icd in thesilt , dl difl'fi~riit depths bf~iif~atli thp scnuiins icfbeix, lo deteiiniiie the>or+: p~e--isine iespouse atvarious points at diffeinig distiinces ftoii, Lhei~ i-hci;:. lii dild 11 ion, t h~, toiiu&tdphv of the silt sui-fiic~ wetsiiiappt'tl. byIpvulliiip. alonx the cent~el~iir of the scoui .ind at a few prof iles atI i~'.ht ,111r;lt~< to ttit, scour. Repe:it 111g this piocess siibst3~irntottic scour

event indicated the surface depression and heave associated with theevent.2.2 Test Procedures, Site Investigation and ResultsPrior to the commencement of the tests, the watel level in the silttank was set at approximately 30mm above the silt level. Tlir lc~brrg wasthen set at the required vertical level and the scour was formed by thvadvance of the gantry at a constant U.06ms-' (see figure 71.Two tests were conducted. the first with the equilibrium height tinair) of the iceberg keel set 0.115m below the silt suiiace, and t.he secondwas set to a depth of O.lb5m below the silt surface. As each test wasconducted, the iceberg initially displaced vertically 1.0 leach itsequilibrium scour depth, and once this was reached, it progressed with .Ilargely steady state motion. The depth ot the first scour vat led hetwt,~n0.005-0.05m (see figure 6) with an average of 0.04m; the 5fcond scourdepth ranged between 0.05 and 0.09m with an average of 0.07m.In the first test, the scour depth was insufficient to tear the surtdceclay layer (except in one localised area), and 50 the danidge un tliesurface was confined to a polished depression following the shdpe of lhvmodel iceberg keel. The deeper scour penetrated the surface and thesurface damage was extensive, consisting of a deep polished scour incisedinto the silt surrounded by surface heave to either side. I.arse blocks ofmaterial were pushed forwards and sideways from the iceberg, which werethen deposited to either side of the scour. Surface heave was alsodetected in front of the head of the deep scour (figures 8 & 9).Subsurface deformation was detected by the digging of trenchfh into thesilt and examining the effect that the scour had had upon fine i 0.001m)layers which were observed in the silt bed (see figures 10). In theshallow scour, the shape of these laminations (perpendicular to the scouraxis) were similar to the surface deformations, being displaced downwardin the centre of the scour. This downward deformation was detectdble at .idepth of 0.2m. or 5 scour depths, and extended approximately to beneaththe edge of the scour. In the deep scour, the laminations also dippeddownward as they approached the centreline of the scour; however, it wasnot possible to trace the laminations to within O.lm of the scourcentreline. In addition, along the axis of the deep scour, a faintlamination at a depth of O.15m was displaced upwards between 0.06 to 0.25min front of the head of the scour. Finally, in one area to the side of thedeep scour, a curved feature was detected whose position and shape was

consistent with the formation of a slip circle.Pore pressure changes were also measured in the vicinity of the shallowscour (figures 11). These pore pressure responses all consisted of a largeshort term response as the iceberg passed close by the transducer,followed by a (smaller) long term change of pore pressure. The magnitudeof the short term response was up to 6kPa, or greater than the shearstrength of the material. At this stage, no attempts have been made toquantitatively analyze these data.3. DISCUSSION OF RESULTS AND COMPARISON WITH THEORETICAL AND FULL SCALEThe data produced by these two model scour events are largelyqualitative in nature, and thus a qualitative analysis of these resultswill be presented. The first point to be considered the validity of themodelling. Assuming a scale factor n=50 yields a prototype soil strengthvarying between 200 and 500kPa. This is somewhat high. Using n=50 impliesan iceberg width of 20m. scour depths of 2m and 3.75m, and an icebergspeed of 0.42ms-l. These latter sizes are all realistic, and so the eventwhich has been modelled is that of a small to medium iceberg with (in thedeep case) a high draught to width keel ratio, in a strong crusted soil.The second point to be discussed is that of the extent and type ofdamage. The results of the layering deformation and of the pore pressureresponse at large distances from the scouring iceberg indicate a nonlocalisedeffect of the scour. In the case of the shallow scour, thevisible deformations extended down to a depth of 0.2m below the scour, orapproximately 5 times the scour depth. In the case of the deep scour, theinability to detect any layering below the scour implies that this regionhad been so reworked as to obliterate any stratification. Thus, completeremoulding appears to occur down to a depth of at least O.l'in,, or twicethe scour depth. Finally, a significant pore pressure response wasdetected underneath the shallow scour at a depth of 0.27cm beneath and0.15m to the side of the scour centreline; this finding implies thatstress changes may be expected at depths greater than the scour by afactor of 7. However, the stress may have been "attracted" to this regionby the presence below it of the hard tank floor, which can be consideredto represent a bedrock layer.The highest quality empirical data against which these model scours maybe compared is probably that from the excavation of the Manitoba relictscour as reported more fully in Woodworth-Lynas et all19891. The relictscour occurs in clays of glacial Lake Aggassiz, and is presently buried

alini~t 1-in ht~liiw thf p,ininicl -urface. Following its drpositiun. t h clav ~ isintnpieted tu have been subdei-iallv exposed. to the extent that the newIrfhr levi-1S.III~ to a (Irpth 7111 bt'low the, clrfvlibidj las .I consequence, thenew lak~ shoies were some distance awav from the area of interest.). TheIdkc's l rvclrest, iiri~l diowi~rd t tip rcgiuii about 9,400 ytJ;irs ago, rising toA level ot l 1On1 .ihove the foimei lv exposed surface. This implies-, that thesoil WJ:. ovrn'on.-.ol iil.it rd at tlir t imp of the scour. The area was d and finely sl ickensided. andsip.nit icant ielat ive displacement is deir~onstdted based on offset bedding.~~.ssiblv uf sevnal metres. FHIP laniir~atioris ill thp clay have beensrvprelv iewoilvpd and mostlv oblit~,iated, which indicates high strains.These ful l [-.calf resul t3 cornpat t, well with the present mudel results.Whet-?.as no disciete lupture p1ani.s were observed below the clay crust IIIthe iiiodrl lest>, this was pmbdblv due to the relativelv soft nature ofthe sediments. I t1c downward movement of the sediments underneath thesioin in thr iiiodt~l tests is cotisistent with the tormation of luptureplanes 111 the stiff clays in tlu' full scale event. The severe reworkingobsn ved 111thr ful l scalp lest5 av,rff:s with the imp1 led reworklug seen inthe CJSC of the det'p model scour. Finally. the shape of the t~eriu in thedeep %tutu

modelled to a fair degree ot accuracv the scouring of a strong. normallyconsolidated, crusted fine grained seabed by a small iceberg.2) The deformations associated with the model hcouis are extensive dudare observed at many times the scour depth below the scour keel, ds arcthe associated pore pressure (and hence effective stless; changes.3) The theoretical models which mav be applicable to the sroiit problemmust be three dimensional in nature and must allow for deep deformations.4) There is good agreement between the model icebrig scours ,11111 relictscours excavated in Manitoba; this agreement could probably he unmoved hvthe provision of model silt bed more prone to rupture.7. ACKNOWLEDGEMENTSThe authors would like to thank Mr. Don Cdri'vron foi h I:-. .nil in t hrcompletion of the tests and site invpstigatlons. Partial support foi theexperimental apparatus was provided bv National So lences and fc,ii?. I ii~t*i 111sResearch Council of Canada grants no. 3-30760 and j-317b3, whx.11 15gratefully acknowledged.6. REFERENCESClark, J. I., char^, 'T.R., L,andva. J. & Woodworl h-Lvnas. C.M.T. "Pip~l inrRoute Select ion in an Iceberg-Scout-ed Sf.'ibed" e r . hot li Cdii. Geotpc-LConf., Regina, Saskatchewan, plll-13%. Oct. I'J-21, 1'137Clark. J.I. & Guigne, J.Y. "Marine ~eotechnical engineel iiig in C.'ii1dda1',Canadian Geotechn-i~aL Journal, Vol. 25. 173-198, lcJ83Harrison, W.L. Soil Failure Under 1.nc li~ied -j.o~ags, US Army CRUEL,. DAProject lTOb2112A130. Hanover, New Hampshire. l'l72Hodgson, G.J., Lever, J.H., Woodworth-Lvnas, C.M.T. i, I.ewis, C.F.M ieds)The dynamics- ~Jo~ceberg groundins.-and.syourln&. ( Dl.(;:> 1e\pck-Lrt,nt ,i~!cirepetitive mawing of the East!rr- C-an~adian cant 111entaI hheltEnvironmental Studies Research Funds Report No. OVÈ Utt..iw.a.Lewis. C.F.M.I'A8.S& Barrie, J.V. "Geological evidence of icehers giounilin~ .?ndrelated seafloor processes in the Hibernia discovi~iv .11e.1 of Gi.iiidBank, Newfoundland'' P~os: Syn~p. Produc. and T1-~311spoi-t. SYS~: f(5 tt~cHibernia Dlscczcry (W.E.Russel1 & D.5.Mugseridf.e pds. Nflfl. tv Lab.Petroleum Directorate, St. John's, Nfld.. pl46-l&7, 1'~SlPoorooshasb, F. et a1 "A Geotechnical Assessment of Ice Scour ul Sf!dbedSedimei~ts", Canadian Geotech~tical .Journal, In prep., lYY3

Schofield, A.N.London, lq68&. Wroth, C.P. Critical State Soil Mechanics, McGraw-Hill,Scott, R.b. Keynote Address, Proc. Intl. Conf. on Geotech. Centrlfu~eModelling, Paris, April 25-27, 1988Wo~d~Orth-I,~nd~. C.M.T., Bass. D.W. & Bobbitt, J. zentory of upslopeand dowt~slope-&ceberg scoullng,Rfpurt No. 039, Ottawa, 1986Env~ronmental Studles Revolv~ng EluldsWnoiiworth-I was. C.M.T. hi I.Y.Giiign6 "Icehers Scours in the GlaciologicalRecord". Pioc. Intl. Cont. Gldcimdrlne Environm~nts: Piocesses andSediments, tienlosicdl Society. London, March 1989Figure 1Side-scan sonar record of a submarine scour.

Scour Incision SurfaceReworked LaminationsFailure Plants-Figure 2A cross section ot the relict scour excavated in Manitoba(aftel Woudworth-Lynas & Guign6[1989]).0 1 2 3 4 5 IQmetresFOOTINGRIGID WEDGESSHEAR ZONESfigure 3A kinematic model for a 2-dimensional shallow foundation failure.

2o;^150700 Figure 4k*fD150+ @The geometry ofthe model iceberg.ALL DIMENSIONS INMILLIMETRES100VERTICAL SUPPORT STRUTS ATTACHED TO GANTRYFigure 5The mounting systemfor the model iceberg.THIS ARRANGEMENT OF VERTICAL AND HORIZONTAL RAILS ALLOWS THE,ICEBERG TO PITCH AND TO HEAVE. WITH THE VERTICAL AND ROTATIONALSTFFNESSES DETERMINED BY THE SPRING STRENGTHS AND THEVERTICAL SUPPORT STRUT SEPARATIONZ in metresFigure 6The profile of the scourcentrelines, before andafter the scouring event.The scale is magnified bya factor of 50 in thevertical direction. The X.Y, and Z directions are asdefined in figure 10.

Figure 7The model iceberg at thestart of a test.Figure 8The scour left after thedeep incision..\Emf of P,.-.xiff"-qo*pr.**ion,----\I\Figure 9Drawings of the shallow (above) and deep scours.,Tçnsio CracksSurcharg* Aheadof Scour Head

POINT X Y ZFigure 10Cross sections from the scours perpendicular to the axis and ahead ofscour head. The sections are located as in the map above.Dimensions in metres.

HUE IN SECMKtl1l.MPPI 4316 HUE PHISSUIE HISPOMSEm s u m III inPIT 3911 MIE PUSSUUE HISPOMSEPHSSURE I N inScour Centrttm*4377 -1 -MÑ 3901-

MULTIYEAR RIDGE FORCE VARIABILITYR. W. SchreiberT. D. RalstonD. E. EggingExxon Production Research CompanyP. 0. Box 2189Houston, Tx 77252-2189U. S. A.The force required to fail a multiyear ridge against a conicalstructure can vary significantly, depending upon the actual shape of theridge. This paper presents multiyear ridge force statistics usingprofiles of actual multiyear ridge cross sections. Wang's upper boundplasticity approach [l] was generalized to calculate the forcesassociated with the field-measured cross sectional shapes, assuming auniform cross section along the entire length of the ridge. The scatterin the calculated forces is large and represents the effect of thevariation in ridge shapes that exist in the real world.A Monte Carlo computer simulation was developed to incorporate theforce statistics which were expressed as a function of ridge crosssectional parameters, such as keel depth and sail height. The use ofthe simulator to calculate loads on a cone structure for selected returnperiods is discussed. The general procedure can be applied to othertypes of ice features, such as icebergs in the Barents Sea.1. INTRODUCTIONMultiyear ridge forces represent an important design consideration foroffshore structures in the deeper water of the Beaufort and ChukchiSeas. The geometry of the design ridge feature has an obvious,significant impact on the magnitude of the computed force. The typicalapproach used by industry [I, 21 to select a design feature forcomputing ridge forces is to use an idealized ridge cross section [3].The idealized cross section, such as shown on Figure 1, is a symmetricprofile and is completely defined by specifying either a sail height or

a keel depth. This paper will focus on the variability in actual ridgeprofile shapes and the theoretical failure forces associated with theseridge profiles.- - K KEELDEPTH2.0K T FLOE THICKNESSFIGURE 1. Idealized ridge profile (After Wright et al. [3]).2. MULTIYEAR RIDGE GEOMETRYA data base of 137 multiyear ridge profiles was developed from theresults of public and industry-sponsored field programs that date backto 1971. Ridges from these programs were profiled in four geographicareas; the U.S. Beaufort Sea, the southern Canadian Beaufort Sea, theChukchi Sea, and near the Queen Elizabeth Islands in the Canadian HighArctic. Each ridge profile was digitized to produce a numericaldescription of the cross section of the ridge. An algorithm wasdeveloped for calculating the geometric properties (e.g., area, sectionmodulus, and moment of inertia) of each ridge cross section from thedigitized profile.Each ridge profile is indexed according to geographic area, themeasurement device used to obtain the data (e.g., sonar, thermal drill,or impulse radar) and the section completeness. Section completeness ofthe cross section was classified in terms of one of four categories:complete cross section, half cross section, complete-sparse (fivemeasurements per cross section or less) and half-sparse. In the case ofhalf cross sections, a mirror image of the profile about the point ofmaximum keel depth was assumed for obtaining geometric properties.The discussion and calculations in this paper will use the non-sparsecomplete and half cross section profiles from the U.S. Beaufort Sea,Canadian Beaufort Sea, and Chukchi Sea. There are a total of 73 ofthese cross sections, profiled from 60 different multiyear ridges. Ofthe 73 cross sections, 60 were profiled across the entire cross sectionand the remaining 13 were profiled over approximately half the crosssection. The ridges profiled near the Queen Elizabeth Islands appear tobe generically different in cross section (larger for the same sail

height) than the ridges in the other three areas and were not includedin this study.A plot of the maximum sail height and the maximum keel depth for eachof the 73 ridge cross sections is shown on Figure 2. This figure showsthat the majority of the profiles have keels less than 50 ft deep andthat the eight cross sections deeper than 50 ft were all measured in theCanadian Beaufort Sea. Most sail heights are less than 15 ft. Themaximum sail height and keel depth in the data base are about 30 ft and100 ft, respectively. The scatter due to the natural variability of theridges appears to increase with increasing sail height. Furthermore,the keel-to-sail ratio of 3.3:l for the idealized ridge shape appears tofit the data reasonably well with a slight bias toward larger keeldepths for a given sail height.120 J100-IDEALIZEDt- 80-L -I -1à -S; 60-0 -L .40:0 CHUKCHI SEA20-0-- r-- ~ÑÑÑÑÑ * ,0 5 10 15 20 25 30 3 5 40SAIL HEIGHT iFTiA CANADIAN BEAUI-ORT0 US BEAUFORTFIGURE 2.Sail height vs. keel depth.3. DESCRIPTION OF RIDGE LOAD CALCULATIONWang's upper bound plasticity solution [l] for long ridges (Type 1)was adapted to compute failure forces for irregular ridge shapes. Thevelocity field assumed in this plasticity analysis is shown on Figure 3.The rate of energy dissipation for the velocity field consists of thefollowing components:1. Dbr - rate of energy dissipation due to ridge bending2. bs = rate of energy dissipation due to ice sheet bending3. Dw,. = rate of energy dissipation due to ridge weight4. DWs - rate of energy dissipation due to sheet ice weight5. Df = rate of energy dissipation due to friction between ridgeand coneDetails of Wang's upper bound analysis are provided in Reference 1.

CONE DIAMETER AT RIDGECONE DIAMETER AT WATERLINE\ \FIGURE 3. Velocity field for long ridge. Type 1 (After Wang [I])The calculations of the first and third components of energydissipation involve integrations over the cross section of the ridge.To accomplish this for irregular ridge shapes, the ridge cross sectionwas divided into trapezoidal sections, as shown on Figure 4, with thehorizontal width of each section equal to the distance between fieldmeasurements. The field measurements used to define the vertical sidesof the trapezoids consist of either a measurement of sail height, keeldepth, or both. The dissipation components were then calculated byintegrating across each vertical slice and summing the results. In thisanalysis, the cross section was assumed to be constant along the entirelength of the ridge.FIGURE 4. Sample irregular ridge cross section.149

4. VERTICAL RIDGE FORCE RESULTSA vertical ridge failure force was calculated for each of the 73 ridgecross sections. Two upper bounds for the failure force were calculatedfor each ridge; one based on the upper bound plasticity solution forridges and the other based on an ice sheet failure mechanism developedby Ralston [4]. The sheet ice failure load was computed since some ofthe ridge profiles were very wide and plate-like. This shape may givehigher forces using the ridge failure solution than those that would becalculated using a plate failure mechanism. The sheet ice load wascomputed assuming that the sheet ice thickness was equal to the maximumkeel depth of the cross section. The lower of the two forces wasselected as our best upper bound for the failure force for each ridge.In addition, forces were determined for failing the ridge from eitherside. For irregular shaped ridges, the forces are different dependingon which side of the ridge contacts the cone, since rotation of theridge is accounted for in the energy dissipation terms. The relativedifference for different loading directions, however, tended to befairly small.The forces were related statistically to both sail height and keeldepth. Figure 5 shows a plot of the relationship between the verticalforce and sail height. The plot includes the forces computed forfailing the ridge from either side, i.e., a total of 146 calculatedloads. In general, there is a relatively high degree of scatter in thecalculated loads, particularly for higher sail heights. For example,the calculated forces for profiled ridges with 17 to 20 ft sail heightsrange from about 16,000 kips to 135,000 kips, which is almost an orderof magnitude. Most of the forces calculated with the actual ridgeprofiles tend to fall below the curve that represents forces calculatedwith the idealized ridge profile at each sail height.IDEALIZED RIDGEPROFILE -//L A0160ug 120tc2< 80 A CANADIAN BEAUFORT+ 0 US EEAUFORT40 r CHUKCHI SEA00 5 10 15 20 25 30 3 5 4 0SAIL HEIGHT IFTIFIGURE 5. Vertical ridge force vs. sail height.

Figure 6 provides a plot of the relationship between vertical forceand keel depth. This plot indicates a significant correlation betweenthe vertical force and the maximum keel depth as evidenced by the smalldegree of scatter. For keel depths greater than 50 ft, the idealizedridge geometry tends to result in forces greater than the forcescalculated using the actual profiles.-wg 120-cd' 80 A CANADIAN BEAUFORTd+ D US BEAUFORT5 40 Â CHUKCHI SEA>00 20 40 fa0 80 100 120KEEL DEPTH IFTlFIGURE 6. Vertical ridge force vs. keel depth.5. MONTE CARL0 COMPUTER SIMULATIONA Monte Carlo computer simulation was used to calculate multiyearridge forces on conical structures for different return periods. Thesimulation procedure calculates the vertical component of the ridgefailure force. The horizontal component of the force is related to thevertical component in a deterministic manner that depends on the slopeof the conical surface and the ice/structure friction coefficient. Theinput required for the simulation includes a definition of a loadingevent, a means to determine how many loading events occur per year, a(statistical) description of the magnitude or size of the event, and ameans to calculate the load that corresponds to an event of a givensize.Our simulation procedure is based on the "grid analysis" procedurediscussed by Wheeler 151. This is an extreme value technique in whichthe largest multiyear ridge sail height is identified within each gridof multiyear ice (in this work a grid is a square 1320 ft x 1320 ftarea) that is recorded in stereo photographs. These photographs must berepresentative of ice conditions in a given region. A "loading event"is thus defined to occur whenever the structure sweeps out a 1320 ft x1320 ft area of multiyear ice. The number of events per year is thendetermined by the area of multiyear ice that moves past the structure

each year. In the present work, results are presented for an assumedfixed number of loading events per year (N - 1, 10, 100, 200).For each load event that occurs in the simulation, the notion of sizeof the multiyear ridge is determined by a sample multiyear ridge sailheight that is drawn from a statistical distribution of multiyear ridgesail heights. This distribution is derived from a grid analysis of alarge number of stereo photographs. In the present calculations, themultiyear ridge sail height distribution is normal with a mean height of9.0 ft and a standard deviation of 4.5 ft.The relationship between vertical ridge failure forces and multiyearridge sail heights is derived from a statistical analysis of the datadiscussed in the previous section and presented in Figure 5. Ananalogous procedure based on ridge keels rather than sails would avoidmuch of the calculated force data scatter (compare Figures 5 and 6).However, the technology needed to effectively develop a statisticalkeel-based event description on a large spatial basis is not presentlyavailable.A regression equation was used to define the best fit to the data inFigure 5. The force scatter about the best fit line was statisticallyrepresented by a residual term which was described by a normal randomvariable with a mean of zero and a standard deviation that increaseswith ridge size. Since there was relatively limited data, particularlyat higher sail heights, the data were grouped in bins with a fixed width(sail height range). The force scatter in each bin was treatedadditively, i.e., as a uniform bandwidth.The resulting expressions to represent the relationship betweenvertical ridge force and sail heights were:Vert. Ridge Force = 0.207 * S 2 - 0.132 * S + Residualwhere S - sail height (ft), the force is expressed in kilokips, and theresidual is a normal random variable with mean of zero and a standarddeviation expressed as:Std. Dev. - 0.0349 * S 2 + 0.337 * S + 0.8The vertical ridge force is thus expressed as a statistical function ofthe ridge sail height.

6. SIMULATIONRESULTSA computer simulation was run assuming a fixed number ofridge/structure interactions per year. For comparison purposes, thenumber of interactions evaluated in this work ranged from 1 to 200 peryear. The results are shown on Figure 7 and are plotted as force versusreturn period for a given number of interactions per year, (denoted asN). The solid lines indicate results using the force statistics in thesimulation. The dashed line represents the results for the forcesassociated with the idealized ridge shape shown on Figure 1, with thesail height distribution and other input remaining the same.N = NUMBER OF INTERACTIONS PtR YEAR- ACTUAL RIDGE SHAPES--- IDEALIZED RIDGE SHAPEI I0 10 20 30 40 50 60 70 80 YU 100RETURN PERIOD lYEARSiFIGURE 7. Simulation results.Several trends can be observed from the simulation results. First fora given N, the slope of the curve for return periods greater than 20years is relatively gradual. For instance at N equal to 10, there isonly about a 20 percent difference between the 20-year and 100-yearload. However, the force increases rapidly for short return periods.A second trend can be observed regarding the effect of an increasingnumber of interactions per year. For large N, the simulation resultsare relatively insensitive to moderate increases or decreases in N. Atsmall N, there is a substantial difference in forces for small changesin the number of ridge interactions per year.In comparison with the results for the idealized ridge shape, theforce-statistics results were about 30 percent lower at a 100-year

eturn period with 10 ridge interactions per year. This is due, inpart, to the idealized ridge geometry specified on Figure 1. Thedirection of this result could be anticipated from Figure 5, which showsthat the use of the idealized shape tends to give higher calculatedloads than many of the actual profiles would yield.7. CONCLUSIONS AND REMARKSThis analysis of multiyear ridge failure loads used a data base of 73measured ridge cross sections to illustrate the variability in loadsthat might be expected when ridges fail against an offshore structure.The load calculation method was based on the upper bound plasticityapproach that was published by Wang [I]. Other load calculation methodscould also be applied to this data base of actual ridge cross sectionsto yield analogous statistics on expected load variability. Conclusionsassociated with this work are summarized below:This analysis produced loads that varied by almost a factor of 10for multiyear ridge sail heights that ranged from 17 ft to 20 fthigh.The actual force variability is probably even greater than what wehave calculated since we have included several "uniform"assumptions; such as, using a common bending strength value for allridges, assuming that the cross section of each ridge was uniformalong the length of each ridge, ignoring ridge length effects, etc.0 A statistical description of the load variability can be easilyincluded in design load calculations. The same approach could beapplied to other types of design-level load events, such as icebergimpact loads. For instance in the Barents Sea, icebergs mayconstitute a design concern for future production structures. Toaccount for the variability in iceberg shapes and mass, the icefeature data base should be tailored to providing the type of inputwhich is utilized in the iceberg load calculation procedure andsimulation model. This could include parameters such as freeboard,waterline dimensions, keel depth, mass, and edge thickness profile.0 Knowledge of the force variability will be very important whenfield measurements of actual ridge failure loads are used to judgethe adequacy of theoretical calculation methods. The presentresults suggest that measurement of a maximum sail height andfailure load for a single event would be a very unreliable test ofa theoretical calculation method. However, the reliability of such

a comparison would be greatly improved if the maximum keel depth ofthe ridge were also measured.This calculation approach can readily incorporate an expanding database of ice feature field measurements or improvements in loadcalculation methodology. It can also be applied to specificregions (e.g., Beaufort Sea, Chukchi Sea, Barents Sea) where icefeature geometries may be limited by their source or formationhistory.8. REFERENCES1. Wang, Y.S., "Analysis and Model Tests of Pressure Ridges FailingAgainst Conical Structures," IAHR Ice Symposium 1984, Hamburg,August 27-31, 1984.2. API Bulletin RP-2N, "Recommended Practice for Planning,Designing, and Constructing Fixed Offshore Structures in IceEnvironments," June 1, 1988.3. Wright, B., Hnatink, J. and Kovacs, A., "Multiyear PressureRidges in the Canadian Beaufort Sea," Proc. POAC'79, Trondheim(1979), Vol. I.4. Ralston, T. D., "Ice Force Design Considerations for ConicalOffshore Structures," Proc. POAC'77, 1977.5. Wheeler, J. D., "Ridge Statistics from Aerial Stereophotography,"Proc. POAC'81, Quebec (1981). Vol. 111.

STUDY OF THE BEHAVIOUR OF ICE MASSESIN MARINE ENVIRONMENTSRaffaele RomagnoliAssistant ProfessorPolitecnico di TorinoITALYRiccardo VarvelliAssociate ProfessorPolitecnico di TorinoITALYABSTRACTParticularly referring to the field of the offshore research of hydrocarbonsin the Arctic regions, the paper presents a new combined approach to thestudy of the interaction phenomena ice vs structure, and of the hydrodynamicsof the ice masses. The problem has been studied and solved on the basis ofthe macroelement approach, with particular attention to the hydrodynamicalanalysis of the single ice masses, and to the interaction ice mass vs structure.The drift forces, the damping coefficients, the retardation functions,and the frequency-independent added masses of ice objects in the nearby ofoffshore structures are included in the computations, in order to allow acareful study and simulation of the possible collision phenomena between theice mass and the structure of the oil rigs. The paper relies upon a characterizationof both the mathematical and the experimental stages of the research.1. INTRODUCTION TO THE PROBLEMThe behaviour of the ice masses in the sea waves can be described with goodaccuracy and approximation by employing a deal of consolidated approaches,already optimized for the performance of hydrodynamical analyses of offshorestructures (e.g.the sink-source techniques, the semi-analytical methods).Some Authors have successfully adopted the macroelement method in order tostudy the hydrodynamical problem for simple configurations (e-g. icebergs

and floes, approximable by plates and cylinders), by using the coaxial ringelement modelling (Kokkinowrachos, 1978: Kokkinowrachos et a1 ., 1980 aboveall). The macroelement method also allows careful analyses of the hydrodynamicalinteraction phenomena ice vs ice and ice vs offshore structures; theexisting literature presents a great amount of practical cases and applications,where the mentioned technique of approach is also extended to the caseof the study of the interaction between vertical and subvertical solids ofrevolution (Kokkinowrachos et al., 1986 above all).2. ANALYTICAL FORMULATION OF THE PROBLEMWith the aim of giving a unitary general formulation of the boundary valueproblem for families of different cases of both ice mass and ice mass-structureconfigurations, the startpoint of the theoretical know how comes to bethe mathematical expression of the complex velocity potential of the flowfield around multibody configurations, when regular wave trains excite setsor groups of N freely floating ice masses in the nearby of offshore structuresfixed to the sea bottom. Referring to an axisymmetric configuration ofthe said bodies, the defined velocity potential can be expressed as follows:Sja(x,y,z)Sjo(.k.)= spatial and time coordinates;= circular wave frequency;= stationary part of the P potential;= potential of the undisturbed incident wave;= diffraction potential;= radiation potential coming from the oscillation of the k bodyin the direction j in still water, also in presence of all theother bodies;= complex velocity amplitude of the k body in the j th mode.

The exciting forces and moments can be determined by solving the diffractionproblem described by the velocity potential, which is basically function ofthe undisturbed gravity wave component and of the diffraction component. Thehydrodynamical parameters ( in particular the damping coefficients and the addedmasses) can be studied by checking the hydrodynamical reactions inside theradiation problem. Of course the velocity potentials have to satisfy: 1) theLaplace condition over the field domain, 2) the linearized boundary conditionson the undisturbed sea surface, 3) the kinematic boundary conditions both onthe sea floor and on the wetted surface of each of the considered objects.The above defined diffraction and radiation potentials have to satisfy theradiation condition at the infinite limits. The profile Go and the velocitypotential Po of each undisturbed incident wave train with circular frequency0, height H, total wave number W, heading angle A, in water depth D can be expressedrespectively as:Po(x,y,z,t) = -i *g * cosh (W * z)"(r^-coih'Tw"*"!)i' *Go(x.y,t)where the frequency and the wave number stay in the relation:0 = sqrt [(g * W * tanh (W * D)] (4)On the basis of the knowledge of the velocity potentials, it is possible tocompute the exciting and the hydrodynamical reaction forces for each of theconsidered bodies/objects. For the movable bodies the pertinent equation ofmotion has to be formulated in detail.3. FORMULATION OF THE MACROELEMENT METHOD AND DEVELOPMENT OF THE STUDYReferring to the complete analytical descriptions given by Kokkinowrachos,1978, Kokkinowrachos et al., 1980, and Kokkinowrachos et al., 1986, it can bepointed out - first of all - that the macroelement approach subdivides thefluid mass into coaxial ring elements bounded by the free sea surface, the

sea floor and the horizontal surface of the steps, the meridian being approximatedby a stepped curve. The velocity potentials of the diffraction and radiationproblem come to be computed for any of the macroelements by the variableseparation method, selectively applied to the Laplace equation concerningthe flow field. By using the Fourier series form, the outcoming expressionsmust satisfy the kinematic boundary conditions on the horizontal limits of theconsidered bodies, the radiation condition at the infinity, the kinematic conditionon the sea floor, and the linearized conditions at the sea surface.The systems of equations which allow the computation of the unknown Fouriercoefficients directly come from the formulation of the remaining boundary conditionat the vertical limit for each step, and from the imposition of themathematical continuity of the potential and of its 1st derivative at theboundary of the neighbouring elements. For the interaction problems involvinggroups of ice objects and masses, the multiple scattering physical modellingis adopted in the fully numerical way. Considering a gravity wave system withvelocity potential Pv interacting with a group of N bodies of revolution, whenthe k-th body is only excited by the incident wave train the total velocitypotential expressed as Pv+Pk(ko), [where Pk(ko) is the zero-order scatteringradiated by the body], is the solution of the boundary-value problem for theconsidered individual body. The summation: sum(k=l ,N) (Pk(ko) ) represents the1st approximation to the total scattered amount of the global system. The saidk-th body, in response to the generated waves of the zero-order scatteringfrom the other bodies, comes to radiate 1st order waves in a way that the outcomingtotal velocity potential: Pk(kl)+sum(k=l,N)(Pk(klo)) [with k + kt]satisfies the required boundary condition in the local coordinate system ofthe k-th body. It is possible to extend the procedure up to the w-th order ofscattering, achieving - in general - that the total wave amount scattered bythe k-th body is given by the smation: sum(w=O,oo)(Pk(kw)), and that thetotal wave amount scattered by the global system is given by the double sum:sum(k=l ,N)sum(w=O,oo)(Pk(kw)).As far as the diffraction problem of multibody systems in regular waves isconcerned, Pv (as expressed in the above formulation) goes to have the meaningof the So potential of the undisturbed incident wave train, and Pk(k) themeaning of the Sm diffraction potential. Keeping considering a set of N vert-

ical bodies of revolution, excited by a regular wave train, when the modellingof the flow around the k-th body is performed by coaxial elements, the g-thorder potential in the infinite ring element of the k-th body [with respectto the local coordinate system] can be computed by assembling the diffractionand the radiation terms, which are given - in a polar system - respectivelyby the expressions:the generical quantity ~..(r,v,z) being a summation function of the Fouriercoefficients, the water depth, the circular wave frequency, the gravity acceleration,as a result of integration in polar coordinates by using the Besselfunction fundamental theorems. The unknowns are usually: the Fourier coefficients.They can be computed for any generical formulation of the problemby imposing the fulfillment of the kinematic boundary conditions on the surfacesof each of the components of the global system, starting from the zeroorderpotentials and the corresponding derivatives. Moreover the use of theBessel functions involves further solution advantages, since additional mathematicalproject-oriented theorems let expressing the potentials in terms ofmuch more opportune local coordinate systems, proper of the considered k-thbody. When facing the study of the collision phenomena between the ice massesand the offshore rig structure, the description in the time domain of the motionof the floating ice masses comes to be indispensible; among the possiblesolution techniques, the impulse response function technique allows carefulformulations of the equations of motion for a body, considered as a real linearoscillator (after Cumins, 1962). The sum is assembled of a deal of termsinvolving: a) the retardation functions, in their integral expression; b) themass total contribution [also including the frequency-independent term, whichis function of the circular wave frequency, of time, and of the retardationfunctions, including the corresponding damping coefficients]; c) the hydrostaticrestoring coefficients and the corresponding motion components. Thetime domain analysis can also take into consideration nonlinear forces and

effects, such as wind(s), currents and current changes, wave perturbations,and other non-climatic factors. The evaluation of the mean drift forces isperformed by direct integration methods, by summating the average-in-timevalues of the terms which include the effects of the wave elevation, of themasses, of the positions of the considered bodieslobjects, of the correspondingpoints on the surface, of other climatic factors. Both the retardationfunctions and the frequency-independent added masses in the contact pointsand sites are required for the aim of careful characterizations of the collisionphenomena and probability (ice mass vs offshore rig structure).4. EXAMPLES OF APPLICATIONA two-year research stage has been developed so far, in order to study andto solve the radiation and diffraction problem for axisymmetric cylindricalobjects and circular plates arbitrarily located in the 3-0 space. Calibrationstages have been repeated on the basis of the availability of real data, com-ing from Kokkinowrachos et al., 1986, and already checked by the Authors inthe recent past (Romagnoli et al., 1988). The results of parametric analysesof the influence of the draftlradius ratio and of the water depthlradius ratioare shown in Fig. 1, referring to the case of an ice floe modelled as a caseof floating circular plate; the study is extended to the case of bergy bitsand icebergs (having ratios draft/radius greater than 0.5).The behaviour andthe influence of added masses and damping coefficients is described in Fig. 1A(where the case water depthlradius = 1 is considered); Fig. 1B examines thetransfer functions of the heave motion while varying the ratio water depth//radius. Fig. 2, for the case of a group of initially coexisting ice floes inmutual vicinity, examines the hydrodynamic effects and the behaviour of boththe added masses and the damping coefficients, and compares the obtained res-ults with the case of no mutual interactions. It is immediate to see that notnegligible differences come out, especially for high ratios interaxislradius.Fig. 3 shows the obtained horizontal drift forces for a set of 5 differentwave headings (0° 30° 45O, 60° 90°) concerning a group of ice plates inclose vicinity, the specified angle being referred to the gravity center line.Sets of curves of this kind can be easily obtained for more complex geometries.

1........................ADDED MASSWATER DENS.*DISPLAC.VOL.depthlradius = 1DRAFT/RADIUSCIRCULAR WAVE FREQ.*SQRT(RADIUS/GRAVITY ACCELER. )DAMPING COEFFICIENT//[WATER DENSITY*DISPLAC.VOL.*SQRT(GRAVITYACCELER./RADIUS)]2depthlradius = 1DRAFT/RADIUS00 2 4CIRCULAR WAVE FREQ.*SQRT(RADIUS/GRAVITY ACCELER. )Figure 1A.Analysis of the influence of the added masses and of the dampingcoefficients (for the case of a single ice floe).1TRANSFER ----------------- FUNCTION0.5*WAVE HEIGHTdraftlradius = 0.20.500 2 4CIRCULAR WAVE FREQ.*SQRT(RADIUS/GRAVITY ACCELER.)Figure 1B.Diagram of the transfer functions (for the case of a single icefloe), for the heave motion.

+0.5draftlradius = 0.2ADDED MASS........................WATER DENS.*DISPLAC.VOL.0-0.50 2 4CIRCULAR WAVE FREQ.*SQRT(RADIUS/GRAVITY ACC. )draftlradius = 0.2DAMPING COEFFICIENT1/[WATER DENSITY*DISPLAC.VOL.*SQRT(GRAVITYACCELER-/RADIUS) I04- 10 2 4CIRCULAR WAVE FREQ.*SQRT(RADIUS/GRAVITY ACC. )Figure 2.Analysis of the influence of added masses and damping coefficientsin the case of 4 square-placed (interaxislradius~ 2) floating icefloes, with the wave train perpendicular to a side of the square;[1=single ice floe; Z=interaxis/radius=2.2; 3=interaxis/radius=3;4=interaxis/radius=6].

CIRCULAR WAVE FREQUENCY*SQRT(RADIUS/GRAVITY ACCELER.)Figure 3.Diagram of the horizontal drift forces for 5 different wave headings,for a 3ice-plate pattern, as schematized below. In the alignedposition: draft/radius=0.2; depth/radius=2.5; interaxis/radius==3.6; the angle is referred to the gravity center line.water density=1.03 kg/& 3

Fig. 4 shows the obtained results which concern the hydrodynamic analysisof ice masses in the nearby of offshore structures fixed to the sea floor,and also at prefixed finite distances from them. In particular the figuredepicts the behaviour of added masses and damping coefficients for the surgeand the heave motions. For some frequency values negative values have comeout for the surge added mass; this fact can be explained by considering thefrequent wave trapping phenomena which occur in the space separating the submergedobjects from the sea surface.5. DISCUSSION OF THE RESULTSExtensive testing and calibrating stages of an original simulator wereperformed. The adopted modelling technique has shown to be able to allow agood fitting to the physical problem, which is much better than other alreadydeveloped modelling schemes.The water depth value has shown to influence the hydrodynamic parametersand the resulting motions strongly. In the case of 4 to 10 interacting icebodies, not negligible resonance effects have been checked, occurring in thespace interval included between the forward and the backward bodies definedreferring to the incident wave direction.As far as the drift forces are concerned, it has been checked and verifiedthat, for the cylinders of a group which are firstly affected by the sea wavetrain(s), quite high drift forces come to be generated. As far as the interactionice-structure is concerned, the surge motion has shown to have thegreatest influence upon the hydrodynamic parameters, much more than theheave motion; other kinds of motions have not shown to be influent in anyappreciable manner.The simulator can be successfully used in order to analyze and forecastthe collision conditions between the ice mass and the offshore oil structures:a further implementation stage is going to introduce the capability of acomplete computational analysis of the retardation functions and of the significantfrequency-independent added masses in all the contact positions. Astatistical implementation of the deterministic formulations is also at thestudy, in order to introduce the possibility of a wider use of the simulator.

60000ADDEDMASS(t)D* = distance iceberg-fixed structure (case of direct interaction)30000DAMP I NGCOEFF.(tls)15000000 1 2CIRCULAR WAVE FREQ. (radls)CIRCULAR WAVE FREQ. (radls)60000ADDEDMASS(t)HEAVE 12000DAMP I NGCOEFF.(tls)600000CIRCULAR WAVE FREQ. (radls)CIRCULAR WAVE FREQ. (radls)Figure 4. Diagram of added masses and damping coefficients (for surge andwavesheave motions) proper of an iceberg near an offshore structure,(fixed to the sea floor, as schematized below); the main data arethe following: iceberg mass=displaced volume=60000 t; iceberg rad-ius=35 m; gyration radius=22 m; water depth=45 m; struct..width=40 mr¥"/ sea floor \ Ii cebkrgfixed structure

6. CONCLUSIONThe study has been faced of the behaviour of ice masses in marine environrents.New and original analysis instruments have been built up and optimized,in order to solve the hydrodynamic and interaction ice-structure problem, byadopting the macroelement method for the spatial modelling of axisymmetricobjectslbodies spatially located in arbitrary positions.The problem has shown to require a quite heavy mathematical formulation,which has to be supported and validated interactively by a good deal of significantand reliable real data.7. REFERENCESCumins, W.E. (1962). The impulse response function and ship motions, SchiffstechnikPubl. Ed.. Vol. 9. 268. 1962.Kokkinowrachos, K. (1978). Hydrodynamic analysis of large offshore structures,5th International Ocean Development Conference, Tokyo, Proc., 1, 360-367.Kokkinowrachos, K., Asorakos, S. and Mavrakos, S. ( 1980). Belastungen undBewegungen grossvolumiger Seebauwerke durch Wellen, Research Report n. 2905North-Rhine Westphalia, Westdeutscher Verlag, Opladen, 146, 1980.Kokkinowrachos, K., Thanos, I. and Zibell, H.G. (1986). The hydrodynamic interactionbetween several vertical bodies of revolution in waves, 5th InternationalOffshore Mechanics and Arctic Engineering Conference (O.M.A.E. 1986),Tokyo, Proc., 3, 431-438.Kokkinowrachos, K., Thanos, I. and Zibell, H.G. (1986). The behaviour of icemasses in waves, VTT International Symposium Polartech '86, Helsinki, Proc.,1, 340-358.Romagnoli, R. and Varvelli, R. (1988). Study of the influence of rubble fieldsand pile-ups on the interactions between the ice and the structure of thedrilling rigs, International Symposium Polartech '88, Trondheim, Proc., 1,451-462.

ANALYSIS OF SEA ICE EKEFT IN A COASTAL ICE ZONEPiper A. SmithEnsign, USNOceanography-.Annapolis, Maryland 21401USAABSTRACTFrun March to July 1982, a satellite transmitting weather station wasdeployed in the coastal ice zone (CTZ) 150 km north of Alaska. Sea ice inthis area may be influenced by synoptic scale winds, mesoscale winds(created by Brooks Range mountain barrier effects), ocean currents, andcoastal shearing and ampaction transmitted through internal ice stresses.These influences oo~plicate ice movement predictions in the CIZ; hcwver,the use of mesoscale network anpkd winds, rather than synoptic scalewinds, accounts for many of the influences and shplifies the predictionprocess. Lbta was wllectd to cupte mesoscale pmssure m r k win%,,surface (3m) winds, and ice velocity. Speed ratios and turning anglesbetween ccqmtd network geostrophic winds, surface winds, and ice driftwere ampared. A plotting algorithm was tirpleroenbed to superimposemesoscale wind vectors on the buoy's track. Also, in late April, a largelead developed along the Canadian Archipelago which resulted in anapparent notation of the entire ice sheet in the Beaufort Sea and anincrease in ice velocity in the study area.According to Zubovls law, sea ice should travel in the same directionand at 1% of the speed of the qeostrophic wind. this estimate is for freeice drift, such that the internal ice stresses are negligible. Also, theeffects of currents are ignored. On a short time scale (less than a

iionth) , in an open ocean, over 70% of the variance in ice motion can beexplained by the geostrophic wind (IhorTKlite and Colony, 1982). Icemotion in the vicinity of a land mass cannot be explained by rules forfree ocean ice drift. 'Biomdike and Colony (1982) defined the regionwithin 400 km of shore where internal ice stress plays an inportant roleas the axsbl ice zone (CIZ) . In aiklition to internal stress in the CIZalong the northern Alaskan coast, snail atmospheric scale phenomena suchas mountain barrier barcclinity, corner effects, and sea breezes are oftenmissed by synoptic scale analyses. It has been shown that mesoocaleqeostrophic wind estimates are more accurate for ice drift predictions inthe U Z (Lipma, 1988). The turning angles and speed ratios between themesoscale wind vectors and ice velocity vectors in the CIZ are not known.Also, it has not hemhew significant otkr influemesf such asinternal ice stresses and coastal ice shearing and axpaction are in CIZice drift predictions.The buoy travelled westward in the Beaufort Sea frcn the 142*W to the157'W meridian, rcughly along the 72'N parallel, in water 2 km deep (Seefig. 1). The Beaufort Sea circulation is dominated by the Beaufort gyre,a clockwise system.M=Laren, et.al., (1987) estimated that the ocean gyreaccounts for up to 50% of the long hnn ice mvement in the CanadianBasin, specifically 5 to 6 Ian of ice drift everyday.About 110 km fromNorthern Alaskan shore, seaward of the 50m isobath, the Beaufort Seaundercurrent has a mean eastward flow toward 10O0T at an average of .015m\s (Aagaard, 1984). Lipana (1988) showed evidence that thisundercurrent reaches the surface.The winds are the most significant influence on the ice drift. Winds,initially driven by atmospheric pressure gradients, are modified bythermal and oroqrachic effects, such as sea breezes (Kozo, 1982) andmountain barrier baroclinity (Scftwerdtfeger, 1974, Kbzo, 1984).The local movement of the ice is affected by the general motion of theentire basin ice sheet, to an extent determined by the consolidation ofthe ice. In the northern hemisphere, along the northern edge of an east-west oriented coastline, a westerly surface wind will cause a netsouthad transprt and a consolidation of the ice agahst the land mass.This consolidation will restrict the response of the ice to the ensuingwind stress. The fractures and leads in the Beaufort ice pack allow a net

northwan3 mvemnt of the ice without anpaction or a restriction inmovemmt. An easterly wird will muse a net northward tranqmrt of theice am3 a 1- of the ice floes nsw the coast. This 1axeni.q willallcw th marshom ie to move mm freely in mspmse to the nexteasterly w id stmss.An additional inflm on the locd ie &ifts unicpe to the th am31-tionof thisstu3ywastheopenhgof a 1- lead inthe Amticpackjust wst of the Canadian Archiplago.The fracture was either the resultof a storm suqe (Kozof 1988) or the shearing stress of the Mufort gyre.T?E fracture was first noted on 4 April 1982. The lead began an27 April 1982 am3 stabilized by 15 May 1982f at a length of qmximamy1000 Ian am3 a width of 80 Ian.Total Drift, March-July, 1982lS7O lSS" 1 SO 0 145' 141'Fig 1. Total buoy drift and mesonet triangles.

lb gather datal an autarated heather station using an AK3X mtaCollection Platfonu system was 1- to a TlKS-N/MlU series satellite.The station has l2 f h per day r- by Servioe NGCSl with anaccuracy of 3 km (Fqmlds et-al. 1982). The station w l l surface ~win3 velocity, surface r-e and tmpenhE, pcsition, and magneticdata f m 1 Mamh 1982 to 11 July 1982. The surf- wird velocitydata was kad 22 June 1982.syrqtic scale winis uere ampted twice daily f m NW &ace map.Mescsale wir& were calculated frm the twu msmet triangles (See fig.1.). In ach msm& triangle, the pmssures at the autarated beatherstation and t w land ~ stations uere masurd am3 adjusted to sea levelvalues using the h-icequation:=ptexp(%) (1)where&isthesealevelp-lmisthemasurda-icpressu~, g is the acceleration due to gravityl az is the height above Bleavel and T is the absolute tmpenture.Cram=r*s rule was used to detemhe the pressure gradient at the centerof the triangle. The air density (p) was estimated using the Ideal GasIaw for the average masurd tmpentures (T) at the three stations andU.S.stamkd Atmcqheric pressure (p = 1013.3nb).T'? =m (2)The Coriolis pammtxx (f) was calculated base3 on the average lati-muse the wird flcw in the ~JEI typically had a radius of mhEgmater than 300 km, gextn@ic bale was aswed (Wzo, 1982) and thewird velocity vectors (v) wxe calculated using the gec&r@ic wirdequation:p is the air densityl $ is the atmaqbric pressure gradient, ~IKIf v is the Coriolis force.FYan 1 March to 9 Junel the msomt triangle had base-vertices at Jagoand Naxwhal Island. The third vertex was the autmated beather stationwhich driW fnxn l41.g0W to 148.2'W. FYan 9 June to 11 July, the basevertices uere NaJXhal1sland and mht m. Again the thixd wasthe autanated beather station dch &iM f m 148.2'W ta 157. OoW (See

fig. 1). The wind v&rs were calculated every 3 hcurs. The wind .stmss-p-theak-ityandvwasthewindm.Thedragccefficient (q) was estimated to be -0026 in the CCZ of the Eeaufort sea((Werlandt 1985).The ice drift velccity was calculated daily based on the rhmb linedishme between the daily cbqe in lxq pcsitions. The spied ntisbetwen the gecdqhic w M (Vg) an3 the ice drift (Vi) and between thesurface wind (Vs) and the ice drift (Vi) were calculated for each day.The msults were divided a~~ tn westerly and easterly winis an3avemgd for each mnth. !lhe turning angles (d) between the -cwhfi (Vg) and the ice drift pi) and between the surface wind (Vs) and icedrie (Vi) were also aculaw for each day. Ehch mnth8s data wasplotted in a scaikeqmm.~ m ~ i c ~ d a t a f m t h e ~ ~ t o a r e f - m k w a san Wcation of the orientation of the on-ice boy. The cbangingorientation of the buoy was plotted over tim and shd the rotaticm ofthe ice floe.mta cm the axumeme, duration, and extent of the lead west of theCanadian -pelago was cbtained fmn satellia imagery (KOZO andTo-, 1988).Ideallyt the surface whxls a d be 45e to the left of the -cwMt having a demeasd velccity due to the surface frictiont andt thus,a decres& Coriolis force. Hwever, the ice should m e 45- to the rightof the surface wMt turning in reqmnse to Coriolis. So, the dativeeffect M d be a 0- tumirq angle betwesn the gesixqhic wind and icedrift. Observing the scatteqrams (See Fig. 21, the March and Aprilturning angles average arourd Oot but are not consistent. For May andJune, when the ice has meltd and demqled fmn the coast, so as toclcser m l e a free drift situationt the 0' tumirq angle is mreconsistent. Using Zubvls law for amparison, the ice shmld m e at 1%of the gembqhic wind. ?he first rcw of figures in Table 1 shmm themnthly average of sped ratics divided into easterly and -1y wind

0 60 120 180 240 300 360GEOSTROPHIC WIND-. ..-J0 0 ~ 6 0120 180 240 300 360GEOSTROPHIC WIND1-21 JUNE 19822408 1805 240w 12. *0 60 120 180 240 300 360GEOSTROPHIC WIND00 60 120 180 240 300 360GEOSTROPHIC WINDFig 2. Geostrophic wind to ice velocity turning angle scattergrams.MARCH, 1982 APRIL, 19820.0 60 120 180 240 300 360SURFACE WINDI0 60 120 180 240 300 3600 60 120 180 240 300 360SURFACE WINDSURFACE WINDFig 3. Surface wind to ice velocity turning angle scattergrams.17 3

ampnenb. The t&al average is .009# slightly less than Zubm'sesthte for fme drift, prcbbly hcause this ice was mre mlidated,ice. Wing this transition pied fran spring to sumer, the icelaxem ardAlso mte that the ratio is always higher forthe easterly wb3s as qpc6ed to the westerly w-. The Wedx2rly win%-use a curpaction of ice against the mest ard a restriction of &ion.%mlywb3s-usetheicetomawayfmthed&bthepck ice. satellite imagery meals that during the stdy pericd the pdcice axtairm-3 mmy fmctures ard leads; thusl the pack ice was not a rigidbcurdaq to inhibit the mrthwaxd flcw of ice.Wle 1. Wbxl to Ice Drift Speal FaticsE!axh && B Y- E - W - E H - E b' - E-007 -005 .OK? -004 -012 -006 -014-008 -001 -015 -007 -024 .OD -030As above, in the ideal sihation, ice mes 45' to the right ofthe surface wM. Fkpolds (1985) shmd that the ice dri£t 30' to theright of the surface wid in the Maqinal Ice Zone WZ) of the ScuUmmming Sea.The MIZ is the zone between pack ice ard cpm ice waterr thetransition zcm between 0% & 100% ice cover. %serving the scatkqmms(See Fig. 3)# the ice nuved 40' to 60' to the right of the surface wid.-ofW-tedM-hqladWWcoastlh orientation of the mrthe.m Alaskan share (alq 115-T) . Forthe predanhately easterly wMrthe ice auld mt maintain a head -ingto the left of 295-T. Fkpolds (1985) that the ice in the MI2moved at -04 of the surface wbxk. In the CIZ, ciuring the spring tosmmer Witim picd, the ice wed on an average of -014 of the&ace wid. The CIZ shaild have a 1- wid to ice speed ratio because-the ice is mre mlidated than the ice in the J3aing Sea MIZ.ohervingtheseam3~ofFi~ in!Cable 1, thevalues -asthey wmach the mmths, hcause the ice is beaming lessmlidated. Also, the values for the easterly wb3s are amsktentlyhigher t2-m the values for e l y wb3sr again due to the westerly w Mice ampction against the cnast.The ice drift &ara&&stics chaqed gradually f m the sprig tosmmsr season. The Wting ard dkmmzction of Mvidual floes alltheice to mve with the wid at a great speed with less mi-. %nature of the ice drift was also chanqd by the develqnmt of an ice lead

along the Canadian Archipelago. The magnetic heading data from the buoyshows that the ice floe rotated an average of .03'/day counterclockwiseprior to the fracture. This cyclonic vorticity could be the result of theopposing shearing stress from the land fast ice on the westward driftingfloe. Fron 4 April to 10 April, during which period the fracture firstappeared an satellite imagery, the ice rotated 5.7'/day clockwise. Iheentire ice sheet containing this floe, now freed from the shore, wasmoving in response to the Beaufort gyre. After the initial fracture ofthe ice, the floe regained its counterclockwise rotation, possibly becauset h e & l w d e ~ ~ ~ - m l ~ ~ W t h e M i c e146" 149 144" 143" 142ÂFig 4 (a). Ice drift and mesoscale wind vectors, May.Fig 4 (b). Ice drift and mesoscale wind vectors, June-July 9.175

sheet velocity. Although the ice fra-early in Aprilt thel & d d & ~ i n & t o i b W w i ~ o f 8 O h ~ i l a ~easterly wind came during the pericd of 27 April to 3 May (Kozo am3mqerson, 1988). &fore this e of the leadt the ice med at ahout.OE of the surface wid; inwdiately after the openimg of the lead, theice began wing at aka& -025 of the surface wid.% daily mesecde wind vectors were sqerhpsed on the buoy ice trackfor May am3 Jm data (See Fig. 4). In Mayt the ice floe travelled at anangle to the right of the wind vector. % tumhg angles deawsd asthe wind blew f m the same direction for a longer pericd of the. NotethetworeversalsinMay. % ~ i c & e w W ~ o n w ~ m ~were easterly during these two mi-, but the -enetwork WWwere westerly, because of a n ~~~tain &crier effect f m the Etmoks Pange(Lipmat 1988t Kozot 1988). The ice drift reflected the msoscde widdirection. In Junet the wid vectors were even clc6er to the ice tracktan Mcation that ice drift predictions in the CIZ shculd be shpler inthe warner mni3~ as the &ion mre and mre resables free drift.1) In the CIZ during the spring to sumer transition, the ice drifts ata him pnxntqe of the wind speed and at a mre consistent tumhgangle as the sumx season ~~~.2) In the CIZ during this transition pericdt the average ice driftsped was -009 of the gesbx@dc w id speed with a 0- turnirg angle.3) In the CIZ during this transition picdl the average ice driftspeed was -014 of the surface w id speed with a 50' right tumhg angle.4) % lead which opmed a l q the Canadian Archiplago in late April1982, resulted in an initial clodwise rutation of the ice sheet and aswtahed hcmase of ice to wind speed ratio.5) The -e gextn@ic wid is a better starting point for icedrift predictions than the synoptic scale wid or, the &£fia toobtain, highly variable surface wind.6) In e t i m to the -e wind velocityt the following nust betaken into account predictiq the ice drift in a CIZ: coastlineorientationt wird direction in relation to the coastlinet wind fetcht theof the year, am3 Mi& characteristics of the enth ice sheet(fractums and leads).

mzol T.L. (1982). An cbemational dxiy of sea bmes along theAlaskan Wufort Sea M: Part lf J. of M. Metsl 211 891-905.mzof T.L. (1984). Mesosmle wird along the Alaskan Wufortmzof T.L.ard L.J. Torgersm (1988). The rule of altermtirg cyclonesard anticyclones in triqgerirq sea ice fractum in the GmdianArctic Basin, Pruc. Ninth Intl. Synp. on Icel wm1 Japanf 23-271988f Intl. Asscc. for Hydraulic Bseamh Cartn. on IcePrcblmsf ed. Hircshi SaeJci, HoJ&aido UniveJsity, 633-642.mzof T.L. (1988). m e effects cn wird velocities, ocean currenk,ard sea ice drift in the E?eaufort Sea axsbl zme, Ninth Intl. W.FWC-87 (in press, editd by Sackinger ard Jeffries, Univ. ofAlaska, Failbnks).r.,ipana, P.A. (1988). -ted weather sixtion drift in the AlaskanE!eaufort Sea axsbl ice zmef Ninth Intl. W. KIAC-87 (in p-,edited by SacJhger ard Jeffries, Univ. of Alaska).A.S., M.C. Serreze, ard R.G. Barry (1987). SWSond variationsof the sea ice &ion in the Gmadian Basin ard their hplications,GecphyS. W. I.&.141 ll23-ll26.0~erlar-d~ J.E. (1985). AbKqbric bcur&ry layer &rwture ard dragcoefficient over sea icel J. Geqhys. Res., 90, 9029-9049.Ff,eynolds, M.# C.H. Rxse, and J.E. Cverlard (1985). Ice drift ardmgimal mrulogy in the scuthem Bring Sea, F&sults f m MIZEXWest, J. GecphySl 90, 11967-11981.Wndike, A.S. ard R. Colony (1982). Sea ice &ionin n?spIse topxtnqhic whds, J. Geqhys. Res., 87# 5845-5852.%ondike, A.S., R. Colony, ard E.A. Mcmz (1983). Arctic Ocean EUoymqraml mta mrt 01 Jan 1982- 31 Dez 1982, mix sci- m,Univ. of Wash., Seattle, 72-8.schedtf~, W. (1974). Mamtain barrier effect on the flm of mleair north of the Ewo0k.s Range, Pruc. 24th Alaskan Sci.Geqhys. Inst., Univ. of Alaska, mixbankst 204-208.

AN UPWARD LOOKING SONAR ICE DRAFT SERIESTorgny VinjeNorwegian Polar ResearchInstitute1330 Oslo LufthavnNORWAYABSTRACTAn upward looking sonar has been used for ice draftmeasurements in the main core of the East Greenland Ice DriftStream at 75O N and 12O W. The basic equations for ice draftcalculations and the accuracy of the measurements arediscussed. Some samples of the one year long recordings aregiven together with the probability density of the ice draftdistribution for the summer and winter periods. Preliminarycalculations indicate that the flux of ice across the 75thparallel amounts to 3120 km3 year-'. This corresponds to 70%of the estimated average ice flux of 4480 km3 year-I passingthe 80th parallel in the Fram Strait.1. INTRODUCTIONBecause of the great variability in the ice thicknessdistribution, relatively frequent observations from in situinstruments are necessary to obtain a good basis forstatistical calculations and budget studies of an ice field.Moored upward looking sonars (ULS) with recording intervalsof 5-10 minutes seem in this connection to represent aninteresting tool.

2. INSTRUMENTThe upward looking sonar (ES-300-11) was manufactured byCHR. Michelsens Institute (CMI), Bergen. The instrumentspecification and mooring configuration are given in Table 1and in Fig. 1.Table 1Technical specifications of CMI ES-300-11.Operational depth ................................ 20-70 mSonar beam width ................................. 5.0 degOperational acoustic frequency ................... 300 kHzResolution.......................................-0.1 mPressure transducer range........ ................ 20-70 mResolution ....................................... 0.02 mTilt (XY) resolution .............................1 degData recording interval .......................... 4 minData recorder ........................... Sea Data Model 610Storing capacity (300 ft cassette) ............. -550 daysTotal length of instrument .......................1.70 m0.55 mDiameter of float..... ...........................Diameter of cylinder ............................. 0.16 mWeight in air, without float. .................... 58 kgTotal weight in air w./float ..................... 79 kgNet buoyancy in sea water ........................ -55 kg

3. RECORDING SPECIFICATIONS3.1. Sonic transit timeThe distance from the sonar head to the underside of the iceis based on four sonar shots of which the two most equaltransit times are stored. As one series of observations isperformed every 4 minutes, this corresponds to about 130,000pairs of ice draft observations per year. The average of thetwo stored transit times (Sl and S2) is used as basis for thecalculation of the ice draft. The mean one-way transit time S(s) is given by the formula:provided by the manufacturer.Observations where the first stored transit time exceeds0.05 s and where the difference between the two storedtransit times exceeds 0.001 s have been deleted. A transittime difference of 0.001 s corresponds to a draft differenceof about 1.4 m. In addition, we have deleted observationswhere the average transit time indicates reflection fromobjects more than 1 m above the water surface (here denotedas negative draft larger than 1 m). The latter filteringexcludes abnormal recordings (possibly due to scattering ofthe return signal) but includes negative recordings which maybe expected due to wave effects in the ice margin. With anULS depth of 50 m the sonar beam, having an aperture of 5degrees, will have a circular footprint with a diameter of4-5 m and is thus capable of detecting the water surface infairly narrow leads. This indicates that wave effects, notbeing detected by the pressure transducer, may be reflectedin the sonar signal. The registrations show that the majorityof scattered negative draft records observed duringconditions with an open ice cover becomes less than 0.5 mafter the filtering has been applied (Cf Vinje and Berge1989 ) .

The speed of sound in water is determined from the equationgiven by Kinsler and Frey in "Fundamentals of Acoustics". Anerror of one degree C in the water temperature yields acorresponding ice draft error of 0.33 m. As we have noregistration of temperature in the actual water column, wehave applied a sound velocity of 1442 m s-I corresponding toa water temperature of -l.OO C and a salinity of 33 per milleat the average depth of 25 m. A one per mille error in thesalinity corresponds to an error in the ice draft of 0.12 m.(These parameters will be adjusted later on whenoceanographic recordings become available.)Control of the accuracy of the calculated ice draft isprovided by the registrations collected during conditionswith open, calm water above the sonar during summerconditions. (Cf. Fig 2 where a connecting line has beendrawn between the recordings. A broken line indicates thatthree or more consecutive recordings have been filtered out).3.2. Instrument depth variationsThe maximum variation of the instrument depth during theperiod (365 days) was close to 30 m. This variation is in allprobability due to a variable drag on the 1200 m long mooringline caused by changing current velocities. Smaller depthvariations, probably caused by the tides, are clearly seen inthe recordings (Vinje and Berge 1989).The range of the pressure transducer was exceeded on anumber of occasions when the ULS was forced down to depthsbelow 70 m. For practical reasons it is also difficult todetermine the accurate level of operation in advance duringdeep see deployments. To secure a continuous operation ofthe ULS it is therefore important to have a pressuretransducer with a sufficient wide range.

The pressure is given in numerical units varying between 0and 4095 (0-70 m). Recordings above 4095 have been deleted.The pressure (P) is given in pascal bywhere Po is the observed numerical unit. A Digiquartz 8060D.S. has been used as reference for the calibration of thepressure transducer.3.3. The tiltThe tilt is recorded and given directly in degrees withinthe range of O0 - 4S0. The vertical orientation of theinstrument turned out to be very stable with deviationsmainly below 3 degrees. This was to some extent unexpected,but indicates that the instruments buoyancy balance isinfluenced to a small extent by the inclination of the 1200 mlong mooring line.A tilt of e.g. 10 deg. corresponds to a correction of 0.8 mwhile the majority of the tilts, which are less than 3degrees, corresponds to a correction of 0.07m. The tiltingeffect is corrected for in the calculations of the draft (seebelow).4. DEPLOYMENT AND RETRIEVALThe ULS was deployed at a nominal depth of 45 m in the maincore of the East Greenland Ice Drift Stream. The instrumentwas attached to the top of a current meter mooring of E.Fahrbach, Alfred-Wegener Institute for Polar and MarineResearch (AWI). The instrument was deployed from R/VPolarstern at 75O03.4'N and 12O09.2'W on 22 June 1987 at0930 UT and retrieved from the same ship on 20 June 1988 at1800 UT.

5. ICE DRAFT DISTRIBUTIONSThe ice draft (D) was calculated from the relationshipwhere Dp is the depth calculated from the pressure, Ds is thedistance from the sonar head to the underside of the ice ascalculated from the sonar transit times, and 0.13 is thedistance between the sonar head and the pressure transducerin the ULS housing. Dp is calculated from the formulawhere P is the recorded pressure estimated from (2), A is theatmospheric pressure read from weather maps, o is the densityof the water = 1026 kg m3 for a 33 per mille salinitycontent, and g is the gravity constant 9.829 m s-*. Ds iscalculated from the formulawhere S is the mean one-way sonar transit time to theunderside of the ice calculated from (I), V is the speed ofsound (=I442 m s-I), and T is the observed tilt.Figs. 3 and 4 give the frequency distribution of the variousice drafts observed for June-October and November-May withinbins of 20 cm. There is a clear bimodal distribution for thewarmer season with a marked maximum thickness observed in thearea between 0 and 0.4 m . The distribution of the thickerice is far more flat with a maximum around 2 metres. Thedistribution for the colder season indicates a marked maximumof thinner ice with thicknesses between 0.2 m and 1.0 m and apeak between 0.2 m and 0.4 m. Again the distribution of thethicker ice is very flat, though indicating a secondarymaximum around 3 m. The maximum draft observed was 34 m,otherwise the average maximum drafts were observed between20 m and 25 m .The series have been divided into 15-day intervals for

statistical calculations. The 15 day mean ice drafts varybetween 1.36 m and 3.93 m with an annual average of 2.38 m.The series indicate no systematic seasonal variation. (CfVinje and Berge 1989). This suggests that the export ofthicker ice from the Arctic Ocean is of a sporadic charactermasking the seasonal thickness variation due to melting andfreezing .6. VOLUME TRANSPORTSAssuming the density of water and ice to be 1025 kg and 920kg m-3, respectively, we get an annual average ice thicknessof 2.65 m. This corresponds to about 66% of the averge icethickness of 4 m as observed further north in the FramStrait (Vinje and Finnekssa 1986).Assuming the width of the East Greenland Current to be 220km at 75ON and applying the observed annual average driftspeed of 0.17 m s-l, we obtain a preliminary ice volumetransport past this latitude of 3120 km3 year-',corresponding to 70 % of the estimated average ice transportof 4480 km3 year"' passing the 80th parallel in the FramStrait (ibid.). A better estimate of the volume transportwill be made later on the aid of the contemporary currentmeter measurements.A downstream reduction in ice thickness and volume transportshould be expected. This reflects the effect of leakage ofice along the eastern margins of the East Greenland IceDrift Stream caused by e.g eddy formation as well as the neteffect of melting and freezing in the main ice stream (Moritz1988).It is supposed that contemporary series at differentlatitudes would serve as a good basis for a better under-standing of the interannual variability in the ice thicknessand the ice budget of this important meridional ice flux.

7. REFERENCESM0ritz.R.E. 1988: The Ice Budget of the Greenland Sea.Technical Report: APL-UW TR 8812.Vinje,T.E and T.Berge 1989: Upward Looking Sonar Recordingsat 75O N - 12O W from 22 June 1987 to 20 June 1988. DataReport Norsk Polarisnstitutt Rapportserie Nr.51.Vinje,T.E. and 0 FinnekAsa 1986: The Ice Transport throughthe Pram Strait. Norsk Polarinstitutt Skrifter Nr. 186.

Fig. 1Upward looking sonar arrangements for ice draft measurements.Fig. 2Sample of typical ice draft recordings.18 6

Sum rn e r6 8 10 12ice thickness (m)Probability density distribution of ice drafts for June-October.Winter2 4 6 8 10 12ice thickness (m)Fig. 4Probability density distribution of ice drafts for November-Hay.18 7

CERTAIN PROPERTIES OF SPECTRALLY INTEGRATEDAND SPECTRAL TRANSMITTANCES OF FRESHWATER ICEFROM 400-700 NMS.J. BolsengaGreat Lakes Environmental ResearchLaboratoryAnn Arbor, MI 48105-1593 USAABSTRACTConsiderable information is available on the transmittance ofphotosynthetically active radiation (PAR: 400-700 nm) through sea ice,whereas relatively little is known about PAR transmittance throughfreshwater ice. Transmittances of PAR through some common freshwater icetypes (including clear ice, refrozen slush, and snow ice) are reportedfrom studies using instruments which measure both spectral (2-10 nmincrements) and spectrally integrated transmittances over this range.Snow causes the greatest attenuation of radiation, often reducingtransmittances to 10% or less over the spectrum as a result of even lightcovers (2-8 cm). Clear ice showed transmittances of 80-95s for thespectrally integrated data and from 65 to nearly 95% for the spectraldata. Transmittances of other ice types were bounded by the clearice/snow-covered-ice transmittance range. Comparisons between thespectral and spectrally integrated data sets show specific applicationsfor each type of measurement.1. INTRODUCTIONInformation on the transmittance of incident photosynthetically activeirradiance (PAR: 400-700 nm) through sea ice is plentiful. Some of thesestudies have combined ice optics with under-ice ecology (e.g. Maykut andGrenfell, 1975; Perovich et al, 1986; Palmisano et al, 1987; SooHoo et al,1987) while others have included only sea ice optics (Grenfell and Maykut,18 8

1977, Gilbert and Buntzen, 1986, Grenfell and Perovich, 1986). Similarstudies on the transmittance of PAR through freshwater ice are not asnumerous and not nearly as well advanced Recent studies, using qualitysensors, include Maguire, 1975a,b and Bolsenga, 1978 and 1981. Many earlyfreshwater ice studies used substandard sensors and methods which renderthe results questionable. The sea ice studies cited above have usedspectroradiometers to measure incident and transmitted radiation, whereasthe freshwater studies have used instruments which measure incident andtransmitted radiation integrated over the 400-700 run range. This papersummarizes and highlights the more important properties of the integratedfreshwater ice transmittance measurements and provides some new spectraltransmittance data collected with a scanning underwater spectroradiometer.The measurements are from both large and small freshwater lakes including,and in the geographical area of, the North American Laurentian GreatLakes. The results compare the two types of measurements (integrated andspectral), discuss their relative usefulness, and project possible futureresearch with respect to freshwater ice transmittance.2. INSTRUMENTATION & METHODSTwo separate instrumentation systems were used. radiation sensorsconsisting of topside and underwater quantum sensors (hereafter called the"integrated sensor w ), which measured radiation integrated over the PARspectrum, and an underwater scanning (400-850 run) spectroradiometer forspectral measurements. All of the sensors were manufactured by the Li CorCorporation (Lincoln, Nebraska USA). Measurements reported in this paperwere made at a distance of about 2 cm under the ice bottom. Measurementsat greater depths will be reported elsewhere.The underwater quantum sensor was light and required only an "L-shaped"arm fabricated from 3.2 cm diameter white plastic pipe, liberallyperforated for ease in submerging, to carry the sensor (Figure 1). Thesensor was located approximately 80 cm from the borehole and wasadjustable to a level position which could be checked topside by an aboveicespirit level. A platform equipped with three large screws was used tohold and level the arm.The suspension device for the heavy (25 kg in air) underwater

spectroradiometer consisted of sections of 5.1 cm diameter aluminum pipefor vertical control and a hinged member to move the instrument to anFigure 1. The L-shaped arm used to support the integrated sensor (400-700mil) Depth of the arm was adjusted for ice thickness by means of a slipjointon the vertical member.Figure 2. The underwater spectroradiometer with buoyancy floats,horizontal folding arm, and vertical depth-adjustment member.

undisturbed area 2 m away from an access hole in the ice (Figure 2). Thespectroradiometer was guided under the ice to the full length of the armand the vertical member locked into a surface tripod (Figure 3). Floatsattached to the instrument provided neutral buoyancy. The instrument wasFigure 3. The tripod securing the vertical member of thespectroradiometer system.attached to the horizontal arm by a shackle which allowed free horizontalmovement for automatic leveling. Neutral buoyancy and leveling wereachieved prior to field operations in a laboratory tank. Verticalmovement to acquire readings at various depths was accomplished to a depthof 5 m by adding additional sections of measured and marked pipe; atgreater depths the unit was lowered by marked line. Typically a scan wastaken in air, at depths of approximately 2 cm under the ice and at 1, 2,3, 5, and 10 m under the ice surface, and at the bottom. The sequence wasrepeated in reverse with a scan in air completing the operation. Total19 1

time for a complete operation varied from 7-10 mm. During that tine,uniform sky conditions, as indicated by visual observations and by thebeginning and ending air scans were required. Scans were not used wherechanging sky conditions accounted for variability of greater than 3-4% inthe repeat transmittance values at various depths.3. TRANSMITTANCESTransmittances are reported for clear ice, snow covered ice, refrozenslush, and white ice (refrozen slush, snow ice)-clear ice combinations(Table 1). Clear ice showed the highest transmittances of all the icetypes measured. However, the amount of radiation penetrating a given icecover varied widely depending on the type of clear ice measured (crack andbubble structure) and the cloud cover. The transmittances vary from 0.70to 0.95 for the integrated sensor (Table 1, Cases 1,2) with the averagetransmittances of the spectral values (Cases 3,4) falling within thatrange (0.79-0.87). Cloud cover influenced clear ice transmittancessignificantly. In one situation, the integrated sensor was positionedunder 36 cm of clear ice (Case 2). Under clear skies, two ratios of 0.95were obtained. At the same site on the following day when 10/lOths cloudcover prevailed during the entire period, the ratios remained in a narrow0 70 - 0.76 range. Figure 4 shows two clear ice spectral data sets. Eventhough the top ice layer of the sample for Trace 1 exhibited extensivebubble structure (Table 1, Case 3, Note b), the transmittances remainedabove 0.70 throughout most of the spectral range. Skies were clear duringthe measurements and the average transmittance (0.87) compares favorablywith the integrated clear sky measurements. Trace 2 in Figure 4 showstransmittances through another clear ice location (Table 1, Case 4) withstippled surface. The values are about 3-10% lower than the ice in Trace 1likely because the stippled surface affords more of a diffuse reflectorthan the surface in Trace 1.A snow cover of just a few centimeters in depth attenuates most of theincoming radiation to an underlying ice surface. Measurements were madeat two locations where snow-covered and snow-free clear ice were locatedin the same area (Table 1; Cases 1,5; and Cases 4,8). Using theintegrated sensor under a 3 cm snow cover (Case 5), ratios of transmittedto incident radiation were reduced by over 70% from the snow-free surface(Case 1). Comparison of average transmittances of the snow covered vs.19 2

Table 1. Case number (0, sensor type, ice type and thickness, integratedsensor transmittance (T), maximal transmittance of spectral sensor (MaxT), maximal transmittance wavelength (A), and average spectraltransmittance from 400-700 mil.C Sensor Ice Type/Thickness(cm) T Max T, X (mil) Avg TClear Ice1) Integ Clear/28 (a) 0.77-0.892) Integ Clear/36 0.70-0 953) Spect Clr + semi clr (b)/25.5+8(c)4) Spect Clear/21 (d)Snow Covered Ice5) Integ Snw cvd/28+3 (a)6) Integ Snw cvd/37+2+1 (el7) Integ Snw cvd/43+3+1 (f)8) Spect Snw cvd/21+7-8 (dlWhite Ice9) Integ Refroz slush/27Clear/White Ice Combination10) Integ Clr + ref slsh/38+4 0.5811) Integ Clr + ref slsh/37+2 0.6612) Spect Clr + wht ice/6.5+18 0.54 (570) 0.4713) Spect Clr + snw ice/13+7 0.52 (562) 0.50(a) 3 cm wind-packed snow over one area, 0 cm snow nearby. Measurementsfrom same borehole;(b) Clear ice is classified as having few bubbles and cracks. The semiclear ice contained a dense structure of evenly distributed elongatedbubbles oriented perpendicular to the ice surface;(c) Stratigraphy from bottom to top layers for all cases;(d) Clear ice with stippled surface, 7-8 cm snow over one area, 0 cm snownearby. Measurements from same borehole.(el 37 cm clear ice, 2 cm refrozen slush, 1 cm new snow;(f) 43 cm clear ice, 3 cm refrozen slush, 1 cm granular metamorphosedsnow.

snow-free ice as measured by the spectroradiometer shows a nearly 80%reduction in transmittance (Table 1, Cases 4,8; Figure 4; Traces 2,3).Maximal transmittances shifted 22 nm higher for the snow covered ice. Tofurther illustrate the effect of snow on PAR transmittance, snow wasremoved from the ice/snow combination listed in Table 1, Case 6. Theratio of under-ice to above-ice radiation rose from 0 18, with undisturbedsnow, to 0.66, with the snow removed.Trace 170Trace 26040Trace 4Trace 510-Trace 30-- ,400 450 500 550 600 650 700Wavelength (nm)Figure 4. Spectral transmittances through 33.5 cm of clear ice with thetop 8 cm exhibiting an extensive bubble structure (Trace 1); through 21 cmof clear ice with a stippled surface (Trace 2), and the same 21 cm ofclear ice covered by 7-8 cm of snow (Trace 3) Spectral transmittances of18 cm of white ice over 6.5 cm of clear ice (Trace 4) and 7 cm of snow iceover 13 cm of clear ice (Trace 5).The term white ice includes the more specific ice types snow ice andrefrozen slush. Snow ice forms from upward water seepage through stresscracks in an existing ice cover loaded with a snow layer, whichsubsequently refreezes. Refrozen slush forms with mild temperatures or

ain which reduce a snow cover to slush, which subsequently refreezes.Only one measurement of an ice cover composed completely of white ice, inthis case refrozen slush, is available (Table 1, Case 9). Measurementswith the integrated sensor showed transmittance ratios which varieddepending on the bubble content and albedo of the ice with lowertransmittances obtained in an area of higher ice albedo. Measurements ofclear/white ice combinations are shown in Table 1 (Cases 10-13) and Figure4 (Traces 4 & 5). Average transmittances of the spectral measurements, areconsistent with transmittances from the integrated sensor, taking intoaccount differences in stratigraphy.Extinction coefficients, k (cm-1) , for representative integrated sensorvalues in this study and from Maguire (1975a,b) areClear ice 0.0006 to 0 02 + 0.003,Combinations of clear ice, white ice, snow 0 027 to 0.059;Snow, new soft 0.10 + 0.02;Snow, hard powder 0 500 + 0.05.4. DATA APPLICATIONS AND FUTURE STUDIES4.1 Spectrally integrated dataIn a recent under-ice ecology program (Bolsenga s, 19881, PAR at theair/water and ice/water interfaces was estimated, using a limited numberof on-site measurements and many of the previously collected measurementsdescribed above with some suprising results (Bolsenga and Vanderploeg,1989). The site was a large (162 tan2 surface area) bay of Lake Michigan,USA before, during, and after ice cover Incident total solar radiationwas measured approximately 35 tan from the measurement site Incident PARwas computed from an empirical equation To compute the amount of PARentering the water column through snow and ice, the ice types, amount ofsnow on the ice, their general abundance and location, and the position ofthe ice edge were observed from the surface (aircraft or satellite imagerycould have been used); ice thickness and stratigraphy were measured.Observations of snow and ice-type, abundance, and location were collectedby an individual with experience in measuring PAR transmittance throughsimilar types of ice and ice-snow combinations making assignment of

estimated transmittance values as accurate as possible. Transmittanceswere then weighted according to the areal coverage of each type.The estimated transmittances during February and March (months with icecover) were higher than expected for two reasons: 1) larger amounts ofclear, snow-free ice over the bay than expected, and 2) both ice covermonths included periods of open water. The lack of snowcover was causedby high winds blowing snow from the surface and by above freezingtemperatures and rain for a portion of the ice-covered period. Figure 5shows that even though the transmittances during ice cover decreasedsignificantly, transmitted PAR does not show the precipitous decreasesmeasured on many small, heavily snow-covered lakes. In addition, highmonthly incident PAR during the ice-covered months, compared to the openwatermonths, contributes to the smooth transition in transmitted PAR fromfall to winter to spring Without high incident PAR, transmitted PARduring the ice-covered months would have exhibited a significant decrease,but not as much as would be expected for a many north temperate inlandlakes which are normally totally snow-coveredIt is unlikely that much additional work on spectrally integrated PARtransmittance is warranted for the ice types and thicknesses alreadyexamined. The existing information enables experienced observers toestimate the PAR transmittance of large or small areas from minimal datasuch as snow thickness and extent, ice thickness, type, and coverage. Inareas with ice conditions dissimilar to those already measured, additionalstudy would be required to provide the baseline data necessary forreasonably accurate estimates.^,Oct Nov Dec Jan Feb Mar AprTime (months)Figure 5 Transmittances (T) and transmitted PAR estimated for an undericeecology pilot program.

