Mechanics of Impact Pile Driving - vulcanhammer.info

this document downloaded fromvulcanhammer.infothe website aboutVulcan Iron WorksInc. and the piledriving equipment itmanufacturedTerms and Conditions of Use:All of the information, data and computer software (“information”)presented on this web site is for general information only. While everyeffort will be made to insure its accuracy, this information should notbe used or relied on for any specific application without independent,competent professional examination and verification of its accuracy, suitabilityand applicability by a licensed professional. Anyone making useof this information does so at his or her own risk and assumes any and allliability resulting from such use. The entire risk as to quality or usability ofthe information contained within is with the reader. In no event will this webpage or webmaster be held liable, nor does this web page or its webmasterprovide insurance against liability, for any damages including lost profits, lostsavings or any other incidental or consequential damages arising from the useor inability to use the information contained within.Visit our companion sitehttp://www.vulcanhammer.orgThis site is not an official site of Prentice-Hall, Pile Buck, or Vulcan FoundationEquipment. All references to sources of software, equipment, parts, service orrepairs do not constitute an endorsement.

MECHANICS OF IMPACT PILE DRIVINGJERRY FRANK PAROLAB.S., University of Illinois, 1962M.S., University of Illinois, 1963THESISSubmitted in partial fulfillment of the requirementsFor the degree of Doctor of Philosophy in Civil Engineeringin the Graduate College of theUniversity of Illinois at Urbana-Chmpaign , 1970Urbana, Illinois

MECHANICS OF IMPACT PILE DRIVINGJerry Frank Parola, Ph.D.Department of Civil EngineeringUniversity of Illinois, 1970Impact pile driving was studied by utilizing longitudinalwave propagation theory as an analytical tool.Field data from piledriving jobs was used to establish the validity and usefulness of theanalytical techniques developed herein.The theoretical treatment of the dynamics of impact pile drivingincluded an analysis of both the force generated at the head of the pileand the response of the pile tip to a generated force pulse.A modelconsisting of a hammer system operating on the head of an infinitely longpile was used to determine both the pile force pulse and the transmit-tedenergy.The model was used to make a dimensionless parameter study ofthe factors influencing force and energy.The driver system consisted ofconcentrated masses for both the ram and the drivehead and an energy absorbingspring (both linear and nonlinear) for the hammer cushion.Soil and pile responses were investigated with respect to anarbitrary force pulse in order to assess the variables controlling pilepenetration and load capacity.Special emphasis is placed on soil andpile response at the pile tip; the soil model includes viscous damping,mass and an elast5.c-plastic spring.Characteristics of the hammer-pile-soilsystem as a whole aresummarized.Theoretical results using wave propagation theory are com-pared with both case histories and commonly used dynamic formulas.Cor-relation of wave analyses and field case histories are used to support theconclusion that wave propagation theory is the proper theoretical tool forpile driving analysis.

iiiThe writer would like to acknowledge Professor Y.T. Davisson forhis suggestions and guidance during the analysis of the data. ProfessorV. J. McDonald and Mr. J. Sterner are acknowledged for their effort andguidance offered during the programming and use of the analog computer.Acknowledgment is also extended to members of the writer'scommittee, Professors R. B. Peck and A. R. Robinson, for their suggestionsduring the preparation of this manuscript.

TABLE OF CONTENTSACKNOIIILEDGE~ENTS ..........................LIST OF TABLES . ..........................LIST OF FIGURES ..........................NOTA'TION ..............................Pageiiivivi ixiCIIAPTER1 . INTRODUCTION ......................1.1 Scope .......................1.2 Impact Pile Driving ................1.3 Single-Pile Analysis ................1.11 Purposes ......................2 . 'THE PILE IiAMMER AS A FORCE GENERATOR ..........2.1 Introduction ....................2.2 Basic Equations ...................2.3 Linear Cushion ...................2.4 Bilinear Cushion ..................2.5 Nonlinearcushion .................3 . PILE AND SOIL RESPONSE .................3.1 Introduction ....................3.2 Dynamic Behavior of Soils .............3.3 Basic Equations ..................3.4 Tip Response of Pile and Soil ...........3.5 Effect of Soil Resistance Along Pile Length ....

CHAPTERPage4 . CHARACTERISTICS OF HAMMER-PILESOIL SYSTEMAFFECTING PILE DRIVING BEHAVIOR ............ 1244.1 Introduction ..................-1244.2 Pile Hammer . ................... 1244.3 Pile ....................... 1384.4 Soil Resistance .................. 1554.5 Design Tool .................... 1644.6 Wave Equation Analysis VersusEner~Fomulas .................. 167CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH .... 1735.1 Conclusions .................... 1735.2 Suggestions for Future Research . ......... 179APPENDIX. .............A . REVIEW OF SINGLE-PILE: ANALYSIS 190B . ANALOG COMPUTER PROGRAM FOR FORCE GENERATOR ...... 225C . ANALOG COMPUTER PROGRAM FOR PILE TIP .......... 231

LIST OF TABLESTablePageIMPACI PILE-DRIVER DATA .................. 8TABULATION OF PILE IMPEDANCES AND PILE TYPES ....... 28A COMPARISON OF CUSHION STIFFNESSES FORIMPEDANCE MATCH AND LIMIT OF PEAK PILE FORCE 46.......ENERGY LOSS OF BILINEAR CUSHION . ............. 52EFFECT OF BILINEAR CUSHION ON PEAK PILEFORCE AND PULSE DURATION ................. 55TABULATION OF PROBLEMS INVESTIGATEDFOR NONLINEAR CUSHIONS .................. 58EQUIVALENT LINEAR CUSHION FOR PEAK PILE FDRCE ....... 71SUMMARY OF DYNAMIC TEST RESULTS . ............. 80PILE IMPEDANCE AND PILE TYPES FOR THE TIPMODEL INVESTIGATION . ................... 92INCIDENT FORCE PULSE AND ENERGIES FOR TIP MODEL ...... 95CASES INVESTIGATED FOR WAVE SHAPE EFFTCT ......... 105SOIL DAMPING AT OPTIMUM ENERGY TRANSMISSION . ....... 112CASES ASSOCIATED WITH SOIL SPRING QUAKX ANDSPRING FORCE DEFLECTION SHAPE . .............. 114COMPARISON OF WAVE EQUATION ANALYSIS ANDENERGY FORMULAS . ..................... 170TABULATION OF PILE ENERGY FORMULAS ............ 194INPUT AND OUTPUT- WAVE EQUATION ANALYSIS . ........ 213INPUT DATA FOR DIESEL HAMMERS ............... 216

LIST OF FICURESFigurePage'1.1 SCHE4ATIC DIAGRAMS OF IMPACT PILE DRIVERS . ........ 51.2 TYPICAL FORCE INPUT TO PILE HEAD ............. 101.3 EFFECT OF PILE FORCE PULSE ON PILE PENETRATION . ..... 122.1 MODEL OF FORCE GENERATOR ................. 182.2 PILE FORCE PULSE WITH AND 'JITHOUT HAMMER CUSHION ..... 212.3 DYNAMIC LOAD-DEFORMATION RELATIONSHIPSFOR KAMMER CUSHION .................... 222.4 FREE-BODY DIAGRAM OF FORCE GENERATOR MODEL ........ 242.5 SCHEMATIC OF PILE-HAMMER RESPONSE . ............ 292.6 ;PILE AND HAMMER RESPONSE FOR = 5'AND LINEAE CUSHION .................... 31IMPEDANCE RATIO FOR PILE-HAMMER SYSTEM .......... 33GENERATED PILE FORCE SUMMARY FOR LINEAR CUSHION ...... 37PEAK PILE FORCE VERSUS IMPEDANCE RATIO .......... 39RELATIONSHIP OF PEAK PILE FORCE WITH HAKYERCHARACTERISTICS AND PILE IMPEDANCES . ........... 141RAM VELOCITY AT IMPACT .................. li3PEAK PILE FORCE VERSUS PIIE IMPEDANCEFOR DIFFERENT RAM WEIGHTS . ................ 47TIME DURATION OF FORCE PULSE AS A FUNCTION OFH W R AND PILE CHARACTERISTICS .............. 50EFFECT OF BILINEAR CUSHION ON PILE FORCE ......... 511REAL AND ASSUMED CURVES FOR PINE PLYWOOD CUSHION ..... 59ASSUMED PINE PLYWOOD CUSHIONS FOR DIFFEFtENT HMRS .... 60REAL AND ASSUMED CURVES FOR ALUMINUM-MICARTA CUSHION ... 61ASSUMED ALUMINUM-MICARTACUSHIONS FORDIFFERENT HAMMERS ..................... 62

viiiFigurePage2.19 COMPARISON OF PINE PLYWOOD AND ALUMINUM-MICARTA.CUSHIONS FOR VULCAN NO. 1 HAMMER ............. 642.20 PEAK PILE FORCE FOR PINE PLYWOODAND ALUMINUM-MICARTA CUSHIONS. .............. 652.21 GENERATED FORCE PULSE FOR VULCAN NO. 1 HAMMERWITH ALUMINUM-MICARTA OR PINE PLYWOOD CUSHION. ...... 672.22 SCHEMATIC COMPARISON OF EQUIVALENT LINEAR CUSHIONSTIFFNESS WITH RESPECT TO PEAK PILE FORCEAND TIME DURATION. 74....................3.1 PILE ANE SOIL TIP MODEL. ................. 783.2 LOAD-DEFORMATION CHARACTERISTICS OF SOIL MODEL ...... 833.3 FREE-BODY DIAGRAM OF PILE AND SOIL TIP MODEL ....... 893.4 TIME DURATION OF PULSE LENGTH. .............. 943.5 EFFECT OF SOIL MASS ON NET TIP DEFORMATION ........ 993.6 COMPARISON OF REFZECTED FORCE PULSE RESPONSEFOR DIFFERENT SOIL MASSES. ................ 1003.7 NET SET RESPONSE OF THE PILJ! TIP FOR PILEIMPEDANCE OF 3000 lbs-sec ................. 102in.3.8 EFFECT OF WAVE SHAPE ON PILE PENETRATION FORPILE IMPEDANCE OF 3000 lbs-sec .............. 106in.3.9 REFLECTED FORCE PULSES FOR CASE 3-B WITHPILE IMPEDANCE OF 3000 lbs-sec ............. .I10in.3.10 EFFECT OF SOIL QUAKE ON PENETRATION FORPILE IMPEDANCE OF 1000 Ibs-sec .............. 115in.3.11 EFFECT OF SOIL QUAKE ON PENETRATION FORPILE IMPEDANCE OF 3000 lbs-sec/in. ............ 1163.12 EFFECT OF SOIL QUAKE ON PENETRATION FORPILE IMPEDANCE OF 6000 1bs-sec/in. ............ 1173.13 EFFECT OF SOIL SPRING FORCE SHAPE ONPILE PENETRATION ..................... 118

Pi gurePage3.14 EXAMPLE PROBLEM FOR THE EFFECT OF SOILRESISTANCE ALONG PILE ................... 1203.15 EFFECT OF QUAKE AND DAMPING ALONG THE PILEON PILE TIP FORCE ..................... 1234.2 FIELD STUDY ]..EFFECT OF INPUT ENERGY ON PILE RESPONSE . .. 1304.3 EFFECT OF GENERATED FORCE PULSE ON PILERESPONSE FOR A GIVEN ENERGY LEVEL ............. 1324.4 LACK OF PILE ENERGY M PRODUCE EFFICIENTDRIVING FOR HIGH PILE PEAK FORCES ............. 1344.5 FIELD STUDY 2 . EFFECT OF HAMMER CUSMIONON PILE DRIVING ...................... 1374.6 EFFECT OF PILE IMPEDANCE ON DRIVINGCAPABILITY AT DIFFERENT ENERGY LEVELS 140...........4.7 FIELD STUDY 3 . EFFECT OF PILE AREAON DRIVING CAPABILITY ................... 1424.8 . FIELD STUDY 4 . CONCRETING PIPE PILES TO IMPROVEIMPEDANCE AND ACHIEVE THE DESIRED CAPACITY ........ 1434.10 EFF'ECT OF DIFFERENT PILE IMPEDANCE WITHINPILE LENGTH 148........................4.11 FIELD STUDY 6 . EFFECT OF DAMAGE ON PILE DRIVING ..... 1504.12 EFFECT OF PILE LENGTH ON DRIVING ............. 1524.13 EFFECT OF PILE LENGTH ON FORCE PULSE ........... 1544.14 FIELD STUDY 7 . EFFECT OF THE PERCENTAGE OFPOINT BEARING RFSISTANCE 157.................4.15 EFFECT OF SOIL QUAKE ON PILE RESPONSE ........... 1594.16 EFFECT OF SOIL DAMPING ON PILE RESPONSE .......... 1614.17 FIELD STUDY 8 . USE OF WAVE EQUATION ANALYSISIN DESIGN FOR SOIL EXHIBITING FREEZE ........... 1634.18 WAVE EQUATION ANALYSIS OF PROPOSED 12 WF 106 PILE ..... 166

XPageIMPACT MODELS . ...................... 199HAMMER-PILE-SOIL SYSTEM . ................. 200VARIABLE FORCE PULSE FOR A GIVEN ENERGY INPUT . ...... 203SMITH'S MATHEMATICAL MODEL ................ 206FORCE TRANSMISSION IN PILE MODEL ............. 208COMPARISON OF GENERATED PILE FORCE PULSES . ........ 211RELATIONSHlP BETWEEN HAMMER EFFICIENCY AND SPEED ..... 214IDEALIZED FORCE-TIME CURVE FOR A DIESEL HAMMER ...... 218TYPICAL RESULTS OF THE WAVE EQUATION ANALYSIS ....... 221SIMPLIFIED PILE MODEL ................... 223ANALOG COMPUTER PROGRAM FOR FORCEGENERATOR ........ 226ANALOG COMPUTER PROGRAM FOR PILE TIP MODEL ........ 232

SymbolUnitsdimensionless impedance coefficientcross-sectional area of pilecross-sectional area of concrete pileeffective area of pistoncross-sectional area of steel pilecross-sectional area of wood pilearea of cushionaccelerationdimens'ionless weight coefficientrecoverable deformation of drivehead andpile headrecoverable deformetion of pile.recoverable deformation of soilslope of a regression line (dimensionless)intercept of a regression linedeformation of spring (m) at time interval (t)pile energy coefficientram displacement coefficientpile force coefficientpeak pile force coefficientpeak pile force coefficientpile head displacement coefficient

SymbolUnitsC1C2arbitrary coefficientsarbitrary coefficientsc0viscous damping at soil tipc velocity of wave propagation L/T~(rn,t) displacement of mass (m) at time interval (t) L~'(m,t) plastic displacement of soil spring (m) at time Linterval (t)EtEiECtransmitted energy to the pilekinetic hammer energy at ram impactsecant modulus of hammer cushionE t rated hammer energyrE~E~E~reflected energy at pile tiptransmitted energy at soil tip.incident energy of pile force pulseFT/LE pile modulus of elasticity F/L~e coefficient of restitution 1-etemporary set representing lossese fe thammer efficiencytransmission efficiencyF(t) force pulse input into top of pile FF(m,t) forceininternalspring (m) attimeinterval(t) F-F force applied by theoretical steam or air pressure Frequired at hammer

xiiiSymbolUnitspile forcepeak pile forcereflected pile force pulseincident pile force pulsearbitrary functions representing force wavesarbitrary functions representing force wavesacceleration of gravityheight of ram fall, ram strokeimpedance ratioviscous damping factor for soilviscous damping factor for soil along the pile'slengthviscous damping factor for soil tip.modified viscous damping factor for soilpile spring stiffness of mass (m)T/LT/LT/LF/Lsoil spring stiffness for mass (m)elastic cushion spring stiffnessloading stiffness of bilinear hammer cushionunloading stiffness of bilinear hauuner cushionequivalent linear loading stiffness for peakpile forceequivalent linear loading stiffness for timedurationequivalent linear loading stiffness for recommendedsecant modulusF/LF/LF/LF/LF/L