4 2 Spectral dataOne principal application for spectral data is with detailed under-iceecology programs Such studies will almost always require on-site,spectral data since varying atmospheric conditions, metamorphosis of theice/snow surfaces, and variable stratigraphy of the ice from location tolocation will affect the depth of the biota as well as their horizontallocation Freshwater zooplankton often adjust their position in the watercolumn according to both the quantity and wavelengths of radiationavailable Estimates of spectrally integrated PAR as described above willcontinue to be useful for pilot studies and large area estimates of PARtransmittance, but detailed studies such as those in the polar regions asdescribed in the introduction will continue to use on-site, spectralmeasurements. It is possible that fiber optic probes could be used. Somespeculation exists, for example, that light penetration in candled icecovers is considerably higher along crystal boundaries (Bolsenga et al.,1989), thus creating favorable environments for the biota in thoseconcentrated areas.5 ACKNOWLEDGMENTMr David Norton of the Great Lakes Environmental Research Laboratorydesigned and fabricated the instrument support systems and assisted in themeasurements. GLERL Contribution # 650.6 REFERENCESBolsenga, S J. and H A Vanderploeg 1989. Estimating photosyntheticallyactive irradiance to open and ice-covered freshwater lakes: Methods andpreliminary results, submitted for publication.Bolsenga, S.J., J.E Gannon, G. Kennedy, D C. Norton, and C E.Herdendorf. 1989. ROV Dives Under Great Lakes Ice. Cold Regions Scienceand Technology. 16-89-93.Bolsenga, S. J , H.A Vanderploeg, M.A. Quigley, and G L. Fahnenstiel1988 An under ice ecology pilot program, operations and preliminaryscientific results Journal of Great Lakes Research g:372-76

Bolsenga, S J 1981 Radiation transmittance through lake ice in the 400-700 nm range J Glaciol. 27-57-66Bolsenga, S J. 1978 Photosynthetically active radiation transmissionthrough ice NOAA Technical Memorandum ERL GLERL-18, Boulder, ColoGilbert, G.D and R.R Buntzen. 1986 In-situ measurements of the opticalproperties of arctic sea ice SPIE Vol 637, Ocean Optics VIII 252-263Grenfell, T C and G.A Maykut 1977. The optical properties of ice andsnow in the Arctic basin Journal of Glacioloig 445-463Grenfell, T.C and D K. Perovich. 1986 Optical properties of ice and snowin the polar oceans. 11: Theoretical calculations SPIE Vol 637, OceanOptics VIII 242-251.Maguire, R.J 1975a Effects of ice and snow cover on transmission oflight in lakes. Inland Waters Directorate, Canada Centre for InlandWaters, Tech. Bull. No. 54 6Maguire, R.J 1975b Light transmission through snow and ice InlandWaters Directorate, Canada Centre for Inland Waters, Tech. Bull.No. 91:4.Maykut, G A. and T C. Grenfell. 1975 The spectral distribution of lightbeneath first-year sea ice in the Arctic Ocean. Limology andOceanography z:554-563.Palmisano, A C., J.B. SooHoo, R.L. Moe, and C.W Sullivan. 1987. Sea icemicrobial communities. VII. Changes in under-ice spectral irradianceduring the development of Antarctic sea ice microalgal communities.Mar.Eco1. Prog. Ser. %:165-173Perovich, D K , G.A. Maykut, and T.C. Grenfell. 1986. Optical properties ofice and snow in the polar oceans. I' Observations. SPIE Vol. 637, OceanOptics VIII:232-241.Roulet, N T. and W.P. Adams 1984 Illustration of the spatial variability oflight entering a lake using an empirical model Hydrobiologia,Vol. 67, No. 74, pp 67-74.SooHoo, J.B., A.C. Palmisano, S.T. Kottmeier, M P Lizotte, S.L SooHoo, andC.W. Sullivan 1987. Spectral light absorption and quantum yield ofphotosynthesis in sea ice microalgae and a bloom of Phaeocystispouchetiifrom McMurdo Sound, Antarctica. Mar. Ecol. Prog. Ser. %:175-189.Stewart, K.M. and B.E. Brockett. 1984. Transmission of light through ice andsnow of Adirondack lakes, New York. Verh. Internat. Verein. Limol., Vol.22, pp. 72-76.

FRACTURE TOUGHNESS OF S2 COLUMNARFRESHWATER ICE: CRACK LENGTH ANDSPECIMEN SIZE EFFECTS - PART I1J.P. DempseyAssociate ProfessorY. Wei and S. DeFrancoResearch AssistantsR. Ruben and R. FrachettiNSF Undergraduate TraineesDepartment of Civil andEnvironmental EngineeringClarkson UniversityPotsdam, NY 13676U.S.A.ABSTRACT. .Wedge loaded compact tension (WLCT) specimens were tested to investigate the influenceof both crack length and specimen size versus grain size on the fracture toughnessof S2 columnar freshwater ice. For one grain size and one specific crack orientation, thecrack length was varied as a function of the grain size, ranging over a major portion ofthe length of the specimen. The crack length effects on the critical-energy-release-rate(GI=) were studied in this way for three specimen sizes. Two parallel research efforts havealready been completed using S2 ice but different loading configurations (Bentley et al.,1988; Dempsey et al., 1989). These previous studies and this study allow preliminaryobservations to be made concerning the influence of specimen size and the comparativemerits of the energy approach. The overall objective is to obtain a criterion for theminimum dimension in terms of grain size in order for small scale yielding conditions toapply.1 INTRODUCTIONIn this study, reproducible values for critical toughness corresponding to the initiationof a stationary macrocrack are sought. In this context it is assumed that prior to loadingno previous crack growth has occurred. Following crack initiation, the crack motion orpropagation must be essentially planar. Assuming that the crack-microstructure orientationis kept fixed, and that the geometrical dimensions of the test specimen are "largeenough n with respect to the rnicrostructure (so that the assumptions of continuum mechanicsare valid), then the value of K, (the stress intensity factor) or G\ (the energyrelease rate) at which a stationary macrocrack extends in a given material should beindependent of the size and shape of the test specimen and the method of loading. Thevalue obtained for the fracture toughness could then be regarded as a material property.An approach that is directly meaningful for anisotropic materials is one in which the

Figure 1: The Wedge Loaded Compact Tension Geometry.critical state at the initiation of unstable crack growth is identified in terms of a criticalenergy-release-rate(GI=). If the compliance C of the wedge loaded compact tension(WLCT) specimen used in the fracture toughness tests reported in this paper (Figure1) is identified through V = CP, where V is the load-line crack-opening-displacement(COD) between the pins, and C is the slope reciprocal of the load-deflection curve ata particular value of the crack length (the specimen compliance), then it is well knownthat the energy release rate is given by,where P, b a, and h are defined in Figure 1. The fracture toughness testing ~rocedurethen resolves itself into determining the compliance of the specimen as a function of cracklength and measuring the gradient of the resultant curve at the appropriate initial cracklength.Two parallel research efforts recently completed are relevant to the present study. Bentleyet al. (1988) tested very large floating WLCT specimens cut out of S2 ice sheets grownin the ice basin at the U.S. Army Cold Regions Research and Engineering Laboratory(USACRREL), Hanover, N.H. The crack lengths to grain size ratio (a/dau) were ex-tremely large in these tests (note that again only one grain size was involved). Dernpseyet al. (1989) - Part I tested the same ice harvested from the basin at USACRREL usingsingle-edge-notched bend (SENB) specimens; either the four-point-bend (4 pt) orthree-point-bend (3 pt) loading configurations were used. In Part I, for one grain size,a distinct size effect and crack length effect were found. The crack orientation in boththese studies and in the present investigation was such that the plane of the crack was200

perpendicular to the plane of the ice sheet (see Figure 1).S2 type ice is one of the two major types of congelation ice formed during quiet (nonturbulent)freezing of lake water (Gow, 1986). S2 ice sheets are composed predominantlyof vertically-elongated, columnar crystals exhibiting mainly horizontally oriented c-axes(Michel and Ramseier, 1971). The present fracture toughness investigation and associatedstudies (see Part I) should serve to elucidate the influence of the microstructural features(the size and shape of the crystals) and the textural characteristics (the c-axis orientationdistribution) on the mechanical properties. The textural characteristics of the S2 icetested here closely resembles those portrayed by Bentley et al. (1988).2 EXPERIMENTAL PROCEDUREIn this investigation, the effects of crack length versus grain size and of the specimenlength versus grain size were again studied, using a distinctly different specimen geometry.Moreover, instead of pursuing values for the apparent fracture toughness KQ (Denipseyet al., 1988), values for the critical energy release rate G\c were sought. Wedge loadedcompact tension (WLCT) specimens were used (see Figure 1). The specimen sizes andassociated test type are briefly summarized in Table 1. Note that the specimen size wasvaried only in terms of the width w and the length b (see Figure 1); the thickness h(length of the crack front) was not varied. The average grain size (dew) of the S2 icetested was 2.2mm, the test temperature was fixed at -1O0C, and a crosshead velocit,y of7.62 mm/min was used for all the ice tests, giving an average times to failure (t,) of 1.3,2.4, and 1.8 s for Sizes 11, 111, and IV, respectively.The seeded, columnar ice was grown at Clarkson using tap water and a tank measuring1.2 x 1.2 x 1.0m. The microstructural information gathered was very similar tothat presented by Bentley et al. (1988), viz., vertical, columnar features; c-axes of thecolumnar grains uniformly sized with random horizontal or near horizont,al orientation.The average grain diameter of the columnar grains was 1.6 15 0.1rnm at the top and 2.9 0.2mm at the bottom, showing a slight increase in grain size in the growth direction.The meltwater conductivity was 2.40 * 0.13 x lO^i2-'~m-~ at -lO°C indicating a lowlevel of dissolved impurities in the specimens. The low porosity of the ice is indicated byan average density of 0.910 zt 0.003 g/ml.1 b = 2w = 4s = 8d = lOe: See Fieiire " 1No. of CrackLengthsSizeII1IllIVb(mm)51102153204b/dW23466992666Tests per CrackLengthTable 1: WLCT Tests (h = 63mm; 2a = 30')

Details concerning the harvesting of the ice, machining of the specimens, the methodused to fabricate a sharp crack, typical preparation, testing and observation time intervals,and method of data acquisition are to be found in Part I.The crack-mouth-opening-displacement (CMOD) was measured in all of the tests usingan MTS clip gage (MTS 632.03B-30). Measuring the CMOD rather than the line-loadcrack-opening-displacement (V) complicates the energy analysis presented in the nextsection; however, this is a difficulty that has been faced by many researchers to date(Vcerman and Muller, 1972; Saxena and Hudak, 1978).Size I (Table 1) could not be machined as desired; the ice repeatedly cracked whilethe pin holes were being drilled. The end face of each WLCT specimen (see Figure 1)rebled on a granite slab which was lubricated with a low temperature teflon spray toapproximate smooth, frictionless end conditions. The pins were loaded by a wedge (seeFigure 1) of included angle 30° this method of loading creates compression (Q = Pm/2)parallel to the crack. This compression promotes straight crack growth. The slidingcoefficient of friction given by p = tan (k between the wedge and pins (hard steel on hardsteel) was determined by completing a set of calibration tests on a brittle polymer, PMMA(poly rnethylmethacrylate), using both the WLCT and the four-poilit-bend geometry.3 ENERGY ANALYSIS AND CALIBRATIONThe energy release rate expression in (1) is based on the load-line COD compliancebetween the pins ((7); in the tests reported in this paper, however, the COD is measuredl>v a clip gage at tlie crack moutli (the CMOD). Moreover, P in (1) refers specificallyto the opening load. Experimentally, the CMOD compliance (Cg) is determined IromV, = PmCg, where V, is the CMOD measured by the clip gages, and Pm is the load onthe wedge. Noting also that the load line COD is given by V = PC, it is possible torelate V to Vg by assuming that tlie rotation axis is at a position r(bÑa below the cracktip (Veerman and Muller, 1972),where z is the distance of the clip-on gage from the specimen surface. A value of r equalto zero is used in the present-analysis. For an isotropic material and small crack lengths,a non-zero value of r is more correct (Saxena and Hudak, 1978). However, the erroris not great in taking r equal to zero, assuming elastic deformations. It readily followsthat C = (Pm/P) fC,. Since Cg is experimentally determined, it remains to relate theopening load P to the machine load Pm on the wedge, considered to have an includedangle of 2a. If the coefficient of friction between the pins and wedge is denoted by p= tan (k, the required relation is given by P = Pm/2 tan(a + 6). Finally, the modifiedenergy release rate expression is given by

Figure 2: Critical-Energy-Release-Rate vs Crack Length for PMMA.The angle of friction in Eq. (3) is unknown and is not reliably determined by lookingup a handbook. For this reason two series of calibration tests using both the 4pt bendfracture configuration and the WLCT geometry were completed. Five 4pt bend testsusing PMMA established ICIc = 1626 Â 111 kPa6 and E6, = 3.93 !z 0.09 GPa forthis material; EL is the effective elastic modulus determined from the load-CMODcurve (a description of the associated analysis is provided in Part I, Dempsey et al.,1989). From these tests it is reasonable to assume that the associated PMMA criticalenergy-release-rateGIc = I

4 Gk FOR S2 ICEThe load-CMOD (P,,, vs V,) plots for the S2 ice WLCT fracture tests revealed adiverse and complicated range of behavior. For crack lengths ranging up to half thespecimen length, there was evidence of "pop-in" fractures. In these cases, the loaddisplacementcurve showed a sudden extension for either constant or often decreasingload. In some tests, the crack initiation or extension occurred relatively stably, and theassociated P,,, vs V, curve evidenced a different slowly rising constant slope. This stableextension then typically arrested, followed by a second or third stage of loading withoutcrack growth. For fabricated crack lengths greater than half the specimen length, theload-displacement plots were very irregular. The procedure adopted in this paper wasto identify the maximum machine load PM associated with macroscopic unstable crackinitiation; the GI value for PM is denoted here by GIc.The compliance expressions for sizes II-IV obtained from the above Pm vs V, plots weregiven by, respectively,The expression in (3), along with (5), = 9' and Pm = PM gave the critical-energyrelease-ratevalues for S2 ice. The Gic values thus determined for the S2 ice tested areshown in Figure 3 for Sizes II-IV. Certain P,,, vs V, plots were judged to be too irregular;they are indicated by solid data points in Figure 3; these points were therefore excludedfrom consideration when the average values were computed.For very short or very long cracks, there is a trend in Figure 3 for the Glc values tobe low, while for intermediate crack lengths, a plateau for each size (albeit with a fairamount of scatter) is observed. As the crack (or uncracked ligament) length to grainsize ratio decreases (a/dav or (b- a)/dav), the fracture energy decreases, with the lowerlimit being either the energy for fracture along an easy cleavage plane of a single grain(GSc = 27,; = 0.218 J/m 2 ), or along a grain boundary (G,t = 27,~ = 0.130 J/m2), where7~~ and 7,b are specific free surface energies provided by Ketcham and Hobbs (1969). Theplateau values (dc = 2ypc) are clearly indicated on Figure 3, which presents all of thefracture energy information vs a/&,. Clearly, the fracture energy controlling strengthdepends both on the aidan ratio, as well as the specimen size (the b/dm ratio).5 DISCUSSIONFor an average grain size of 2.2mm, a test temperature of -lO°C the wedge-loacledcompact-tension(WLCT) geometry is used in this paper to examine the effects of specimensize and crack length on the critical-energy-release-rate GIc. These GIc values correspondto the initiation of an initially stationary crack formed by freezing a razor bladein a notch cut by a bandsaw (see Part I, Dempsey et al., 1989). Each fracture event was20 4

Size I11Figure 3: Fracture Energy vs Crack LengthJGrain Size for Sizes 11, 111, and IVunstable, with rapid crack propagation following carck growth initiation. Only one crackorientation vs the microstructure was studied, and the ice tliickness was approximately63mm.The energy analysis presented in this paper, including the determination of the criticalenergy-release-rate(GI=), involves no assumption of isotropy. Any assumption of isof I opyfor the S2 ice being tested in this paper is not valid. In Part 1, Dcmpsey et al. (D89)reviewed the literature to date on the fracture toughness testing of S2 ice. This reviewindicated that the ice fracture mechanics community has placed a somewhat burdensome20 5

eliance on measuring the critical stress-intensity-factor (A\=). Because associated sizeeffect and specimen geometry effect studies were non-existent, and because of the useof K-expressions appropriate only for isotropic materials, Dempsey et al. (1988) choseto identify the critical stress-intensity-factor information to date by the symbol KQ,implying an apparent or conditional fracture toughness.A feature of the compliance analysis presented was the need to monitor the load vsload-line COD (P vs V). This information, in turn, gave a direct indication of fractureinitiation events that could not be interpreted in terms of linear elastic fracture mechanics(LEFM), namely because certain P vs V linearity requirements were not met.Part I included a discussion of relevant specimen size criteria. There is little reason torepeat that discussion here, since the thrust of this paper (Part 11) has been to employthe more fundamental energy approach to deduce the critical-energy-release-rate Gic.Clearly, there is a need to account for the particular crack orientation vs microstructuralanisotropy if valid Iclc results are to be obtained. The latter task is equally important,since K-expressions can be superposed.Several difficulties were encountered in this study which require further investigation.First, the Gic calibration for the PMMA exhibited more crack length/specimen lengthdependence than expected. Second, the determination of the load-line COD versus theclip-gage COD (V vs V,}, which is critical to the energy approach, was not acconlplishedwith total confidence using the chosen geometry. These two difficulties require furtherexperimentation, and more reasoning concerning suitable compliance expressions6 CONCLUSIONSThe main conclusion from this study is that there is a clear crack length and specimensize effect. The information presented in this paper, it must be remembered, is specific toone ice thickness (63mm), one grain size, one crack front orientation in S2 ice, a particulartest temperature and loading rate, and a specific test geometry. However, in terms ofKQ, and for the 4pt and 3pt loading configurations, a distinct crack length and specimensize effect was found in Part I, Dempsey et al. (1989). The only differences betweenPart I1 and Part I are the ice thickness (63mm here vs 45mm) the specimen geometry(WLCT vs 4pt,3pt), and the average grain size (2.2mm vs 3mm).The scatter in the fracture toughness testing literature for S2 ice (reviewed in Pait I),based on the above conclusion, is evidently partially caused by crack length and specimensize effects. The influence of different specimen geometries has yet to be shown. The highdegree of scatter is understandable, since the data presented in Parts I and I1 suggestthat the specimen sizes tested to date (excluding the work by Bentley et al., 1988) havebeen sub-size. This possibility is in all likelihood applicable in differing degrees to allother ice types, be they equiaxed-granular, (doped) model ices, or sea ice.

7 ACKNOWLEDGEMENTThis work has been supported in part by the U.S. National Science Foundation underGrant No. MSM-86-18798 and in part by the U.S. Army under Contract No. DACA89-88-K-0013.8 REFERENCESBentley, D.L., Dempsey, J.P., Sodhi, D.S., and Wei, Y., 1988. Fracture of S2 colun~narfreshwater ice: floating double cantilever beam tests, Proceedings of the 9th InternationalIAIIR Symposium on Ice, Sapporo, Japan, Vol. 1, pp. 152-161.Dempsey, J.P. Nigam, D., and Cole, D.M., 1988. The flexure and fracture of macrocrystallineSl type freshwater ice. Proceedings of the 7th International OMAE Conference,Houston, Vol. IV, pp. 39-46.Dempsey, J P., Y. Wei, S. DeFranco, R. Ruben and R. Frachetti, 1989. Fracture toughnessof S2 columnar freshwater ice: crack length and specimen size effects - Part I.Proceedings of the Sth International OWE Conference, The Hague, The Netherlands,Vol. IV, pp. 83-89.Gow, A.J., 1986. Orientation textures in ice sheets of quietly frozen lakes. Journal ofCrystal Growth, Vol. 74, pp. 247-258.Ketcham, W.M. and Hobbs, P.V., 1969. An experimental determination of the surfaceenergies of ice Philosophical Magazine, Vol. 19, pp. 1161-1173.Michel, B. and Ramseier, R.O., 1971. Classification of river and lake ice. CanadianGeotechnical Journal, Vol. 8, pp. 36-45.Saxena, A. and Hudak, S.J., 1978. Review and extension of compliance informationfor common crack growth specimens. International Journal of Fracture, Vol. 14, pp.453-468.Veerman, C.C. and T. Muller, 1972. The location of the apparent rotation axis in notchedbend testing. Engineering Fracture Mechanics, Vol. 4, pp. 25-32.

ELASTIC PROPERTIES OF FRAZIL ICE FROM THEWEDDELL SEA. ANTARCTICAManfred A. LangeStaff ScientistHarald ~ellmann'Staff ScientistJacqueline A. Richter-MengeResearch EngineerStephen F. AckleyChief, Snow and Ice BranchAlfred-Wegener-Institute forPolar and Marine ResearchD2850 Bremerhaven, FRGUS-Army Cold Regions Researchand Engineering LaboratoryLyme RoadHanover, NH 03755, USA1) now at: DFVLR, Raumsimulation, Postfach 906058,5000 Kdn, FRGABSTRACTWe present data on the elastic properties of Antarctic sea ice from the Weddell Sea area. The datahave been obtained through measurements of compressional- and shear-wave velocities on frazil ice atultrasonic frequencies (1 MHz). Sample (total) porosities range from 2 to 9% and salinities from 2.3 to7.1 ppt. The measured compressional- and shear-wave velocities lie at 3.6 to 3.8km/s and at 1.4 to1.9km/s, respectively. The shear-wave velocities of the present samples lie significantly below thoseobtained under similar experimental conditions for Arctic frazil ice. The resulting elastic constants rangebetween 5 to 9GPa, 7.5 to lOGPa, 1.5 to 3.2GPa and 0.32 to 0.42 for Young's modulus, bulk modulus,shear modulus and Poisson ratio, respectively Initial tangent moduli, obtained in compression tests onthe same samples, are in good agreement with or slightly above the dynamic Young's moduli.1. INTRODUCTIONWhile the mechanical properties of Arctic sea ice have been studied in some detail (e.g., Mellor,1986), there is relatively little information on sea ice from the Antarctic. This is mainly due to the currentlack of commercial activities in Antarctica. As well, there is only limited perennial sea ice present thatcould be readily probed in the summer and sampling of sea ice during austral winter has been scarce.However, operations of ice-going (research) vessels require some basic knowledge of mechanicalproperties of Antarctic sea ice. In light of the significant differences of Arctic versus Antarctic sea ice(e g., Lewis and Weeks, 1971), simple extrapolation of Arctic results to Antarctic conditions seemsinadequate. Finally, currently available data have been obtained primarily for sea ice of columnartexture. Thus, there is a need for elastic/mechanical data for Antarctic sea ice in general and for frazilice of granular texture in particular (Cox and Weeks, 1988).

During the Winter-Weddell-Sea-Project 1986 (=WWSP '86) on RV "Polarstern", we obtained a sufficientnumber of sea ice cores to carry out an investigation into the mechanical properties of Antarcticsea ice from the eastern and south-eastern Weddell Sea. In this pilot project, we measured compressional-and shear-wave velocities (P- and S-wave velocities) at a frequency of 1 MHz as well as the densityand salinity on samples of about 0.1m in diameter and 0.25m length (approx. 4" and lo", resp.).Thesame samples were subsequently used in compression tests under a variety of temperature- and strainrateconditions (the latter are reported in a companion paper by Richter-Menge et al., this volume) Thispresents us with the rare opportunity to compare elastic properties of sea ice as obtained under static(in compression tests) and dynamic conditions (through ultrasonic wave velocities). In order to avoidanisotropy effects and to gain data on ice other than columnar, we limited our sample material to ice ofgranular texture (frazil ice).Measurements of P- and S-wave velocities in conjunction with density determinations allow thecomputation of elastic constants. Aside from presenting these results for the first time, other aims of thisstudy are:(i) to compare the present data with results for Arctic sea ice, which were obtained under similar experimentalconditions and(ii) to relate elastic constants obtained in compression tests to the dynamic moduli of the samesamples.2. EXPERIMENTAL TECHNIQUES; METHODSThe sample materiial was obtained in the eastern and south-eastern part of the Weddell Sea (forsample locations, see Lange et al., 1989). Of the two 4-cores taken at each station, one was analyzedfor texture and other properties on board 'Polarstern' (cf. Lange et al., 1989) and one was archived.Based on the stratigraphy of the first core, sections of granular ice at least 0.25m length were selectedfrom archive cores of identical stations. After visual inspection on a light table, the final samples werecut and horizontal thin sections at top and bottom surfaces were fabricated for detailed texturalanalysis.Commercially available ultrasonic transducers (Krautkramer) of 1 MHz nominal frequency were directlyfrozen to the top and bottom surface of each core sample in a specially designed apparatus(details of this and other components of our experimental set up can be found in Hellmann, unpublished).Thus, we measured ultrasonic velocities parallel to the growth direction of the ice Square signalsof about 2 psec width were generated by a pulse generator and were fed through the transmitterinto the sample. The signals were received by the opposite transducer and transmitted through an oscilloscopeto a digital signal recorder (SMR-2; Scientific Instruments); the latter also triggered the pulsegenerator. On the digital signal recorder, travel times of P- and S-waves were recorded at an accuracyof < 0.1 psec. Sample lengths were measured to about 1/10 rnm after the transducers were frozen tothe sample, directly between top and bottom surfaces. This results in an overall error of < 1% in themeasured P- and S-wave velocities The measurements were performed in a cold laboratory at -12'~

(in a few cases, because of high attenuation in the samples, measurements were done at -28'~; seebelow), after the samples had sufficient time to equilibrate (at least one day).Densities were obtained by weighing accurately lathed and milled samples (prior to the compressiontests) and determining their volume After the compression tests, vertical thin sections were preparedfor those samples that had remained mechanically intact and bulk salinities were measured fromthe molten samples.Salinities and densities were then used to calculate total porosity, as well as brine and air porositiyfollowing Cox and Weeks (1983).The elastic constants (Young's modulus E, bulk modulus K, shear modulus G and Poisson ration)were computed from the densities? and the compressional- (=VJ- and shear-wave velocities (=Vs):3. RESULTS AND DISCUSSIONSFigures la and 1 b give compressional- and shear-wave velocities plotted against total porosity (= P)for 23 of our samples. Of our 25 samples, two could not be measured at all because of strong signalattenuation and for 6, values could only be obtained, after the samples had been cooled down to -28'~.However, since the data of Hellmann (unpublished) demonstrate that there is only a 1.9% and a 3.8%increase in V and V respectively, when measured at -12'~ versus -28'~, we do not distinguish be-Ptween our measurements at these two temperatures.The large scatter in the data (Fig. 1) is probably caused by both experimental problems and effectsof sample inhomogeneities and/or sample anisotropy. The experimental problems arise because of theuse of very long samples (appr. 0.25m) and because of difficulties in the coupling between sample andtransducer This leads to seismograms that are usually difficult to interprete, i.e. the correct selection ofthe first arrival is not always possible These problems are more severe in the case of shear-wave mea-surements, where a good coupling between sample and transducer is essential for reasonable dataquality.The relatively large size also results in less homogeneous samples than desirable. This means thatthe effects of porosity on V and V are sometimes masked by other effects, which are caused by textu-Pral inhomogeneities of the samples (this is currently under investigation; Lange, in prep.). While we arewell aware that ultrasonic measurements should be performed on much smaller samples (Mellor, 1983),our approach of using identical samples for dynamic and static measurements left no other alternativethan the one chosen.

AFigure 1 Compressional- (a) and shear-wave velocities (b) obtained in ultrasonic measurements at1MHz at -12'~ plotted against (total) sample porosity. Also shown are regression fits for data ofHellmann (unpublished; here and in the following figures denoted by dashed lines) on Arctic frazilice. (c) gives V versus VsP

The presently observed shear-wave velocities are significantly smaller than those reported by Hell-mann (unpublished). Whether the generally higher brine volumes in our Antarctic versus Hellmann'sArctic samples (brine porosities lie at 3.29+01.3% versus 1.1830.6% for the present versus Hellmann'sdata, respectively) alone caused this discrepancy, is not certain. Domenico (1976) demonstrates thatthe water saturation of porous sand (approximately equivalent to the amount of brine porosity in oursamples) does not influence the value of V significantly. Thus, we have to attribute the lower values ofV relative to Hellmann's data to a combination of effects probably caused by higher bulk salinities(mean values lie at 2.5231.3 ppt versus 4.4131.3 ppt for Hellmann's and the present samples, respec-tively), experimental difficulties and the larger sample inhomogeneities in the present samples.With the exception of three data points (with V > 3.75km/s), our data show a weak relationshipPbetween compressional- and shear- wave velocities consisting of the expected increase in V withPincreasing VsFigure 2a gives Young's modulus E (computed after equation 1) as a function of P for our data. Thelarge scatter in E as seen in the figure results from the relatively large scatter in VAlso shown are theresults of Hellmann (unpublished) for Arctic frazil ice (dashed line) as well as of Tabata (1958; horizon-tally hatched box) and of Abele and Frankenstein (1967; vertically hatched box; both after Mellor, 1983).With regard to this graph, we note the following points:(i) About half of our data agree reasonably well with those of Hellmann, Tabata and Abele andFrankenstein;(ii) the other half of our data fall within the range of Young's moduli obtained for Arctic sea ice of un-specified temperature and porosity (5 603 1.93 GPa; values range between 1.7 and 9.1 GPa; ) asgiven in Weeks and Assur (1967).Figures 2b - 2d show the other elastic constants that can be derived from the V and V measure-Pments (equations 24). Aside from the data of Hellmann (unpublished), there is little data in the existingliterature to compare our results with. Again, Weeks and Assur (1967) give values for the shear modulusG and Poisson ration for Arctic sea ice of unspecified total porosity and temperature. G in this compila-tion varies between 0.6 and 3 GPa (2.052 0 73 GPa) and n between 0.25 and 0.38 (0.33 + 0 05). Bothmean values lie at the lower range of our results, while Hellmann's (unpublished) data for the shearmodulus lie above our values, the latter again probably indicating the influence of lower shear-wave ve-locities in the Antarctic samples -Hellmann's (unpublished) lower bulk moduli and Poisson ratios (Fig.2b and 2d; equ. 2 and 4) may be attributed to higher shear-wave velocities in his samples (Fig. 1 b).The Poisson ratiov is the only elastic constant in our (and Hellmann's data) that shows an increasewith increasing porosities (Fig. 2d). This is surprising at first sight, but as noted by, e.g. Mellor (1983), vcan be expressed in terms of E and K:Since an increase in brine volume (as a consequence of increasing porosity) will not significantlyaffect the value of K (Fig. 2b), the variation in v with porosity is primarily controlled by the correspond-

Figure 2

Figure 2: Elastic constants derived form the V -V data of Fig. 1 in relation to sample porosity AlsoP sshown are results of Hellmann (unpublished) and regression fits to his data, results of Tabata(1958; horizontally hatched box in 2a), of Abele and Frankenstein (1967, vertically hatched box inFig. 2a) and data compiled by Weeks and Assur (1967; shown are mean values as heavy dotsand standard deviations as thin lines at unspecified porosities in Fig 's 2a, 2c and 2d).

ing variation in Young's modulus. Thus, while E decreases with increasing P, v will increase withincreasing porosity.Figure 3a gives the initial tangent modulus Ei as a function of porosity as obtained in the compres-sion tests at -5 and -12OC and strain rates of 10'~ and 10'~ s"(see Richter-Menge et al., this volume).Also shown are two mean values and standard deviations of initial tangent moduli for tests on Arcticmulti-year columnar ice at the same strain rates (Cox et al., 1984). Ei is obtained as the initial gradient inthe stress-strain curve of a compression test and is regarded as an elastic modulus comparable toYoung's modulus (Mellor, 1983):The agreement between Cox et al.'s (1984) and our data is good (this applies also to the valuesgreater IOGPa, which were also encountered by Cox et al ).Figure 3b gives a comparison between Ei and Young's moduli for identical samples As can beseen, the values of both elastic moduli fall nearly into the same range. However, they are far from a di-rect, one-to-one correspondence between each other. The Ei data for the 10'~ s^data lie slightlyabove the corresponding Young's moduli. The initial tangent moduli show neither a clear temperalure-nor a strain rate effect However, because of the more brittle behavior of sea ice at high loading rates,the higher-strain-rate data appear to represent the true elastic component of the deformation in thecompression tests in a more consistent fashion.4. CONCLUSIONSWe present the first data on elastic constants for frazil ice of granular texture from the Weddell Sea,Antarctica. The constants are computed from measured compressional- and shear-wave velocities at-12'~. V and V show no particular trend with increasing (total) porosity. The absence of a wellPdefined relation between sonic velocities and porosity might be caused by the influences of samplegeometry and/or the inhomogeneous nature of our samples and consequently the resulting materialproperties that masked any (possibly) existing trend in the data. The present data partly agree withthose of Hellrnann (unpublished), which were obtained under similar conditions on Arctic frazil samplesThe major difference lies in significantly lower shear-wave velocities in the Antarctic versus the Arcticsamples. Whether or not this is related to higher mean salinities and higher brine porosities or to greatersample inhomogeneities in the present samples is not clear at present.As a consequence of lower shear-wave velocities, the computed elastic constants of the presentsamples show the expected behavior in comparison to those of Hellrnann (unpublished). The Young'smoduli partly agree, shear moduli are smaller, and bulk moduli and Poisson ratios are generally largerthan those of Arctic sea ice, respectively. Due to the poor dependence of V and V on porosity, therePis no clear trend of elastic constants versus porosity However, the data can be better explained by adecrease in elastic constants with increasing porosity than by increasing constants with increasingporosity, except for the Poisson ratio. The latter would better be explained by the reverse trend Weeksand Assur (1967) and Mellor (1983) hypothesized such a trend without presenting experimental evi-

~0,70 00 I 717 --m-:TrrT7 17-,-rr- 7 i ~0.0 40.0 80 U 120 0Porosity, o/oo- 7I00 L ,7T7 r r m - - - - 8 8 3 , r 8 I , ,-- - ~ - > - --8 74 00 5 00 b 00 7.00 U 00 !J 1)uYoung's mod., GPciFigure 3: Initial tangent moduli as obtained in compression tests under a variety of conditions (see textand Richter-Menge et al., this volume) plotted against sample porosity (a) and given in relation toYoung's moduli as measured on the same samples (b). Also shown are results (mean and stan-dard deviation) of tests on Arctic multi-year columnar sea ice of Cox et al (1984). Data obtainedat strain rates of 10'~ s" are given as closed circles and those at 10'~ s" as open circles.

dence. Comparison with other studies on Arctic (mostly columnar) sea ice shows that our values lieboth at the lower and the higher range of reported Young's moduli and are higher than other publishedshear moduli and Poisson ratios.The initial tangent modulus, obtained in compression tests under a variety of test conditions(Richter-Menge et al., this volume), decrease with increasing porosities. They agree well with data onArctic multi-year columnar sea ice (Cox et al., 1984). The agreement with the dynamic Young's moduli,obtained on the same samples is good Data at strain rates of lo4 s" however, are consistently higherthan the Young's moduli and are regarded as a better representation of the elastic constants than thoseobtained at lo^ s''.Acknowledgements: We would like to thank the crew of "Polarstern" for their assistance in obtainingthe sample material during WWSP '86. Thanks are also due to the technical personnel at the Alfred-Wegener-Institute (P. Mursch and U. Vogel) and at CRREL (N Perron). This is contribution no. 173 ofthe Alfred-Wegener-Institute for Polar and Marine Research.ReferencesAbele, C. and Frankenstein, G. (1967). Snow and ice properties as related to runways in Antarctica.CRREL Techn. Rep. 176.Cox, G F N. and Weeks, W F. (1983). Equations for determining the gas and brine volumes in sea icesamples, J. Glac. 29(102), 306-316.Cox, G.F.N. and Weeks, W.F. (1988). Profile properties of undeformed first-year sea ice, CRREL Rep.88-13.Domenico, S.N. (1976). Effect of brine-gas mixture on velocity in an unconsolidated sand reservoir,Geophysics, 41, 882-894.Lange, M.A., Ackley, S.F., Wadhams, P., Dieckmann, G S. and Eicken, H. (1989). Development of seaice in the Weddell Sea, Antarctica, Ann. Glac. 12,92-96.Lewis, L.E. and Weeks, W.F. (1971) Sea ice: Some polar contrasts, in Deakon, G. (ed.) Symposium onAntarctic Ice and Water Masses, SCAR, 23-34.Mellor, M. (1983). Mechanical behavior of sea ice, CRREL Mon. 83-1.Tabata, T (1958). Studies on the visco-elastic properties of sea ice, in: Arctic Sea Ice, U.S. Nat. Acad.of Sciences, Nat. Res. Counc., Publ no. 598. 139-147.Weeks, W.F. and Assur, A (1967). The mechanical properties of sea ice, CRREL Mon. II-C3.

TEMPERATURE, SALINITY, AND DENSITY PROFILESIN A FAST ICE SHEET IN LIAO DONG BAYLi Zhijun (M. Sc.)Institute of Marine EnvironmentalProtection, SOASui Jixue (M. Sc.) P.O. Box 303, DalianYan Decheng (Engineer)CHINAMeng Guanglin (Engineer)ABSTRACTSome vertical profiles of ice basic physical parameters inwhole ice thickness were carried out in a fast ice sheet insidea harbour in Liao Dong Bay over the winter 1986-1987. Thisreport presents the observation methods, results as well asthe vertical profiles of ice and water temperatures, icesalinity, ice density and grain size. More detail descriptionsconcentrate on the changes of ice temperature and thicknesswith following factors: daily air temperature,water temperatureunder the ice, snow cover, and episodes of relative "cold u or"warmw periods over the winter.1. INTRODUCTIONThe potential oil and gas resouces under the sea bottom hasmade sea ice engineering properties one of the importantsubjects in Liao Dong Bay. The overall ice force and local icepressure on marine structures depend mainly on three factors:ice physical properties; ice mechanical properties; and thestiffness and shape of the structures. Because thermal dynamicconditions change frequently in nature, changes in the icephysical properties occur. Therefore, it is important that weknow the physical properties under natural conditions forstuding ice engineering (Kivisild, H.R. 1975). Many observationsabout the properties of sea ice have been made abroad(Weeks, W.F. and Gow, A.J. 1978; Richter-Menge, J.A. and

Cox, G.F.N. 1985; Tucker HI, W.B. etc 1985). But there are somedifferences between these findings and the ice in Liao DongBay. For example, the salinity, density and thickness aredifferent. A study of the properties of the fast ice sheetinside a harbour ( water depth was about 7 m and salinity wasabout 29-30 '% ) in Liao Dong Bay has been completed. Theresults are essential data for further research of ice mechanicsand ice forces on marine structures in this area.2. METHODS OF OBSERVATIONThe ice sheet was 22 cm in thickness before Jan. 9, 1987 andreached 43 cm in the middle the month. Two sections and fivevertical profiles were obtained at five sites. Fig. la and lb.There were 12 temperature probes in each vertical profile atdepths of 3, 8, 13, 18, 23, 28, 33, 38, 43, 53, 78 and 103 cmbelow the ice surface.The vertical temperature profiles were made in-situ. Otherprofiles of ice salinity, density and grain size were measuredfrom one vertical cut column which was sawed into five centi-meters thick pieces in the vertical for these measurements.The temperature probe was made from a copper-cupron thermo-couple. The advantages of this system are fast response andsmall volume. Its useful measurement range covers the icetemperature interval -20 to 0 OC,and the resolution is 0.1 OC.Only one reference point, the melting temperature of freshwater ice, is needed. The thermometer reading at this point isbasinFig.1-a Location of fiveSampling Sites219Fig.1-b Location of 12Temp. Probes

Each piece from a vertical cut column was placed into asealed plastic bottle, melted and allowed to warm to roomtemperature. The salinity values were obtained from conducti-vity measurements of the water by a WUS salinometer.Ice density was simply made by using V.V.Shuleykin methodwhich based on the differences between the volumes of freshwater and kerosene when a ice piece sank in them (V.V.Shuleykin1953).Grain size analysis of the ice column was much more involved.The column was stored in a white box and moved into cold roomas soon as possible. Then a 0.5-1.0 cm thick section was cutfrom the column alone; the vertical and horizontal directionswith a handsaw. One of two faces of thin section was smoothedand frozen on a glass slide and thinned to about 0.2-0.5 mm.Atthis thickness, the section was viewed between crossed polar-oids and photographed. From this work,grain sizes were measured3. OBSERVATIONS3.1 Daily changes of vertical temperature profilesIn a vertical temperature profile, the ice temperature nearthe surface was controlled by the air temperature over the iceand the ice temperature in the lower part of the ice was con-trolled by the sea water temperature at the ice-water interface.The water temperature was constant at -1.5*0.1 OC. Due tofrequent variations in the air temperature, the fluctuations ofice temperature were very complex in the upper part (0-30 cm)of the ice, whereas the temperature in the lower part(30-45 cm)approached a liner distribution. Ice temperature data arepresented in Figures 2 through 6. At Sites Tand TI the snowwas removed from the ice surface. The change in temperature ofthe ice mainly depended on the fluctuation of the air tempera-ture. The snow cover influenced the ice temperature as well asduring ice growth and decay. From Fig. 2 and 4, the airpenetration depth was 30 cm. Below this depth, the ice tempera-ture was constant.3.2 Profiles of salinity, density and grain sizeTn a fast ice sheet the salinity profile usually has a highsalinity in the upper and lower portions which gives it a "CfI

Ice Temp. (OC)-8 -6 -4 -2 0(5) 23:30Ice-WaterSurfaceFig.2 Change Process ofTemp. Profile atSite I on Jan.18(1) 6:50(2) 10:oo(3) 14:30Ice-WaterSurfaceFig.3 ChangetoProcess ofTemp. Profile atSite IV on Jan.18Date and TimeJan. 19Remarks-2- 4-6-2 Affected from13 -4 - air temp.2 8 1 s - .-- ---^ -2- = - - - -. .-58 -2. - - = - -- -.Affected from43 -2 -253 -2-- = --Const. temp.78 -2. - z - :- . of water*103 -2- - = 'Fig.4 Temp. Curves at Different Depth at Site I on Jan.18221

I Jan.8 I Jan.9 I Jan.101 Jan.ll 1 Jan.12 lJan.13 lJan.142 14 2 14 2 14 2 14 2 14 2 14 2 144-20-Ice Temperature (OC)-10 -6 - 20 -10 -6 - 20 -10 -6 - 2 01 :OO. 22:30Ice-WaterIce-WaterJan. 1 1 Jan. 12 Jan. 13Fig.5 Change Processes of A i r Temperature, and Ice VerticalTemperature Profiles, Thickness in a "Cold" EpisodeT-l4IIce Temperature (OC)Fig.6 Change Processes of Air Temperature, and Ice VerticalTemperature Profiles in a "Warmw Episode

shape. The ice salinity depends on the salinity of the seawater and the ice growth rate. When the new ice was formed,its growth was fast, so grain size and brine packages weresmaller. The upper layer contained granular ice with a smallgrain size and high salinity. After the ice cover formed, thegrowth rate decreased resulting in less brine entrapment, moregravity drainage and a lower ice salinity. Through geometricselection the ice structure changed from granular to columnar.Because of the slower growth rate, grains were larger. Thesalinity was hifner in the bottom of ice sheet due to itsproximity to the sea water and the pressence of a porousskeletal layer. On Jan.9 it became colder. The growth ratesuddenly increased and a layer of granular ice with highersalinity was formed again. Therefore, the salinity profile wascomposed of a number of "C-shapest1 in vertical. The grain sizewould corresponding change.Ice density varied over a small range and the mean densitywas about 0.9 R/cm3. The vertical profiles of salinity ,densityand grain size are presented in Fig.7.Density ( g/cm3)Salinity (%)Fig.7 Vertical Profiles of Salinity,Density and Grain Size

4. CONCLUSIONS1. The temperature profile can be divided into two parts. Inthe upper part, the ice temperature was controlled by the airtemperature and had very obvious and complex fluctuations. Inthe lower part, it was controlled by the water temperature andwas charisterized by zero fluctuation.2. The snow cover insulated the ice and affected the icetemperature, growth, and decay.3. The growth history of the fast ice sheet can be dividedinto two stages which were confirmed by thickness measurements,and profiles of salinity and grain size.5. ACKNOWLEDGEMENTThanks are extended to Prof. Wu Ziwang for his support inobservation equipments and Mr. Zhang Mingyuan, Ms. Wang Jinbo,Mr. Gao Shugang and Mr. Yu Yonghai for their assistance in theinvestigation.6. REFERENCESKivisild, H.R. (1975). Ice mechanics, Proceedings of POAC 75,Proc., 1 , 287-314.Richter-Menge, J.A. and Cox, G.F.N. (1985). Structure,salinityand density of multi-year sea ice pressure ridges,Proceedingsof 4th OMAE, 194-198.Shuleykin, V.V. (1953). Marine physics. (in Chinese, 1963,464 PP. 1.Tucker in, W.B. etc (1985). Physical properties of sea ice inthe Greenland Sea,Proceedings of PCAC 85, Proc,, 1 , 177-188.Weeks, W.F. and Gow, A.J. (1978). Preferred crystal orienta-tions in the fast ice along the margins of the Arctic Ocean,Journal of Geophysical Research,Vol. 1 , 83.C10, 5105-51 21.

CREEP BEHAVIOUR OF DAMAGED ICE UNDER UNIAXIALCOMPRESSION: A PRELIMINARY STUDYJ. M~YSSOM~~~P. DuvalLabratoire de Glaciologie etGeophysique de 1'Enviromement(C.N.R.S.), B.P.9638402 St.Martin-d'H&res Cedex FRANCEABSTRACTPolycrystalline initially isotropic equiaxed ice samples weresubmitted to constant strain-rate uniaxial compression tests until acertain amount of damage was reached. Then these samples underwentcreep tests under constant uniaxial compressive stress, at levelsselected so that further increase in microcrack density wasnegligible. The results obtained give an order of magnitude for theeffect of distributed microcracks on the creep rate of ice, and arediscussed using the concepts of Continuum Damage Mechanics.1. INTRODUCTIONAt very low strain-rates (Z i s'l ) ice is generally modelled asa visco-elastic material (Ashby and Duval, 1985). Strain decompositioninto a pure elastic component ee and a time dependent strain is assumed.The later is generally split in two parts: a recoverable strain edcommonly termed "delayed elastic strain", and a permanent strain ec,which will be referred to as the "creep strain" in the following.At higher strain-rates the visco-elastic deformation is often accompaniedby cracking. The transition between brittle (sudden failure)and ductile (continuous microcracking) behaviour depends on stress-state (tensile/mpressive), strain-rate level, temperature and grainsize (Gold, 1972; Cole, 1985). In many situations of practicalinterest, such as ice-structure interaction, ice undergoes more orless rapid compressive loading. Constant strain-rate compression testsshow that brittle fracture may occur by axial splitting (quasiinstantaneous macroscopic fracture) or shear faulting after a certain

amount of internal microcracking is reached. In the same testingconditions, ductile behaviour, characterized by the softening branchof the stress-strain curve, is associated with the development of anarray of uniformly distributed microcracks. These cracks havedimensions of the order of the grain size, with preferentialorientation along the compression axis. They do not propagate butincrease in number during the tests (Gold, 1972 ; Hallam et al.,1987), and the ratio "number of intergranular / number ofintragranular" cracks increases with strain-rate (Gold, 1972; Cole,1988; Kalifa et al., 1989).Continuum Damage Mechanics provides a suitable framework for thedevelopment of constitutive models describing the progressivedegradation of the properties of ice undergoing such homogeneouslydistributed microcracking. It has been only recently introduced in thefield of Ice Mechanics (Karr, 1985; Sunder, 1986; Sjolind, 1987; Choiand Karr, 1989; McKenna et al., 1989; Pulkkinen, 1989; Santaoja,1989). The essential features of a damage model are: a) definition ofdamage as an internal state variable; b) description of the mechanicalbehaviour of ice for a given state of damage; c) description of damageevolution (damage growth) versus state variables or associated forces.The knowledge of how damage affects the creep properties of ice isobviously essential at stage (b). If damage growth is to be related tosome nucleation criterion, either stress based (Hallam, 1987) orstrain based (Sinha, 1984) a correct estimate of the elastic strain isneeded, and thus an experimental checking of a damage growth modelnecessitates solving stage (b).The present study is an attempt to quantify the influence of damageon the creep properties of ice by means of conventional creep testsperformed under uniaxial constant compression on already damaged icesamples.2. EXPERIMENTAL PROCEDURE2.1 Preparation of the samplesPolycrystalline ice was obtained from a mixture of distilled and deaeratedwater and sieved snow, following the procedure described byHallam et al. (1987). The resulting ice had an isotropic structure, auniform grain size of 4 mm on average, and was apparently free of airbubbles. Cylindical samples, 60 mm in diameter and 120 mm long, weremachined then stored at -10C for at least 5 days before testing. Thesame conditions of preparation were strictly respected for all the

samples in order to keep the same grain size in all tests.2.2 Ice damagingDamaged ice was obtained using the 500 kN servohydraulic pressrecently installed at LGGE. Uniaxial compression tests were performedat constant strain-rate of 5x10 * s' , and at a temperature of -lo0 C.In order to prevent the occurence of brittle failure due to possiblemisalignment, and to ensure the application of a uniform compressionat the platen-ice interfaces, the ice was pre-stressed at 0.5 MPa for30 min before processing. The axial strain was deduced from themeasurement of the relative displacement of the platens using a LVDT.The axial stress was derived from the measurement of the axial forcerecorded by a piezo-electric sensor. The tests were ended with acomplete unloading sequence at different points on the typical stressstraincurve (before peak stress, just after peak, on the nearhorizontalplateau). One of the stress-strain curves (sample No.13)is shown in Figure 1.BED 2 4 6 H G 8 - 3Figure 1. Typical stress-strain curveUniaxial strain (xlO )227

2.3 Creep testsThe samples were tested under constant uniaxial compressionimnediatly after the end of the damaging procedure. As stress-controlof the 500 kN press was not yet available, the creep tests were performedusing an apparatus especially designed for torsion-compressiontesting, a description of which was given by Duval (1976).Given the aim of this study, it was essential to prevent theoriginal state of damage of the samples from increasing during thecreep tests. To this end, a maximum load of 1.8 ma, always less thanhalf the stress recorded at the end of the damaging phase, wasprescribed. This maximum load was applied in successive steps, theduration of which was such that the corresponding minimum creep-ratewas reached. Finally, each creep test was ended by progressiveunloading.3. EXPERIMENTAL RESULTSThe results of this preliminary study are summarized in Tables 1-2.Table 1 shows the main characteristics of the stress-strain curvesobtained during the damaging phase at the constant applied strain-rateof 5x10 '* s' : E is the apparent initial Young's modulus measured uponloading ; o , e are the axial stress and strain at peak (whenP Preached); o, E. are the stress and strain values at the end of thetest; E is the apparent Young's modulus measured from the final totalunloading.Table 1. Summary of constant strain-rate compression tests for polycrystallineice (5 =5x10' '" s-I , grain diam. =4m, ~=-10' C) .Sample

Table 2 gives the values of the minimum creep-rates 6; and correspondingcompressive stresses o recorded during the creep tests. Sample 293was not submitted to the damaging procedure and serves as a creep-ratereference.Table 2. Creep tests results(uniaxial compression, damaged samples, T =-10C)SampleNO.stress a 3MPaNO.e minimum3x10- s-(*) undamaged sampleThe results in Table 2 are drawn on a Log/Log plot in Figure 2. Thisfigure shows that, for the same sample, the minimum creep strain-rateversus axial stress may be modelled using Glen's relation 5 =AO" withexponent n very close to 3. Uniaxial compression induces anisotropicdamage (at least until the peak stress is reached), but as all thesamples were damaged under the same stress-state conditions we mayreasonably assume that their state of damage was characterized by asingle scalar parameter D. Thus, adopting n =3 , Glen's creep law maybe written as:which relation is only valid in a uniaxial situation.The corresponding curves are drawn in solid lines on Figure 2. Thevalues of A(D )/A, where A corresponds to undamaged ice (A =3.5x10'MP~^ s1=0.011 bar^ a" from sample 29), are given in Table 3.

05 1.0 2.0Axial stress (M Po)Figure 2. Minimum creep-rates for damaged samples (-10' C)4. CREEP-RATE PREDICTIONS FROM DAMAGE MECHANICSThe elastic behaviour of damaged ice is expressed by:0 = [K] ee (2where 0 and geare the principal stress and elastic strain vectors (inthe uniaxial case), and K is the matrix of the damaged stiffnesses.Under uniaxial compression a , microcracks form preferentially parallelto axis 3 and are assumed to be oriented at random in sections perpendicularto this axis. Thus K may be viewed as the matrix of a trans-verseley isotropic medium, and is written in inverse form as:

where E is the damaged Young's modulus along the compression axis,3and v is the apparent (damaged) Poisson's ratio.-Following Chaboche (1988), the effective stress g is defined by:where KO is the undamaged elasticity matrix .E and v being the undamaged moduli, and using the notation:the principal effective stresses derived from (4) are given by:-(uniaxial case: o = o = O), and the effective deviatoric stresses 5'1 2are related to the deviatoric stresses o' by:Duval (1976) gave experimental proofs of the multiaxial extension ofGlen's relation for undamaged ice in the form:According to Chaboche (1988), the influence of damage on the creep-behaviour is simply expressed by replacing g with g in the potential S,which from (7) and (8) is thenreplacedwith $ = (k/(l-D))"@. Thecreep strain rate which results is then, from (8):Sunder (1986), SjUlind (1987), Choi and Karr (1989), McKenna et al.(1989) and Pulkkinen (1989) take into account the influence of damageon creep rate by replacing g with directly in the expression for Ec3derived from (8): the resulting creep rate is still given by relation(9), but with m =n ,instead of n+1.Since v was not measured during the experiments, the values of 6"a 3for the samples whose damage was stopped near the peak stress, may beroughly assessed by assuming that the peak stress corresponds to theoccurence of positive dilatancy, i.e. v = 1/2. The values of A(D)/Ao-a

derived from (9), with v = 1/3, v = 1/2 ()L = 9/8), m = 3 or 4, and(1-D) estimated from the measured values of E/E (with E = 9500 MPa)are given in Table 3.Table 3. Creep-rate enhancing factor A(D)/AoSampleDerived from (9)with: ?.=9/8, n=3, andDerived from Fig.25. DISCUSSIONThe very few experimental results obtained do not allow definiteconclusions to be drawn on the influence of damage on the creep-rateof ice. Nevertheless the comparison of the A(D)/A values in Table 3,for samples 18-19-28 damaged up to the peak on the stress-strain curve,seems to indicate that taking m=3 in relation (9) would be better thanm=4. This would support the intuitive concept of effective stressesacting on the undamaged material. The two highest creep strain-rates,recorded on samples 13-17, should be looked at very cautiously aslocalization of the deformation was detected on thin sections whichwere made at the end of the creep tests. Examination of Table 2 showsthat this process did not progress during the creep tests (if it wereso, an apparent increase of Glen's law exponent n or coefficient Ashould be observed). A calculation of the creep-rate at the end of thedamaging procedure, using relation (1) with the measured value of A(D),gives .C* =3.8x10" s' ' for sample 13 ( which seems quite reasonablesince the applied strain-rate was 5x10' ' s" ' ) , but Z = 1.4~10' s'for sample 17. This would imply that additional damage was induced inthis sample during the first load step of the creep test. It must benoted that this explanation contradicts the basic assumption of DamageMechanics which states that damage does not grow during re-loading upto the stress at which unloading was started.

SjOlind (1987) assumes a reduced influence of damage on the creeprateand derives a relation (similar to (9)) in which the damage parameteris reduced by a factor c

Choi, K. and Karr, D.G. (1989). A damage mechanics model for uniaxialcreep and cyclic loading of polycrystalline ice. 8th 1nt.Conf. onOffshore Mechanics and Arctic Engineering, The Hague, Proc., 4, 75-82.Cole, D.M. (1985). Grain size and the compressive strength of ice, J.of Energy Resources Technology, 107, 369-374.Cole, D.M. (1988). Crack nucleation in polycrystalline ice, Cold RegionsScience and Technology, 15, 79-87.Duval, P. (1976). Lois de fluage transitoire ou permanent de la glacepolycristalline pour divers etats de contrainte, Annales de G6o-physique, IV, 32, 335-350.Gold, L.W. (1972). The failure process in columnar-grained ice, Tech.paper No.369, Div. of Building Research, NRCC-Ottawa.Hallam, S.D. (1987). The role of fracture in limiting ice forces, IAHRWorking Group on Ice Forces, 3rd State of the Art Report 87-17, 1-33.Hallam, S.D, Duval, P. andAshby, M.F. (1987). Astudyof cracks inpolycrystalline ice under uniaxial compression, Journal de Physique,Colloque Cl, Suppl.No.3, 48, 303-311.Kalifa, P., Duval, P. and Ricard, M. (1989). Crack nucleation in polycrystallineice under compressive stress states, 8th Int. Conf. onOffshore Mechanics and Arctic Engineering, The Hague, Proc., 4, 13-21.Karr,D.G. (1985). A damage mechanics model for uniaxial deformation ofice, J. of Energy Resources Technology, 107, 363-368.McKema, R.F., Meyssonnier, J. and Jordaan, I.J. (1989). Peak pressuresfrom a damage model for ice in compression, 8th 1nt.Conf. on OffshoreMechanics and Arctic Engineering, The Hague, Proc., 4, 67-73.Pulkkinen, E. (1989). Rate-sensitive damage and cracking model for ice,8th 1nt.Conf. on Offshore Mechanics and Arctic Engineering, TheHague, Proc., 4, 47-53.Santaoja, K. (1989). Continuum damage mechanics approach to describethe multidirectional microcracking of ice, 8th 1nt.Conf. on OffshoreMechanics and Arctic Engineering, The Hague, Proc., 4, 55-65.Sinha, N.K. (1984). Intercrystalline cracking, grain-boundary sliding,and delayed elasticity at high temperatures, J. Materials Science,19, 359-376.SjGlind,S.G. (1987). A constitutive model for ice as a damaging visco-elastic material, Cold Regions Science and Technology, 41, 247-262.Sunder, S.S. (1986). An integrated constitutive theory for the mecha-nical behaviour of sea ice : micromechanical interpretation,lrstInt. Conf. on Ice Technology (ITCV86), Cambridge (Mass.,USA), Proc.,87-102.

MAJOR DIFFERENCES IN THE FAILURE MODES OF AN ICE SHEETON AN INCLINED PLANE: LABORATORY TESTSB. MichelF. PicardUniversite Lava1Departement de Genie civilFaculte des Sciences et de GenieSainte-Foy (Quebec)G1K 7P4ABSTRACTLaboratory tests were performed in a 4m x 4.6m tank where a planarindenter inclined from -45- to +45O with the vertical was pushed in a S2ice sheet, about 4cm thick. Failures mechanisms were observed and thevertical and horizontal components of the resulting initial forces weremeasured in function of time.In the brittle range the ice cover deforms very little before failure,which occurs when radial cracks and a circumferential crack are appearing.The theory of elastic failure of an unfractured infinite ice sheet on anelastic foundation is the closest to explain the results.In the ductile range there is a very important deformation of the icesheet before failure and the forces are much lower than those measured forfast loading rates. Radial cracks are appearing much before the collapseof the ice sheet by formation of the circumferential crack. The theory offailure of wedges on an elastic foundation gives the best explanation forthe values of the maximum measured forces.In upward icebreaking, the size of the broken ice pieces, after thefirst peak, are larger by about 30% in the ductile failure mode comparedto the brittle one. They are very large in downward icebreaking in theductile failure mode.1. INTRODUCTIONThere have been numerous articles published in the last ten years on thesubject of the action of ice on inclined structures. Most are theoretical

ut a few deal with laboratory tests on conical or planar structures.There is also a considerable body of knowledge on the action of ice on thebow of ships, which is also relevant to this question.However, none of these studies or tests makes a distinction between thebrittle or ductile modes of failure which is paramount in the determinationof the forces which are developped. Every study takes for grantedthat there is a unique mode of failure of an ice sheet acting on aninclined structure and no distinction is ever made in the results for thismajor factor.In this paper, we will show from simple laboratory tests with real iceacting on an inclined plane that the difference between failure in thebrittle or ductile modes is major both in failure mechanisms, in size ofbroken pieces and in the resulting forces on the indenter.2. LABORATORY TESTSA total of eighty three tests were carried out in a cold room waterbasin with a surface area of 4m by 4,6m as shown in Figure 1.The basin was built within a steel frame acting as a loading press towhich an ice sheet is attached. The water depth is 60m. The ice sheet isproduced by seeding and growing S2 ice of uniform structure and thicknessvarying from 3 to 4cm.uniformly distributed.Crystal sizes were 2mm on the average and veryOne side of the ice sheet was freely floating and directly aligned withthe initial position of the indenter.The indenter width was either 10cm or 20cm and its angle with thevertical for downward or upward icebreaking could take the followingvalues:loo, 20° 30 and &So. This indenter was pushed by an hydraulicram with a stroke of 1,83111. As shown on Figure 1, three load cells wereused to measure the horizontal and vertical components of the loadingforce. A potentiometer measured the distances. The ram was operated withspeed as low as 0,04cm s-I in the ductile range and up to 6cm s-I in thebrittle range, so that there is a variation of two orders of magnitude inthe loading rates.Compare to the width of the indenters the tests aremade at strain rates varying from 3 x l~'~s"^ in the ductile range up to5 x 10~s'~ in the brittle range.The data acquisition system is made of a HP-3497A control unit and anIBM PC-AT. This system is taking fifteen measurements per second on eachrecording channel.

3. PROGRAM OF TESTINGThe objective of the tests was to obtain the first and peak force on aninclined indenter. The variables could be expressed in dimensionless formas:where:F : maximum horizontal force exerted at the first peak;a : flexural strength of ice;h : ice thickness;b : indenter width;a : angle of indenter with the vertical (plus or minus);E : strain rate.A total of 83 tests were made. The first serie of 42 tests was carriedout in the brittle range. The second one contained 32 tests in theductile range. Finally, 9 tests were made with a = 45' and a = -45' andvariable indentation rates.For each ice sheet that was formed, beam tests were made in upward anddownward ice breaking in order to obtain the value of a to be used in theinterpretation of data. The cantilever beams were loaded with a charriottravelling at the same speed as the indenter of the corresponding test.The beams has a length and a width relatively 10 and 5 times the thicknessof the ice sheet.4. RESULTS OF TESTSWe will not give all the results in this short paper and we refer to thecomplete experimental work (Picard, 1987).For each test, the horizontal and the vertical forces were recorded andthe broken ice sheet was reconstituted afterwards to determine thefracture lines. A video film was also taken to analyse and record themode of failure in each test.

4.1 Failure in the brittle mode; upward breakingThe results for a typical test in this mode is shown in Figure 2.As the indenter touches the lower edge if the ice sheet the loadincrease very quickly to a given value most probably associated with theformation of the first radial cracks. In a typical test, two radialcracks appear starting at an angle (about 30') with the corners of theflat indenter. A fraction of a second later, a circumferential crack isformed and the peak load is attained as shown on the graph. In a fewtests, there was only one central radial crack formed at the beginning ofloading but the peak load was always measured with the formation of thecircumferential crack.4.2 Failure in the brittle mode; downward breakingOne result is shown on Figure 3. In that typical case, only one radialcrack is formed at the center, a fraction of a second before thecircumferential cracks appears and gives the peak loading condition. Theloading pattern is very similar to that observed in the upward breakingmode. In many cases two cracks are formed instead of one at the initialcontact with the indenter.4.3 Failure in the ductile mode; upward breakingA typical test is shown in Figure 4. Contrary to the brittle failuremode, the load increases in a regular manner up to failure. In this caseonly one radial crack is formed at the beginning of loading. The icesheet, then divided in two, is pushed upward and subjected to considerabledeformation that can be observed with the naked eye, before failure by theformation of a circumferential crack. The time to failure is about oneorder of magnitude higher than for brittle failure (about 20 secondscompared to I or 2 seconds). There are also a few tests where two radialscrack are formed at the beginning of loading, but very few compared tobrittle failure.The circumferential crack is formed farther away from the indenter thanfor brittle failure and the broken ice pieces are much larger.

4.4 Failure in the ductile mode; downward breakingThe tests could not be completed in the experimental basin but it isinteresting to note that the ice sheet after forming one radial crackdeformed right down to the bottom of the lower edge of the indenterwithout forming a circumferential crack and producing a peak load.Secondary cracks appeared at the walls of the basin and it was obviousthat these walls were interfering with the breaking process. The brokenice pieces were very large.5. INTERPRETATION OF RESULTS5.1 Flexural strength of iceThe results of the beam tests gave an average strength of the ice of0,9-MPA in the brittle range. The same value was found either in upwardor downward icebreaking. For the tests at the same speed as that of theindenter in the ductile range the resisting moment at failure was found tobe approximately 507 higher than that found in the brittle range,verifying well the fact that the beam section was fully plastified beforefailure in the ductile range. A reference value of 0.9 MPA was taken tomake an interpretation of all the tests, even those in the ductile range.5.2 Horizontal ForceThe results of measurements of the maximum horizontal force are shown inFigure 5 for the three cases experimented. A linear regression was madein each case in function of tg(9O0-a). There is a lot of dispersion andaverage correlation in the results. The equations of regression are thefollowing:a) Upward breaking: brittle failureoh 2= 0,93 tan (9O0-a) + 0.79b) Downward breaking: brittle failure= 0,72 tan (90'-a) + 1,53oh *

c) Upward breaking: ductile failure= 0,75 tan (9O0-a) + 0.09oh 2These equations are valid only for angles higher than a = loo. Belowthis value crushing only would occur on the model. This is rather a lowlimit angle compared to results obtained elsewhere, but it can beexplained by the low friction value of the indenter surface with the ice.In comparing results for upward and downward icebreakings in the brittlerange, it can be seen that they are approximately the same. The forcerequired to break the ice is a little higher in downward icebreaking fora = lo0, where the facing is close to the vertical.There is a large difference in the results between upward failure in thebrittle range compared to the ductile range. At a = 45- the force exertedin the brittle range is about two times higher. At a = loo it is reducedto 1,4 times higher.In the brittle range, the failure force can be approximated with thetheory of failure of a semi-infinite sheet having a vertical load on theedge. The vertical force V forming the circumferential crack is given byNevel, 1972:The horizontal load is related to the vertical load by geometry(Frederking, 1979)wherecotan a + p1 - p cotan a

whenis the friction coefficient between the indenter surface and theice.It can then be concluded that, under brittle conditions, the firstradial cracks do not separate the ice in fully independant wedges but thatthe shear stresses and vertical deformations are transmitted to thelateral wedges so that the full axial moments are developped to fail theice in forming a complete circumferential crack.In the ductile range, the wedges are subjected to considerabledeformation and can be observed to become completely separated. TheFrederking (1979) analysis for the case we have observed in some testswith a central truncated wedge gives a force equal to approximately:This gives values in the lower range of our results. If we approximateNevel (1972) theory to only two 90" wedges, we obtain approximatelyThis is much closer to our results for a = 20° 30 and 4S0.5.3 Size of broken piecesAfter each test, the broken ice pieces were replaced to form the initialsheet, so that the position of all cracks could be recorded.The average radius of the circumferential crack in the brittle range is1.1 t 0.3 m. The average of computed characteristic lengths for each icesheet is 0.9 t 0.1 m. The theory of failure of a vertical load on afloating semi-infinite plate shows that the circumferential crack shouldoccur at a length of 0.8L where L is the characteristic length. Thepresence of a horizontal component as well as the fact that there areradial cracks in the ice sheet before circumferential failure, couldexplain this difference.For upward icebreaking in the ductile range, the radius of thecircumferential crack is 1.3 t 0.3 m; about 30% higher than under brittleconditions. In general, the broken ice pieces are larger than underbrittle conditions but not by a very large margin.However, for downward icebreaking, the ice pieces are very large and inmost cases, only a radial crack is formed and no circumferential crack

appears before the test has to be stopped. Again this can be explained bythe fact that under larger deformations, the ice sheet which is floodeddoes not act as a plate on an elastic foundation because the verticalupward pressure under the ice becomes a constant which is small when theice is flooded.CONCLUSIONSThe tests carried out in upward and downward icebreaking in the brittlerange gave approximately the same results for corresponding inclinationswith the vertical. The theory of failure of a semi-infinite plate on anelastic foundation with a vertical edge load is the best to explain themeasured values for the maximum horizontal force.At low speeds, the ice behaves in a ductile manner and there is animportant vertical deformation before failure. In the upward icebreakingmode the maximum force can be obtained with the theory of a vertical loadacting on two separated 90" wedges. This is the most important type offailure which was observed. The load is then only about 60% as large asthat obtained for brittle conditions; all other conditions being alike.The broken ice pieces were about 30% larger than under brittle conditions.For downward icebreaking in the ductile mode, the deformation becamevery large and no circumferential fracture was observed before the testswere stopped when the ice sheet moved under the indenter. The loads weresmall and the broken ice pieces were very large.Although these tests were made to determine only the characteristics ofthe first loading event on an inclined structure, they do give importantsignals as to the results to be expected for continuous icebreaking whenboth the forces needed to overturn the broken ice pieces and to slide themup or down a structure or a ship are important.It is obvious that these latter forces would also be much different inthe ductile or brittle mode. because of the difference in the size of thebroken ice pieces. This would be particularly so for downward icebreaking, with a ship for example, when a ductile failure is consideredinstead of the brittle one which occurs in nature.REFERENCESFrederking, R. (1979). Dynamic Ice Forces on an Inclined Structure, Proc.IUTAM Symposium "Physics and Mechanics of Ice", Copenhagen, Denmark,pp. 104-116.

Nevel, D.E. (1972). The Ultimate Failure of a Floating Ice Sheet, Proc.IAHR Symposium of Ice and its Action on Hydraulic Structures, Leningrad,pp. 17-22.Picard, F. (1987). Etude experimentale de l'interaction entre une nappede glace flottante et une structure inclines, ' M.Sc. Thesis, UniversitkLaval, Sainte-Foy, Quebec, 256 p.

Details of indenter support1 - Structure32 - HydraulicBasin ram \-,/4 - Indenter5 - support of the indenter6 - Linear potentiometerFig. 1 - Experimental set-up of indentation basin.

Test no E2S30F--0 1 2 3 4 5 6 7 8 9Time (s)-[cm] b-396-Indenter width ...................... 20 cmIndenter speed ................... 7.2 cmlsIce thickness .................... 4.0 cmCirc. crack radius ................. 1.5 mUpward flexural strength ....... 9.6 E05 PaDownward flexural strength ... 9 5 E05 PaFailure linesFig. 2 - Results of 20' upward breaking test in the brittle failure mode.

Test no E6A130FTlÑÑÑÑÑ[cml L 396ÑÑÑÑÑÑÑFailure linesIndenter width ................... 20 cmIndenter speed ................. 6 5 cmlsIce thickness ....................... 3.1 cmCirc. crack radius ................ 1.3 mUpward flexural strength ...... 1.1 E06 PaDownward flexural strength ... 9.2 E05 PaFig. 3 - Results of 30' downwward breaking test in the brittle failure mode.

Test no ElAS20D0Indenter width ................... 20 CmIndenter speed ..................Ice thickness ...................... 3.7 Cf7-ICirc. crack radius ................. 1.7 mUpward flexural strength ......Downward flexural strength ...3.6 E-02 Cm/S1.2 € Pa1.1 € PaFailure linesFig. 4 - Results of 20' upward breaking test in the ductile failure mode.

tan (90O - a)Upward ice breaking (brittle failure)tan (90' - a)Downward ice breaking (brittle failure)tan (90" - a)Upward ice breaking (ductile failure)Fig. 5 - Maximum horizontal force exerted byice on an inclined plane.

PRESSUHE-MELTING OF ICEBo NordellResearcherDepartment of Water ResourcesEngineering (WHEL)LuleA University of TechnologyS-951 87 LULEASWEDENABSTRACTThe pressure-melting curve of ice is often found in literature dealingwith ice problems. This curve originates from the excellent experimentalworks of G.Tammann (1903) and P.V.Bridgman (1912). The method used meansthat ice at constant temperature is submitted to an external pressure. Whenincreasing the pressure a sudden volume change occurs, the pressure-meltingpoint is reached. Results from their works are summarized in this paper.An alternative experimental method was used in this study. Water is confinedin a filled up pressure tank. The water is then cooled from an initialtemperature of OC. The ice formed creates a pressure increase in theice-water mixture. At any temperature a corresponding pressure occurs atphase equilibrium. The temperature and the pressure are measured in theice-water mixture. The results are in good agreement with earlier measurements.The method used, which is easy to handle even with this prototypeequipment, should be more accurate than the old method since one possiblesource of error (the external pressure) is eliminated. The method could beused for other substances than pure water.1. BACKGROUNDAt WREL the interest in pressure-melting originates from the constructionof an ice-powered cart Nordell (1986, 1987). The driving force of this cartis the pressure-volume-work of freezing water. The cart which has a weightof 200 kg, incl. driver, reaches a speed of about 70 km/h. The water volumeis 27 1 and the maximum pressure is limited to 25 MPa this being the maxi-

mum strength of the pressure tank. The maximum driving distance is limitedto 400 m.Riley (1988) tells that Faraday described pressure-melting in 1860. Thevery first laboratory experiments on pressure-melting of ice (Ih) were performedby G.Tammann (1903). who also discovered ice I1 and ice 111. Thiswork was followed by F.V. Bridgman (1912).Tammann and Bridgman used a method where a small volume of ice, at iso-thermal conditions, is compressed by a piston. The pressure is slowlyincreased and when the volume of the ice suddenly decreases the pressure-melting point is reached. This procedure is then repeated for ice at diffe-rent temperatures. The excellent work of Tammann was pioneering. The pres-sure and the temperature were measured with an accuracy of 10 bars and 0.1c respectively. The phase diagrams of ice Ih and temperature-pressure datawhich are frequently presented in literature on ice physics originate fromthe works of Tammann and Bridgman. More recent measurements on melting-pressure of ice Ih have not been found.2. AIMThe aim is to study melting-pressure of ice in the temperature range ofoc to -22° in a laboratory test.The melting-pressure is seen as the maximum pressure obtained when waterin a filled up, confined container is cooled below 0 OC. The lower densityof the ice formed results in a pressure raise. At any constant water temperaturethe pressure becomes constant at phase equilibrium. A temperatureincrease means melting and a lowered temperature means that ice is formeduntil a new corresponding pressure occurs. Thus the pressure is created bythe freezing water itself. The temperature and the pressure are detected inthe ice-water mixture.3. THEORYThe theory of thermodynamics gives a theoretical explanation of pressure-melting. The Clausius-Clapeyron equation (1) gives the general solution forone substance with two phases at phase equilibrium (ph.e).

where P (Pa) and T (K) are pressure and temperature respectively and L(J/kg = Nm/kg) is the latent heat. The specific volumes v = 1/p (m3/kg)where p is the density. The specific volume depends only on the changes inpressure and temperature. The liquid phase is denoted by 1 and s denotesthe solid phase. The thermal volume change is defined at constant pressure,see eq.(2) and the compressional volume change is defined at constanttemperature, eq. (31.The relative volume change (aV/V) is equal to the relative specific volumechange (Sv/v). The coefficient of thermal volume expansion is a (1/K)and K (l/Pa) is the compressibility. To calculate the specific volumechanges of two phases at phase equilibrium, eqs. (2) and (3) are added foreach of the two phases. Eq.(4) and eq.(5) are the differential equationsfor the volume changes of the water phase (w) and the ice phase (i).The solutions of eqs.(4) and (5) are given by the following expressions.c cwhere F(T)-BT = A+C K(P)-~P = -K+C . The constants e 1 and e 2,where e is the base of the natural logarithm, result in a new constant C .It is presumed that the total mass (m = V/v) and the total volume (V) ofwater + ice are constant i.e. SV=am=O, see eq.(8) and eq.(9)

With eqs.(B) and (9) the frozen part (m.) of the total mass (m=l) can beexpressed:where v is the specific volume of the ice-water mixture (water) at ini-tial conditions, 0° and 0 Pa. Finally, eqs. (6) and (7) into eq. (1) resultin eq.(ll) which defines the melting-pressure curve.Eq. (11) is solved numerically starting at P = 0 (Pa) och T = 0 ( 0. Foreach pressure step, the corresponding temperature step is calculated.The used parametric expressions of a, K and L, listed below, are deter-mined from regression analysis of experimental data in cited literature.Hobbs (1974) gives the latent heat of fusion, L. The thermal volumeexpansion of ice, a. is from Hobbs (1974) and the corresponding value ofwater, a is found in Angel1 (1980). (after Zhelesnyi, 1969). The densityof water from Boni (1983) and the density of ice from Bridgman (1912) at0"~ and 0 Pa give v and vi from which the integration constants aredetermined. The integration constants C.and C are determined by solvingeq. (6) and eq. (7) for the boundary condition v(T=O,P=O)=l/p.For performed calculations the pressure step 1 0 (Pa) was used. The cal-culations are summarized in Table l. The temperature, pressure, density andthe volumes of the two phases are given at phase equilibrium. The calcula-ted temperature-pressure gradient is ST/SP = -7.369- 10' OC/P~ (-7.369- 10'~bar) between 0 and lo4 Pa (0 - 0.1 bar). The calculated melting-pressurecurve is presented in the diagrams of Figure 2 to facilitate a comparisionwith experimental data.

Table 1. Calculated melting-pressure, density and volumeX ofan ice-water mixture at phase equilibria.'emperature pressure density vo 1 umeice waterice water(OC) ( bar ( kg/m3 (XI4. EXPERIMENTAL STUDY4.1 Set-upThe pressure-melting tests were carried out in a freezer. Pure degassedwater is confined in a filled-up steel cylinder. The temperature and thepressure were measured in the mixture. The freezer was equipped with twoheaters, each of 100 W. By using the cooling system of the freezer, theheaters and two fans a stable mixed air temperature was obtained inside thefreezer. The temperature was controlled by a thermostat.The pressure tank, a cylinder of stainless acid-proof steel, has a volumeof 50 ml. During the tests the water filled steel cylinder was placed inthe freezer, on a shaking-table to avoid temperature layering in the mixture.The size and shape of the steel cylinder are given in Figure 1. Thetemperature sensor (PT-100) is mounted through the left lid. The temperatureis measured 25 mm into the ice-water mixture. The accuracy is f0.02 "C

at oc and k0.05 c at -16.95"~.The pressure gauge is mounted on the opposite lid. The piezo-electricsensor is in hydraulic contact with the mixture. Since the pressure gaugeis made for temperatures above -5 c the electronic part of the pressuregauge is heat insulated and heated by a heat-cable. The temperature insidethe insulation which is kept constant at oc is controlled by a thermostat.The accuracy of the pressure sensor is 0.25% which means a maximum error of0.55 MPa = 5.5 bars.Figure 1. Section and plan drawing of the pressure-tank, of acid-proofstainless steel, used for the melting-pressure measurements atWL. Length-scales in mm. To the left of the section thetemperature gauge is seen. To the right, the hole for the piezoelectricpressure-gauge is seen. O-rings are used to tighten thelids. After Larsson (1988).4.2 ResultsThe experimental data of this study are compared to the data obtained byTammann (1903). Tammann (1910) and Bridgman (1912) in Table 2. The experimentaldata are also compared with the calculated melting-pressure curve,Figure 2, and found to be in good agreement. These curves also demonstratethe differences and similarities between the results of the four laboratorytests. The calculated temperature/pressure gradient is aT/aP = -7.369. lo-''c/P~ (-7.369- 10'~ 'C/bar), between 0 and lo4 Pa (0 - 0. 1 bar). 8T/aP atoc and atmospheric pressure is many times discussed. Offenbacher (1981)suggests -7.4- 10'~ "C/bar.The calculated curve. Figure 2, is closer to older measurements than itis to this study. The reason is probably that the old K-values of Bridgman(1912) are used in the calculations.