SymbolUnitskssoil spring stiffness at pile tipAL segment length L9. cushion stack length LL length of pile Li, length of pile, measured from head to center of Ldriving resistanceM pile mass FT2/Lm 1ram mass FT*/Lm 2drivehead mass FT~/Lm soil mass at pile tip FT~/Lmass number as used in Smith's lumped mass-spring 1modelN power of instantaneous pile velocity 1coefficient of restitutionmean pressure of steam or airsoil quakequake for soil along the pile's lengthquake at soil tipstatic ultimate soil resistance and pile capacityload carried by pile point resistanceload carried by pile frictionultimate soil resistance at pile tipF/ Lfi0total soil resistance with respect to time (t)static ultimate soil resistance as determinedby TomkoF

SymbolUnitsXVR(m,t)RstaticRdynamicrsTttotal soil resistance on mass (m)static soil resistancedynamic soil resistanceroots of an equationnet set per hammer blowpsuedo ram periodreal timetime interval number as used in Smith's lumpedmass-spring modelselected time duration of force pulsetd0A tuVapproximate time pulse durationtime when velocity at top of pile is zerotime intervallongitudinal displacement of bar in x directionparticle velocity in pilev~v~reflected particle velocity in pileincident particle velocity in pileV ram impact velocity0? velocity of rigid body pilev(rn,t)WWlW2velocity of mass (m) at time interval (t)soil weight at pile tipram weightdrivehead weight

, SymbolUnitsweight of mass (m)weight of pilerm co-ordinate in nondimensional expressionsfirst derivative of ram co-ordinate innondimensional expressionsFFLLsecond derivative of ram co-ordinate innondimensional expressionsdrivehead co-ordinate in nondimensionalexpressionsfirst derivative of drivehead co-ordinate innondimensional expressionssecond derivative of drivehead co-ordinate innondimensional expressionspile tip displacementram co-ordinateram velocityram accelerationdrivehead co-ordinatedrivehead velbcitydrivehead accelerationpile head co-ordinatedimensionless timemaximum free-tip pile displacementmaximum free-tip displacement for a sine pulsepile mass per unit volumepile impedance

CHAPTER 1INTRODUCTION1.1 Scope .The purpose of this dissertation is to investigate analyticallythe mechanics of impact pile driving with the goals of increasing theability of the engineer to design a pile foundation and aiding the con-tractor in proper selection of eqflipment.These goals will be accom-plished by considering the behavior of single piles.The design of all pile foundations depends upon load capacityand settlement criteria as well as feasibility of installation. Therefore,the ultimate goal is a general understanding of pile-soil interactionduring installation and the interaction of superstructure, pilesand soil after construction.With the exception of a few isolated in-stances, group behavior has been physically difficult and financiallyimpossible to investigate in detail. As a consequence, an understanding- of single-pile behavior plus theory, model studies and judgment re-garding the relationship between a single pile and a pile group must berelied on in order to produce an acceptable design.The dynanics of driving piles with impact hammers is investigatedby considering both the force pulse generated at the head of the pileand the response of the pile tip to a generated force pulse.It ispossible to obtain significant results by studying incident waves onlyat both the pile head and pile tip; an analytical model using an in-finitely long pile serves to eliminate reflected waves from the far end.

-A model consisting of a hammer system operating on the head of an in-finitely long pile is utilized for determining both the pile force pulseand the transmitted energ,-.The driver system consists of concentratedmasses for the ram and drivehead and an energy absorbing spring (bothlinear and nonlinear) for the hammer cushion.Next, soil and pile response is investigated with respect to anarbitrary force pulse in order to determine the characteristics of pile-penetration and load capacity.Special emphasis is placed on soil andpile response at the pile tip; $he soil model includes viscous damping,mass, and an elastic-plastic spring.The characteristics of the hammer-pile-soilsystem as a whole aredescribed after the elements of the mechanics of impact pile driving arestudied.Theoretical results using wave propagation theory are comparedwith both case histories and commonly used dynamic formulas.Correla-tions of wave equation analyses and field case histories are used toinvestigate the validity and usefulness of the wave propagation conceptas the proper theoretical framework for pile driving analysis.-The mechanics of pile driving deserves investigation for the en-lightenment of both foundation engineers and pile contractors.The foun-dation engineer is concerned with the performance of a pile foundation.In an effort to predict pile performance, the engineer has allocatedto pile drivers a rather unique dual role, that of a driving tool andthat of a measuring instrument.Although the pile driver's primaryrole is pile installation, the pile driver is also used as a measuringinstrument, i.e. the resistance to penetration in terms of hammer blowsper inch is used as a measure of the pile's ability to support load.

3Of course, the engineer must be able to predict similarities and differencesbetween pile behavior during driving and under static load inorder to make the pile driver an effective measuring tool.With an understanding of the mechanics of pile driving in conjunctionwith experience, the pile contractor can install the optimumpile foundation, i.e. the one with the lowest cost providing the desiredfoundation performance.The cost of the pile foundation includes not-only the amount of pile material needed, but also the driving expensewhich involves driving time, pile damage, and replacing damaged or in-adequate piles.The pile driving contractor should be able to choosethe proper equipment along with the pile that, as well as being inaccordance with the technical specifications, can be installed in themost expeditious and economical manner.The foundation engineer must also have a working knowledge ofpile installation in order to write satisfactory and rational specifi-cations.With an understanding of the mechanics of pile driving, theengineer can avoid unnecessary restrictions in the specifications to.- prevent a cost burden on the pile contract. The restrictions in thespecifications can include limitations on hammer size, pile type andpile dimensions.1.2 Impact Pile DrivingOne of the oldest and simplest methods of driving a pile is bythe use of a drop hammer.Drop hammers, now rarely used, were preva-lent before the twentieth century.The disadvantage of the drop weighttechnique is the long driving time because of the time consumed be-

- tween blows to raise the ram by power winching. In order to achieve anincrease in pile penetration rates, hammer development has been directedtoward applying the driving energy at a faster rate.A faster enerarate is associated with a larger number of hammer blows supplied in aperiod of time (blow rate).The desire for faster driving rates led to the single-actingsteam hmer. The Vulcan single-acting steam hammer introduced in 1887-. (~ulcan Iron Works, 1927) is the forerunner of modern impact hammers.Tn-stead of being raised by a power winch, the ram is lifted by steam pres-sure which is regulated to apply an upward force on a piston connectedto the ram.The valving mechanism exhausts steam at the top of strokeand allows the ram to fall by gravity through a stroke h before impact.A schematic of both the drop and single-acting hammers is presented inFigure l.la.The major components of the pile hammer are the ram, ham-mer cushion and drive head. The ram with an impact velocity, V im-0'parts the energy and force pulse to the pile through the hammer cushionand drive head.+ Several years after development of the single-acting hammer,double-acting and differential hammers were introduced to increase theblow rate.Hammers of these types not only use pressure to lift the rambut also increase the downward acceleration of the ram by adding forceto the gravity force (~i~ure l.lb).Differential and double-actinghammers commonly have half the stroke and twice the blow rate of thecomparable single-acting hammer.With the development of portable air compressors, the substitutionof air pressure for steam pressure has now become comon practice.The

PistonAir orAir or SteamPressureWinch(Drop Hammer)Steam PressurePiston...Compressed Air(optional)[HammerHeadPilePile- Drop and Single- Differential and Double- DieselActing Iiamners Acting Hammers Hammers\A;i/V(a) (b (c)Figure 1.1 SCHEMATIC DIAGW OFIMPACT PILE: DRIVERS

-use of air pressure is accomplished without change in the hammermecha-nism because operating pressures of both air and steam are commonly 100to 120 psi.Recently, a hydraulically powered differential hammer hasbecome operational with the ports sized to be consistent with fluid pressuresof 3000 to 5000 psi.The most recent aevelopment in impact hammers is the dieselpowered driver introduced in Germany prior to World War 11. The inte--grally powered diesel hammer is currently popular because it requiresless equipment and manpower than steam or air hammers.The diesel ham-mer utilizes the combustion of diesel fuel to lift the ram.The hammerram serves as the piston, compressing air on the downward stroke afterthe intake valve is closed.The atomized diesel oil explodes upon therise in temperature of the compressed air which results from the ramdrop.Impact of the ram on the anvil is approximately simultaneous withcombustion of the diesel oil; therefore, the force driving the anvil isa combination of combustion and impact (Figure 1.1~). The combustion-force also drives the ram upwards to the top of its stroke. The dieselhammer can be open-ended at the cylinder top or closed-ended with anair chamber (bounce chamber). On the up stroke, air is compressed inthe bounce chamber and thus shortens the stroke and increases the blowrate.Vibratory pile drivers are also in common use, but they are notimpact hammers.They produce a combination of axial oscillations andstatic thrust as discussed by Smart (1969).Impact hammers are normally rated or sized according to theequivalent potential enera available at the top of their stroke.

. Energy ratings for drop or single-acting hammers are readily defined;e.g. E = W h where E is the rated h&er enera, W1 is ram weight andr 1 rh is the stroke (height of ram fall). However, energy ratings for double-acting or differential hammers must also account for the effect of the-downward thrust in addition to gravity, e.g. E = W h + &I where F isr 1the force applied by the theoretical steam or air pressure required atthe hammer.- Diesel hammer ratings are complicated by the unknown effective-ness of the combustion force and the variability of the ram stroke underfield conditions; therefore, confusion exists regarding the rating ofdiesel hammers.. Rated energy for open-end diesel harmers is determinedby the maximum ram drop.For closed-end diesels, the ratings are estab-lished from the equivalent stroke which is the actual stroke plus anequivalent increment of stroke based on the energy stored in the bouncechamber.The common range in rated energies per blow for impact drivers isfrom 5,000 ft-lbs to '120,000 ft-lbs; the most common values lie between- 15,000 ft-lbs and 40,000 ft-lbs. For offshore driving, there is -a needfor larger hammer sizes than are now available.Commonly used impacthammers have blow rates varying from 40 to 200 blows per minute whereasthat for drop hammers is 5 to 20 blows per minute.Single-acting andopen-end diesel hammers commonly operate at 40-60 blows/minute and dif-ferential, double-acting and closed-end diesel hammers at 80-120 blows/minute.Pile-driver data for the hammers currently available in theUnited States are given in Table 1 .l.

-Tlblc 1.1IWACT PIE-DRIVER DATAstro,.ItRstCd Ha** B~WS R.tc6 Wclght 'rot* ~ , ~ ~ ~ t h A.S.H.E. Stem SfreEnerg,'. oT per Energ,' Striking Velght, of AIr Boiler orlilr, or Ratingrt-lb ~mer sire ~lp ~n in. parts. lb lb ti-r cn. H.P.iloac. in.Enera over 100.000 R-lbI80,OCO vuican 060 single-act. 62 36 60.000 121.000 18'6.1 L626 7110130.000 HcKlcrnau>-Terry S-LO Single-act. 55 39 bO.OOO 96.000 16'0'' ..130 (2)L 103.900120.0~0 Vui"&"375 150 L 72.100OLO Slnnle-sct. 60 36 LO.OOO 87.500 11'11" 31100 531113.L78 Supcr-Yuleu, LOOC Dlrlerenti~l 100 16 112 L0,000 83.000 16'9" 1659 700120 (2)369.300150 5 61.Loo18.750 Vulean 016 Sln~,le-act. 60 36 16.250 30,250 11.6'' 1290 210110-6B,l5O Ra,mond3 28.1000000 Siniile-act. b6 39 15,000 23.000 -- ..LL.500 ~cbe 85lL0 2 112 21,000K22 Diesel L5-60. 98 b.850 10.600 13'h" -- .. -. -. 1b.100L2.000 "*CanOIL Single-act. 60 36 IL,WO 27,500 1L.6" 1282 200110 3 2L,200b0.600 ~awcnd 000 Slngle-act. 50 39 12.500 21,000 15'7" --70 135 2 112 22.50039.800 &lnc.E-22 ~lcael L2-60 "la b.850 10,0511 12101/2. -- .. .. ..37,100 HeYicrnnn-Terry SlL Sinillc-act. 60 32 1b.000 31.600 iL.10'' 1260 190 13,900100 3 23.00016.000 Supr-vuicm lbOC Dlrrercntlai 103 15 112 111.000 27.98b 12'3" 11.25 211iL0 3 22.00032.500 McKlcrnan-Term 810 Sinsle-act. 55 39 10.000 22,200 li'l" 1000 1b080 2 112 18.00032.500 Yule-010 Slngle-act. 50 39 10.000 18.150 15.0'' 1002 151105 2 112 18.00032.500 Rwmnd00 Single-act. 50 39 10,000 18.500 15'0'' -.32.000 HcKlernen-Terry DE-LO Dicecl L8 96 6,000 11,215 15'0" -- 25 125 2-- .. -- 18,00030.225 YUCM OR slnglc-.ct. 50 39 9.300 16.165 15'0" 1020 -. ll.3nO100 2 112 16.800- .L3 11620393916 112nla3918nlrr9698-.19;200 supr-vuicon18.250 Link-Belt0 Double-act. 110 261183 Double-act. 95 1906 Single-act. 60 3665c ~irrcrentlal 111 15 112LbO Mesel 86-90 36 718S5 Single-act. 60 3916,250 n ~ ~ i c ~ ~ - ~ ~ ~ ~16.0~ ~ ~ l DE-20 u me~cl ~ ~ 48 ~ 96 - ~ ~ ~ ~C5 Compound 110 185OC MCCcrcntial 120 15 1125Y Mlfcrential 120 15 1121 Single-act. 60 36312 Diracl ]DO-105 30 7181083 Double-act. 105 191 Double-act. 125 2116.000 kern^-^^^^.I5 ,100 sup=-vulcm15,100 Vvlcm15 .OOO VUCM15.000 Link-Belt13.100 1BKiernm-Terry12.125 Uoion9.000 H C K ~ ~ ~ ~ ~ - T ~ ~ ~9,OW NeKlcrnen-Term8,800 McKlernur-Terry8.150 YEKIemn-T~rry8.28C Union8,100 Link-BeltEnergy 5.000 To 10.000 m-lbEnere Under 5,QOO n-lb4.900 Yvlcm COW00 Dillerentlal 238 10900 5.000 6'.9" 5803;600 mim3 DouBlc&et. 160 lb15 18 1 112700 h.700 6'1" 3001,9003.600 ilc~iernm.~~~~ 1 DouBle-et. 225 9112-800 5.000 6.1" L ~ O 1 .llL 1.600LL5 mfon 6 Double-set. 3b0 763 loo I 1121W1,700386 m1.m COHlOOA Dlffcrcntial 303 6 910 3'10" 15 - 1001003lb 210356 UeKlernul-Rrry 3 Double-set. boo 5 3/L 68786675 b'lo"L12*110 11 8 60 1 200320 U~ton 1A Double-wt. LOO 6100 1801505'40 3'1" 10 - 100-3lb 160E, - =at.a .t=i**ng energ,' in foot-pound-; w1 - reisbt o< .triung parts ioRun vc'sbta or bop b-er. vul Imn 5W to 10.~0 ib. rlth rui.b~. .tio*ca therecore vul.bl.-. ..

Rated hammer energy is only an index to hammer capability.Theactual energy available at impact is more indicative of hammer capabilitythan rated energy; the energy at impact is less than the rated energybecause of mechanical losses due to friction, pre-admission of steam orair, etc.. .The hammer kinetic energy at impact may be expressed as1 W1E. = - - V where V is the ram velocity at impact and g is the ac-1 2 g o 0celeration of gravity. The ratio of energy at impact to rated energy isE.1defined as hammer efficiency, i.e. e = - x 100%. Some widely acceptedbut undocumented hammer efficiencies are given by Chellis (1961) asfollows :fE7-Hammer Type Hammer Efficiency, ef, %DropTrigger ReleaseWinchSingle-ActingDouble and Differential Acting 75 to 85Diesel 100The dynamic response of ram, anvil, hammer cushion, drive headand pile determines how much of the energy available at impact is trans-mitted to the pile. The efficiency of transmission may be defined asEte = --x 100%where E is the energy transmitted to the pile. A fewt E. t1field measurements and calculations indicate transmission efficienciesof 50 to 90 percent should be common.A typical force pulse delivered to the pile head by an impacthammer is shown in Figure 1.26~. Durations of 20 to 50 milliseconds arecommon with pile peak forces in the range of 100 to 1000 kips.As noted