TAMMANN (1903)I ITAMMANN (1910)IIBRIDGMAN (1912)7THIS STUDY (1988)I I-30 -20 -10 0temperature (C)-30 -20 -10 0temperature (C)Figure 2. Measured melting-pressures of ice from Tammann (19031, Tamrnann(1910), Bridgman (1912) and this study (1988). The drawn curve,in all the diagrams, is the calculated melting-pressure. Calculateddata of this curve are listed in Table 1.As a consequence of subcooling pressures lower than 575 bars (>-4.5 c),see Table 2, were measured during the melting phase. Subcooling of ice I11probably occurs below -22"~ since the expected maximum pressure was notobtained.

The accuracy of the performed melting-pressure mesurements is slightlyimproved since Tammann (1903). Tammann gives the accuracy of 210 bars forthe pressure measurements and 20. 1 c for the temperature. In this studythe corresponding values are k5.5 bars and ±(0.0 to 0.05)~~ respectively.TABLE 2. Measured melting-pressure of ice. After T amam (19031,Tanmmnn (1910). Bridgman (1912) and this study (1988).Tammann (1903)(OC)(bar)Tammann (1910) [Bridgman (1912)(OC) (bar) 1 (OC) (bar)This study(OC) (bar)m=melt ingf=freezing5. DISCUSSION OF RESULTSAs a mental experiment, what happens if a sudden volume decrease of thetotal volume (ice+water) occurs?. See Table 1 and assume that the initialconditions are -5C and and 632 bars, i.e. phase equilibrium. The volumechange causes a pressure increase, assume up to 747 bars. The temperatureof the ice-water mixture is still -5 "C and thus the phases are not atequilibrium. The melting point of the ice is -6'~ and thus the ice startsto melt. Consequently the pressure falls until phase equilibrium isreached at 632 bars.This mental experiment implies that a minor volume change of the totalvolume does not change the melting-pressure at phase equilibrium. This isof importance since the volume of the pressure tank is slightly changingduring the test. There is a thermal volume change of the pressure tank andthere is also a volume change depending on pressure change. These changesare opposite to each other since the pressure increases when the watertemperature is lowered.

6. CONCLUSIONSThe melting-pressure of ice has been measured in a laboratory test. Inearlier measurements an external pressure was used to find the meltingpressureof a small volume of ice at constant temperature. In this studythe method used was quite different in principal. Water is confined in afilled up steel-cylinder which Is subjected to cooling. The ice formedresults in a pressure increase. At phase equilibrium the temperature andthe corresponding pressure are measured.Measured data are in good agreement with earlier measurements by Tammannand Bridgman. The method used, which is easy to handle even with thisprototype equipment, should be more accurate than the old method since onepossible source of error (the external pressure) is eliminated. The methodcould be used for other substances than pure water.The melting-pressure calculations are based on old measurements of K.This value is taken from Bridgman as he gives K for both ice and wateralong the curve which means that they are linked to each other. A smalldifference of one of the K-values result in a large deviation from thepresented curve.7. ACKNOWLEDGMENTThis study was performed as part of a study to find applications of thepressure-volume work of freezing water as demonstrated in the ice-motor ofthe ice-powered cart. The project was funded by COLDTECH in Luleg, Sweden.I would like to acknowledge Lena Molin at the University of Kalmar,Sweden, who made the first tests on the prototype equipment and KjellLarsson at WFEL who carried out the measurements after tests and calibrationsof the test equipment. I also would like to acknowledge prof. AndersSellgren for his valuable comments upon this paper.

8. REFERENCESANGELL C.A. (1980). Supercooled and superheated water. Dept. Chemistry.Purdue Univ., West Lafayette, Indiana, 47907 USA.BRIDGHAN, P.V. (1911/12). Water in the liquid and five solid forms, underpressure. Amer. Acad. Arts and Sci. Proc. V. 47 (1911/12). p. 441-558.mNI, P. et a1 (1983). Properties of the solid-liquid interface layer ofgrowing ice cristals. A dynamic light scattering study. Phys. Rev. Am.V. 28, No. 5, 1983 p. 2953-67.HOBBS, Peter V. (1974). Ice Physics. Clarendon Press. Oxford. 1974.LARSSON, Kjell (1988). (in Swedish). Measurements of melting-pressure ofice. (Matning av istryck). Internal report No 1988:04. WREL, LuleS.University of Technology, LuleS., Sweden.LARSSON, Kjell, ISAKSSON, Niklas (1988). (in Swedish). The Ice Thermometer.(Is-termometern). WREL-Report Ser. B, No 34, M.Sc Thesis, report No1988:092E. Lule.5 University of Technology, LuleS., Sweden.NORDELL, Bo (1986). (in Swedish). The Ice Motor. (Ismotorn - Hydrauliskkraftoverforing av istryck). Technical report No 1986:06T, WREL, Lule&University of TEchnology, Lule&, Sweden.NORDELL, Bo (1987). The Ice Motor. Presented at the Fifth InternationalSvedala Symposium. Association for Ecological Design, May 21-23 1987.Svedala, Sweden. Internal Report No 1987:04. Dept. Water ResourcesEngineering. Lule.5 University of Technology.OFFENBACHER, Elmer L. (1981). What is the temperature change in pressuremelting? Cold Region Science and Technology, 4(1981), pp. 155-156.RILEY, Frank (1988). A snowball's chance. New Scientist 14 January 1988.TAMMANN, Gustav (1903). (in German). A Contribution to the Science of PhaseChanges. (Kristallisieren und Schmeltzen. Ein Beitrag zur Lehre der Anderungdes Aggregatzustandes). Verlag von Johan Ambrosius Earth. Leipzig.TAMMANN, Gustav (1910). (in German). On the Behavior of Water at HighPressures and Low Temperatures. (her das Verhalten des Wassers bei hohenDrucken und tiefern Temperaturen). Zeitschrift fur Physikalische Chemie,V. 72 (1910). p. 609-630.

SOME LABORATORY TEST RESULTS ON THE CREEPBEHAVIOUR OF FRESH WATER ICEPius PalathingalResearch EngineerDepartment of Offshore TechnologyTechnical University of Hamburg-HarburgEissendorfer Strasse 422100 Hamburg (joFederal Republic of GermanyABSTRACTIn a series of plate bending tests on fresh water polycrystalline ice platesunder constant temperature the validity of the parameters, estimated by GrabeC 2 I for a five parameter nonlinear material model . has been investigated force plate strips. The results show that the Grabe's parameters together with thenvariant theory constitute a good method for prediction of the creep behaviour.Nevertheless there is a certain deviation between the test results and the theor)at the ends of the plates because of the edge effect.In a series of compression creep tests on prismatic ice specimens the influenceof age of ice on the creep behaviour in the first 8 days after it's formation hasbeen studied. A hardening of the material has been observed in the first 6 daysand after that a relatively stable behaviour. In a series of cyclic compression testson prismatic ice specimens a convergence of creep rate and total strain to acertain steady state has been noticed.1. INTRODUCTIONSince the reality of hidden natural resources in the polar region becameknown, the interest in this area has tremendously increased. The difficulties intransporting the conventional building materials to this area and the difficultiesof these materials to adjust with the e\treme climatic conditions are acting ascataljsers for the use of ice. the most available material in this area, as abuilding material.Bj sudden loading ice seems to be brittle and even by a stress near to it'sfracture stress the deformation is not high. But in case of long term loadingce shows a strong creep behaviour and the deformation can be very high evenfor a stress. which is far below it's fracture stress.The Fig. la and Ib showqualitatively the creep behaviour of polycrystalline ice under constant compressionand constant temperature. For ice as a construction material the tertiary periodcan be avoided. The total strain up to that period can be divided into threeparts- an instantaneous elastic part ( Â e,ast,c ), a primary period with adecreasing creep rate ( & ) and a secondary period with constantcreep rate( Â stat,onary 1 - as follows

Creep fracture1Strain rate E ' I IFigure la & Ib. Creep behaviour of polycrystalline ice under constant stressand temperature.Already a large number of investigations has been done in the area of uniaxialcreep behaviour of ice, e.g. [ 2 I & [ 6 I. Many material models have been suggestedby different authors. Among them the five parameter nonlinear model used byGrabe( Burger model ) ( Fig 2 ) seems to be very good for representing the uniaxialcreep behaviour of fresh water polycrystalline ice up to the end of it'ssecondary stageFigure 2. Five parameter nonlinear model for iceHe has suggested that the total strain under a constant stress andtemperature can be calculated using the following equation:where f\ , . 7) , El , E ->-, and n are material constants and 0 is a reference stress.

After a certain time the creep process enters into the secondary stage ofconstant creep rate. In this stage the total creep rate can be represented by thefollowing equation:The material constants n and I) have been evaluated by Grabe using uniaxialcompression tests on prismatic specimens for temperatures between - 1 0 ~and - 2 0 . ~ The creep rate range was between 108 s ' and 3.10 -' s ' andthe corresponding stress range was between 0.3 MPa and 1.2 MPa. The identifiedvalue for n is 3.2 . The parameter T) is very much dependent on thetemperature. For a temperature of -IS C and a reference stress of 1 Pa, it is1.414 10 26 (S).Some work has also been done in the recent years on multiaxial creepproblems, e.g. C 3 I, C 5 I & [ 11 I. In the following a simplified ice plate problemis examined in detail. Some test results on ageing of ice and the effect of cyclicloading is also presented.2. BENDING OF ICE PLATE STRIPS2.1 Theoretical approachUnder the asumption that the material is isotropic it is possible to expressthe secondary creep rate as a function of stress and for a multiaxial stresscondition we can write the generalized equation as follows:According to the Caley- Hamilton principle the right side of Eq . (4) can belimited to the third order. Then we get0 0 awhere I., I2 , I are stress invariantsNow asuming that the creep rate isindependent on the superposition of ahydrostatic pressure and the material is incompressible and moreover that theinfluence of the third invariant can be neglected [ 4 I&[ 10 I ,we obtainwhere s.. is the stress deviator and 1; is it's second invariant.1By asiming that in thecase of uniaxial stress the formula ( 6 ) gives thesame result as ( 3 ) C 8 I, we obtain for a multiaxial stressNow we consider a plate strip as shown in Fig.3.When this plate strip will beloaded with a constant static load along it's length as shown in Fig.4 , we geta field in the middle part of the plate( Field 1 ) with a constant bending moment.

Figure 3. Deflection of a plate strip under a constant bending momentAsuming that the deflection of the plate is very small as compared with thethickness of the plate and applying Eq ( 7 ). we obtain the principal stressNow asuming the compatibility condition of Euler-Bernoulli for it's crosssection,we getwhere is the curvature rate.Using Eqs. ( 9 ) and ( 8 ) and integrating along the thickness, we obtain thebending moment per unit length as follows:and the curvature rate is2.2 Experimental Procedure2.2.1 Specimen PreperationFirst of all the ice monocrystals were produced in an ice machine. The crystalswere later crushed into small pieces and sieved into crystals of maximum 5 mmdimension. This was brought into a mould, and, after it is densified, water atoc was poured till it became saturated. The freezing followed at a temperatureof future tests. After 24 hours of freezing the specimen were taken out of themould and were brought into the required dimensions by means of mechanicalshaping methods.This procedure resulted in the formation of small crystals. That means thatthe specimen had a large number of crystals which would characterize thespecimen more isotropic. This procedure also resulted in specimen with low airporosity and with out thermal stresses. The density of the specimes producedby this procedure was 0.84 * 0.015 g/cm

2.2.2 Experimental set upThe experimental set up is as shown in Fig. 41-3 Number of fne~~urlngIce75 , 100 , 75Field 1HFigure 4 Experimental set up for the measuring of curvature of plate stripsunder constant bending moment along it's length.The ice plate was placed on two cylindrical rods, which were fixed to thetable. The plate was then loaded along the whole length with static loads. Theload transmission takes place through the two cylindrical rods on top of theplate producing a constant bending moment in the field I along the wholelength The deflection of the plate was measured at three points (measuringpoints 1 to 3 ) using inductive deflection transducers and was recorded continuouslyon a multi chanel recorder. The experiments had been done for six differentbending moments ( Ml to M6 ) at a constant temperature of -15~. For eachexperiment a new virgin specimen had been used. The plate thickness was 17mmfor the tests with bending moments Ml and M2 , 19mm for M4. and 20mm forM3, M 5 and M6 The stresses on the surface of the plate for different bendingmoments were between 0.5 MPa and 0.7Mpa, which were clearly within thepermissible range of the model The duration of the experiments was between42 and 48 hours.

2 2 3 Results and commentsSome results of the experiments are shown in the Fig 5 and 6 . Here thecurvatures at the three measuring points are plotted against the time. In thesefigures, the instantaneous elastic part is followed by the primary stage withdecreasing creep rate. After 3 to 5 hours the creep behaviour enters into asecondary stage of constant creep rate. In Fig. 7 the curvature rates in thesecondary stage are plotted with respect to the corresponding bending moments.The curves calculated with Eq. ( 11 ) are also shown in the Fig. 7.' 1M aMoment= 217 Nm. T :-15-c-0.24 t, = 17 mm'Number of measuring pomts7 ,0 L 8 12 16 20 Ã 28 32 36 LO LL L8Time [hiFigure 5. Creep of ice plate strip for a bending moment of 27.7 Nm.er ofMeasuring PointsFigure 6. Creep of ice plate strip for a bending moment of 48.6 Nm.

0 I I I I I25 30 35 1.0 1.5 50Moment [NrnlFigure 7. Creep bending of ice plate strips at a temperature -1.S0c.A, o and X are measured values at the measuring points 1,2 and 3respectively.n = 3.2- Calculated curves with Eq ( 11 ). = ...,oz6sAs expected there is a reseasonable agreement between the test results andthe calculated values at the middle part of the plate ( measuring point 3 ). Butthe curvature rate is showing an increasing tendency towards the edges becauseof the edge effect. No microcracking was observed during the e~periments.3. AGEING OF ICE AND INFLUENCE OF CYCLIC LOADINGDuring the search for the reasons of bad reproducibility of experimentalresults on fresh water ice specimens, it is suspected that the ice specimens areundergoing an age hardening process in the initial da)s after it's formation.Compression test results on prismatic polycrystalline fresh water ice specimens( LxBxT = 180x90x80mm 3 ) with different ages at a constant temperature of-ISC and a constant compression stress of 1.0 MPa ( Fig. 8 ) indicate that thissuspicion is correct.

0 2 4 6 8 10 12 1L 16 18 Zb 22 26TimelhlFigure 8 Age-hardening of fresh water polycq stalline ice at -1s0cEven though there is not much change in the rate of creep during thesecondary stage, it can clearly be noticed that a stabilized creep condition isreached for an age of 162 h The test results at -20'~ and -10'~ exhibitedsimilar behaviour.0, : IMPa1: -1S'C :0,3"C I-",Age of ire at the beginning 192h1. Cycle0.010 - 2. cycle3 Cycle0 40 2 L 6 8 I0 12 1L 16 18 20 22 21TimelhlFigure 9 Influence of cyclic compression loading on fresh water polycrystalline ice.266

A series of cyclic loading creep tests have also been carried out with similarprismatic specimens as described above. In these tests each specimen wasrepeatedly compressed at an interval of one hour at a constant temperature of-15'~ and a constant stress of 1.0 MPa for a duration of 24 hours. The creepcurves of one such test is given in Fig 9 Here also the change of secondarycreep rate is not much. But there are considerable changes in the primarycreep stage. The period of primary creep stage is decreasing with the numberof cycles The decrease in the total strain between the first and second cycleis quite high while the decrease between second and third cjcle is not high. Ingeneral. a convergence of creep rate and total creep to a certain stable conditionis noticeable This tendency is well known for metallic structures [ 1 1 & [7 14. CONCLUSIONTaking into account the importance of ice as a construction material and thelack of enough research work in the field of ice plates, an attempt has beenmade to investigate a specific ice plate problem. As an intermediate step betweenuniaxial and multiaxial creep problems, a simplified plate problem ( plate strip)has been investigated both analytically and experimentally. The validity of theBurger material model and it's parameters from the uniaxial case have beenchecked for the plate strips. The results show that this model together withthe invariant theorj constitutes a good prediction method for the creep behaviourof polycrj stalline ice plate stripsA series of compression experiments on polyciystalline prismatic ice specimenshas shown a considerable amount of age hardening behaviour in the first 6dajs after the freezing of the specimens Further experiments with cycliccompression loading on specimens of similar type have shown the tendency ofconvergence of creep rate and total creep to stable values as that observed inmetallic structures.5. REFERENCES1. Frederick. C.O. & Amstrong. P J. ( I066 ). Convergent internal stress andsteady cjclic states of stress. J. Strain Analysis, 154-159.2.Grabe. G ( 1087 ). Zum Tragverhalten von verstarktem Eis. VDI Verlag.Dusseldorf ( Ph D thesis ).3 Hausler F.U. ( 1988 ) Beitrag zur Ermittlung der Krafte bei Eisbrechernunter besonderer Berucksichtigung der Anisotropie des Eises und seinerVersagenseigenschaften unter inehrachsiger Beanspruchung,TUHH ( Ph.D thesis )4 Johnson. A.E. ( 1962 ). Creep under Complex Stress Systems at elevatedTemperature, Proceedings, Inst. of Mechanical Engineers, London5 Mahrenholtz. 0, Konig. J.A., Palathingal, P. ( 198

7.Mroz, 2. ( 1971 ). On the theory of steady plastic cycles in structures, 1stSMIRT Conf., Berlin, Paper L 5/6.BOdqvist, F.K.G. and Hult, J.( 1962 >. Kriechfestigkeit metallischer Werkstoffe.Springer Verlag, Berlin-Heidelberg-New York.Y.Palathingal, P . & Mahrenholtz, 0. ( 1988 ) Langzeitverhalten vonfaserverstarkten Eisplatten und Eisscheiben. THUU Report.10. Prager, W. ( 1945 ). Strain Hardening under Combind Stress. Journal ofApplied Physics,16ll.Szyszkowski, W. & Glockner, P.G. ( 1986 ) On a multiaxial constitutive lawfor ice, Mechanics of Materials . 5, 47-71.AcknowledgementThis work was carried out under the grant 525-3991-POLMinister for Science and Technology ( FR Germany ).0037 of the Federal

COMPARISON OF THE COMPRESSIVE STRENGTH OF ANTARCTIC FRAZILICE AND COLUMNAR SALINE ICE GROWN IN THE LABORATORYJacqueline A. Richter-MengeStephen F. AckleyUS Army Cold Regions Research andEngineering LaboratoryHanover, NH 03755 USAManfred A. LangeAlfred-Wegener-Institute for Polarand Marine ResearchBremerhaven, FRGABSTRACTUnconfined, uniaxial compression tests were performed on frazil sea icesamples collected in the Weddell Sea, Antarctica. The tests were done at aconstant strain rate ofs-I and at temperatures of -3, -5 and -10'C.Data from the frazil ice tests were compared to results from tests doneunder the same conditions on transversely isotropic, columnar saline ice.The approximate grain sizes of the frazil and columnar ice were 1 and 10mill, respectively. The results of this work indicate that the frazil icegenerally has a higher strength than columnar ice loaded in the plane ofthe sheet. Tests done by other researchers on freshwater, equiaxed poly-crystalline ice have also shown the compressive strength to vary inverselywith grain size according to the Hall-Petch relationship; o=(d) -'I2 Applicationof this relationship to the sea ice we tested indicates that theresults from these freshwater ice tests at a strain rate of 10- s-I cannotbe directly extended to explain the variation in compressive strengthbetween the frazil and columnar sea ice. We speculate that this may be dueto either (1) the influence that the increased ductility of sea ice has onthe relationship between strength and grain size at 1 0s ,(2) thatanother microstructural parameter (e.g. the thickness of the ice betweenbrine inclusions) may be the controlling factor in determining sea icestrength, or (3) that the dominant mechanisms driving deformation vary witheach ice type.

1. INTRODUCTIONThe development of models to predict ice-structure interaction for designpurposes requires information on the mechanical behavior of ice under complexloading states. Much of this information comes from small-scalelaboratory tests designed to gain an understanding of the mechanisms ofdeformation. The results of these tests must be extended from the microtothe macro-scale for application in large-scale loading problems, Ideallythis extension should be made using ice of similar characteristics. Forexample, when considering large-scale loading problems that involve Arcticfirst-year sea ice, laboratory tests done on columnar, saline ice should beapplicable. A loading problem in an Antarctic scenario, on the other hand,would be likely to involve frazil ice because of the large quantities ofthis ice type found in this environment (Gow et al., 1987, Lange et al.,in press). While the columnar and frazil saline ice both contain air andbrine, the frazil ice is characterized by its granular appearance.Realistically, much of the work that has been done in the laboratory todetermine the failure process of ice on the micro-scale has involved theuse of freshwater, equiaxed ice with an extremely low air volume and nobrine. This ice differs significantly from both columnar and frazil salineice. The freshwater ice constitutes a single-phase system, while thesaline ice types represent multi-phase systems. Given the lack of data onthe failure process in both columnar and frazil saline ice, however, itbecomes tempting to base explanations of the failure processes of these icetypes on the freshwater, equiaxed ice test results. To date, no work hasbeen done to indicate whether this extension is appropriate. Consideringthe fundamental difference between the freshwater and saline ice, the extensionis not intuitively straightforward.This work represents an initial effort to investigate the (dis)similaritiesbetween the mechanical behavior of saline and freshwater ice types.We present the results of constant-strain-rate compression tests done onfrazil and transversely isotropic, columnar saline ice. The results arecompared with published results on freshwater, equiaxed ice tests, focusingon the relationship between peak stress and grain size.2 ICE PROPERTIESThe frazil ice that we tested was collected in the Weddell Sea, Antarctica.The columnar ice was grown in the laboratory, and it has been shownto accurately model the behavior of unaligned, columnar first-year sea icefound in the Arctic (Richter-Menge, 1986; Kuehn, 1988). The properties of

Table 1. Comparison of ice properties. All values represent averages.Salinity Density [at -2O0C] Grain Size(PP~) ( g/cm3 (mm)Frazil 4.37 ? 1.34Columnar 3.28 Â 1.10the frazil and saline, columnar ice are summarized in Table 1 Figures 1and 2 show the characteristics of the crystal structure of each ice type.The most notable difference between these ice types is their crystalstructure. As confirmed by thin-section analysis, the frazil ice is granularand equiaxed with the c-axes oriented randomly. The columnar ice ischaracterized by a long vertical axis, extending in the growth direction ofthe ice. The c-axes of the columnar ice are oriented in the horizontalplane and are unaligned. As a result of these characteristics, the frazilice behaves isotropically (independent of direction), while the columnarice exhibits transverse isotropy (isotropy limited to the horizontalplane). The variation in the structure of the ice is also apparent in theaverage grain size. The grains in the frazil ice are an order of magnitudesmaller than the cross-sectional dimension of the columnar grains. Theaverage salinities and densities of the frazil and columnar ice are comparable.One other significant difference between the frazil and columnarFigure 1. Typical crystal structure of the frazil ice collected in theWeddell Sea, Antarctica.271

a. Horizontal thin section. b. Vertical thin section (growth direction).Figure 2. Typical crystal structure of the columnar, saline ice grown inthe laboratory.ice is that the brine inclusions in the frazil ice are intergranular. Thebrine pockets in the columnar ice, on the other hand, are intragranular.The ice that was collected for sampling was obtained using 10.2-cm,cylindrical core barrels (Rand and Mellor, 1985). The frazil ice sampleswere cored in the vertical direction, while the columnar ice samples werehorizontally cored. We chose to sample the columnar ice in the plane ofthe ice sheet because, with the ice oriented in this direction, a compressiveload applied along the cylindrical axis of the sample will tend tocreate cracks parallel to the short axis of the ice crystals. We felt thatunder these loading conditions, the influence of grain size would be similarin the frazil and columnar ice.3. TEST PARAMETERSAll of the tests were done at CRREL using a closed-loop, electro-hydraulictesting machine with a load frame capacity of 2.2 UN. The loadingactuator used in these tests had a 1.1-MN capacity. The samples weremachined to high tolerances, endcapped, and tested according to the methodsdescribed in Mellor et al. (1984) and Cole et al. (1985). Displacement

measurements up to peak stress were made using transducers mounted directlyon the ice. The displacement measurements used for the feedback controland for post-peak data were obtained via an extensometer mounted on theendcaps adjacent to the ice-endcap bond.The samples were loaded in constant-strain-rate compression along their1cylindrical axis. All tests were done at a strain rate of 1 0 s . Thesamples were tested at a constant temperature of either -3, -5 or -1O0C. Atotal of 13 tests were completed on frazil ice samples, and 9 tests weredone on the columnar ice.4. TEST RESULTSThe combined results of the tests are given in Figure 3, a plot of compressivestrength or peak stress versus porosity at the test temperature,The porosity of the ice is a combined measurement of the air and brinevolume in the ice. It is calculated using the equations derived by Cox andWeeks (1983). Note that for convenience we have combined data from threedifferent test temperatures. We do this assuming that the primary influenceof the temperature increase over this range is to increase the sampleporosity. For comparison, we have also included results from Sinha's work(1986) on young Arctic frazil ice. Sinha's tests were also done under controlledlaboratory conditions at strain rate of 1 0 s and temperature of- 1O0C.Figure 3 indicates that there is a comparable decrease in compressivestrength with an increase in porosity for both ice types. It also indi-. . -- 0 Sinho (1986) Test Temp =-IOC-l l l l l l l l l l l0 20 40 60 8 0 100 120Porosity (%.)Figure 3. Peak compressive stress versus porosity for saline ice samples.Closed symbols represent columnar ice structure and open symbolsindicate frazil ice structure. All samples were tested at astrain rate of 1 0 s .

cates that the strength of the frazil ice is consistently higher at a givenporosity. For example, comparative strengths of the frazil and columnarice at a porosity of 60 ppt are 5.3 and 4.2 MPa, respectively.5. DISCUSSIONOur results indicate that grain size may influence the compressive be-havior of saline ice. The 1-nun-grain-size frazil ice is consistentlystronger than the 10-mm-grain-size columnar ice at comparable porosities.Inverse relationships between grain size and strength have been observed inmany materials. This includes freshwater, equiaxed polycrystalline icewith a porosity = 0. This grain size-strength relationship is welldescribed by the Hall-Petch relationship: o-k(d)-'".Using the Hall-Petchrelationship, we have plotted the average peak compressive strength of thefrazil and columnar saline ice from our results versus the inverse of thesquare root of grain size in Figure 4. Included in this plot are resultsfrom tests on freshwater, equiaxed ice taken from Cole (1987) and Schulsonand Cannon (1984). The data used from these references are from tests done1at a strain rate of s . Cole performed his series of tests at a tem-perature of -5"C, and Schulson and Cannon (1984) performed their tests at-10°C The slope of the lines that represent the k value in the Hall-Petchrelationship are shown above each set of test data.It is clear from this figure that the relationship between grain size andpeak compressive strength at a strain rate ofis much less pronouncedGrain Size' (mm)"'2Figure 4. Comparison of the relationship between peak compressive stressand grain size for different ice types tested at a strain rateof 10' s'. The analysis is based on the Hall-Fetch relationship; ~-kd'~".274

I I 1. I 52 0- 2 5-2 8r 3 1-333 5-384 1-4 9- 5 0-59Cole. 1985Ill1 IIO-~Strain Rate (s')10"Figure 5. Peak compressive stress versus strain rate for freshwater,equiaxed ice samples tested by Cole (1987). The k value for theHall-Fetch relationship is indicated at strain rates rangingfrom 10" to 10'~ s".for the saline ice. One potential explanation of this difference can beseen in a figure taken from Cole (1987) (Figure 5). This figure shows thatthe freshwater ice at a strain rate of s-I exhibits the greatestvariation in strength with a change in grain size. According to Cole (personalcommunication), the ductilehrittle character of the ice at thisstrain rate was dependent on grain size. The finer-grained ice at thisstrain rate still exhibited some ductile characteristics while the coarsergrained ice failed in an explosively brittle manner. At strain rates oflo-' s-I and s-I, the characteristics of the failure were relativelyindependent of grain size. The ice behaved in a ductile manner at thelower strain rate and in a brittle manner at the higher strain rate, regardlessof grain size. This variation is reflected in the k values(Figure 5). The values of k at lo-' and s-I are much less than thevalue at 1 0 s that was used in our analysis. If we assume thatk - 3.0, based on Cole's results at lo-' and s-I, the expected increasein strength in the saline ice tests is 2.0 MPa -- much closer to theobserved variation of 1.1 MPa. Saline ice is intrinsically more plasticthan freshwater ice due to the inclusion of brine. The observations madefrom Cole's work might indicate that, with the more compliant saline ice,the frazil and columnar ice were behaving similarly at the strain rate of1 0 s . At a higher strain rate, we might observe a variation inbehavior under loading that is more dependent on grain size. We plan to do275

more testing of both the frazil and the columnar ice over a wider range ofstrain rates to determine whether this is a reasonable explanation.A second, and somewhat related, hypothesis which might explain the differencein the results between the freshwater and saline ice test is thatdifferent microstructural parameters control the failure processes in thesaline ice. Both Cole (1988) and Schulson (1986) suggested that theobserved relationship between strength and grain size in freshwater ice isbased on the controlling influence that grain size has on the formation ofmicrocracks within the material. Note that the mechanisms that theseauthors propose as an explanation of the grain size dependency describeseveral different processes. The explanations put forward seem quiteplausible in a single phase system such as freshwater ice, where theindividual grains are free of voids and the ice contains no brine. Thesaline ice, however, is a multiphase system. Within each grain of thecolumnar ice there is a system of ice platelets and brine pockets. Thebrine pockets contain either a highly concentrated saline brine solutionor, if the brine has drained, air. In the frazil ice, pockets of highbrine concentration are found between the individual ice crystals. Thesenetworks of brine inclusions may interrupt the progress and influence ofcracks and dislocations in the saline ice. They may also significantlyalter the internal stress distribution in the loaded ice sample. Hence, wemight expect that another microstructural parameter, such as the distancebetween brine pockets, controls the failure process in saline ice.One additional and very important factor that cannot be overlooked isthat the frazil and columnar ice differ in their fundamental crystal texture,the frazil being equiaxed granular and the columnar consisting ofelongated grains. The freshwater tests that we have used for comparisonconsider the grain size effect in samples of one texture. No work has beendone to specifically determine the failure process in either the granularor columnar saline ice. While freshwater ice has been studied extensivelyas an equiaxed, polycrystalline aggregate, the work done on columnar,freshwater ice is limited (Gold, 1970). Gold's work should be extendedusing current test techniques and equipment.6. CONCLUSIONSCompression tests on saline frazil and columnar ice at a strain rate of10-3 s-l . indicate that the finer-grained frazil ice reaches a consistentlyhigher strength than the columnar ice at comparative porosities. Aninverse relationship between strength and grain size has also been reportedin several studies on freshwater, equiaxed ice. This relationship is much

more pronounced, however, in the freshwater ice test results. Thisdifference may be due to the presence of brine in the saline ice and itsinfluence on the deformational processes in this multi-phase system. Whilewe can only speculate as to the specific influence of the brine inclusionsuntil more careful work is done, we can conclude that the results ofstudies on freshwater ice cannot be directly extended to explain the variationin strength between the columnar and frazil saline ice. Studies needto be initiated to investigate the failure process in both columnar andfrazil saline ice, specifically. Until such work is completed, cautionshould be taken in developing hypotheses that interpret the behavior ofsaline ice based on freshwater ice studies.7. REFERENCESCole, D.M. (1988). Crack nucleation in polycrystalline ice, Cold RegionsScience and Technology, 15 (1988), 79-87.Cole, D.M. (1987). Strain-rate and grain size effects in ice, J. Glaciology,33 (115), 274-280.Cole, D.M., L.D. Gould and W.D. Burch (1985). A system for mounting endcaps on ice specimens, J. Glaciology, 31 (log), 362-365.Cox, G.F.N. and W.F. Weeks (1983). Equations for determining the gas andbrine volumes in sea ice samples, J. Glaciology, 29 (2), 306-316.Gold, L.W. (1970). Process of failure in ice, Canadian GeotechnicalJournal, 7, 405 (1970), 405-413.Gow, A.J., S.F. Ackley, K.R. Buck and K.M. Golden (1987). Physical andstructural characteristics of Weddell Sea pack ice, Cold Regions Researchand Engineering Laboratory, CRREL Report 87-14.Kuehn, G.A. (1988). The structure and properties of laboratory-grown salineice and first year sea ice, Presented at Dartmouth College, Thayer Schoolof Engineering, June 21 and 22, 1988.Lange, M.A., S.F. Ackley, P. Wadhams, G.S. Dieckmann and H. Eicken (inpress). Development of sea ice in the Weddell Sea, Antarctica, Annals ofGlaciology.Mellor, M., G.F.N. Cox and H.W. Bosworth (1984). Mechanical properties ofmulti-year sea ice: Testing techniques, Cold Regions Research and EngineeringLaboratory, CRREL Report 84-8.Rand, J. and M. Mellor (1985). Ice-coring augers for shallow depthsampling, Cold Regions Research and Engineering Laboratory, CRREL Report85-21.

Richter-Menge, J.A. (1986). Comparison of the compressive behavior ofnaturally and laboratory-grown saline ice, Proceedings of Second Workshopon Ice Penetration Technology, June, 1986, Monterey, CA, 331-350.Schulson, E.M. (1986). The fracture of ice Ih, Presented at the VIIthInternational Conference on the Physics and Chemistry of Ice, Grenoble,France, September 1-5, 1986.Schulson, E.M. and N.P. Cannon (1984). The effect of grain size on the compressivestrength of ice, IAHR '84, Hamburg, W. Germany, Proc., 29-38.Sinha, N.K. (1986) Young arctic frazil sea ice: Field and laboratorystrength tests, Journal of Materials Science, 21(5).8. ACKNOWLEDGEMENTSThis is contribution No. 170 of the Alfred-Wegener-Institute for Polarand Marine Research.

A LABORATORY INVESTIGATION OF THE FRACTUREOF MULTI-YEAR SEA ICE UNDER TRIAXIALSTRESSES AT -20 OC AND -40 "CP R SammondsAssoc. Research Assist.Rock and Ice Physics LaboratoryDepartment of Geological SciencesUniversity College LondonS A F Murrell Gower Street LONDONReader in Geophysical WC1E 6BTMechanicsENGLANDABSTRACTThe fracture of multi-year sea ice is being investigated inour laboratory under triaxial compression using a new lowtemperature, high pressure testing cell. In this paper theresults of 45 tests are presented which were carried out onmulti-year sea ice collected off Buckingham Island in theCanadian Arctic Archipelago. Constant displacement ratecompressive 'strength' tests were performed on this ice at -20deg C and -40 deg C, at confining pressures up to 30 MPa andat strain rates up to 10-2 /s. The effects of confiningpressure on the fracture of ice are discussed and comparisonsare made with results obtained at -10 deg C, presentedpreviously.1. INTRODUCTIONMulti-year sea ice floes are the most abundant thick icefeature in the Arctic Ocean and in many locations represent thegreatest hazard to offshore operations. However by comparisonwith first year sea ice the mechanical properties, and inparticular the fracture, of multi-year sea ice are not wellcharacterized, whilst the number of laboratory studies of thismaterial under complex stress states are few (see for instanceCox and Richter-Menge [1986], Sinha [1985]).In general, fracture is strongly dependent on the triaxialityof the applied stress field. As our interest is primarily inthe fracture of ice, the principal test technique we employ is

the conventional triaxial test. In this test a specimen isloaded under a hydrostatic pressure applied by a fluid mediumand an additional uniaxial load is applied by an externalactuator.Much of our understanding of the behaviour of brittlematerials has come from the laboratory study of rock fractureusing the triaxial test (Murrell, 1965). The influence ofconfining pressure on rock deformation has been observed tohave two important effects. Firstly the compressive fracturestrength increases with an increase in confining pressure;secondly the mode of failure changes from brittle fracture tocataclastic flow and then to plastic flow with increasingpressure. This behaviour has been successfully described byGriffith fracture theories (Murrell and Digby, 1970).However, ice on earth exists at high homologous temperatures,commonly above 0.95 of the melting temperature, and itsmechanical behaviour is highly strain-rate sensitive. Triaxialcompression tests on multi-year sea ice at -10 deg C (Sammondset al. 1989), and on pure granular ice at -20 deg C (Rist etal. 19881, showed that only at comparatively high strain ratesof 10-2 /s did ice exhibit the shear faulting commonly observedin rock specimens under compression, whilst the strength of iceexhibited little pressure dependence. In addition thereappeared to be no evidence of cataclastic flow occurring athigher confining pressures. Our investigations have now beenextended to lower temperatures and in this paper results of theconfined strength of multi-year sea ice at -20 and -40 deg Care presented.2. ICE DESCRIPTIONThe multi-year sea ice tested in this programme came from asingle floe off Buckingham Island in the Canadian ArcticArchipelago, collected during a British Petroleum expedition.Cores of multi-year sea ice 1m long by 325 mm diameter takenfrom the floe were flown back to London and stored in a -28 degC cold warehouse.The thickness of the floe was found (by coring) to be 7 m. Asalinity profile for the floe obtained from melted testspecimens is given in Fig. 1. The top 0.2 m of the floeconsisted of bubbly ice (average density 850 kg/m3), with

Depth Relative to Sea Level (mlFig. 1. Average salinity profile of the multi-year floepredominantly fine-grained polycrystalline ice (grain sizeapproximately 1-2 mm) in the uppermost portion. In the next0.05 m a columnar structure was rapidly established with agrain size (column width) of 3 to 7 mm. The average density oftest specimens taken from the floe was 899 kg/m3 (standarddeviation 12 kg/m3). Further details will be published at alater date (see Sammonds, 1988).For these tests, specimens were taken mostly from the samelocation at an unridged portion of the floe and mostly at thesame depth below the surface (0.8 - 1.6m). They were cored inthe plane of the ice floe (i.e. horizontal specimens) and inthe direction of magnetic north. A typical thin section of atest specimen is given in Fig. 2. This shows predominantlycolumnar grains across the section with the characteristicsubstructure and brine pockets running in line with with thecolumnar grains. At this depth little c-axis alignment in thehorizontal plane was evident.Fig. 2.Thin section through atypical horizontal multiyearsea ice test specimen(40 nun diameter) viewedunder crossed polars (takenfrom 0.1 m below sea level,1.2 m below ice surface).

3. EXPERIMENTAL PROCEDUREA schematic diagram of the triaxial testing apparatus used,is shown in Fig. 3. A 100 kN servo-controlled actuator loads aram assembly contained in a pressure vessel, 1 tonne in mass.The apparatus is located inside a -20 deg C cold room, but isindependently cooled by refrigerant circulating in a coilaround the vessel.Pressure Vesselvent for HighPPessurc GasTransducer HoleFig. 3.The triaxialtestingcellRetaining NutHigh Pressureas Inlet/OutletCooling co11for CirculatingA test specimen 100 mm long by 40 mm diameter is used whichis enclosed in an indium metal jacket to exclude the confiningmedium (nitrogen gas) from cracks and pores. The apparatus iscapable of performing tests at pressures up to 300 MPa, temperaturesdown to -90 deg C and at strain rates in the range 10-9/s to lo-' /s.The vessel design incorporates a pressure-balanced ramwhereby high pressure gas is vented above the ram shoulder(below seal A) whilst the pressure below the shoulder (betweenseals B and C) is maintained at atmospheric pressure. Theactuator is therefore only required to apply the differentialload to the specimen. Differential load is measured by anexternal load cell. Specimen displacement is measuredexternally by a displacement transducer mounted on the ram. Thesum of specimen and ram deformation is measured, but the latter

eing elastic and proportional to the applied load iscontinuously subtracted from the displacement signal within theservo-control loop and thereby eliminated. A more detaileddescription is given by Sammonds et al. (1989).The standard triaxial test procedure was employed. Here theconfining pressure is pumped to a set value and maintained,then the actuator is advanced at a constant rate. Jacketedspecimens were checked for leaks before and after testing.Cylindrical specimens were cored as required using a pillardrill and stored at U.C.L. at -40 deg C. Immediately prior totesting, specimen cores were sectioned for analysis. Specimenends were machined flat and parallel (with an end parallelismof 0.02-0.04mm). The cylindrical surface was left in the coredcondition. Density was determined from linear dimensions andspecimen mass. The ice was then jacketed, the ram and specimenaligned and lowered into the vessel.At the end of the test, specimens were sectioned toinvestigate the nature of deformation and of the crackingactivity using optical microscopy. Afterwards the entirespecimen would be melted to determine salinity from which brineand air volumes would be determined.4. RESULTS AND DISCUSSION29 strength tests have been conducted at -20 +/-I deg C and 16strength tests at -40 +/-2 deg C at strain rates between/s and /s and at confining pressures up to 30 MPa +/- 3per cent. Four main types of deformation were observed. (i)Axial splitting at high strain rates (of 10-2 /s) underuniaxial test conditions. (ii) Shear fracture at low confiningpressures (see Fig. 4). (iii) Plastic deformation accompaniedby substantial cracking activity at higher confining pressures.(iv) Plastic flow without cracking at the highest confiningpressures.A series of stress strain curves illustrating this pattern ofbehaviour is shown in Fig. 5 for multi-year sea ice deformed at10-2 /s and -20 deg C. At 4 MPa confining pressure (A) the testspecimen failed abruptly by shear faulting, the actuator wentout of control, before recovering as sliding took place on theinclined plane of fracture. For a confining pressure of 7 MPa(B), specimen failure occurred by a combined ductile shearing

Fig. 4.Example of a horizontally coredmulti-year sea ice specimenthat has failed by the formationof a shear fractureunder confined compression at-10 deg C, a strain rate of10-*/s and a confining pressureof 2 MPa. Note the shearfracture is at an angle ofappromately 45 deg to theprincipal compressive stressaxis which implies that fracturestrength is independent ofconfining pressure at thistemperature.2 5200n A Confining Pressure 4 MPa2- B Confining Pressure 7 MPa15 C Confining Pressure 20 MPainf!!n1050Nominal Strain (x)Fig. 5. Differential stress/strain curves illustrating thedeformation behaviour of multi-year sea ice at a strain rate of10-2 /s at -20 deg C under varying confining pressure.

and barrelling deformation, with intense cracking activity inthe shear zone. At 20 MPa (C) creep deformation occurred withno visible cracking activity. The post failure strain softeningfor curve C is not nearly so marked as for curve B. Inaddition, the peak stress for C was low, but this may be852 kglma ) .-20 deg C areare presentedexplained by the low density of this specimen (atIn Fig. 6a the results of the confined tests atgiven, and in Fig. 6b those at -40 deg C. Theseas principal stress map plots (Hallam, 1986). Abe used to describe the yield stress of ice asstrain rate:e = c 0snpower law cana function ofwhere a. is the applied shear stress, C and n are constants.The values for these constants, determined empirically, aregiven on the plots. On the failure map this is represented bylines of constant shear stress for particular creep strainrates. The fracture envelope has been calculated using afailure criterion presented by Hallam (1986):(2)The equation is derived from fracture mechanics and crackinteraction considerations where L characterizes crack growth,and u is the friction coefficient. A value of 0.1 has been usedat -40 deg C in accordance with Bowden and Tabor (1986), avalue which is consistent with the experimental values foundfrom the triaxial tests.There is considerable variability in the results, which isexpected of multi-year sea ice, perhaps caused by variations inthe amount of granular ice contained in the predominantlycolumnar-grained specimens (Richter-Menge et al. 1986). Howeverthere would appear to be a strong contrast between the data at-20 deg and at -40 deg C.In Fig. 6a for multi-year sea ice deformation at -20 deg C itcan be seen that the data points lie approximately along thecorresponding creep envelope. This would of course be expectedin the creep regime, where aside from pressure melting effects,confining pressure should have only a small influence on peakstresses measured in strength tests. However if the data at anominal strain rate lo-= /s are examined it can be seen thatthe although there is a transition from an abrupt brittle

AXIAL STRESS If060 50 40 30I+Â4 :DATA4 10--2 /s 4 :X lo--3 /S# 10'-4 /SW lo'- /S..... WEE? ENVELOPES. 4LOGlCtÑ6.1 n-3.0,' 4+ :-2 -3 -4-5'-5-4 -3 -2- 30LOG STRAIN RATEFig. 6a. Principal Stress Map. Multi-Year Sea Ice -40 deg C.LOS STRAIN RATEFig. 6b. Principal Stress Map. Multi-Year Sea Ice -40 deg C.286

fracture (at the lower confining pressures) through to creepwithout visible cracking occurring (at the higher confiningpressures), the maximum differential stresses measured exhibitlittle dependence on confining pressure. Again the data pointsall lie approximately on the creep surface for this strainrate. The transition from brittle to ductile behaviour isobserved but the strength alters little. The behaviour issimilar to that observed for confined compression tests onmulti-year sea ice at -10 deg C (Sammonds et al. 1988). Theuniaxial compression data at lo-* /s shows a greater scatter,but some of this scatter is due to the existence of two failuremodes - shear failure at higher stresses, and axial splittingat lower stresses.In Fig. 6b for multi-year sea ice deformation at -40 deg C itcan be seen that the tests performed at this temperature and astrain rate of /s appear to exhibit quite differentbehaviour. There would now appear to be a marked pressuredependence of the fracture strength. Instead of lying along thecreep envelopes, where the creep envelopes are truncated by theAshby-Hallam theoretical fracture envelope, the data points lieclose to this fracture envelope.There are few published studies on the fracture of sea iceunder triaxial stresses with which to compare this work. Thedata of Cox and Richter-Menge (1986) for multi-year sea ice andof Richter-Menge et. al. (1986) for first-year sea ice arelargely in the ductile regime and obtained using a proportionalloading triaxial cell. However the data of the former, obtainedat -20 deg C and at strain rates of lo-Â /s and /s, are inreasonable agreement with the results presented here. Resultsgiven by Blair (1987) for columnar-grains saline ice deformedat high strain rates (loe2 /s to lo2 /s) at -10 OC indicate theconfined strength of sea ice continues to increase with strainrate, which is what we would anticipate at this temperature.5. CONCLUSIONSWe believe it is only at lower temperatures (of -40 deg C) andat high strain rates that multi-year sea ice specimens deformedin the laboratory begin to exhibit mechanical behaviourassociated with the deformation of hard rocks. At highhomologous temperatures, close to the melting point, the

maximum differential stresses observed for fracture and forductile deformation are similar. This would imply that at thesetemperatures fracture occurs after the stress required forgeneral plasticity has been reached. We are planning to conductfurther experiments, particularly at the lower temperatures andhigher strain rates, to test this proposal.REFERENCESBlair, S. (1987). Mechanical properties of first-year sea iceat intermediate strain rates, POAC 87, Fairbanks, Alaska.Bowden, F.P. and Tabor, D. (1986). The Friction and Lubricationof Solids, Vol. 1, Clarenden Press, Oxford.Cox, C.F.N. and Richter-Menge, J.A. (1986). Confinedcompressive strength of multi-year pressure ridge sea icesamples, Proc. 5th Int. Offshore Mechanics and ArcticEngineering Symposium, Tokyo, pp. 365-371.Hallam S.D. (1986). The role of fracture in limiting iceforces, IAHR Ice Symposium, Iowa, Proc. Vol. 2, pp. 288-319.Murrell S.A.F. (1965). The effect of triaxial stress systems onthe strength of rocks at atmospheric temperatures, Geophys.J. R. astr. SOC. Vol 10, 231-281.Murrell S.A.F. and Digby P.J. (1970). The theory of brittlefracture initiation under triaxial stress conditions, Part I,Geophys. J. R. astr. SOC. Vol 29, 309-334.Richter-Menge et al. (1986). Triaxial testing of first-year seaice. CRREL Report 86-16, Corps of Engineers, Hanover, N.H.Rist, M.A., Murrell S.A.F. and Sammonds, P.R. (1988).Experimental results on the failure of polycrystalline iceunder triaxial stress conditions, IAHR Ice Symposium,Sapporo, Proc. Vol. 1, pp. 118-127.Sammonds, P.R., (1988). PhD Thesis, University of London.Sammonds, P.R., Murrell, S.A.F. & Rist M.A. (1989). Fracture ofmulti-year sea ice under triaxial stresses, JOMAE (in press)Sinha, N.K. (1985). Confined strength and deformation ofsecond-year sea ice, Can. J. Civ. Eng. Vol 11, pp 82-91.ACKNOWLEDGEMENTSWe wish to thank Dr N Riley of the BP Research Centre forassistance with specimen preparation. This research was fundedby BP Petroleum Development and the Department of GeologicalSciences, U.C.L. We thank BP for permission to publish the paper

STRENGTH PROFILESOF DAKSHIN GANGOTRI ICE SHELF IN EASTERNAN rARCTICASatya S SharmaDeputy DirectorResearch and Development Establishment(Engineers) Dighi, Pune-411015.INDIA.ABSTRACTDuring the first wintering by Indian Scientists in Antarctica in 1984, yearround measurements of strength profile of snow cover up to depths of 1.25to 1.5m from surface were carried out on Dakshin Gangotri Ice Shelf inEastern Antarctica around the Indian Antarctic Research Station OakshinGangotri (70Â 05's 12OE), covering an area of 625 sq km. Ten to fifteenstrength profiles per month were taken at different locations with the helpof Swiss Ram msonde and the values of Ra m hardness so obtained at differentdepths were averaged for each profile for depth intervals of 15 cm, 30 cm,45 c m and 60 cm and the same were converted to obtain unconfined compressivestrength profiles of the snow cover during different periods of theyear.It is seen that the snow cover below 45 cm has generally high strengththroughout the year, whereas the strength of snow cover from 0 to 30 cmis highly dependent on the period of the year. This layer from 0 to 30 cmshows a general increase in strength from March through October with peakvalues achieved between 3une to September. The strength decrease graduallyfrom November to February which is the warm period in Antarctica.The strength profile values can be utilised to assess trafficability of wheeledand tracked vehicles during different periods on the ice shelf. They alsoindicate the load bearing capacity of the surface for landing of light weightto mcdiu m weight dircrafLs.I

1. INTRODUCTIONS~ruiiijLli polllc ul 51mw covri on ii~~ n'c sliell is iinpoi'LdriL froinmanypoints ol' viov liku .is~ex,iin:nt ul lriil1ic~l~iliLy I'or wheeled and trackedvcllldc'i,II~:~I~IIII~~o .iii~l coir.lnirl~on oll.i~iili~ii~ II~~IIIIII:~ I'or~II~I~~-~~III(~~IKJand ski-lariiljri~~ d1rcri.il'Ls, ds well

tratlon of a cone under impact of known energy.It has found extensiveappllcaLlon for estlmatlnq avalanche dangrr and for tlotormlnliy allowablewlicitsl luiiila on iir~ll'icl~Uy co mpiicled snowpdve merits (U edd and oLtiers,1975). It is one of the few hardness measuring Instruments which is notlimited to testing only the surface hardness of snow but may quite conve-niently be used to determine snow hardness at any depth.However, itsvalues are more reliable upto snow having Ram hardness below 800 kgs orunconfined compressive strength of 12.53 kg/cm 2 (Abele, 1963).The Ram msonde (Fig 1) consists of sections of light metal pipe assembledinto a hollow shaft.meter of 2 cm.of 4 c m and a height of 3.5 c m.Each pipe section Is 1m long and has an outside dia-One of .these sections has 60Â conical tip with a diameterBecause the cone diameter is slightly largerthan the outside shaft diameter, the friction between shaft and snow canbe disregarded, so that only the cone resistance has to be considered duringthe process of driving.A mete1 rod 55 cm long, mounted on top of thepenetrometer, guides the driving ham mer. The ham mer of weight W is raisedby hand to a certain height H, which is read on the guide rod, and thendropped freely. The penetration S after each blow of the driving hammerIs read and the number of blows required for getting a certain penetration(in this case 5 cm) is determined. The resistance to penetration R In kgm ay be expressed as :-R = WHIS + W + Q (kg) (1)Where WH = Energy of hammer blows, W = Weight of hammer, H = Heightof fall, S = Penetration from one hammer blow and Q = Weight of penetrom eter.The important assumption made in this case has been that the penetrometerassembly is completely elastic and slight friction between the guiderod and the ham m er is considered negligible.2.1 Ra m hardness R and Unconfined compressive strength.The Ram hardness R of snow so obtained can be utilised for assessmentof unconfined co mpressive strength ^Ã in kg/c m 2 by the following relationgiven by Abele (1963) for milled snow:

1he above relaLion has llie IimiLations that il is valid for milled snow andit qivcs uli~orifi~~od co[iipr'c~,',ivc ~;1rcii~)lIi or llul I~l'~iri~ig eLipiiciLy wlticli werequire for llie purpose of Held app1i.ciitions.However, for practical purpose,laking the sdfety ractor inlo account, Lhe values so obtained may safelybe utiUsed JS confined compressive s~reriyth.3. MEASUREMENIS CARRIED OUT3.1 Dakshin Gangotri Ice ShelfThe Dakshin Gangotri (DG) Ice Shelf is part of the unnamed ice shelf inAntarctica, extending from 69O 50' S to 70Â 45's width wise, and 8' 30'Eto 13OE length wise, along the periphery. It has Fimbullsen Ice Shelf onits west and Lazarev Ice Shelf on its east. The complete ice shelf runsalong the Princess Astrid coast in a zig zag manner. Extent wise, its averagewidth is 70 km and length along the coast 150 km (fig .2). It is a flat toppedice shelf having a gradual southward ascent from sea edge to its point oforigin at the foot of the Schirmacher oasis which is the Strand crack regionof tlie shelf. There is no station functioning at present on this shelf exceptthe Indian station Dakshin Canyotri at 70Â 05'5 12O F which was establishedin Jdn-Feb 1984. Tlie other station in the general area is Lazarev at 69O59' 5 12O 35' E belonging to Soviet Union, which was abondoned by themI eiir1y sixties and piarts of wliieli lidve been seen on icebergs in the lastfew years. (Sharma, 1986).The shelf originates from Schirmacher oasis which is an open patch ofground on a hillock located at about 90 kms from the northern edge of theDG Ice Slielf towards south. The current Soviet Union station Novolazarevskayais located on the oasis at an altitude of 105 m at the foot of a glacier.The DC Ice Shelf stdrts from the foot of the North wall of the Schirmacharoasis which is the Strand crack region or the hinge region of the shelf andhas a large number of crevasses and lakes of varying depths. From theStrand crack region to the coastal edge, the .shelf is uniformly sloping withthe ~ivernije yrddieril beinq 60 m in 100 km. Along the edge of the shelf,there are two high grounds of height 70 m to 80 m which are permanentlycovered with ice.The thickness of the ice in the general area varies from 374 m to 447m (Korotkevich and others, 1978). No systematic measurements on the movementof the shelf have been carried out, however, from visual observations

Fig 2 - Layout of Dakshin Gangotri Ice Shelf

it is presumed that the movement of the shelf is not very significant inthe region of Dakshin Gangotri station.3.2 Ram hardness measurementsStrength profile measurements with the help of Swiss Ram msonde werecarried out in the general area of the shelf around Dakshin Gangotri station.Wooden poles of height 3 to 4 m were erected at intervals of 7 to 10 kmIn the general area of 18 to 20 km south from the coastal edge, A totalnumber of 8 poles were erected covering a total area of 625 square km onthe ice shelf.of 1.25 to 1.5 mStrength .profile with the help of Ram msonde up to a depthwere taken at each site of the pole during 1984 at a fre-quency of two to three times a month, depending on the availability of clearweather.for 5 c mFor getting a fair idea of the strength, number of strokes requiredpenetration of the cone was taken as the basis of measurements.The Ram hardness values for each 5 cm upto a depth of 105 cm were cal-culated for each month and minimum, maximum and average values of RIn the brackets of 15 cm are tabulated In table 1. As a part of study andanalysis, the hardness and unconfined compressive strength values for depthIntervals of 30, 45 and 60 cm were calculated and the average values ofRobtained for each ,month are plotted In figure 3 and the strength profilesin the depth Intervals of 15, 30, 45 and 60 cm are plotted In figure 4.Fig 3 -Average values of R (kg) and2(kglcm ) for 1984 on DG Ice Shelf

4. DISCUSSION ON THE RESULTSThe measurements so carried out were primarily aimed at obtaining strengthprofile of snow cover in Llic Q~~IMT~II i~n'i~ ol' mciisuremcnL.However, a studyof the hardness values obtained give some interesting indications which couldbe of use in the year-round exploration of the general area. The patternobserved and inferences drawn are described below:-i) There Is a general increase in hardness from March to 3une with27.44 kglcm ) being achievedhigher values of above 229 kgs (fT" =between 3une to October (fig.3).During November there isa rapid fall of hardness where the lowest value of hardness of2143 kgs (S" = 5.51 kglcm ) is achieved in December and similarlow values are observed till February i.e.sum mer.during the Antarcticii) The top 15 cm of snow cover or the snow surface is highly sensitiveto radiation.of 50 kg or less (a- =Very low values of Ram hardness of the order21.15 kglcm ) (minimum values) are obser-ved during the period of polar day i.e between November toFebruary, though some sporadic low values may also be observedduring mid-winter months as observed in May 84, which maybe due to profiles being taken im mediately after a snowfall.On the other hand, very high values of surface hardness are observedduring polar night and the months following the polar night.The highest surface hardness with average value of R as 7722kg (O"" = 12.39 kglcm ) was observed in Aug 84 which incidentallywas the coldest month on DC Ice Shelf with minimum temperatureon the shelf going down to -55OC.ill) Increase in strength with low temperature and decrease withhigh temperalure is pronounced in snow layer from 0 to 30 cm.The layer between 30 to 45 cm also shows some increase anddecrease but the extent to which it shows is comparatively verylow. This layer may be said to be a dividing layer between thegenerally strong snow cover which is below 45 cm and generallysensitive snow cover which is above 30 cm.

Table 1 - Ram hardness R (kg) of Dakshin Gangotri Ice Shelf in 1984 at 15 cm intervals.DEPTH JANUARY FEBXUARY ' ;',ARCH APRIL MAY JUXFRO". MIN "AX AV NIil MAX AV MIS MAX AV .11N MAX AV HIN MAX A'/ MIX MAX AVSUSFACE-----------------------.---...-----..-------------.--.-----.-----..-.------.-..------~::c;:.I~£: :, :zu2:!,JULY AL:LST s:,--.,~U N !L-i.i A'l Xi!: !'AX AV :!IN350 3£ 772 37 255 137 17,.. L: ..-- 3. OcTIsER ' -. 7.,T=sf. AV 1::;159 110 87- . ZX4GC149 319 216 151 208 186 91159 133 31270 192 5121.1. 159 119674 262 47527 360 95800 599 177

Fig 4 - Average values of R (kg) for 1984 a t different intervals.

Due Lu ruliiUvely liiijh values of liardness available between Aprilto October, when the surface hardness generally remains above2100 kg (0'= 4.05 kg/cm ) or more, it is possible to use wheeledand tracked vehicles in the general area which have Nominal2Ground Pressure (NCI1) less lhdii 2 kglcm .During the peak winter period (3un - Sep), comparatively verylittle efforts in terms of compaction and levelling of the surfacewill be required for preparing a runway for wheel landing aircrafts.For some light weight aircrafts like C47, merely levelling ofthe surface may be sufficient for landing during this period,as seen from the data of C47 given by Abele (1968).For any construcUon/InstallaUon, the depth of the foundationshould be minimum 45 to 50 cm below the surface where aminimum value of 0' = 5.85 kg/c m 2 of bearing capacity isavailable.5. CONCLUSIONStrength profiling of snow-cover was carried out on Dakshin Gangotri IceShelf for the first time during 1984 with a view to assess the general increaseand decrease of strength of the snow cover with respect to the period ofthe year. Studies on these lines are continuing.The strength values obtained on the DG Ice Shelf give a fair indicationabout the bearing capacity and load carrying capacity of snow cover in variousperiods in a year. The Swiss Ram msonde is a very handy and simple instrumentavailable for such measurements which can effectively be employedfor such purposes on Antarctic ice shelves.The pattern of strength profile observed gives a fair indication about theefforts required for construction of snow roads and runways on the DG IceShelf as well as it helps in deciding the ideal period of construction of suchroads and runways, and their period of use.6. REFERENCESAbele, G (1963). A correlation of unconfined compressive strength and Ramhardness of processed snow, USA,CRREL,TR 85, 12 - 13.

Abele, G .(1968). An experimental snow runway pavement in Antarctica.USA, CRREL, TR 211, 13.Korutkcvicli, Y.S. S.iviiLymjin L.M. .ind Morcv (1978). Drilling thorough theice shelf in the vicinity of Novolazarevskaya. Bulletin of SovientAntarctic Expedition Report N 0.98, Hydro m eteo, Leningrad, 50.Sharma, 5.5. (1986). Criteria for selection-of site for construction of structureson a floating ice shelf in Antarctica - A case study, Internationaloffshore and navigation conference and exhibition, (Polartechf86),Helsinki (Finland), Proc. vol.3 VTT Sy mp. 73, 306Ueda, H.SeUman, P.Abele, G.0975) USA, CRREL, Snow and ice testingequipment, USA, CfUiEL, SR 146, 5.

A FIEID INSTRUMENT FOR FPflCTURE TOUGHNESS TESTINGOF ICEDivision of Structural EngineeringD2pmmnt of civil Eng*ingLuleA University of TechnologyS-951 87 LuldSWEDENABSTRACTThis paper pressrits the development of a portable field test equipmentcall& FIFT (Field Ir&nment for Frazhxe lkskhq). Tk ocinplete m?asure-ment of Q can be made in the field. To obtain this the snort-rod dievron-notched specimen approach is used. The sample preparation is minimized totvm vertical cuts in a &ill& cylidrical specimen. Tk design ideaskehird FIFT and the usefdms of the mtkd are discus&. Six pilotstudies wxe ww on gmn~~ar sea ice at -5Oc to test the mm-ability of FIFT. A 1-the relative brine volume, JV,relaticnship betwen %c and the square nmt ofwas observed.Offshore exploration of oil and gas in arctic regions is still increas-irg. ~ d ~ ~ ~ ~ ~ t h efhed-b i g n oand ice breakinq ships. Cne approach is to model ice/structure interactionsmically wit3 different thmries in W to predict the 1-the stmzhms. In an ice/structure interaction tl-e f-gen=ratdaffeth~depend, in part, on the fracture behaviour of the ice. It is possible, byapplication of a fracture mechanics approach, to predict lower, and there-f m eaxkmically mre favwrable, design lcads. wite the l& of aocinplete fracture mechanics definition, the technique provides fracturetoughness as a useful parameter for many design applications.The fracture toughness can-be characterized by a critical stressgatea & of a kmmn size. The high inintensity factcr, %c. If certain ax-ditions are mt, as disassd Mew,%c is a material pmpx-ty which detamims th stm=ss to prop-300the vicinie of a &

tip prcdxe a mn-1-creep m. If this creep rn is limited in sizeamprdwithotkrdimmsicnsof theusedspcimn, thethxyof 1-elasticity can be used. Not only must the requirements for l£F beaccurate, the specimen size must be large enough for truly poly=rystallinebehaviour of the ice. Otherwise an apparent connection between e.g. grainsize and %c be masurd. A suitable specimen size to grain size ratiois 10, %t is a mhimm of 10 gxahs a q l e is forpolycrystalllne behaviour in ice.This paper presents the ckvelqmmt of a field test quipm~t calledFIFT (Field Instrument for Fracture Testing), Stehn and Franscn (1988).The mmsxarmt of %c is n&e with short-rod chevron-no- sp3zhms.The short-rod chevron-notched specimen approach is a simplified methodfor IEa!3x* plain strain fracture lm@nsss. T h method can ke intests in which very simple loading devices are utilized. This type ofspecimen wits a stable ma& devel-t dur* the first ofm& gnmth. At a critical ma& depth, ace the crack grud3-1 b xmsunstable. The critical crack depth is a constant for a specified gecmetry.Theonly--teristhemload-to£-thsample at a. The short-rod chevron-notched specimen was first proposed byBarker (1977) and (1978). This method has been used by Nixon (1984) tomeasure 1C- of freshwater ice.2. THE SHORT-ROD CHEVRON-NOTCHED SPECIMENThe short-rod chevron-notched specimen oonfiguraticn with contncn nomen-clature is shown in Fig. 1.Initial crack lengthLength of chevron notchthe surfaceCritical crack depthmitical crack widthSpecimen diameterSpecimen lengthChevron secant angleChevron slot thickressFiqure 1. Short-rod chevron-notched fracture toughness specimen. The loadline or the load area is where the opening load is applied inthe mouth of the specimen.

Two methods have been used to load short-rod q¥sedmes~~ In the fl-rst,Barker (1977) applied a load line along the front edges. Barker (1978)used the second method where a load cushion was inserted to a deptha, = 0.482 B and thus applying pressure over a load area in the slot, seeFig. 1.If LiIEar Elastic FrxAUre (m) dtials are assm2d,Bubsey et al. (1982) gives the stress-intensity factor for the load linemethod asm a x .) y-ln^ = qw(l-v2Here YL is a dimensicdess mtrical error fuxztion. F- is thpeak load and v is Boissons ratio. Shannon and Munz (1983) presents apolynomial expressim for Y_.Here a = a /W and a = a /W are dimensionless chevron-notch parameters.Equation (2) is valid when 0 l a i 0.4. The Initial crack length, a, isthe paran~ter with the 1- inflm on KIc &&at& by equation (1),Ouchterlony ( 1985).The %c equation for the load area method is derived in a similar way asequation ( 1). Barker ( 1978) gives this asHere A is a dimensionless constant, P- is the peak pressure appliedPover the slot surf-. No error furctim similar to quation (2)exists, but Barker (1978) has evaluated A for specimens with fixed geo-Pmetrical configuration, i.e. a (W/B)-ratio of 1.5, a (aI3)-ratio of 0.5,and a chevron secant angle of 29.It is diffiut to make identical specimens for FIFT e d th ~ a test isdone, depending on the fact that the tests are made in the field. ¥niere

fore, the expression of Y" rarath tlnn A is very handy since it takesPcare of differences in geanetry. However, FIFT is a load cushion andequations (3) and (4) must be used to evaluate %.3. DESIGN OF FIFT3.1 Design considerationsl'k ah of a cmplete ice fracture m c s prqram is to give amswxsto the applicability of LEFM to ice engineering problems. Experimental andanalytical studies must be carried out for a more adequate estimation ofice loads acting on a structure. This is possible by considering the fracturemechanism of ice. The way of safely applying fracture mechanics in themodeling of ice/structure interactions is twofold: first, the whole processof interaction must be described rather than just a part of that process;and second, a basic understanding of the parameters affecting the fracturee c s of ice is reeded. In this paper aily the second statawnt willbe mi-.The main purpose behind the development of FIFT was:1) The specimens should be simple to manufacture and provide a simpletheory for calculation of K,.,2) The test procedure must be simple enough for two men to handle in thefield3) No use of complex load frame or power supply should be required.The short-rod chevron-notched specimen offered several advantages. Thecylindrical form of the specimen is obtained from ordinary core drilling.The load cushion functlcnability is described in section 3.2. When thefirst attempts were made to crack an ice specimen with FIFT, they did notturn out well. As shown in Fig. 2a, it was difficult to make the slot ofthe specimen with such tolerance that the necessary contact pressure wasachieved. Using equation (3) with 1C- = 100 kPaJ'm and a load cushioncontact area of 300mm*(amsmed~w), theestimtedcontact presmrebeoones 1.3 MFa. Thus., if erouqh contact pressure is obtained the state ofstress is sufficient for plastic de£onnaticms h2n33 rn fractu?=ing untilthe contact area has beocroe larger. To overocme this two stiffening plateswxe p l d ketwen the load cushion arxl the ice surf-of the slot, Fig.2b. Theplates had thedimensionA = 80. 65mm 2 , i.e. a l w o f 0.41 Bsoand a height of 0.34 B. The plates were then melted Into the slotwhich gave perfect contact.303

Figure 2. Schematic outline of the -tact problemAs described in the next section, the cushion is very stiff. The loadcushion has to sustain pressures of up to 800 kPa without leaking orbursting. Furfhennore, a stiff loading device gives the opportunity tomasure the f-energy G. If the ld vs r3eflection~ isen a fast x-y plotter or storage oscilloscope, the fracrtxire energy can becalculated. However, this requires a stiff load cushion that does not"explode" as the crack beocmes unstable and the entire specimen cracks.The relatiaxihip between G and %c for p- skah iswhere E is Youngs modulus and v Poisscns ratio. Strictly it is G that is amaterial parameter.3.2 Presentlayout (figure3)The functional design of FIFT is evaluated here. The length of FIFT,measuredfrcmthebottcmoftheloadcushiontothetopoftheloadscrew,is 430 inn. The width f m the electrical pressure gauge to the quickcoupling that connects the flexible tube from the hand pump is 260 inn, seeFig. 3. The total weight is about 1.6 kg.The load cushion is fitted into the vertical slot of the chevron-notchedspzhen. Force is applied on the spzhen by a hard-hld el-icaldrilling machine. Fluid, made of water ad glycol, is depressed f m theload housing into the load cushion, see Fig. 3c. The drilling machinedevelops a torque of 11 Mn and gives 350 or 1100 revolutions per minute.The machine is powerful enough for the flow rate, and therefore the dis-placement rate, to be fairly constant. In IEFM, displacement rate is can-parable with loading rate. 'The displacement rate is both constant withinead-~ test @om14 and is als~repatable £ra time to time. Hcmver,exactly the same rate cannot be achieved since the time to fracture differs30 4

etween individual tests. This can be a drawback, since the rate dependencyof the fracture toughness cannot be studied properly. Itie pressure, i .e.the force acting on the specimen, was measured using a 0-689 kP. (0-100pi ) electrical pressme gauge.When the fluid is ccnipressed into the cushion, it expands. Since it iswelded around its edges and oonparatively small, the cushion is verystiff. The deflection of the cushion is a convex growing bulge. With thestiffening plates ;arranged as displayed by Fig. 2 , the initial crackleqt3-1 a. , is easily msasmed.Figure 3. layout of FIFT. a) General outline, b) Detail of cushion,c) D.3tail of lmdhg ~9xaqmerlt305

4. EXPERIMENTAL PROCEDUREIt was our intenticm to the anplete field quimt, i.e.both FIFT and the wooden frame in the field. However, this was not donebecause the frame was not anpletsd in -tlins. Furthermore, it was mareconvenient to test FIFT the first time in the cold rocms at the universitysixe its -our there axld be mare closely with mticmalinstrumentation.Cores were taken from sea ice f m the Gulf of Bothnia close to LuleACity. Six cones, with a length of 500 mil and with a diameter of 200 inn,were drilled from -the first-year landfast ice. The core orientation wastaken so that the crazk prupagationwas vertical.The-l~in~tmethodwas~to-thegrainsize%mean grain size, averaged over six traverses, was 1.7 inn. The mean elcngaticnratio, that is vertical to horizontal grain size, was 1.1. This indi-cates a regular shape with approximately equal sized grains, i.e. granularice. Specimens had an average density at -l.oOc of 876 kg/m3 .The fabrication of the specimens were made at -~OC, which also was thetESt -tLKe. The de-%bd wiW this Shidy was (W/B)-and (a/B)-ratios of 1.50, (a/B)-ratio of 0.5, a chevron secant angle 0of 2g0, and a chevron slot thickness, t of 6 mil. In the future a bettermanufacturiq method w ill be developed to ensure that the dimension toleranoesare achieved mare -1y.4.2 Test methodThe experimental set up is shown in Fig 4.Figure 4. -tic figure slmwiq the 1- and measuriq -t306

he specimens were tested at -5Oc. ~fter testing and dimensid ineasure-~=I-I~s, ea3-1 specimen was carefully m. The splittE!d anfinnedthat the crack had indeed propagated along the chevron-notch, as itwas intended to do.The crack opening displacement was measured with a system comprising twasupports placed on different sides of the slot, see Fig. 4. Small holeswere drilled into the tcp of the specimen and the supports were frozentight into tkm. 'I'm eleztrical displ-t tmmdmem were attzdd toone support and a rigid plate to the other.Themaximal pressure, P , and the time to fracture, tf, weredefranthe loadvs I3.m -. Fig. 5a skws a Qpical amve. It nust benoted that only the curve, above the dotted line, corresponds to the loadacting on the specimen. The dotted line, with extension upwards and down-wards, represents the stiffness of the load cushion, i.e. the pressurerequired to bulge the m ined cushion. The area under the curve in Fig.5b represents the fracture energy G.LOAD 'IN)300 -200 -Dl SPLACEMENT*100 200 300 (urn1Figure 5. Typical a) load vs tune curve and b) load vs crack openingdisplacement curve4.3 ResultsIn order to be able to interpret the results with LEFM, the maximal valueof the crack tip creep -, r , is limited to 1/50 of the critical specimendimension. In this case it is the chevron slot thickness t = 6 inn. Themaximum value of rg , -' 3 to Timm and Frd&&q (1986) and N b n ~and Schulson (1986), is

Taking values for the variables in equation ( 6) as B = 1.62 10' s"Pa-3, E = 8 GFa (Yq's d u l u for gx-anular ice) am3 a critical stressintensity factor of 75 kPafm, the tine at which r' equals one fiftieth ofthe slot thickness (= 0.12 mm) beocmes t _ = 103 s. The 1- test tinewas about 2 s. Thus, r" is limited in size and a IEFM analysis is valid.This investigation conposes a far too small number of tests to show apossible connection between K,,, and e.g. porosity. However, Fig. 6 showsthe test results mther with a best-fit line based on a regressionanalysis. The functional relationship has the formHere Vb is the relative brine volume in wt and KIc (&datedby equa-tion (3) ) is in kPafm. The correlation coefficient for this line (r 2 ) is0.83.Timm and Fb&e&hq (1982) -ted a omvhzirg dezease of tkfracture tcqhmss with increase of brine ¥volume This is consistent withthe fact that tensile strength decreases as porosity increases, describedby Wlor ( 1983), since Kc is proportional to strength when the cracklength is constant.Figure 6. Fracture toughness KIc vs J'Vb5. DISCUSSION AND CONCLUSIONSLEFM seems to be safely wlicable with the short-rod chevron-notchedgeonetrics used in this test. The size of the specimen is big enough forplycrystalline behavicur and the time to fracture is not so long that thecrack tip creep zcne beoones to large.308

We believe that the general design of FIFT is very goal. Tests can easilybe wormed in-situ since m LEI-ture mitive equi-t is d.FIFT will work well even when wet since there are no Darts that can freezeand unwanted ice is easily removed. Rirthermore, the anpressing fluid ismade of anti-fr€eInbrtwX (water and glycol) and will rmt dramticallychange its viscosity at low temperatures. The heat achieved when puttingthloadcushionhicka j & t i s ~ t o ~ t h e & M ~ ~between the stiffening plates and the chevron slot, see Fig. 2.Since no error function similar to equation (2) exists for the load areamethod and the stiffening plates used for FIFT were not big enough, theresults presented In Fig. 6 suffers frun filaocuracy. In the future eitheran error function or a rearrangement of FIFT so that the line load case isachieved will be needed.Another source of error occurs when the applied load is measured as theinternal pressure of the load cushion. This rquims a very accurate cali-bration of the load cushion. The relationship between measured internalpressue ad the fora= cbtzdnd frun a load cell was acperhentally deter-mired. If ore of the stiffening plates, see Fig. 2, is nodified to includea snail load cell, the applied force can be determined directly. If boththe load cushion and the stiffening plates are made bigger, the result willbe a more evenly spred pressure over the whole width B of the slot. Fur-ther, the requirements behind equations (1)-(4) will then be fulfilled. Thedevelopment of a progressed version of FIFT is hoped to Improve the frac-ture toughness testing for sea ice. The following conclusions can be made:(1) A field instrument for fracture testing (FIFT) was developed and usedsuoosssfully to determine the fracture touchiness. The loading deviceis sufficiently stiff so that measurements of the fracture energy canbe made.(2) FIFT is easy to handle and together with the specimen pmpam1tionsthe complete measurements can be made In the field.(3) The 1- elastic fracture lnxhmia amzept was srxwn to beapplicable for the calculation of %c.The writers gratefully acknowledge the financial support provided by theSwedish Council for Building Research and by Coldtech, a foundation inLad& wilA the aim t~ pramte te3xmlcgy for -ionswith mld Wte.Ms wish to thank professor Finn Ouchterlcny at the Swedish DetenteResearch Foundation and professor Lennart Elfgren at the division ofStructural ESiginsertng for their helpful oannents on the manuscript.309

REFERENCESBarker, L.M. (1977). A simplified mettcd for m i r q plam strain fm-ture toughness. Engineering Fracture Machanics, Vol. 9, pp. 361-369.Barker, L.M.(1978). Short rod Kc measurements of M0. Fracture nsdi-anics of ceramics. EUiM by Eradt, Hassdmn and Large, Vd. 3,pp. 483-494.Bubsey, R.T., Munz, D., Pierce, W.S.,and Shannon, J.L. (1982). Cunpliancecalibration of the short rod d-evrln-rntch sp32hm for fracture tulgh-ness testing in brittle materials. International Journal of F'racture,Vol. 18, No. 2, pp. 125-133.Mellor, M. (1983). Mechanical behaviour of sea ice. U.S. Army Cold RegionsFksear& and F3-gimXdrg ~ t m y a2RET.l , t4mqmph 83-1, 93 gp.Nixcm, W.A.(1984). Sane aspects of -the engineering properties of ice.Ph.D. Thesis, Cambridge University.Nixon, W.A., and Schulscn, E.M. (1986). Fracture toughness of fresh waterice as a Krction of 1-rate. Ice tedrnlcgy. Pme&irgs of -the1st Intematicnal Conference, Cambridge, Springer-Verlag Berlin, pp.287-296.Ouchterlony, F. (1985). Evaluation formulas for rock fracture toughnesstesting with standard core specimens. Swedish &tonic researchfoundation, Box 32058, 126 11 Stocktolm, Report DS 1985:2, 82 pp.Shanncn, J.L., and-, D.G. (1983). Specimensizeandgeometryeffectsonfracture toucftmess of aluminium oxide measured with short-rod and short-bar chevron-notched specimens. Chevron-notched specimens. Edited byUnderwood, Frieman & Baratta, A% Special Technical Publication 855,pp. 270-280Stehn, L., and Fransscn, L. (1988). A field instrument for fracture toughnesstesting of ice. Technical -report 1988:35T, Division of StructuralEngineering, LuleA University of Technology, LuleA 1988, 22 pp.Timoo, G.W., and Frederking, R.M.W. (1982). Flexural strength and fracture¥toughnes of sea ice. Cold Regions Science and Technology, No. 8, pp.35-41TiJico, G.W., and -, R.M.W. (1986). The effects of anisotropy andm t b fraztum tnqhms (%c) of fresh wa*ice.Proceedings of the Fifth International Offshore Mechanics and ArcticEngineering Symposiun, C W , Tokyo, Vol. IV, pp. 341-348

DYNAMIC RESPONSE OF AN ICEBEAMWITH FLOODING WATER EFFECTs. L. wang,Graduate Studentc. R. Hazell,ProfessorC. C. Hsiung,ProfessorDepartment of Mechnical EngineeringTechnical University of Nova ScotiaB.0.BOX 1000Halifax, Nova Scotia,B3J 2x4 CANADAABSTRACTA system of a cantilever beam on an elastic foundation with floodingwater on the upper surface of its free end is considered. The distributionof flooding water is assumed depending initially on the time rate E and thelocation x. The effect of flooding water is determined by employingcomponent mode synthesis and an asymptotic method.1. INTRODUCTIONIn this paper, a system of a cantilever beam on an elastic foundationwith flooding water on the upper surface of its free end is considered.This class of problem occurs when an icebreaker moves on a huge floatingice cover and breaks its edge. Because of the existence of flooding water,the effective mass and stiffness of this beam system will change. The freevibration behavior and the dynamic response of the icebeam will beaffected.To solve this problem, it is assumed that the distribution of floodingwater along the beam depends initially on the time rate 6 = To/ T

According to the distribution of flooding water, the icebeam is dividedinto two parts: ( 1 ) without flooding water the behavior of the beam canbe described by a system of linear differential equations, ( 2 ) withflooding water the behavior of the beam will be described by a system ofnonlinear differential equations containing the small parameter E. Then,two groups of equations will be matched at the connected section forcontinuity. Finally, the governing equation is obtained with smallparameter & for the whole system. Thus, the problem can be solved by theasymptotic method 121. Studying the expressions of the natural freqency,the mode shape function and the response, the effect of flooding water canbe determined.2. GOVERNING EQUATIONA system of an ice cantilever beam on an elastic foundation is shown inFig.1.Fig.1 The Cantilever Beam System with Elastic FoundationAccording to the distribution of flooding water, the beam system isdivided into two parts: one has no flooding water, and the other does. Twocoordinate systems are used to describe two different parts. According tothe component mode synthesis method [31, the deflection function Wi(x,t)can be expressed aswherenW2 (X2,t) = Â qS(x2) qs(t)s =mm and n are integers.At the connected section ofthe two parts, the continuity conditions areNow dealing with each part of this beam system, the kinetic energy forthe first part of the beam (without flooding water) isT = (1/2) 1^ZS ^(tl Gs

The potential energy due to the strain and buoyant force isFor the second part of the beam (with flooding water), based onassumptions stated in the introduction, the flooding water mass can beexpressed asThen, the kinetic energy can be expressed ass = m, m+1, ... n. (9)The potential energy in the second part of the beam is given as followsSubstituting T and U into Lagrange's equation:d/dt ( a~/aq(t) ) - a~/a~~(t) + au/aq1(t) = Q_

we obtainor in matrix formand Qi is the generalized force, for Qi(x) = P ll)i(x,) + R (l)'i(x,)i = 1,2,. . .,m,.. .n,moment.where P is the shear force and R is the bendingj=l,2;The degree of freedom can be reduced from n to n-3 by substituting thefollowing transformThe matrix [Dl is determined by the continuity conditions at the connectedsection. Finally, we obtain the governing equation for the whole systemNoting that the function f(t) is contained in matrix [MI and [s*].Considering only the flooded portion, the generalized force (Q*) =[PITfQ*) = (Y*) = constant vector. By using linear transformation (6) =[q) + [T), where the constant vector [TI is called the translationalvector satisfying the equationequation (17) becomesf(t1 is related to the time rate E = to/tl and it represents the masschange effect of the whole system due to the flooding water.Therefore, it is assumed that f(t) can be expressed as

Since the time rate = To / Tl

To solve the non-linear differential equation (27), the asymptotic methodis employed and the following assumptions have to be made as in Ref[3]:(i) Undamped harmonic oscillations with frequency CO. depending only ontwo arbitrary constants are possible in the unperturbed system (28).(ii) The only solution corresponding to equilibrium in the unperturbedsystem is the trivial solution tl (t) , & (t) . . . (t) = 0.(iii) Neither the frequency 0). nor any of its overtones 2Uj, 30) j' ...kc0 ., ... are equal to any of the natural frequencies CO,, an,. .. Wj1,COj1,...0)n_3 of the unperturbed system ( absence of internal resonance ).Under those circumstances, we can construct the asymptotic expansionin which a and C = ( 6l.t t 6 ) are determined by the differential1equationsda/dt = E A, (a) t E' A, (a) + E3 . . .dc/dt = 0) + E Bl (a) + E2 B2 (a) + E3 .. .1Equation(30) represents the approximate asymptotic formulae for particularsolutions corresponding to monofrequency oscillations which, for small E,are close to the normal unperturbed oscillation (29) with frequency (0..3Due to the existence of the perturbing force - E Fr in the systen (27),there would appear a series of particular solutions uS(j) in the generalsolution (30), and both amplititude a and full phase C = ( (O.t + 9 ) would3no longer remain constant but would be determined by equations (31).(Note that the case of resonance is not discussed here). Once solvingequations (30) (31), we can obtain the frequency (O.(a), the generalizedIcoordinate C(t), the deflection function Wl(xi,t) and other quantities.4. NUMERICAL RESULTSTo demonstrate the effect of flooding water, computation of a cantileverbeam system was carried out for (Fig. 1)E = 5.025x108 ~/m' ; Ll=9m; ~ - , = l m ; b = l m ; h*=0.2m ; D = (l-rs/r-)h* = 1.6xl0-~ m; p = 920 kg/m3; po = lo3 kg/m3; g =9.807 m/s2; h(x2) = ax2: a: A function of initial velocity VO.Assuming that for each part of the beam the deflection is expressed asfollows :

From the connected conditions we have the [PI matrixWith the translational vector (T) = [T1,T2lT = [ -3.5767E-5, 9.5253E-3 ]^and initial conditions W(0) = Wo, dW(O)/dt = vo , the following solutionsare obtained by three different approaches from the governing equation(27) with small parameter 6:(i)The solution of unperturbed system:For unperturbed system (without flooding water effect), which is governedby equation (28), the solution isWith initial conditions W(0) = 1.6x102 m, dW(O)/dt = 0, constants a and ca redetermined by following equations for CO0 1Combining equations (16) and (la), equations (32) gives the deflectionfunction for each part of the beam.(ii) The first approximation:The solution of equation (27) will be different from that of unperturbedsystem because of existence of term - E Fr (perturbing force). For thefirst approximation,we assume that the term -EF will only influence theamplititude a and the full phase C = ( CO,t + 0 ).solution of the following form for the perturbed system:Therefore, we have aCs(t) = (ps(J) a cos c(s = I, 2, . . . , n-3)where, a and c are determined by equations

In this case, the solutions close to the first order natural frequency COolare( 0 (a) = COO + E Bl(a)The solutions close to the second order natural frequency(0 arewhere constants Sll,S12 and SX,S22 are determined by initial conditionsW(0) = 1.6xl0-~m, dW(O)/dt = 0.(iii) the second approximation:Differing from the first approximation, in the second approximation weassume that the term - E Fr not only influences the variables a, andC = ( CO.t + 9) but also produces the particular solution us(1) (a,c).Therefore, we have a solution of following form:ts(t) = vS(j) a cos((0.t t 9) + & (a, (0.t + 9)Here a and C are determined by equationsII(5, j = 1, 2, . . ., n-3)In this case, the solutions close to the first order natural frequency COO]are

wherea = Siland c = [COO + Bi(a) E + B2(a) E2 I t + St2The solutions close to the second order natural frequency COO arewhere constants Sn,S12 and Szl,S22 are determined by initial conditionsW(0) = 1.6~10"~ m, dW(O)/dt = 0.Table. 1 shows the frequencies for three different approaches, andFig. 2 and Fig. 3 show both the deflection W(xi,t) and the momentM,(xi,t)for the entire beam by the method of the first approximation (theline with squares), the second approximation (the line with prisms) or theunperturbed one (the slid line), respectitvely.TABLE. 1 The Natural frequencya = 0.5 I The Unperturbed I The First 1 The SecondE = 0.011428 I System I Approximation 1 Appproximationw-0005w0 005-0 015 -0,005-0 025 -0 015-0 035 -0.0250.0 2.0 4.0 6.0 8.0 10.0 XFig 2 (a) The 1st-order deflection0.0 2.0 4.0 6.0 8,O 10.0 XFig.2 (b) The 2nd-order deflection

00 2.0 4,O 60 8.0 100 x 0.0 20 4.0 6,O 8.0 10,O XFig,3 (a) The lit-order momentFig.3 (b) The 2nd-order moment5. CONCLUSIONS(1) The flooding water effect depends very much on the parameters OC and Ein the frequency domain and the dynamic behavior of the beam system.(2) The flooding water influnces the shape and the phase for both of thebzam deflection and moment. The higher the frequency is the moresignificant the influence is.(3) There is no special effect for the deflection or for the moment at theflooded end of the beam.REFERENCE[I] Luk, C.H. (1988). A Three-Dimensional Plasticity and Momentum Model forShip Resistance in Level Ice, ASME 7th International Coference onOffshore Mechanics and Arctic Engineering, Houston, February.[21 Bogoliubov, N.N. and Mitropolsky, Y.A. (1961). Asymptotic Methods in theTheory of Non-Linear Oscillation, Hindustan Publishing Corp., Delhi India.131 Thomson, W.T. (1981). Theory of Vibration with Application,2nd Ed.,Prentice-Hall Inc .[41 Kerr, A.D. (1986). Response of Floating Ice Beams and Plates with PartialFlooding, Ice Technology. Proceedings of the 1st International Conference,Cambridge, Mass. USA, June.[S] Peirce, T.H. (1978). Arctic Marine Technology: A Review of Ship Resistancein Ice, The Royal Institution of Naval Architects.