I+-1 0.05 SecondsTime(a) Single Hammer BlowPile at RestEynami cForce r(.- Z 1 \ 1I I t0.75 SecondsTimeHammerWeight(b) Several Hammer BlowsFigure 1.2TYPICAL FORCE INPUTTO PILE HEAD

in Figure l.2b, pile oscillations are damped very quickly and one hammerblow has no effect on succeeding blows; therefore, the mechanics of im-pact pile driving may be investigated with respect to the events associatedwith a single impact.Blow rates of 300-600 blows/minute would be re-quired before piles with typical lengths could be kept in steady motionmaking it necessary to analyze a sequence of blows.For a given hammer-pile-soilsystem, maximizing the energy trans-- mittcd to the pile is the first step towards maximizing pile penetrationper blow.However, the transmitted energy must also be in an acceptableform (force pulse shape) in order to maximize pile penetration.Forexample, consider the point bearing pile shown in Figure 1.3a and thegenerated force pulse versus ultimate tip resistance R as shown inFigure 1.3b.Pile penetration will occur when the pile peak forcegenerntcd by the impact hammer exceeds the ultimate soil resistance atthe pile tip.In fact, if the tip resistance is rigid-plastic, pene-tration will occur ffi long as the peak force exceeds 0.5 R, as will beshown later.If the peak force is less than 0.5 R, then only enough.-soil resistance is mobilized to counteract the pile force and no netixovemcnt of the pile point results even if the transmitted pile energyhas been maximized.For the friction pile (Figure 1.3c), the pile force pulse isettenuated with depth by the soil resistance along the pile's length.Because of attenuation, very low peak force may reach the pile tip; however,no force is necessary to overcome the tip resistance.Pile penetration is controlled by the magnitude and duration ofthe generated force in the pile with respect to the response ofthe soil.

RSoil TipUltimate Point Bearing FrictionResistance Pile Pile(a) (b) (c)Figure 1.3 EFFECT OF PILE FORCE: PULSEON PILE PENEEJLTION

-The ram-cushion-drivehead-pile sysr,em controls the force pulse generatedin the pile head.Therefore, a pile hammer may be considered to be aforce pulse generator.1.3 - Single-Pile AnalysisCurrent methods of analyzing a single pile can be grouped in-two general categories, namely, static and dynamic.A review bf theseanalytical methods is given in Appendix A; only a brief summary of theconcepts is presented here.A static analysis of pile point bearing and skin friction israther limited in scope because information is obtained with respectto load capacity only.No information is obtained on driving characteris-tics.However, a static analysis is a valuable tool for determinationof driving characteristics when used in conjunction with a dynamicanalysis, as will be shown later.A dynamic analysis is the proper tool to investigate the.-mechanics of impact pile driving.analysis that differ in concept:However, there are three methods of(1) Dynamic ener@y formulae based onsimple energy considerations, probably the oldest method of pileanalysis; (2) Wave equation analysis based on one-dimensional wavepropagation; (3) A method utilizing measured force and accelerationat the pile head.In all cases, dynamic analyses are used to predictstatic load capacity.In order to use a dynamic analysis to predict static load ca-pacity, a knowledge of the relationship between static and dynamic soilresistance is necessary.Dynamic versus static behavior is complex and

-can be determined only qualitatively.Correlation studies of dynamic andstatic soil resistance are difficult because of the infinite variety ofsoil profiles as well as the variety of single soil properties.Addi-tional complicating factors that affect soil properties are the pileshape, pile volume and method of pile installation.The experience andjudgment of the engineer in selecting appropriate soil data input fordynamic analysis are critical to the success of the analysis.-Several examples of soil type.wil1 help illustrate the soil be-havior encountered.For dense and submerged cohesionless soils, eitherfine or coarse-grained, dynamic resistance may greatly exceed staticresistance (~ang, 1956 and Yang, 1970) because of temporary negativepore pressures due to rapid dilation of the soil structure.The oppositeeffect is observed in loose cohcsionless soils where pile driving causestemporary positive pore pressures which reduce soil resistance.Conse-quently, the dissipation of excess pore pressures results in a gain orloss of strength with time after driving.For dense soils, dynamic re-.-sistance is greater than static resistance, whereas dynamic resistanceis less than static for loose soils. Pile driving disturbance of co-hesive soils produces the same effect as in loose cohesionless soil,namely, lower dynamic soil resistance than subsequent static soil resistance.In this thesis, special emphasis is placed on the wave equationanalysis of pile driving, although other methods are also discussed inAppendix A.Recent investigations have shown that analyses involvingimpact and wave transloission theory represent the best techniques nowavailable.The wave equation analysis provides a theoretical framework

within which all practical pile driving experience can be properlyassessed.The investigations reported in this thesis are based on thetheory of wave propagation and the behavior of single piles driven withpure impact hemmers.Diesel hammers are considered beyond the scope ofthis dissertation.-1.4 PurposesGenerally, the purpose of this dissertation is to investigateanalytically the mechanics of pile driving.More specifically,' thisdissertation covers :1. The parameters controlling the force pulse deliveredto the head of a pile, both with respect to maximizibgenergy transmission and maximizing pile penetration(Chapter 2).2. Soil resistance parameters governing pile penetration(Chapter 3).3. Characteristics of pile hemmer, pile and soilresistance affecting pile driving behavior, namely,pile penetration and capacity (Chapter 4).14. A comparison of results from wave transmission theorywith case histories and also with commonly useddynamic formulas (Chapter 4).The foregoing purposes are accomplished by independent idealized studiesof the parameters controlling the generated force pulse in the pile head.and the soil resistance parameters at the pile tip.The behavior of

the hammer-pile-soilsystem as a whole is then summarized and explainedusing both the idealized theoretical studies and the wave equation analy-sis; case histories are used to support the summary.The wave equationanalysis is a numerical technique applied to a lumped mass-spring model;it is an analysis of the entire system, but it does not facilitate anunderstanding of the controlling parameters.It will be shown that theidealized studies in Chapters 2 and 3 lead directly to pile design andhmer selection criteria.

CHAPTER 2THE PIJX HAMMER AS A FORCE GENERATOR2.1 IntroductionThe objective of this chapter is to investigate the effects ofthe various parameters controlling the force pulse delivered to the pilehead, with respect both to maximizing energy transmission and maximizin(:-pile penetration. The shape of the generated force pulse and the energyin the pile head are the decisive factors for overcoming soil resistanceand achieving maximum pile penetration (net set per hammer blow).A pro-.cedure will. be developed for matching the driving equipment and pile soas to impart maximum energy to the pile head; however, as maximum transmittedenergy alone does not guarantee the best hammer-pile combinationfor maximizing pile penetration, the shape of the force pulse is alsogiven consideration.In ordcr to establish a basis for investigating driving equipment,only the generated force pulse will be considered; no extraneous effectswill. be included.The effects of wave reflections will be considered inthe following chapter after the basis of the generated force pulse isestablished.The model of the force generator used herein is shown in Figure2.1. The driving mechanism consists of point masses for the rm anddrivehead, whereas the hammer cushion is assumed massless.Several dif-ferent approximations are made regarding the stress-strain characteris-tics, including linear elastic, linear inelastic and nonlinear inelastic.