THE MEASUREMENT OF "ELASTIC COEFFICIENTS" OFBOHAI SEA ICE UNDER UNIAXIAL COMPRESSIONShen, WuP:ofessorLi, Guang-WeiEngineerLiu, Chun-HouEngineerDalian University of TechnologyDalian, Liaoning, 116024, ChinaDalian University of TechnologyDalian, Liaoning, 116024, ChinaBohai Oil CompanyTianjin, ChinaABSTRACTIn order to solve the problems associated with ice-resisting oil platformsin Bohai Sea, following measurements of "elastic coefficients" under uniaxialcompression for sea ice of Liaodong Gulf were performed in laboratory. The testcontents invo1ve:using different ice (single layer and multi-layerice),whichcollected from different sea regions, at different temperatures(268, 263, 258K),under different strain-rates(~=l.~xl~~, 7.5x104, 5.0x104, 2.5x10~,1.0xlo5 sl). The measured "elastic coefficients" are: En- the initial tangentmodulus of origin of stress-strain curve; E o.the secant modulus of stress-strain curve corresponding to the half of ultimate stress; P I, ~2-the strainratios between the strains in transverse columnar direction and columnar di-rection respectively and the strain in loading direction.The results of different measuring conditions were compared mutually. Itwassatisfactorily found that the "elastic coefficientsl'vary regularly with thetest temperatures and strain-rates, and that coefficients differ from e achother for different collected regions of ice and orientation of specimen.The project supported by National Natural Science Foudation of China.1. INTRODUCTIONThe regions of Liaodong Gulf of Bohai Sea are rich in resource of petroleum.In order to exploit this resourse, it is necessary to built various offshorestructures there. Since these regions are frozen in different degree everywin-ter, and the freezing period generally lasted three months or over, the iceload is the most important controlling load in the design of the offshore sttuctures.The physical and mechanical properties of sea ice are the main parame-ters for determining thp ice load. Therefore, since 1984, the Research Divi-321

sion of Ice Mechanics of Dalian University of Technology(DUT) had been mea-suring following physical and mechanical properties of sea ice:the ice cry-stalline structure, salinity, flexural strength, fracture toughness, creepproperty, uniaxial tension and compression strength as we11 as their sensiti-vity to strain-rate, etc. Early in 1988, DUT cooperated with Bohai Oil com-pany(B0C) to measure above ice properties for different sea regions of Liao-dong Gulf of Bohai Sea in laboratory. These data provide important basis forthe investigation of constitutive theorem of sea ice and the design of off-shore structures of Bohai Oil Field. This paper only introduce the measure-ment of elastic modulus and lateral deformation coefficients of sea ice withdifferent strain-rates.The "elastic coefficients" discussed in this paper is defined as the elas-tic modulus and strain ratio measured in laboratory by short term experimentand using static method. To measuring elastic modulus of ice under uniaxialcompression is difficult. The main difficulties are that the stress- straincurve varies considerablly and it is very sensitive to the strain-rate ( orstress-rate) and ice temperature, and that it is difficult to obtain obviouslinear elastic stage. Sinha (1982) had performed the measurement under cons-tant strain-rate and stress-rate. Hedefined the initial modulus as following:it is thesecant modulus between the origin and the point on the initial st3ge corresponding to stress level 0 =0.5 or 1.0 MN m 2 and denoted resp eclively by Eor or El,,. The result show that they increase with an increaseof the rate. J.A. Richter (1984) reported the work of measuring initial tan-oential modulus under uniaxial compression, she verified the following con-clusion pointed out by Mellor (1983):the reliable initial tangent modulusmay be obtained only after the longitudinal strain of guace length stage sec-tion on the ice sample had been measured. These results also expressed thatE, increases with the strain rate. According to the non-linear property,Sin-ha(1986) proposed to replace the general Young's modulus (he ca1ledit"effec-tive modulus") with the deformation modulus, and proposed to take the nameof failure modulus, E - uf/ef, which is useful in engineering practice, hereof and Eare respectively the stress and strain corresponding to failurepint. Frederking and Timco (1988) also deem that two moduli can be defined, atangent modulus, E , which is tangent to the stress-strain curve at a parti-cular point, and a secant modulus, E , drawn from the origin to a particularpoint. The secant modulus to the failure point ( ef, a ) is refered to as theffailure modulus. They deem that the failure modulus E is a good approximationof the average tangent modulus and reflects the intrinsic stiffness of theice,i.e. temperature, grain size, etc. The values of Ef scattered in a rangefrom0.9 to 8.3 GPa, it also possess a tendency of increasing with strain rate. Ac-cording to international suggestion standard which laid down by Schwarz eta1

(1981), the authors performed uniaxial compression test for cylinderical icesamples and directly measured deformationof the guage length stage of icesam-pie by extensometers. From the plot two moduli can be defined, aninitialtan-gent modulus, En, which is obtained from the slope of the longer or shorterinitial straight line stage, and a secant modulus, E , which is obtained fromthe origin and the point corresponding to half failure stress, it is referredto as half failure modulus E The results presented that, E and E 0.5funder different conditionshave obvious sensitivity to the temperature and-in-rate, they scattered in the ranges of 1.6310.65 and 0.86-6.80 GPa formul-ti-layer ice, 1.75 - 9.66 and 0.72 - 5.47 GPa for single-layer ice respecti-vely. The reasons of taking half failure point are: 1) When the deformationof sample reached to this point, the sample had appeared internal cracks andentered an obvious expanding stage (non-linear stage). 2) the authors refer-red to the concrete standard, for the concrete and ice have similarities.By comparing the result in this paper with the materials collected byLaineyand Tinawi (1984), it may be seen that: the result in this paper is conside-rably differ from Butkovich's (1956~59) result; and E E in thispaper areY'close to the regressive result obtained by Hausler (1981), but E is obviou-sly different from it. (in this paper, E is a little greater than E ). Theauthors had compared the modulus E k f calculated from the nominal strainbe-tween the upper and lower board mats with EOsf, and discovered that Ebr,isless in one order than E 05f This comparison more clearly shows that calcu-lating the Young's modulus must use the sample deformation in gauge lengthstage. Owing to the ambiguous of Young's modulus of ice under uniaxial com-pression, many experts used the flexural experiment,itwill be discussedlater.The lateral deformation coefficient is generally called Poisson's ratiowhen the deformation is within elastic stage. Owing to the non-linearproper-ty of stress-strain curve in many cases, it is also called strainratio,whichis defined as the ratio of lateral strain to axial strain of the sampleinthesame gauge length stage. Inoue et.a1.(1988) investigated the strength and st-rain ratio of Antarctic sea ice under uniaxial compression, and obtained thestrain ratios, pf , correspondidng to upper yield point or failure stress,andpo5, corresponding to half upper yield stress, the results express obvioustime effect, i.e. possess sensitivity to strain-rate. Murat and Lainey (1982)obtained the Poisson's ratio by measuring the surface lateral and longitudinalstrain of the simply supported beams loaded at two points as pure bending,theresults also express the sensitivity to temperature and stress-rate. In thispaper, the authors use piand p2 to signify the strain ratios correspondingto half ultimate stress (112 0 ) or half failure point for transverse colum-nar direction and columnar direction respectively. The results listed in thetables denote that the \ii is 2 - 4 times greater than \i^.

2. COLLECTION, STORAGE, TRANSPORTATION OF ICE BLOCKS AND PREPARING OF ICESAMPLESFrom Jan. to Feb. 1988, ice breaker sailed two times in Liaodong Gulf ofBohai Sea, and collected ice blocks from five regions, A, B, C, E, F (Fig.1).Figure 1. Map of ice collecting points in Liaodong Gulf of Bohai SeaThe dimensions of ice blocks are 50 cm x 30 cm x natural thickness(cm), thenatural thickness is about 30 cm in B, C, E regions, but is about 50 cm in A,F regions. The ice blocks packed in the plastic bags and stored in the refrigerators(at a temperature of -20 "C) in the breaker. After the breaker cartedanchor on the wharf, the plastic bags were put into wooden boxes andtransportedimmediately by a refrigerated car to the cold storage of laboratoryof DUT and refrigerated with the temperature lower than -15 OC. On the way oftransportation, there was brine drainage a little, but after stored underthistemperature, there was no longer brine drainage. The ice specimen generallywas prepared within 48 hours before a test. The ice blocks first were cut to120 mm x 120 mm cubes by saw in accordance with the requirement of test, andthen were cut into cylinderical form with a diameter D = 100 mm and length L= 250 mm on the C620 lathe. The processing quality of cylindrical specimenswere checked in cold storage. The specimen which had been finished packed inplastic bags and sealed well in order to avoid sublimation. Twenty four hoursbefore lest, the specimen was put into constant temperature refrigeratorwiththe same temperature of test, in order to ensure the required temperature fortest.3. THE CRYSTALLINE FABRIC, DENSITY AND SALINITY OF ICE

The authors undertook the measurement of crystalline fabric and grain sizefor the ice on the breaker (at midnight in order to utilize the lower temperature)and in the cold storage of DUT respectively according to followingprocesses: the thin pieces of ice were cut from ice blocks in accordancewiththe orientations of longitudinal (perpendicular to sea surface) and transversal(parallel to sea surface) directions respectively; the pieces were groundto 0.5 mm in thickness and attachedto aglass slide; then put it in a rectangularpolarized scope to survey. It was found that in B, C, E regions,theicecrystalline structure in upper layer (about 7 cm in thickness) appeared asgrained ice, but the ice crystalline structure of lower layer appeared as columnarice. The crystal grains increase in average diameter with the increaseof distance from upper surface, the average diameters are from 7.0 to 9.0mm.According to Michel's classification method the ice in these regions is calledsingle-layer ice. In A, F regions the ice crystalline structure appearedas alternative fabric of granular and columnar ice layers, every layerisabout3--5 cm in thickness, and the diameters of grain are 2.0 -- 2.5mm.Theicein these regions is called multi-layer ice according to above classification.In order to obtain the densities of sea ice, the measurement on diameter,height and weight for every specimen was undertaken as soon as the specimento be prepared well. The averase densities of the single-layer ice is 0.769- 0.837 g/cm3, and the multi-layer ice is 0.796 - 0.840 g/cm3. The salinitiesof the single-layer ice is 4.924 - 8.052 %o, and the multi-layer ice is2.170- 9.300 %ã4. EXPERIMENT SYSTEMAll of the uniaxial experiments were performed in the cold chamber of ZDMK300 kN low temperature test machine, the controlled sensitivity of temperatureis  0.5 'C. Before test, the ice specimen was put in the constant temperaturerefrigerator and keep the temperature as testing temperature at least24 hours, the controlled sensitivity of temperature is also  0.5 'C. TheYJY- II:ype and YZU type extensometers (i.e. displacement transducers) were locatedon the specimen for measuring the longitudinal and lateral strainsrespectively.The YHD-50 displacement meter was used to control the strain rate. ABHR-4 type load transducer was installed between the upper mat and the loadingend of test machine for displaying loading values. These transducerstransform the physical quantities of load and displacement to the electricsignal,which leaded out from the cold chamber through connecting terminals toDY-15 type dynamic strain indicator, then input to LZ3-204 type X-Y recorderin order to plot various curves, at the same time, input to data acquisitionsystem of APPLE-11 type mini-computer for real treatment or store.Before tes-

ting, the output values of every transducers was calibrated by using TENS0type displacement calibrator in a corresponding temperature condition whichthe test required. In addition, during calibration, two displacement transdwcers which connected abreast in order to eliminate the eccentric effect.Whentesting, above mentioned transducers were installed symmetrically on both sidesof ice specimen to measure the longitudinal displacement Ax (x definedasthe loading direction). Two transdusers should be used to measure the deformationsof Y and Z directions (Y and Z defined as the directions perpendicularand parallel to the columnar axis of ice crystal respectively), thus, twostrain ratios pi and ~9 may be obtained. After AID transformation, all theinformationsof data were acquisited and stored by mini-computer, at the sametime to plot P - Ax, P - Ay, P - AZ, Ax - t curves by X-Y recorders.5. MEASURING CONTENTS AND RESULTSAccording to object of investigation the authors performed the uniaxialcom-pression test for the following three cases: 1) The horizontal compressiontests (loading direction parallel to the sea surface), which are identicalin strain-rate ( ?= 5.0 x 10sl), but are different in temperatures; 2) Thehorizontal compression tests which are identical in temperature (T = 263 K),but are different in strain-rates; 3) The compression tests in two directions(horizontal and vertical), but under same strain-rate ( = 5.0 x 10-~s-' ) andsame temperature (T = 268 K ).From the slope of initial straight stage of o- E curve, the initial tangent modulus was obtained and denoted by En. Fromthe straight line connected the origin with the point corresponding to 1/20( a is failure stress), the secant modulus was obtained and called half fai-lure modulus, it is denoted by EOsf. The results demonstrate that both Eoand Eo.5f possessing the sensitivity to strain-rate. In addition, the resultsdisplay the following facts: For the single-layer ice, the tangent modulus En= 3.96 GPa when the test temperature T = 263 K and subjected to horizontaldi-rection compression with strain-rate & = 1.0 xs! When the strain-ratedecreases, the value of En only decreases a little, from 3.96 GPa reduces to3.74 GPa, and Eo.5f increases a little, from 2.37 GPa raises to 2.82 GPa.Butwhen the strain-rate decreases to 2.5 x lo-' s-I, Eo and EOssf reduces to 2.87GPa and 1.56 GPa respectively. When the strain-rate continuously reduces toless than 2.5 x s-I, Eo and Eo. have no considerable variation. For themulti-layer ice, when under same test temperature and loading conditions, andwhen the stra~n-rate in the range of k = 1.0 x l~-~s-l- 2.5 x ~o-~s-', both Eoand Eo.5f have no various variation only increase or decrease a little. How-ever, when the strain-rate reduces to 1.0 x 1 0 s En ~ decreases rapidly to2.72 GPa, and Eo.5f, decreases to 1.05 GPa(see Table 6).

Table 1. The measured values of moduli by using different methods (multilayersea ice, diameters of grain: 2.0 - 2.5 mm, average densities:0.796 - 0.840 g/cm3, salinities: 2.170 - 9.300 %,. T=263 K).Note: 1) E unit in GPa. 2) The unit of strain-rate is in s-l.3) Each column represents the data from one specimen.- The half failure modulus calculated from the relative dis-4, E"5fplacement between upper and lower mats.Table 2. The values of moduli E under identical strain-rate (~.ox~o-~s-')but in different temperatures (single-layer sea ice, average diametersof columnar crystal:7.0 - 9.0 mm, average densities:0.769- 0.837 g/cm3, salinities:4.924 - 8.052 %,. horizontal compression),E unit in GPa.Temperature] 268 K (-5OC) 1 263 K (-1O0C) 1 258 K (-15'C)ModuliAverage 1 2.42 2.04 1 3.74 2.82 1 6.33 4.24Table 3. The valued- f strain ratios PI and under identical strain-rate= 5.0~10 's- but in different temperatures (single-layer sea ice,horizontal compression).Average 1 0.25 0.06 1 0.26 0.06 1 0.36 0.19In order to inquire about the difference of moduli obtained from nominalstrain and guage-strain respectively, at the same time the authors measuredthe relative displacement between upper and lower mats to obtain the nominal327

Table 4. The values of moduli E in identical temperature T = 263 K but underdifferent strain-rates (single-layer sea ice, horizontal compression),E unit in GPa, strain-rate unit in s-'.StrainrateModuliAverageTable 5. The values of strain ratios p;and \i^in identical temperature T =263 K but under different strain-rates (single-layer sea ice, horizontalcompression), strain-rate unit in s l .StrainrateStrainratiosAverageTable 6. The values of moduli E in identical temperature T = 263 K but underdifferent strain-rates ( multi-layer sea ice horizontal compression),E unit in GPa, strain-rate unit in s .V5f5.69 2.752.11 1.08Moduli 8.47 2.505.65 2.82- -- -Average 15.48 2.29half failure modulus E b f . The results show that E b f is far less thanEorr about one order of magnitude (see table 1).From the ratio of longitudinal strain to two lateral strains correspondingto 1/2o the strain ratios pl and pzwere obtained (Y and Z direction resm

Table 7. The values of strain ratios pi and p; in identical temperature T =263 K but under different strain-rates (multi-layer sea ice, horizontalcompression), strain-rate unit in s .StrainrateStrainratio1.0 x l o37.5 x lo4 I 5.0 x lo4 ' 2.5 x lo4I I I I IPl P2 V\ P2 Pi P2 PI P20.21 0.11- -- -0.46 0.220.17 0.070.17 0.140.09 0.030.11 0.07- -0.34 0.100.17 0.120.14 0.101.0 x lo5Average 10.21 0.11 10.27 0.14 10.10 0.05 0.22 0.11 10.25 0.21PiP20.26 0.21- -- -Note:Owing to its features of multi-layer sea ice, it is difficult todistinguish the columnar direction of ice crystal, only by comparingthe values of strain ratios while the smalleronewill be p->.Table 8. The values of moduli E and compressive strength om in identicaltemperature T = 268 K and same strain-rate t = 5.0 x 104s1 butunder different compressive directions (multi-layer sea ice).Compressive 1horizontalverticaldirectionModuli andcompressivestrengthAverageTable 9. The values of moduli E and compressive strength of single- andmultilayersea ice in identical temperature T = 263 K , same strain-rate= 5.0 x 10^sland under same horizontal compression.~ c type e1 single-layer Imulti-layerModuli andcompressivestrengthAveragepectively). The results show that is about 2 - 4 times greater than P2The chief reason for using the lateral deformation corresponding to 112 oto measure the strain ratio is that the deformation of sea ice in initiallinear stage is very small, so that, the transducer can not reach required

e 10. The values of moduli and compressive strength of single- and multilayersea ice in identical temperature T = 263 K, same strain-ratek = 1.0 x l ~ s and - ~ under same horizontal compression.Ice type 1 single-layer 1 multi-layerModuli andcompressivestrengthEo (GPa) Eo. 5f (GPal3.965.304.262.952.592.382.412.64om(MPa)4.443.152.755.06En (GPa) Eo. 5f(GPa)5.692.118.475.652.751.082.502.820 ,,,(MPa)3.243.064.812.17Average4.122.513.855.482.29 3.32accuracy.All the results of En, EOQ, band pnare listed in Tables 1 - 10.6. CONCLUSION AND DISCUSSION6.1 For the initial linear elastic stage of stress-strain curve of ice underuniaxial compression is very short and rapidly curved with decreasing slope,so it seems that using the half failure modulus Ensf to express the elasto-plasticity of sea ice is reasonable.6.2 Both the "elastic moduli" Eo and EO5,: of sea ice possessobvious sensi-tivity to temperature, the values increase with the decreasing in temperature.6.3 The values of ultimate stress and moduli En and E5ffor the horizontaland vertical directions measured in laboratory are very close to each other,and are identical with the results measured in field. This does not conformwith the usual recognition on the mechanical properties of columnar crystalice. The causes will be a pending question to be investigated further.6.4 The data of strain ratiop and p were scattered slightly, and thereare1 2no regularity of variation. From the average value, plis about 0.3 andu2isabout 0.1.7. ACKNOWLEDGEMENTThe author express heartfelt gratitude for the supports of BOC, engineerZhang Tao participated in a great number works from beginning to end. In themeantime, the authors are also deeply grateful to following colleaguesofDUT,they are: associate professor Li Hongsheng, engineer Sun Xiutang, Liu Weibo,engineering master Yue Qianjin, associate engineer Ping Xugao, Chang Cheng,Peng Wei, they supported this work with all their strength. The authors thankespecially technician Li Lun, he always kept the cold storage in agood state.

8. REFERENCESFrederking,R.M.W. and Timco, G.W. (1983). On measuring flexural propertiesofice using cantilever beams, Annals of Glaciology, 58-65.Frederking, R.M.W., Timco, G.W., Jeffries,M.O. and Sackinger, W.M. (1988).Initial measurements of physical and mechanical properties of ice from Hobson'sice island, IAHR 9th Int. Sym. on Ice, 1, 188-198.Inoue, M., Yamaguchi, Y. and Ebinuma, T. (1988). Mechanical properties of antarcticsea ice, IAHR 9th Int. Sym. on Ice, 1, 162-176.Jeffries, M.O., Sackinger, W.M., Frederking, R.M.W. and Timco, G.W. (1988).Initial mechanical and physical-structural property measurements of old seaand brackish ice from Wand Hunt Ice Shelf, Canada, IAHR 9th Int. Sym. onIce,1, 177-187.Lainey, L. and Tinawi, R. (1984). The mechanical properties of sea ice-A compilationof available data, Canadian Journal of Civil Engineering, Vol.ll,4, 884-923.Mellor, M. and Cole, D.M. (1982). Deformation and failure of ice under constantstress or constant strain-rate, Cold Regions Science and Technology,5, 201-219.Mellor, M. (1983). Mechanical behavior of sea ice, U.S. Army Cold RegionsResearch and Engineering Laboratory, Monograph 83-1.Richter, J.A. (1984). Static determination of Young's modulus in sea ice,Cold Regions Science and Technology, 9, 283-286.Schwarz, J. (Chairman), Frederking, R., Gavrillo, V ., Petrov, I.G., Hirayama,K.-I., Mellor, M., Tryde, P. and Vaudrey, K.D. (1981). Standardized testingmethods for measuring mechanical properties of ice, Cold Regions Scienceand Technology, 4, 245-253.Sinha, N.K. (1982). Constant strain- and stress-rate compressive strength ofcolumnar-grained ice, Journal of Materials Science, 17, 785-802.Sinha, N.K. (1986). Young arctic frazil sea ice: field and laboratory strengthtests, Journal of Materials Science. 21, 1533-1546.

PLANE STRAIN FRACTURE TOUGHNESS KIcOF SEA ICEZhang Mingyuan,Meng Guanglin~Yan Decheng.Yu YonghaiInstitute of Marine EnvironmentalProtection, SOA, Dalian, China.ABSTRACTIn this text, a test item in small scale is narrated. Researchof the said test is chiefly to determine the fracture toughnessof sea ice. The range of plane strain fracture toughnessK c obtained through measuring in the test is 11-77 KN/m3I2andthe average value is 32 rn/m3l2. It is obtained from the testresult that there is a close relation between the fracture toughnessof sea ice and the loading speed, ice crystalline particlesand test temperature of sea ice. These factors rather greatlyaffect the critical value of stress strength factor KIC .The result indicates that the KIc value presents that when loadingspeed increasee, KIC value decreases and when temperaturerises, KIC value also decreases.1. THEORECTICAL BASIS OF KIc TESTIn fracture mechanics, looking in a microscale, it can besaid that when the normal tension load exceeds the bound strengthbetween atoms, crack begins to spread. When tension exceedsB critical value, a crack begins to develop. Commonly acritical stress strength factor K., is used to describe thiscritical value state. KIc is the measurement of the capacity ofa materiel to prevent the development of loss of stability dueto cracking.As early as in the year 1920. ~riffith" assumed that whenthe strain energy releasing rate came up to or exceeded the criticalenergy equal to the energy needed to form a new crack,

(41cracks begun to spread, For ty years later, Orowan'-^-'and Irwinsuggested that for sticky materials, the value of work aasociatedwith crack spreading should be equal to the sum of thework due to surface energy and plastic and uiscous, that iswhere,dF = dw-du : dw = work done by external force;du = variation of strain energy; G = strain energyreleasing rate; dc = increasing amount of crackdevelopment (original crack length = 2c); = surfaceenergy; p = work associated with the plastic andviscous flow.Releasing rate of crack body strain energy G is with relationto stress intensity factor KIc .for plane stress (2)G =2(1-v )E for plane strain (5)Irwin ^ has put forward the famous crack end stress, approximateexpression of displacement field and famous concept ofstress field strength factor thus to enable the analysis ofcrack end stress and displacement field to render with mathematics.As crack development strength is the concept obtainedon the base of analysis of energy, it has the meaning of universalapplication. It thus lays down the theorectical basis forfracture mechanics.Fracture mechanics is a new and developing science developedonly in recent ten of twenty years. At the beginning, it hasbeen used for materials such as metals and concrete etc. andrather late on sea ice. Internationally, in the year 1963, Gold,L.W. '-'-'used thermal shocking method to form ice crack on an iceplate beginning the study of ice fracure mechanics. Liu, H.W.and Loop, Spew. published an article "Fracture Toughness ofFresh Water Ice" obtaining the result that KIc increased withthe decreasoment of test temperatures and loading rates. In theyear 1977, Goodman of England mad a measurement on creep rupture

of river ice of sea ice and surface strain. In the same year,Vaudrey of America also made certain work on fracture ice engineering.In the year 1979* Hamaza of canadaL6] published planestrain fracture toughness (KIc) data of fresh water ice. In theyear 1980Ã Urabe* N et a1 of Japan also published an article ofsea ice fracture to~ghness'~). In our country, study of applicationof fracture mechanics to sea ice is more less. In theyear 1986, in the 5th Offshore Mechanics and Pole Region Engineering(OMAE) Symposium, Shen Wu et a1 published the paper of"Fracture Toughness of Bonal Bay sea ice (81.2 MEASUREMENTS AND TEST METHODMeasurement and testing of fracture toughness KIc is theearliest studied parameter of fracture mechanics and are themethod developed rather maturely. In the year 1981* AmericanSociety for Test Materials (ASTM) issued E599-81 "Standard TestMethod for Plane Strain Fracture Toughness of Metalline Materials."^At present, many countries hare adopted 8399-81 as standardtest method. In the year 1978, our country issued the firststandard test method of the Ministry of Metallurgical Industry.American E599-81 latest standard test method is basicallyadopted for this method.2.1 Form of the Test Sample.There are two kinds of standard test samples often used forsea ice : a ?-point bending beam and a compact tensile testpiece. The 3-point bending beam has been adopted for thistest, because it has several advantages: 1) test installationis simple and our present equipment can be utilized; 2) the compncttensile specimen is inconvenient to process and also difficultto centre, but there is no such problem on 3-point bending;3) since the important character of 5-point bending testsample is the stability of BE'*~(l-a/w)~ making the 3-pointbending test sample specially advantageous in the analysis ofJ integral. The 3-point bending test sample is shown in Fig.1-

Fig.13-point Bending Test Sample2.2 Preparation of Test SampleIn order to maintain the ice sample in the state of naturalcondition and not to be affected by external factors, we havechosen an in-situ test method. On January, 1987. site measurements and test on sea ice plane strain fracture toughnesswas carried out on coastal sea area of Ea Yu Quan a t LiaodongEay, Laboratory facilities was established at the pool side ofNew Port of Ea Yu Quan and test samples were taken from Fortpool. Refer to Pig.2 for the location.Pig.2Location of SamplingThe time of sampling was chosen at the period of flourishingice. At that time. ice in the Fort pool was 40 cm and more inthickness. Simultaneously, ice temperature, salinity, density

nnd ice crystal structure were also measured this is not possible,or to make out a basical assurance to ensure the qualityof test.In total have three series of original ice been chosen forthis, all of which were flat fast ice in the Port pool, whichwere separately marked with Pn7-., , F87-2 and No.P87-lice was of rather small ice crystalline particles with diametersof 3nun. NO.P~~-~ and P ice were of ice crystalline particles,87-3which were a little bit bigger than the ice particle of p87-1and about 5mm. When preparing ice samples, a gas saw and electrichand saw were firstly used to cut the original ice from theice plate later an electric disk saw was used to meticulouslyprocess big pieces of ice to standard test samples. The size oftest sample was 10X10X60 (cm3). Bach series of test sample included5 pieces. The test samples processed into shape were putinto a low temperature refrigerator for freezing for one day ormore to have them sufficiently frozen to attain equilibrium temperaturefor test use. Before testing, the single side notchwith depth a, thickness W, width B, span L, span height ratioL/W,a/W were carefully measured. After completion of measuring,test was then carried out according to E399-81 method.i912.Hest Instruments and EquipmentThis test was carried out on the sea ice pressure test machinemanufactured by Marine Instruments Research Institute. The machinewas equipped with load sensor suitable for automatic recording*Model ZW-11 displacement meter, x-y function recorderand ?pen recorder etc. First, electric quantity of load quantitywas amplified via mechanical resistor strain gage and thenmade input into the recorder to make the curves of ram speed v-t,load quantity p-t and pressure-deformation p-v. This instrumentis reliable and rather superior in consecutive automatic recording.3 TEST RESULTS AMD DISCUSSION, 1.5x10 ,In this test, 6 kinds of loading speed 2.4~102.5~10"~, 4.5~10-\ 7.6~10""' and 2.8~10"~ cm/s and 5 kinds oftemperature (267,263,261,255 and 248k) have been used. The tests

where made on 3 kinds of ice of different type and a total of130 test samples have been made.The value of plane strain fracture toughness KIc was calculatedwith the following formula 191 ;wherePO - maximum fracture loading ascertained in experiment (N):B - thickness of test sample (mm) : S - span of inflection support(mm) : W - higth of test sample (mm) : a - length of crack(mm)The waximum valve of KIc obtained through measurements andtest calculation, is 83~~/m^~ , minimum value is 7XN/m3I2 andmost of them are between 20-40m/m~'~ . As to test result, seeTable 1 for details the value in the Table is the average valueof 5 data.Table 1 Plane Strain Fracture Toughness of Sea IceRam speedS B g S W S B W B E 040 B 0( cm/s S M Y Y

The values of plane strain fracture toughness KIC of sea iceobtained in this test is basically in conformity with KIc valuesmeasured and tested by foreign countries and is smallerthan the KIc value of fresh water ice. L~~Analysis and discussion are made on the result of test asf 01 1 ows :"'1.1Requirement of Test Sample SizeIn order to satisfy the condition of plane strain and hope toobtain a vacid and stable plane strain fracture toughness KKon ice, requrement for size of thickness E, length of crack aend width of tough belt (W-a) is7.2 Relation between Sea Ice Plane Strain FractureToughness KIc and Sea Ice TemperatureOther investigations shows that there exists a relation betweensea ice plane strain fracture toughness KIc and sea icetemperature. Within certain limits, the lower the sea ice temperatureis, the greater the sea ice fracture toughness KIcbecomes (see fig.3). This kind of relation is similar to thatfound between compressive strength of sea ice and temperature.When the temperature is lower than a certain valve, this relationis no longer in existence and when the temperature decreaseseven more, the strength is also decreasing. '6J It is foundfrom individual datum that some of them is not completely inconformity with this condition, which we consider is caused bythe ice sample itself being not too similar.

Fig.?Relation between Sea Ice Temperaturet and KT,,7.7 Relation between KIc and Ham SpeedThis investigation shows that the slower the ram speed. thehigher the value of sea ice fracture toughness KIc . see Fig.4.However. there la an exaeption. which la similar to the conditionof temperature mentioned above.Deformation Speed ( cm/s )Fig.4 Relation between Deformation Speed and KE339

'5.4 Relation between KK and Size of Ice Crystalline Particle.From the tests, it is also possible to sag that under thesame condition, there appears quite different values on thefracture toughness. In general, when temperature and loadingspeed are all the same, for big ice crystalline particle, thereappears a rather great fracture toughness value. Fw-, havegranvar ice with particle diameter 5mm, Fa7^ and F87-5 arecolumn shaped ice with particle diameter 'jam, the value ofFen and obtained through measuring is greater than thatF87-17.5 Problem of Orientartion of Crack Plane.Fracture toughness of materials that is anisotropic usuallyis concerned of the orientation of crack and direction ofspreading. An anisotropic material is concerned with the directionof mechanical processing or variation of crystalline particle.In this test, the direction of the notch of test sampleis perpendicular to the direction of sea level and parallelwith the direction of the growth of ice crystal. This kind ofcut ice is easy to crack causing the value obtained throughmeasuring from it to incline to a little bit small. If the notchis perpendicular to the direction of the ice crystals, thevalue obtained through measuring will be a little bit greater.Sea ice is an anisotropic body, because the thickness of iceonly 40crn~ therefore only the former condition has been measuredand as to the later one, on account of the measure of icethickness being not long enough to make test sample, it has notbeen measured.4 CONCLUSIONS4.1 The limit of plane strain fracture toughness KIc obtainedthrough measuring in this test is 11-77KN/m3/* and theaverage is 32KN/m3/2 .4.2 Within certain limits, KK increases with descending ten>perature.

4.3 KIP increases with decreasing of ram speed.5 REFERENCES1 ) Chen Chi et al, Engineering Fracture Dynamics (Volume One),1977, National Defence Industry Publishing House, 290-296.(2) Griffith, A. A. 1924, Theory of Rupture, Proc of the 1stInternational Congress for Applied Mechanics, Delft. 55-63.(3] Oroman, E. 1950, Fatigue and Fracture of Metals, PROC. MIT.SYMP.* 139.(4) Irwin, G.R., Analysis of Stresses and Strains near the Endof a Crack Transversing a Plate* J. App. Mech., Vol.24, N3,1957, 361-564.151 Gold, L. W., Crack Formation in Ice Plates by Thermal Shock,Can. J. of Physics, Vol.41 , 1963, 1712-1728.16) Hamza, H. and Muggeridge, D.E., Plane Strain Fracture Toughness(KIc) of Fresh Water Ice POAC 79. Vol.1, 1979, 697-707[7J Urabe, N., et ale Fracture Toughness of Sea Ice Cold RegionsScience and Technology* 3, 1980 pp. 29-37.(8] Shen, W. and Lin, S.Z., "Fracture Toughness of Bohai BaySea Ice", Proceedings of 5th International Symposium on OffshoreMechanics and Arctic Engineering, 1986, Vol. IV, pp.354-557.(9) ASTM, Standard Test Method for Plane Strain Fracture Toughnepsof Metallic Materials. Annual Book of ASTM StandardsE399-81, 1981 , 592-622.(10) Parsons, B-L. and Snellen, J-B** Fracture Toughness of FreshWater Prototype Ice and Crarbamide Model Ice POAC85V01.19 1985, 128-1 57.

ON A FINITE ELEMENT MODELFOR FREEZING AND THAWING SOILSK. AxelssonProfessorS. KnutssonAssociate ProfessorB. NystrBmGraduate StudentD. ShengGraduate StudentDepartment of Civil EngineeringLuleA University of TchnologyS-951 87 LuleiSWEDENABSTRACTThe paper presents a programmed finite element model for two-dimensionalfreezing and thawing problems in soils. The phase change has been implicitlyaccounted for by the means of an apparent heat capacity and an effectivethermal conductivity. This does not only take into consideration thetemperature-dependency of the thermal properties, but also the latent heatreleased at the freezing temperature. Comparison between numerical results,analytical solutions and laboratory tests are also provided in the paper.The comparison shows that the finite element model gives satisfactoryestimation of the phase-change depth and temperature distribution, even forlarge values of the latent heat.1. INTRODUCTIONNumerical difficulties to model the freezing and thawing procedure insoils are encountered when the phase change is taken into consideration.Firstly the thermal properties may significantly change due to freezing,which leads to a non-linear transient heat conduction problem. Secondly thelatent heat released at the freezing front gives rise to the discontinuityof the enthalpy, as a result, the heat conduction equation is violated atthis point. In addition, the phase-change front is a moving boundary withtime, and may disappear and re-appear in the domain of interest, thus,special numerical treatment to track this moving boundary is required.Basically, there are two principal classes of approaches used to solvethis type of problems, the moving grid and the fixed grid methods, /Crank(19841, Ockendon et al. (1975), and Wilson (1982)/. In the moving gridmethods, the position of the moving front is determined at each time step,and the numerical mesh is rearranged so that appropriate numerical detail is3 4 2

preserved. These methods usually provide excellent accuracy, but, on theother hand, are used mainly in one-dimensional problems and can not copywith appearing-disappearing phases, /Crank (1981, 19841, Djomehri (1988) andStorti (1988)/.In the fixed grid approach, the problem is reformulated in such a way thatthe phase-change condition is implicitly bound up in a new form of thegoverning equations. Therefore, it is not necessary to track the movingboundary directly, instead, the position is determined a posteriori from thetemperature field. To accomplish such a reformulation, one way is to use theenthalpy as the main unknown and the temperature is obtained from theinverse temperature-enthalpy relationship. An alternative way is to use thetemperature-enthalpy relationship to define an apparent heat capacity, whichincludes the effects of both the sensible and the latent heat, and the heatdiffusion equation is assumed to be valid across the phase change front withthis apparent heat capacity, /Comini et al. (1977). Crank (1984) andDalhuijsen (1986)/.In this paper, a finite element model based on the fixed grid approach fortwo-dimensional freezing and thawing problems is formulated. The phasechange is implicitly accounted for in the enthalpy definition, and thelatent heat evolution is treated in terms of an apparent, temperaturedependentheat capacity. The integral averaging technique suggested byLemmon (1981) is used to obtain the apparent heat capacity.The model has been programmed on a PC for small scale problems. Thecomputed temperatures are compared with both analytical solutions andlaboratory tests.2. MATHEMATICAL FORMULATION2.1 Statement of the problemTwo-dimensional freezing or thawing problems can be described by Fig.1, inwhich a certain domain 0 is divided by an internal moving boundary into twosubregions 0 and 0 , representing unfrozen and frozen soil respectively.Figure 1. Freezing or thawing system with moving boundary (s).343

The transient heat conduction equation in domain Q and Q is generallywritten in the formwhere K is the thermal conductivity (W/m.K), C the volumetric heat capacity(J/~~K), T the temperature (K), Q the internal heat generation rate (w/m3),and t the time (sec).Generally, the thermal properties K and C are temperature-dependentparameters. Particularly, K and C may vary considerably during the freezingof soils. Also for frozen soils, the thermal properties may exhibit a signi-ficant temperature-dependency. This particularly holds for fine grainedsoils. The reason is that the thermal properties K and C are both stronglyinfluenced by the temperature-dependent water content in the soil. Thermalproperties of soils and factors influencing them have been comprehensivelydiscussed by Farouki (1986).The temperature-dependency of the thermal properties results in a non-linear transient heat conduction equation. This non-linearity is oftenapproximated by assuming K and C to be step wise constant for a number ofchosen temperature zone. A common used assumption, which is also adopted inthe model presented here, is that K and C have constant values above andbelow freezing temperature respectively.The velocity of the moving boundary (s) is controlled by the phase-changecondition (i.e. the so-called Stefan condition)where K and K denote the thermal conductivity of unfrozen and frozen soilurespectively, n is the normal direction of s, L is the effective latentheat, and T is the freezing temperature.The boundary conditions considered in the model includewhere K can stand for K or Kdepending on the temperatures on the boundauf'ries; g(t) represents the specified temperature, q(t) the imposed heat flux,a(t) the convective heat transfer coefficient, T(t) the surfacetemperature; and 1 and 1 are the direction cosines of the outward normal tox Y

the boundaries.2.2 The enthalpy and the apparent heat capacityThe enthalpy H is defined as the sum of the sensible heat and the latentheat required for a phase change. If we assume that the latent heat isreleased in a small temperature interval around the freezing point, and plotthe heat capacity as a function of the temperature. Fig. 2a, the enthalpyrepresents the whole area under the curve. By using a temperature intervalfor the phase change, the infinite value of the derivative of the enthalpywith respect to the temperature at the freezing point can be avoided.Fig. 2b shows the relation between the inverse of K and temperature. Thereason why 1/K is used in this diagram is due to the fact that the effectivethermal conductivity between two points in two different materials isobserved to be a series type of average (analogous to series electricalcircuit 1, /Lemon (1981 )/.Figure 2. Constitutive relations and the enthalpyFor freezing and thawing problems with a finite freezing interval [T fl'T I ( T 2 T), the enthalpy can be expressed asf 2where C is the volumetric heat capacity in the freezing interval, and T isa reference temperature. In the case of one-point freezing, i.e. Tf~= Tf29Eq. (4b) disappears, and the enthalpy exhibits a jump at the freezing point.

With the above nomenclatures, we can define an apparent heat capacity asThe derivative dWdT in Eq. (5) can be directly evaluated by Eq. (4) or ifthe freezing range [T~' - T 1 is fairly large. Otherwise, this directc 1evaluation will give rise to the possibility of the temperature at a nodalpoint skipping the phase-change temperature interval in a single time stepof numerical computations, IDjomehri (1988)/. To make sure that the phasechange is not omitted, the averaging techniques suggested by Lemmon (1981)have been used in the model. Defining n as the direction normal to theinterface, the apparent heat capacity is evaluated with reference to thisdirection byIn order to find the effective thermal conductivity in those elementswhere the phase change takes place, a similar averaging technique suggestedby Lemmon (1981) is used here(aw/aX)'+ OW/~~)' 'I'+ (a~/ay) 21where W=J'(l/K)dT. As shown in Fig. 2b, W represents the area under the 1/K,T diagram. Obviously, Eq. (7) is valid for all the elements in the domain.Before applying Eq. (6) and Eq. (7) for evaluating the apparent heatcapacity and the effective thermal conductivity, we first calculate thenodal values of H and W within an element by Eq.(4) or by use of Fig. 2. Thevariation of H and W within the element is approximated in terms of the sameassumed interpolation function as used for T. If linear triangular elementsare used, the three nodal values of H (or W) within an element define aplane, through which the spatial variation aH/ax and aH/ay are single valuedin the element.2.3 Finite element formulation and time discretizationWith the definitions of the apparent heat capacity and the effectivethermal conductivity, we now can write the heat conduction Eqs. (1) and (2)in a single quasilinear parabolic equationMultiplying Eq. 8 by an arbitrary test function

Integration by parts leads towhere I-' is the boundary of the domain 0, and m is its outward normaldirection.Let the unknown T be approximated throughout the domain at any time t bythe relationshipwhere N are the usual shape functions defined piece wise element byelement, and T is the temperature at the nodal point 1.In the Galerkin method the test function o is replaced by the shapefunctions N . Substituting Eq. (11) into Eq. (10) and replacing is by Niresult in a system of ordinary differential equations of the formwhere K and C are the conductivity and capacity matrices, respectively, T isthe temperature vector, T is the time derivative of T, and F is the heatsupply vector. Typical matrix elements of K, C, and F arewhere 0e is the element region, re and re refer only to those elements withexternal boundaries on which conditions (3a) and (3b) are specified respectively.It is important to mention that the heat capacity matrix C, which isanalogous to the mass matrices of dynamic problems in structural mechanics,can be lumped to a diagonal matrix using Newton-Cotes rule. Dalhuijsen(1986) claimed that the use of a lumped heat capacity matrix does not onlyhave computational advantages, but also results in a greater accuracy of thecomputed temperature fields. For linear triangular finite elements, thislumping yields

where A is the element area. The lumped heat capacity matrix has beenadopted in the presented finite element model.To solve the set of ordinary differential equations (13). a two-stepDupont I1 scheme has been used for the time discretization in the model,which givesThis leads to the following recurrence formulaeAlthough Hogge (1981) and Thomas et dl. (1984) claim that this Dupont I1scheme is unconditionally stable, has a high accuracy and is free fromoscillations, the authors find that large time steps may result in lowaccuracy and even steady state heat flow, especially for small elements. Thereason for this is that, when the element area A rather small and the timeestep is relatively large, the second term in Eq. (17) which represents theeffect of the heat capacity, will become negligible compared with theconductivity term and the heat-supply term, thus results in a steady stateheat flow. In order to avoid this problem, the following restriction on thetime stepping has been used, /Sheng et al. (1989)/.where a is a non-dimensional value greater than unit. The maximum andminimum values are selected from all the elements in the domain of interest.Obviously Eq. (18) is not self-starting. In the presented model, an Eulerbackwardscheme is utilized to find the second start-temperature vectorwhere TI denotes the initial temperature vector, which is known over thewhole domain. Eq. (20) requires an iteration solution scheme.2.4 Computational aspectsThe finite element model described in section 2. 1 to 2.3 has beenprogrammed in FORTRAN 77 on a PC for the time being. Linear triangularelements are used so that the variation of T, H and W within each element

are constant, thus both the apparent heat capacity and the effective thermalconductivity are single valued within an element. This is important becausethe position-dependent values of C* and K* within an element (e.g. forisoparametric elements) will result in difficulties in the numericalintegration for the matrices K and C.The computational scheme of the mode1 is outlined in Fig. 3.INPUT DATA (INITIAL CONDIION,MATERIAL PROPERTIES,~~~)~-1-TIME STEPPING CONDITION ~~.191Â¥ICOMPUTE THE NODAL VALUES OF H AND W BY Eq.4 OR Fig.2 ]+-1-1 COMPUTE c AND* BY Eqs. 6,7-1-[COMPUTE K(T), C(T) AND F(T) BY Eqs. 13,14,151-1-1COMPUTE THE UP-DATE CAND*COMPUTE THE UP-DATE K, c AND FIFigure 3. Flow chart for the computational scheme, t denotes the stop time.3. NUMERICAL EXAMPLES3.1 Comparison with the Neumann solutionAs a first example, we consider a one-dimensional freezing problem whichwas solved exactly by Neumann in 1860. The position of the phase changefront by the Neumann solution is, e.g. given by Carslaw and Jaeger (1959)where K denotes the diffusivity of unfrozen soil, and t is the time. Theconstant y is determined by the following implicit equation

where K denotes the diffusivity of frozen soil, T is the initial groundstemperature, T the freezing temperature and T the ground surface temperasture.When 7 is determined, it is also possible to calculate the temperaturedistribution in both frozen and unfrozen regions, see Cawslaw et dl. (1959).In Fig. 4 the position of the phase-change front (frost penetration) iscompared with the result from the Neumann solution. The temperature obtainedfrom the numerical model are compared with those analytically determined inFig. 5. The soil properties used in this example refer to soil 1 in Table 1.The initial ground temperature is ~ O C , and the ground surface temperature is-5'~. The time step used in this computation is 3600 seconds.Since the maximum depth involved in the computation is only down to 1.0meter, where an insulated boundary is assumed, the discrepancy between theTable 1Thermal and physical properties of the example soilsSoilKW/mKK W/mKC MJ/m3KC MJ/~~K r kgfm3w %L MJ/m3soil 11.161.423.002.20154125.4130.5soil 20.951.372.902.10143026.3125.0soil 31.772.483.632. 19141062.1 301.0(rd is the soil density, and w is the water content.)Ir !7i0 2 4 ft B 10TIME In) x 1tTFig. 4 Position of the phasechangefront .Fig. 5 Temperature historiesat different depths.

numerical and analytical results increases with depth, which can be seen inFig. 5. At depths far above the insulated boundary, the numerical resultsand the Neumann solution are in an excellent agreement. which is to beexpected since the Neumann solution is valid for semi-infinite domain.As a second example, we consider a two-dimensional problem. A frequentlyasked question by engineers is: "when can a one-dimensional model, e.g. theNeumann solution, be used to predict the frost or thaw penetration in aground with the surface of the type illustrated in Fig. 6a?" Of course theanswer depends on what distance the calculation is performed from thebending point and how steep the slope is. In Fig. 6b the ratio of the frostpenetration by two-dimensional model to that by one-dimensional model isplotted as a function of the distance from the bending point and the slopeangle. The soil properties refer to soil 2 in Table 1.*. - - - . ..- limitell b0U"d.q $so S, - Two-Olnxn*teo.1 .d"llonFig. 6 Relationship between the frost depth obtained by one- and twodimensionalmethods as a function of the slope angle and the distance3.2 Comparison with laboratory testsThe laboratory device CBT (Constant Boundary Temperatures) oedometer isdesigned originally for studying the development of pore pressure in thawingsoils, /Axelsson (1987)/. The cylindrical frozen soil sample is subjected toa positive temperature at one end, and a negative at the other. Thetemperature distribution as well as the pore pressure is measured during atest. Fig. 7 shows a CBT oedometer.The heat flow in the sample is assumed to be one-dimensional so that theanalysis is only needed in the centre of the sample. As an example, we testthe soil 3 in Table 1. The calculated and measured temperature histories atdifferent levels are shown in Fig. 8. The comparison indicates that thefinite element model works well even for large values of latent heat value.

FLUIDFLUID1 - aLaboratory teç-3 ,I I1TIMEucFig. 7 A CBT oedometer.Fig. 8 Comparison with laboratory test. CONCLUSIONS AND FURTHER WORKAs mentioned in the introduction, the presented finite element model isbased on the fixed grid approach so that the front tracking, which may leadeither to refinement of the finite element mesh (or remeshing if necessary)at each time step or to special numerical treatment for the phase-changecondition as well as for the heat diffusion equation itself in theneighbourhood of the moving boundary, has been successfully avoided. As aresult, not only has the numerical work been simplified considerably, butalso the problem is generalized to two dimensions.As we have seen in the previous section, the model is supported by theanalytical solution i. e. the Neumann solution for one-dimensional problems.The laboratory tests also show agreement with the numerical results.The model has been programmed temporarily on a personal computer, and itis only available for small scale problems. In addition, the preprocessor(for the automatic mesh generation) and the postprocessor (for the managementof the computed results) are still in progress. The implementation to aworking station computer net work as well as the development of the preprocessorand the postprocessor for the programme are the work in the nextstep.5. REFERENCESAxelsson, K. and Ryden, C.G. - Experimental determination of pore pressure352

development in thawing soil, 9th Int. Conf. on Port and Ocean Engineeringunder Arctic Conditions (POAC 87). Fairbanks, Alaska, 17-21 August 1987.Carslaw, H.S. and Jaeger, J.C. - Conduction of heat in solids, 2nd edn,Clarendon Press, Oxford, 1959.Comini, G., Guidice, S.D., Lewis, R.W. and Zienkiewics, O.C. - Finiteelement solution of non-linear heat conduction problems with specialreference to phase change, Int. J. Numer. Methods Eng., 12, 1191-1195(1977).Crank, J. - How to deal with moving boundaries in thermal problems, inNumerical methods in Heat Transfer (R.W. Lewis, K. Morgan and 0. C.Zienkiewicz, Eds), Wiley, New York, 177-200 (1981 1.Crank, J. - Free and moving boundary problems, Clarendon Press, Oxford, 1984.Dalhuijsen, A.J. and Segal, A. - Comparison of finite element techniques forsolidification problems, Int. J. Numer. Methods Eng., 23, 1807-1829, 1986.Djomehri, M. J. and George, J.H. - Application of the moving finite elementmethods to moving boundary Stefan problems, Comput. Methods. Appl. Mech.Eng. 71, 125-136 (1988).Farouki, 0.T. - Thermal properties of soils, Trans Tech Publications,Clausthal-Zellerfeld, 1986.Hogge, M. - A comparison of two- and three-level integration schemes fornon-linear heat conduction, in Numerical Methods in Heat Transfer (R.W.Lewis, K. Morgan and 0.C. Zienkiewics, Eds), Wiley, New York, 75-90 (1981).Lemmon, E.C. - Multidimensional integral phase change approximation forfinite element conduction codes, in Numerical Methods in Heat Transfer,(R.W. Lewis, K. Morgan and 0.C. Zienkiewicz, Eds), Wiley, New York,201-213 (1981).Ockendon, J.R. and Hodgkins, W.R. (eds) - Moving boundary problems in heatflow and diffusion, Oxford University Press, Oxford, 1975.Sheng, D.C., Axelsson, K. and Knutsson, S. - Verification of a weak solutionfor two-dimensional freezing problems, Proceedings 6th Int. Conf. onNumerical Methods in Thermal Problems, July, 1989, Swansea (in press).Storti. M., Crivelli, A. and Idelsohn, S.R. - An efficient tangent schemefor solving phase-change problems, Comput. Methods Appl. Mech. Eng. 66,65-86 ( 1988).Thomas, B. G. , Samarasekera, I. V. and Brimacombe, J. K. - Comparison ofnumerical modeling techniques for complex two-dimensional, transient heatconductionproblems, Met. Trans. B, 15, 307-318 (1984).Wilson, A.D., Solomon, A.D. and Boggs, P.T. (eds) - Moving boundaryproblems. Academic Press, New York, 1982.Zienkiewics, 0. C. - The finite element method. 3rd edn., McGraw-Hill,London, 1977.

ICE FLOE DISTRIBUTIONS --Mikko LensuResearch scientistFinnish Institute ofMarine ResearchBox 33,SF-00931 Helsinki FINLANDABSTRACTThe applicability of logarithmic normal distribution to thedescription of ice floe fields is investigated. Analysis of twosets of floe data and a series of ice breakup simulationresults reveals that the section of medium-sized floes is ingood agreement with lognormality.1. INTRODUCTIONThe size and shape of ice floes concern many fields of iceresearch, especially when dynamics, melting and suchgeometrical properties as maximum floe packing have to beexplained and modelled. Ice floe distributions are relevante.g. to collisional rheologies and wave attenuation theoriesbut the development of theories has been hampered by theinadequacy of existing knowledge. Floe distributions have beenstudied every once in a while but no definite lines of studyhave yet emerged. Most authors have been content withpresenting empirical distributions and have not made anysuggestions about their possible analytical properties. Otherstatistical aspects of ice fields, especially the spatialdistribution of ice ridges or leads and the thicknessdistribution of ice, have been subjects of more intenseempirical and analytical studies.Qualitatively taken, a fair number of probabilitydistributions suggest themselves. Weeks et al. (1980) proposeda negative exponential distribution, which was adopted as a

working hypothesis by Lepparanta (1981,1983). Rothrock andThorndike (1984) proposed power distribution, which was thenemployed by Perovich (1983) in his treatment of lateralmelting. Vinje (1977) made extensive studies in the Fram Straitregion, but his distributions show such a great variation thatit seems to deny all simple analytical generalizations.2. FLOE MEASURES AND FLOE DISTRIBUTIONS2.1. Floe measuresIn practice, the size of floes can be expressed in one of twoways: as floe area or as some measure of diameter. However, thediameter of floes can be defined in many ways. The shape of icefloes and the search for the best diameter measures arethemselves subjects of study and will not be discussed in thepresent context (see Lepparanta 1983, Rothrock and Thorndike1984 or Herdan 1953). Area is an unambiguous and more suitablemeasure for describing the breakup process since the total areais conserved.2.2. Number and areal distributionsA given sample of floes can be described either by a numberdistribution (relative number) or by an areal distribution(relative areal coverage). Number measures are more commonlyused, but they usually overemphasize the very small floes,whose great abundance is not in proportion to their importance.Also their mean values are usually less suitable to representof "a typical floe w and they are strongly dependent on theminimum floe size determined, for instance, by the resolutionof photographs. They are also theoretically problematic sincethe number of floes may well be infinite and the distributionnonnormalizable. In contrast areal distributions are alwaysnormalizable. For a number distribution f(x), where x is thefloe area, the corresponding areal distribution is given bywhere EXP stands for the expectation (mean). This relation doesnot hold if x denotes some measure other than area. The mean ofg is subsequently called the areal mean of f and similarly for

any other parameter.2.3. Power and exponential distributionsThe fact that aerial photographs at different scales are easilyconfused with each other has prompted the suggestion that thiskind of self-similarity should have explanative value (e.g.Rothrock and Thorndike 1984). One proposal is the use of powerdistributions, i.e. the distribution f should be proportionalto x u and the cumulative distribution F to x ( ~ ."Theseindeed do have the property that F(x)/F(kx) is constant forconstant k, which is one mathematical formulation ofself-similarity.Power distributions naturally result from processes in whichthe smallest floes continue to disintegrate further while thelarger ones remain as they are. However, this assumption isunrealistic when applied to ice floe fields, which are formedby a branching process in which every floe has a nonzerobreaking probability.In addition, the power function cannot be rendered into aneat normalizable distribution function since the integraldiverges either in zero or in infinity. Some modification isunavoidable, but any modification tends to lack the physicalmotivation which the power law itself has.Another distribution that has frequently been suggested isthe negative exponential distribution, f(x)=ae ax , which haspreviously been applied in many areas. Ridge spacings, forexample, have been found to follow this distribution, whichcorroborates the hypothesis of the random spatial occurrence ofridges (Hibler et a1 (1972)). It is natural to suggest that theoccurrence of cracks in an ice field follows a similar randompattern. This leads to the Poisson field, which consists ofrandomly oriented and randomly occurring lines (Rothrock andThorndike (1984)). The diameters of the circles inscribed inthe polygonal pieces formed thereby obey the exponential law.However, once again, the random processes leading toexponential distribution do not take into account thecumulative, branching nature of floe breakup.

3. LOGARITHMIC NORMAL DISTRIBUTION3.1. Grounds for the lognormal distributionIf the logarithm of a random variable is normally distributed,the variable itself follows a logarithmic normal distributionand has the expression1 1 lnx-lnpf(x) =x lnu fi ~xP[-z( lnu 2] .This distribution has been extensively used in the engineeringsciences and biology, especially for describing distributionsproduced by breakage or aggregation (eg Epstein (1948), Koch(1966, 1969 ) ). Such use can be justified as follows. Accordingto the central limit theorem of the probability theory, thedistribution of the sum of N independent random variablesapproaches normal distribution under very general preconditionsas N increases (see e.g. von Mises (1964)). On the other hand,in a breakup process the particle sizes (here, floe areas) area product of random events, so the floe area distribution at agiven stage of evolution can be considered as a result of Nreduction events: area=areaoRIR 2...R,,. This means that thelogarithm of the floe area is a sum of random variables. Iftheir distribution approaches normality the relative areadistribution approaches loqnormality. If floes are described bya measure for diameter rather than area the distribution isstill lognormal. However, considering the case of ice floefields, the applicability of this reasoning demands that everyfloe should have equal breaking probability.3.2. Parameters of the lognormal distributionThe parameters 4 and u can be interpreted as the geometric meanand the geometric standard deviation (Irani and Callis (1966)).is also the median of the distribution (but not the mode) andu is independent of scale. It is more informative to scale thelognormal distribution so that the geometric mean is 1. Fromnow on we shall systematically use this scaled form. Theparameters of lognormal distribution are collected in Table 1.By taking a logarithm from both sides of (2), it is seen that,on a logarithmic paper, lognormal distribution appears as a

second order polynomial.TABLE 1. The parameters of the lognormal distribution with 4-1Geometric meanGeometric standard deviationMean valueStandard deviationMedianMode50% confidence intervalAreal meanAreal standard deviationAreal medianAreal modeGeometric areal meanGeometric areal standard dev.exp(_ln1 2u)(exp2( 21n u) -exp( ln2u) )'I23.3. Time evolutionLet us suppose that an ensemble of floes follows a lognormaldistribution with parameters wand a . Subsequently every floewith the respective area x is broken further to yield alognormal distribution with parameters w2x and u2 where p2

4. FLOE DATA STUDIES4.1. The dataThe floe data was obtained from two sets of 10 aerialphotographs taken during the melting period in the Bay ofBothnia. One set was taken on 21 April and one on 19 May 1982.Both sets covered an area of 360 km 2 . The floes with a maximumdiameter of less than 100 m could not be measured. The numberof measured floes was about 1700 in both cases. The shapefactors and elongations of these floes and the distribution ofthe diameter measure used have been analysed by Lepparanta(1982). Here, we concentrate on the floe area.The abundance of very large and very small floes wasconsiderable in both cases and the exact floe distribution isknown for only a small percentage of all floes. (Table 2).Table 2. Ice compactness and abundance of large and small floes.A small floe is one with a diameter of 100 m or less. A largefloe is one whose area is greater than 10 per cent of the maximumobserved floe area (Lepparanta 1982).1 Case Compactness Small floes % Large floes %of ice areaof ice areaApril 21 0.84 18 49May 19 0.69 71 7Table 3. The parameters of the distribution and lognormal fits(scaled data).CaseApril 21All floesFloes < max/10Fitting curveApril 21All floesFloes < max/10Fitting curveGeometric mean10.9250.66110.9740.8338Geometric standarddeviation4.1303.5603.7573.0072.8592.5954.2. LognormalityBecause of the cutoff of small floes and the small number oflarge floes it is questionable whether any reliable conclusionsabout the possible analytical form of the floe distributionscan be made. Nevertheless lognormal curves fitted with the data

are presented in Figure 1 and the parameters in Table 3. Theyare seen to be in relatively good agreement.Figure 1. The relative number distributions of floe area forApril 21 (top) and May 19 (bottom). The geometric mean isscaled to 1.

Table 4: The statistical parameters of the two floe sets whenthe geometric mean is scaled to 1.CaseApril 21May 19ParameterAll FloesFloesfloes

4.3. Parameter studiesThe parameters of the floe data scaled by the geometrical meanare given in Table 5. Table 6 gives the agreement between somerelations in Table 1 and the data. It is seen that theagreement is better in May and is considerably improved whenthe largest floes are discarded, indicating that lognormalityis very nearly satisfied for the middle section of thedistribution.4.4. Time evolutionThe two sets of aerial photographs were taken at an interval ofone month from two areas located close to each other. For thisreason it is interesting to observe how the distributions havechanged. It was noted above that the conformity with thelognormality hypothesis improved. In Table 8 the parameters ofthe two cases are compared. It is evident that, although theoverall distribution has changed, the distribution of themedium-sized floes has not. The fact that the geometricstandard deviations are no greater in May than in April aspredicted in 3.3 is understandable since the maximum size hasdecreased but the minimum (measured) size is the same in bothcases.5. SIMULATING THE FLOE DISTRIBUTIONS5.1. The simulation procedureBecause of the sparsity of data on floe distributions, a seriesof computer simulations was run to establish whether thedeveloping floe field obeys the lognormal law, and if so, howthe parameters of the lognormal law evolve.The simulations consisted of a stepwise partition of a squarewith an area of lo6 units into a given number of rectangles.The normal series included partitions into 20, 50, 100, 200 and400 and the partitions were repeated until an ensemble of 8000had been created. The data included the area, dimensions andlocation of the floes in the base area. The process could bevery freely regulated by the properties of the floes. Here weconsider only the basic simulation case where every floe had anequal probability of breaking. The number of floes can be used

tto define a time parameter by n=e , assuming a breaking rateof one breakup per floe per unit of time.5.2. Large and small floesTable 9 gives the statistics of the large and small floes.Although the size of the maximum floe decreases, the relativearea of the largest floes remains approximately constantbetween 4 and 5. Thus the relative area of 49 per cent of thelarge floes in the April 21 case considered in section 4 can beattributed to the randomness of the breakup process. However,although the number of small floes increases rapidly their areagrows slowly since the minimum size decreases and, in thepartition into 400 floes, they still cover only one per cent ofthe total area. Thus the partition would have to be into a fargreater number of floes than in the simulation cases if we areto create an ensemble similar in this respect to the previouslyconsidered case of May 19 where the overwhelming majority ofarea was covered by small floes.Table 7: Relative abundancies of large and small floes in thebasic simulation case.5.3. Parameters of the whole ensembleAll mean values were found to decrease exponentially with thetime parameter whereas the standard deviations increasedexponentially. However, the agreement between the parametersand the relations in Table 1 deterioriated exponentially.Consequently, as a whole, instead of developing towards alognormal distribution, the ensemble becomes increasingly lesslognormally distributed. Even so, the ratio of median andgeometric mean improves from 1.31 to 1.16. Thus the equalityof the median to the geometric mean is not in itself a reliable

indicator of lognormality. The situation did not improveessentially when the parameters were calculated for thesections of small floes only. From the cumulative distributionsit was apparent that the small floes obey the power law werywell (Fig 2).Table 8: The ratios of the statistical parameters to thosecalculated according to the relations in Table 1 from thegeometric standard deviations and geometric means; ratios ofmeans and medians.ParameterFloes > Floes > Floes > Floes >max/20 max/lOO max/500 max/lOOOmean value 1 0.969 I 0.916 I 0.874 1 0.8751 areal mean 0.820 1 0.675 1 0.759 0.945 1standard dev.0.756 0.710 0.799 0.916geom. areal mean 0.911 0.784 0.731 0.770qeom.mean / median 1.170 1.192 1.212 1.204geom areal mean / 1.061 0.991 0.901 0.871areal medianFigure 2. The cumulative distributions of the basic simulationseries.5.4. Distribution of the large floesThe sections of the large floes were in good agreement withlognormality. Some parameters are compared in Table 8. However,the agreement did not improve when the largest floes were

omitted from the ensemble (as in Table 5); on the contrary, itbecame less satisfactory, indicating that the large floesmentioned in the cases in section 4 follow a different breakupprocess than the smaller ones.6. CONCLUSIONSFrom the comparison of the simulation results and the floe datapresented in section 4 it is evident that a hypothesis oftotally random breakup can be evoked to account for thedistribution of medium-sized floes in the cases studied. Theagreement between the distribution and lognormality improvesduring the evolution while the proportion the relative amountof largest floes that apparently follow a different breakuppattern decreases.REFERENCESEpstein, B. (1948). Logarithmico-normal distribution inbreakage of solids, Journal Industrial and EngineeringChemistry 40:12.Herdan, G. (1953). Small Particle Statistics, Elsevier,Amsterdam.Hibler, W.D., Weeks W.F. and Mock, J.S. (1972). Statisticalaspects of sea-ice ridge distributions, J.Geophys.Res. 77.Irani, R.R. and Callis, C.F (1963). Particle Size: Measurement,Interpretation and Application, John Wiley and Sons, NewYork.Koch, A.L. (1966). The logarithm in biology: mechanismsgenerating the log-normal distribution exactly, J.Theor.Bio112:2.Koch, A.L. (1969). The logarithm in Biology 11: Dist-ributionsSimulating the Log-Normal, J.Theor.Bio1. 23:Z.Lepparanta, M. (1981). On the structure and mechanics of packice in the Bothnian Bay. Finn. Mar. Res. 248.Lepparanta, M. (1983). Size and shpae of ice floes in theBaltic Sea in spring. Geophysica 19:Z.Perovich, D.K. (1983). On the summer decay of a sea ice cover.Ph.D. thesis, University of Washington.Rothrock, D.A. and Thorndike, A.S. (1984). Measuring the sea

ice floe size distribution. J.Ge0phys.Re.s 89:C4.Weeks, W.F., Tucker, W.B. and Frank, M. (1980).Characterization of surface roughness and floe geometry ofsea ice cover over the continental shelves of the Beaufortand Chukchi Seas. In Pritchard, R.S. (ed.). Sea Ice Processesand Models, Univ. of Washington press, Seattle.Vinje, T.E. (1977). Sea Ice Studies in theSpitsbergen-Greenland area. Landsat report E77-10206. US Dep.of Com. Natl. Tech. Inf. Service.von Mises, R. (1964). Mathematical Theory of Probability andStatistics, Academic Press, New York.

EVALUATION OF CONSTITUTIVE LAWS FOR SEA ICE WITHAPPLICATION TO ADAM'S ISLANDMichael P Montemurro University of Waterloo CanadaWaterloo, CanadaJon F. SykesN2L 3G1ABSTRACTThree constitutive laws were compared for use in the estimation of loads due to slow-moving first-year ice on an offshore structure. A one-dimensional analysis was performedto evaluate the three laws: two based on viscous-plastic rheology and the third based oncreep rheology. The value of the viscosity was found to be the most crit,ical parameter inthe analysis. Dat,a for Adam's Island, which is located at the tip of Navy Board Inlet, wasused to evaluate the performance of the model. Averaged wind, ocean, and displacement,data were used to estimate an ice force on the island of 91 MN at an azimuth of 21°INTRODUCTIONOne of the crucial conlponents in t,he design of a structure in Arctic waters is theestimation of ice forces to which it will be subjected A st,ructure within the Arctic icepack will be exposed to four types of loads (Sanderson,1984): static loads due to slowlymovingfirst-year ice; static loads due to ice features acted on by the slowly-movingfirst-year ice; dynamic loads due to impact with multi-year floes; and dynamic loads dueto the impact of icebergs and bergy bits This paper evaluates different constitutive lawsfor the purpose of estimating the static loads due to first-year ice on an offshore structure.The results are used to estimate t,he ice motion around Adam's Island bet,ween Marchand May of 1985.MODEL DESCRIPTIONThe ice model investigated in this study consists of three components-a momentumbalance, a redistribution function, and a constitut,ive law. The moment,urn balance equa-tion is an application of Newton's Second Law to ice motion and is expressed in vectorform asD- ( r n ~ ) = ~ , + r ~ t F ~ - r n ~ ~ ~ + ~ f f (1)Dtwhere the left-hand side of the equation describes the inertia of the ice. The right-handside is the sum of the applied forces acting on the ice where T, is the wind stress, TÃis the stress due to the interaction of the ocean, fi is the Coriolis force, mgVH is the

force due to ocean tilt, and V

The second form of viscous-plastic constitutive law was derived by Leavitt et al(1984)and involves relating deviatoric stress components to the strain-rates. The constitutivelaw isu;, = 27, (e;, - i;]) + [C - 71 ( 4 k - iL) &I (10)where t,he bulk and shear viscosities are expressed as a function of the ice strengthThe plastic strain-rate ef is det,errnined through the use of a piecewise linear yieldformulation (Thomson et al,l988) which divides the yield surface into a series of chordsthat have gradient vectors N; and are at a perpendicular distance R k from the origin.The "PWL Yield Criterion" becomeswhere k is the hth piecewise segment and j is t,he Cartesian component. The principlevalues for the plast,ic strain-rate according to the associated flow rule then becomeThe advantage of a piecewise linear constitutive law is t,hat it is computationally moreefficient with little loss of accuracy as long as a good linear approximation for the yieldsurface is usedThe viscosities used in both of the viscous-plastic constitutive laws are linear functionsof ice strengt,h. At the onset of plastic behavior, the values of C,,, and Am,,, are directlyrelated to the yield strain-rat,eThe values of the viscosity constants determine the magnitude of the viscous componentfor the ice deformationThe third constitut,ive law is derived based on observations of ice deformation atthe micro-scale. Sea ice is a polycrystalline mat,erial which t.ends t,o deform at. highhomologous temperatures If a load is applied at these temperatures, crystals are freeto orient themselves in order to redistribute the load. On a macro-level the materialappears to deform in a fashion typical of creep The division between creep deformationand plastic deformation is not clear, however it has been shown that both creep andplastic deformation play a part in the irreversible deformation of sea ice.Glen(1955) proposed the first creep model for polycrystalline ice Through experi-mentation, Glen found t,hat for loads varying from 100 kPa to 1 MPa secondary creepis the dominant deformation process He proposed the power law relationship for icedeformationu;,= (~-&)(A~X~[Q/RT]~.)~~ft (16)

.-Table 1: Values of Parameters Used in the Ice Motion ModelParameter Notation Value Sourcedensity of icedensity of airdensity of waterair drag coefficientwater drag coefficientratio of the minor to majoraxis of yield ellipseempirical constant instrength formulationwind velocity : Id AnalysisAdam's Islandocean velocity : Id AnalysisAdam's Islandstrength constant--- ~p, 900 kgm-3 well knownpa 1.2 kgm 3 well knownpw 1028 kgm'3 well knownC,, 1.5 x Frederking et al(1985)Cw 4 0 x lCT3 Frederking et al(1985)e 2 0 Hibler(1979)ua 4 0 ins-I assumeduaz,uti( 40, 2.9ins"'data analysisu 0 078 ms-I assumedt ~ ~ , 0 078 u ~ mi" ~ Frederking et al.(1985)pà 14x106Pa Celej(1986)viscosity constant ,offshore zonenearshore zoneC!, 1.0 x logs Adam's Island dat,aCTrn 1 0 x 10'sin whichis the octahedral strain-rate, vO is a brine correction factor, Q,R and T are thermodynamicproperties, and A is a constant similar to viscosity.EVALUATION OF CONSTITUTIVE LAWSA one-dimensional model was used to evaluate the performance of the viscous-plasticand creep constitutive laws under small-scale motion. The spatial scale used for themodel was in the order of 100n1. A boundary velocity was applied 300111 from shoreand velocity, stress, and thickness distributions were calculated. The terms included inthe momentum balance were the ice inert,ia and the divergence of int,ernal stress. Asummary of parameters used for the analysis is given in Table 1was performed with the forcing averaged over a period of three mont,hs.A transient analysisThe effect in the variation in the viscosit,y paramet,ers Am,,, and Cm in the viscous-plastic rheologies and A in the creep rheology is shown in Figure 1 For each of theseparameters, there is a critical value which changes the behavior of the velocity distribu-tion. If the value of Cm or A is great,er than its critical value or A ,is less than it,scritical value, the velocity gradient becomes constant and the velocity distribution be-comes linear. If Cm or A is less than its critical value or Am,,, is greater than its criticalvalue, t,he velocity dist,ribut,ion exhibits low velocity gradients offshore and high velocit,ygradients nearshore.