1 Vo - Initial Velocity at ImpactConcentrated MassPile Hammer(corce - Generator)ILinear Elastic, LinearInelastic, or Nonlinear~nelestic.DriveheadConcentrated MsssPilePCAInfinite in Len&hPile Impedance = pcAJ,=m(No Reflections)Flgure 2.1MODEL OF FORCE GENERATOR

The ram and drivehead are for practical purposes infinitely stiff corn-, pared to the hammer cushion; therefore, the assumption of lumped massesis justifiable.The force generator operates on the head of an infinitelylong pile which is considered to have distributed mass and elasticity.It will be shown that pile force is a linear function of particle velo-city.The ratio of pile force to the induced velocity in the pile isthe mechanical impedance of the pile (~olsk~, 1963). The pile force can- be written:F = (PCA)V (2.1)whereP = force in the pileV = particle velocity in pilepcA = pile characteristic impedance hereafterreferred to as pile impedancep = pile mass per unit volumec = J,velocity of wave propagationA = cross-sectional area of pileE = pile modulus of elasticity.- Equation 2.1 can be readily derived from the classical one-dimensionalequation of wave propagation (Timoshenko and Goodier, 1951).The model of the infinitely long pile (~igure 2.1) can be usedto investigate the force pulse and energy transmitted to the pile headwithout consideration of reflected force waves from the pile tip.Theeffect of pile tip response on the generated force pulse will be presentedin the following chapter.The input parameters of the force generator include the ram anddrivehead weight, load-deformation relationship of hammer cushion, im-

pedance of the pile and initial velocity of ram at impact.Ram impactvelocity is a function of rated hammer enera and hammer efficiency andnormally ranges from 9 to 15 ft/sec for typical hammers.Experience has shown that a hammer cushion is required to protectthe hmer from damage; however, the inclusion of a cushion alsoaffects the force pulse shape and energy transmitted to the pile.-Housel (1965) showed the effect of a cushion on the generated force pulse.As shown in Figure 2.2, the peak force and pulse shape are grosslyaffected by cushion material.Wood, one of the first materials to be used as a cushion, is incommon use today.Recently, alternating thin discs of aluminum andmicarta have become prominent.Other types of cushion materials such aswire rope, asbestos, etc. are employed in practice; however, the aluminum-micarta and wood cushions represent common limits in load-deformationcharacteristics.The aluminum-micarta assembly is a stiff spring, whereas.-the wood cushion corresponds to a soft spring.The spring constants for various types of cushion blocks are obtainedfrom test results. A typical shape of the dynamic load-deformationcurve for a cushion is shown in Figure 2.3a.The difficulty encounteredin solving analytically for the real load-deformation characteristicswarrants the use of an idealized load-deformation curve (bilinear) asshown in Figure 2.3b.The idealized shape can be readily used where aloading stiffness, kt, can be based on typical values of secant moduliand the unloading stiffness, kU, can be based on typical values of thecoefficient of restitution, e (see Figure 2.3).The unloading curve isfollowed after the peak load is generated; the unloading slope is related

800Force,lkips 4000o 20 40 60 o 20 40 60Time, millisecondsAfter House1 (1965)Figure 2.2 PILE FORCE PULSE WITH AND WITHOUT lWMKER CUSHION

LoadnDeformationa) Real CurveLoadNote : -e = Coefficient ofRestitutionArea BCDArea AEXCDeformationb) Idedized CurveFigure 2.3 DYNAMIC MAD-DEFORMATION RFLATIONSHIPS FOR HAMMER CUSHION

k.to the loading slope and coefficient of restitution, i.e. k = -u 2eThe coefficient of restitution accounts for the energy loss in thecushion material.The force generator will be investigated in terms of three typesof behavior for the hammer cushion:1) linear elastic, referred to hereinas linear, 2) linear inelastic, referred to as bilinear, and 3) nonlinearinelastic, referred to as nonlinear.A comparison of common soft (wood)L and stiff (aluminum-micarta) nonlinear and inelastic cushions for typicalpile hammers will be made.The range of cross sectional pile propertieswill be represented by the variable pile impedance, pcA.2.2 Basic EquationsThe basic differential equations governing the force generator-pile system are developed on the basis of the model shown in Figure 2.4~.-0'The hmer ram and drivehead possess weights W and W and masses1 2 ?L andm respectively. At the instant the ram impacts the hammer cushion,2'with initial velocity V x is considered to be zero. The hammer1cushion is initially treated as a massless elastic spring with stiffnessk; the spring is considered to act in compression only. The driveheadco-ordinate x is considered zero at the instant of impact as is co-2ordinate x describing motion of the pile head. It will be shown that3the infinitely long pile behaves in the model as a dashpot; therefore,x = x and x may be eliminated.2 3 3Forces acting on the ram and drivehead are shown in Figure 2.4b.Only gravity, acceleration and spring forces act on the ram.Similar

(a) Model(b) Free Body DiagramsFigure 2.4 FREE-BODY DIAGRAM OF FORCE GENERATOR MODEL

-forces act on the drivehead in ~ddition to the pile force, pcAi2.Be-cause the pile is infinitely lpng no reflections enter into the analysis;therefore, force on the pile head is controlled only by pile head velo-city, A2, which in turn is controlled only by the force generator.Thedrivehead weight is a small force relative to the forces under discussionand causes unnecessary complications in the analysis; therefore, it hasbeen discarded.Thus, the resulting equations of equilibrium become:Initial conditions are x = x = = 0, and 2 = V . me equations1 2 2 1 0are solved under the condition that k(x -x ) cannot be negative (no1 2tension in the hammer cushion).Equation 2.2 can be expressed in dimensionless form; this has beenaccomplished by utilizing the following definitions:-where T is the psuedo period of the ram on the cushion and z is dimen-sionless time. Substitution of these definitions into Equation 2.2,and rearranging yields the following expressions:

- whereX=x,X=- , X = -2- dx - Wl m" d x - pcAg1, B =-or-. Thedzmdz W2 2initial conditions become: X = X = X = 0, and X = V T .1 2 2 l oEquation 2.3 has been solved using an electronic analog computer;details of the computer program are given in Appendix B.Only the solu-tions involving linear and bilinear hammer cushions can effectively uti-lize the nondimensional form.For nonlinear cushions, the nondimensional-equations were used to solve a particular case.It is noted that if the hammer cushion stiffness is made a functionof (X -X ) for purposes of representing nonlinear cushion behavior, it is1 2possible to substitute the function directly into Equation 2.3 becauseno operations are performed on the functions.Arbitrarily assumed'functions are used to represent the actual load-deformation relationshipsof nonlinear cushions.2.3 Linear Cushion-.Introduction- The study of the linear hammer cushion will be used to investi-gate hmer-pile parameters controlling both maximum eneray and the forcepulse shape transmitted to the pile.Initially, maximum transmittedenergy to the pile will be investigated which involves the impedancematch of hmer and pile.Then, the generated pile force shape will beinvestigated and rela7ed to the impedance match of hmer and pile.For the investigation of pile force pulse and energy theco-efficient, relating ram weight to drivehead weight as shown in Equation2.3, was selected to cover the range of the practical limits of driving

- equipment. The 5 coefficients investigated are 1, 3, 5, 10 and 20;coefficients between 3 and 10 are typical for driving equipment and 5 isa reasonable average value.The Zi coefficient, relati~g pile impedance".and hammer impedance as shown in Equation 2.3, was varied for a particularvalue of % to include very high and low pile impedances with respect tothe driving equipment.The term hammer impedance is defined herein asthe quantityfor purposes of discussion even though this quantitymay not precisely describe the real impedance of the hammer.To facilitate the use of the parameter study results for alltypes of common pile materials, the pile is designated simply by itscharacteristic impedance, pcA.A tabulation of pile impedance for steel,concrete and wood piles and the corresponding dimensions are shown inTable 2.1.The pile impedances listed in Table 2.1 correspond to typicalpile dimensions and are referred to in the presentation of the results.It should be noted that the low pile impedances correspond to light-wallpipe or wood piles, whereas the high impedances correspond to heavy-wallpipe (mandrels), concrete or H-piles.- Pile Enera-Enera transmitted to the pile head can be qualitatively consideredin terms of the ram and drivehead motion as shown in Figure 2.5.First,maximum energy can be delivered to the pile when the pile impedance ismatched with respect to the hammer impedance; the ram and driveheadmotion continues downward to maximum displacement and remains at thatlocation (~i&ure 2.5b).When the pile impedance is higher than thematched impedance (high pile impedance with respect to the hammer impe-dance), the ram motion continues downward to a maximum displacement and

-Table 2.1TABULATION OF PILE IMPEDANCES AND PILE TYPESPilePile EkterialImpedance Steel* Concrete* Wood*P cA Area Area Diameter Width Area Diameterlbs-sec/in. in. 2 in. 2 in. in. in. 2 in.7255(Thin WallPipe23.5 5.5 4.8 82 10.2*The following material properties were used to determine piledimensions from impedances. Subscripts (s = steel, c = concrete,w = wood) are used.c = 16,600 f't/sec (rc); = 1b5s6-- Concrete E = 4.25 x 10 psic = 4.65Cd Klbs-see2ftin.= 11,500 f't/sec (PC.)~ = 30.9 in.6 lbs-sec 2=1.3x10 psi = 1.24ft 4

NoReboundNoReboundlpion Continues- DownwardIIiammerCushionOscillation OscillationRamReboundLow Pile Impedance Matched Pile Impedance High Pile ImpedanceSuFer-Criti calDnmping(a)CriticalDamping(b)Sub-criticalDamping(c)Figure 2.5SCIIEMATIC OF PILE-HAMMER RESPONSE

-rebounds while the drivehead motion is downward as shown in Figure 2.5~.For this case when the ram rebounds, some of the initial kinetic energyis'lostin the rebound; therefore, the energy transmitted to the pile isless than the impact energy of the driver system.For low pile impedance with respect to the matched pile impedancethe ram and drivehead motion continues downward; however, the drivehead-is driven downward at a faster rate than the ram motion (Figure 2.5a).The ram continues downward as the drivehead slows again and producesanother ram blow, whereupon the drivehead oscillatory motion is re-peated.With time, the energy is fully transmitted to the pile; however,the rate at which energy is transmitted decreases with decrebsing pileimpedance.The interference of hammer operations in returning the rumfor another stroke can prevent the energy from being fully transmittedto the pile for the condition of low pile impedance.The hmer and pile response for ij = 5 and a linear elasticcushion can be used to illustrate further the preceding qualitativediscussion.The response of pile cncrpy, rum d-isplacement, pile dis-vplacement and pile force versus dimension1.e~~ time, z, is shown inFigure 2.6.The energy, displacements and force are expressed in termsof coefficients: C = pile energy coefficient, C = ram displacementERcoefficient, Cp = pile head displacement coefficient, and C = pile forceF1coefficient.The procedure for converting the hammer and pile re-sponse into real quantities is explained in Appendix B.The individualcurves are represented bycoefficients relating pile impedance andh-erimpedance, i.e. ii = pcA G/ Jmlk'. The hammer and pile responseshown in Figure 2.6 illustrates the behavior for low, matched and highpile impedance relative to hammer impedance.

Dimensionless Time, zDimensionless Time, zfl = Ram Weight W1/Drivehead Weight W2Figure 2.6PILE AND KAMMER RESPONSE FVR B = 5 AND LINEAR CUSHION

The representative plot of pile energy shown in Figure 2.6shows that when ?i is 4 a good impedance match of hammer and pile exists.The ram and pile displacements occur as expected.In the case of energyloss due to ram rebound as shown for x = 10 (pile impedance greater thanmatched impedance), the pile energy is lower than for the impedancematch condition of = 4.An example of low pile impedance with respect to the matched im--pedance is shown in Figure 2.6 by the curve for ii = 1. The rate of en-ergy transmitted to the pile is less than that for the matched conditionsand the drivehead motion is oscillatory.The pile force pulse also showsa change in pulse shape as compared to the condition of r\ = 11 and 10.It is noted in Figure 2.6 that there is a range incoefficients thatrepresent essentially a match between pile and hammer with respect toenergy.The energy was determined at a time approximately equal to fourtimes the pseudo period of the ram.The most efficient pile-hammer combinations for energy tmns-1mission were determined from the analog computer studies of hammer andwpile response for each % coefficient is shown in the runEe band inFigure 2.7 in terms of an impedance ratio; the impedance ratio is simplythe ratio of the x 6.to coefficient, or IR = A/% = The rangeband for the matched pile impedance represents an efficiency of energytransmission of 90 percent or more.The impedance ratio for matchedpile impedance decreases with an increase in the ratio of ram weightto drivehead weight.Above the impedance match condition shown in Figure 2.7, thepile impedance is high relative to hammer impedance with energy losses

due to ram rebound; therefore, as previously discussed, this is not anefficient energy system.Below the matched condition, the pile impedanceis low relative to hammer impedance and the rate of energy transmissionis lowered.A low rate of energy transmission is not the only disadvan-tage of the low pile impedance condition; possible hammer damage causedby driving the drivehead out from beneath the ram should be considered.-Consideration of hammer damage suggests that it is better to be on thehigh side of the impedance ratio than the low side.In general, the practical range of impedance ratio for matchedpile impedance is 0.60 to 1.10 for typical ratios of ram to drivehead'weight (5 = 3 to 10). This means that for an optimum pile-hammer combinationwith respect to maximum energy transmitted to the pile, the pileimpedance (pcA) is related to the hammer impedance (@)by:-A closed form solution was attempted in order to define the con-ditions of maximum energy transmitted to the pile for the force functiongenerator described herein. The homogeneous solution of Equation 2.3may be written in the form ofrzrz% = c1 e and X2 = c e2where c and c are arbitrary coefficients and r represents the roots1 2of a quartic indicial equation. Three conditions can be determined fromthe roots of the indicial equation:

2201R 2One real and4 2"R +4(IR) - I, - - + - ifi + 1)3 > 0 two imag. rootsE2 3 (2.5)Subcritically dampedg2201R48 1 - 3 real roots4(1,) -IR---2+-+-t(~+1)3=~ - 2equal (2.6)fi E B Critically damped3 real roots4 2&(I,) -IR-: + 1)3 < 0 unequal (2.7)BSupercritically dampedThe conditions of Equations 2.5, 2.6 and 2.7 imply the ram motion" to be oscillatory or deadbeat. With a high pile impedance with respectto the hammer impedance the ram motion is oscillatory and ram reboundoccurs; therefore, this condition of motion is commonly defined as asubcritical damping.The transition of ram mdtion from subcritical tosupercritical damping is the critically damped condition.For the cri-tically damped system or pile-hammer match, the im-pedance ratio of Equation 2.6 can be determined for particular values ofthe 5 coefficient.The relationship between the impedance ratio andcoefficient for the analytical solution is shown in Figure 2.7; theanalytical curve falls within the matched pile impedance zone as deter-.- mined from the analog computer results. The impedance ratios of thecritically damped system for E - > 8 are real values and the maximum valuewas selected.For the special condition where the drivehead weightapproaches zero, i.e. fi = m, the impedance ratio for the criticallydamped pile-hammer system equals 0.5.This value is a lower bound forthe pile-hammer match.For cases where fi < 8, the calculated impe-dance ratios were imaginary values; therefore, the minimum point ofEquation 2.6 with respect to impedance ratio was selected as the criti-

cal condition.A rull explanation of the analytical interpretationof this minimum point criterion is beyond the scope of this presentation.Pile For% -Introduction.The generated pile force with respect to peakvalue, force shape, and duration will be discussed relative to the impedancematch of the pile and hammer, i.e. high pile impedance, matched- impedance and low pile impedance. The hammer variables, such as ramvelocity, ram and drivehead weight, and cushion properties will be investigatedwith respect to the pile impedances given in Table 2.1.In order to facilitate the discussion of piLe force, the generatedpile forces will be summarized for B coefficients of 3, 5, 10 and 20 asshown in Figure 2.8.The force pulse generated for different 5 co-efficients is expressed in terms of the pile force coefficient, C~l 'and dimensionless time, z.Real time can be easily determined by theexpression, t = zT;.however, the pile force is a function of severalvariables as shown in the expression below:Equation 2.8 shows that the pile force is directly proportionalto the force coefficient and inversely proportional to the 5 coefficient.The inverse proportionality of the Ti coefficient does not alter theshape and magnitude of an individual force curve for a particularcoefficient, but it causes an apparent misrepresentation of the rela-tive magnitude of the force curves for different x values.For in-

0.42.620ote :1. Circled3i Coeii.representsthe"MatchedPileImpeBance"1 TIMmemionless Tima, z Mnwruionless Tim ,z0Figure 2.8GlXERM"l'D PILE IORCE BUEHARY FOR LIm CIGRIOA

stance, the low value of the A coefficient has a larger peak pile forcethan the higher 7i coefficient value for a given pile impedance and ramvelocity.The reason for the apparent discrepancy is that the E co-efficient increases at a faster rate than the pile force coefficient,CF1, decreases .For E = 5, Figure 2.8, the ji value of 1 represents a low pileimpedance relative to the hammer impedance; therefore, the pile is- driven out from under the ram resulting in oscillatory and damped pileforces. With an increase in the coefficient to 3 or 6, the impedancesof hammer and pile match and the force pulse is approaching the shape ofa damped sinusoidal wave. With larger coefficients such as 20 or 40,the pile impedance is larger than the hammer impedance; therefore, theram is rebounding and the force pulse is approaching the shape of asine wave. The presentation of the pile forces as shown in Fi.gure 2.8will be used to aid the discussion of generated pile force with re-spect to peak, shape and duration.- Peak Force. The peak pile force can be summarized for B--coefficients of 3, 5, 10 and 20 as shown in Figure 2.9. ,The peak pileforce, FP'following:is related to the pile and hammer characteristics by thewhere C is the peak pile force coefficient. Equation 2.9 and FigureF22.9 can be used to determine peak pile force for a particular pile.With reference to Figure 2.9, the E coefficient has a negligibleeffect on the peak pile force for a given hammer and pile; therefore,generated peak pile forces are nearly independent of drivehead weight. . , . . . . . , . . . . .. . . . , . , . . . . , . , . . . , . , , , ,.,.,.. . ,. ,.,. , .,. . . . .,.. ,. .,.,. ,,.,., . , . ,. . .. , . ,