Figure 1: Effect of variation of viscosity parameter a) piecewise linear viscous piw .P,b) Hibler's v~scous-plastic, c) power-law creep

The bulk and shear viscosities in the viscous-plastic constit,utive law are also funct,ionsof the ice strength so the effect of the variation of ice strength is shown in Figure 2 Aswith the viscosity parameters, there appears to be a critic-;it value for the ice strengthFor strength values less than the critical value, the velocity gradients are low offshoreand high iiearshore~'li.itrihiition becomes linearFor values greater than the critical strength value, tlie velocityIce motion data shows that deformation in nearshore regions is significantly different,from offshore regions Ice tends to deform in narrow bands close to shore therefore thenearsliore velocity gradients are gieater than those in uffsliore regions This phenomenonis similar to that observed in turbulent Hiiicl How where niiirh higher velocity gra~lieiits areobserved close the the fluid l~oundaries In the regions of the fluid far frniu the boundary,flow is turbulent and viscosities tend tu he higli. close t,o the fluid boundaries, flow islaminar and the viscosities are reduced. Tins sugg~sts that viscosities for sea ice couldvary as well. When ire interacts with shore boundaries, the deformation is dominatedl~y out-of-plane i~~ecl~anisnis which tend tu cause large strain-ratesTo represent thisphenomenon in a plane stress case, the viscosities close to the shoreline should be reducedto reflect this high deformation rate Figure 3 illustrates the use of a zonal values for C','n the velocity distribution Vrn is givrii a large value at the outer model boundary andis reduced within 100 in of t,he shore The- result is a low velocity gradient at the out,er~oundaries and a high gradient close to the shoreANALYSIS OF ADAM'S ISLANDAdam's Island is a small island located off the tip of Navy Poard Inlet at the inter-settint with Lancaster Sound. Ice cnnditims around tlie island have heen stiirlied toexaiiiiiie the effect,s of small-scale ice cleformation (Freclerking et al,l984.198.5,l986) Theire motion model described by Equations (1) to (5) was used to estimat,e the force that theice v;v k ev'rts on t,he island The parameters used in the analysis are given in Tahle 1The ice displarement, wind, and orean data were

Figure 2' Effect of var~at~on of the ice strength a) piecewise linear viscous plastic, b)111bler's viscous-plastic

9e-07 rVelocity Distributionoi 050 100 150 200 250 :x hiThickness Distribution161.41.2Figure 3: Effect of the use of zonal viscosities374

.-,/,,,.,,,,,,,,,,,..,./ j , , , # ,,,,,,,,, ,, ,,,,. ~adam a Lland Vrlin-nt i~;,i~~i,~,~,,.,,- , ,I I,,, --,,dk - ,,,,,,,,,, '.............................................................................. - I....................................... :!Figure 4Model Results For Adam s Island

on the south shore The calculated force on the Island is 91 MN at an azimuth of 21'which is comparable to the results given in Frederking et al(1986)CONCLUSIONSThe choice of constitutive law is critical for modelling ice at small-scales. The mostimportant parameter in the constitutive law formulation was found to be the viscosit,y.Values for viscosity used for modelling large-scale ice motion are unable to describesmall-scale ice deformati .-: '. ,oastal boundaries because t,he deformation mechanismsare different For small-scale ice mot,ion modelling., the viscosities must he reduced inzones close to the nearshore regions where t,here are high velocity gradients The resultsof the ice motion model with zonal viscosities for Ailam's Island show t,hat the bulk ofthe deformation dries indeed occur within the zones of lower viscositiesREFERENCES[I] Cushon. J D. Modelling and Sensitivity Analysis of Ice Motion Near Adam's Island,M.A.Sc. Thesis, University of Waterloo, Waterloo, Ontario, 113pp , 1985.121 Frederking, R , Sayed, M , Wessel, E , Child, A J., and Bradford, D Ice Interactionwith Adam's Island, Winter 1983-1983, Proceedings for IAHR International Symposiumon Ice, Int,ernational Association for Hydraulic Research, Hamburg, Vol3, pp 187-201, 1984131 Frederking, R , Wessel, E , Maxwell, J B , Prinsenberg, S and Sayed, M Ire Interactzonuizth Adam's Island, Winter 1983-1984, Canadian Journal of Civil Engineering,Vol 13(2), pp 140-149, 198641 Frederking, R., Wessel, E , Maxwell, J B , Prinsenberg, S and Sayed, M Ice Interactionwith Adam's Island, IVtntir 1984-198.7, Proceedings for IAHR InternationalSymposium on Ice, International Association for Hydraulic Research, Iowa Cit,y,Iowa, pp. 127-143, 19865 Glen, J W. The Creep of Polycrifitalhuf Ice, Proceedings of the Royal Society ofLondon, London, Series A, Vol 228, No 117.5, pp 519.538, 1955(61 Hibler, W D A Viscous Sea Ice Law as a Stoch^shr Average of Plasticity, Journalof Geophysical Research, Vol. 82, No. 27, pp. 3932-3938, 19777 Hibler, W. D A Dynamic Thern~odynainzc Model Sea Ice Model, Journal of PhysicalOceanography, Vol 9(4), pp 815-846, 1979181 Leavit,t, E., Sykes J. F , Aubin F., Krakowski E., Grandia I

DYNAMIC AND IHEEMODYNAMIC M3DELLING OF SEA ICE INOQBSTALSEASAnders CrostedtHead of OceanographicResearchSwedish Meteorological aridHydrological InstituteS--601 76 Norrkbpiny, SwedenABSTRACTIn the present paper sons basic thennodynamic and dynamic aspects of icein coastal seas are discussed using a one-dimensional sea ice-ocean model.Variations in the on-off shore directions are considered, and the ideas areapplied to the Bothnian Bay, where ridging due to southerly winds is a cornncnfeature. It is concluded that a one-dimensional model approach can beused, giving realistic information about cooling, ice formation, growth anddecay. Horizontal gradients in the sea and in the ice imply, however, thata two- or three-dimensional model is generally needed, particularly for theinitial advance of the ice edge and for the ice deformation calculation.1. INTRODUCTIONThe sea ice in a seni-enclosed sea as the Bothnian Bay may vary considerably.Due to different forcing the ice may rapidly cover the basin or decaydue to ridging or melting. The formation, growth and decay of the ice istherefore an intricate balance of both thermal and dynamic variations.The sea ice cover is also influenced by the presence of coastal processesas, for exanple, compression during on-shore ice drift- and formation ofpolynyas during off-shore ice drift. The vertical structure of sea ice isillustrated in Fiqure 1, where two thin sections are shown. The ice coreswere sampled during BEPERS (Bothnian Bay Experiment in Preparaticn forERS-1) in March, 1988, and illustrate the importance of considering mechan-ical processes when studying sea ice. The ice core data from BEPEFS arefurther discussed by Fransson et al. (1989).

Dote : 880305Station : AB70 -Fah ,\^ TypBrokenstNChrecDate : 880309Station : AB9Type1cMult,layeredGFigure1. Vertical thin sections of sea ice taken during the BEPERS-88experiment. The different ice types are:C = Columnar Ice, and G = Granular Ice.The purpose with the present paper is to discuss sons basic aspects otthe thermal winter regime, including sea ice, in a serni-enclosed basin.Only variations in the on-off shore directions will be considered (Figure2), and the ideas will be applied to the Bothnian Bay. The calculations arebased on a coupled one-dimensional sea ice-ocean nodel developed by Chistedt( 1989 b) .Net heatexchangeISun radiation Sun radiationto water , toice\ /Figure 2. A sketch of the problem under consideration.378

'Fhe the- winter regh of the hltic Sea has recently keen investigatedby Onstedt (1989 a). In that study the severe winter of 1986187 wasanalyzed using a mathematical &el, which divided the hltic Sea intothirteen subbasins. Sea ice was not dealt with in the dels, insteadbundary conditions for an 0p.n water surface were applid all throu@ theseason, and the water tenpratwes were put equal to the freezing pintwhen they were belm freezing. Reasonable results were achieved, but it wasconclwled that sea ice had to be consider& in sane of the thirteen subbasins.For example, the calculations indicate3 that sea ice could delayspring warming for mre than one mnth in the mthnian hy.The ice fomticn is partly dw to vertical gr& ard prtly due tohorizontal advance. In general, ice fornntion starts in the mthnian Jhy inNovenker when the radiaticn dw to the sun is mall. 'Fhe correspnding&el respnse (see Onstedt, 1989 b for equations etc.) to typical earlywinter ccmditicns is illustrate3 in Figures 3 ard 4.xFigure 3.Mcdel shlaticn of iceE-!l228 O& 0 30 60 90 120 150 Time (days1 formation during calmwind conditions butwith variable air ta-~peratures. 'Ihe threecases are:(a) an air tenperatweof -5 OC and a net heatlass of 66 W m-2,(b) an air t-rature60 of -10 OC and a net0 30 60 90 120 19Time(days)and (c) an air tenpratureof -25 OC and anet heat lass of 166

The &sic assqtlon is that the sea temperature is equal to the freezingtemprature. Tke sky is covered with clouds, ad the relative humidity is90 %. The first test is given in Figure 3, where the wind is pt to zeroam3 the air temperatwe is varled. The horizontal qrmth illustrates thatthe &sin will te amst lce-covered withm one and tw weeks respzctlvely,In the case of alr t-ratures of -25 OC and -5 OC. If the cloud~nessdecreases, the freezeup keccmes, of course, m& Tore rapid.Figure 4. We1 shlation of ice formatim during cmstant air temperature(-5 OC) kut with variable wid speed. The three cases are: (a) awind sped of 5 m-I and a net heat loss of 147 W m-2, (b) a windspd of 10 m-l am3 a net heat 1- of 240 W r2, am3 (c) a windsped of 25 ms-I and a net heat loss of 517 W nr2.

If mnd effects are added to the &el(Figure 4), one has to keep inmirri that besides ridging the net heat losses change, as bath a i tempera- ~ture and wlnd enter into the heat flux equations. Frm the figure one cannotice h a the first ice fomtim phase rapidly increases the ice concen-tration. The ice thickness during this phase is a hst mstant due totreating the thickness as mean of new and old ice. At a certain ice mcen-tration the horlmntal advance is decreased, and ridging dramtically iri-creases the thickness. Curing the ridging phase the ice drift is highlyinfluenced by the shore and decreases slwly to zero due to ice pressure.It should also k note3 that even thouqh the net heat flux is larger vhenthe wind is blwing, the time to cover the hsin is mch larqer due to icedefomtim.4. ICE DEXXYTk ice decay includes break-up, vertical rce1ti.x~ an3 horizontal retreat.Saw respse characteristics are d~cussed belm for the case of an alnnsticeaver& &sin with a mean ice thickness of 0.5 m.considered 1s mel-ing without winds (~igure 5).The first situation0 30 60 90 120 150 T~me (days)Fiqure 5.We1 sh1atia-s ofbreak-up and mltingice during calm windconditions and cmstantair tenpratu-e(5 Oc), kt withvariable heat fluxesdue to sun radiaticq.The far cases are:(a) no sun radiationan3 a net heat lossof 34 W m-2, (b) asun radiatim of 50 Wm-2 and a net heatqain of 16 W K2, (c)a sun radiatim oflCâ‚ W m-2 and a netheat qain of 66 Wm-*, and (d) a sunradiaaon of 150 Wrn-? and a net heatqain of 166 W r2.

wan the figure one can notice the inprtance of sun radiation for thedecay of tke ice cover. If also wind is intrducd (Figure 6), the icemncentration decreases even faster. Winds therefore strongly influenceshw fast the ie will decay in the &el. me figures also illustrate thatthe min decrease is practed to cccur in the ice ancentration and not inthe ice thickness. This is also in agreement with what om can obeme£ra ice charts.Figure 6. Me1 sinulations of break-up and mlting ice during mnstant airtemperature ( 5 OC) ht with variable wind speds. The three casesare: (a) a wini sped of 5 rnsl ad a net heat gain of 56 Ii nr 2 ,(b) a wind s@ of 10 m-I and a net heat gain of 103 W nr 2 , and(c) a wind sped of 25 m-l and a net heat gain of 244 w r2.

The f o l l chapter ~ presents data fran d y me verificatim study.Further studies can ke f d m anstedt (1989 b). In figure 7, calculatedad obsemed ice data are sham. In Figure 7 a, the ie mentratim areillustratd. Rapid freezing events are mxlelled and observed in the kegin-nirq of the ice season. In the calculations the ice ccncentratiom sm,haever, to ke overesthated. This is prohbly due to the presence of l-zontal gradients in the sea, whi& is not taken into account in the presatthm-.In late January a perid with ridging is ncdelled, and later thesea is frozm over again. In April the spring warmi-starts wit31 a rapiddecrease in ice concentration due to melting and ice deformation.-- 19 Date~DEC~WL JAN FEB-~ MAR APR MAY 197s1.0k- E2 0.8 -206-5 0.4--lDECm JAN FEB MAR APR MAY 1975Figure 7. Calculated (dashed lines) and observed (fully drawn lines) datafor the ice winter of 1974175.The results fran the winter of 1974175 shm that tb &elseaas to sb-late the ice evolution realistically. me min deviation between calmla-tiom ad olxematicns is asscciated with the melting priod, where &elcalculations predict higher ice wncentrations due to new ice formationcapired with the ice chart data. Lkrir~~ April 1975, a sea ice field ex-sriinent fran the Finnish research vessel Aranda t& place. bring thisexperiment ned ice fonmtim bas observed (see Fiqure 1 in Lepp31~11ta and

Onstedt, 1989). The observations thus indicate that new ice formation isunderestimated in the ice chart data, and the model results seen thereforeto be quite correct.6. CONCLUSIONSThe study illustrates that a one-dimensional model approach can reproduceseveral features, which are of importance for the winter ice regime insemi-enclosed seas. The rapid freezing-over in the initial ice phase aswell as ridging and melting can be sinulated. The model gives realisticinformation, but several aspects are oversimplified. For example, ridgingoccurs in the Bothnian Bay in all directions. Hinds from the south causeheavy ridging, but this is also true for winds £ra north-east, which arenot dealt with in the present tmdel. The assumption of a horizontal hamgeneous ocean can also be of doubtful value for the Bothnian Bay, at leastduring initial ice formation, when the coastal areas often reach freezingtemperatures while the open basin is generally one degree Celcius above thefreezing point. These aspects obviously inply that some mre dimensionsshould be considered in the construction of ncdels.7. REFERENCESFransson, L., ~akansson, B., Ctnstedt, A., and Stehn, L. (1989). Sea iceproperties from the icebreaker TOR during BEPERS-88. (Submitted)Lepparanta, M., and Cffistedt, A. (1989). Dynamic coupling of sea ice andwater for an ice field with free boundaries. (Tellus, in press)Cmstedt, A. (1989a). Modelling the Baltic Sea as thirteen sub-basins withvertical resolution. (Tellus, in press)Cmstedt, A. (1989b). A coupled one-dimensional sea iceocean model forsemi-enclosed basins. (Submitted)

The Deformation of Floating Ice Sheets of Variable ThicknessUnder In-plane Compressive LoadingbyT. Takeuchi and L. H. ShapiroGeophysical InstituteUniversity of Alaska FairbanksFairbanks, Alaska 99775-0800ABSTRACTBending occurs in floating ice sheets or floes under in-plane compressive stresses.If the thickness of the ice is irregular due to bottom roughness, bending will belocalized where the thickness has its minimum values [Hallam et al. (1987)l. Thebending stresses at those points will be amplified with respect to those in an ice sheetor floe of uniform thickness, thus reducing the magnitude of the compressive stresswhich the floe can sustain before it fails in bending.In this paper, we present the results of finite element calculations which furtherexamine the effect of bottom roughness on the in-plane compressive stress which amultiyear ice floe can sustain. The floe is assumed to deform as an elastic plate on anelastic foundation under plane strain conditions. The bottom roughness is taken tohave the form of a sine curve with the amplitude and wavelength as variables. Aforce is applied at one end of the floe, and the horizontal displacement is required tobe zero at the other end, to simulate the resistance of a vertical structure. Ourcalculations follow the results of Hallam et al. (19871, showing that the ratio (K)between the tensile stress due to bending and the applied compressive stressincreases rapidly with increasing roughness amplitude. Other variables consideredhere (elastic modulus, wavelength and boundary conditions at the interface with thevertical structure) have little effect on K.

INTRODUCTIONThe objective of this continuing study is to use finite element calculation methodsto examine the influence of the bottom roughness of ice sheets or floes on the loadswhich can be transmitted from moving ice to stationary offshore structures.Multiyear ice floes are of most interest, but the methods and results would apply tofirst year ice floes and ice sheets as well. The long range goal of our work is to extendthe analysis to as wide a range of ice properties and loading conditions as possible.The first results are presented in this paper; they deal with 2-dimensional problemsin which the ice is modeled as a linearly elastic plate with a flat top and a sinusoidalbottom, resting on an elastic foundation.BACKGROUNDIt is well known that the thickness of ice floes and sheets is variable. In first yearice, the variation can arise from the presence of refrozen leads, from the insulatingeffect of an irregularly distributed snow cover, from ridging, and possibly otherfactors. In multiyear ice the primary causes of thickness variations are probablydifferential ablation and the presence of ridge sails and keels. Thickness variationsin a floe which is under an in-plane compressive stress act to localize bendingstresses at thin areas [Hallam et al. (1987)l. The resulting amplification of tensilestresses over a thin area of a floe can be great enough to cause failure at that point ata relatively low value of the compressive stress. This, in turn, places an upper limiton the total force that the floe can transmit to a structure (assuming that the ice canclear from around the structure).

Our idealized floe is based on the form and dimensions of multiyear floes [Weekset al. (1971); Kovacs (1977,1983)l and has the mechanical properties of multiyear ice[Cox and Richter-Menge (1985)l.PURPOSE AND METHODSThe objective of the calculations described here was to determine the influence ofvarious parameters on the value of the stress ratio K, the ratio between themaximum tensile stress (oJ in a floe of variable thickness, and the applied in-planecompressive stress (PI. The general problem is illustrated schematically in Figure 1which shows the interaction between a floe of variable thickness and the verticalface of an offshore structure. This was idealized as shown in Figure 2, in which thesymbols used in this paper are also defined. In some calculations, the contact areabetween the ice sheet and the structure was reduced to represent either an overhangor a submerged ice foot. These are represented by the contact ratios Cu and CL(Table 1 and description below).The floe was modeled as an elastic medium on an elastic foundation, so thatbuoyant forces were included. The maximum thickness of the floe was taken as 6 m,to approximate a thick, multiyear ice floe. The base of the floe was given the form ofa sine curve and, since the sail-to-keel ratio is generally small, the top was assumedto be horizontal.The amplitude and wavelength of the sine curve were the main variables of theproblem. The amplitude was expressed as the ratio hi/h (Figure 2) and thewavelengths were selected to approximate the range of observed irregularities. Theother important variable was the elastic modulus E, which was assumed to either be

constant through the ice sheet or to decrease with depth. The ranges of the variablesfor which calculations were done are shown in Table 1.The boundary condition at the free end of the floe was an in-plane compressivestress which was constant with respect to time. For calculations in which E wasconstant with depth, the compressive stress was uniform with depth. When Edecreased with depth, the stress distribution was varied so that the horizontal strainat the boundary was constant with depth. However, the total applied force was thesame in all cases. We have verified by calculation that, as expected, the nondimensionalstress ratio K is independent of the applied stress P for the elasticproblems considered here.In most of the calculations, the boundary condition at the end of the floe incontact with the structure permitted movement of the ice in a vertical plane only(the "roller" condition in Table 1). For comparison, a few calculations were donewith the ice assumed to be fixed to the structure with no displacement at theboundary. The results are discussed below.The calculations were done with the finite element package "ADINA" (ADINAR&D Inc, 71 Elton Ave., Watertown, MA 02171, U.S.A., 1984). Examples of themeshes used are shown in Figure 2. The main horizontal divisions of the mesh werespaced to scale 0.5 m apart at the thinnest point of the floe, which also determinedthe number of horizontal divisions in the mesh. Thus, the number of horizontaldivisions increased as the amplitude of the irregularity at the base of the ice sheetdecreased. Note that at the thinnest area of the floe the size of the mesh elementswas reduced and their density increased to provide more detail where the tensilestress reached its maximum.

Most of the calculations done to date evaluate the effect of wavelength andamplitude of the sine curve at the base of the floe when the elastic modulus isconstant with depth. A few additional calculations assessed the influence of thechoice of the boundary condition at the end of the floe in contact with the structure,and the value of the elastic modulus and its variation with depth. In addition, as atest of our methods, we modeled the experiments done by Hallam et al. (1987)(Figure 3), with the satisfactory results shown in Figure 4. In Figure 4, K is simplythe reciprocal of the applied boundary stress (01 of Hallam et al.), because the tensilestrength was taken as 1 MPa in that paper.RESULTSEffect of the Amplitude RatioThe effect of the amplitude ratio (hllh) on K is shown in Figure 5 for thewavelengths and values of the parameters indicated. The trend is similar to that inFigure 4 but the magnification of the tensile stress over the crest of the thin area islarger. This probably reflects the difference in the geometry of the bottomirregularity between the two cases.The upper limits of the compressive stress for this case are surprisingly low,according to this calculation. As an example, for the applied stress of 0.5 MPa usedin the calculation, and a tensile strength of 1 MPa, failure would occur over the thinarea of the floe at a value of K of about 2, corresponding to an amplitude ratio ofabout 0.3. This is the upper limit of the amplitude ratio for which a floe could sustaina compressive stress of 0.5 MPa without failure. Conversely, an amplitude ratio ofabout 0.7 implies a value of K near 20 so that, for a tensile strength of 1 MPa, themaximum compressive stress that the floe could sustain would be about 50 kPa.

Effect of the WavelengthThe data used to prepare the plot in Figure 5 can be rearranged to show thedependence of K on the wavelength 1, for values of the amplitude ratio. This hasbeen done in Figure 6, which shows that the magnitude of K does not varysignificantly with wavelength for any particular amplitude ratio. However, thetrends in the data are interesting. K increases slightly with increasing wavelengthat the lowest value of the amplitude ratio, while at the highest ratio it decreasesthrough a larger range. At intermediate amplitude ratios, K appears to passthrough a maximum. The reasons for these variations in K are still to bedetermined.Effect of the Boundary Condition at the IceIStructure InterfaceSeveral calculations were done to evaluate the effect of the choice of a roller orfixed boundary condition at the icelstructure interface. The results are shown inFigure 7 in which the parameters used in the calculation are also given. The Kvalues are consistently higher when the roller boundary condition is used, but thedifferences are small enough to be negligible for the range of variables used in thecalculations.Effect of the Contact RatioThe contact ratio was defined above as the fraction of the surface of a floe which isin contact with the structure. As shown in Figure 8, the contract ratio Cu representsan overhang of the end of the floe, while CL is a submerged ice foot. Calculationswere done for both configurations for one value of the amplitude ratio and twowavelengths. The results are shown in Figure 8, in which the ratio of K to K* (thestress ratio for contact factor C -f- 1) is plotted against the contact ratio (CL or Cu).

Clearly, the decrease in contact area from either the top or bottom of the ice sheethas only a minor effect on the amplification of the tensile stress.The applied compressive stress P was the same in all cases, so that the stress atthe icelstructure interface increased as the contact area decreased, according to theequationFor small contact areas, the amplification of the compressive stress at the interfacecould become large enough to cause local compressive failure of the ice. In that case,it seems likely that the result would be to flatten the end of the floe, returning theproblem to the boundary condition considered above.Effect of Variations in Elastic ModulusIn all the calculations described above the elastic modulus was assumed to beconstant through the floe with a value of 6 GPa. However, calculations were done toevaluate the effects of other constant values of the modulus. The results showed thatK increased by less than 0.8% as E ranged from 6 to 8 GPa.Several calculations were done in which the value of the modulus decreased from6 to 5 GPa with depth through the floe. The values used in the calculations are givenin Table 2. The number of increments through which the change was made variedfrom 2 to 8 with decreasing amplitude ratio [this was done for simplicity since, asnoted above, the mesh was scaled in 0.5 m increments (Figure 2)l. In addition, the 2-step calculation for the highest amplitude ratio was repeated for values of E of 3 GPaand 2 GPa in the lower layer. As noted above, the applied compressive force was the

same as in the other calculations but the stress was scaled so that the horizontalstrain was constant with depth along the boundary.The results of the calculations are shown in Figure 9. The effect of varying thewas not large.sensitive to the chosen value of E. 1SUMMARY AND CON1 !LUSIONSOur calculations reinforce the conclusions c ' Hallam et al. (1987) that bottomroughness is an important factor to the strength f ice floes. Within the limits of thefloe geometry and variables considered here, anc for a reasonable value of the tensilestrength for ice, the tensile stresses due to benc ng over the thinnest area of a floecan be amplified to large multiples of the appliec in-plane compressive stress. Thus,the floe fails in bending at a relatively low value )f the compressive stress.The results of our calculations show that, 1 ithin the constraints of our modelassumptions, and for the range of parameters u ied, the amplitude ratio hi/h of the

ottom roughness has the greatest influence on K, the stress ratio. K increasesrapidly as hllh increases. The wavelength, contact factor and the bonding (or lack ofbonding) at the icelstructure interface are much less important.The stress ratio is independent of the value of the elastic modulus when themodulus is taken as constant with depth in the floe, and it decreases only slightlywhen the modulus decreases with depth. The results suggest that the use of aconstant value for the elastic modulus in calculations such as we have done givesslightly conservative values for the strength of the floe.ACKNOWLEDGMENTSThis study is part of an M.S. Degree project for T. Takeuchi and was funded inpart by his employer, Shimizu Corp. Additional funding was provided by theUniversity of Alaska. We wish to thank Dr. S. Huang and Mr. K. Yamasaki forassistance in the use of the ADINA finite element package. The manuscript wasimproved through the thoughtful comments of Drs. W. Sackinger and W. Harrison.

REFERENCES CITEDCox, G. F. N. and J. A. Richter-Menge, Tensile strength of multi-year pressure ridgesea ice samples; Proc. Offshore Mechanics and Arctic Eng. Symp., Dallas,Texas, Vol 11, pp. 186-193, 1985.Hallarn. S. D.. N. Jones and M. W. Howard. The effect of sub-surface irreeularities onthe strength of multiyear ice; Proc. offshore Mechanics and ~ rctic~n~. Conf.,Houston, Vol. IV, pp. 235-238,1987.Kovacs, A., Sea ice thickness profiling and under-ice oil entrapment; OffshoreTechnology Conf. Proc., Houston, pp. 547-555,1977.Kovacs, A., Characteristics of multiyear pressure ridges; Proc. Ann. Conf. on Portand Ocean Engineering Under Arctic Conditions, Helsinki, Finland, pp. 173-182,1983.Weeks, W. F., A. Kovacs and W. D. Hibler, Pressure ridge characteristics in thearctic coastal environment; Proc. Ann. Conf. on Port and Ocean EngineeringUnder Arctic Conditions, Trondheim, Norway, pp. 152-183,1971.

FIGURE CAPTIONSFigure 1. Schematic diagram of a multiyear ice floe impacting the vertical face of astructure.Figure 2. Idealized model of a 6 m thick (h) multiyear ice floe in 16 m water depth(D). under in-olane comoressive load (P) at one end while the other end isin contact with a vertica'l face where no horizontal displacement can occur.The too of the floe is flat. and the amplitude of the sinusoidal roughness atthe base is hi. Theh? and h3 are used to define the contactfactors (Cu = h2/h, and CL= h3/h); see text for discussion. The meshes forthe cases h-hi = 1 m (top) and h-hi =4 m (bottom) are also shown. Note themore detailed mesh at the thinnest part of the floe.Figure 3. Geometry of the columnar ice samples used in the experiments of Hallamet al. (1987). Dimensions are in centimeters. The notch depth, hl, variedfrom 1.7 cm to 3.3 cm.Figure4. Comparison of the results of finite element calculations (x's) to theexperimental results of Hallam et al. (1987) (solid dots).Figure 5. Stress ratio (K) vs. amplitude ratio (hllh) for various wavelengths. Otherparameters are applied compressive stress P=0.5 MPa, elastic modulusE = 6 GPa, and contact factor C = 1.Figure 6. Data from Figure 5 replotted to show the relationship between stress ratio(K) and wavelength (1) for various amplitude ratios. Other parameters arethe same as in Figure 5.Figure 7. Comparison of the results with "fixed" (x's) and "roller" (solid dots)boundary conditions for wavelength 1 =50 m. Other parameters are thesame as in Figure 5.Figure 8. Comparison of the stress ratio for the contact factors Cu= h2/h andCL= h3/h (indicated by K*) with K for the amplitude ratio hl/h=0.667 andwavelengths of 25 and 50 m. Other parameters are the same as in Figure5.Figure 9. Stress ratio (K) vs. amplitude ratio (h~/h) when the elastic modulus isvariable with depth, as follows: solid dots, E ranges from 6 GPa at thesurface to 5 GPa at the base of the floe; open square, E varies from 6 GPa to3 GPa; open triangle; E varies from 6 GPa to 2 GPa. Results for E constantat 6 GPa are shown by x's for comparison. Other parameters are the sameas Figure 5.

TABLE CAPTIONSTable 1. Parameters of the model and range of variables used in calculations.Table 2. Vertical variation of elastic modulus and applied compressive stress forcalculations of the effect of E variable with depth. Note that the total forceis the same in all cases at 3 X 10Wlm.

FIGURE 3

Experimental Results frcr Hallan et a1x F.E.N. Results--K--e xXÂx %! & @@ I IFIGURE 4

706050 -40 -30 - I=%. x I=%, 0 l=75Ç Â- E=6GPa, P=O.SUPa, C=l, xROLLER-20 -10 -008I 9 , I 1FIGURE 5

10090807060~ h /h=0.833, , 0hi/h=0.667,~h ,/h=0.5- mh, /h=0.333. E=fiCPa. P=0.5HPa. C=lROLLER-A- A- AK=uf/P 50-40 -30 -20 -10 -0xa ax k? IFIGURE 6

1=50ç E=6GPa, P=0. ma,C=l,à HOLLER, x FIXEDÂFIGURE 7

ICE:ICEh2. I1 =&h ,/h=O.667, E=6HPa, P=0.5HPavROLLER,-Pnote: K =stress concentration factor for O

- -1=50H, P=O.5HPa9 C=l, ROLLERx E=fXPa (CON!5?ANT),A0KFIGURE 9

WAVE LENGTH (1) mHAXIHUH THICKNESS (h)AnPLITUDE (h,) m(h,/h)25. 50. 7562. 3, 4. 5(0.3331, (0.5). (0.667). (0.833)CONSTANT ELASTIC MODULUS(El GPaVARIABLE ELASTIC MODULUSTOP GPam n GPaPOISSON'S RATIO (u) 0.3I6, 7, 865.3.2APPLIED LOAD (PI tPa 0.5, 1.0, 3.0IWATER DEPTR (Dl 16TABLE 1

A2L@2HIhl/hzO.WEi GPa6Pi HPa0.5455h,/h=0.667EL GPa6PL HPa0.5455Ei. GPa6hl/h=0.5Pi HPa0.54%-EL GPa-6n250.4%5.6670.51525.80.52735.857f'35.3330.48485.60.50915.714H4,50.45455.40.49095.571ns-Hb-~"75.250-4727 5.429-0.4545 5.2865.143H85-F= XPi XH;=3X 10bN/m=constantTABLE 2

DAMAGE OF ISOTROPIC POLYCRYSTALLINE ICEUNDER MODERATE CONFINING PRESSURESStone, B.M.Jordaan, I. J .Jones, S.JMcKenna, R.F.Faculty of Engineering and Applied ScienceMemorial University of NewfoundlandSt. John's, NE, CanadaInstitute for Marine DynamicsNational Research CouncilSt. John's, NF, CanadaFaculty of Engineering and Applied ScienceMemorial University of NewfoundlandSt. John's, NF, CanadaABSTRACTRecent work on the mechanics of ice under compressive states of stresshas shown the importance of including, in the analysis, the effects ofmicrocracking at high strain-rates.An experimental study of the damage of laboratory produced granular icehas been started. Damage, defined in the present study as the change in theapparent elastic modulus resulting from the initiation and propagation ofmicrocracks, has been determined. The tests, conducted under uniaxialstress and moderate confining pressures, used a constant strain rate inputas the controlling feedback parameter in a closed-loop machine.Preliminary results of the degree of damage, or change in apparent elasticmodulus, as a function of strain rate, and confining pressure are presented.A formulation for enhanced creep due to damage is presented and discussedin light of the experimental results.1.0 INTRODUCTIONThe process of degradation of ice subjected to compressive states ofstress is often referred to as "crushing". A dense array of microcracksforms and the ice can degrade into a powder; if this is associated with acontinuing interaction or indentationwith a structure, the powdered ice canbe extruded from the zone adjacent to the structure. Nowhere has this beenmore vividly illustrated than in the case of the full scale experience withthe Molikpaq structure in the Beaufort Sea, where a 8 m high pile of crushedice formed during an interaction event with a multiyear ice floe (Jefferiesand Wright, 1988).

Ice is an extremely brittle material; this has been recognized in thework of Gold (1963). Measurements by Timco and Frederking (1986) indicatea value of strain energy release rate for tensile cracks (GI=) of the orderof 1 to 2 ~/m'. Ice, in common with other brittle materials such asportland cement paste or concrete, rocks, and sulphur-based concretes, showsa descending branch of the compressive stress-strain curve under conditionsof constant strain rate.The energy required to create new fracture surfaces is very small becauseof the extreme brittleness of ice; this is illustrated by the calculationsof Jordaan and Timco (1988) related to energy consumption in ice crushingby indentation; the creation of fracture surfaces was found to constitute0.1% of the total work, the remainder being consumed in frictionalprocesses associated with the extrusion of the crushed ice. The importanceof these processes must be recognized in an analysis of the damage process.2.0 DAMAGE MECHANICSThe requirements for a damage model for ice are quite demanding. Icecrystals are anisotropic, although isotropy can be introduced in cases whereit is appropriate; for example, granular ice can be regarded as beingstatistically isotropic. A columnar ice sheet with random c-axisorientation in the plane can be treated as isotropic for plane stressanalysis. Even if the ice is initially isotropic, the damage induced canbe anisotropic which must be reflected in the constitutive relations; anexample is shear damage which could be greater on certain planes than onothers. This suggests a vector representation for damage. The cracks inice, even under multiaxial states of stress (Kalifa et al, 1989), tend tobe oriented in the direction of the highest principal compressive stress.Eventually, as the ice becomes more damaged, cracks interact and coalesce,separate particles form, and the ice extrudes as a powder-like material.Anisotropy would tend to disappear in the final stages as the crushed icebegins to "flow". Dilatations will also accompany the process of damagefrom the virgin state to a crushed powder.In the following, a simple scalar damage measure A will be used so as toillustrate the concepts involved. This can be thought of as a measure ofdamage in uniaxial compression or as a response to the axial stress q inthe standard confined compression test (al>a2=a3). A further interpretationis the scalar shear damage measure of Resende and Martin (1984). Areasonable starting point is to consider the changes in elastic modulus asa measure of damage. Thus after damage A, the modulus is E=Eo(l-A) where

EO is the initial elastic modulus. The analysis of the damage process willbe based on an incremental approach in time. At time t, the damage is A(t)and we consider an interval "dt" at time t. A strain energy function W isassumed to exist; then it can be shown (Jordaan and McKenna, 1988) that, forelastic materials:where the superimposed dots indicate rates with respect to time, We - worksupplied by external forces across the boundaries of the element underconsideration, Wd - work dissipated on internal crack surfaces. e.g. byfriction, and G - 8W/aA, the strain energy release rate. It is importantto link the energy of damage to the strain energy; the physical basis of theenergy transfer is the effect of the crack on the elastic strain energyfield. For materials such as ice, which creep, equation (1) must be amendedto include dissipation due to creep, enhanced by the presence of cracks.The time-dependent dissipation across crack faces will also involve creep.3.0 EXPERIMENTAL WORK3.1 Test SpecimensAll tests were conducted using laboratory prepared granular ice. Tominimise the final air content of the ice while maintaining control overgrain size, the following equipment and procedure was developed and used(Figure 1). Bubble free, columnar grained ice produced from distilled,DEAERATORCOLD 1ROOM 1IIIIF I N 4 'H!EXCHANGERFREEZING -1O0C I ICE BATHImWATERAT O°MANIFOLDVACUUM1 PUMPFigure 1. Equipment and procedure, laboratory prepared granular ice.

deionized, and deaerated water frozen unidirectionally was crushed andsieved to produce 2.00 to 3.36 mm seeds. A cylindrical, acrylic mold, 229mm diameter, 303 mm length, was filled with this seed. The bottom of themold, also constructed of acrylic, was sealed with O-rings and equippedwithan air tight valve. The top of the mold consisted of a flexible latexmembrane sealed against the wall of the mold using elastic bands andsilicone high vacuum grease. The filled mold was attached, via rubbertubing, a copper coil heat exchanger, and a 3-way valve, to both a vacuumpump and deaerator.The mold, with seed ice, heat exchanger and connecting tubing, was placedunder a vacuum of 200 to 270 Pa (1.5 to 2.0 torr) for a period of 2 to 3hours. After evacuation, distilled and deionized water cooled to 0" C wastransferred to the deaerator and deaerated for 10 minutes. The mold wasthen completely flooded with this deaerated water via the evacuated tubing,3-way valve and heat exchanger immersed in an ice bath, without any furthercontact with the atmosphere.After flooding, the air tight valve was closed and the mold disconnected.The mold, supported above floor level, was then covered with an insulatingjacket leaving the bottom exposed. Freezing was primarily unidirectionalfrom the exposed bottom up, and was completed in approximately 3 days, ata cold room temperature of -10' C. The ice was removed from the mold byallowing it to warm slightly and slide from the mold.Typically, the freezing procedure produced larger than desired grainsnear the bottom and outside perimeter and a higher density of bubbles nearthe top. To ensure consistent repeatable ice quality, the top and bottom30 nun were removed and discarded. Six cylindrical samples were then cutfrom the large cylinder such that the outside perimeter was also discarded.To cut the cylinders to the desired length with ends parallel andperpendicular to the center axis, a precision V-block jig was used to holdeach sample with its longitudinal centre axis parallel to the longitudinalaxis of the lathe and perpendicular to the cross feed. Both ends were thenfinished using a vertical milling unit and a long end mill. The final testspecimens used measured 54 k .05 mm diameter by 135 k .25 mm length.The crystal structure of each batch of six specimens was checked by takinga thin section at the immediate top and bottom of random specimensthroughout a given batch. The average number of grains per diameter of 54mm of the specimens used was 17 to 22. C-axis orientation was determinedusing a Universal Stage with azimuths and inclinations plotted on a LambertEqual Area Projection. Random C-axis orientation was evident in each case.Density measurements were undertaken to provide a quantitative indication

of airbubble content. A Beckman Model 930 Air Comparison Pyconometer wasused to measure volume of a small sample of the ice and a Mettler PK 300balance to measure mass. This provided a density measurement of 0.917 ?0005 g/cm3 at -4' C. Although the ice produced is relatively transparentthrough the 54 mm diameter, some small bubbles can be seen. Densitymeasurements did not provide an adequate measure of the low air bubblecontent achieved.3.2 Test ProcedureCompression tests were conducted at three strain rates,and5x10"' sec", uniaxially, and at two triaxial confining pressures 2.5 and 5MPa. After peak stress had been reached during the initial loading of thesample, the load was removed and the specimen reloaded to obtain the initialslope and peak stress of the now damaged ice. These tests were supplementedby uniaxial tests where reloadings were applied at successively increasedor decreased strain-rate.An MTS Systems Corporation Model 905 Structural Testing System was usedfor all tests, in combination with a Structural Behaviour EngineeringLaboratories Model 10 Rockwell triaxial cell for the triaxial tests. TwoLVDT's were mounted directly on the sample 180' apart over a gauge lengthof approximately 85 mm using specially designed collars. The two LVDToutputs were averaged to provide both an in-situ measure of strain and toprovide the closed-loop feedback control signal to the MTS servovalve,Load, stroke, averaged in-situ LVDT displacement, confining pressure andtime were recorded and storedusing a microcomputer via a multifunction dataacquisition board. It was found that an acquisition rate of about 75samples/sec/channel was adequate for tests conducted at strain rates of10" to lo5 sec", however at the faster strain rate of 10'~ sec" anacquisition rate of 175 samples/sec/channel was found to be more useful.Over the range of k10V the acquisition board provides a measurement accuracyand resolution of ±0.02% Load and stroke were also plotted in real timeusing an XY plotter. This permitted unloading and reloading atapproximately the same degree of strain during each test.4.0 RESULTSFigures 2 and 3 show typical uniaxial and triaxial stress-strain curvesat a strain rate of Ixl~'^ sec'l showing both the initial loading slope andsubsequent reloadings. Classically, the elastic modulus of a material is

StrainFigure 2. Typical uniaxial test at a strain-rate of 1 x lo'&sec".Figure 3. Typical triaxial test, confining pressure of 5.0 MPa,strain-rate of 1 x lo"* set"'.

given by the slope of the stress strain curve for that material. The slopeof the least squares fit to the data over a chosen range of 0.00005 to0.00035 strain is presented in Table 1. From the original or initialTable 1. Damage A from the formulation E-E (1-A).Uniaxial Triaxial Triaxial(2.5 MPa) (5 MPa)Strain Loading Slope Damage Slope Damage Slope DamageRate E A E A E A(secV1) IGPal (GPal IGPa)1x10~ INITIAL 7.09 - 7.73 - 7.52 -2nd. 6.55 .15 6.45 .143rd. 4.99 .35 5.37 .294th. 4.24 .45 5.60 .265x10"~ INITIAL 5.69 - 6.33 - 6.82 -2nd. 2.77 .51 3.24 .49 3.07 .553rd. 1.97 .65 3.17 .504th. 2.29 .60 2.61 .59loading slope E and the subsequent slope E, the scalar damage measurepreviously discussed has also been calculated. The strains, especially onreloading, will include creep and appropriate corrections have not beenmade.Figures 4 and 5 show similar stress-strain curves (in this case uniaxial)where reloadings were at a strain-rate higher (Figure 4) and lower (Figure5) than the initial loading. In the latter case, the 3 values of plateaustress, i.e. peak stress of the now damaged ice, versus strain-rate areplotted in Figure 6.5.0 DISCUSSIONFigure 2 shows a stress-strain curve for ice at constant strain rate andin uniaxial compression. A striking feature is the fact that the plateauafter the initial peak is almost horizontal. This is indicative ofcontinuing energy dissipation, and subsequent reloading confirms that thestress-strain curve becomes stabilised, i.e. repeats itself if the strainrate is maintained in the subsequent cycle (as shown in the figure). If thestrain rate is increased on a subsequent reloading cycle, the stress attains

6 1UNIAXIALStrainFigure 4. Uniaxial test, first loading strain-rate 5 x 10'~ sec",second 1 x lo"* set"', third 1 x"= set"'.6UNIAXIALT=-IO0C1.95 MPa1.49 MFI- f2= 5 x IO-~ sec-I-g3 = IX 10-5sec-10 I 1 I I I I I0 0.0 1 0.02 0 03 0.04StrainFigure 5. Uniaxial test, first loading 1 x lo'* sec", second5 x 10'~ sec", third 1 x set"'.

0 Jones (1982)--- Sinho (1982)Figure 6. Results of test of Figure 5 for damaged ice compared toresults of Jones (1982) and Sinha (1982) for undamaged ice.a new peak with accompanying damage and subsequent re-stabilisation (Figure4); on the other hand, a decrease in strain rate on reloading (Figure 5)results in the material absorbing energy in dissipative mechanisms.Presumably this is related to enhanced creep due to the presence ofmicrocracks and frictional effects across crack faces; these are in turnrelated to such effects as creep and adhesion at asperities of the surfaces.The stress-strain curves for ice at constant strain-rates will, after aperiod of damage, reach a horizontal plateau; the plateaux illustrated inFigures 2 and 3 can be modelled using nonlinear dashpots (Jordaan andMcKenna, 1989). The flow law for ice (Glen, 1955) is normally given as i= KO" where K and n(4) are constants. For the standard triaxial test(ol>u,-0,). the stress o is replaced by the deviator (ul-03). For a uniaxialdamaged state A, the flow law can be generalised to:where f(A) and n(A) are assumed to increase with A (see also Jordaan, 1989)

If the damage is such that it results only in a reduction in cross-sectionalarea by a factor (1-A) with a corresponding increase in stress to a' froma, with a - a/(\-\), then the creep rate becomes i - ~(u')" - [K/(l-A)"]un,i.e. n is not a function of A . A more detailed analysis by Sinha (1989)also points to the same result, i.e. a final equation of the formThe simple relationship based on areas does not explain the fact thatexperimental observations show the elastic modulus changes by a relativelysmall amount while the proportionality constant in the creep rate changesby several orders of magnitude so that a more thorough analysis isnecessary. In formulating constitutive equations, changes in elasticitymust be modelled as this is the central medium for transferring energy tocrack activity. For the following, only viscous dissipation, given byequation (2). or (3). will be considered, along with elastic strain, i.e.we are considering a Maxwell unit where damage causes a degradation inelasticity and an enhancement of viscous flow.The validity of equations (2) and (3) can be tested by means of resultssuch as those shown in Figure 5. The three plateaux at different strainrates correspond to steady state creep for a given amount of damage havingbeen performed in the first cycle. The values of stress and associatedstrain rates for the damaged ice are plotted on Figure 6 in which they arecompared to the results of Jones (1982) for undamaged granular ice underhigh confining pressures and Sinha's (1982) constants for secondary creepof undamaged columnar-grained ice. Under constant stress, the presentresults for damaged unconfined ice give a strain-rate of approximately 400times that of Jones' values, showing that cracks cause a very significantincrease in creep rate. These initial results appear to be consistent withequation (3).The results presented are initial ones in a series of tests aimed at thecharacterisation of damage in ice under uni- and triaxial stress states.6.0 CONCLUSIONThe importance of damage mechanics in analysis of the ice crushing processat high strain-rates has beenillustrated. Under constant strain-rate afterthe stress reaches an initial peak, damage stabilises as the stress-straincurve reaches an almost horizontal plateau. Reloading at an increased rateproduces a new peak stress and subsequent damage restabilisation. Reloading

at a lower rate results in the material absorbing energy in availabledissipative mechanisms and a reduced plateau stress level results. Damagestabilisation occurred in both uniaxial and triaxial conditions.Measures of damage from the initial and subsequent loading slopes islikely to include creep, enhanced on reloading by the presence ofmicrocracks from previous damage. Crack density may prove to be a moreuseful measure of damage. A test technique to characterise enhanced creepusing an analytical model based on a non-linear dashpot appears promising.ACKNOWLEDGEMENTSThe assistance of Mr. M. Johnson, Mr. K. Kennedy and Mr. D. Scott withthe experimental program and data analysis, and that of Dr. R. Gagnon forhis helpful comments on laboratory prepared ice and related densitymeasurements, is gratefully acknowledged.The use of the triaxial cell made possible by Dr. B. Michel of UniversithLava1 and Dr. J.-P. Nadreau is greatly appreciated.Support for this research from the Natural Sciences and EngineeringResearch Council of Canada, The National Research Council of Canada,Institute for Marine Dynamics and from Mobil Oil Canada Properties Limitedis gratefully acknowledged.REFERENCESGlen, J.W. 1955. The Creep of Polycrystalline Ice. Proceedings of theRoyal Society of London, Vol. 228, No. 1175, pp. 519-538.Gold, L.W. 1963. Crack Formation in Ice Plates by Thermal Shock. CanadianJournal of Physics, Vol. 41, pp. 1712-1728.Jefferies, M.G. and Wright, W.H. 1988. Dynamic Response of 'Molikpaq' toIce-Structure Interaction. In Proceedings of the Seventh (1988)International Offshore Mechanics and Arctic Engineering Symposium, Vol.4, New York, American Society of Mechanical Engineers, pp. 201-220.Jones, S.J. 1982. The Confined Compressive Strength of PolycrystallineIce. Journal of Glaciology, Vol. 28, No. 98, pp. 171-177.Jordaan, I.J. 1989. Damage Processes in Ice. Canadian Congress of AppliedMechanics, 28 May - 2 June, 1989, Ottawa, Canada.Jordaan, I.J. and McKenna, R.F. 1988. Modelling of Progressive Damage inIce. Proceedings, International Association for Hydraulic Research (IAHR)Symposium on Ice, Sapporo, Japan, August, Vol. 11, pp. 585-624.Jordaan, I.J. and McKenna, R.F. 1989. Constitutive Relations for the Creep

of Ice. Proceedings, International Association for Hydraulic Research(IAHR) Symposium on Ice, Sapporo, Japan, August, Vol. 111, in press.Jordaan, I.J. and Timco, G.W. 1988. Dynamics of the Ice-Crushing Process.Journal of Glaciology, Vol. 34, No. 118, pp. 318-326.Kalifa, P., Duval, P. and Ricard, M. 1989. Crack Nucleation inPolycrystalline Ice Under Compressive States. Proceedings OffshoreMechanics and Arctic Engineering (OMAE) Symposium, A.S.M.E., Vol. 4,pp.13-21.Resende, L. and Martin, J.B. 1984. A Progressive Damage Continuum Modelfor Granular Materials. Computer Methods in Applied Mechanics andEngineering, Vol. 42, pp. 1-18.Sinha, N.K. 1982. Delayed Elastic Strain Criterion for First Cracks inIce. Symposium on Deformation and Failure of Granular Materials, Aug. 31- Sept. 3, Delft, Netherlands.Sinha, N.K. 1989. Ice and Steel - A Comparison of Creep and Failure.Proceedings, Mechanics of Creep Brittle Materials (Euromech 239), August,Leicester, England (in press).Timco, G.W. and Frederking, R.M.W. 1986. The Effects of Anisotropy andMicrocracks on the Fracture Toughness (Krc) of Freshwater Ice.Proceedings of the Fifth (1986) International Offshore Mechanics andArctic Engineering (OMAE) Symposium, Vol. 4, New York, A.S.M.E., pp.341-348.

THE TRANSFER FUNCTION APPROACH FOR ASTRUCTURE SUBJECTED TO ICE CRUSHINGG.W. TimcoR.M.W. FrederkingS.K. SinghNational Research CouncilOttawa, OntarioMemorial UniversitySt. John's, NewfoundlandCANADACANADAABSTRACTA test program has been performed to investigate the suitability andreliability of the transfer function approach in determining ice loads onflexible structures. A simple cylindrical structure was modelled with acompliant foundation and the loads on both the structure and its foundationwere measured during ice/structure interaction events. The dynamics of thestructure were determined by step-unloading experiments in ice-free water.Assuming that the structure behaved as a single-degree-of-freedom oscillator,foundation loads (which include the dynamics of the structure) werecalculated using Fourier techniques. These were compared to experimentallymeasured values. The results of the test program indicate that this approachis useful only if the frequency of the loading events is not at all close tothe natural frequency of the structure. At or near resonance conditions, thistechnique cannot be used to predict accurately the loads or the dynamicbehaviour of the loading events.1.0 INTRODUCTIONIn many field situations where a slender structure (such as a lighthouse)is subjected to ice loading during winter months, a knowledge of the iceforces is important. In most of these situations the structure is fairlylight and loading events can occur with frequency components near the natural(resonant) frequency of the structure. During resonance, the ice loads whichare transmitted to the foundation of the structure can be greatly amplified.The amount of amplification depends upon the natural frequency and dampingcharacteristics of the structure. To try to measure these characteristics ofthe system, a number of step-unloading or "plucking" tests are usuallyperformed during the summer months. By appropriate analysis, a "transfer

function" can be determined which can give an indication of the dynamicamplification of the structure due to resonance processes. The main problemwith this approach is that the plucking tests are performed when thestructure is in open water which is free from ice. During the winter months,however, ice surrounds the structure. Since the ice may influence the dynamicbehaviour of the structure, there is no guarantee that the ice-free transferfunction represents the correct transfer function during ice loading events.To try to address this problem, a test series was performed in a modellingbasin. In the tests a slender model was instrumented to measure both the iceforcing loads and the foundation loads. The model, which was designed to becompletely rigid within itself, rests on a compliant foundation. By usingthis experimental arrangement, the general applicability and reliability ofthe transfer function approach in ice crushing can be investigated.2.0 THEORYA structure which is built on a flexible foundation can, as a firstapproximation, be considered as a Single Degree Of Freedom (SDOF) oscillator.This is represented as a mass connected to a spring which provides arestoring force proportional to the amplitude of the displacement, and adamper which acts to remove energy from the system in proportion to thevelocity of motion (see Figure 1). The dynamic response for this system canbe characterized by the mass m, the stiffness k and the amount of damping c.The equation of motion for this oscillator is (dough and Penzien, 1975)where x = x(t) represents the displacement of the mass, 2 and x are its firstand second time derivatives, and p(t) represents the time varying excitationforce (i.e. the ice loading on the structure). This equation is asimplification of the actual system. For a SDOF oscillator, the naturalfrequency of free vibration, fN, is given asFor an offshore structure, the ice loading on the structure at the waterline is equivalent to p(t), the measured force on the structure. If thestructure and foundation are completely rigid, the load transmitted to thefoundation would be simply p(t). However, if there is some compliance in

Figure 1 : Schematic showing a single degreeof freedom (SDOF) oscillator.applied "excitation" ice load p(t) (see Figure 1).the system the ice loading onthe structure may "excite it" andcause it to move in response tothe loading. If the frequency ofthe ice loading is at or near thenatural frequency (fN)of thestructure, a condition ofresonance occurs and themovementof the structure will cause anincrease in the loading on thefoundation. The "foundationresponse" load q(t) is notnecessarily the same as theClearly, the nature ofthe response is dependent upon the dynamic characteristics of the structureand its foundation. The foundation response q(t) can be related to theforcing function p(t) by the impulse response function of the structure h(t),by the convolution integralIt is more convenient to transform this relationship into the frequencydomain asIf the structure is assumed to behave as a SDOF oscillator, the frequencyresponse function H(f) can be determined by performing a step-unloading, orplucking" experiment. In this, the structure is loaded with a static loadwhich is released abruptly. From the vibration response of the structure,the natural frequency fN and critical damping ratio (c-c/4mrfN) can bedetermined. Tests of this type have been performed in the field onlighthouses (Haynes,1986) and bridge piers (Lipsett and Montgomery,1979) andin the laboratory on model structures (Maattanen,1983; Frederking and Timco,1987). From the tests, the amplitude of the frequency response function, orthe "transfer function" can be determined as

By using equations (4) and (5) and appropriate Fourier analysis it ispossible to determine q(t) if p(t) is known or vice versa. If this methodcould be substantiated with respect to ice loading events, it could be a verypowerful tool for determining ice forces on a structure and its foundation.3.0 EXPERIMENTALIn order to investigate this, it is necessary to design a system containinga structure mounted on a compliant foundation and subjected to ice forces.In addition, both the applied (ice) load and the load at the foundation mustbe measured. In these tests, a simple cylindrical pile of 6 cm diameter waschosen to represent a slender vertical-sided structure. This pile wasdirectly mounted to a dynamometer which measured the ice forces on thestructure at the water line (i.e. p(t)). The natural frequency of thisassembly was greater than 80 Hz. The base of the dynamometer was mountedthrough a compliance simulator to a second dynamometer which measured thefoundation or response forces (i.e. q(t)). Note that the system is rigid inthe vertical direction. This allows the experiment to be performed with thedynamometers and compliant foundation mounted above the structure (see Figure2). This arrangement avoids the problems inherent in waterproofing themeasuring instrumentation. It does not at all adversely influence the testresults. The compliance simulator is the same one used in a previous studyby the authors (Frederking and Timco, 1987) with the addition of a dashpotwhich allowed some adjustment to the damping characteristics of the system.A separate mechanism allowed adjustment of the natural frequency of thesystem. In the test program fà varied from 10.7 to 55.7 Hz and (" varied from3.8% to 8%.In addition to the dynamometers which measured the total forces in thehorizontal plane, an accelerometer and displacement gauge were included inthe instrumentation package (Figure 2). This whole arrangement was mountedon the main carriage in the NRC Hydraulics Laboratory ice modelling facility(Pratte and Timco,1981). By moving the carriage, relative interaction speeds(s) between the ice and the structure were obtainable up to 65 cm-sl. Theoutput from the transducers were sampled at a rate of 250 Hz. A 100 Hz anti-aliasing filter was used in the data acquisition hardware. The data werestored in digital form for subsequent analysis and signal processing.In testing, the stiffness and damping characteristics of the structure wereset by adjusting the compliance simulator. Then, a step-unloading test was

-ICE-FOUNDATIONDYNAMOMETER all)COMPLIANCESIMULATORFigure 2 : Schematic diagram showing theexperimental arrangement.performed from which the impulseresponse function h(t) wasmeasured. The Fourier transformof this gave the frequencyresponse function H(f)(seeFigure 3). The structure was thenmoved along the length of thetank relative to the fixed icesheet. The data acquisitionsystem was started only when thecarriage was at the desired testspeed. The model ice used in thetest series was EG/AD/S(Timco, 1986).iceThis model icerepresents well, on a reducedscale, thecrushing, flexuralandfracture behaviour of sea ice.For all the tests, an average icethickness (h.)of 3.7 cm wasused. The flexural strength of the ice was 50 kPa for all test series exceptone where the strength was reduced to 30 kPa. In total 34 separate test runswere performed with parametric variations of the stiffness, damping, speed,and flexural strength.TIME (s)10 25FREQUENCY (Hz)Figure 3 : Time series decay and amplitude transfer function from oneof the step-unloading tests giving f,, - 17.6 Hz and (Â - 4.5 8.

4.0 RESULTS AND DISCUSSIONThe full test results of this program are too lengthy to be published here,but they will be published in a subsequent publication. In this paper onlyone of the experimental arrangements with hi - 3.7 cm, fà - 17.6 Hz and ( -4.5% will be used.When ice crushes, there are definite time-series variations of the loadwhich are cyclic in nature. To evaluate the present test results, it isimportant to consider the characteristic frequency of the ice crushingprocess. This can be found by measuring the ice loads on a completely rigidstructure where there is no feedback between the structure-ice system. Thenthe measured crushing frequency does not depend upon the structuralcharacteristics. It is possible to determine the characteristic frequency ofcrushing for any given speed. Sodhi and Morris (1984) have performed anextensive set of model tests on a rigid structure to investigate this Theyfound that, as a rule-of- thumb, the characteristic crushing frequency ( fC) isrelated to the ice thickness (hl) and interaction rate (or speed) (s) by fc= K s/h, where K has a value ranging from approximately 3 to 5. For thepresent test series with h - 3.7 cm, this crushing frequency would be givenas fc = s where f is in Hz and s is in cm-s". This approach will be used topredict the characteristic crushing frequency of the ice.In the evaluation of the present test results three separate cases willbe examined : Case 1 where the characteristic crushing frequency is lowerthan the natural frequency ; Case 2 where the characteristic crushingfrequency is close to the natural frequency ; and Case 3 where thecharacteristic frequency is higher than the natural frequency of the system.Figure 4 shows a time-series of the load variations of the forcingfunction p(t), the measured response function q(t) and the calculatedresponse function n(t) for the conditions where f is much lower than fu (Case1). Included on the figure are the variance spectral densities for each timeseries.For this test h = 3.5 cm and s = 5 cm -s so the predictedcharacteristic crushing frequency (f) would be as 5 Hz. Examining thespectral density plots indicates that this is not so. Even at this relativelylow speed of 5 cm-s 1 there is considerable energy in the frequency rangeabove 5 Hz. There appears to be a feed-back mechanism in effect which forcesthe structure to vibrate at a frequency close to the resonance frequency ofthe structure. In essence then, the forcing function p(t) is not simply a

function of time alone; it is also a function of the characteristics of thestructure. A comparison of the measured and predicted foundation responseindicates that the correspondence between them is not too good. It is seenthat the compensation techniques has amplified the frequency components inthe frequency range close to fà to such an extent that it is the peakfrequency in the predicted time-series.FORCINGFUNCTION~ ( t )2400 lÑÑÑÑÑÑÑÑÑÑSPECTRAL 1 1DENSITY[N2/HzlMEASUREDRESPONSEFUNCTIONCALCULATEDRESPONSEFUNCTIONn(l)1NI24002400o-1600 'ÑÑÑÑÑÑÑÑÑTIME (s)10SPECTRALDENSITY[N2/HzlSPECTRALDENSITY[N2/Hzlok0 20 40I 05 x105FREQUENCY (Hz)Figure 4 : Time-series and spectral density functions for Case 1 wherethe predicted characteristic crushing frequency is lower than thenatural frequency of the structure (s - 5 cm-s l ).Figure 5 shows a time-series of the load variations for the condition whenthe natural frequency of the structure is similar to the characteristiccrushing frequency of the ice (Case 2). For this test, the structuralcharacteristics of the system were the same as in the previous test but s -18 cm-s'l (so f s= 18 Hz). There are three things to note. First, it is quiteevident that the foundation loads are significantly higher than the iceforcing loads. The amplification effects on the ice load on the foundationare pronounced. Second, the calculated response function has a maximum valuewhich is much larger than the measured foundation load. It is clear that theFFT approach significantly overpredicts the foundation load. This indicatesthat there is additional damping introduced into the system, probably due tothe crushed ice surrounding the structure during ice loading events. Third,although the frequency content are similar for all three time-series, theamplitude of the calculated variance spectral densities are quite different.

FORCINGFUNCTION~(1)IN1SPECTRALDENSITY[N2/HzlMEASUREDRESPONSEFUNCTIONq(1)IN1SPECTRALDENSITY[N2/Hz]CALCULATEDRESPONSEFUNCTIONnil)IN10 5TIME (s)SPECTRAL 1 1DENSITY[N2/Hzl00 20 40FREQUENCY (Hz)Figure 5 : Time-series and spectral density functions for Case 2 wherethe predicted characteristic crushing frequency is close to the naturalfrequency of the structure (s - 18 cm-s").FORCINGFUNCTIONP(t)IN1600-SPECTRALDENSITY[NVHz]MEASUREDRESPONSEFUNCTION---q(t) 0IN1CALCULATEDRESPONSEFUNCTIONn(t)SPECTRALDENSITY[N2/Hz]600 12 x104oIN] 0 1 ou-TIME [s]SPECTRALDENSITYlN2/Hz]0 20 40FREQUENY [Hz]Figure 6 : Time-series and spectral density functions for Case 3 wherethe predicted characteristic crushing frequency is higher than thenatural frequency of the structure (s - 60 cm-s").

Figure 6 shows a time-series of the load variations and the spectraldensities for the condition when the characteristic crushing frequency of theice is higher than the natural frequency of the structure (Case 3). For thistest, the structural characteristics of the system were the same as in theprevious test with s - 60 cm-s'l (so f, = 60 Hz). Once again the peakfrequency is close to 17 Hz, indicating that the structural characteristicsare influencing the loading event.. -- -CALCULATED7 I- + +3I -MEASURED1 10(f./f.)Figure 7 shows a plot of theratio of the peak foundationload to the peak forcing loadversus the ratio of thecharacteristic to the naturalfrequency (fc/fy) for the wholetest series with fà = 17.6 andr - 4.5 %.Both the measuredand the calculated foundationloads are shown. From thisfigure it is clear that thisFigure 7technique does not give a good: Performance curve of the measuredand calculatedoeak foundation loadwhere the estimate of the foundationcalculated load uses the transfer function load, especially in the regionapproach ..with a SDOF oscillator model.where the predictedcharacteristic frequency is close to the natural frequency. The data inFigure 7 show a general overprediction of the foundation load in this testseries. This was generally true in the other test series (for structures withdifferent frequency and damping characteristics); however, in some instances,the SDOF model underpredicted the foundation loads.Clearly the wholeprocess of ice crushing on flexible structures is complex. This complexitymakes the use of the SDOF oscillator model not reliable in many cases.From the foregoing discussion it is evident that there are many factors whichinfluence the ice and foundation loads and the treatment of this problem.There are two which should specifically be identified. First, the dampingcharacteristics of the transfer function are not as predicted by the SDOFmodel. The actual transfer function is much more complex than that inferredfrom a SDOF oscillator. It is conjectured that the crushed ice layer (seeJordaan and Timco, 1988) surrounding the structure serves to change thedamping of the system. Second, from the spectral characteristics of the timeseries,it is evident that the structural characteristics significantly

70 - ---influence the load on the60-structure. In fact there50appears to be a type of "lock-> 0 o FLEXIBLE STRUCTUREin" phenomenon which extends$ 3oi \?ZZ? over a very wide range ofrr"- 20interaction rates. Figure 8^- 1 . , H-n 100 5 0 5 20 25 30 35 40 45 50 55 60 65 70INTERACTION RATE (cmls)shows an overall comparison ofthe peak forcing frequency ~.measured in this test seriesversus the interaction rate.Figure 8 : Comparison of the peak frequency The Curve illustrating theversus the interaction rate showing the general trend for a rigidlock-in" phenomenon of the peak frequencyover a wide range of interaction rates.structure (Sodhi and Morris,1984) is also shown. It isclear that in this test series the peak frequency is constant over a widerange of interaction rates. Similar behaviour has been measured in othermodel tests on flexible structures (Tsuchiya et al, 1985) and was recentlyobserved in large scale vibrations of the Gulf Resources structure Molikpaqin the Canadian Beaufort Sea (Jeffries and Wright, 1988). The generaldisagreement in Figure 8 between the test results on a flexible structure andon a rigid structure indicate that the forcing function p(t) contains acomponent that depends on the oscillator response. This gives the pooragreement shown in Figure 7.5.0 SUMMARY AND CONCLUSIONSA simple analysis has been performed to compare, in ice loading events,the measured foundation load time-series and spectral density with thatcalculated using Fourier techniques assuming a SDOF system. The resultsindicate that only in certain circumstances will this approach be useful inestimating the maximum loads transferred to the foundation in ice/structureinteraction events. The simple model of a single-degree-of-freedom oscillatoris quite inadequate to predict the frequency content of the time-series. Thisis most likely due to ice-induced damping. In using this technique it wouldappear that it may give reasonable results as long as (1) the structurebehaves in a manner similar to a SDOF oscillator, and (2) the frequency ofthe forcing function is not at all close to the natural frequency of thestructure. If either of these conditions are not met, a more complex modelincorporating ice damping and force feedback would have to be used in orderto obtain the correct results.

6.0 ACKNOWLEDGEMENTSThe authors would like to thank R. Bowen for technical assistance in thisprogram. This work was partially funded by the Natural Science andEngineering Research Council of Canada through an Operating Grant to GUT.This grant made it possible for S.K. Singh to participate in this researchprogram.7.0 REFERENCESClough, R.W. and Penzien, J. 1975. Dynamics of Structures, McGraw-Hill Inc.,New York, N.Y., U.S.A.Frederking, R.M.W. and Timco, G.W. 1987. Ice Loads on a Rigid Structure witha Compliant Foundation. Proc. POAC 87, Vol 3,pp 393-402. Fairbanks,Alaska.Haynes, F.D. 1986. Vibration Analysis of the Yamachiche Lighthouse. Int. J.of Analytical and Experimental Model Analysis, Vol 1, No 2, pp 9-18.Jeffries, M.G. and Wright, W.H. 1988. Dynamic Response of "Molikpaq" to Ice-Structure Interaction. Proc. OMAE 88, Vol 4, pp 201-220.Jordaan, I. J. and Timco, G.W. 1988. Dynamics of the Ice Crushing Process.J. Glac. 34, No. 118, pp 318-326.Lipsett, A.W. and Montgomery, C.J. 1979. Dynamic Structural Response of aMassive Bridge Pier. Alberta Research Council Internal Report SWE-79/04,Edmonton, Alberta, CanadaMaattanen, M. 1983. Dynamic Ice-Structure Interaction During ContinuousCrushing. U.S. Army CRREL Report 83-5 Hanover, N.H., U.S.A.Pratte, B.D. and Timco, G.W. 1981. A New Model Basin for the Testing ofIce-Structure Interaction. Proc. POAC 81, Vol, pp 857-866, Quebec City,Canada.Sodhi, D.S. and Morris,C.E. 1984. Ice Forces on Rigid Vertical CylindricalStructures. US Army CRREL Report 84-33, Hanover, N.H , USA.Timco, G.W. 1986. EG/AD/S: A New Type of Model Ice for RefrigeratedTowing Tanks. Cold Regions Science and Technology. Vol 12, pp 175-195.Tsuchiya, M., Kanie, S., Ikejui, K. and Yoshida,A. 1985. An ExperimentalStudy of Ice-Structure Interaction. Proc. Offshore Technology Conf. OTCHouston, Texas, USA

CONSTITUTIVE MODELING OF POLYCRYSTALLINE ICEMao S. WuResearch AssistantS. Shyam SunderAssociate ProfessorMassachusetts Institute of TechnologyDepartment of Civil EngineeringRoom 1-274Cambridge, MA 021 39U S.A.ABSTRACTThis paper examines the constituent elements of a numerical model for simulating ice-stuctureinteraction processes. The discussion emphasizes the fundamental element of the model, i.e., theconstitutive model, and elucidates the physical basis of a flow model for polycrystalline ice proposed byShyam Sunder and Wu (1989a, b) Also discussed is the physical interpretation of material parametersand their determination from standard tests on ice, and the validation of the predictive capabilities of thenumerical model.1 INTRODUCTIONThe ultimate objective of numerical modeling as applied to ice-structure interaction is the prediction ofice loads on structures. Within this broad objective at least two roles can be identified for a numericalmodel. The first is the simulation of field-scale problems without necessarily having to conduct field-scaleexperiments. This allows one to explore the sensititvity of the ice-structure response to various inputparameters associated with the structure, materials, and environment at comparatively little cost.Furthermore, a wide range of behaviors can be studied under controlled conditions, particularly thoserelated to extreme conditions of loadingA second role is to help establish more rational engineering design procedures that lead to safe andeconomical systems For instance, a parametric study enables the identification of field parameters (suchas the speed of ice feature, ice strength and interaction geometry) that have the most significant effect onthe predicted ice force. These parameters could be obtained with the greatest accuracy in the field, thusimproving the accuracy of prediction. Furthermore, if a significant parameter is structure-related, then thestructure can be optimized to minimize ice forces. From such studies parametric formulae can also beestablished for design purposes.The relationships between various elements of a numencal model are discussed in Section 2.Constitutive modeling is discussed in Section 3. This attempts to establish the link betweenphenomenology and the physical mechanisms operating on the microscale The procedures required forthe determination of model parameters and the validation of the numerical model are reviewed in Section

4. The last section summarizes the authors' view on current and future research in constitutive modelingas applied to numerical modeling.2. CONSTITUTIVE ELEMENTS OF A NUMERICAL MODELBecause of the many complexities that must be taken into account in a typical ice mechanics problem,solution by numerical simulations Is often necessary First, ice is a complex material occurring naturally athigh homologous temperatures, and may have several physical mechanisms operating on the microscalesimultaneously. It may contain cracks, voids, brine channels, and may be texturally anisotropic. Second,the environmental, loading, and ice-structure interface conditions must be taken into account asappropriate boundary and initial conditions These include temperature, velocity of ice feature, and thegeometry of contact and the coefficient of friction between ice and structure. Third, the complexgeometries of ice and indenter complicate the prediction of ice forces further. In some problems, the mostInportant parameters are the aspect ratio (between indenter width and thickness of ice feature) andstructural geometry (indenter with vertical or inclined face).Depending on these parameters ice displays a wide rande of behaviors including transient creep,steady-state creep, tertiary creep and brittle fracture. During indentation or impact, these complexbehaviors can cause ice to fail by creep, crushing, cracking, spalling and buckling The deformation modemap of Palmer et a1 (1983), reproduced in Fig. 1, schematically shows the influence of strain rate andaspect ratio on the deformation mode. It shows that ice fails by creep at strain rates below about loe4 s-l,while at higher strain rates it can fail by a variety of modes ranging from crushing for aspect ratios lessthan about 0.5 to radial and circumferential cracking for aspect ratios greater than about 10Approximate analytical methods for indentation problems based on the plastic limit analysis (e g ,Ralston, 1978) and the reference-stress model (e.g., Ponter et al., 1983) suffer from the drawback thatnot all the parameters can be simultaneously analyzed. It is in this respect that numerical models usingthe finite element and boundary element methods offer a definite advantage (Jordaan, 1986). Recentwork by Shyam Sunder et al. (1989c), which combines a flow model and a smeared cracking model oftensile failure in a finite element framework, is a step towards the study of ice-structure interaction in theductile-to-brittle transition region.a-1 ' ' 'U I 1 Â 10 .mCONTACT an*-LAFig. 1 Deformation Mode Map(Reproduced From Palmer et al. (1983))

The constituent elements or building blocks of a numerical model are the constitutive, finite element (orboundary element), and the system models. At the lowest level is the constitutive model whirh d-terminesthe response of a material under load. Two distinct types of constitutive models exist- the macroscopicmodel and the micromechanical model.In the macroscopic approach, constitutive relations are derived for the particles of the continuum interms of macroscopic quantities. A continuum particle refers to a representative volume of theneighborhood of a material point. The representative volume is regarded as uniform and subjected toboundary conditions which are compatible with the overall stress and deformation fields. In apolycrystalline material the representative volume must be appropriately small compared to the overalldimensions of the material body, and yet sufficiently large to ensure overall homogeneity of itsconstitutent grains, thus permitting the overall behavior to be adequately described.A macroscopic model ranges from the purely phenomenological to the purely physical (ormicrostructural). An example of the former is one of the many classical spring-dashpot models, while thedislocation kink model developed by Goodman et al. (1981) for steady-state creep of ice falls into thesecond category In a physically motivated approach, the constitutive relations are derived from theviewpoint of the underlying physical mechanisms (which may be represented phenomenologically bysprings and dashpots) The flow models of Sinha (1978), Michel (1978), and Ashby and Duval (1985) forpolycrystalline ice are in this category.In the micromechanical approach, constitutive relations are derived for suitable "microelements" of arepresentative volume sample. Taking plasticity in metals as an example, where if the overall inelasticityis due to slip over crystallographic planes in individual crystals, one approach is to derive the constitutiverelations for the microelements using local parameters, e.g., the rates of slip in the various slip systems interms of the resolved shear stresses. Using the relations between the local quantities for a typicalmicroelement and the macroscopic quantities, the overall response can then be extracted by using someaveraging technique. However, the precise nature of the slip systems operating in polycrystalline Ice Isnot yet fully resolved (see Duval et al., 1983). Also. damage processes which may contribute significantlyto the total deformation are not fully known. For these reasons and the fact that the micromechanicalapproach demands substantial computational effort, only macroscopic models are discussedsubsequently.It is necessary to incorporate the constitutive model in a finite element framework. This enforcesequilibrium of nodal forces and moments as well as compatibility of displacements at the nodes. Thechoice of a particular finite element type (e.g., plane linear or quadratic isoparametric element) dependson the problem at hand and the requirements of accuracy, efficiency, stability and good convergencecharacteristics. Viscoplastic models based on internal variables are generally stiff, and require efficienttime-integration scheme for solution. This generally demands a minimal acceptable level of accuracy,since a typical problem may involve hundreds of elements and solving the creep and damage constitutiveequations for all the elements is costlyFinally, at the uppermost level is the system model which encompasses the entire ice feature and thestructure. This involves the task of problem definition, i e., the translation of a complex engineeringproblem into a mathematical model. The system model is then integrated with the finite element andconstitutive models into an overall numerical model. This involves optimizing the mesh design using thefinite elements. Special elements may be used to simulate the ice-structure interface and crack-tip

egions. Material constitutive laws and appropriate boundary conditions are specified for the elements.3. PHENOMENOLOGICAL AND PHYSICAL MODELS OF CONSTITUTIVE BEHAVIORTo facilitate the description of physical models of ice deformation, the molecular structure of ice is brieflyreviewed here, following Glen (1968) The form of ice at low pressures, i.e. ice 1-h, has a hexagonalstructure An oxygen atom occupies a point of the hexagonal lattice and is bonded by hydrogen to fourother oxygen atoms located at the corners of an approximately regular tetrahedron. Each oxygen atom isclosely associated with two hydrogen atoms at a distance of about 0.95 A, and is also linked to two otherhydrogen atoms at a distance of about 1 76 A. The oxygen atoms are concentrated on the basal planesto which the principal hexagonal axis (c-axis) is perpendicular.The structure of ice 1-h is such that the oxygen atoms are crystallographically ordered with the positionof the hydrogen atoms obeying the Bernal-Fowler rules which state that (i) only two hydrogen atoms areassociated with each oxygen atom and that they can occupy any of the four tetrahedral links between theoxygen atoms, and (ii) only one hydrogen atom can lie between any pair of oxygen atoms A breach ofthe first rule produces ionic defects' a negative ion (OH)., or a positive ion (HgO)+. A breach of the secondrule produces Bjerrum defects a D-defect, I e., a bond with two protons on it, or an L-defect, i e., a bondwith no protons on it.The sizes, shapes and orientations of crystals in a polycrystal can vary, giving rise to different types ofice. Two of the most common freshwater ice types are the S-2 columnar-grained ice with preferredhorizontal orientation of c-axes, and the T-1 snow ice with equiaxed grains and a random orientation ofc-axes. The discussion in the following sections is restricted to freshwater polycrystalline ice.3 1 Steady-State and Transient CreepSince elastic deformation in polycrystalline ice is well characterized by the classical Hooke's law, onlycreep deformation is discussed in this paper. Alternative physical mechanisms leading to creep havebeen proposed by various researchers Michel (1978) has proposed that creep occurs by dislocationmultiplication and the preferred slip of ice crystals on basal planes The unfavorably oriented crystals willinitially rotate to an orientation favoring basal slip, and the overall deformation is accomodated by localboundary sliding. This model can describe elastic behavior as well as transient and steady-state creep.On the other hand, Sinha (1978) has argued that transient creep (delayed elasticity) is the directconsequence of grain boundary sliding, while steady-state viscous creep is due to basal slip only. Duvalet a1 (1983) suggested that slip must occur on both basal and nonbasal planes for extensive creepdeformation to occur. Since the resistance to slip on nonbasal planes is much larger than that on basalplanes (at least sixty times at -1O0C), as can be inferred from experimental data on the plasticity ofmonocrystals (Duval et al., 1983), the basal planes initially bear much of the load which is subsequentlytransferred to the nonbasal planes. This results in transient creep. Steady-state creep occurs when thereis a balanced interaction between the basal and nonbasal deformation systems. However, apart frombasal slip the precise deformation systems have yet to be determined. Duval et al (1983) suggestedpossibilities involving slip on the prismatic and pyramidal planes (nonbasal slip), as well as climb of basaldislocations onto ~rismatic lanes

3.2 Constitutive Modeling of FlowThe discussion above underlines the fundamental differences of the various approaches. More recently,Shyam Sunder and Wu (1989a. b) have developed a flow model for polycrystalline ice based onthermodynamics with internal variables as proposed by Coleman and Gurtin (1967). This model departsfrom previous models in two ways. First, it recognizes that knowledge of the physical mechanisms ofcreep in polycrystalline is incomplete, and consequently describes the plausible mechanisms in terms ofcertain hard and soft deformation systems. This general approach agrees with that of Sinha (1978), sincegrain boundary sliding and basal slip may be considered as the soft and hard systems, respectively, andAshby and Duval (1985), who consider basal slip and nonbasal slip as the soft and hard systemsSecond, it is consistent with thermodynamic principles. The internal structural change or rearrangementthat occurs during creep deformation is accompanied by energy storage and dissipation, and must satisfythe thermodynamic law of dissipation. Furthermore, the model satisfies (i) dimensional requirements atsmall stresses, i.e., dimensionless creep curves can be constructed from properly non-dimensionalizedvariables of time, strain and strain-rate (Ashby and Duval, 1985), and (ii) correspondence requirementsbetween constant-stress creep tests and constant strain-rate tests, i.e., a creep curve can be constructedfrom a family of stress-strain curves, and vice versa (Mellor and Cole, 1983).In the model the total strain rate is additively decomposed into three components associated withelasticity, transient creep and steady-state creep The evolution of transient creep is attributed to thegeneration of certain back and drag stresses that resist the applied stress. The back stress is a longrange elastic stress which may arise from the development of local inhomogeneities such as the polarizeddistribution of dislocations resulting from dislocation pile-ups at grain boundaries, and stressconcentrations at triple points resulting from grain boundary sliding. Duval et al (1983) have associatedthe development of back stress with the directional stress transfer from the basal system to the nonbasalsystem Under load it is the soft system which initially sustains a greater load or deformation. Asdeformation progresses, the hard system becomes more dominant and the material in effect hardens.Based on these considerations, the back stress in the proposed model is taken to represent ananisotropic flow resistance which increases as the hard deformation system becomes increasingly activein resisting flow. This is accompanied by an increasing isotropic resistance or drag stress to flow. Thiscontribution to hardening may arise from dislocations interacting on parallel and intersecting planes, orfrom the formation of cell walls.During loading the stress driving transient creep is the applied stress reduced by the back and dragstresses. Permanent irreversible deformation occurs simultaneously and this is associated with "steadystate"creep deformation. Upon unloading, the back and drag stresses are not instantaneously recovered,rather, they cause reverse transient creep to occur. Thus, an important difference between the proposedmodel and that of Ashby and Duval (1985) is that transient creep (or anelasticity) is associated directlywith the interference of the back and drag stresses on flow processes, while irrecoverable creep is directlyassociated with the steady-state component of creep.Power Law Creep - In the model of Shyam Sunder and Wu (1989a, b), only small strains and rotations

are considered. Additive decomposition of the total strain rate into recoverable and irrecoverablecomponents then yields:where E, E , F, and E denote the total strain, elastic strain, transient strain, and steady-state creep strains,respectively. The superposed dot denotes the time derivative. The instantaneous elastic strain is given bythe stress divided by Young's modulus. The equation describing irrecoverable steady-state creep at lowstresses (e.g., between 0 1 MPa and 2 MPa at -1 O0C) is the power law given by:where i is a reference strain rate (set equal to unity), and N, o, and V denote the power law index, thestress, and a temperature dependent stress factor, respectively. For the temperature range ofapproximately -40° to -1O0C, the stress factor obeys the Arrhenius law.where V Q, R and T denote a temperature independent constant, the activation energy for steady-statecreep, the universal gas constant and the temperature in Kelvin, respectively The activation energy Qhas been found to lie in the range 60 to 80 KJ mol-I within the stated temperature range. Close to thefreezing point, Q increases, possibly due to the effect of grain boundary melting. The power law index Ngenerally equals three for the stated stress range, although it can vary from one at very low stresses to avalue greater than three beyond about 2 MPa. Goodman et al 's (1981) deformation mode map suggeststhat diffusion creep is the deformation mechanism at very low stresses (e g. c 0 1 MPa at -1O0C), while athigh stresses (e.g. > 2 MPa at -10°C the rate limiting mechanism for dislocation glide is the nucleation ofkink pairs on dislocation linesFrom an analysis of both creep and hardness data for randomly oriented polycrystalline ice. Barnes etal. (1971) have used the hyperbolic sine function to describe steady-state creep behavior over the range0.1 MPa to 10 MPa, corresponding approximately to about 10"9 s'l to 10"' s-l, i e£, k0 = A'(sinh on)^ exp [-Q/(RT)]where for the temperature range of -8° to -14'C, a, N, Q and A' have been determined to be 0.254(MP~)-', 3.08, 78.1 KJ mol~l and 3.14 x 101 s-', respectivelyEquations (2) and (4) are phenomenological equations However, they are consistent with a physicalmodel of steady-state deformation proposed by Goodman et al (1981). This model is motivated by Glen's(1968) idea that the motion of dislocations through the ice lattice is made difficult by the creation ofdefects (ionic and Bjerrum defects) The protons are believed to be randomly arranged about the oxygenatoms according to the Bernal-Fowler rules. This randomness suggests that as a dislocation movesthrouah the lattice, breaches of the rules will be made with the creation of defects If the randomly

arranged protons are frozen on the bonds, Glen (1968) found that the shear stress required to move thedislocation is about a tenth of the shear modulus. As Ice creeps at a much lower stress at highhomologous temperatures, it is suggested that the protons must be capable of rearrangement to yield afavorable configuration ahead of the dislocationAccording to the model of Goodman et a1 (1981), an initially straight dislocation advances by thenucleation of kink pairs at places where the proton configuration just ahead of the dislocation is favorable,i.e., no defects are created. The dislocation is advanced by the drift of the kink pairs which are annihilatedwhen they encounter kinks of opposite sign. The advance is possible only if the local proton configurationis favorable. At low stresses and high homologous temperatures (but above the stress level at whichdiffusional creep is dominant) the rate limiting mechanism is proton rearrangement As the temperaturedecreases, and at high stresses, the rate of proton rearrangement decreases and kink nucleation itselfbecomes rate limiting At absolute zero the protons are immobile and the rate limiting mechanism isdefection creation itself, with a flow stress close to the ideal strengthThe shear strain rate is given by the Orowan equation:where p, b and vdi denote the mobile dislocation density, the Burger's vector of dislocation, and thedislocation velocity, respectively At low stresses where proton rearrangement is rate limiting, Goodmanet a1 (1981) used an expression for v d which is inversely proportional to temperature, but proportionalto the shear stress o, and the term exp[-F/(RT)], where F denotes the energy associated with the kinkand the formation and motion of a Bjerrum defect The mobile dislocation velocity is taken to beproportional to 3. Substituting the expressions for vdls and p in Eq. (5) yields an expression for the shearstrain rate:where a, v, k and G denote the kink height, the vibration frequency associated with protonrearrangement, the Boltzmann's constant, and the temperature dependent shear modulus. Theparameter a is the only 'empirical' constant in Eq (6), and can be determined from effective shear strainrate versus shear stress data obtained from constant strain rate tests.It can be shown that the variation of the term t/(Gq) with temperature is negligible compared with thecorresponding variation in exp[-F/(kT)]. Consequently , the power law creep with N = 3 as stated in Eq. (2)is a good approximation of Eq (6) at low stresses. Indeed, the shear stress and shear strain rate in Eq.(6) can be converted to equivalent axial quantities using the relations = 3'12 and o = 0/3"~, and acomparison between Eqs (2) and (6) then yields'The values of the parameters provided in Goodman et a1 (1981) are: a. = 1.2 x to"=, a-b = 4.52 x 10''~m, (t/v,,) = 6.36 x tot6 s, k = 1 38 x J K-I. For T = 263.15 K, G is estimated to be 3.048 GPa using

an equation contained in Goodman et al (1981). The parameter V is then estimated to be 1 20 KPa fromEq (7), which agrees with the value (1.21 KPa) used in Shyam Sunder and Wu (1989a, b) for Q = 78 1KJ mol-l.At higher stresses kink nucleation becomes rate limiting, and the physical model developed byGoodman et al. (1981) appears to describe well the data presented in Barnes et al. (1971) It predictsthat the shear strain rate tends to infinity as the shear stress approaches the ideal shear strength. Itshould be noted that the hyperbolic sine equation (Eq 4) also describes well the steady-state response athigh stress levels. The physical model, however, predicts a dislocation velocity about an order ofmagnitude less than that determined experimentally. This issue has been studied by Whitworth (1983),who shows that the predicted and measured values of the dislocation velocity are compatible if basal slipoccurs on planes of the glide set (between closely spaced planes of water molecules), instead of on theshuffle set (between widely spaced planes of water molecules) as assumed in the model of Goodman etal. (1981).Transient Creep.-- The transient creep rate equation in Shyam Sunder and Wu (1989a, b) is aphenomenological analogue of the Orowan equation Since transient creep is associated with structuralevolution leading to the Interference of flow by internal stresses, it may be considered to be driven by areduced stress measure. The reduced stress in the proposed model is taken to be (o- R)/B, where R isthe back stress and B is a non-dimensional "drag stress". The evolution for transient creep is then'where V is the temperature dependent stress factor given by Eq (3). Sinha (1978) has determined theactivation energy for columnar-grained S-2 Ice to be equal to that for steady-state creep. For an evolvingstructure, evolution equations must be proposed for R and B.The back stress opposes the applied stress and gives rise to directional or kinematic hardening, amuch quoted example being the Bauschinger effect in metal plasticity The classical hardening rule ofPrager (1949) relates the rate of back stress linearly to the creep strain rate k . On the other hand,nonlinear time recovery can be introduced by use of the Bailey-Orowan equation, i ewhere hl is a hardening constant and f, is a static recovery function. Equation (9) can be furthergeneralized to include dynamic recovery by requiring h, to be a function of the variables (0, R, T). Anequation similar to Eq. (9) has been used in the physical model of Derby and Ashby (1987) for primarycreep in f.c.c. metals, but the recovery function fl is a function of physical parameters pertaining to theassumed process of recovery. In the model of Shyam Sunder and Wu (1989a, b), the time rate of theback stress is linearly related to the transient strain rate, recovery being implicit since the transient strainrate decays to zero at steady state. The uniaxial form of the equation is:

where A is a constant The parameter AE may be interpreted as an anelastic modulus During a creeptest, the maximum recoverable strain at steady state (assuming no tertiary creep) is given by o/E +o/(AE), and consequently the applied stress per unit maximum recoverable strain is given by EAI(1 + A),which may be interpreted as a "relaxed modulus". The initial value of the back stress is taken to be zerofor an annealed material or for a material that has recovered from prior loading.The non-dimensional drag stress, on the other hand, is associated with the isotropic deformationresistance of the material. Its evolution may also take a form similar to Eq (9), in which the rate of B islinearly related to the equivalent transient strain rate. In uniaxial form, this equation isB= H E k, = H E [(o - R)/(Bv)]~ (1 1)where H is a hardening parameter. This formulation suggests that the rate of B is directly proportional tothe rate of the equivalent back stress, I.e., the two internal stresses are coupled However, dimensionalconsiderations suggest that the parameter H in Eq (11) equals H /(o - R) This phenomenologicalformulation leads to a proper dimensionless form of Eq. (ll), as shown in Shyam Sunder and Wu(1989a). The initial value B represents the isotropic resistance to flow in the initial state of the material.4 PARAMETER DETERMINATION AND MODEL VALIDATIONThe model of Shyam Sunder and Wu (1989a, b) contains a total of six parameters: E, N, V A B andft. The activation energy Q is regarded as a property of creep deformation. Except for the Young'smodulus, these parameters can be determined from simple constant-stress creep tests or constant strainrate tests. Determination of the first three parameters E, N and V follows standard procedures. Young'smodulus can be determinded using static and dynamic methods. The power law index N is generallytaken to be three for stresses in the range of 0.1 MPa - 2 MPa; this value agrees with the theoreticalmodel based on the Orowan equation. It also agrees with flow stresslstrain rate data of constant strainrate tests, as reported in Duval et al. (1983). The activation energy Q can be determined from minimumcreep strain rate data for creep tests conducted at the same load but at different temperatures. KnowingQ and N, the stress factor Vo can be determined from the flow stresslstrain rate data.The parameter AE can be estimated from the maximum transient strain at steady state, i.e :This, however, requires the maximum transient strain to be inferred from the creep data by subtracting theelastic and irrecoverable viscous strain from the total strain (see Fig. 2). An alternative procedure is bymeasuring the maximum recoverable strain in a creep recovery tests, since the applied stress per unitmaximum recoverable strain is given by EA/(l + A).

â ‚Maximum Recoverable Deformation = u/E (1 + 11A)'/A(::::Transient CreepPower Law Creeo 1Fig. 2 Identification of Parameters From Constant Stress Creep TestThe parameter B is a measure of the initial isotropic resistance to creep (see Fig. 2) Its value can bedetermined in the following manner. The initial creep strain is the sum of the initial transient andirreversible creep strain rates'Measurement of the initial creep rate therefore provides an estimate of Bo, Finally, the hardeningconstant H can be estimated form the entire creep curve using the integrated form of Eq. (1 1) (see ShyamSunder and Wu, 1989a).To use a numerical model in a predictive mode, it is necessary to verify its predictions Specifically, thefollowing verification procedures may be followed-1. The structure of the constitutive model can be verified by comparing model predictions withdifferent data sets, which may correspond to either the same or different types of ice. Forexample, the different data sets may reflect different growth conditions or different grainstructures Different types of ice generally require different parameter values forcharacterizing their constitutive behavior2 Material parameters determined from a specific type of test and for specific test conditionsshould generate a model prediction close to the measured reponse The robustness of theparameters should be examined by studying the change in predicted response with changein parameter values. A robust parameter is one in which a small change in a parametervalue does not cause significant change in the predicted response This avoids gross errorsif the material parameters are not obtained with great accuracy.3. Material parameters determined from a specific type of test should generate reasonablygood predictions of the measured response for the same type of test but for different testconditions The limitations of the model should be examined by studying its pred~ctions for awide range of conditions.4 The model predictions generated from a given set of parameters should ideally comparewell, or at least consistent in trend, with the measured response for different types of test,e.g , the verification of ice response under stress or strain rate jump, cyclic loading, andchange inanfining pressure.5. The predictions of the numerical model should be verified against model test results.Considerations should be given to scale effects, especially if the loading conditions permitfracture.

6. Verification with field scale test data should ultimately justify the nuencal approach Avalidated numerical model can then be used with some confidence for sensitivity study, orthe predictions of Ice response under extreme loading conditions.For items 1 and 2 above, Shyam Sunder and Wu (1989a) have verified their model predictions againstthe creep data of Sinha (1978) and Jacka (1984). Since their equations satisfy non-dimensional as well ascorrespondence requirements, verification procedures stated in items 3 and 4 have also been carried outto some extent. Model verifications involving more complicated loading history such as small and largestress jumps during forward and reverse creep have been attempted, but are preliminary in nature due tothe lack of test data5. CONCLUSIONSThis paper discusses the relationships between constitutive, finite element, and system modeling in anumerical framework for the study of ice-structure interactions. Constitutive modeling of flow Inpolycrystalline ice is discussed in some detail. It is suggested that a physically motivatedphenomenological model is generally adequate for solving an initial- and boundary-valued problem usingnumerical simulations. To make further progress, other, but no less important physical mechanisms suchas recrystallization and damage, should be included in the analysis The constituive modeling of flowdamage processes, of particular importance in the ductile-to-brittle transition regime of ice deformation, isunder investigation by the authors.6. ACKNOWLEDGEMENTSThe authors would like to acknowledge financial support from AMOCO, ARCO, BP America, CONOCOand MOBIL through MIT's Center for Scientific Excellence In Offshore Engineering, and the U.S.Department of the Interior, Minerals Management Service.7 REFERENCESAshby, M.F and Duval, P. (1985). The creep of polycrystalline ice, Cold Regions Science andTechnology, 11, 285-300.Barnes, P., tabor, D. and Walker, J C.F. (1971). The friction and creep of polycrystalline ice, Proc Roy.Soc Lond. A, 324, 127-155.Coleman, B.D. and Gurtin, M E. (1967). Thermodynamics with internal variables, Journal of ChemicalPhysics, Vol 47, No. 2, 597-613Derby, 9. and Ashby, M.F. (1987) A microstructural model for primary creep, Acta Metallurgica, Vol. 35,NO 6. 1349-1353.Duval, P., Ashby, M.F. and Anderman, I. (1983). Rate-controlling processes in the creep of polycrystallineice, Journal of Physical Chemistry, Vol. 87, No. 21, 4066-4074.

Glen. J.W. (1968). The effect of hydrogen disorder on dislocation movement and plastic deformation ofice, Phys. Kondens. Mater., 7, 43-51Goodman, D.J., Frost, H.J., and Ashby, M F (1981). The plasticity of polycrystalline ice, PhilosophicalMagazine, Vol. 43, No. 3,665-695.Jacka, T.H. (1984). The time and strain required for the development of minimum strain rates in ice, ColdRegions Science and Technology, 8, 261 -268.Jordaan, I.J. (1986). Numerical and finite element techniques in calculation of ice-structure interaction,Proc. IAHR Symp on Ice, Iowa City, Iowa, Vol II, 405-440Mellor, M. and Cole, D. (1983). Stress/strain/time relations for ice under uniaxial compression, ColdRegions Science and Technology, 6,207-230Michel, 6. (1978). A mechanical model of creep of polycrystalline ice, Canadian Geotechnical Journal,VOl 15. 155-170.Palmer, A.C. et al. (1983). Fracture and its role in determining ice forces on offshore structures, Annals ofGlaciology, 44, 216-221.Ponter, A.R.S. et al. (1983). The forces exerted by a moving ice sheet on an offshore structure, ColdRegions Science and Technology, 8, 109-118Prager, W. (1949). Recent developments in the mathematical theory of plasticity, Journal of AppliedPhysics, VOI 20, NO 3, 235-241.Ralston, T.D. (1978) An analysis of ice sheet indentation, Symp. on Ice Problems, Vol. I, Lulea, Sweden,13-31.Shyam Sunder, S. and Wu, M.S (1989a). A differential flow model for polycrystalline ice, Cold RegionsScience and Technology, 16, 45-62.Shyam Sunder, S. and Wu, M.S (1989b) A multiaxial differential model of flow in orthotropicpolycrystalline ice, Submitted for PublicationShyam Sunder, S., Wu, MS. and Chen, C W (1989~) Numerical modeling of rate processes duringice-structure interaction, Submitted for Publication.Sinha, N.K. (1978). Rheology of columnar-grained ice, Experimental Mechanics, 18(12), 464-470.Whitworth, R.W. (1983). Velocity of dislocations in ice on (0 0 0 1) and (1 0 1 0) planes, Journal ofPhysical Chemistry, Vol. 87, No. 21, 4074-4078.

A VISCO-PIASTIC CRliEP iWELFOR STATIC ICE LOAJS ANALYSIS:u Jizu3r0f essorTicnij .i-n UniversityP.R. CHINAznen XingLecturerABSTRACTIn the paper the theory of viscoplasticity is used foranalysis of sea ice loads, and a mathematical creep modelunder uniaxial stress condition is extended to a triaxialformulation. The maximum static ice forces on a singlerectangular pile are calculated according to this modelby using the nonlinear finite element method. The resultsare compared to those from other sources. The model seemsto be more realistic and reasonable than those in presentuse such as the plastic limit analysis method and thereference stress method.1. GENERALIce is a natural material with the normal temperatureadjacent to its melting point under the environmentalconditions. The mechanical properties of sea ice are sensitiveto a number of factors such as: type of ice, size andorientation of ice crystals, strain rate, salinity, porosity,temperature and so on. Sea ice is elastic, plastic, viscousor brittle, depending upon different ranges of the strainrate. It would therefore be unfeasible to build up anuniversal model to describe all of the mechanical behavioursof ice.Experimental investigations indicate, however, that under

certain external conditions, only one (in some cases itmay be two) among those above mentioned behaviours of iceis usually predominant. The others are not important andcan be ignored in the calculations. The modelling and anaysisof ice are hence simplified, and this is just what we havedone in the modelling of some commonly used engineeringmaterials (concrete, steel and plastics).The plastic and viscous deformations of ice usually takeplace simultaneously and perhaps equally significantly whenan ice sheet is moving extremely slowly against a structure.It would not be realistic to predict such a phenomenon byconsidering only one of these deformation modes. Comparedto the results by some present methods like the plasticlimit analysis method and the reference stress method, theviscoplasticity theory then may be more realistic inconsidering both time and loading path dependence of thestates of stress and strain.It would be significant to look into the mechanism ofinteraction between ice and structure when the ice sheetmoves extremely slowly against the structure. This impliesa possible maximum static ice load on the structure anda critical state for the structural design. The situationcould be expected in the Bohai Gulf when either the tidalcurrent velocity comes to a reverse (that would happen twicea day in the Gulf) or the structure is forzen in ice ina rather cold year. For higher ice velocities, the ice forceswould be lower than the peak value due to the crackes effectin the ice sheet. In the later case and for a flexiblestructure, however, the dynamic interaction between iceand structure may become serious. The intensive structuralvibration and fatigue failure may even happen. This makesanother critical state for the structural design, but itis not in the scope of this paper (Xu, 1986).2. APPLICATION OF VISCOPLASTICITY THEORYBeing distinguished from rheology and plasticity,viscoplasticity considers both the viscous and plasticbehaviours of a material. The viscous properties of the

material introduce a time dependence of the states of stressand strain. The plastic properties, on the other hand, makethese states dependent on the loading path. Consideringthe interaction between viscous and plastic behavioursconsequently makes up a particular branch of appliedmechanics-viscoplasticity.For an elastic/viscoplastic material, which implies thatthe viscous properties of the material becomes manifestonly after the passage to the plastic state and that theseproperties are not essential in elastic regions, it willbe assumed that the strain rate can be resolved into anelastic and inelastic partThe inelastic part of the strain rate, which is denotedPby Eij , represents combined viscous and plastic effects.The constitutive equations for an elastic/viscoplasticmaterial may have the following form (Perzyna, 1966):C. - < 1 /3>~~&j,where G, E and are the shear modulus, Young's modulusand Poisson's ratio of the material respectively; yo isa viscosity constant; S-a - = ( t/3)ei jis1 9Kronecker's delta. S is a nonlinear monotonously increasingnonnegative function of F and is defined as follows:0 for F

(75; and the state of plastic strain f: . The parameterK is the strain hardening parameter.It will be much more convenient to write the constitutiveequations (2) in the slightly different form1 - 2uE01 &j +where )> = yo/ k .To discuss theconstitutive equations more accuratelylet us consider the inelastic part of the relations (5)In the case of F>0, squaring both sides of Eq. (61, anddenoting by 1; = (l/2)â‚ &; the invariant of the inelasticstrain-rate tensor, we obtainIf the inverse function of $ exists and is denoted by GI,from Eqs (4) and (7 1,we haveThe Eq. (8) represents the dynamic failure surface of anelastic/viscoplastic material, and the feature of strainrate dependence is shown in the equation.It can be seen from Eqs (6) and (8) that the inelasticstrain-rate tensor considered as a vector in thenine-dimensional stress space is always directed along thenormal to the subsequent dynamic loading surface (Fig.1).For elastic/visco-(perfectly plastic) material, If is aconstant c. The function F does not depend on the strainand has the form:~=f(^,) -c (9)

According to the inelastic part of Eq. (2), we haveIf c=0, we can see that there will be a certain amount ofstrain rate under any stress level. This is the state ofcreep.3. CONSTITUTING THE THREE-DIMENSIONAL ICECREEP EQUATIONS BY USING VISCOPLASTICITYLet us assume the one-dimensional ice creep equation inthe form:where fcP is the inelastic strain, A is a parameter dependingon the size of ice grain and the temperature of ice, P isa function of stress u, T is the function of time t. Derivingboth sides of Eq. (11) by t, we obtainIn the special case of creep, i.e. c=0, we square bothsides of Eq. (10) and obtainFor one-dimensional states, Eq. (13) leads to the relationAccording to the experimental results (Lindholm, 1965)it can be assumed that there is a single curve relationshipwhich is independent of the state of stress, between (I:)and f for an elastic/visco-(perfectly plastic) material.447

So Eq. (12) is equivalent to Eq. (14). The functions yoand

where )Of(#) = x$,({) +% f,(f),~hese functions can be determinedfrom Eqs (15) and (16) as follows:Let us consider a slow-moving ice sheet against a singlerectangular pile (Fig.2). The width of the pile is 4m andthe thickness of the ice sheet is 0.7m. The grain size ofthe ice is 4mm. The boundary condition between the pileand the ice sheet is stiff. In Fiq.3 there are two ice forcedisplacement curves with different ice velocities by usingnonlinear three-dimensional finite element method. Theice velocities are O.OOOlcm/s for curve A and 0.001 cm/sfor curve B. The ice forces are 6.59 and 13.9MN for curveA and B, respectively. It is obvious that the velocitiesof ice effect the ice forces under the state of creep.The results are compared with those from other methodunder the same condition. They are shown in the Table 1.Table 1. ComparisonIof results with different methodsViscoplastic Plastic limit ReferenceImethod proposedin this papertce velocitycm/s1Ice force16.59 13.9MN5. CONCLUSIONSViscoplasticity can be used for calculation of ice loadsin the state of creep. It would be more reasonable because

it consider the viscous cind plastic properties of icesimultaneously. The proposed model gives a little largerice forces than the reference stress method. The resultsare different from those of plasic limit analysis methodbecause the creep takes an important role when a slow-movingice sheet moves against a structure.6. ACKNOWLEDGMENTThis paper is on the basis of a research program supportedby the National Natural Science Foundation of China.Lindholm, U.S. (1965). Dynamic deformation of metals, Behaviorof Metals under Dynamic Loading.Perzyna, P. (1966). Fundamental problems in viscoplasticity,Recent Advances in Applied Mechanics, 9, 243-377, AcademicPress.Sinha, N.K. (1981). Deformation behavior of ice-like materialsin engineering applications, International Symposium onthe Mechanical Behaviour of Structural Media, Ottawa.Ontario, 419-430.Xu, J. (1986). The structural vibration induced by sea icein Chinese), Ocean Engineering.

Fiq.1Dynamic loading surface and strain rate vector(1) Subsequent dynamic loading surface(2) Initial yield surface (F=0)\ 1 STRUCTUREFiq.2Problem definitionDISPLACEMENT(cm)Fig.3Ice force - displacement curves

DYNAMIC ICE LOADSON THE GREAT BELT WESTERN BRIDGEF.T. ChristensenDanish Hydraulic InstituteDK-2970 Hairsholm, DenmarkN. -E. Ottesen HansenLICengineering A/SDK-2900 Hellerup, DenmarkS. Spangenberg andL.J. VincentsenThe Great Belt Link Ltd.DK-1601 Copenhagen V, DenmarkABSTRACTThe planned bridge across the western channel of the Great Beltin Denmark will experience some unique conditions with respect toice loading. It is placed in open waters, and in a seasonal icezone. Due to this, it will experience ice floe impacts at allincidence angles. Some of the ice floes are large enough to causea sustained failure process inducing dynamic vibrations of thebridge piers. This paper describes a preliminary analysis of thedynamic behaviour of one of the proposed pier designs. The dynamicamplification of the intermittent ice forces was found to bedetermining for the response level.

1 . INTRODUCTIONDuring the period 1989-1995 a fixed link will be built across the18 km wide Great Belt. At the particular site of the link theGreat Belt is divided into two channels, called the EasternChannel and the Western Channel. They are separated by the islandof Sprog0, see Figure 1.Figure 1. The planned bridge and tunnel system across the GreatBelt.A 6 km long bridge will be built across the Western Channel, anda 7 km railway tunnel will be built underneath the eastern channel.The tunnel and the bridge will link up at Sprog0. At a laterstage, a road bridge will be built across the eastern channel.The Great Belt is a mild ice zone with about one of three wintershaving any ice at all. Nevertheless, with design probabilities of-5exceedance of 10 per year the ice loads together with ship col-lision loads become governing for the design. The water depth inthe Western Channel is in the range of 23-27 metres.In order to quantify ice forces during oblique ice attack on thepiers of the Western Bridge, a model test programme has been car-ried out. The results are reported by Christensen et al. (1989).

Two types of piers were tested in level ice. One was a twin-leg-ged design with cylindrical legs of 6 m diameter and a centre-to-centre spacing of 15.6 m in full scale. The other pier was anoblong mono -legged design with the same outer dimensions as thetwin-legged pier. The tests were carried out at a scale of1:14.76 with a target ice thickness of 65 mm and a target uniaxialcompressive ice strength of 129 kPa at model scale. The testresults were presented earlier (Christensen et. al., 1989).At the two lower test velocities, buckling failure occurred, andthe proximity of the two legs created a limitation of the bucklingload. Two individual, but simultaneous, buckling processeswould interfere near the centreline and thereby limit the bucklingload. Another limit load is the one corresponding to "fullinteraction" where the ice buckles as if the two legs were actuallyone solid (mono-legged) structure. At the high test velocitycrushing failure occurred.The measured forces were corrected to account for the desiredstrength and thickness, and they were scaled in accordance withthe formula by Schwarz et al. (1974), i.e. along a logarithmicslope of -0.2 in a pressure area diagram. Strengths were scaledlinearly.Natural frequency tests were carried out to investigate whetheror not the ice load measurements are affected by the natural frequency(eigenfrequency) of the experimental set-up. The naturalfrequency of both model types was established in two horizontaldirections by impact tests with the model connected to the towingcarriage. The models were cleared of ice during the impact tests.In both cases the natural frequency was about 14 Hz.Frequency spectra were computed in order to find out whether ornot significant amounts of energy are concentrated around thenatural frequency. Tests at low velocites showed no concentrationof energy near the natural frequency. Tests at the high velocityshowed a concentration near 14 Hz, but it was ignored in the staticanalysis. An interpretation of the crushing loads as static

loads is conservative because the damping of the model pier wasslightly less than that of the full scale piers. The magnitude ofthe crushing loads from a static interpretation was described byChristensen et al. (1989).2. DYNAMIC ANALYSISAn analysis of the dynamic behaviour of a deepwater pier for thecomposite superstructure was carried out. There was no dynamicamplification in the model tests in which buckling failure tookplace, because the typical frequencies observed during model icebuckling did not coincide with the natural frequency of the modelpier. In full scale, however, the frequencies observed duringbuckling will coincide with the natural frequency of the pier-soil system, and so the question of dynamic amplification be-comes important.Applying the force spectrum determined from buckling tests, adynamic amplification of 4.6 may be experienced. In the worstcase, where the peaks of the force spectrum and the mechanicaltransfer function coincide an amplification of 6 may be experienced.The first eigenfrequencies and eiqenfunctions are calculated fora typical bridge pier. The selected deep water pier is located inthe middle of the Western Channel at 26.0 m water depth and thelevel of the bearings is +22.26 m. The total height of the struc-ture is approximately 48 m, see Figure 2. A finite element pro-gramme was employed for the calculation of the first modes. Thebridge pier was subdivided into 24 beam elements in order to de-scribe the varying mass and stiffness properties (bending andshear) along the shaft and caisson. Young's modulus for the con-2Crete was taken to be 40,000 MN/m .

The girder substructure interactionsare represented by means oflinear springs and lumped masses.The springs describe the girderstiffness for horizontal transla-tion perpendicular to the bridgeand rotation along the girder axis.The bridge can dilate freely overthe pier.xThe soil-structure interaction isin accordance with Det norske Veritas"Rules for the Design, Constructionand Inspection of Off-shore Structures, Appendix 9, DynamicAnalysis". The interaction ismodelled by means of a continuumFigure 2 Isometric view ofapproach, which includes lumped the bridge substructure.masses, linear springs and dampingratios for the foundation subsoil. The approach is dependent onthe size of the shear modulus of the soil. The shear modulus hasbeen estimated from the stated empirical relationship for theupper moraine clay in the layered soil profile.The stiffness of the girder is less than 1% of the soil stiffnessso the motion of a substructure will only influence the adjacentsubstructures to a minor degree. Further the bearing betweensuperstructure and the bridge pier is a kind of pendulum parallelto the bridge.Direction 1st Mode 2nd Mode(Hz)(Hz)X-perpendicular to the bridgeY-parallel with the bridgeTable 1 Eigenfrequencies for the first two modes.457

The calculated eigenfrequencies are shown in Table 1. The reasonthat the eigenfrequency in the direction parallel to the bridgeis larger than transverse to the bridge is that this motion isdecoupled from the girder structure. The first two modes are depictedin Figure 3. It can be seen that the first mode eigenfunctionsrepresent the rocking movement and the second mode eigenfunctionsrepresent the foundation translation. Bending of theshaft influences the shape of the eigenfunction.The actual response of the structure for excitation near theeigenfrequencies depends on the damping. The damping ratios differwith the different materials and also with mode and vibrationamplitude in the soil. The damping calculations are based on thedamping ratios in Table 2.LEVEL! mFigure 3 The first and second eigenfunctions. Deflections arenormalized with the maximum deflection.

MATERIALDAMPING MODE OF DAMPINGTYPE VIBRATION RATIO (%)Girder Internal - 3.0Concrete in shaftand caissonInternal - 3.0Fill in shaft andcaissonWaterSoilSoilSoilInternal - 3.0Radiationand viscous - 1.0Radiation Rocking 1.4Radiation Translation 11.3Internal - 3.5Table 2 Damping ratios for the different structure materials.The generalized damping is calculated for the different eigenfunctions,see Table 3. Although the soil damping may seem largedue to the magnitude of the damping ratio, respect must be paidto the mode shape and the variations of damping with the level.The large damping ratio for radiation damping of translatory vibrationscontributes very little to the generalized damping ofthe first mode because this mode has very little translation atthe foundation level. Combining these two effects, the resultsshow that the dominating contribution originates from the dampingof the reinforced concrete 3%.Direction 1st Mode 2nd Mode(%I (%)X-perpendicular to the bridgeY-parallel to the bridgeTable 3 Generalized damping ratios for the first two modes.459

The damping ratios presented in Table 3 are very close to thedamping ratios measured on the Norwegian offshore platforms ofthe GBS type. So although the damping is small it is consideredto be very realistic.Combining the eigenfrequency and the damping ratio, the frequencytransfer function can be established for each mode as depicted inFigure 4. Dynamic amplification of the ice load becomes signifi-cant if the ice load spectrum has large energy contents aroundthe eigenfrequency peaks.2 MODEy - DtR.2 MODEx- DIR.-FREQUENCY ( Hz )Figure 4 Frequency transfer functions for the first two modes.The soil-structure interaction, which is governed by the soilshear modulus, influences the magnitude of the eigenvalues andthe shape of the modes. In the above calculations the equivalentelastic subqrade modulus and damping ratios have been reduced by50% due to the soil layering. This results in a subqrade modulusin the range of 35 to 50 M N / for ~ rocking and sliding movementrespectively. Calculations with half and double the soil shearmodulus showed a ±25 change in the eiqenfrequencies.

3. OBSERVED DYNAMIC BEHAVIOUR IN ICE MODEL TESTSThe tests made at the Hamburgische Schiffbau-Versuchsanstalt GmbHhad some inherent dynamic effects, due to the elastic suspensionof the model. The measured eigenfrequency of the model was 14 Hzwhich in full scale corresponds to 3.6 Hz. The damping ratio wasestimated from the natural frequency time series to be 0.02 forthe bridge pier.Figure 5 shows a typical recorded force spectrum in a test wherecrushing is the dominating failure mode. The major part of theenergy is concentrated around a frequency of 12 Hz, reflectingthe natural frequency of the model pier. For pure resonance thedynamic amplification factor would be 1/(2-0.02)=25. The spectrumin Figure 5 shows an amplification of roughly 840/50~ 17, whichis in good agreement when the sensitivity to peak width (with theforce spectrum narrowly distributed around the natural frequency)and damping ratio is considered. An excerpt from a typical time-series of crushing forces is shown in Figure 6. The mean forcevalue has been subtracted when calculating the spectrum in Figure5.Figure 7 shows a typical spectrum of recorded forces in a testwhere buckling is the dominating failure mode. The energy is concentratedaround a frequency of 2 Hz, reflecting a "buckling frequency"associated with the velocity and mechanical characteristicsof the ice. There is a smaller concentration around 12 Hz,but this only reflects dynamic vibrations of the pier after suddenchanges in applied load, e.g. after failure of the ice. Thissmaller peak is consequently ignored in the further calculations.Since the "buckling frequency" is considerably smaller than thefirst eiyenfrequency of the model pier, dynamic amplification isnot included in the model test results on buckling.

4. DYNAMIC ICE BUCKLING LOADSIt is assumed that the dominating frequency in the buckling processis directly proportional to the velocity of the advancingice sheet. Even though the ice strength is rate dependent, thisassumption should give reasonable frequency estimates. This meanswith the currents present in the Great Belt that resonance can beexpected between the buckling and the basic natural frequenciesof the bridge.Figure 8 shows a typical time-series of recorded resultant forcein a test where buckling is the dominant mode of failure. It isinteresting to note the buckling event covering the right half ofthis figure. A surprisingly regular variation pattern is maintainedfor about 18 cycles over about 13 seconds. The correspondingfrequency is 1.4 Hz, (= 0.35 Hz full scale) . Note that thespectrum in Figure 7, which is based on a test with twice thevelocity, has a peak frequency about twice that dominating inFigure 9. The vibration with 18 cycles was the longest observedin all the tests.It appears that in full scale values the dominating frequency inthe buckling process (with the design ice cover) may be estimatedas fb = V/0.14 m, where V. is the velocity of the ice. Excitationat the eigenfrequencies of 1.1 Hz and 1.4 Hz calculated earlierwould then take place at velocities of 0.15 m/s and 0.20m/s, respectively. These are very common velocities in the GreatBelt. The necessary kinetic energy of the ice floes for a 15 secondbuckling event can be possessed by floes typically more thanroughly 400 m in diameter.Taking the spectrum from Figure 5 ignoring the peak near 12 Hzand converting it to full scale values (by multiplying forceswith 1096 and frequencies with 0.26) the lower curve in Figure 9is obtained. Multiplying this force spectrum with the mechanicaltransfer function for the first mode the response spectrum isfound. It is shown as the upper curve in Figure 9, and clearlyreveals a substantial response near the natural frequency.

-400.5n 2nc"u mTest 3950 - CrushingLoadcell no.1Force spectrum in attack directionTwin-leg pierVelocity 260 nun~secAttack angle 90 deg(Model scale values)Hz0 .n-i n-rm-n "l-Tinn^ - - - - -70.0 10.0 a. o sa o 40.0 so. nFigure 5Typical force spectrum for crushing.3 8IFigure 6'\ / Twin-legged pierTest 3950 - CrushingVeLocit:l 260 mn/secAttach %ole 90 SeqTise ? Hodel scale values.-Typical time-series for crushing.Force spectrum in attack direct~on12Twin-leg pier=Velocity 26 nun/secBO- AttacK angle 90 deg 40(Model scale values)a0 0.0 10.0 20.0 30.0 d0.0 50.0Figure 7Typical force spectrum for buckling.Figure 8Typical time-series for buckling.463

The effective dynamic amplification factor can then be found bycalculating the ratio of the rms values for the two spectra. Withthe shown curves an estimate of 4.6 results. Due to the velocitydependence of the buckling frequency, the peak of the (lower)force spectrum may shift to other values. The "worst case" wouldbe for the peaks to coincide, which they do for common ice velocitiesas explained earlier. By shifting the lower peak in Figure9 to a peak frequency of 1.1 Hz a dynamic amplification factor of6 is found for the ice bucklinq loads. This is a substantial amplificationwhen applied on for instance the force time seriesshown in Figure 8.It is seen that the amplitude of the force fluctuations are 0.4times the average force value. With a dynamic amplification of 6this means a maximum response of 1 + 6 x 0.4 = 3.4 times theaverage response, and a dynamic load factor of 3.4/1.4 = 2.43.This means that in scaling to the Great Belt Bridge, the forcesfor buckling obtained by the same scaling which was used forcrushing shall be multiplied by 2.43 in order to get the equivalentstatic force. This is substantial. However, the above calculationshave the inherent assumption that all frequencies are inphase.0 1 2 3 4 5Figure 9Response spectrum in full scale values.

Taking proper care of the phase differences when the peak frequencycoincides with the resonance frequency of the piers, andonly assuming 18 load cycles as a maximum, a simulation hasresulted in an amplification of 3.80 times the mean force.The corrected budget for the amplification then becomes 1 + 3.8 x0.4 = 2.52 and a dynamic load factor of 2.52/1.4 = 1.80. Thismeans that the full scale forces extrapolated from the modeltests for the buckling situation shall be multiplied by 1.80 inorder to account for the dynamic amplification.The model ice used in the laboratory tests is generally believedto have less flaws and cracks in it than its corresponding fullscale ice. This can be explained by the fact that the full scaleice has undergone morphological changes for months before reachingthe full thickness. This means that the energy will be spreadslightly more in the full scale spectrum, and as such the abovedynamic amplification factors are conservative.5. CONCLUSIONSFrom the above analyses it is realized that the dynamic effectswill play an important role in the response of the bridge piersto ice loads.For crushing failure, the forces resulting from the model studycan be applied directly.For buckling failure, the forces resulting from the model studyshall be multiplied by 1.8, in order to account for dynamic amplification.This result has been based on force records fromtests with a zero degree angle of incidence of the ice only.Note that the pier investigated in this paper need not be the oneselected for the Western Bridge. The choice of substructure lay-out is expected to take place in the early summer of 1989.

ACKNOWLEDGEMENTThe presented analysis was carried out on behalf of The GreatBelt Link Ltd. Their permission to publish the result is grate-fully acknowledged.REFERENCESChristensen, F.T., N.-E. Ottese !n Hansen, K-U. Evers, S. Spangenbergand L.J. Vincentsen (1989), "Design of the Great Belt WesternBridge for Ice Forces", Proc. 8th int. conf. on Offshore Mechanicsand Arctic Engineering (OMAE-89), Vol. 4, the Hague, theNetherlands.Schwarz, J., K.-I. Hirayama and H.C. Wu (19741, "Effect of IceThickness on Ice Forces", Proc. 6 ' th Of fshore Technology Conference(OTC-74), Paper OTC 2048, pp. 145-155, Houston, Texas,U.S.A.

THE USE OF RESIDUAL STRENGTH IN THE CALCULATIONOF GLOBAL CRUSHING FORCES ON WIDE STRUCTURESJ. F. DorrisShell Development CompanyHouston, TexasU.S.A.ABSTRACTIce crushing loads are often estimated by an empirical approach developed to predict iceforces on bridge piers The application of this methodology to u-ide structures overpredicts forcesmeasured in the field. The overprediction is due to fundamental differences between the indentationtests used to develop the methodology and actual field conditions encountered by wide structures Asan alternative to the current crushing methodology, it is proposed that the post peak residual strengthmeasured in unconfined compression tests under ductile conditions be used as an upper bound foreffective pressure in global load calculations Data are presented which define the residual strength formulti-year ice. Comparisons are made between the residual strength and effective pressures inferredfrom field measurements1. INTRODUCTIONIce load methodologies seek to relate ice forces on a structure to some ice parameter whichcharacterizes its strength. The ice strength parameter is determined from standard mechanical testsand is very sensitive to the sample's physical properties such as salinity, porosity, and crystal structureThe type of test used to measure strength depends on the assumed failure mode If, for example,crushing is the assumed failure mode, then uniaxial compression tests are a logcal choice andcompressive strength is an appropriate strength parameter.Of all ice load methodologies, crushing is most widely used since it provides an upper boundon ice loads. The crushing methodology is an empirical approach derived from indentation tests Theeffective pressure (total load/contact area) is related to the unconfined compressive strength by meansof empirically derived parameters which account for confinement and rate effects This approach wasdeveloped to predict ice forces on bridge piers and works well where the ratio of structure diameter(D) to ice thickness (h) is small, generally D/h < 10.However, the discovery of oil in Arctic regions created interest in structures large enough tosupport drilling activities These structures are necessarily wide and typically have Dlh ratios of 20 andgreater. The application of the crushing methodology to wide structures yields total forces andeffective pressures much greater than actually measured in the field As a result the recent trend in

ice load prediction has been to move away from small scale mechanical tests and toward directapplication of field measurements While it is agreed that field measurements should be the final judgeof the merit of any ice load methodology, they are expensive, risky, and subject to large uncertaintyFurthermore, the measurement of the "design" event is left entirely to chanceThe purpose of this paper is lo argue that crushing loads on wide structures can be estimateddirectly from small scale mechanical tests The argument is based on consideration of the strainsoftening observed in compression tests conducted under ductile test conditions, and use of the postpeak residual stress as the strength parameter.2. UNIAXIAL COMPRESSION OF MULTI-YE\R ICEThe mechanical response of ice in compression can cover the \&hole range of materialrespon'-ie from ductile 10 hriule depending on its r.iie of loading At lo!v strain riites the response isductile and the stress strain curve is chardcteii/ed by .I rise in stress to a peak ialue follov.ed by adecrease to a fairly constant post peak Jalue The non-monotonic nature ol the stress strain curve isdue to the softening of the ice from microcracking The stress strain curve for ice under ductileconditions can be characterized by t\\o strength parameters (1) the peak or unconfined compressivestrength (ac) which is associated with small -drains and undamaged ice and (2) the post peak orresidual strength (an) which is associated uith large strains and damaged ice. At high strain rates theresponse is brittle and the stress strain curie is characterized by a sharp rise to a peak value wherecatastrophic failure of the sample occursAttention in ice mechanics has focused primarily on the measurement of peak stress valuessince the peak values are thought to yield the highest ice loads Consequently little attention has beengiven to the measurement of the residual strength The most extensive data available on residualstrength are found in three indu-itry funded projects (Cox, et al (1984), Cox, el a1 (1985),GEOTECH (1985)) administered by Shell Development Company These projects investigate theuniaxial compression of multi-year ice over a range of temperatures and strain rates All test samplesare loaded to failure or 5 percent striun

LOO meFig 1 - Unconfined compressive strength (MPa)vs. strain rate (llsec)Fig 2 - Residual strength (MPa) vs. strain rate(Ilsec).Figures 1 and 2 show the variation of unconfined compressive strength and residual strengthwith strain rate for two temperatures Large scatter is found in multi-year ice samples so that meanvalues are used to define strength The vertical bars denote one standard deviation Data from thethree programs mentioned above are used to calculate mean values, and the number of tests at eachtest condition varies from 18 to 70 tests. The residual strength is defined as the stress measured at5 percent axial strain. The decrease in strength beyond lO^/sec in Figure 1 and the absence ofresidual strength values at lO^Isec in Figure 2 indicate that the ductile to brittle transition point foruniaxial stress is at approximately lO^/secThe most notable feature of Figure 2 is the apparent rate independence of the residualstrength. Statistical t-tests are used to compare mean values at different levels of constant strain rateand constant temperature The comparisons are tested at a 99 percent confidence level and show thatthe unconfined residual strength is independent of strain rate and increases with decreasingtemperature If residual strength is assumed to be rate independent, then ail samples at a giventemperature can be combined to yieldwhere 0 is temperature measured in "C and a, is measured in MPaA possible micromechanical explanation for the rate independence of the unconfinedresidual strength is friction At large strains, where microcrack density is high, the frictional slip ofopposite faces of microcracks could be the dominant mechanism for energy dissipation. Frictionalmaterials (e g., granular materials) are generally regarded as rate independent For ice, the coefficientof friction increases with decreasing temperature This would explain the increase in residual strengthwnh a decrease in temperature seen in Equation 1

3. INDENTATION TESTSThe estimation of global crushing loads is essentially an empiiical approach derived fromedge indentation tests of ice sheetscompression testsResults from these tests are qualitatively similar to unconfinedPlots of the maximum effective pressure (total loadlarea) as a function ofindentation velocity shows a maximum pressure at some critical velocity which marks the transitionfrom a ductile to brittle failure mode.propagation of a damaged zone of fissured iceThe ductile mode is characterized by the initiation andThe force history is smooth and resembles the stressstrain curve of an ice sample in the ductile mode The brittle mode is characteri~ed by the propagationof large cracks and the flaking of ice off the sheetrise to a peak followed by an jagged response at a louer force levelindentation is given by Michel and Toussaint (1977)The force history in the brittle mode has a sharpA deiailed discussion of sheet4. GLOBAL CRUSHING LOADSThe effective pressurecompressive strength (oc) by the equation,[P) from global crushing loads is related to the unconfinedHere I and ic are empirical factors obtained from indentation tests of ice sheetsThe essential problem in applying Equation (2) is choosing the correct value of ucunconfined compressive strength is rate dependentindentation velocity (v)TheConsequently its choice should be related toThis is accomplished by defining an effective strain rate (e) which can beobtained by scaling the indentation velocity by some length characteristic of the problem. hlichel andToussaint (1977), for example, recommend e = u/(-^D) v.hile Ralston (1979) recommends 6 = u/(2D).The contact factor (fc)depends on the effective strain ratecontact is maintained throughout the penetrationin Equation (2) accounts for the post peak decrease in load andAt low strain rates where the ductile failure mode occurs goodIn this case values for the contact factor should benear 1 At high strain rates %here brittle failure dominates, splitting and flaking reduce the effectivecontact area. Here values for fc are less than 1. Figure 3 illustrates the contact factors recommendedby hlichel and Toussaint and the factors recommended by Ralston The solid line in Figure 3represents a rough upper bound obtained b! connecting recommended values for €=lo-s/s and€=lo-3Ise

UpperBound--8 -7 -6 -5 -4 -3 -2Log10Fie 3 - Contact factor vs strain rateThe indentation factor (I) in Equation (2) accounts for strength increases resulting from theconfinement of the interaction zone by the surrounding ice sheet Values for I range from 1 to 3 forisotropic materials. For narrow structures the in plane confinement is high and values of I near 3 arereasonable. For wide structures the in-plane confinement is lower and values of I near 1 arereasonable Plastic limit analysis has been applied to provide analytical support for the values of Iquoted aboveThe application of Equation (2) to the prediction of global crushing loads on wide structuresgreatly overpredicts measured global loads. The discrepancy between predicted and measured forcesis often explained by size effects and non-simultaneous failure. These explanations are conceptuallyreasonable but difficult to quantify and apply. Furthermore evidence exists which suggests that theseconcepts may not be applicable. In a comparison between crushing strengths of laboratory test samplesand full thickness ice sheet samples, Petrie and Poplin (1986) report no significant reduction instrength with increasing volume. In a discussion of the dynamic response of the Molikpaq, Jefferiesand Wright (1988) report that during crushing events the pressures recorded from panels locatedacross the width of the Molikpaq were in phase and of similar magnitude indicative of simultaneousfailure5. APPLICATION OF RESIDUAL STRENGTHAs an alternative to size effects and non-simultaneous failure, we propose that theoverprediction of global crushing loads is due to the failure to properly account for strain softening.This failure stems directly from fundamental differences between the rather idealized conditions ofindentation tests and the actual loading conditions encountered by wide structures in the field.The initial boundary conditions for sheet indentation tests are good contact with undamagedice over the entire indentor width At t=O a velocity jump is specified These conditions give rise tothe initial impulsive force peaks seen in indentation tests. The peak force should be related to the

unconfined compressive strength since the strain is small and the ice is undamaged. The subsequentdecrease in force is accounted for by the contact factor The reduced force level should be related tothe residual strength since the strain is large and the ice is damaged The product fcuc can beinterpreted as a reduced strength parameter. This product is shown in Figures 4 and 5 for 8 = -5'Cand 8 = -20° by multiplying the unconfined cornpressive strengths from Figure 1 by the contactfactors from Figure 3 The reduced strengths predicted by the Ralston (1979) and Michel andToussaint (1977) contact factors are maximum near the ductile to brittle transition point butoverestimate the residual strength there by a factor of 3 Better agreement is found by replacing thediscretized contact factors by the upper bound from Figure 3 but its maximum value occurs below theductile to brittle transition point There is no physical basis for the variation of the reduced strengthparameter seen in Figures 4 and 5 and the choice of the effective strain rate is rather arbitraryConsequently both the contact factor and effective strain rate should he viewed as calibration factorsused to reconcile unconfmed compressive strength with pressures from sheet indentation testssuch, their extension to applications beyond the scope of sheet indentation tests is questionableAsf' *c0 = -20 deg CContact FactorsRalstonResidualStrength-A-Fig. 4 - Reduced strength (MPa) \s strain rate(llsec) (6 = -S°CFig. 5 - Reduced strength (MPa) vs strain rate(llsec) (6 = -20°CIt is difficult to imagine a global load scenario for a wide structure where the initial conditionswould ever coincide with the initial conditions specified for sheet indentation tests Consider firstwinter conditions. In this case the initial contact between the structure and undamaged ice is good.However, in winter conditions the ice is initially at rest and the far field stresses which drive the icebuild up over a period of hours or even days Upon breakout, the ice in the vicinity of the structurehas been subject to accelerating strain rates This condition is similar to an ice sample in a soft testmachine where strengths can be considerably less than those measured by a stiff machine It isprobable that peak strengths are never realized in the winter under accelerating strain conditions andice stress could even approach the residual strength from below if the period of strain acceleration wassufficiently long.

Consider now the summer irnpact of a floe into a wide structure. This situation is quitedifferent from edge indentation tests since the contact area tor the impact increases throughout thepenetration At initial contact there is a jump in velocity The contact pressure is high but the totalload is small At initial contact unconfined compressive strength is the appropriate parameter since thestrain is small and the ice is undamaged As penetration proceeds the contact area and total loadcontinue to increase while pressures decrease due to strain softening At large penetrations, residualstrength is the appropriate strength parameter In this example the maximum load would be associatedwith residual strength rather than the unconfined compressive strengthFrom the above discussion it appears that the unconfined compressive strength has littlesignificance for the calculation of global crushing lodds on wide structures Furthermore the reducedstrength (fcoc) is shown to consistentl~ cner predict the strain softening actually observed in thelaborator). It is recommended that the reduced strength he replaced directly by the residual strengthfor global load calculations involving large strain For nide structures (Dlh > 10) where confinementof the ice sheet is small. 1=1 is suitable Thus, the effective crushing pressure (P) on a wide structure isThis effective pressure is independent of indentation velocity and only depends ontemperature It is assumed that the maximum global loads will occur from pure crushing (I e , ductilefailure) The presence of other failure modes such as splitting or buckling will act to relieve stress sothat the residual strength should be viewed as an upper bound6. COMPARISON WITH MEASURED LOADSThere are wo ice load measurement programs which can provide a comparison betweenmeasured loads and predictions based on residual strength Jefferies and Wright (19S8) discuss theforces from multi-year floes in contiict with the Molikpaq in the winter of 1985-86 Danielewicz andBlanchet (1987) describe the impact of multi-\ear floes against Hans Island during the summers of1980 and 19816.1. Winter LoadsTable 1 summarizes the peak loads of four events which induced a dynamic response of theMolikpaq All events except for the May 12 event had low velocities typical of winter conditions TheMay 12 velocity is described as 0.2 mlsec slowing to 0 mlsec. This description along with the late dateof the event indicates that the event is momentum driven which is more typical of breakup and summerconditions Furthermore the May 12 ice is described as first year with a multi-year inclusion whereasthe other events involved multi-)ear ice Despite these differences the May 12 event is included heresince its failure mode (crushing) is the same as the others

Table IMOLIKPAQ LOADSFailure v Peak Load Est Pressure Temp Res. StrengthEvent Mode (m/s) (MN) (Mpa) (deg C) (MPa)Mar 07-Crushing 06 230 0.35 - 1 05 -10 1 42Mar 08 Crushing 02 320 0.48 - 1 45 -10 1 42Apr 12 Crushing 05 >500 >O 76 - 2 27 -5 1.28May 12 Crushing 20 - 00 250 038- 114 -5 128Effective pressure for the Molikpaq loads is estimated by dividing peak load by structurediameter (D=l10 m) and ice thickness Thickness values are not reported by Jeffenes andWnght (1988) but Sanderson (1988) reports that the range 2m

Other notable winter ice loads have been measured for first year ice events. Strilchuk (1977)reports a maximum pressure of 1 1 MPa measured by pressure panels located in the vicinity of levelfirst year ice interacting with a rubble pile around Netserk F-40. Metge (1976) estimates that apressure of .83 MPa was required to move the artificial island Adgo P-25 during the winter of1975-76. If it is assumed that crystallographic distinctions between ice types diminish at large strainsdue to damage, then the multi-year residual strength for -1O0C (i.e., a, = 1.42 MPa) provides a goodupper bound for the pressures quoted above.6.2 Summer LoadsTable 2 summarizes the peak forces measured on Hans Island for direct uncushionedimpacts which produced the largest load;). The force history of each event is obtained fromaccelerometers attached to the floe and an estimation of the floe massHowever, in order to relatemeasured forces to an effective pressure some assumptions about the pressure variation duringpenetration and the evolution of the contact width are required.Table 2HANS ISLAND LOADSMeasuredSimulated (n=15)Event "0 h Dm Fm Po P(.94) D(.94)(mis) (m) ( 4 (MN) (MPa) (MPa) ( 4In their discussion of the failure modes for the direct uncushioned events. Danielewicz andBlanchet (1987) observe crushing along with localized bending, cracking, and rubble formation as theload rises to us peak value At the end of this initial phase, a significant reduction in load is observedand is attributed to a flexural failure over a larger area in the vicinity of the contact zone. Subsequentfailure is primarily ridging A schematic diagram of the force history for a direct uncushioned impact isshown in Figure 7. Here T denotes the time between initial contact and the first flexural failure Theforce history for 0 5 t/T & 1 is simulated in the following.

Fig 7 - Schematic force history for direct uncushioned impacts at Hans IslandAt initial contact ue assume the contact width is zero and the contact pressure is at itsrnaximum since the ice is initially undamaged As penetration proceeds the contact uidth grows andthe ice softens At t/T = 1 a flexural failure occurs Here the contact pressure drops to zero and thecontact width reaches us maximum value. These assumptions require the contact pressure tomonotonically decrease to zero and the contact width to monotonically increase for 0 t/T 5 1.Two simple functions, which satisfy these criteria are a quarter period cosine and a power law.Using these simple functions, the initial portion of the force history can be simulated by,F(t/T) = PDh = (P,,D,,,Ii) - cos - , 0 s à 5 1,(;)" (;) Twhere Po denotes the initial contact pressure and Dm denotes the maximum contact width Smallvalues of n yield peak forces near t/T = 0 while large values yield peak forces near t/T = 1 The forcehistory in Figure 7 indicates a large \;ilue of n is required. We arbitrarily choose n = 15 which yields apeak force at t/T = ,94. Normali~ed plots of contact pressure, contact width and force are shown inFigure 8 for n = 15 The initial pressure (Po) can be adjusted so that the rnaximum measuredforces (F,,,) in Table 2 match the maximum value of Equation 4 Values of Po for each event alongwith the effective pressure and contact width at t/T -= 94 are listed in Table 2.

Hans Island Simulationn=15Fig. 8 - Normalized histories for contact pressure, contact width and forceThe estimated effective pressure associated with the peak force (I e , PC. 94)) is plotted inFigure 9 for each event. The uncertainties reported by Danielewicz and Blanchet (1987) for surfacearea, acceleration and contact width translate into a 30 percent uncertainty in effective pressure.Effective pressures estimated from residual and unconfined compressive strengths are also shown inFigure 9 for comparison. These values are obtained by assuming an average ice temperature of -Sac.The recommendations of Ralston (1979) and Michel and Toussaint (1977) are used to choose contactfactors and effective strain rates.The initial velocity uO is used to estimate strain rate since;~l~(;)d(+) is small compared to initial velocity where m is the floe mass Although the ratioD(.94)/h is small for two of the three events, we assume the confinement is small and take 1=1. Thisassumption is supported by the elastic analysis of a diametrically compressed disk which shows analmost constant tensile stress normal to the loading diameter. Further support is given by the tendencyfor floes to split normal to the contact area under impact conditions.

Inflective Pressure (MPa)Hans Island LoadsEstimatedPressureFig 9 - Hans Island loadsIn Figure 9, the predictions based on residual strength and unconfined compressive strengthshow better agreement with each other since the residual strength and reduced strength, fc ¡c are incloser agreement at high strain rates. However, the residual strength prediction provides a slightlybetter bound for the estimated effective pressuresFinally, Figure 9 illustrates the effective pressures estimated by Vivatrat and Kreider (1981)for ridge building The residual stress and ridge building pressures provide upper and lower bounds onthe estimated effective pressures inferred from the simulation. These bounds arise from considerationof the mixed failure modes observed in the initial stages of the force history For thin floes, theflexural rigidity would be small and buckling would dominate with little crushing present As thicknessincreases, flexural rigidity increases and higher pressures are required to induce flexural failure. It isexpected that the upper bound on pressure would be the residual stress which represents a purecrushing failure at large strains This point of view is supported by Figure 9 which shows the thickestfloe yielding the highest contact pressure.This simple simulation is not intended as a proof but rather is presented as a heuristicargument to illustrate that ice structure interactions are processes involving strain softening and loadhistory which cannot be modeled with a single strength parameter. Indeed the initial contact stresses inTable 2 are similar to unconfined compressive strengths while the contact stresses at peak forces aresimilar to residual strengths In this case the peak force is not associated with peak contact stresswhich is contrary to the notion that peak contact stresseslstrengths yield peak loads7. CONCLUSIONArguments are presented which show the crushing equation as derived from sheetindentation tests is inappropriate for estimating global crushing pressure on wide structures As analternative it is proposed that the residual strength measured in unconfined compression tests underductile conditions be used directly as an upper bound for global pressure on wide structures Thismeasure of strength agrees more closely with measured field data and makes for a more physicallyconsistent strength parameter.

ACKNOWLEDGMENTThe permission of Shell Oil Company to publish this paper and the critical review ofM hl. Winkler is gratefully acknowledgedREFERENCESCox, G F S., Richter-Menge, J A , Weeks, W F , Mellor, M , and Bosworth, H. \V (1984) TheMechanical Properties of Multi-Year Sea Ice, Phase I. Test Results, Report 84-9, Cold Regions Res.Eng. Lab , Hanover, NH, USACox, G, F N , Richter-Menge, J A . Weeks, it' F , Bosworth, H., Perron, N , hlellor, M., andDurrel, G. (1985). The Mechanical Properties of Multi-Year Sea Ice, Phase I1 Test Results,Report 85-16, Cold Regions Res Eng Lab, Hanover, NH, USADanielewicz, B \V. and Blanche!, D (1987). Measurements of Multi-Year Ice Levels on Hans IslandDuring 1980 and 1981, Proceedings of 9th Int Conf on Port and Ocean Eng Under ArcticConditions, Fairbanks, Alaska, U.S.A.GEOTECHnical resources (1985)to Program Participants, Calgary, Alberta, Canada1985 Multi-Year Ridge Ice Laboratory Test Program, ConfidentialJefferies, M G and \Vr~ght, \V H (1988). Dynamic Response of "hlolikpaq" to Ice-StructureInteraction, Proceedings of 7th Int Conf on Offshore hlechanics and Arctic Engineering, Houston,Texas, U.S.AMetge, M. (1976). Ice Conditions and Ice Defense at Netserk B-44 and Adgo P-25 During theWinter of 1974-75, APOA Project 104, Imperial Oil Ltd , Calgary, Alberta, CanadaMichel, B and Toussaint, N. (1977).J Glaciologv, Vol 19, No. 81Mechanisms and Theory of Indentation of Ice Plates,Petrie, D. H. and Poplin, J P (1986) Comparison of Small Scale and Large Scale Sea Ice Strengths,Proceedings of Int Assoc. of Hydraulic Research Ice Symposium, Iowa City, Iowa, U.S.A.Ralston, T. D (1979). Sea Ice Loads, Technical Seminar on Alaskan Beaufort Sea Gravel IslandDesign, Presented by Exxon Company, U.S.A.Sanderson, T. J 0 (1988) Ice Mechanics - Risks to Offshore Structures, Graham and TrolmanLimited, London, U K

Strilchuk. A. R. (1977). Ice Pressure Measurements - Netserk F-40, 1975-76, APOA Project 105,Imperial Oil Limited, Calgary, Alberta, Canada.Vivatrat, V. and Kreider, J. R. (1981) Ice Force Prediction Using a Limited Driving ForceApproach, Proceedings of Offshore Technology Conf., OTC Paper 4115, Houston, Texas, U S A

ON THE RELATIONSHIP BETWEEN GLOBAL ANDLOCAL ICE CRUSHING LOADSShell Development CompanyHouston, TexasU.S.A.Shell Development CompanyHouston, TexasU.S.A.ABSTRACTA connection between local and global ice loads is developed based on mechanical properties ofice This connection suggests the observed variation in ice contact pressure with area as seenbetween laboratory and field measurements to be entirely a function of strain history, rate effects,and confining stress. Results from this paper discount the importance of assigning ice a size effect inorder to explain the observed difference between small and large scale ice contact pressures.Mechanical property results are presented from tests performed to study the dependency of postpeakice strength on both confining stress and loading rate. Based on consideration of these and othersmall scale test results, a physical connection is made between basic mechanical properties and theobserved variation in contact pressure during actual large scale indentation This connection is usedto develop a conceptual pressure-area model for crushing failure This model suggests an inverserelationship between pressure and area having an upper limit which depends on the peak confinedcompressive strength and a lower limit defined by the unconfined residual compressive strength Thepressure values contained between these limns provide an upper bound for all failure modes. Basedon this model, the interpretation of existing field measurement data are studied and questionedaccordingly.INTRODUCTIONCurrent industry and research trends towards explaining the discrepancy between local and globalice loads have emphasi~ed the existence of a size effect Furthermore, the procedure used tocalculate both local and global loads has been to consider ice loading as a single event and not as acontinuous process In this paper, the observed variation in contact stress with area is studied, and,instead, a connection between the "observed" size effect and small scale mechanical property tests isdeveloped. Based on this connection, the calculation of ice loads hill be shown to be a function ofthe complete deformational processTest results from a testing program to consider the effects of high loading rate and confining stresson multiyear ice strength are presented and discussed This program considered loading rates up to10-Vsec and confining pressures up to 10 MPa. The results from this testing program are uniqueand, to our knowledge, the only such results of their kind. These test results are used to develop aconceptual pressure-area model which shows the observed variation in stress to result entirely fromdifferences in strain history, loading rate, and confining stress

Because of the sometimes large disparity between measured and computed ice loads, there hasbeen a trend towards the direct use of measured held data as structure design criteria. Although werealize the need for realistic ice load criteria, we question the direct application of ice loads measuredin the field without a complete understanding of the physics or verification from models. In somecases, measured "crushing" loads may not be upper bounds as a result of insufficient driving force orelse addition of other non-crushing failure modes.We believe that peak ice loads for ice-structure contact with vertical, or near vertical walls, occurfrom a crushing failure mode Our conceptual pressure-area model assumes pure crushing as thefailure mode and, for many applications, may represent an upper bound for these type of structuresPossibly, greater loads could result from the addition of rubble pile formation and/or ice clearing;however, these are not considered hereThis paper will begin with a discussion of the mechanical properties of ice considering variation inloading rate and confining stress Heuristic arguments are then used to develop a connectionbetween small scale test results and the variation of contact pressure expected during indentation.Based on this connection, a pressure-area model is conceptualized which shows the relationshipbetween global and local ice loads to be a function of strain history, rate effects, and confining stressBased on this conceptual model, the interpretation of existing measurement data are studied andapplication questioned. Finally, conclusions and recommendations for future work are presented.THE MECHANICAL RESPONSE OF ICE UNDER COMPRESSIONThe mechanical response of ice under compression covers the whole range of material responsefrom ductile to brittle depending on its rate of loadingAt low strain rate (e), the response is ductile,and the stress strain curve is characterized by a rise in stress to a peak value followed by a decrease toa fairly constant post peak value The non-monotonic nature of the stress strain curve is due tosoftening of the ice from progressive damage of the microstructure.dominant softening mechanism is microcrackingconditions can be characterised by two strength parametersUnder uniaxial stress, theThe stress strain curve for ice under ductile(1) the peak strength (o\i) which isassociated with small strain and undamaged ice, and (2) the residual strength (up) which is associatedwith large strains and damaged icehistoryClearly, under ductile conditions, the strength of ice depends onAt high strain rates, the response is brittle, and the stress strain curve is characterized by asharp rise to a peak value \\here catastrophic failure of the sample occursUniaxial strength parameters for mulnyear ice have been presented by Dorm (1989) and arereproduced in Figures 1 and 2 for peak strength and residual strength, respectively The decrease instrength at c =lo-2/sec in Figure 1 and the absence of residual strength values at 10-2isec in Figure 2indicate that the ductile to brittle transition point for uniaxial stress is at approximately lO^/sec.

LOGjo&Fig. 1 - Unconfined compressive strength (MPa) vs strain rate (llsec)-----I-.. ""IFig. 2 - Unconfined residual strength (MPa) vs. strain rate (llsec)The effect of confinement on the mechanical response of ice is illustrated by developing yieldsurfaces which typically plot the deviator~c stress a, - a3 as a function of confining pressure. Here,a, denotes the axial stress of a cylindrical test sample, and a3 denotes the radial confining stress.

:ooU3 MPa 10Yield surfaces are usually developed from peak strength values since those values are thought toproduce the largest loads A yield surface for multiyear ice developed from peak stress values isshown in Figure 3 The uniaxial strength values are from Figure 1, and the confined strength values,u3 7t 0, are from four tests conducted in a triaxial test program on multiyear ice(OI-~S~M MPa121.E-03Isec-e-1.E-02Isec-4&-Fig 3 - Yield surface for peak multiyear strengthThe same tests are used to develop the yield surfaces based on residual strength shown in Figure 4.A notable difference between the two types of yield surfaces is that residual strength values do notexist at low pressure and high strain rates. This is a direct result of the ductile to brittle transition andimplies that a generalized yield surface which accounts for strain hardening and softening should becomplemented with a failure surface which separates ductile response from brittle failure. One suchfailure surface is shown in Figure 4 which indicates that the presence of confinement shifts thetransition point to higher strain rates

I , I I I2 4 6 8 100, MPaFig 4 - Yield surface for residual multiyear strengthPrevious work by Ralston (1978) and others has constructed yield surfaces from peak strength\dues alone and made no distinction between yielding and failure As a result, only peak stressvalues can be realized, and strain softening, which is clearly demonstrated in the laboratory, isignored This point of view sees ice-structure interactions as an event. Peak stress is reached andfailure occurs despite the observation that ice can still carry load in the post peak region over a widerange of pressure and strain rateThe distinction between failure surtaces and yield suifaces suggests a different approach tomodeling ice-structure interrictions Under ductile condnions. the ice remains as a continuum If asui~able constitutive model \bas a\ailable to describe the stress-strainbehavior under ductileconditions, then finite elementuor other numerical techniques could be employed to solve boundaryvalue problems. The maximum load for a specific problem would occur v~hen the solution fails onthe failure surface. This point of view sees ice structure interactions as a process in~olving strainsoftening and strain history over a range of strengths hound above b) the peak strength and below bythe residual strengthImplementation of the approach \s,ould require mechanical tests under brittleconditions to define the failure surface and mechanical tests under ductile conditions to defineconsumlive parameters, particularly the procure, strain rate dependence of peak and residualstrenethsA CONCEPTUAL PRESSURE-AREA CURVE FOR ICEIce load calculations fall into two categories'(1) local loads which govern the design of shellthickness and bulkhead spacing, and (2) global loads which control the sliding resistance of the

structure. Contact pressures from local loads are typically high and occur over small areas, whileglobal pressures are much lower and occur over large areas. Local and global pressures are oftenconsidered to be unrelated phenomena due to the large differences in their magnitudes. However,from a physical point of view, it seems logical that, at intermediate areas, global and local pressuresshould meetEarlier in this conference, Dorris (1989) suggested the indentation stress for wide aspect, or Dlt,ratios to be a function- of strain history For conditions of low confinement, Dorris showed theindentation pressure for large areas to be entirely a function of the unconfined residual strength, OR.For these conditions, the peak strength, OM, is seen to be of relatively little importance, since uM isonly realized during the initial contact stage at which time area is also small.This work has been generalized here to consider a multiaxial stress state In the following, aconceptual pressure area curve is developed to provide a connection between local and globalpressures The connection is based on consideration of the stress-strain curve obtained under ductileconditions.Consider first small areas. Contact with small areas is usually associated with initial contact, and,as the indenter penetrates into an ice feature, the initial contact stress is expected to be high. Here,the ice is undamaged and the strain is small The appropriate strength parameter in this case is thepeak strength OM Since uM is rate dependent, the contact pressure should also be rate dependent.Small contact areas are usually highly constrained by surrounding ice so that the contact pressurewould also be sensitive to confinement. Thus, for small areas, the contact pressure would have thefunctional form, P = f(h, e, a3) An example of this case is the crushing equation developed fromsheet indentation tests Here, confinement is accounted for by the indentation factor, rate isaccounted for by the contact factor, and strength is accounted for by the unconfined compressivestrength.Consider now large areas To generate contact over large areas of a structure, large deformationand significant damage of the ice feature are likely to have occurred Here the residual stress is theappropriate strength parameter For sufficiently large deformations, the stress strain curie is flat, andmemory of peak stress has faded. Thus, history effects can be ignored. Large contact areas willcover the full thickness of most ice features and extend laterally for distances many times greaterthan the thickness, so that the effect of confinement is likely to be small The residual strength withzero confinement has previously been shown to be rate independent Thus, for lar2e areas aconceptual model for contact pressure would be P =/(ad Dorris (1989). for example, has arguedthat P = OR is an upper bound for large contact areasData and empirical models (e.g., crushing eqn and Dorris, 1989) exist for both large and smallscales. The model for each extreme chooses as us strength parameter a characteristic valuemeasured from small scale mechanical tests under ductile conditions Intuitively, it seems that, atintermediate contact areas, ice strength would vary between the two strength parameters. A modelfor intermediate areas would necessarily be more complex than the examples discussed above sincestrain-softening and load history would be required to describe the transition in strength. Formonotonic loading, the current strain is a suitable measure of these effects. Since OM and OR dependon pressure and strain rate, it is expected that contact pressure at intermediate areas would also

depend on confining pressure and strain rate. Thus, a conceptual model for contact pressure atintermediate areas would be P = f(as 5 a S cry, e, e, 03) An example of this model would be theone proposed in the previous section The dependence on strain would describe the evolution of theyield surfaces in Figure 3 to the yield surfaces in Figure 4 provided that the stress state remainsbounded by the failure surfaceBased on this work. the conceptual pressure summarized in Figure 5 has been developed.Annotated on this figure are regions of small, intermediate, and large contact area and the associatedfunctional form expected for indentation pressure. The model proposed for intermediate areas issufficiently general to cover the entire range of contact area. In the extreme limits of small and largeareas, the intermediate model should produce results similar to the simpler empirical modelsproposed for these extremes Figure 5 serves only to illustrate where different approaches areapplicable and what variables are important The terms "small" and "large" are relative to specificapplications and should not be taken out of context. We refer to small as applications involving smallstrain, undamaged ice, and high confinement and large as applications involving large strain,damaged ice, and low confinement The actual pressure for a given area can only be determined bya particular application. For this reason, we question the wisdom of plotting contact pressure solelyas a function of contact area without regard to boundary conditions, geometry, strain history, etc.CONCEPTUAL PRESSURE vs. AREA CURVEFORPURE CRUSHINGSmall Area : I' = ~ ( c Q ~ , c T - ~ , ~ )Intermediate Area : P = ~(o~

COMPARISON WITH EXISTING PRESSURE-AREA OBSERVATIONSThe observed dependency of small scale peak- and postpeak-ice pressures on confining stressseriously questions the validity of a single pressure-area relationship. Sanderson (1986) hassuggested such a relationship based on plotting much of the publicly available ice load measurementsonto a single figure. This figure is reproduced here as Figure 6. The inverse relationship betweenpressure and area observed in this curve has been attributed by both Sanderson (1986) and Hallam(1986) to ice having an inherent size effect Croasdale (1988) has further tried to incorporate failuremode variability to explain the 013'-ened dataa1000FIRST YEAR SEA ICE100. Laboratory & In situ testsIslands & structuresLiJtKMULTI YEAR SEA ICE2 10 Hans IslandId C/lorn. 120I- 012Id 2Q 0.01-0.001iu 5 10-4 10-3 10-1 lo0 lo1 102 lo3 lo4 105 lo6 10'CONTACT AREA m2Fig h - Pre^sur~-~irea relationship ..ifter Sanderbon (1986)We believe that the ohseried relationship hci-~een pressure and area can be explained by theconceptual pressure-area model de\eloped in the foregoing section Pressures from this modelshould provide an upper bound since only cru?hing pressure is considered As has been discussed,ice strength for a given area is a function of strain history, rate effects, and confining stress.Depending upon the relative influence ot each of these effects, different pressures could be observedfor similar contact areas. The influence of confining stress can be seen by study of Figure 7 For thetho geometries shoun in this figure, the contact stress for the partially confined case is expected to beless than that for the fully confined caseThe influence of strain history can be seen by study ofFigure 8. The contact stress beneath the partially embedded indenter is expected to be less thanbeneath the indenter in initial contact with the ice surface. This difference is expected based on thestrain history of the partially embedded caseThese two examples show contact stress to be anon-unique function of area. For small and intermediate areas, the resulting contact stress for all ofthese geometries is expected be a function of loading rate as shown by the small scale triaxial testresults.

Fig. 7 - Effect of confining stress on contactstress, (a) fully confined (b) partiallyconfinedFig 8 - Effect of strain history on contactstress (a) with no strain history (b) mthstrain historyConsidering the values plotted in Figure 6, these data essentially fall into tho categories small scaleand large scale Intermediate scale areas are not discussed in the context of the Figure 6 data sincewe question if measurements over intermediate scale areas as defined here have ever been made Inthe following, these data values, for small and large scales, are briefly discussed and placed in contextwith the pressure-area model conceptuali~ed hereThe small scale data plotted in Figure 6 are derived primarily from laboratory tests, icebreakerimpact tests, and field measurementsBased on the foregoing study of the mechanical behavior ofice, these high pressures most probably result from a combination of high confining stress and rapidloading rate The triaxial tests presented here have peak strengths well below the maximum pressuresshown in Figure 6, but this is due to insufficient confining pressure and loading rate Jones (1982)conducted triaxial tests with confining pressure up to 40 MPa and strain rates up to 1.4 x 102/sec.Those results are more in line with the maximum pressures in Figure 6 In the case of the icebreaker tests, contact pressure values need to be used with caution since pressures associated withlarger areas may be ship energy limited. For the case of field indentation pressures, data values arefor small aspect ratios and good initial contact with undeformed iceThese conditions are consistentwith our notion of "small" and correlate with peak triaxial strengths despite large differences inactual contact areas.

The large scale data plotted in Figure 6 are derived primarily from Hans Island and for very largeareas are inferred from mesoscale ice dynamic models An additional grouping of data values hasbeen plotted on this figure corresponding lo the observed peak stress range inferred by Dorris (1989)from Gulf Canada Molikpaq data published by Jefferies and Wnght (1988). As discussed by Dorris,the stress range computed from the Nlolikpaq data is very similar to the contact stress that would bepredicted from the unconfined residual compressive strength For reference, the unconfined residualcompressive strength from small scale tests has been superimposed onto this figure. The horizontalline shown corresponds to a residual stress range between 1 28 and 1 71 MPa for ice temperatures of-5 and -20 degrees, respectively The magnitude of the ice pressures inferred from the Molikpaqmeasurements are expected based on the conceptual pressure-area model postulated here. For theMohkpaq contact conditions, the aspect ratio of the contact area is large and so are deformations.For these conditions, confinement is expected to be minimal, and the contact stress is expected to bedominated by the unconfined residual strength, ergThe inclusion of data from Hans Island in Figure 6 illustrates the importance of considering failuremodes. These data, which show lower stresses than those inferred from the Molikpaq, correspond tomultimodal failure conditions As discussed b) Dorris (1989), the unconfined residual stress shouldserve as an upper bound to these data Additionally, the driving force in the Hans Island data ismiited by the available kinetic energy Most of the Hans Island impacts also involved glancing blowsor were cushioned bv smaller floes.Finally, the pressure-area relationship postulated here is not expected to be valid in the mesoscaleregion identified in Figure 6. This region includes refrozen leads and polynas The stress to closethese features may be governed by sheet ice buckling rather than by pure crushing as considered inthe pressure-area model conceptualized hereCONCLUSION AND RECOMMENDATIONSArguments have been made, and a conceptual model postulated, showing a connection betweenlocal and global crushing loads for ice. Using inaxial test results, a relationship has been shownbetween this pressure-area relationship and small scale laboratory test data This model suggests aninverse relationship between pressure and area having an upper limit which depends upon the peakconfined compressive strength and lower limit defined by the unconfined residual compressivestrengthQualitatively, the model provides a physical understanding of the observed variation in pressurewith contact area. This model is expected to provide a realistic upper bound for observed icepressures across the entire range of indentation geometries considered. Finally, comparison ofmeasured field data to this postulated pressure-area curve suggests that, in some instances, measuredvalues may be limited by failure modes other than crushing and, thus, are not necessarily associatedwith maximum pressureThe triaxial test data described in this paper are part of a larger set of test results recently obtainedby Shell Development Company, To our knowledge, these tests represent the only such results of

their kind. Ongoing work plans include the application of these results into the development of arealistic constitutive model for ice and planned future implementation into a multipurpose finiteelement codeREFERENCESCroasdale, K. R. (19881, Ice Forces Current Practices, Proceedmg of the 7th Int Conf. onOffshore Mechanics and Arctic Engineering, Houston, Texas, LSADorris, J F (1989). The L'se of Residual Strength in the Calculation of Crushing loads on WideStructures, to be presented at The 10th Int. Conf on Port and Ocean Engineering L'nder ArcticConditions. ~ulea SwedenHallam, S. D (1986), The Role of Fracture in Limning Ice Forces, Proceedings of the 8th IntSymposium on Ice, IAHR, Io\ia City, Iowa, USAJefferies, M G and Wright, \V H (198S1, Dynamic Response of "Molikpaq" to Ice-StructureInteraction, Proceedings of the 7th Int Conf on Offshore Mechanics and Arctic Engineering,Houston, Texas, USAJones, S. J. (19821, The Confined Compressive Strength of Polycrystalline Ice, Journal ofGlaciology, V. 28, No. 98, pp 171-177.Ralston, T. D (1978). An Analysis of Ice Sheet Indentation, 4th Int IAHR Symposium on IceProblems, ~ulea SwedenSanderson, T J 0 (1986), A Pressure-Area Curve for Ice, Proceedings of the 8th Int Symposiumon Ice, IAHR, Iowa City, Iowa, LSA

PARAMETRIC STUDY OF ICEBERG IMPACT LOADSDat DuthinhGroup Leader,Ice EngineeringCentre for ColdOceanResources EngineeringMemorial University of NewfoundlandSt. John's, NF, A1B 3x5 CANADAABSTRACTAn analytical model was used to investigate the influence of variousparameters on the load caused by the impact of an iceberg on a gravitybased structure. The most important parameters are the velocity and theindentor shape of the iceberg. Therefore, more field observations ofthese quantities are recommended. Also, ice strength is important. Thevariation of strength at small contact areas is unimportant and the useof strength values at high contact areas is recommended. Collisions occurmostly in the brittle range where ice strength is independent of strainrate. However, in the final stages of the collision, the variation in icestrength with strain rate may affect the maximum impact load.It is possible to control the geometry of the collision zone to someextent by surrounding the structure with load attenuators, which slow thecolliding berg down gradually. In general, the simplifying assumptionthat all load attenuators involved in an impact behave identically is agood assumption.1. INTRODUCTIONIceberg impact loads are one of the design criteria for the gravitybased structure (GBS) proposed for the Hibernia oil field offshoreNewfoundland. The calculation of a design load for iceberg impact mustaccount for the random characteristics of icebergs. To this end variousprobabilistic models have been proposed [Duthinh and Fuglem (1988).Johnson and Nevel (1985)). This study takes a different approach andestablishes the sensitivity of impact loads to various properties of

icebergs as well as of the structure and its foundation. The parametricstudy, undertaken with a computer model described below and a range ofvariables deemed reasonable, shows which parameters influence the impactload the most and therefore, deserve further definition by fieldmeasurements.The geometry of the interaction turns out to be a significant factor inthe impact load and is studied in some detail for the case of a structureequipped with load attenuators.2. IMPACT LOAD MODELSClosed Form ModelMuch insight can be gained from a simple model which accounts for themost important physical aspects of the iceberg-fixed structure collisionproblem. In the case of a tabular (rectangular) iceberg with a constantice crushing strength colliding head-on with a triangular indentor, theimpact force Q is (Duthinh, 1984):where U= kinetic energy of the bergK, = 2 sb tan a = ice-structure interaction stiffnessK = structure stiffnessK = 16(l-V)ER = foundation translation stiffness(7-8V)(l+v)K = 4ER3 = foundation rotation stiffness3h 2 (1-VZ)2a = angle of load attenuating wedgeb = vertical contact length (berg height)s = ice crushing strengthE = soil elastic modulusV = soil Poisson's ratioR = foundation radius.This equation assumes elastic behaviour of the structure and itsfoundation and is thus valid, as a first approximation, at the operationalstress level. The ultimate resistance of the structure would call uponpermanent, plastic deformations and the above equation would no longerapply.

Equation (1) shows that the energy absorbed by the various mechanismsinvolved (ice crushing, structure and foundation straining) depends on therelative stiffness of these mechanisms. In most cases K,

Effect of Contact AreaIt is well known that ice strength 0 decreases as contact area Aincreases (Sanderson, 1988). The largest tests of iceberg crushingstrength were conducted at Pond Inlet and remain proprietary (Johnson andBenoit, 1987). To study the effect of constant area, the impact model wasexercised with the following strength-contact area relationship obtainedfrom sea ice (Karp, 1980):0 S A

Effect of TemperatureAs the structure penetrates into the iceberg, it encounters ice atdifferent temperatures, and therefore, different strengths.Diemand(1984) noticed that the colder ice of the core (between -15 and -20%) liescloser to the surface of a berg in warm water than in cold water, due tothe more rapid ablation of the warm, outer layers in warm water. Goodrich(1987) measured temperatures on three icebergs. The greatest temperaturegradient occurs in the outermost 4 or 5m which also show the greatestseasonal fluctuations. Below 15m the temperature is virtually constantat -10 t 2¡for two icebergs and slightly warmer for the third.Lachance and Michel (1987) propose the following relationship betweentemperature 6 in degree C and the crushing strength 0in the brittle range for a constant strain rate(MPa) of iceberg iceo = 2.50 + 1.19 18]0-55 (4)In the following example, the impact model assumes, for simplicity, alinear increase in strength with penetration depth do = 7.0 + 0.75 d MPa d < 4.0mo = 10 MPa d 2 4.0mAn iceberg of mass 7.5 x lo9 kg (including added mass) impacts a GBS at0.5m/s. The "prow" of the berg is modelled as a horizontal wedge indentorof angle 112O whereas the structure is either a vertical wedge shaped loadattenuator of angle 900 or a circular load attenuator of radius 8.4m.(Sonar profiles of icebergs show that wedge shaped indentors are notuncommon). The following maximum impact force F, the impact duration tand the maximum penetration d are obtained.Triangular attenuatorF(MN)t(s)Constant o = 7.0 MPa 544 13.7o as in (5) 612 12.0Circular attenuator --o as in (5) 748 8.27 3.03The assumption of constant ice strength equal to its surface value canunderestimate the impact force significantly depending on the temperatureand strength gradients with depth.

4. PARAMETRIC STUDYParameters were varied about the four following base cases all involvingthe same berg:Berg mass "- 10 million tonnes (.including added mass)Berg velocity = 0.5 mlsIce strength = 7.0 MPaFour different geometry combinations were studied, resulting in impactforce F:a) A truncated wedge shaped berg of angle 28 and snub length 1 versusa triangular indentor of angle 2a.a = 45" 8 = 560 1 = 6.0m F = 713 MNb) A truncated wedge berg versus a cylindrical indentor of diameter D.D = 16m B = 56" 1 = 6.Om F = 891 MNc) A wedge berg versus a triangular indentor.a = 45"6 = 56" F = 659 MNd) A wedze berg versus a circular indentor.D = 16m 0 = 560 F = 778 MNThe parameters are realistic and based on the author's consultation withvarious industry sources.ResultsThe results depend on the choice of the base case and the range ofvariation of the parameters. In Figures 1-4, the steeper the curve, themore sensitive the impact load to the parameter considered. Icebergvelocity and indentor shape are the most important parameters.5. IMPACT ON S E W . LOAD ATTENUATORSThe parametric study shows the importance of the geometry of thecolliding bodies. In this section, a more detailed model is developedthat accounts for impact on several 90 degree wedge load attenuators. Dueto the overall curvature of the structure, impact does not usually occursimultaneously but rather, consecutively on adjacent indentors, nor is theangle of attack the same. However, calculations are greatly simplifiedif all attenuators can be treated identically in a multiple indentor

impact. This will be referred to as the straight structure, simultaneousimpact case. [These load attenuators are assumed rigid, in contrast tothe low strength bumpers proposed by Wishahy (1987)l.Impact on Two Adjacent Load Attenuators (Fig. 5)The iceberg chosen for this example has a mass of 4 million tons, avelocity of 0.5 m/s, a rectangular vertical contact depth of 10m and aconstant ice strength of 4.0 MPa.Case -.Penetration Depth (m) Impact Force (MN)ingle attenuator 3.54 283) Two attenuators,straight structure,simultaneous impact 2.50) Curved structure,symmetrical impact3) Curved structure,consecutive impactImpact on Three Adjacent Load Attenuators (Fig. 6)Such an impact requires deeper penetration. Therefore, the example bergis doubled in mass to 8 million tons and the vertical contact depth halvedto 5 m.Case Penetration Depth (m) Impact Force (MN)Single attenuator 7.07 2834) Three attenuators,straight structure,simultaneous impact 4.085) Curved structure,symmetrical impact 3.486) Curved structure,asymmetrical impactIt is clear that only a very energetic iceberg with a sharp profile canindent to the depth required by case 6).In case 6) the third attenuatoronly gets hit near the end of the collision, at an angle much differentfrom the first attenuator. This explains the relatively large differencebetween the impact force obtained in 4) and in 6). The iceberg is assumedto continue in its linear path without rotation during the impact.

Impact on Four Adjacent Load Attenuators (Fig. 7)The same iceberg is used as with three attenuators.Case Penetration Depth (m) Impact Force (MN)7) Straight structure,simultaneous impact 3.54 5668) Curved structure,symmetrical impact 4.61The indentors are not deep enough to allow the case of four indentorsbeing hit one after the other.DiscussionThe load attenuators work by slowing the iceberg down gradually anddecreasing its kinetic energy over a longer time and distance than for abare structure. Large collisions would involve several attenuators, theeffectiveness of which increases with their number, for a given geometry.The assumption that all load attenuators involved in an impact behaveidentically is good, thus simplifying calculations.6. CLOSUREAn analytical model was used to investigate the influence of variousparameters on the load caused by the impact of an iceberg on a gravitybased structure. The most important parameters are the velocity and theindentor shape of the iceberg. Therefore, more field observations ofthese quantities are recommended. Also, ice strength is important. Thevariation of strength at small contact areas is unimportant and the useof strength values at high contact areas is recommended. Collisions occurmostly in the brittle range where ice strength is independent of strainrate. However, in the final stages of the collision, the variation in icestrength with strain rate may affect the maximum impact load.It is possible to control the geometry of the collision zone to someextent by surrounding the structure with load attenuators, which slow thecolliding berg down gradually. In general, the assumption that all loadattenuators involved in an impact behave identically is a good assumption.

REFERENCESDiemand, D. (1984). Iceberg Temperatures In The North Atlantic:Theoretical And Measured. Cold Regions Science and Technology, V. 9.Duthinh. D. (1984). The Head-on Impact Of An Iceberg On A Vertical GravityBased Structure. Specialty Conf. on Computer Methods in Offshore Eng.,CSCE, Halifax, N.S.Duthinh, D. and Fuglem. M. (1988). Iceberg-Structure Interaction: Force,Energy And Probability. IAHR Ice Symposium, Sapporo, Japan.Duthinh, D. and Marsden, S. (1986). Iceberg Impact Load On A Gravity BasedStructure. Fourth Int. Cont. Cold Regions Eng. ASCE, Anchorage, Alaska.Goodrich. L.E. (1987). Core Temperature Measurements On Three ArcticIcebergs. Proc. OMAE. V. 4.Johnson, R.C. and Benoit, J.R. (1987). Iceberg Impact Strength. Proc.OTC. V.4.Johnson, R.C. and Nevel, D.E. (1985). Ice Impact Structural Design Loads.POAC 85, V.2.Karp. L.B. (1480). Concept Development Of A Concrete Structure Founded InThe Ice-Stressed Chukchi Sea. University of California at Berkeley,Technical Report 8.Khezsin. D.E.. Likhomanov, V.A. and Kurdyumov, V.A. (1976). DeterminationOf Specific Breakup Energy And Contact Pressures Produced By The ImpactOf A Solid Against Ice. USA CRREL TL539.Lachance, J. and Michel 11987). Experimental Study Of The BrittleBehaviour Of Iceberg Ice. POAC 87.Nevel, D.E. (1986). Iceberg Impact Forces. IAHR Ice Symposium, Iowacity.Sanderson, T.J.O. (1'388). Ice Mechanics. Graham & Trotman.Tunik, A. (1987). Impact Ice Loads On Offshore Structures. POAC 87, V.I.Wishahy, M.A. (1987). Methods For Minimizing Iceberg Impact Loads OnGravity Base Structures Iceberg Bumpers: Conceptual Design. OMAE, V.4.

Ec * structure stlffnusv = bwg wl

Sfructur* berg 1-60 -40-0OJFIG 3WEDGE BERG VERSUS WEDGE STRUCTUREBore structureD- 120 mAD -650% AF -153%FIG 4 WEDGE BERG VERSUS CYLINDRICAL STRUCTURE502

AN ICE-STRUCTOKE INTERACTION KIDELBASED ON OBSERVATIONS IN THE GULF OF BOTHNIAAlf EnqelbrektsonVBB-SWECOBox 5038S-102 41 STOCKHOLMSWEDENABSTRACTOn the basis of experiences from studies of ice-structure interaction inthe Gulf of Bothnia a model has been outlined for the characterizationof periodic ice forces associated with resonant structural vibrations.A generalized ice force time-history is proposed to be used for engineeringpurposes, and the model is discussed in terms of ice mechanics. It appearsthat the basic features of the model are of a generic character and thatthe suggested ice force equations are relevant, in principle, to casesof static as weU as of dynamic structural response.1. LONG-TERM STUDIES OF ICE-STRUCTURE INTERACTIONFor about 30 years ice action on offshore lighthouse structures in theGulf of Bothnia has been increasingly studied. Largely, each decade representsa specific stage of development.During the 1960's the studies were quite unsophisticated: sinply a follwupof the performance of the structures when affected by drifting ice,ice-piling, icing etc. On the basis of the rather poor knwledge of iceaction at that stage and, apparently, a portion of good intuition, iceforces were predicted rather closely to the optimum risk level. A fewcases of damage gave fairly clear indications as regards particular iceconditions, requiring adjustments of the design loads.

During the 70's the problem of ice-induced vibrations was realized andthe most strongly affected structure was instrumented. Vibration recordssampled during that decade, together with the continued follow-up and analysisof a few cases of static and dynamic overloading of Finnish and Swedishlighthouses, improved the understanding of ice-structure interaction considerably.During the 80's the studies have been expanded appreciably, quantitativelyas well as qualitatively. Taking advantage of the Gulf of Bothnia as aconvenient facility for Arctic research, several independent ice studyprojects with international participation have been conducted and someare in progress. The product is a continuous inflow of parametricallywell-defined data and subsequent improvements of the bases for ice-forcepredictions for Arctic areas, whereever the fundamental ice parameterscan be quantified and where ice conditions are not essentially differentfrom those prevailing in the Gulf of Bothnia.2. RECENT STUDIESIn 1985 the studies of ice-structure interaction were intensified in thata joint study project was agreed between Arco, Exxon and Mobil (USA), NorwegianContractors, Canadian Coast Guard, Mitsubishi, the Swedish NationalIndustrial Board, Hamburgische Schiffbau-Versuchsanstalt and VBB. Thelatter two companies, cooperating with the Swedish Administration of Shippingand Navigation and with the University of LuleA obtained financial andadvisory support for a comprehensively extended field study of ice-structureinteraction, by employing some large lighthouses in the Bothnian Bay asobjects for data sampling and other abservations.The instrumentation of the lighthouses was improved and during a threeyears' period the database was greatly enlarged, and suitable analysismethods were developed for transformation of measured structural responseto ice forces. Since the instrumented lighthouse structures serve, in principle,as full-scale elastic obstacles and measurement devices with calibratedconstitutive properties, static as well as dynamic relations betweenthe structural response and the ice forces can be determined within uncertaintyranges that are judged to be quite acceptable from an engineeringviewpoint.

Two years of development, including trial operations and refinements, resultedin an elaborate system for data acquisition and processing, basedon the following elements:* Accelerometer and inclinometer systems including computers, filters,tape recorders, etc, for sampling of response data in the form of recordsof acceleration and inclination (in principle two types of accelerograms).Figure 1.Sampling of ice data in connection with an event of indentation

* Video camera systems, coordinated with the above systems, for observationofice movements etc.* Signal processing procedures especially developed for the analysis ofthe rather complex data records, involving separation of signals in respectof frequencies as well as directions. (The lack of reference points onthe open sea and the strongly vibrational character of the structural responsenecessitate that very small gravity related signals must be distin-guished in the inclinometer records, containing predominantly signals causedby horizontal inertia due to the strong vibrations.)* Constitutive models of the lighthouses, calibrated by pull tests etc,for transformation of response data to ice force time-histories.* Field sampling and laboratory investigation of ice data (Figure 1).3. ICE FORCE TIME-HISTORIES DERIVED FROM RECORDS OF OBSERVED STRUCTURALRESPONSEThe records of structural response data and the corresponding ice forcetime-histories studied so far present a fairly clear picture of the mechanismof ice-structure interaction from the mechanical point of view. Onthe basis of these data the mechanism can be modelled mathematically interms of ice force and response time-histories. By selecting simple characteristics,such as the maximum and minimum ice forces as key parameters,the relationships can be normalized, resulting in a set of ice force expressionsfor engineering applications.Obviously, the type of ice-structure interaction that involves dynamicstructural response and, particularly, resonant vibrations is a more complexmanifestation of ice action than stationary ice pressure or steady-stateindentation. This presentation will still originate from the dynamic typeof ice structure interaction and it will be demonstrated, that the varioustypes of ice action are closely related. By way of introduction some iceforce records from a large offshore lighthouse in the Bothnian Bay areshown. The diameter of the cylindrical structure is 7.2 m (Figure 1).

4284.3kN ICE FORCE FFigure 2. Condensed ice force time-history from an event of indentationthrough an ice floe drifting with a speed of 0.04-0.06 m/s. Four differentphases are observed: Initial indentation with increasing interface width,steady-state indentation without major structural dynamics, indentationassociated with a greatly fluctuating ice force and, finally, a phase ofload decay.2ADISPLACEMENT AT WL (mm)v-- /--2.3140.0 TIME (s) 150.0Figure 3.The sequence 140-150 s from the above record displayed in anextended time scale together with the corresponding time-history of structuraldisplacement at the ice force level. (Positive for displacement inthe ice force direction.)During this short sequence the ice-structure interaction changes froman almost "static" mode to a mode associated with periodic fluctuationof the ice force as well as the structural displacement. The latter phaseis initiated by a sudden load peak followed by a load drop. The correspondingamplitude of the structural response motion is sufficient for startingthe periodic phase of the ice-structure interaction, associated with increasingamplitudes of structural deflection until energy equilibrium is reached.The frequency of vibration is very close to the fundamental natural frequencyof the structure and the vibrations are of a typically resonant character.

The study of numerous records of strong vibrations and associated periodicice forces has provided unambiguous evidence on the following points:* When an ice cover is being indented by a flexible structure and failsmainly in a crushing mode, so-called self-induced vibrations occur frequently.The resonant vibrations are coupled to a periodic fluctuation of theresultant ice force.* If the drift speed is not much lower than the maximum velocity of thestructural vibrations, the frequency of the predominant structural oscillationsdetermines the frequency of the load fluctuations. Obviously, thestructural vibration induces the periodicity of the ice force, that inturn amplifies the vibration and so on, until the energy consumption dueto danping becomes equal to the energy input from the resonant load.When the vibration amplitudes are below the threshold, where the periodicinteraction becomes significant, the resultant ice load also fluctuates,but the amplitudes are comparatively small and the fluctuations are moreirregular. The character of the load is almost the same for a rigid structureas for a flexible one and the deflection of the latter is essentiallystatic. Whereas a distinction is made betwen static and dynamic structuralresponse during indentation, it should be kept in mind that the ice forceduring indentation is always more or less dynamic.* The most important feature of the ice force time-history during periodicindentation associated with resonant vibrations is the sudden drop of theresultant force after reaching the peak of each load cycle. Another importantobservation is that the time-averaged resultant ice force appearsto be essentially equal to the ice force during non-periodic indentationof the same ice-floe. The maximum, mean and minimum ice forces (F-,Fo, Fin) are therefore suitable key parameters for characterization ofa sequence of periodic as well as non-periodic ice-structure interaction.* The periodic ice force can be characterized in a spectral form, by meansof Fourier analysis, i.e. by breaking down the force time-history intocomponent sine waves, the amplitudes and phases of which can be representedin a spectral form. In Figure 4 the power density spectrum of the sequencepreviously displayed in Figure 2 is shown as an example. The spectrum clear-

ly demonstrates the strong coupling between the structural oscillationsand the ice force fluctuations. The component waves of the ice force timehistoryhave their frequencies predominantly concentrated at the fundamentalstructural frequency 2.34 Hz and its multiples, an observation that willbe further referred to, when generalizing the ice force time-history fordesign purposes.Figure 4.0 01 I I I I I0 0 4 00 8 00 FREQUENCY f(ftfl2 00Typical power density spectrum of ice forces associated withresonant structural vibrations.2. OBSERVED BEHAVIOUR OF DRIFTING ICE DURING INDENTATIONThe following observations are based mainly on studies of video recordsfrom events of strong ice action associated with continuous as well asperiodic indentation of ice-sheets with thicknesses of 0.5-1.0 m. Occasionaldirect visual observations are also referred to.* The load limiting mode of ice failure is crushing. Occasionally, theload limit is set by splitting, associated with more or less radial cracks(seen from the centre of the structure). However, splitting does not occurcontinuously and can therefore not be relied upon for design purposes.Consequently, crushing across the whole width of the structure can be regardedas the ultimate load limiting mechanism, at least when dealing withconditions similar to those prevailing in the Bothnian Bay. In waters wherethere are multiyear ice ridges the utlimate loads exerted by such ridgesare sometimes limited by other failure modes than crushing, but in otherrespects the Bothnian Bay conditions are broadly representative for Arcticareas.

* The crack propagation and crushing take place within a short distancefrom the ice-structure interface. Normally, it has the character of pulverisationof the ice. From laboratory experiments we have learned thatsuch a pulverisation is the final phase in a course of initial fracturegrowth, progressive cracking and final collapse of the ice structure.* Obviously the cracking and pulverisation are more or less outspread inspace and time, which is associated with a corresponding limitation andvariation of the interface contact. At a certain instant the contact isconcentrated at limited spots or zones. At each zone the ice is stressedto a condition between ductile strain and cracking, and the phases aremore or less different from one zone to another. This phase differenceor non-simultaneous failure is a key feature in our following considerations.* Basically, the large scale mode of ice failure appears to be that ofcrushing in case of static structural response as well as in case of strongvibrations. The non-uniform distribution of failure zones has sometimesbeen discerned in the video records, but the resolution is, of course,not sufficient for allowing details such as the periodicity of the crushingand the local phase difference to be distinguished.5. A GENERIC M3DEL OF ICE-STRUCTURE INTERACTIONIt is particularly in the light of recent experiences from the field studiesin the Bothnian Bay that all the findings seem to converge towards basicallyone single mode of ice-structure interaction during indentation. Basedon a few variants of that mode, simple explanations can be found for variousforms of interaction such as steady-state indentation, periodic indentationassociated with strong structural vibrations and even interaction withunbroken ice to some extent.A generic model of ice-structure interaction is therefore proposed, withreference to the following categories of supporting material.* The above-mentioned observations of the mode of ice failure and the observationsof structural response and ice force time-histories, enabling amathematical characterization of "static and dynamic" ice forces againststructures in the Bothnian Bay.

* Current knowledge regarding relations between ice strength, strain andstrain-rate as well as reported observations concerning apparent relationsbetween ice forces and the size of the interface area, the aspect ratioetc.* Observations and qualitative explanations, admittedly hypothetical tosome extent, regarding the details of the transient ice stress and failureconditions close to the interface.The model has the following basic features:* During the course of indentation the contact between the ice and thestructure is predominantly concentrated at local zones, the location ofwhich vary with time.* At each temporary contact zone the ice undergoes at least one cycle oftransient conditions, from increasing stress associated with ductile behaviourto cracking and pulverisation. The load cycles at different contactzones are more or less out of phase.One extreme is a random phase distribution (although there is, most likely,a certain coupling between adjacent contact zones due to interactive stressconditions). The opposite extreme is synchronized load cycles at the variouscontact zones.During a course of steady-state indentation (when the indentor does notoscillate) the local zones are consecutively undergoing their individualstress cycles, the rate being determined by the ice drift velocity. Thisparameter also determines the strain-rate and, therefore, it probably influencesthe ice strength and the amplitude of the contact forces. Sincethe time distribution of the load impulses, represented by the local contactforces, has a random feature, the global load on a large interface areawill be rather uniform and correspond to the average contact force. Incase of a smaller interface and only a few contact zones, the majorityof the contact forces nay be in phase occasionally and the global forceis likely to be fluctuating irregularly. The maximum effective contactpressure will exceed the pressure associated with a large area. For otherwisehomogeneous ice conditions the maximum value will be determined by

the ice drift velocity and the random phasing, thus by the duration ofthe indentation.The widely observed size effect on the effective pressure may thus be explainedby the phase distribution of local contact forces. However, fornarrow indentors the effect of confinement due to unstressed ice adjacentto the interface should not be neglected. There are strong indicationspointing at confinement effects in some cases of over-loading when narrowstructures have been damaged. The aspect ratios have, however, not exceededthe order of 4 in those cases.* During a course of periodic rate of indentation the vibrating indentorinfluences the local load pulses largely. The structural movements affectthe strain-rate and coordinate the local pulses, as illustrated in Figures5 and 6.RELATIVE VELOCITY V-V,STRAIN RATCBRITTLETRANSITIONDUCTILE"3"sFigure 5. During each cycle of structural oscillation the relative velocityand the strain-rate (as well as the strain) passes to and fro over theranges corresponding to ductile deformation, fracture growth and brittlefailure.

STRUCTURALDEFLECTIOND-E :The structure moves backwards after the precedingcoordinated ice failure. The strainrateis high, the contact reduced and theice force passes its minimum.The structure slows down and then turns,the strain-rate decreases and the contactpressure increases to a peak before the forwardvelocity increases and the structuretends to move ahead from the ice.The structure decelerates, the contact pressureincreases once more in a ductile manneruntil a sudden coordinated failure occurs,when the ice strength is being exceeded.The global peak load is therefore composed of relatively well-coordinatedlocal pulses. The peaks of the individual load cycles may reach the limitcorresponding to the maximum strength of the ice almost simultaneously.During the phase when the structure moves in the ice drift direction theonloading is soft and the strain-rate is initially rather low. Therefore,the ice strength may come close to its optimum before the coordinated failure,and the peak load may reach the same order as in case of any initial failureover a smooth interface. Actually, no cases have yet been observed, wheresuch an initial peak has exceeded the peaks during subsequent resonantvibrations.Beside the build-up of the peak load the sudden stress drop followingthe peak is the most important feature as regards the periodic ice-structureinteraction. This stress drop occurs almost simultaneously at various contactzones and is the strongest coordinating factor. The mechanism of coordinationis quite understandable, considering the brittleness o the ice afterthe fracture nucleation, leading to progressive cracking not only withinthe induvidual fractured zones but also leading to progressive collapseswhen the load at one collapsed zone is overtaken by adjacent zones.The obvious lower limit of the minimum force, locally and globally, is zero.However, our observations indicate, that the global load drop is normally

of the order of 50 per cent of the peak load in case of strong resonantvibrations, and that 75 per cent of the peak load is an extreme value.6. GENERALIZED CHARACTERIZATION OF ICE FORCE TIME-HISTORIES FORENGINEERING PURPOSESIn respect of the choice of key parameters the development of ice forceformulae for engineering purposes can be approached in two steps:* Characterization of a generalized load time-history normalized to thekey ice force parameters F , F~, Fin or the corresponding "effectivepressure" parameters pmX, pot pmin.* Formulation of relationships between the above load parameters and fundamentalparameters for characterization of ice conditions.It is recognized that a more or less probabilistic approach must be considered,for the latter step in particular. However, generalized relationshipsmay very well be formulated deterministically, assessing approximateuncertainty ranges for the parameters until sufficient data have been acquiredfor enabling a refined probabilistic approach.With reference to the Fourier analyses of ice force time-histories andthe example of an ice force spectrum given in Figure 4, the following sinipleexpression has been chosen for characterization of a generalized time-historyof the effective ice pressure:~(t) = p0 + zpn. cos(nCJ1t + @J (1)The loading function can thus be represented by a constant and a numberof sine waves with n = 1, 2, 3, 4 etc., the angular frequencies n LJ1 ofwhich are multiples of the fundamental structural frequency Wl.For most engineering purposes four sine waves are sufficient for obtaininga realistic generalization of the loading function, as demonstrated inFigure 7.

Figure 7. Comparison of an ice pressure sequence from the record shownin Figure 3 and the corresponding generalized function (below), composedof a constant pressure and four sine waves. The normalized constants arepl/pmx = 0.110, pipmax = 0.165, p3/pmax = 0.050, p4/pmx = 0.040 andthe phase angles are 5.38, 2.24, 4.62 and 3.66 radians respectively, forEquation (1) can be applied to ice-structure interaction associated withdynamic as well as static structural response. Steady-state indentationis represented by the first term and in case of resonant vibrations thesine terms are to be included. The use of the maximum effective pressureas a normalizing parameter is motivated by its close relation to the maximumice strength before fracturing.The next problem is to establish a reliable relationship between theeffective pressure and a well-defined ice strength parameter. We may referto the classical Korzhavins formula and setp=k Sa k ~ kp. .(2)where fum is the uniaxial compressive ice strength averaged over the thickness.For relatively large cylindrical structures as those referred to abovethe effects of shape (kn) and of lateral confinement (k,.) need not be assessedexplicitly and the relationship can simply be expressed by one factor k = p/£In case of invariable interface area and ice strength the time functionof k is obtained from Eq. 1 :k(t) = ko + Zkn. cos(n~+t + on) (3)

It follows from the above that the factor k varies strongly with themode of ice-structure interaction. Typical maximum and mean values duringsequences of saturated resonant vibrations are 0.6 and 0.4, respectively.7. CONCLUSIONS AND OUTLOOKSPrevious experiences and future objectives of the ongoing ice force studiesin the Gulf of Bothnia may be briefly summed-up as follows:* The model outlined in Sections 5 and 6 for the characterization of staticand dynamic ice structure interaction, including the proposed generalizedice force equations, is intended to provide engineers with an improvedbasis for the design of offshore structures including installed equipment.A simplified spectral presentation of the ice force function has been chosen.This is for practical reasons and for allowing transperancy, but a moreconplete spectral presentation, including higher-frequency components ifneeded, might be incorporated in the future work.* In addition to the observation that a generalized ice force functioncan be expressed in terms of a few key parameters, such as the maximum,mean and minimum ice force amplitudes during a sequence of periodic interaction,it is important to note that the basic features of the functioncan be explained in terms of ice mechanics. Key elements are the interac-tive cycling of the interface pressure, the variation of the constitutiveproperties of the ice during each load cycle, the synchronism of ice failuresat local zones, the strain-rate dependence etc. Further investigationsof these relations will be performed by means of a system of ice forcesensing panels, enabling separation of local pressures in time and space.* In the first approach the ice force relationships have been expressedmainly in a deterministic manner, the probabilistic aspects covered onlyby indicating fairly broad ranges of uncertainty and expected spread. Theseranges are based on the long-term experiences from the Gulf of Bothnia.The experiences are, however, sufficient only for very rough probabilisticquantifications. Acquisition of more data, for improved probabilistic considerationsis therefore programmed to become an important part of futureactivities.

DETERMINATION OF THE ICE LOAd O.\l PILES OF-FIXED OFFSHORE STRUCTURESM.G.GladkovRes. OffrThe 3.E.VedeneevAll-Union riesearchInstitute of HydraulicEngineering ( VNIIG) ,LeningradUSSRABSTRACTBased on the author's experimental data on the strength of grainad andfibrous sea ice ( constituents of typical first-year arctic ice field), the upperbounds of the ultimate load which may occur during ice interactionwith vertical piles of various shapes iivere established. These bounas areto be used for determining the ice load.A simple and convenient expression is derived for predicting the horizontalforce exerted by ice on vertical piles of fixed offshore structuresusing the ice temperature, salinity, thickness and texture data as well asthose on pile shapes and widths and conditions at the ice-pile contact.1. INTRODUCTIONAllowance for the maximum forces occurring during ice-,^ile interactionis a must for engineering design of safe and cost-effective fixed offshorestructures. To resist these forces, the piles must be capable to inducecrushing the ice fields acting on them.The maxiinuin horizontal force exerted by ice on a vertical pile andoccurring, as is known from Peyton ( 1968) and Taylor ( 1981) et al., atthe ice-pile contact area due to the ice plastic failure may be rather easilyestimated within the framework of the plastic limit analysis as reportedin detail by Reinicke ( 1980) . However, this necessitates the availability ofthe reliable data on uniaxial loading strength of natural ice which can beobtained in a ~nanner as shown in Figure I.

Figure 1. Uniaxial loadin2 tests of the ice sheet.2. LNIAXIAL LOADING STRENGTH OF SEA ICEThe experimental part of the present puper zives the follo..in" relation-ships between the ,naxiinu.il strength of sea ice in uniaxial coin,->ressionand that in uniaxial tension defined in Figure 1 byC., T , C ,'rzC / C = 3.7; T / C = 1.23; T / C = ,: for fibrous ice ( 1)c/c = 1; T / c = T / C = ~ A for grained ice ( 2)The magnitude of the ratio C /C is found directly from uniaxial corn-7: Xpression tests. The test results obtained are shown in Figure 2. The ~n~-ixi-mum uniaxial compressive strengths take place at different critical strainrates & which depends on the ice texture and temperature and loadingdirection (in case of fibrous ice) (Table 1). The influence of the salinityon & is not detected.The .nawtude of T/C is found indirectly from flexural tests.Uniaxial compression and flexural tests are performed on carefully pre-pared prismatic speciinens of fibrous and grained ice ( constituents of thetypical arctic first-year ice field) under closely controlled conditions accordingto the IAHR recommendations ( 1960) .

aAUTHORFREDERKING and TIMCO(4983)A VAUDREY (1977)5 10 15 20V/.Fijure 2.Uniaxial coiiipressive stren>th of sea ice versus brine -volume:1, 3 - fibrous ice ( 1 - Cz., 3 - CX) ; 2 - jrained ice.

Fibrous ice-'-- -GrLiined ice10 describe the sc~ice behr~vio~ir the parabolic yield function, discuss-ed by Reitnicke 'ind r^cilston ( 197,'), is used which represented in the Car-tesic1n coot-dintites ~yste.~i IIQSit1 c~ise ot i-ihuie strainstitc- lot-l,~:ii-i c~iso of plane stressesTlie t-iuit~ericcil values of the coefficients of functions (3) and ( 1) calcu-lated by the use of ( 1) i^nd ( 2) are Aiven in Table 2.Inblf? 2.Coefficients--a!a3%'t'ield f~inction coefficients for seii ice."ibrous ice- >0.) 1 Cx--02.89 C "v-'I11.78 CXL2. cil-10.54 CxI--Coefficients valuesGrained ice1.5 C-'1.5 c"'-'>9 C L2 c-l2 c-1

- THE ULTIMATE LdAdThe scope of this pcper is li.mtec; cnl,' to tile upper bounds c.nc:lysis ofthe ultiiiiate load occurring duriti~ inneiiti~.tion of the ice -.ieet ul coiistL~iitt.iic~ness oy vertical rizic'i fldt, ivec~~e-siii~poc~ 'AII~ circ~llar iiicientersare in perfect contact ,~itl'i tile ice. To estii.kito tin-' influence ol ice cd-~ i i ~ i ifree~ii-i.: to the ;>ile at the ice-indenter contact, ootl-i free s1i~.ic~gi.~ nd

( a) The brine volume 3 , /oovhere S ( the ice salinity, loo) and t ( the ice temperature, C ) arefound using the data either on actual or calculated temperature and salinitydistributions over the ice field thickness. These data correspond to theperiod of time with the greatest ice effects observed within the constructionsite. And if the data mentioned are unavailable, the linear temperaturedistribution froin ta at the ice fielc! surface to 2OC belo*: zero at the icefield bottom and also the un1for.n salinity over the ice field thickness areaccepted. "The teili,3erature ta can be determined usin2 the air temperature,thickness of snoi".' cover and wind velocity cata by thennodynamic methods,etc.( b) The ultimate loadwhere F /( C b h) is the value found from Table 3 as dependent on thex xpile shape, ice texture, i-ispect ratio a/lh ( at b/h < 1 ~>-e select plune strainand at b/h > J ^.'Q select plane stress) and also on the conditions at theice-pile contact; ( C ) is the value deterinined a s a function of the brinevolume fro.ii Figure 2 ( curve Li is for grained ice; curve 3 is for fibrousice) .Using the ulti.ncite load values obtained for dl layers b;e determine theice field load on the pile of a given shape-nl?/b = [+ ( ~ ~ / b1 =1h) ] 11, k~N/n-,(5)"vhere nI-th layer, 1-1is the number of layers, ( ~ / b h) is the ultimate load for theThe values of F'/bis the ice field thickness.calculated by expression ( 5) give the upper boundof the load on the pile on the siae of the ice field that is in yerfect con-tact with the pile. Additional factors such as the actud-1 contact conditionsbehveey-i the ice and .iile the vdue of the aspect ratio, dependence of

the criticcil strain rate on the ice field structure and teinperature etc. leadto the decretise in the design ice loi.id (1s compared to that calculated intliis ctiicilysis. The tiictors ,iientioneci ccin be i~-llo..eci for by introciucingthe s,~eci~-il coefficients such as kL and I

vvhere III is tlie i-ihclpe factor for the pile ~ctlcukj-ted by the expressiont i =1 - ( 1 - cd liiO) ( d.lb> 0 + (2.6-1) for flat and ~~fcicd piles.vitli the angle A = ( 45 - 1Li-i) ( for circulc~r piles 0O) underfree slippage coi~clitions and by 111 = 1 for fieit *lid .ed:c.-slleiped piles(lnd in = 1.22, + f> ;L^J for ctrculcir ,>iles 'under Lidliusio~i coiiditions.h-xprcsssion ( 6) is trcinsfornied into tile for.11~ tla for c,~lcul~-ititl~ie lion-zotltal force exerted by first-ye'irstructu-es at b/h 2 3ice on vertical ,~ile=. of. fixed oifsnorcThe relative error in the force co-lcukutcd by toriln.ila ( 7) does not ex-ceed ID,o at the confidence lev-el of d.95. JLICIIaccuracy for calculiititn~P is undoubtedly sufficient especially in the lizlit of the fdct th'it tlie vcilu-es of the input data. are fo-r fro.,i be1112 specified uith the ~t-eater ~~ccut-a-CY.The method of the niti.~iu.te load u;Jper bound proved to be simple cmdefficient in deter,iiinit~~ the ice load on the bi^sis of the ice stre,i~th d'ita.Since the desizn values of the ice 1oiici are influenced by tliese dih, ti10. iLi-lysis is to ;:)v bisect on tl ie roli,. blo stre, I ;ti I ci ~"u'~.~ctet-i.~tics o;~t iedin the,. field.Frederkin~, A?. and Tiii-ico, G.W. ( 1 ~ 3 . ) Unioxtal coi~i~ircssivo strc~ti :tliand defor.nation of Beaufort Sea ice, Nat. ..Ses. Cou.ici1 Catiddu., dl\'.Build. Res., TA No. 115U, U9-90.Goldin, A.L. and Gladkov', h1.G. ( 19~;~) . iJeter,.linin~ tlie ice load on de-ments of ,ilarine engineering structures, Hydrotekl~t~iclieskoe 5troitelstv0,7, 27-29.Peyton, H.A. ( 1958). Ice ana marine structures, Ocean Industry, 3, 12,12-21..

Skndartii'ation ot testing ,netliocis for ice problems, ,~ro,~osed by WorkingGroup of IAHR Section on Ice Problems ( 1980), J. of Hydraulic iqes.,18, 2, 153-165.T.P. ( 1981) . An experitnenfc.il investigation of the crushingstrength of ice, The (ith Int. Conf. on Port and OCLY~I Engineering undei/kctic Cond. ( POAC'81) , Quebe c, Proc., 1, 332-AIL>.Vaudrey, K.U. ( 1977) . Ice engineering-study of related [properties of float-i n sea ice sheets and summary of elastic and viscoelcistic analyses,Civil En:;. Lab., Ti< No. boo, Port Huene.

A NUMERICAL MODEL FOR PREDICTING THE RESPONSE OFCONCRETE GRAVITY PLATFORMS TO ICEBERG IMPACTKjell HoltheDr ingSINTEF Division of Structural EngineeringN-7034 Trondheim - NORWAYABSTRACTAn efficient special purpose computer program for predicting the dynamic response ofconcrete platforms to iceberg impact has been developed, based on a three dimensional timedomain analysis of the coupled iceberg-platform system.A simple ice crushing model with no elastic deformation for the ice is used. The totalinteraction force is expressed as the product of a uniform area-dependent pressure and theprojected contact area.Local deformation of a column at the area of impact may be included in the analysisbased on linear shell theory and the time dependent impact area.The platform is described by one or several stiff volume structures interconnected withflexible column structures and a deck structure at the top. The soil is described as an assemblyof linear elastic springs.Simulations of the dynamic response are presented in computer plots for two typicalconcrete gravity platforms. Normalized results are given for the main forces and stresses fordifferent iceberg masses and local iceberg geometries.The present work has been a part of a comprehensive arctic research program for ESSONorge a.s.1. INTRODUCTIONOne of the main uncertainties in the design of arctic offshore platforms is the forceinteraction between the platform and the ice. Of special interest in areas such as the BarentsSea, is the collision between a concrete gravity platform and an iceberg to evaluate the designof such a platform.Several papers have been published analysing ice impact forces against gravity platforms.More recent studies are performed by Bass et al. (1985) using a three-degree-of-freedommodel; by Johnson and Nevel (1985); by Brown et al. (1986) including locally generatedpressure and by Cheang and Lam (1987) including a finite element analysis for the soilresponse. In recent papers Nevel (1987) and Croasdale (1988) give an overview of thedevelopment of ice load theories.In the present work, the main goal has been to develop an efficient special purposecomputer program to perform parametric iceberg-platform interaction studies. A possibleiceberg-platform situation is shown in Figure 1 where the iceberg may hit the caisson or onecolumn.

Figure 1Problem definitionThe numerical model considers an eccentric but radially directed impact with 6 degreesof freedom of motion for the iceberg and a simple 3-dimensional beam finite element modelfor the platform. The model also includes a simplified computation of local shell stressesbased on a uniform interaction pressure. The name of the computer program is ISIS.The present work has been a part of the comprehensive arctic research program ESARC("ESSO/SINTEF Arctic Research Program"). The ESARC program is outlined by Setchfield(1986) and by Mset and Wold (1989).2. ICEBERG MODELThe response of the iceberg during the time of impact is described by a simple icecrushing model, as shown in Figure 2.At the global level an inertia relation including both iceberg and hydrodynamic mass isestablished between forces and accelerations at the center of gravity (CG) for the 6 degrees offreedom of the iceberg in the iceberg coordinate system (b-axes). The iceberg is defined by itsmass and a horizontal shape which in the present model may be circular or rectangular. Anaccurate determination of the added mass of the iceberg is rather difficult and beyond thescope of this work. However, based on results given by Vugts (1968), the added mass of theiceberg is taken as 50 per cent of its mass for the three translational degrees of freedom.Buoyancy stiffness of the iceberg for rotation about the xb-and y,-axis and vertical translationis included. In case of a rectangular shaped iceberg these axes are parallel to the length andwidth of the iceberg (through the CG point).At the local level a relation is established between the ice indentation depth and thehorizontal interaction force based on the local shape of the iceberg and the diameter of theplatform at the point of impact.The horizontal interaction force, F , is calculated as the product of an ice mean pressure,pc, and the projected contact area, A , as follows (ice crushing model):It is assumed that the impact is head-on, that is, the front of the iceberg at the impact areais perpendicular to the iceberg velocity (x-axis parallel to velocity direction, no frictionaleffects). It is also assumed that the cylindrical shape of the platform at the contact area isunchanged during impact with respect to the ice indentation. The projected contact area will528

then be a function of the indentation depth, the platform diameter and the local geometry ofthe iceberg. In the present study the effective pressure is a function of the projected area. Thepressure-area relationship for ice impact (sudden, relatively short duration) is a very complexproblem and little public information is available. For purposes of illustrating the capabilityof the ISIS program, a fit to Sanderson's pressure-area data (1986) is assumed, although thedata are derived from various ice failure modes and ice types. This is given as follows:Here, a reference pressure value of p.., = 7.5 MPa is used to correspond to the referencearea A = 1 m2. The interaction force, which is nonlinear, may thus finally be expressed bythe indentation depth, A, (for a given iceberg local geometry and platform diameter).Since the direction of the interaction force may be eccentric with respect to the CG of theiceberg, rotation of the iceberg about its horizontal axes and the vertical axis may occur.GLOBAL LEVELRectangularCircularstructurevelocity direction^-icebergPlan viewSide viewLOCAL LEVEL@ Plan viewA- indentation depthASide view- projectedcontact areaGlobal level parameters:Local level parameters:length of iceberg D - diameter of platformwidth of icebergho - initial interaction heightdiameter of iceberg circular shapeheight of iceberg p, - upper interaction angleeccentricity in horizontal plane (y-direction) p, - lower interaction angleeccentricity along vertical axiscenter of gravity of the icebergiceberg coordinate system at CG (b-axes)platform coordinate system at point of impact(n-axes)angle between x- and x-axisFigure 2 Iceberg impact model

3. PLATFORM AND SOIL MODELThe soil is described by four linear elastic springs (vertical, horizontal, rocking andtorsion), with stiffness based on the secant modulus of the soil. Stiffness proportionaldamping is included in the soil model, but there is no mass associated with the soil description.However, both damping and mass forces for the soil are expected to be small compared tothe stiffness forces.The platform is represented and described by a few basic objects; such as volume,column and deck structure. The volume object is considered completely rigid and describesthe caisson with a circular, rectangular or triangular base area with a certain height. Both thecolumn(s) and the deck object are modelled by a system of linear straight beam elementsrigidly connected at nodal points. At each nodal point 6 degrees of freedom are defined;tranlations in, and rotations about each of the 3 orthogonal global axes. One column maytypically be modelled by 3 or 4 beam elements. The deck may alternatively be described by acompletely rigid volume object.The total mass of the platform includes consistent masses from the beam elements, masscontributions from the volumes and any additional mass contribution specified at nodal points(topside equipment and facilities). Both structural and hydrodynamic masses are considered.Structural damping is included to damp out high frequency local structural oscillationsand is due to internal friction in the material itself, and in the connections between thestructural components. The associated damping forces are described as a Rayleigh type darnpingwith a stiffness proportional damping matrix for each finite element.Hydrodynamic damping is not included. It is expected that both structural and hydrodynamicdamping forces will be small compared to the stiffness and mass forces during the timeof the iceberg impact.4. LOCAL SHELL MODELLinear local shell response in the cylinder wall is included in the present analysis, by amethod reported by Holmas (1987). Based on linear thin shell analysis employing Donnelltheory with trigonometric series solution for a long uniform cylinder, local shell stresses anddeformation are computed at the point of impact. The loading for the local shell analysiscorresponds to the actual mean pressure and loading area according to the iceberg indentationdepth at each point of time. Obviously, the present local shell analysis represents an approximationto the real shell problem with respect to loading, geometry and reinforced concretematerial behaviour. However, with a distance from the impact point to the cylinder endsgreater than twice the cylinder diameter, the stress deviation from a more accurate linear shellanalysis is found to be in the range of 10 to 15 per cent.5. SOLUTION PROCEDUREIn matrix notation the total dynamic equation of motion of the platform (P) and theiceberg (I) may be written as the following well known equations:in which R p is the platform force vector, M p the platform total mass matrix (added massincluded), C " the platform structural damping matrix, K p the plat-form structural stiffnessmatrix and rp,rI>,'rp are the platform displacement, velocity and acceleration vectors,respectively.5 30

R1 = MI? + K'r' ( at the point of impact) (iceberg) (4)where R' is the iceberg force vector (6 elements), MI the iceberg total mass matrix (6x6),K1 the buoyancy matrix and 6, IP are the iceberg displacement and acceleration vectors,respectively.For the platform all degrees of freedom are referred to a global coordinate system (notshown in Figure 2) except for the interaction point where the degrees of freedom (3 translationaland 3 rotational) are referred to the n-axes. For the iceberg the total mass matrix containsonly the 6 diagonal terms and the buoyancy stiffness matrix contains only 3 terms (horizontalrotational and vertical translation) with respect to the b-axes. Based on well known geometricalrelations the mass and stiffness matrix of the iceberg are transformed from the CG pointand b-axes to the impact point and the n-axes.Note that all elements in R p and R1 are zero except the one corresponding to the nonlinearice-platform interaction force (numbered as the last element in R p and R1) which links the twoequations together.An incremental form of the total equilibrium equations from time t to time t + At is usedto solve the dynamic problem employing the well known Newmark I3 method with varyingtime steps (if necessary) and constant average acceleration. At each point of time a veryefficient equilibrium iteration procedure is used to ensure equilibrium of the nonlinear impactforce. A skyline representation of all matrices is also employed to speed up the solutionprocedure.6. NUMERICAL EXAMPLESTwo examples are presented to demonstrate the capabilities of the present numericalmodel included in the ISIS program. The two examples describe iceberg-platform interactionat water depths 100 m and 250 m, see Figures 3 and 7, respectively. North Sea type gravity-(width)20 m^-I25 m- -I15 m3Soil:35 m-^I50m iTtrans '7'rot(The iceberg shape is squarein the horizontal plane)x-dir+ 98.2m1Figure 3 100 m water depth, iceberg-caisson interaction531

ased structures were assumed in the analysis to provide examples of the ISIS computations.In both examples, the deck is modelled as being completely rigid.The 100 m water depth example is studied for 4 iceberg masses (500, 1000, 2000 and4000 Mkg) with a velocity of 0.3 d s hitting the caisson at an interaction depth of 75 m. Bothimpact in the x-direction (interaction with one cylinder) and in the y-direction (interactionwith 4 cylinders simultaneously) are considered. The 500 Mkg iceberg is floating in a stableconfiguration with a keel depth of 82 m which gives the interaction point at 66 m water depthfor this iceberg.Figures 4 and 5 show the relative results of the ISIS time simulation for the icebergplatforminteraction force and the base shear force, respectively. As seen, the forces are quitesimilar, but for the 1000 Mkg iceberg in the y-direction the maximum soil force is about 45percent higher than the y-direction interaction force due to local oscillation of the caisson.Impact in y-direction will give maximum impact forces about 3 times higher than impact inx-direction for this case because of the larger contact area.DEPTH 100 METERSCAISSON IMPACT1 v-dir.ST-DEPTH 100 METERSCAISSON IMPACTE 000 1000 2000V4000 Mkg7x-dir.4000 Mk0 2 4 6 6 1 0 1 2TIME SFigure 4 Iceberg-platform interactionforce (relative to max x-dir. forcefor the 1000 Mkg iceberg)0 2 4 6 8 1 0TIME SFigure 5 Base shear force (relative to maxx-dir. interaction force value forthe 1000 Mkg iceberg)DEPTH 100 METERSCAISSON IMPACT0 2 4 6 0 1 0 1 2TIME SFigure 6 Kinetic (K) and crushing (C) energy for x-dir. impact(relative to initial kinetic energy for the 1000 Mkg iceberg)532

The relative magnitude of the forces is highly dependent on the assumed input forpressure-area curve, soil and structure stiffness and structure geometry. As a consequence ofthe Sanderson's pressure vs. area curve, the maximum impact force is relatively insensitivewith respect to the iceberg mass in this example.Figure 6 shows both the kinetic energy and the crushing energy (relative values) of theiceberg during the impact. As the volume of the iceberg increases from 500 to 2000 Mkg theiceberg crushing energy after the impact increases from about 50 per cent to about 85 per centof the initial kinetic energy of the iceberg. This is caused by the location of the center ofgravity of the iceberg relative to the interaction point and the rotational inertia of the iceberg.Thus, with the iceberg geometries used in the 100 m water depth example the kinetic energy(iceberg rotation) after the eccentric impact will be relatively higher for the 500 Mkg icebergthan for the 4000 Mkg iceberg.Figure 7250 rn water depth, iceberg-column interactionIn the 250 m depth example three different initial iceberg interaction heights (10 m, 30 mand 50 m) are considered and the iceberg hits one column at a depth of 50 m. The slope ofthe interaction angles, see Figure 2, is 45 degrees. Figure 8 shows the interaction force andthe base shear force (relative values). Again, the maximum soil force is somewhat higher (upto 30 per cent) than the corresponding interaction force. Figure 9 depicts the nonlinear interactionforce versus the ice indentation according to the present ice crushing model (relativevalues). As seen, the interaction force increases very rapidly at the start of the impact. Thekinetic and crushing energy (relative values) during the impact are given in Figure 10. Asmight be expected the results for the three cases in Figure 10 are quite similar. The smallincrease in the kinetic energy at the end of the impact is caused by an increasing icebergvelocity in the reversed direction.533

DEPTH 250 METERSCOLUMN IMPACT7DEPTH 250 METERSCOLUMN IMPACT- 550m 30m10m0 5 10 15 20TIME SFigure 8 Interaction and base force(relative to rnax interaction forcefor the 10 m height case)- 5 10 2 4 6 0 1 0ICE INDENTATION N ICE (RELATIVE1Figure 9 Interaction force versus iceindentation (relative to maxvalues for the 10 m height case)-1 00+>a -6DEPTH 250 METERSCOLUMN IMPACT4>mY 205 10 15TIME SFigure 10 Kinetic (K) and crushing (C) energy(relative to initial kinetic energy)DEPTH 250 METERS6, COLUMN IMPACTBending0 5 10 15 20TIME SFigure 11 Shell stresses at interaction point for the 10 m height case(SXTOTAL = SX + SM + SSTATIC) (relative to rnax value of STO)

Shell axial stresses (relative values) at the outer and inner surface of the interaction pointfor the 10 m interaction height case are given in Figure 11. With the present column diameterand thickness, a relatively high compression stress (hydrostatic stress included) in the circumferentialdirection occurs. In the longitudinal direction, the total stress is composed of abending moment dynamic stress and a static stress in addition to the shell theory basedlongitudinal stress. Figure 12 shows the relative maximum stress values as a function of theinteraction height. The maximum stresses are less sensitive to the interaction height variationthan the maximum interaction force.Finally, the relative deck displacement in the ice velocity direction is shown in Figure 13.In the present example the amplitude of the local platform oscillation is less than 10 per centof the total displacement.6,DEPTH 250 METERSCOLUMN IMPACT1DEPTH 250 METERSo, COLUMN IMPACT- a-1 0ST00 10 20 30 40 50INTERACTION HEIGHT MFigure 12 Maximum shell stresses(relative to the max. STO-valuefor the 10 m height case)50 5 10 15TIME SFigure 13 Deck displacement in icebergvelocity direction(relative to the max value for the10 m height case)7. CONCLUSIONSThe present iceberg-structure interaction model simulates iceberg collision with a concretegravity platform. By considering the response of both the iceberg and the platform simultaneouslyin the time domain, dynamic forces and moments in the platform are determined. Thepresent ice force model is simple with its clear shortcomings (uniform and radial static icepressure and fixed location of interaction force). In addition, many of the more complexhydrodynamic effects are omitted. However, despite the simplicity of the model, it should bewell suited for evaluating iceberg-platform interaction consequences as better input informationbecomes available.

8. REFERENCESBass, D., Gaskill, H. and Riggs, N. (1985). Analysis of iceberg impactswith gravity base structures at Hibemia, 4th. Int. Offshore Mech. and Arctic Engn.Conference (OMAE'85), Dallas, Vol. 2,255-259.Brown, T.G., Kocaman, A,, Punj, V. and Bercha, F.G. (1986). Iceberg-structure interactionglobal and local loads, 5th Inst. Offshore Mech. and Arctic Engn. Conference(OMAE186), Tokyo, Vol. 4,555-560.Cheang, L.C. and Lam, I.P. (1987). Design of gravity structures under iceberg loading, 6thInt. Offshore Mech. and Engn. Conference (OMAE'87), Houston, Vol. 4,55-62.Croasdale, K.R. (1988). Ice force: Current practices. 7th Int. OffshoreMech. and Engn. Conference (OMAE'88), Houston, Vol. 4, 133- 15 1.Holmas, T. (1987). Implementation of tubular joint flexibility in global frame analysis.Report no. 87-1, Division of Structural Engineering, NTH, Trondheim, Norway.Johnson, R.C. and Nevel, D.E. (1985). Ice impact structural design loads, 8th Int. Conf. onPort and Ocean Engineering under Arctic Conditions (POAC'85), Vol. 2.Loset, S. and Wold, M. (1989). ESARC-An arctic research program for the Barents Sea,10th Int. Conf. on Port and Ocean Engineering under Arctic Conditions (POAC '89),Lulea, Sweden (in press).Nevel, D.E. (1987). Iceberg impact forces, 3rd state-of-the-art report, special report 87-17(edited by T.J.O. Sanderson), U.S. army cold regions research and engineeringlaboratory, New Hampshire.Sanderson, T.J.O. (1986). A pressure area curve for ice, IAHR Symposium on Ice,IOWA City, Iowa.Setchfiled, T.L. (1986). Esso-SINTEF Norwegian Arctic Research Program,POLAR TECH '86, Helsinki, Finland.Vugts, J.K. (1968). The hydrodynamic coefficients for swaying, heaving and rollingcylinders in a free surface, Int. Shipbuilding Progr., Vol. 15,251-276.

THE PRIMARY STUDY OF ICEFORCE ON THE STRUCTURE IN BOHAI SEAli Xiao-huiEngineerShen WuProfessorChina Northeast BuildingDesign InstituteDalian Institute ofTechnologyABSTRACTIn the winters of 83/84/85/86/87, in order to investigate the mechanicaland physical properties of ice in Liaodong Gulf of Bohai Sea,a series experiments were carried out. Results considered the anisotropyof ice, and calculation of ice forces on an isolated pile and amulti-pile structure in creep mode, using a finite element method.A new Bound Theorem in structural limit analysis was introduced andvariable solution to the isolated pile problem was given. Upon comparisonbetween experimental data and calculation results were agreewithin twenty percent.1. IntroductionThe accumulated evidence of ice damage to the offshore structuresis substantial in high latitudes areas. There are accidents from abroadthat icebergs or ice floes damaged offshore structures and drillingplatforms. The similar cases occured in Bohai Sea. Recently therewas an incident in Liaohe Petroleum Field in Liaoning Province wherea gas pipe was broken by a moving sheet of floating ice, which causeda fire. These events showed clearly that it is imperative to conductresearch on the ice forces on offshore structures.CllThe forces acting on fixed structures were classified into 4 types ,(1) Static pressure from expanding or contracting ice sheets. Thistype of movement, caused by air temperature changes, induces importantinternal stresses in the ice external reactions to the structures.(2) Impact of moving ice sheets, pressure ridges and ice islands.This movement may be caused by wind and, or, water currents. They areparticularly important for large ice masses of cold ice in slow movement.One of the most severe conditions is slowly moving large continuousice masses.(3) Pressure due to unconsoIidated ice accumulation. When the sizesof floes are small, the floes will accumulate together under the influenceof wind and currents.(4) Vertical force exerted by ice. The main cause is the movementof an ice sheet adhering to a structure, due to a variation in waterlevel. Vertical forces may also caused by the weight of ice collarsadhering to the structures.Only the second type of ice forces is studied in this paper.In the winters of 83/84/85/86/87, to investigate the physical andmechanical properties of ice in Bayu Harbour, Liaohe River Mouth, Huludao,Juhua Island in Liaodong Gulf of Bohai Sea, a series of experimentswere carried out in the Laboratory of Strength of Materials inDalian Institute of technology (DID. Making use of the results of the--------Project supported by the Science Fund of the Chinese Academy of Sciences.

experiments, which considered the anisotropy of ice, a finite elementmethod was used to calculate the impact of drifting ice in thecreep mode, deriving the ice force on an isolated pile and on a multipilestructure. Meanwhile, a new Bound Theorem in structural limitanalysis was introduced and a variational solution to the problem ofice movement towards an isolated pile was given. Comparison of resultswith the formula recommended by ~aeki'gave agreement within twentypercent.2. Material IdeaizationThere are many paperscwhich study the effect on elastic modulus,compressive strength and fracture toughness caused by the existance ofbrine volumes and air bubbles. Treating ice as a kind of defect medium,by means of Weibull's statistical theory, W. ~hen~~bt.al inves -tigated scale effects in sea ice. For simplicity and convenience, seaice was thought of as a homogeneous, continuous and incompressive solidmaterial.The anisotropy of ice arise because of the coiumnar-grained natureof its crystals. The sea ice of Bohai Sea which has been studied isthe S, type" First, it is transversely elasticlly isotropic, that is,istropy in the x-y plane, orthotropy in the x-z plane(Fig.1). Second, sea ice is yield-anisotropic. Its yeild function f iswherea's are constants which can be determined by six confined compressiontests at constant strain-rate c 6 'In the strict sense, the elastic modulus of all materials is differentin tension and compression. The affection of bimodulus is quitelarge?^Because compression is dominant in this paper , all elastic moduliwers regarded as compressive, in spite of the stress state.The viscoelastic natures of ice make the contitutive relations COBplex. For ice, Norton's Law is basically applicable.3. Part of Theory3.1 Basic Constitutive RelationsA typical uniaxial creep-time curve of ice is shown in Fig.2. thesecond part and most of third part satisfy Norton's Law,E, a a( c/~-a.Ã u (3-1-1)where e. is creep strain-rate, a. is unit stress, a,N is constant, uis uniaxial stress.Total strain e iswhere Em is effective elastic modulus.The second ten u/EÃ of Eqn(3-1-2) is much smatter than first one,can be neglected.

For multi-axial condition, defined anisotropic effective stress andstrain are~=3/2/i&+a.t) J- ( 3-1-3)a- depends on a, --a''4with multi-axial Norton'se. = 4(cs /y. 1"assuming thatto== "^ /d-nLawconsidering Eqn.(3-1-11 and (3-1-5)¥fl-igthat is,1 = 3 ~ / 2(a1+at))È~''-( /G''3.2 Finite Element MethodFrom virtual work priciple, the fundamental equations of finite methodare (initial strain method)where (Q is initial strain vector.In creep problem, the creep strain (t} was treated as initial strain(0.4. Part of Calcution4.1 Iteritive AlgorithmThe initial strain finite element method is used in the catcutat'on.The method was proposed first by Medeloson, Hirschberg and Mensonmindproceeded in a stepwise fashion as follows.Step 1. At time t=0 determine the elastic solution of the problemby setting {£,)=(?)= in Eqn(3-2-1). This gives the nodal displacementsand stresses at the start of processing.Step 2. assume that stresses obtained in step 1 remain constant overa small increment of time A t and calculate the increments of creepstrain that occurs in the increment of time by using Eqn.(3-1-9),Step 3. Use the creep strain increments obtained in step 2 to determinethe new creep strains and the end of the time increment by means

Then determine the stresses at the end of time increment by sustitutingthe creep strains into Eqn(3-2-1) and solving them.Step 4. Test the stresses against their existing values at the beginningof the time increment. If they are large than a preset fractionof existing stresses, repeat step 2 step 3 with a smaller time increment.If the stresses are less than or equal to the preset fractionof the existing stresses, goto step 5.Step 5. Add another time of increment and repeat steps 2, 3, 4. Continuein this manner until a stationary state has been achieved.4.2 The Selection of Time Increment c'elBecause the running time of computer is proportional to the numbersof time increments, the selection of a proper length of time is important.In order to get similar precision in every increment oftime, the varying length of time increment is selected,wheret is a time increment ratio, and satisfiesTo avoid the oscillation of solution, generally, the change of everytime increment is equal to less than half the former one,atm 5 l-wth (4-2 -3)The increment of time should satisfy Eqn(4-2-1) and (4-2-3) at thesame time.4.3 Calculation Examplesa) Isolated pile caseClllAccording to the experimental data, Saeki recommended the estimatedformula of ice pressure on isolated pile,where K' is a scale effect factor (Shown in Fig.. 3), C--shape factor(5.0 for circular pile, 6.8 for rectangular pile), W-- width of pile,h--thickness of ice sheet,~compressive strength of sea ice.For sea ice of Liaodong Gulf the peak of compressive strength occorsat i =4. 0x10"' sec"' (Fig. 4)!1a1A sketch of Bohai Sea and Liaodong Gulf is shown in Fig.5. All theconstants such as a,N,E and determined in experiments are, a=l.85*10 ,N=3.01, E =3.5GPa,JU =0.3As regards the constants a's is referred to.For different strain-rates, the comparison between results by Saekitsformula and finite element method is shown in Fig.?. The comparisonof the case V/4D=8.0*10~ sec"' for different diameters is shownin Fig.8. The mesh is shown in Fig.6.b) Multi-pile structureThe representative case of a multi-pile structure is a two-pile one. If the distance of two piles is over five times the diameter of the pile, the ice force is the same as that of Eqn(4-3-1) (C=6.8, W=ZDtdistance of two piles). If the distance is less than 5D, the compa-

ison is shown in Fig.95.A Variational SolutionLO]Qian Lingxi and Zhong Wanxie induced a Bound Theorem, summed theextreme load of structure up to get a stationary solution,~=f~(a;^i~.a~T/(

[4] V. Shen et.al.,The Experimental Investigations of Scale Effectof Bohai Sea Ice,Proceedings of The Sixth (1987) Internationaloffshore Mechanics and Arctic Engineering (OMAE) Symposium, vol.IV, ppp. 173--179.[5] S.L. Bai, Master Thesis, 1986, DIT.[6] S. S. Sunder, J. Ganguly and S.K. Ting, Anisotropy Sea Ice Indentationin the Creeping Mode, Pro. OMAE Sym.,VolIV.[I] 1. Wu, The structural Elements Model for t he Strength of Solids, Acta Mechanica Solida Sinica, 1983, No.4[a] W. Shen, Z. H. Zhang and Ji X., The Study of K and K forUsing a Compact Compression Test Specimen, at Hulu Is land, BohaiChina, ASCE EMD Specialty Conference, Buffalo, USA, 1987.[9] H. Karus, Creep Analysis, A Wiley-Intersci ence Publication,[lo] Li Yue, Eiastic~viscoplastic Model and it s Application, HZ86-02.[11] 1. Saeki et. al., Total Ice Forces on the Clusters of CylindricalPiles, Proc.5 OMAE Sym., VolIV .[12] V., Shen, et.al., The Strain-rate Sensitivity of Strength ofBohai Bay One-Year Ice Under Uniaxial Compression, Jour. of DIT,Vol. 23.[ 131 1. H. Tsien (L.X.Qian), V. S. Tsoon(V.X. Zhong), The LimitAnalysis in Solid Mechanics and Suggested Generialized VariationalPrinciple, Acta Mechanica Sinica, Vol.6.

t. Time C Dlmsnelonlees IFlg.2A Typical Creep-time curve

F1g.4 Unlaxlal Compressive Tee-t1 . 5 Sketch of Bohol See

Saekl'a Formula+ ~ ~ u l tof e finiteElement Method0-100mFig.6Mesh of Finite Element-- --Fig.7Comparison between Results6.8l la-Fig.8 Comparison for Different DiameterI I I I- 7 -6 -3 loa?Flg.9 Comparison for two-Pile Case (the distance oftwo-pi 1e=o

CALCULATION OF ICEBERG IMPACT FORCESRoy C. JohnsonAnton ProdanovicMobil Research and Development Corp.Offshore EngineeringP.0. Box 819047Dallas, Texas 75381-9047USAABSTRACTDevelopment of petroleum resources located on the Grand Banksmeans that icebergs must be considered. Platforms must either becapable of withstanding iceberg impact forces or withdrawing fromthe path of the drifting iceberg. For a large, permanent productionplatform like the one proposed for Hibernia, icebergimpacts are to be resisted.For the structural designer, the starting point is specificationof the design loads to be resisted by a given structure. Severaldeterministic algorithms that were considered during thisinvestigation are outlined and reviewed. One of these approacheswas selected to form the core of a stochastic computer programfor iceberg impact loads. This paper summarizes the procedureundertaken to select the deterministic iceberg impact loadalgorithm and the reasons for the selection that was made.Examples are given to illustrate the differences among thevarious methods. The platform used in the examples is thatproposed for production of the Hibernia field located off theCanadian east coast.INTRODUCTIONFor a large, fixed production platform like the Hibernia GBS,loads imposed by colliding icebergs dominate feasibility. Bothglobal and local effects must be considered. During an event,such as an iceberg colliding with a GBS, the maximum ice loadagainst the platform is the global load. This load must notcause the platform to overturn or slide along the sea floor.Thus, global loads govern platform stability. Global loads arelimited by some physical condition or process as discussed byCroasdale and Marcellus [I]. Local effects of the same impactare used to design individual elements, such as ice wall thickness,within the platform. The main emphasis in the presentpaper is a comparison of possible methods to compute the globaliceberg load resulting from an iceberg-GBS interaction.

BACKGROUNDPrior to initiating the activities leading to development ofthe various approximations for iceberg impact loads on a GBS,several guidelines need to be developed. It is important thatthese guidelines are understood for they form the "keel w uponwhich the various methods are built. These are:1. the model should build upon past experience (ifpossible) ;2. the model should be simple;3. the model should use as much actual iceberg data aspossible; and4. where actual data is unavailable, the model should bebased on an assumption that is conservative.A considerable amount of iceberg data existed when the mathmodels were investigated. For example, Mobil and its Hiberniapartners had funded several proprietary data gathering fieldprojects including iceberg size, shape (both above and belowthe water surface), drift speed, flux and strength.Additionally, other data bases, such as the U.S. Coast GuardInternational Ice Patrol Bulletins, were also available.Stochastic approaches for determining structural loads producedby icebergs impacting a platform have been the subject ofseveral investigations. At the core of all such probabilisticapproaches is the deterministic algorithm used to predict theresulting load for any specific interaction. It is thesedeterministic math models that will be investigated in thispaper.MATH MODELSFour iceberg load computation methods are presented anddiscussed as deterministic algorithms for computing theresulting impact force for a single iceberg colliding with theplatform. The following description of these methods islimited to describing the fundamental approach and underlyingassumptions for each math model. Additional details may befound in the appendices.Method I. Purely Centric Impact. The scenario in which adrifting iceberg has a velocity vector that is always directedtowards the geometric centroidal axis of the GBS is depicted inFigure 1 with 9 =O. The simplest of all possible math models[2] for icebergloading is also the most conservative (that ofa radial collision with no eccentricities). The method appliedfor this case is based on the concept of limited momentum, orlimited kinetic energy.Key assumptions are:1. the GBS is both rigid and immovable, and2. the iceberg kinetic energy just prior to impact isabsorbed by crushing ice during the impact.

Method 11. Quasicentric Imwact Using Limited Momentum. Inorder to reduce the inherent conservatism associated withassuming that all icebergs collide with the GBS with noeccentricity and that all the iceberg kinetic energy isabsorbed by crushing ice, the above approach is modified toinclude iceberg eccentricity. In addition to the firstassumption for Method I above, other key ones added are:1. the iceberg rotates about the point of initial contactwith the GBS,2. small displacement theory applies, and3. work done crushing ice during the impact plus rotationalenergy remaining with the iceberg after the event isequal to the initial translational kinetic energy.Method 111. Quasicentric Impact Awwroximated as CentricImwact. This method is quite similar to that above except allimpacts are approximated as centric impacts with equivalentmasses. The first assumptions of both previous methods areaugmented by:1. the impact force is in the direction of the velocityat the point of contact, e.g., constant direction.Method IV. Stew-by-Stew Integration of Equations of Motion.This algorithm is the most general one considered during thisstudy. By removing restraints on the iceberg motion in thehorizontal plane and treating the iceberg as an axisymmetricbody, both iceberg and structure eccentricities are includedin the formulation. Key assumptions, in addition to that ofthe rigid, immovable GBS, include:1. the total force consists of a normal component(crushing) and a tangential component (shearing);2. the normal force is equal to the contact area timesthe pressure which is a function of the contact area;3. the tangential force opposes motion between the twobodies and is based on a local shearing pressureproportional to the normal pressure.EXAMPLE PROBLEMUsing the load computation procedures presented, global icebergimpact loads are computed for a specific iceberg colliding witha smooth, cylindrical GBS configuration of similar size tothose proposed for use at Hibernia. It has a nominal diameterof 100m and loads are computed for various degrees of impacteccentricity as shown in Figure 1. Iceberg parameters are:mass = 900,000 tonnesspeed = 1.39mpsiceberg shape (L = 0, a = 73O, p = 45O)r /r = 0.59ize crushing pressure = p = 6MPahydrodynamic interaction coefficient = ch = 0.5.

Results of the numerical computations are presented in Figure2. Several significant effects of the various algorithms areevident. The most obvious is that Method I produces an upperbound,albeit not mathematically rigorous, on the globalimpact load. It is easily concluded that use of Method Iwould result in an overly conservative estimate of the load.Methods I1 and I11 produce quite similar results. For purelycentric impacts, results are the same as for Method I. Sinceonly iceberg eccentricity is included in the formulations andsince the force on the GBS is a radial force, the load doesnot go to zero at full eccentricity. Between the two extremeeccentricities, loads are higher for Method I1 than for Method111. The reason is that in Method I1 the equations of motionare used only to develop an expression for energy remainingwith the iceberg in rotation. This energy is, in effect,subtracted from the total energy and the remaining energy isabsorbed by crushing ice and the math model is stillessentially a one degree of freedom model. Method 111, on theother hand, allows two degrees of freedom and is lessrestrictive than Method I1 at all eccentricities except at theextremes.Method IV was developed to eliminate the obvious conservatismassociated with large eccentricity in either of Methods I1 or111. Whereas the previous algorithms use a single stepintegration from contact to maximum load, Method IV solves thegoverning equations of motion at specific time intervals frominitial contact through the entire event until either theiceberg is stopped or loses contact with the structure.Results from this method are more theoretically pleasing thanthose associated with previously discussed methods. Tofacilitate as direct a comparison of the various methods aspossible, no tangential force was considered in the exampleproblem using Method IV. The effect of including a tangentialforce is generally to decrease the time of contact between thetwo bodies by increasing the rotation of the iceberg (icebergrolls off GBS more rapidly).SELECTION OF ONE METHODThe goal of the engineer is to design and construct for bothsafety and economy. He must consider both of these goals.For iceberg impact load specification, a stochastic approachis recommended so that a return period, or some otherprobabilistic basis, for the design load can be specified.Keeping in mind the criteria for a desirable math model listedin the Introduction, selection of one of the four candidatemethods is not difficult. There is no existing data baseavailable documenting icebergs colliding with large fixedstructures. Therefore, the three criteria are that the methodshould be simple, based on as much actual data as possible,and where assumptions need to be made they should beconservative.

Method I is about as simple as possible, but its use iseliminated because it is overly conservative and will not leadto a cost effective design. Method IV is the most rational ofthe remaining three. Its use is eliminated from considerationat the present because of the unknown global shearing strengthof iceberg ice. The crushing strength is based on relativelylarge scale field tests 131. A separate sensitivity study wasperformed using various assumptions to compute tangentialforces. Study conclusions were that until physical testingcan be done to substantiate one of the tangential forcemodels, the degree of conservatism, or lack of it, is unknown.Method I11 is selected over the remaining candidate becausethere are fewer assumptions made, it is internally consistentand less restrictive that Method 11. The facts that MethodI11 is easily programmed and, as the basic component of astochastic algorithm, is computationally fast are additionalbenefits.CONCLUSIONSeveral deterministic methods for computing global icebergimpact load on a fixed platform have been reviewed anddiscussed. Differences in computed loads are highlighted byexample. A set of guidelines are presented to aid in theselection of a particular approach for use at any particulartime. Discussion of the relative merits of each approach isused to select one method for use today to establish designcriteria. Subsequently, based on availability of futureexperimental data, a different method may be selected.REFERENCESCroasdale, K.R. and Marcellus, R.W., "Ice Forces on LargeMarine Structuresnt proceedings, IAHR InternationalSymposium on Ice, Quebec City, Vol. 2, pp 755-765, 1981.Johnson, R.C. and Nevel, D.E., "Ice Impact StructuralDesign Loads," Proceedings, POAC 85, Volume 2, pp569-578, Narssarssuaq, Greenland, September, 1985.Johnson, R.C. and Benoit, J.R., "Iceberg ImpactStrength," Proceedings, 19th OTC, OTC 5599, ~ol. 4, pp417-423, April, 1987.Nevel, D.E., "Iceberg Impact Forces," Proceedings, IAHRIce Symposium 1986, Iowa City, Iowa, 1986.

APPENDIX ADEVELOPMENT OF QUASI-STATIC MATH MODELSMethod I, Purely Centric ImpactLimited momentum, or kinetic energy, forms the basis for thismodel. The platform is assumed to be both rigid and immovable.The iceberg is assumed to have only a linear drift velocity.It is also assumed that the iceberg mass (including addedmass) and the shape of the iceberg at the point of interactionwith the platform are known.The method assumes that theiceberg motion is completely stopped by the platform andequates the change in kinetic energy, from its initial valueto zero, to the work done "crushing n ice. Mathematically,2 Y1/2 (1 + ch) MV = / p A dy = p Vol (Al)0where ch is a hydrodynamic interaction coefficient, M is theiceberg mass, V is the iceberg velocity immediately prior toimpact, p is the ice "crushing w pressure, A is the contactarea, y is the penetration distance that the platform indentsthe iceberg, and Vol is the volume of crushed ice.The vacrushinqta strength, p, is not a laboratory determinedquantity from confined or unconfined tests. "Crushing" coversmany factors that can occur during indentation in the field.These are splitting, spalling, pulverizing and subsequentclearing of the crushed ice. To develop a value for p to beused in design, a set of field indentation tests wereperformed [3] on a grounded iceberg in the Canadian arctic.For the areas of interest, p is assumed to be a constant.Therefore, the right hand side of Equation A1 is reduced to ptimes Vol.Making use of the local geometry of the impact area andEquation Al, the maximum, penetration and of the structureinto the iceberg and the corresponding contact area aredetermined. The predicted load isMethod 11, Quasieccentric Impact using Limited Momentum.This algorithm is a simple extension of the first method. Theextension recognizes that typically icebergs will collide witha GBS with some horizontal eccentricity.Consider the interaction of the iceberg shown in Figure A1with a fixed, rigid structure. Let the initial eccentricityof the iceberg, yo, be as shown in the figure. The equationsof motion are- ( l+ch) Max = Fx (A3(l+ch)Ma = FY Y(A4(l+cr)Ia = Fx yo - Fy xo, (A51

where I is the polar moment of inertia about the center ofgravity of the iceberg and c is the associated hydrodynamicinteraction coefficient . substitution of Equations A3 and A4into A5 yieldsThe initial conditions are v = V, v = 0 and 0 = 0. Assumingthat x and y are constant ?or smalx rotation, integration of~quati8n A6When the iceberg contacts the platform, it is assumed that theiceberg rotates through a small angle, $, about the contactpoint and that no slippage between the two bodies occurs andtheref oreVX = " Yo(A8)Substituting Equations A8 and A9 into A7 and rearrangingproduceswhereThe kinetic energy of the iceberg is2 2r 2 = xo + yo . (A121Substitution of Equations A8, A9 and All into the expressionfor the iceberg kinetic energy, A13, produceswhere r = (l+c) I/(l+ch)M.gEquating kinetic energy prior to impact with that remainingwith the iceberg, in rotation, plus the work done by"crushing w ice against the platform producesThis equation is solved for the volume of crushed ice. Basedon the interaction geometry, the penetration of the platforminto the iceberg and contact area between the iceberg andplatform are obtained. Iceberg load is then determined fromEquation A2.

APPENDIX BDEVELOPMENT OF MATH MODEL FOR METHOD IVIn this method the impact is simulated by a step-by-stepintegration of the governing equations of motion of theiceberg (Equations A16 - A18 with the right hand side of A17equal to F ). Newmark's beta method was used to perform theintegratioiy.During the impact simulation, forces, iceberg motion(location, velocity and acceleration) and energy losses arecomputed.The iceberg was modeled with three degrees of freedom wherethe iceberg was permitted to rotate about an axisperpendicular to the water surface and translate in a planeparallel to the water surface.ASSUMPTIONSTwo additional assumptions have been made during developmentof the analytical approach for modeling the dynamicinteraction of an iceberg colliding with a GBS. These are* Iceberg is axisymmetric and consists of a centraldisk sandwiched between two truncated cones (seeFigure Bl) , and* The total force on the structure can be computedbased on the contact area, an average pressureacting over the contact area and a constant crushingor shearing coefficient of friction between the icemass and structure.ICEBERG GEOMETRYThe iceberg geometry has been idealized as a central disksandwiched between two truncated wedges as shown in Figure Bl.The resulting shape is axisymmetric. The berg is specified bya mass (m) and the geometric parameters L, a and B.The radius of the central disk is determined from thefollowing equation which was derived from iceberg data.where R = central disk radius (meters), andm = iceberg mass (tonnes).CONTACT AREAFor computational purposes the iceberg shape depicted inFigure Bl is subdivided into a number of disks of constantradii. The contact area is developed for a single disk andthen computationally each disk is treated separately and thetotal area determined by summing all the single disk contactareas.

Contact Area Determination. Consider a single disk of radiusR and thickness t interacting with a rigid cylinder. The ice(disk) is assumed to behave as a rigid plastic material. Theinitial geometry is shown in Figure Bla with the coordinatesystem origin being at the structure's center and the centerof the ice disk being located on the negative x axis such thatthe ice disk just touches the structure. The interaction isspecified globally by assigning an initial velocity to the icewith 0 < 9 < 90".At some time during the interaction, the ice has CGcoordinates x , y as shown in either Figures B2b or B2c, andvelocity vt. ~t hme t, determine the coordinates of points A& B, shown in Figure B2, by simultaneously solving EquationsB2 and B3.2(x-x) + (y-yt)2 = R~2x+ y2=Rs 2Having found the coordinates of points A and B, we next solvefor the coordinates of those points on the extremity of thestructure to which the current velocity vector direction istangent. These points are called C and D. For each disk thecontact area is found by multiplying the central angle, r.,subtended by the two innermost points (determined fromA, B, C, D) by the product of the structural radius and diskthickness.FORCES ON STRUCTURESSince this is a dynamics problem and since the iceberg is thebody of mathematical interest, the forces computed areactually forces acting on the iceberg. Structure forces aresimply equal, and opposite, to those forces being calculated.The computed force lies in the x-y plane and is calculated asthe vector sum of two components: (1) the normal componentthat acts in the same direction as the straight line joiningthe centers of the structure and iceberg; and (2) thetangential component which acts along the interface betweenthe structure and iceberg in a direction that opposes therelative motion between the two bodies. These forces arecomputed as the product of a pressure and area.Normal Pressure. Since the contact area, at any time, iscomputed prior to any force computations, a pressure-arearelationship can be used to prescribe an effective, nominalice pressure, p. This procedure recognizes, and allows for,incorporation of the so-called scale effect. Anypressure-area relationship can be used.Shearinq Pressure. There is no test data available on icebergice to indicate what the shearing pressure should be as iceslides along the surface of a structure and is extruded at theedges of the ice-structure contact. Furthermore, thestructure's surface roughness would also affect the value. Itis, however, recognized that such a pressure, shearing stress,

must exist. In the present work this shearing pressure hasbeen assumed to be directly proportional to the normalpressure and is given bywhere T = shearing pressure,1 = coefficient of proportionality (includingcrushing coefficient of friction and surfaceroughness effects).DIRECTION OF ICEBERG MOTION(a1 GBS(bl IMPACT PLAN VIEWFIGURE 1. GBS AT IMPACT1500METHOD I0 15 30 45 60 75 90ECCENTRICIlY, eB (DEGREES)FIGURE 2. COMPARISON OF METHODS

,ICEBERG MOTION AT IMPENDING IMPACTFIGURE A1. GEOMETRY FOR METHODS II AND Ill@ (-j-#>3IL A SECTION A-AFIGURE B1. GEOMETRY FOR METHOD IV:a1 INITIAL GEOMETRY lbl INTERACTION GEOMETRY 1cI ALTERNATE INTERACTION GEOMETRYFIGURE B2. CONTACT AREA AND ICEBERG VELOCITY

Movses J. KaldjianProfessorThe University of MichiganNaval Arch. & Marine Eng.Ann Arbor, MI 48109-2145U.S.A.ABSTRACTExperimentallyobtained data on ice-sheet/structureinteractions loads are few in number and costly to obtain. Toextend this data bank, mathematical models are prepared andanalyzed numerically.The study covers parameters to analyzevarious waterline displacement boundaries, the effects of sharpforward ridges, artificially induced cracks, etc.The floating ice-sheet is studied as a large, rectangular,continuous plate supported by springs (equivalent buoyancy).The plate is held at the far edge and waterline displacementboundary condition applied at the middle of the near edge.The models are analyzed using finite element techniques. Non-linear property and geometry effects are also considered.Preliminary work results indicate that the stress anddisplacement patterns improve with modified waterline geometrywhich produces lower breaking forces to develop in ice,especially when it is coupled with radial precuts at strategiclocations.1. INTRODUCTION AND BACKGROUNDEvery year many new offshore structures are being planned andconstructed. Some of these are slated for cold regions, likethe Beaufort Sea, where the menacing presence of floating icewill pose a seasonal hazard to them and to ships [I] that play avital role in their operation and maintenance.

A number of investigators [5,6] have studied analytically theproblem of ice forces on inclined structures.Frederking and Timco [2] using experimental small scalemodels, discovered that analytical results consistently underpredict ice/structure interaction forces. They also report thatin ice/structure interaction the maximum breaking load wasassociated with the formation of radial cracks in the ice-sheetin front of the inclined plane, Fig. l(a).Further experiments with built-in cracks had conclusivelyverified their observation.The presence of built-in radialcracks reduced the maximum breaking load by half as shown inFig. 16. Work at The University of Michigan using finiteelement analysis with and without built-in cracks [31 showedgood agreement with the experimental data obtained by Frederkingand Timco.Thus, through numerical analysis, we can calculate thelocation of maximum flexural stress in the ice-sheet. Firinghigh pressure hot water jets to these spots (or possiblybuilding sharp ridges forward of the structure at these points),or using a mechanical device similar to Ditch Witch machine asdone by Manikian et al.[4], will precipitate formation of radialcracks and thereby reduce the value of the maximum breakingforce that an offshore structure has to withstand.2. PROBLEM DEFINITION AND NUMERICAL APPROACHThis study covers mechanically induced pre-cracks and threeseparate displacement boundaries to accommodate different waterline geometry. Mathematical models of the floating ice-sheet asa large, rectangular, continuous plate supported by springs(equivalent buoyancy) were prepared. The plate was held at thefar edge and a displacement boundary condition appliedstatically at the middle of the near edge.The displacementboundary condition will be that of the contact edge geometry ofthe offshore, or ship structure.The mathematical model was analyzed using the finite elementprogram ADINA.Both linear and non-linear analyses wereperformed. The resulting displacement fields and the stressesin the critical elements are presented graphically in thispaper.

3. FINITE ELEMENT MODELSThe finite element model to perform the analysis of theice/structure interaction is shown in Fig. 2 (b). Experimentalwork of Frederking and Timco [Z] formed the basis of themathematical model. The ice-sheet was 7m wide, 5m long and0.048111 thick as seen in Fig. 2 (a), with an elastic modulus of240,000 kPa and Poisson's ratio of 0.333.Because of symmetry the finite element (FE) model needed to behalf as large. The FE model discretization for ADINA is shownpresented in Fig. 2 (b). The ice-sheet is treated as supportedby elastic foundation. The buoyancy produced by the water islumped at the nodal points using truss (line) elements.The FE model is made of 134 nodal points, 134 truss and 35 8-node shell elements. This study considered three differentphysical situations, namely:Series I.Series 11.Series 13.(Continuous) ice-sheet with no cracks,(Pre-crack 1) a t the centerline of symmetry,(Pre-crack 3) half a meter away from above.Each series was displacement loaded on edge of contact, at threeseparate locations, namely A, B, and C.The value used for the displacement load, which is consideredto be more realistic than edge force loading, was -. 0005m and0.0100m in the y- and z- directions respectively. Thedisplacement points and the pre-crack locations discussed aboveare shown marked in Fig. 2 (a) .4. RESULTS AND OBSERVATIONSThe displacement results for all the three FE series are shownplotted in Figs 3 through 6. These figures show very clearlythat the presence of the pre-cracks substantially alters thedeflection configuration of the ice field. On the other hand,the location of the applied displacement points seemed to effectto a lesser degree the displacement pattern.Fig. 6 shows the deflections of the linear study with that ofthe non-linear (primarily geometric). Larger displacements wereused here to bring out the differences between them. The most

highly stressed elements, eight in all, shown numbered in Fig.2(b), were those in contact with the displacement points and thepre-cracks.Figs. 7 through 10 show the maximum stresses in these elementstabulated graphically for all the three series and thedisplacement points mentioned earlier. The stresses in Figs. 7to 10 correspond to the deflections in Figs. 3 to 6respectively, and are in compression.It is observed that the presence of pre-cracks as seen inElement 7, does increase the stress level, and since the applieddisplacement is always the same, it can be concluded that itw i l l break first. Likewise, the applied displacement locationseems to play an important role and can be very critical as seenin Element 4 of Figs. 7 and 8. This points to the importance ofthe water line contact configuration.The finite element technique is indeed a very useful andpowerful tool to study ice/structure interaction. Full scalemodel with nonlinear material properties of sea ice on anoffshore structure need be studied.Radial precuts using hot water jets, or some other mechanicaldevice, placed at strategic locations look very promising.5. REFERENCESl.Enkvist, Ernst, "On the Ice Resistance Encountered by ShipsOperating in the Continuous Mode of Ice-breaking," TheSwedish Academy of Engineering Sciences in Finland, ReportNo. 24, Helsinki: Keskuskirjapaino Oy, 1972.2 .Frederking, R.M.W., and Timco, G.W., "Quantitative Analysis ofIce-sheet Failure Against an Inclined Plane," Proc. 4thInternational Offshore Mechanics and Arctic EngineeringSymposium, ASME, Dallas, pp. 160-169, 1985.3.Kaldjian, M.J., "Ice-sheet Failure Against Inclined andConical Surfaces," -1 of Cwters & Structm, Vol.26, No. 1/2, June 1987.4 .Manikian, V., and McDonald, G.N., "Method for Weakening theIce Cover in Northern Rivers," Civil Engineering in theArctic Offshoreof the Conference Arctic '85,ASCE San Francisco, CAI March 1985.5.Ralstonf T.D., "Ice Force Design Considerations for ConicalOff-Shore Structures, " P r o c e e u 4th International560

conference on Port and Ocean Engineering under ArcticConditions, St. John's, Newfoundland, pp. 741-752, 1978.6.Sorensenr C., "Interaction Between Floating Ice-sheets andSloping Structures," Institute of Hydrodynamics and HydraulicEngineering, Technical University of Denmark, Series PaperNo. 19, 1978.

BROKENSLABSRADIALCRACKSINCLINEDRADIALCIRCUMFERENTIAL?RE-CUT0.47 m0.50 mSECONDARYIREAKCIRCUMI ERENCRACKDIRECTION OFICE MOVEMENT," -rzoo ,-, 2001-1TIME. s TIME. ISCHEMATIC OF ICE BEHAVIOR11 RADIAL ?RE-CUIS bl CIRCUMFERENTIAL PHI-CUTS(a)Fig. 1. Ice Behavior and Model Test Results for a 45-DegUpward-Breaking Inclined Plane

CE SHEET(.048m thick)canter line of symm.5m(a). Ice Cover and Offshore Structure Test Layout.- = Displacement Point; = Precrack Location5.0m(b). F. E. Model showing Displ. & Precrack Locations.Fig. 2. Ice Cover Test Layout & the Finite Element Model (ADINA).

Applied displ. at point AApplied displ at point AApplied displ. at pant BAppl~ed dlspl at point BAppl~ed dlspl. at point CAppl~ed displ. at po~nt CFig, 3. Deflected Ice F~eld xIO0 (for Dz-.OlOOm & Dy=- 0005m) Fig. 4. Deflected Ice Fleld x100 (for Dz=.OlOOm & Dy=- 0005m)I. Model with no Precrack I1 Model with Precrack 1

Applied displ. at polnt AApplied Displ. at point BApplied displ. at point BAppl~ed dlspl at point CDlspl. at B, nonlinear material & geometryFig. 5 Deflected Ice Field x100 (for Dz=.OlOOm a Dy=-.0005m) Fig. 6. Deflected Ice F~eld x25 (for Dz=.0400m a Dy--.002Om)13. Model with Precrack 3 l3.B Llnear & Nonlinear Model wlth Precrack 3.

1 2 3 4 5 6 7Fig. 7. Stresses Due to Displs. at A, B, and CI. Model with no CracksElement Numbers1 2 3 4 5 6 7 8 Element NumbersFig. 8. Stresses Due to Displs. at A, B, C11. Model with Precrack 1.

1 2 3 4 5 6 7 8ElementNumbnFig. 9. Stresses Due to Displs. at A, B, C13. Model with Precrack 3.1 2 3 4 5 6 7 8ElemOIltN~IllbWSFig. 10. Stresses Due to Displs. at Bl3.B Model, Linear & Nonlinear.

TRANSVERSE STATIC ICE PRESSURE CM BRIDGE PIERSBertil LofquistDr. Sc. (Eng.)Royal Inst. of Tech.,Hydr. Ehgrg.,S-100 44 StockholmSWEDENIn the research of ice pressure on bridge piers mast attention hashem dbxcted to the laqilxdiml dynmic faxes fran f l a w ice.In Sweden no case is known where a pier has been tilted or moved bythe ice in its laqilxdiml dimction. m, there am a few casesof movement in the transverse direction due to action of static forcesfrom extended ice-Sheets. These lateral forces seem to be caused bythermal variations in the ice or by water-level variations. Verylittle is known of the real magnitude of these forces under differentconditions but a few observed incidents may give sun guidance.THERMAL ICE PRESSUREA theoretical approach to the prublein of transverse thermal icepressure on a pier is likely to give very high figures, much higherthan might be passible according to experience. A bridge pier whichis subjected to unilateral pressure - as for example close to an openice-channel ought to get higher pressure per linear meter due to theside-effects than a supposed extended structure as a dan-frcnt tn thesame position. In the appendi-ic a calculation based on elastic conditionsshows that a single pier should get many times higher specificpressure than the fictive dam, especially with great distance A to theshore.The maximum thermal ice pressure on a dam may be in the order of200-300 kN/m. In 14 undamaged bridges In northern Sweden for examplethe design values for transverse pressure on the piers varies from8 to 71 kN/m. It seems to be no consistency in these figures.A number of factors may explain this great difference between theoryand practice, the meet Important be-ice en both sides of the pier,

snow cover, various original cracks and stresses in the ice andbuckling of the ice-sheet. An incident at the Hjulsta-bridge inJanuary 1953 shows that sometimes thermal pressure of importanoe mayoccur (Haggm 1958).^.. If-Ice channel#&Figure 1. Bridge across the Malar-lake at Hjulsta, east ofStockhDImThe bridge has a swing span across the fairway and an ice-channelwas broken. The air temperature rose from -20 to -6'~ in about 12hours. Very little snow covered the ice-sheet, 22 on thick. The southstopping pier was pressed 4-5 an close to the swing span. Some movementcould also be observed on the adjoining piers, which were foundedon wooden piles. The stopping pier was founded on firm bottom. Thei ' q force was calculated to 3CW kN, to 270 kN/m.The ice pressure could have been higher than this value as the contactpressure against the swing span could not be estimated.The seven piers and the long embankment on the south side -ateagainst the expansion of the ice-sheet. The effective distance A inthe appendix is here 600-700 m. Interesting is that the north stoppingpier did not move. The distance A is 200-300 m, thus less than thehalf, all other factors beeing almost the same. The size of the icesheetand its extension along the bridge seems consequently to be onedetermining factor for transverse thermal ice pressure on bridge piers.There are two old references from North America (Barnes, 1928). Inone case a 30 on thick ice-sheet between two piers, 27 m apart, expandedand formed an arch, 0.9 m high. The horizontal pressure fromthe ice was calculated to 320 kN/m. In the otter case a bri- withice on only one side was tilted 5 an and was kept in this positionas a train passed. Ice thickness was 30 an and calculated ice pressure270 kN/m.

The Swedish A t i o n s from 1987 regardiq lateral thermal icepressure (Lofquist, 1987) have the following paraqraph~.Unilateral thermal ice pressure will be greatest on piers closeto an open ice-channel. The transverse ice pressure may beestimated as a force I = i a, uniformly distributed on thelength a meter (a s horizon& length of the piers cross section).The value of i for fresh-water ice vary normally between50 and 300 kN/k. The highest figure may be attained for a pierclose to an open channel already by about 30 cm thick, ice ifthe ice-sheet has a large extension parallell to the bridge.For a pier number of less than 4 m, a = 4 m should be applied.If a high number of il is applied for a pier close to an openchannel, adjoining piers may be computed for i1/3, miniiam ilbeeing 50 kN/m.High ice pressure effects often one side of the pier only, whichmay be considered.In order to counteract extreme ice pressure and movement of piertope along the bridge the fixed and movable bearings can be designedso that several piers co-operate, for instance by means ofstops.ICE PRESSURE BY WATER LEVEL VARIATIONSLarge water-level variations develop cracks in the ice-sheet alongthe share and a tendency of expansion pp-rpend-icular to the share-line.If there is an open channel further out, the ice-sheet will move inthis direction. Otherwise the ice can be pressed up on the shore.Corresponding ice forces alone may be rather limited normally and maycause trouble for smaller objects mostly. Fig. 2 shows how transverseice-loads can be set up between two piers due to rising water-level.Very little is known of the magnitude of these forces under differentconditions. It is rather easy to calculate on various models of trus-ses and arches but more difficult to judge the value of the models inan actual case. An example is given in the following case (Lofquist,1963).Figure 2.Example of possible ice Ipads from water level variations.

Figure 3.Bridge across the Une-river, Lycksele, northern Sweden.In February 1959 the top of the pier no. 6 was pushed by the ice30 cm bringing the nuvable bearing to fall down on the ice and steelgirders to bend down on pier. The middle pier no. 4 had fixed bearingand was unmoved. The piers on both sides of the middle pier had movedtowardstheshores.The bridge is a continuous steel-girder bridge in 8 spans. Pier no.6 consists of a wooden caisson, stone-filled, and on top of this a dryrubble wall.The thickness of the ice was 0.6-1.2 m outside the bridge. In theopenings on both sides of pier 6 the thickness was 1.1 m and close tothe pier 2.4 m. Sane khw be£ the hiht the daily vat-iatim ofthe water-level had been up to 1.0-1.5 m.In fig. 4 a model is proposed with a=3 m, b=14 m, and l:n=l/3. Riseof water-level = 1 m. Disregarding the uplift on the parts a, thehorizontal pressure is H = 14 . 3 . 1/2 = 210 kN/m.The vertical forceis 70 kN/m. Pier no. 6 could resist only about 110 kN/m. It is notknown whether the forces in reality had developed according to themodel in fig. 4 or in sane other way.Figure 4.Proposed model of ice forces.It is interesting to note that the movements has been directed againstthe shore on both sides. The opposite direction is usually to be ex-pected. The explanation might be that an open channel was lacking571

and~t%ice&dbewwon%-onmsih.The Swedish reocninendations from 1987 regarding this type oftransverse ice pressure have two paragraphs:1. Water-level variations leads to broken and thickened ice aroundand between bridge piers. Unilateral horizontal pressure due toarch- or truss-action may be estimated at maximum 200 kN/m.2. This force may act unilateral against piers in one or more spans.COMBINED ACTION OF THERMAL AND WATER LEVEL VARIATIONSThe two types of transverse pressure which has been described seemto have co-operated at the Kusfors railway-bridge.Figure 5. Railway bridge across the Skellefte river at Kusfors,North Sweden.In 1974 it was observed that the top of one middle pier had roved10-15 an in direction from the abutment. In 1977 corresponding pieron the other side had also moved 10-15 an from the abutment. Due tosbrt-tim regulation of the flow in the river the daily variationsof the water-level where 0.2-0.7 m sometimes up to 1.0 m. Overturningforce for the middle piers was estimated at only about 300 kN in total,which may explain the movements. There is a relatively large ice-field"behind" the piers on both sides and the mid-stream channel is openseme periods.During the winter 1979-80 amtinous ni~asureinents of one middle pierwere carried out (Cederwall and RehnstrCm, 1981). The Movements werecorrelated to the variations of air JCTperature and water-level. The

influence of temperature doninated somewhat over the other factors.Under the bridge the ice was 1.0 m thick and free from snow. Outsidethe bridge the thickness was 1.0 m and snow cover 0-5 a. Thus CQI-ditions for high thermal pressure were at hand.The Swedish reconnendaticns 1987 regarding transverse ice loads arebased upon rather few field evidences. However, the bridge designersdemand sane reasonable design values and soneone has to do the judgemerit.Hopefully additional field evidences will be published in courseof time go that more specific values for different conditions can beestablished and lessen guesswork.REFERENCESBarnes, H.T. Ice Engineering.Montreal 1928.Cederwall, K., RehnstrCm, A. Report of measurement of a piers move-merits in the railway bridge at Kusfors. Lul& Uhiversity of Techno-logy, Div. of Structural Engineering 1981 (in Swedish).Hagg&d, S. ice pressure on a bridge pier. V8g- och VattenbvqgarenNo 3, 1958 (in Swedish).LOfquist, B. Ice pressure on bridge piers. Reocinnsndations andccnroents on the choice of design values. Swedish National RoadAanlnistraticn 1987 (in Swedish).LOfquist, B. Report on ice pressure on pier No. 6 in bridge acrossUne-river, Lycksele. Swedish Naticnal Road Administration 1963(in Swedish, not published).

APPENDIXIce channelBRIDGE PIER CLOSE TO AN OPEN ICE CHANNEL---- ' IT,-,' -- - -Ice shed, Ih'ickne5 sElasi. modal. =E1 a d = ice pressure onlp = 0-ipAdo fictive dam1. The ice-sheet expands a length A . Suppose elastic behaviourof the ice and full restraint at the shore. The ice pressureagainst a fictive dam-front is2. The horizontal "settlement" of the pier according to a formulafrom Soil Mechanics (Bousslnesq) is3. (1) and (2) give i = 1.25 id A/a (3)4. For example A = 60 m and a = 6m, i = 12.5 id. Under elasticoonditicns the ice pressure on the pier per linear meter shouldbe 12.5 times the pressure on a dam in the same alignment.5. The real deformations In the ice are mainly not elastic butviscous which probably will give a lower relation factor. However,the distance A still remains an iJicortant parameter, asbeing deciding for the extension of the ice-sheet against theopen channel.

MEASUREMENTS OF LOAD TRANSMISSION THROUGH GROUNDED ICE RUBBLEA.R. MarshallOcean Engineering Research GroupMemorial University of NewfoundlandSt. John's, NfldK.R. CroasdaleESSO Resources Canada Ltd.Calgary, AlbertaR.M. Frederking & M. Sayed I.J. JordaanInstitute for Research in Construction Ocean Engineering Research GroupNational Research Council of Canada Memorial University of NfldOttawa, OntarioSt. John's, NfldJ.P. Nadreau (*)Centre for Cold Ocean Resources Engineering (C-CORE)Memorial University of NewfoundlandSt. John's, NfldABSTRACT :During the winter of 1986/87 a full scale field study of ice rubble wasconducted at ESSO's CRI (Caisson Retained Island) at a drilling location inthe Beaufort Sea. The aim was to obtain ice rubble characteristics and loadtransmission data so that a theoretical model could be developed, and thispaper summarizes the collected field data.Data was collected from stress sensors on the caissons, pressure panels inthe rubble, pressure sensors in the sea ice, strain rosettes, thermocouplearrays, movement surveys, and rubble profile surveys. Local pressures of 4MPa were measured at the CRI during initial rubble formation but by latewinter the surrounding grounded rubble had reduced the contact pressures tonegligible values. The thermocouple array data showed that the rubblerefrozen layer thickness can exceed 3 m with growth rates in excess of 1.5cm/day. Northward movement of the landfast sea ice produced pressureagainst the rubble, reaching a peak average of 360 kPa and survey dataindicates a generally northward deformation of the entire rubble field.1.0 INTRODUCTIONThe movement of sea ice against a wide structure, such as an artificialisland, produces piles of broken ice called ice rubble. If such pilesbecome sufficiently firmly grounded, subsequent movements will not dislodgethem, and a grounded ice rubble field will form. Artificial islands in theBeaufort Sea often become surrounded by such rubble fields and experience* Presently at NSERC (Natural Sciences and Engineering Research Council)

shows that the rubble fields tend to protect structures from subsequent iceloads. This behaviour might be used to advantage in the design and operationof offshore structures but a thorough understanding of load transmissionthrough grounded ice rubble is first required. To date, some full scaledata is publicly available (Nelson et al, 1976; Strilchuk, 1977; K.R.Croasdale and Associates, 1985) but much of the work done is proprietary.During the winter of 1986/87 a collaborative, full scale, field measurementprogram was undertaken at ESSO's CRI (Caisson Retained Island) atKaubvik. The objective was to collect full scale rubble field data thatcould be used to analytically model force transmission through groundedrubble. Such data was collected and is presented here in summarised form.2.0 SITE DESCRIPTIONKaubvik is located in the southern Beaufort Sea, 120 km northwest ofTuktoyaktuk, at the 18 m depth contour. The nearest land is Pelly Islandsome 26 km to the south. The sea ice usually grows to 2 m thick by themiddle of May (Parker, 1987) but when cored on April 10th 1987, it was only1.5 m thick, implying an end of winter ice thickness of about 165 cm.Historically, Kaubvik is within the landfast ice margin (Markham, 1982) andduring the winter of 1986/87 Kaubvik became landfast by the second week inJanuary. The rubble field that formed prior to this was substantial (seefig 5) and did not grow significantly during the remainder of the winter.The CRI itself is octagonal with eight steel caissons retaining a centralsand core. As the water depth was greater than 9 m, a circular, underwater,berm with a design slope of 12:l was constructed to support the caissons.The caissons have steeply sloping sides, and at the waterline the islanddiameter is 112 m "across the flats".3.0 LANDFAST ICE PRESSUREOn behalf of C-CORE, R. Duckworth of B.P. International Ltd installedthree pressure sensor rosettes in the level sea ice 180 m southeast of theCRI. Each rosette contained three 7.5 cm diam, mercury filled pressuresensors (see Duckworth et al, 1988), frozen into the ice at a depth of 0.6 m(approximate neutral axis). The stress measured by each sensor was recordedon a data logger every 2 minutes over a one month period. The highestrecorded stress was 550 kPa and the largest calculated principal stress was570 kPa (same event). One sensor in each of the rosettes was oriented tomeasure stress approximately in the direction of sea ice expansion and in

all cases these sensors gave the largest pressure readings. An intermittentfault with the data logger resulted in the loss of some of the data, leaving168,000 valid stress readings. The data loss prevents the three principalstresses from being averaged over the entire month but such averaging can bedone with the three sensors oriented in the direction of ice expansion (seefig 1). This is expected to be within 85% of the average principal stressJULIAN DAYSFig 1.Pressure averaged from three sensors oriented along the line ofsea ice expansion. Plot covers entire data collection period.and from this three important characteristics are apparent:- The pressure fluctuates daily as a result of daily temperature cycling.In each rosette the sensor oriented in the direction of thermalexpansion consistently measured by far the largest pressures, indicat-ing that these stresses represent actual rubble field loading, notbiaxial thermal stresses.- Although most of the time the pressure changes were gradual, onoccasion all the sensors indicated, rapid fluctuations of up to 200kPa.The rapid pressure fluctuations are reminiscent of brittlefailure but they occur at pressures well below the usual ductile tobrittle transition range (1.5 MPa , Sanderson, 1984).It is expectedthat this is a result of vertical ice sheet displacement and/orcracking near the rubble field edge.- An "event" occurs between days 114 and 118.5, and on day 123.5, atwhich times the pressure drops to a low level. Analysis of sea icetemperature at a depth of 0.6 m shows that this corresponds to periodsof minimal thermal expansion of the ice sheet.

4.0 RUBBLE PRESSURE DISTRIBUTIONIn January, four pressure panel arrays containing a total of 14 panelswere installed in the rubble. The panels were placed within the refrozenlayer and panels from three sources were used, 0.5 x 2.1 m Exxon panels, 1 xI m and 1 x 2 m Ideal panels, and 0.46 m diameter Arctec panels. They wereall of the flat, strain gauge type with width to thickness ratios from11.5:l to 40:l. Data collection rates varied between arrays, with databeing recorded at 10, 15, and 30 minute intervals.Several pressure "events" were detected and one of the most significant ofthese happened one day after installation of the North-west Exxon array. Arubble building event occurred in which new rubble overtopped existingrubble and covered Exxon panels #3 and #4 with piles up to 5 m high. Thestresses measured by the NW Exxon panels are shown in fig 2, where panels#1,#2,#3 and #4 were 15, 10, 20 and 35 m away from the rubble field edgerespectively. During this event panels on the NW caisson were protected byJULIAN DAYSFig 2.Stress panel output from the North-west Exxon array during arubble building event.substantial rubble accumulations but a shearbar panel on the west caissonmeasured peak pressures up to 40 kPa through rubble accumulations 50 m wide.Unfortunately, difficulties with calibrating some of the panels within therubble, and damage to some of the strain gauged elements within the panels,limits the accuracy of the stress data to -+ 50%. All the panels showedgenerally low stresses, but the limit on data accuracy prevents reliableassessment of the spatial stress distributions within the rubble.

5.0 CRI ICE PRESSURESThe CRI consists of 8, water ballasted, steel caissons arranged in a ringand held together by tensioned wire ropes. The central core of the islandis filled with sand which provides the working surface for drilling, as wellas sliding resistance against ice forces. Each caisson is equipped withvarious sensors including two types of external ice pressure sensor. Thedesign global ice pressure is 1.7 MPa (2 m thick ice) and the design localpressure is 4.8 MPa. The ice pressure sensors are two different sizes,0.165 m diameter "Microcells" (27 operational) and 0.5 m x 2.1 m "Shearbars"(5 operational). Each shearbar panel thus has 50 times the area of amicrocell and both types of sensor measure averaged pressure normal to0.0 1.0 3 0 3 0 4.0 5.0 6 0WEEKS SINCE OCT. 16, 1986Fig 3 Microcell peak pressure data including the maximum recorded (4.1MPa).After October 27 the sensor was protected by rubble.the caisson wall (see figs 3 and 4). Various geotechnical sensors were alsoinstalled but they did not detect any soil response to ice loading events.Until January, the sensors were scanned at a minimum rate of 6 times perminute with the calculated 5 minute average, variance, and peak pressuresbeing recorded. After shut down of operations in mid January, a remotelogging system was used which recorded raw data at a constant rate.The maximum microcell pressure was 4.1 MPa and the maximum shearbarpressure was 0.5 MPa. Both were measured at the Northwest Caisson but

(see fig 5). At most locations the generally northward movement is; in thedirection of sea ice expansion, away from the CRI, and down the berm slope.The survey posts were usually on top of rubble sails so that tilting of thesails may have contributed up to 0.1 m of the measured horizontal displacements.\ I CAISSON 1SCALE OF ICE MOVEMENT, mFig 5Results of movement survey showing locations of survey postswithin the rubble field, measured horizontal movements and (inbrackets) the measured settlements.7.0 ICE RUBBLE STRAINSIn early March 1986, a strain array was installed in a valley, 125 msouth-east of the CRI centre. The site was a patch of level ice that formedas a result of sea water flooding behind the outer sail (ie. at sea level).The short thermocouple array was located nearby, and at installation, therefrozen layer was 2.7 m thick. The strain array consisted of 6 LVDT's(linear variable differential transformers) that measured relative movementbetween 4 posts in the ice surface. The posts were arranged to form theapexes of an equilateral triangle (30 cm apart) with a fourth post in themiddle. The centre post held 3 LVDT's, each outer post held 1 LVDT, andover the 51 day field period, 7300 hourly strain measurements were recorded.The array has been treated as two delta rosettes. One rosette containingthe outer three LVDT's and the other containing the inner three LVDT's. Theprincipal strains were calculated with the following result;

- The magnitude of the inner rosette strains was about twice that of theouter rosette.- The largest principal strains were tensile with a slope change thatcorresponds to a drop in sea ice pressure between days 114 and 118.- The smallest principal "strains n correlate with surface ice temperatureand appear to be due to thermal expansion and contraction of the ice.The discrepancy between the output of the inner and outer rosettes is notunderstood, but in both cases large tensile strains are recorded. Becauseof the viscous nature of ice and the differences in strain magnitudes, it isdifficult to calculate the level of stress in the ice from the strain data.The trends, however, are the same for both rosettes.A positive slopeindicates a compressive stress, and a negative slope indicates a tensilestress. It is thus apparent that during the period of low sea ice pressurebetween days 114 and 118 (see fig I), the surface ice at the array wassubject to compressive stress (see fig 6).When sea ice pressure resumed onday 118, the stress again became tensile. This was not expected and mayhave resulted from the effects of a nearby crack or from some formrefrozen layer bending.,0005 770 75 BO 85 90 95 100 105 110 115 120 1JULIAN DAYSFig 6 Maximum (positive) and minimum (negative) principal strainsmeasured by the outer rosette.8.0 ICE RUBBLE TEMPERATURESOn March 11, two thermocouple arrays were installed in the ice rubble nearthe strain array. A 12 m array in a rubble sail measured temperatures at 14

elevations, and a 3 m array in a valley measured temperatures at 13 eleva-tions.Over a 51 day period 33,000 hourly temperature measurements wererecorded and both arrays initially penetrated into unrefrozen rubble. Fromthe temperature versus depth profiles, the position of the freezing frontcould be determined (see fig 7), and from successive profiles the growthrateof the refrozen layer was calculated. For sea ice, accumulated degree daysversus the ice thickness squared is a linear relationship (Parker, 1987).By May 2 about 2900 degree days had accumulated since the rubble formationand the refrozen layer was 3 m thick in the valley and 3.85 m thick underthe sail with averaged growth rates of 1.7 cm/day and 2.7 cm/dayrespectively. The temperature versus depth profiles also show the thermalgradients above the freezing front and this enables one to calculate therate of heat flow.unfrozen rubble keel was liquid water.0.00-0.25-0.50-0.75--1.00E -125g -1.50On-175-2.00-2.25- 2.50-2.75From this it was calculated that only 12% of the- 3.00 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2TEMPERATURE (Deg. C)fig 7Temperature versus depth profile from the short thermocouplearray, midnight day 83-84.9.0 RUBBLE PROFILE DATAThe surface of the rubble field consists of an irregular series ofsails and valleys (see fig 8). A total of 89 ice rubble elevations weremeasured along 7 survey lines covering a combined distance of 540 m. Theaverage height of the 27 sails surveyed was 3.8 m and the maximum observed(not along survey lines) sail height was 9 m.Eight holes were drilled to establish the rubble thickness. This was

done to the southeast of the CRI and started on the floating, broken anduneven ice (disturbed zone) adjacent to the grounded rubble. The averagethickness of the disturbed zone ice was 3.3 m (5 holes) and drilling intothe rubble established that the rubble was grounded, even under a valley.In April the rubble iceblock thickness was measured at various distancesfrom the CRI. The thicknesses increased from 0.2 m, 10 m from the CRI, to0.75 m at a distance of 75 m from the CRI.DISTANCE (m)Fig 8East survey line # 2 carried out to the south east of the CRI10.0 CONCLUSIONSThe CRI and ice rubble field provide useful platforms for studyingforce transmission through ice rubble, and large scale ice indentation.Readings from the two sizes of pressure panel on the CRI clearly showthat peak effective ice pressure increases with smaller contact area.Thermally induced sea ice movements can cause significant ice loads.Substantial pressure decrease after the formation of grounded rubbleindicates that this protects the CRI.A rapidly formed refrozen layer exists in the rubble and this should beaccounted for in any theoretical models.The refrozen layer was thickest under the sail, suggesting that despitethe insulation provided by the sail, reduced rubble porosity under thesail allows greater refrozen thickness with less heat loss.0.2 m thick ice formed grounded rubble piles in 9 m deep water.

11.0 REFERENCESDuckworth, R. and Westermann, P.H. (1988)."Stress And Strain MeasurementsIn Ice. Field Techniques", Polar Instrumentation Workshop, Monterey,24 PgsK.R. Croasdale and Associates (1985)."Ice Investigations At A Beaufort SeaCaisson, 1985", Report for NRC and U.S. Dept of the Interior, 129 pgsMarkham, W.E. (1982)."Artificial Islands And Fast Ice A DOE Report OnCostal Ice Conditions In The Beaufort Sea", Environment Canada,Atmospheric Environment Service, Downsview, Ontario, 13 pgsNelson, R.D. and Sackinger, W.M. (1976)."Ice Stress Measurements At ADGOAnd Netserk, 1974-1975", APOA Project Report 104, 73 pgsParker, M.N. (1987)."Ice Thickness Climatology For Northern Canada",Scientific Services Report, Atmospheric Environment Service, 53 pgsSanderson, T.J.O. (1984)."Theoretical And Measured Forces On Wide Struc-tures", IAHR State-of-the-Art Report on Ice Forces, 32 pgsStrilchuk, A.R. (1977)."Ice Pressure Measurements Netserk F-40 1975-76",APOA Project Report 105, 279 pgs

THE SENSITIVITY AND UNCERTAINTYANALYSIS OF AN ICEBERG STRUCTURECOLLISION MODELDavid A. PinturJon F. SykesUniversit,~ of Wat,erlooWaterloo, CanadaN2L 3G1ABSTRACTThe Hibernia oil field is characterized by not only its vast oil potent,ial, but alsoits severe environmental condit.ions, the great,est being the threat posed by icebergs.There exists a need for an accurate prediction of iceberg collision loads on drilling andproduction structures in both a deterministic and a probabilistic sense.A dynamic collision model is utilized which incorporat,es the iceberg hydrodynamicsand force-penetration properties, the effect of waves, and the structure and foundationcoupled response. This paper develops the sensitivity equations for the local sensitivityof the contact force response to each of the input parameters. Referred to as the adjointformulation, the sensit,ivities are calculat,ed in the equivalent of one additional run oft,he model. Combining t,he sensitivity coefficients in a Moment Method technique, aprobabilistic model is t,hen developed t,o predict the uncertainty of the contact force.A "most,-likely" scenario of an eccent,ric collision is present.ed. Relative to all ot,l~ermotion components of the system, the adjoint response reveals that t,he iceberg's surgevelocity during the init,ial collision phase exerts the greatest importance on the maxi-mum cont,act force. In the uncertaint,~ analysis, comparable force dist,ributions t,o thatof the Lat,in Hypercube technique are predicted, but in a fraction of the computer time.1. INTRODUCTIONLocated 315 kilomet,res east-southeast of St,. John's, Newfoundland, the Hiberniaoil field poses unique design challenges for any structure drilling in the region. Present,inga constant threat to the drilling operations is the constant flux of icebergs fromGreenland, ranging in size from 10 tonne bergy bits, to 6 million tonne monoliths.With the conceptual approval of a fixed gravity base structure (GBS) for Hibernia,consideration must now be given to developing design criteria. In the absence of documentedcollisions, and the fact that a structure of this type has never been built to

withstand iceberg impacts, a thorough parametric st,udy of a nun~erical simulation isrequired. Existing iceberg-collision models have demonstrated uncertainty associatedwith eccentric collisions, wave effects, and ice-st,ructure compliance (Pintur 1988); how-ever, due to the inherent complexities of the deterministic models, uncertainty analyseshave not been included in the simulations. Probabilistic models do exist, (Reddy et01 1980, Maies 1984), but tend to greatly oversimplify the collision process and mayneglect the above-mentioned uncertainties.This paper develops an efficient method for calculating the sensitivity of each of themodel parameters to the force response, and then utilizes these sensitivity coefficientsin an uncertainty analysis.2. MODEL OVERVIEWThe numerical development presented in this paper is adapt,ed to the STRIKEmodel (Pintur 1988, Acres, 1986). Briefly, the model is a 12 degree-of-freedom non-linear syst,en~ incorporating t,he hydrodynamic motion of both the iceberg and structure(through the conservation of linear and angular momentum), coupled with the foun-dation stiffness and damping. The contact point between the iceberg and GBS isrepresented by normal and tangential non-linear springs relating the force exerted onthe iceberg and t,he structure as a function of their respective distances penetrated intoeach of the masses. This relationship makes it possible to simulate any type of contactconfiguration by pre-defining the force-penetration characteristics of both masses.Accounting for the functional dependence of the stat,e variables, the continuous formof the problem is stated aswhere 6, 6, and 6 are the displacement, velocity and acceleration vectors respectively;M, C, and K are the lumped mass, damping and stiffness mat,rices, and F is t,heexternal force vect,or. The state vectors represent t,he centre of mass motions in thesurge (z),sway (y), heave (z) translational directions, and in the roll (0=), pitch (ai,),and yaw (0,) rotational directions.Added mass terms are included in M to represent the inertial effects of tlie waterwhich is decelerat,ed along with the iceberg, and in some respects, to estimat,e thewater's cushioning effect. Although studies have indicated a time dependency of theseadded mass t,erms (Isaacson 1985), constant values have been assumed.External driving forces include second order water drag, wave forces, fluid-inducedpitch and roll moment,^, form and surface drag, and a buoyancy force. By discretizingthe iceberg into n stacked disks of varying diameters, the net wave force acting on theiceberg is

where s, is the elevation from the sea bed t,o t,he it* disk, & and C'M are the dragand inertia coefficients, D, and A, are the disk diameter and circular area, p is thefluid densit,y, and u and u are the horizontal wave velocity and acceleration vectorscalculat,ed from St,oke's second order wave theory.The st,iffness matrix in (1) represents the global bending and torsion stiffness ofthe structure as well as the force penet,ration relationship of the contact point. In thenumerical simulation, the stiffness properties are represented as a force vect,or Fk = K6,which is treated as a driving force t,o the system.A discrete solution technique is then implemented based upon Newmark's methodof constant acceleration over a time interval At. At an arbitrary time t, an implicitsolution for the displacement vector is det,ermined fromfollowed by an explicit calculation for the velocity and acceleration components,respectively. The recursive nature of (3) causes the solution to propagate through timefrom initial conditions at t = to, and is referred t,o as the forward problem. Nonlinearitiesin the STRIKE model necessit,ate an iterative solution scheme at each timestep.Over m time st.eps, the forward problem can be expressed in canonical matrix formin terms of a "stiffness" matrix A and a global load vector R of dimension 3n1n,where,.m ..m4 = ((61,61,61)1', (62,2,2)7", ... ,(6"',6 ,6 )T)T. (6)The solution domain of (5) is convenient for developing the sensitivity equations.3. THE ADJOINT SENSITIVITY SOLUTIONThe model's out,put can be defined in terms of a performance measure P, which irgeneral is a funct,ion of bot,h the system parameters a, and t,he stat,e variables 4,

9~In this paper P represents t,he maximum global contact force, P = max IF'I. Theperformance function sensitivity to a perturbat,ion of an arbitrary parameter ak, canbe found by differentiation of (7),@ 9~ +- 94dni 9ak 99

adjoint solution is unique for a given performance function; t,herefore once calculated,the performance sensitivity in (13) requires only an explicit, linear solut,ion for eachparameter.4. THE UNCERTAINTY SOLUTIONAn uncertainty analysis assesses the statistical variance in the performance functiondue to the variation of the model parameters. This uncertainty can be calculated usingeither full distribution techniques such as the Latin Hypercube (Iman and C!onover1980), or a Moment Method (McKenna el 01. 1987). The former implies a complet,especification of each parameter's probability distribution function, and requires repeatedrealizations of the forward state problem until all of the parameters have beenrepresented; the latter assumes that the parameter mean and variance describe theparameter distribution. In the Moment Method, a first order Taylor series expansionof the performance function deterniines the mean fi and variance of P,(IP11 = E{P(a)} = P(a,,). and Var(P) = -C(a)-,At Twhere C is the covariance matrix of the parameters (t. and dP,'AfT is the vector ofsensitivity coefficients calculated using (13).From (15) it is evident that a parameter having a relatively small variance will contribut,esignificantly to the performance uncertainty if that parameter has a relativelylarge sensitivity coefficient.(\pclaT(15)5. AN ECCENTRIC ICEBERG COLLISIONRelative to a head-on collision, eccent,ric collisions generally inflict less impact loadsdue to induced rotational motions of the iceberg; however, an eccentric collision has thegreatest probability of occurrence. Thus in a risk analysis, this type of scenario maygovern the design. The following section presents an eccentric collision of a medium-sizeiceberg with a large gravity base structure.Table 1 sunlmarizes the main input data for the eccentric collision. The gravitybase struct,ure data is from Acres (1986). To expediate iceberg crusliing. load attenuatingdevices in the form of concrete wedges were located around the structure. Theglobal stiffness characteristics were derived from a finite element analysis, and includethe effects of torsion, bending, and shear. Relevant foundation parameters were itsgeometric damping and stiffness properties, developed from elastic half-space theory(Whitman and Ricliart 1967) assuming a shear modulus of 110 MPa. For simplicity,linear force-displacement response was assumed at the foundat,ion.The collision eccentricity is measured in the horizont,al water plane. From the geonietryof the impact rrgion, iceberg force-penetrat,ion curves were generated in t,helocal normal and tangential directions. The fundamental assumption is that the ice

fails only in a uniaxial crushing mode, which is reasonable at high strain rates. Using aprocedure outlined by Cammaert et 01. (1983), the depth of penetration was increment,allyrelated to t,he crushed ice volume, which in turn was relat,ed to the penetrationforce. A constant ice strength of 4 Af Pa was assumed,5.1 Forward State SolutionA five second animation sequence is presented in figure 1, revealing a clockwiserotational yaw acceleration. From a time history response (figure 2) tlie maximumcontact force was ,155 giga-Newtons at 2.0 seconds, after which time hysteretic motionoccurred due to the continued driving force exerted on the iceberg by the waves. Thepenetration distance of the structure into the iceberg was 2.23 and 1.83 metres in thelocal normal and tangential directions respectively. A plot of the iceberg and structure'sacceleration response histories is presented in figure 3.5.2 Adjoint State SolutionThe adjoint solution was initiated at the time of maximum contact force using atime step of -.025 seconds. For a twelve degree-of-freedom model, thirty-six uniqueadjoint components were determined, relating the temporal importance of each of thestate variables to the performance function. It is interest,ing to note that the normalizedshape of the displacement, velocity and accelerat,ion adjoint coniponents are identical,however it is their magnitudes that determine their relative importance. For example,the velocit,y components (figure 4) and more specifically, the iceberg surge velocity, hasthe greatest positive influence on the force, relative to the other components. Similarly,the sway motion exerts a negative influence on t,he contact force, such that a slightincrease in the acceleration causes a decrease in t,he maximum force; the most significantchange occurring at 1.05 seconds. The rotational mot,ions exerts posit,ive effects, with aslight initial perturbation of the pitch and yaw motions inducing the greatest increasein the cont,act force.Having a much greater stiffness than (,hat of tlie iceberg, the structure's dynamicproperties are evident in its damped oscillatory adjoin! response. TI].- ereateqt import,anceof t,hese motions occurred at 1.5 seconds for the translational components and1.75 seconds for the rotational conlponents.5.3 Discussion of Sensitivity ResultsThe most sensitive of the paramet,ers were t,hose relat,ing t,o t,he iceberg motion andwave characterist,ics, and are (in order of importance): the initial velocity components(surge, pitch and yaw motions), the normal force-penetration relationship, the addedmass (surge direction) and actual mass, t,he mass moments of inertia (about all 3 axes),

and the init,ial pitch and yaw accelerations. Similarly, the wave parameters were thewave height, direction of propagation, and the iceberg inertial and drag coefficients.The least sensitive of the iceberg parameters were the initial accelerations and theadded-mass terms in the sway and heave direct,ions, as well as the drag coefficients.Except for the normal force-penetration relationship of the GBS, the structureexhibited negligible influence on the cont,act force. Similarly, the damping and stiffnessresponse of the foundation proved to have negligible influence on the contact force;however, the foundation stiffness in the surge direction did had a marginal effect. Thevelocity of the current had zero effect on the contact force.Caution must be observed in the interpretation of the adjoint sensitivity coefficient,s,for they represent the localized first-order effect of each parameter on the performancefunction. For highly non-linear paramet,ers, the sensitivit,ies may vary significantly fordifferent values of the paramet,er.5.4 Discussion of the UncertaintyFor illustration purposes, a simplified analysis was undertaken, in which the modelparameters are assumed to be independent of each other, such that the covariancematrix of (15) was reduced to a diagonal of each paramet,er's variation. Furthern~ore, itwas assumed that the uncertain parameters were normally distributed with a coefficientof variat,ion of .10 of their respective means as defined in tlie forward problem. Onlythe following parameters (all relating t,o the iceberg) were assumed to contribute tothe uncertainty of the contact force: the initial surge velocity, the inertial and dragcoefficients (wave force terms), the mass and added mass, and t,he moments of inertiaabout all three axes.The non-linearity of the parameters over the range of 3 standard deviations was firstass,essed. Non-linear behaviour was observed for the moment of inertia parameters, theiceberg mass and the initial surge velocity. The time of maximum force remainedst.ationary for all parameters, wit,h the exception of the surge velocity, in which thepeak contact force ranged from 1.4 to 2.8 seconds.The Moment Method technique was then compared to the Latin Hypercube tech-nique. Using 40 realizations, the lath t,echnique predicted a mean of 152.8 MN for tliemaximum contact force, with a standard deviat,ion of 14.1 MN. Alternatively, in onerun of the bot,h the forward and backward problems, combined wit,h a summation of(15), the uncertainty of t,he contact force was determined in the Moment Method; morespecifically, a mean of 154.5 MN and a standard deviat,ion of 14.9 MN. This representeda relative error of 5.4 percent compared to t,he variance of the Lat,in Hypercube analy-sis. This slight discrepancy can be partly attributed to the highly non-linear nature ofthe initial surge velocit,~.

6.0 CONCLUSIONSThis paper has presented a most-likely scenario of an eccentric collision. From thetime histories of the adjoint solutions, it was shown that the iceberg surge velocity dur-ing the initial period of the collision exerted the greatest importance on the maximumcontact force relative to all other motion components of the system. The parameterswhich exhibited the greatest effect on the maximum contact force were those parame-ters relating to the iceberg and wave properties. Of importance was the iceberg force-penetration relationship. A separate sensitivity analysis. however, is recomn~ended toassess t,he parameters which affect the generation of the curve, for example, the localgeometry of the contact area.For a subspace of iceberg parameters, the uncertainty analysis demonstrated theMoment Method's efficacy relative to the Latin Hypercube technique. In the equiv-alent of two runs of the forward problem, the Moment Met,hod predicted a responseuncertainty 6 percent greater than the Latin Hypercube uncertainty, with the lattertechnique requiring 40 forward simulations before its statistics stabilized. Further re-search into the parameter correlation is recommended, before a complete uncertaintyanalysis can be undertaken7. REFERENCES[I] Acres Consulting Services Limited, 1986, Global Ice Forces on n Gravity BaseStructure. Final Report to Pet ro Canada Limited (proprietary ).[2] Cammaert, A. B. , . T. Wong, D.D. Curtis, 1983, "Impact of Icebergs on OffshoreGravity and Floating Platforms", POAC '83, Helsinki, Finland.[3] In~an, R.L, and W.J. C'onover, 1980, "Small Sample Sensitivity Analysis Techniquesfor Computer Models, With an Application to Risk Assessment,", Cornmumcationsin Statistics, Theory and Methods. A9(17), 1749-1842.141 Isaacson, M. de St. Q., 198.5, "Iceberg Interactions with Offshore Structures", CivilEngineering in the Arctic Offshore, Arctic '85 Proc., San Francisco, 276-284.[S] Maes, M.A., I.J. Jordaan, J.R. Appleby, and P. Fidjest01, 1984, "Risk Assessment,of Ice Loading for Fixed Structures", OWE Proc. 3, New Orleans.161 McKenna, R.F., N.R. Thomson, J.F. Sykes, 1987, "Uncertainty of Sumnier IreDrift Forecasts", POAC 1987, Fairbanks, Alaska.[7] Pintur, D.A. , 1988, "The Sensitivity and Uncertainty Analysis of an IcebergStructure Collision Model for Hibernia ", MASc Thesis, University of Waterloo,Ontario, Canada.[El Reddy, D.V., M. Arockiasamy, P.S. Cheema, and N.P. Riggs, 1980, "Monte CarloSimulation of Iceberg Impact Probabilit,ies", CRST 1, 293-297, Amsterdam.[9] Whitman, R.V. and F.E. Richart Jr., 1967, "Design Procedures for Dynamically-Loaded Foundations", ASCE Journal Vol 93, No. $M6, November.

Table 1: Summary of Input Data for Eccentric Collision -ICEBERGMass [tonnesl 10 000~dded mass coefficient 0.5Drag coefficient [kg/m] 1.2~,In,Iit[kg~m2](x1010) 1.3,9.45,5.83Initial iceberg velocity [m/sec] 2.0Ocean current [m/sec] 2.0Wave height and length - [m] .. 5.0, 150.Iceberg & [kg/m] 1.4z, y, z soil stiffaus [N/m](x lo9)STRUCTURE3.4~ 10"439., 439.. 514.Structure radius [ml 98.Bending stiffness [N/m\ 2.82el2Torsion stiffness IN/m/m] . . . . 1.5~15Collision eccentricity [mi 24.543.3, 43.3, 57.1s,. s,, 9, soil stiffness [N . m/rad\ (x1014)z, y, z soil damping coefficients [N s/m\ (x lo9)9=, Hi,, 9, soil damping coefficients [N . s/m] (x 10") , .- Normal Contact Forcer ____-- Tangential Contact ForceHorizontal Wave Force on IcebergFigure 1:Animationof Eccentric Collision-2Tine [sees}-A) 1 2 3 4Figure 2: Time History of Force ResponseIceberg-0.04Figure 3:Iceberg andStructure AccelerationResponse(translational [m/sec2],angular [rods/sec2])0 0.5 I 1.5 2 2.5

ICEBERG COMPONENTSFigure 4:Time Histories of the Adjoint Velocity Components595

AN ICE FAILURE MODEL INCORPORATING SIZE EFFECTSMohamed SayedRobert M.W. FrederkingInstitute for Research in ConstructionNational Research Council of CanadaOttawa, K1 A OR6CANADAABSTRACTA new criterion for the brittle failure of ice is proposed. By including astress gradient, strength of ice becomes size dependent. Calculations arecarried out for an idealized indentation. The resulting pressure-arearelationship shows reasonable agreement with field and laboratorymeasurements.1. INTRODUCTIONA wide variety of failure modes may take place when ice impinges on astructure. Failure modes and the resulting forces depend on numerousfactors such as geometry, size, velocity, temperature and type of ice. Thisstudy is concerned with the brittle failure of ice, which may occur during localindentation.A comprehensive review of local ice pressures has been recently given bylyer (1988). One important observation is that failure stresses decrease assize increases, even when geometrical similarity is maintained. Thisbehaviour is often referred to as "size effect" or "pressure-area" dependence.A number of analytical solutions has been developed to predict ice failurestresses (for example Varsta, 1983 and Riska, 1987). The calculations,however, do not predict a "size effect". Empirical corrections have to beused (see lyer, 1988).

A new failure criterion that includes a stress gradient is proposed in thispaper. Solution of an indentation problem is then developed. The resultingfailure stresses, which are size dependent, are compared to availablemeasurements.2. PROPOSED FAILURE CRITERIONSeveral studies have dealt with developing failure criteria for ice based onlaboratory tests of small samples. For example, formulas were developed byMichel and Toussaint (1977), Croasdale et al. (1977), Reinicke and Ralston(1977), Ralston (1978), Karr and Das (1983), Timco and Frederking (1984and 1986), and Nadreau and Michel (1986). These formulas demonstrate agood fit for experimental results of multiaxial tests but do not include a "size"effect.Introducing a stress gradient in a failure criterion would result in a strengthsizedependence. There are no reported studies so far on stress gradienteffects on ice failure. However, related studies of the brittle failure of rockwere reported by Hodgson and Cook (1970) and Brown and Gonano (1975).They found that stress gradient increases strength and produces a sizeeffect.Sturman et al. (1965) tested concrete samples under uniaxial eccentriccompressive loading. Failure stress (strength) and strain were found toincrease in the presence of the strain gradient produced by eccentric loading.The strain gradient was also observed to suppress cracking. Thoseobservations imply that a natural length or size effect may exist becauseincluding a strain or stress gradient in a failure criterion would render itdimensional.A simple failure criterion is considered here to illustrate how a stressgradient may be incorporated, thus bringing in a size effect. The formula ofTimco and Frederking (1986) is reduced to the following equation for thecase of plane stresswhere o, and o, are the principal stresses, and the constant K is a material

property. The value of K depends on ice type, salinity, temperature andstrain rate. Equation (1) may be extended to include the magnitude of thestress gradient 121which should increase the strength. This approach isin agreement with the experimental results of Sturman (1965), and theobservations of Hodgson and Cook (1970), and Brown and Gonano (1975).Thus, a simple criterion may be expressed aswhere C is a positive constant. The value of C, like that of K, shoulddepend on ice type, salinity, temperature and strain rate. Equation (2)should be viewed as a tentative attempt to include a stress gradient in thefailure criterion. There are no data to determine the power to which thegradient [:]should be raised, or if other stress gradients" )should be included. A sketch of the failure envelopes( [ ax, 1according to equation (2) is shown in Figure 1. It should be noted that theexperiments of Sturman et at (1965) were limited to uniaxial compression.INCREASINGa (7.-----0, TENSION'/TENSION"1COMPRESSIONFigure 1. Sketch of failure envelopes\

The failure envelopes in Figure 1 are extended into the compressioncompressionand compression-tension zones. There are no data to guidethe choice of failure envelopes in the tension-tension zone.All stresses in equation (1) can be nondimensionlized with respect to areference stress (K for example). Thus, geometrically similar problems wouldresult in the same failure stresses, regardless of size. Alternatively the termC Ñ1 in equation (2) would be proportional to I" where I is a reference( :2J[ :z2 Jlength (such as an indentor's width). The term C Ñ1would decrease,and consequently stresses decrease, as size increases. The pressure-arearelationship predicted by equation (2) and the appropriate values of C and Kare further examined in the following section.3. INDENTATION ANALYSISAn indentation problem is used here to examine the stresses predicted byequation (2). Figure 2 shows the idealization used to calculate the elasticFIXEDFigure 2. Sketch showing geometry and boundary conditions

stresses. Displacements are assumed to be parabolic along a length Irepresenting half the indentor's width. This loading case was chosen toavoid the unrealistically high stresses at the indentor's corners in the case ofuniformly imposed displacement. A plane stress solution was obtainednumerically using the finite element program PDEJPROTRAN.Calculated stresses were normalized with respect to Young's modulus E,and lengths with respect to 1. Solution for one case was obtained using adimensionless displacement of 10"~ at the centre line. The principalstresses ol and 02, as well as the gradient of ol, 2) were calculated.Failure stresses were determined by substituting these values in equation(2). Calculations were done for a range of values of C/12. Failure occurswhen the left hand side (LHS) of equation (2) at any point reaches the valueof K. Thus, the maximum value (LHS) , corresponds to failure of ice.This always occurred over a local area in the neighbourhood of a pointlocated 0.25 I below the indentor and 0.78 I from the centre line. Since theLHS of equation (2) contains only quadratic terms of stress or stressgradient, stresses are multiplied by/K^d-HS),.,,,, to give failure values.Stresses were then normalized with respect to so, which is the averagefailure stress for a very large indentor (obtained by letting l+ w). Thereforethe value of K would not affect the resulting normalized stresses.The resulting average normal stress on the indentor at failure is plottedversus I 'IC in Figure 3. It should be noted that failure mode may changeas stresses increase (e.g. failure can occur at the centre line). This wouldgive an upper limit for the stress in Figure 3, for small values of I 'IC. Thepreceding discussion gives only an outline of the calculations because ofspace limitations.4. COMPARISON WITH MEASUREMENTSThe present failure criterion (equation 2) and indentation analysiscorrespond to a simple case of plane stress. Nonetheless, the predictedstress-area relationship is compared to more complex cases of field andlaboratory measurements here. This comparison is aimed at examining the

0.01 0.1 1 .oPICFigure 3. Nondimensional pressure area relationshiptrends of predicted stresses and to give some indication of the appropriatevalues for material properties to be used in equation (2).Laboratory measurements by Varsta (1983), field indentation tests byJohnson and Benoit (1987) and the M.V. Arctic ramming trials (Riska andFrederking, 1987) are compared to the calculations in Figure 4. The resultsof Johnson and Benoit (1987) are presented here in a dimensional form byassuming that the uniaxial strength, which they used as a reference, to be 7MPa. The values of so and C are adjusted to obtain the best fit of the data.nt108I I I I- TUNNEL 1, TEST 5 -TUNNEL 3, TEST 2--0a TUNNEL 4, TEST 2o o A TUNNEL 4, TEST 3 ---- -0 I I I I0.0 1 .o 2.0 3 0 4 0 5 0AREA, m *Figure 4a. Iceberg indentation tests, Johnson and Benoit (1987)--

n COsa: 8--303a: 3 56;nw 4 -03 -82 2 ->

not be suitable to suggest values appropriate for full-scale conditions.The present failure criterion (equation (2)) also agrees with the results ofWang and Poplin (1986) and Petrie and Poplin (1986). They measured fullscale strength of ice sheets and found them similar to those obtained fromlaboratory testing of small ice samples. Those findings led to questioningthe existence of size effect. Those full scale and laboratory tests, however,utilized uniform stress distributions, i.e. no stress gradient. In the absence ofa stress gradient, the measurements should show no size effect, accordingto the present failure criterion. This explanation reconciles the apparentlyconflicting observations of strength-size dependence (lyer, 1988) with thoseof Wang and Poplin (1986) and Petrie and Poplin (1986).5. CONCLUSIONA new criterion for the brittle failure of ice is proposed. This criterionaccounts for size effects by including a stress gradient. Thus, failure at anypoint would depend on stress conditions both at the point itself and in itsneighbourhood.The choice of the failure criterion is motivated by early tests that indicatethat a stress gradient increases the compressive brittle strength of concreteand rock. Only a simple formula for the plane stress case is presented.More elaborate formulas dealing with more complex stress situations may bedeveloped in a similar manner. There is not enough information, however, todetermine the precise form of the stress gradient terms. Therefore, only asimple plausible choice of one such term is made.Analysis of an indentation problem illustrates the manner in which failurestresses decrease with increasing size, or contact area. Field and laboratorymeasurements confirm the predicted trends and give a range of values formaterial constants.6. ACKNOWLEDGEMENTSThis paper is a contribution from the Institute for Research in Construction,National Research Council Canada.

7. REFERENCESBrown, E.T. and Gonano, L.P. (1975). An analysis of size effect behaviourin brittle rock, Proceedings of the 2nd Australia-New Zealand Conferenceon Geomechanics, Institution of Engineers, Sydney, Australia, No. 7514,139-143.Croasdale, K.R., Morgenstern, N.R. and Nuttal, J.B. (1977). Indentation teststo investigate ice pressures on vertical piers, J. Glaciology, 19 (81), 301-312.Hodgson, K. and Cook, N.G.W. (1970). The effects of size and stressgradient on the strength of rock, Proceedings of the 2nd Congress of theInt. Society for Rock Mechanics, Belgrad, 21-26 September 1970, 2, 31-34.lyer, S.H. (1988). A state of the art review of local ice loads for the designof offshore structures, Proceedings of the 9th International Symposium onIce, International Association for Hydraulic Research (IAHR), Sapporo,Japan, 23-27 August 1988, 2, 509-566.Johnson, R.C. and Benoit, J.R. (1987). Iceberg impact tests, Proceedings ofthe Offshore Technology Conference, Houston, 417-423.Karr, D.G. and Das, S.C. (1983). Limit analysis of ice sheet indentation, J.of Energy Resources Technology, 105, 352-355.Michel, 6. and Toussaint, N. (1977). Mechanisms and theory of identation ofice plates, J. Glaciology, 19 (81), 285-300.Nadreau, J-P. and Michel, 6. (1986). Yield and failure envelope for iceunder multiaxial compressive stresses, Cold Regions Science andTechnology, 13, 75-82.Petrie, D.H. and Poplin, J.P. (1986). Comparison of small-scale and largescalesea ice strength, Proceedings of the International Association forHydraulic Research (IAHR), Iowa City, Iowa, 18-22 August 1986, I, 265-277.Ralston, T.D. (1978). An analysis of ice sheet indentation, Proceedings ofthe International Association for Hydraulic Research (IAHR) Symposiumon Ice, Lulea, Sweden, 1, 13-31.Reinicke, K.M. and Ralston, T.D. (1977). Plastic limit analysis with ananisotropic, parabolic yield function, Int. J. Rock Mech., Minning Sci. andGeomech. Abstr., 14, 147-154.Riska, K. (1987). On the mechanics of the ramming interaction between aship and a massive ice floe, Technical Research Centre of Finland,Espoo, publication 43, 86p.

Riska K. and Frederking, R.M.W. (1987).Development of a model forpenetration into ice, Espoo 1987, Report of the Joint Research ProjectArrangement #1 between Technical Research Centre of Finland andNational Research Council of Canada. 57pSturman, G.M., Shah, S.P. and Winter, G. (1965). Effects of flexural straingradients on microcracking and stress-strain behaviour of concrete, J. ofthe American Concrete Institute, 62 (8), 805-822.Timco, G.W. and Frederking, R.M.W. (1984). An investigation of the failureenvelope of granular/discontinuous columnar sea ice, Cold RegionsScience and Technology, 9, 17-27.Timco, G.W. and Frederking, R.M.W. (1986). Confined compression tests:outlining the failure envelope of columnar sea ice, Cold Regions Scienceand Technology, 12 (I), 13-28.Varsta, P. (1983). On the mechanics of ice load on ships in level ice in theBaltic Sea, Technical Research Centre of Finland, Espoo, Publication 11,91 p.Wang, Y.S. and Poplin, J.P. (1986). Laboratory compression tests of seaice at slow strain rates from a field test program, Proceedings of the 5thInternational Offshore Mechanics and Arctic Engineering Symposium,Tokyo, Japan, 13-17 April 1986, 4, 379-384.

THF. CHARACTERISTICS OF BOHAIICE LOAD ANALYSING METHODWane Qin-jianSenior EngineerBohai Engineering Design Co. ChinaZhu Jun-sunProfessor~ong-ji University Shanghai ChinaABSTRACTThe authors think that there are about three kinds of ice load in thework. 1. Moving ice sheets (wind generated) .2. Collision with floating ice blocks. (current generated.)3. Moving ice sheet (water level variations) generated by the tide.As the Bohai ice load belongs to third kind, its move law and ice forceare determined by means of analysing current, tide and wind. What has beenmentioned above is explained in this paper.picture 1

1. INTRODUCTIONThe first steel platform in Bohai was built in 1956. Later, a similarplatform was overthrown by an unprecedented sea ice in Bohai of 50 yearsrecurrence in 1969. Since then, special attention has always been paid tothe sea ice load on platforms in Bohai by the designers. large scale measurementand observation of sea ice were carried out and the characteristicsand mechanical properties of sea ice were studied. At the sametime,the existing methods of calculation of ice loads in the world were extensivelycollected and critically compared. The results of such calculationsare quite different and the difference may be as much as five times. Sincethe strength and thickness of sea ice, the freezing process, method of actionas well as the meteorology and geography are different for differentlocations, it is impossible to use a general formula of the sea ice loadfor all locations. In the estimation of the ice load, it is necessary toconsider the meteorology, hydrology and other specific local conditions.2. TYPES OF SEA ICE LOADThe sea ice load can generally be divided into three types, namely:2.1 Stationary typeThe complete huge ice sheet covers almost the entire sea area. It poceasesimmense momentum. Under the action of wind and currentt, it exertsgreat thrust on offshore platform and it forms the most formidable menaceto the platform. As, the sea ice in BONEAR Bay, which has been studied experiencly.The lighthouse at Kemi I1 in Finland is an example of a structurewell suited for such conditions.2.2 Foreign typeThis is the huge block of floating ice coming from elsewhereflowingwith the tide. Once it collides with the platform, it will cause smashingdestruction to the platform. The sea ice along the eastern coast in NorthAmerica is a such example. If the ice block is dragged upstream by a shipto change its cource of motion, it will bypath the platform. Ice forecastis an effective means to avoid accident.2.3 Alternating type

This type generally occurs in the inner sea of the temperate zone wherethe ice moves back and forth regularly with the tide. In Bohai, for example,under the action of half day tide, the sea ice is always in thisstate of movement (see picture 1) from its growth to disappearence by thawing.Its movement has also a certain range.3. THE CHARACTERISTICS OF ICE LOAD IN BOHAI3.1 The breaking and accumulation of sea iceA. The driving force of ice blockThe driving force to move the sea ice can be expressed as follows:P = n(~ + P + P )Sin t P4Sin1 2 3in whichfl- Surface area of ice block(m2)P - Friction force of water current on the under surface area of1ice block, P = 0.5":1 ( kg/m2(kg)V - Current velocity under the ice block (m/s)P - force of water current on the edge of ice blockhP = 50 - VL s2h - ice thickness(kg/m2L - length of ice block in the direction of current (m)P - the force exerted on the ice block due to slope drop of water3surfaceP = 920hislope drop of water surface(m)(kg/m2)P4 - friction force of wind on the top surface of sea icep4 = 0.001 - 0.002 v(kg/m2V - wind velocity(m/~)od - angle of inclination of current with the structure (degree)fi - angle of inclination to previous page of wind with the struc-ture (degree)B. The force of sea ice on the structureThe fdrce of sea ice on the structure can be expressed as follows:F = m.K K R .b.h1 2" cin which rn - shape factor, 0.9 for circular shapeK - local thrust factor 2.51

Kn - contact factor 0.45R - ultimate compressive strength of sea ice 150t/m 2b - width of structure facing the ice (m)h - ice thickness (m)By comparing the above two formulas, it can be know that when P7F, icebreaks, When PC F, ice accumulates.During the early stage of freezing, the ice usually breaks near the platform.As the temperature drops, the ice will increase in thickness, leadingto the accumulation of ice. This time, due to the small size of theice blocks, it will have no sufficient driving force. The ice will mainlybreak due to bending, causing little menace to the platform.3.2 Range of Movement of sea iceBohai is of half day tide, its period is about six hours and the averagevelocity of flow is 1 knot. Assume the velocity of ice is equal to the velocityof flow and the width of sea ice is one nautical mile. Then the rangeof movement of sea ice will be 6 nautical miles, i.e. , the area of seaice acting on the platform is about six square nautical miles. Therefore,in the calculation of sea ice load on the platform, it is necessary to considerthe gydrology and the meteorology of the sea area of the platformand the possible range of movement of sea ice.The magnitude of sea ice force depends upon the driving force of seaice, while the magnitude of driving force depends upon the velocity offlow and the mass of ice block. For a certain mass of ice block, it mainlydepends on the velocity of flow. Hence, the position of water level formaximum ice load should be at half tide of maximum velocity of flow, insteadof high mean tide and no tide when the velocity of flow, is zero. Fora certain area, thickness and strength of sea ice, the magnitude of iceload depends upon the velocity of flow. As to the mechanical propertiesof sea ice, as determined by the rate of load application, it may not appearin the alternating sea ice load.4. PROBABILISTIC METHOD OF ANALYSISThe reliability analysis of structure based on probabilistic principlehas been widely used in the design of offshore structures. As the ice forceis determined by a full probabilistic method, not only the probabilisticdistribution can be used for the load in the reliability analysis ofstructure, but also the choice of ice recurrence period agrees with objec-

tive reality. Introducing the random distribution of thickness and strengthof ice, the long range probabilistic distribution of maximum static iceforce can be solved by statistical experimental method. (the so-called statisticexperimental method is the well-know Monte Carlo simulating method).This is an effective method to solve multi-variable random processproblems.After the samples of random process of thickness and compressive strengthof ice have been determined, they are put into the deterministic impactcomputing model, the sample values of ice force of ice force events canbe obtained. Finally, after the probabilistic statistic analysis of iceforce events, the long range probabilistic distribution of maximum staticice force acting on the structure can be obtained. Putting all the parametersinto the micro-computer, the ice force probability for differentrecurrence period can be obtained with satis-factory results. See simulatingprogram chart.41 Events/year 1IIn the following condition to calculate the static ice forcewith the ice force model41 Record yearly maximum ice force 1J-1 Is there any other event in the year 1-1 Is there any other simulating year 11[Probabilistic distribution of ice force 15. SOME SUGGESTIONS5.1 To provide the forecast at early stage by strengthening continuoussatellite monitor and picture analysis of ice in the sea.5.2 To strengthen the development of new type of transducers of ice forcefor field use (at present, the welding type strain gage, strain type pre-ssure box and calibrated pressure box are generally used).5.3 To strengthen the study of forecast of the change of stress and cm-pressive force in the process of ice growth around the platfm by a com-puter monitor system.

5.4 To strengthen the study of mechanical and rupture mechanical proper-ties of sea ice.5.5 To strenthen the study of the type of platform to resist ice.

REFERENCESWang Qin-Jian, A Analysing Method of Ice Load to Jacket Platform Bo-Hai, 1980, China.Zhu Jun-Sun, A Study of Ice Force to the Offshore Structres in Bohai.OTSC. 1983, China.Zhu Jun-Sun, The Design and Constuction of Jacket Platform, 1973,China.Ministry Communications, The Rual of Port Engineering Chapter 4. "TheLoad". 1987, China.National Dept. of Ocean, Procre of Bohai Sea Ice China.Maattanen, M., Stability of Self-exerted Ice-induced Structural Vibrations,POAC-1977.Langen.T., A General dynamic Analysis Program for Linear StructuresUset's Manna1 SINTEF, Norway, 1977.Carstens.T., Working Group on Ice Forces on Structures, CRREL REPORT,Norway, 1980.T.Ojima, Sane Considerations on the Designing of Arctic Structures,O M , 1986.Groasdale, K.R.,OTC. 1984.The Limiting Driving Force Approach to Ice Loads.Wane Qin-Jim, A Tentative View on Ice Load Applied on Jacket Platformsin Bohai Gulf POAC-83.Mottia. R. Prof. Finland. On the Analytic Solution of ce-indced Vibrationsin a Marine.Borthiwlk, Londom, England. Ice and Iceberg Contingency Planning andManagement for Offore Oil and Gas Operation.

AUTHORS INDEXAckley S.F.Andersson A.Andersson L-0.Arikaynen A.Axelsson K.Backman A.Bailey S.H.Baldauf J.Bales J.T.Barry R.G.Been K.Beletskiy V.Bergdahl L.Bjelm L.Bjorkenstam U.Blackmore R.Z.Bolsenqa S.J.Bruun P .Burak J.P.Carstens T.Cederwall K.Chen A.C.T.Chen X.Chersky I.Chiang K-N.Chin S.N.Christensen F.T.Clark J.I.Clement B.Colony R.Comfort G.Coon M. D .Croasdale K.R.Daerga P-A.DeFranco S.Dempsey J.P.Dickins D.Domaschuk L.Dorris J.F.Duthinh D .Duval P.Egging D. E .Eigenbrod K.D.Elfgren L.Engelbrektsson A.Eriksen K.Erlingsson B.Ettema R.Farmer L.D.208, 269671786962342V0l. 34 410011023103123V0l. 3885V0l. 3627V0l. 318818, Vol. 394331, 6947966814438209086384531331001V0l. 3123445758081991995 4648467, 481492225143943808, 983504896V0l. 310961053199300, 796, Vol. 3Frachetti R.Fransson L.Frederkinq R .M. 420, 575, 596Fulton R.E.908Gagnon J.J. Vol. 3Gartner R.V0l. 3Gjorup P.983Gladkov M.G. 518Goehlich D. 908Gold L.Gram K.G.Granberg H.B.GU Z.X.Haapanen M.E.Hanunarstrom L.Hassinen P.Haugan P.M.Haugum D.Hazel1 C.R.Hellmann H.Hemsley M.J.Holladay J.S.Holthe K.Horjen I.Horrigmoe G.Hsiung C.C.Huard G.Huther M.Hakansson B.Hagqstrom M.Jeffries M.O.Jensen H.Jensen 0.Ji X-H.Jin H.T.Jochmann P.V0l. 3681V0l. 31084975Vol. 3873V0l. 398331120810231042527694, Vol. 3Vol. 331111641164V0l. 37051032, 10631107V0l. 35371084V0l. 3Johannessen O.M. 1073, Vol. 3Johansen 0. 65, 1131Johansson B.Johnsen A.s.Johnson R.C.Jones S. J.Jordaan I.J.Julson A.Jussila M.Kaldjian M.J.Kankanpaa P.Kenyon R.Kheisin D.Knutsson S.Konuk I.Koskinen P.Kouhi J.Kovacs A.KO20 T.L.Kujala P.Lange M . A.Larionov V.Lau P.A.Lee G.C.Lensu M.Lepparanta M.Levit B.Lewis J.E.Li F-C.Li G-W.Li Z.Lindahl J.Lindberg K.

Lindgren M.Lindqvist G.Liu C-H.Liukkonen S.Lobanov A.Loset S.Love J.Lovis S.M.Lozowski E.P.LU M-C.LU Q-M.Lyck L.Lofquist B.Marklund S.Marshall A.R.Mathisen J.P.McKenna R.F.Menq G.Meyer A.Meyssonnier J.Mian F .A.Michel B.Miles M.W.Montemurro M.P.Murrell S.A.F.Myrhauq D.Nadreau J.P.Nelson L.T.Nordell B .Nord6n R .Nystrom B.Nystrom M.08Connell S.Ohlsson U.Olaussen T.Olsen K.B.Omstedt A.Oshima M.Ottesen HansenOverland J.E .Palathingal P.Palmer A.C.Pease C.H.Picard F.Pintur D.A.Poorooshasb F.Prodanovic A.Pilsson I.Rabinowitz P.Ralston T.D.Rasmussen E.B.Raven P.W.J.Reinhardt H.W.Richter-Menqe J.A.Riska K.Romaqnoli R.Ronninq B .Ruben R.Sackinqer W.M.Sammonds P.R.vol. 3N-E. 4537122591237122355861335468851001143V0l. 31180Sandkvist J. Vol. 3Sandven S.1073Sayed M.575, 596Schmidt L.R. 991Schreiber R.W. 143Shapiro L.H. 385Sharma S.S.289Shen W.537Sheng D-C .342Shields D.H. 648Sinqh S.K.420Skagseth 0. Vol. 3Skoqnes K.65Smith P.A.168Sodhi D.S.Vol. 3Soininen H. 764Sorensen K.A. 918Suanaenbera S. 453steh; L. ' 300, 705, Vol. 3Stephens M.J.stone M.Sui J.Sun Y.Sunder S.S.Svensson U.Sykes J.F.Takeuchi T.Tatinclaux J.C.Taylor B.J.Taylor E.Thiqer I.Thompson T.Timco G. W.Tryde P.TSOY L.G.Tunik A.L.3 Vabo H.Varsta P.Varvelli R.Veen C v.d.Vefsnmo S.Vincentsen L.J.Vinje T.Waeqter J.Wanq Q.J.Wanq S .L.Weeks W. F .Wei Y.Welsh J.P.Wessels E.Williams P.M.Winkler M.M.Woodworth-269 Lynas C.M.T.Wortley C.A.wu M.S.wu s.xu J., 1063 Yan D.Yu Y.8734082181084431671367, 586385774441001705Vol. 3420Vol. 3Vol. 3658896Vol. 315685231453178918606311Vol. 31991053Vol. 3638481133

Zakrzewski W.P. Vol. 3Zhagparovich Z .A. 953Zhang L.K. 1084Zhang M. 332Zhu J.X. 606Zimmerman T.J.E.Astrom L .873vol. 3

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