The relationship between peak pile force and impedance ratio(Equation 2.9 and Figure 2.9) can be used to determine the peak forcefor a particular pile impedance, ram weight and cushion stiffness.Toexemplify the interrelationship of parameters, particular values ofpi1.e impedance were selected and peak forces were determined for common--ram weights and cushion stiffnesses as shown in Figure 2.10. Since theeffect of drivehead weight on peak force is negligible, a common 8coefficient of 5 was used to obtain ther results shown in Figure 2.10.The pile impedances selected represent a range of typical pile sectionsvarying from light weight (thin-walled pipe) to heavy weight (mandrel or11-piles) as tabulated in Table 2.1.In terms of pile impedance, thesteel piles can easily account for the full range of impedances inlbs.sec.vestigated, namely 725 to 8700 . Wood piles fall in thein.impedance range of thin-walled pipe, whereas concrete sections correspondto the higher impedance range of steel piles.Peak pile force may be determined by the following expression:where F is a peak force in kips, CF3 is a peak pile force coefficientP(Figure 2.10) which has units of kip-seconds/foot,velocity at impact in feetlsecond.and Vo is ramWith reference to Figure 2.10, the peak pile force generallyincreases with increases in ram velocity, cushion stiffness, ramweight and pile impedance.The ram velocity is directly proportionalto the peak pile force as shown in Equation 2.10.The velocity at

0 l I Pile Im~edcjnceI6Hmer Cushion Stiffness, kxlONote:Fp = [cF3] [ v~ ft/sec] kipslbs/in.Cross-hatching represents zone of impedancematch of pile and hammer.Figure 2.10RELATIONSHIP OF PEAK PILE FORCE WITH HAMMERCHARACTERISTICS AND PILE IMPEDANCES

impact, and therefore the peak force, can be related to the height ofram fall and hmer efficiency for a free-fall drop as shown below:where V is expressed in feet/second and h is in feet. Equation 2.110can be expressed graphically as shown in Figure 2.11 for the practical2 range of hammer efficiency from 30 to 100 percent. The drop height, h,is the actual fall distance of the ram for a sing]-e-acting hemmer.Fora double-acting or differential hammer, the drop height h is the cquivalentheight with consideration of the downward acceleration added byair or steam pressure.The effect of ram weight and cushion s-tiffness for particularpile impedances is shown in Figure 2.10.In general, the peak force in-creases with an increase in both cushion stiffness and ran weight for agiven pile i.mpedance; however, there are limiting conditions beyond- of hammer cushion, the peak force becomes independent of cushion stiff-which the peak forces do not increase.With respect to the limitationsness beyond an upper limiting stiffness, defined herein as the upperI.imit of effective cushion stiffness.For the limitations of the ramweight, peak force becomes independent of ram weight for low pile impe-dances (See Figure 2.10).In order to clarify the meaning of the upper limit of effectivelbs-seccushion stiffness, consider the pile impedance of 725 in as shownin Figure 2.10.For the ram weight of 10,000 lbs, the peak force in-creases with cushion stiffness up to a stiffness of approximately

61 x 10 lbs/in., and thereafter is independent of stiffness. The stiff-6ness of 1 x 10 lbs/in. therefore, represents the upper limit of effectivestiffness. For the light ram (1000 lbs), the upper limit of effective6stiffness is approximately 4 x 10 lbs/in. 'With reference to pile im-lbs-secpedances greater than 725 --,In.of cushion stiffness at higher stiffness levels.peak pile force becomes independentFor instance, the upper-limit of effective cushion stiffness increases with an increase in pileimpedance as shown below:Pile Range in Approximate UpperImpedance Ram Weights Limit of Effectivelbs-sec/in. - lbs . Cushion Stiffness-It should be noted that the lower cushion stiffness corresponds to theheavier ram weight and the higher stiffness corresponds to the lighterram.The impedance match of hammer and pile for maximum energy trans-mission can be superimposed on the results of Figure 2.10.For a givenpile impedance and ram weight, cushion stiffness can be determined forthe impedance match of the hammer and pile; this is shown cross-hatchedin Figure 2.10.For comparison, the range in cushion stiffnesses forthe impedance match condition will be tabulated along with the approxi-mate upper limit of cushion stiffness for maximum pile peak force as

shown in Table 2.2.The cushion stiffness at which the upper limit ofpeak pile force occurs is considerably larger than that for the impedancematch condition.As pile impedance increases, the cushion stiffness forefficient energy transmission approaches that for the approximate limitof peak pile force.The cushion stiffness at which the approximate peakpile force is first attained corresponds to an energy transmission-.efficiency of approximately 80%.The effect of ram weight can be represented by a relationship he-tween pile impedance and peek pile force as shown in Figure 2.12.Thepeak force, expressed in terms of the impact velocity, Vo, was arbi-6trarily determinbd at a cushion stiffness of 20 x 10 lbs/in. As shownin Figure 2.12, the peak force is independent of ram weight at low pileimpedances; however, the ram weight becomes more significant with re-spect to the generated peak force as the pile impedance increases.Figure 2.12 is also representative of the effect of pile impedance-on the generated peak force. Peak pile force increases with an increasein pile impedance. For low values of pile impedance, the generated peakforce spproaches a direct proportion to the increase in pile impedance,i.e. a 50% increase in pile impedance will produce a 50% increase inpeak force.For high pile impedances, peak pile force increases at arate less than the increase in pile impedance.The proportional rela-tionship between peak force and pile impedance is superimposed onFigure 2.12 in order to evaluate the lack of proportionality at highpile impedances.With the proportional relationship line as reference,it is seen that the proportionality between peak force and pile impe-dance decreases with an increase in pile impedance.Also, the propor-

Table 2.2A COWARISON OF CUSHION STIFFNESSESFOR IWEDANCE MATCH ARD LIKT OFPEAK PILE FORCEPile Ram Hammer Cushion Stiffness, Percent ChangeImpedance, Weights k, x 106 lbs/in. in Pile Forcelbs .-sec lbs . from Matched toin. Impedance Match Approximate Limit Limit Conditionof Peek Force12 to 14 78-23%Below Match16 Condition69-BelowMatch

. , , , . , , , . , , , , . . . . . . . , . , . . . . . , . . . . . ,., . .:,. :,, ..: ..; . . ,. ... ,, , . ... . .Pile Impedance,lbs-secinNgure 2.12 PEAK PILE FORCE VERSUS. PILE IMPEDANCEFOR DIFFERENT RAM WEIGHTS

tionality decreases with a decrease in ram weight.For high pile im-pedances, a typical lower limit of proportionality may be 60%, i-e. a50% increase in pile impedance will produce a 30% increase in peak force.Shape and Duration.The effect of pile and hammer parameterson the generated pile force shape and duration will now be considered.Although the drivehead weight has a negligible effect on the-peak pile force, the shape of the force pulse is noticeably affected.For the conditions of high pile impedance (high 21 values) as shown inFigure 2.8, the force pulses for all B coefficients are nearly sinu-soidal and the pulse durations are nearly equal.As pile impedanceapproaches the matched condition, the pulse becomes skewed and approachesa damped sinusoidal shape.In addition, duration of pulse is larger asthe B coefficient increases (or drivehead weight decreases).Theskewed trend is also prevalent for the low pile impedance condition(lower than impedance match) and the force becomes oscillatory.-For the force pulse curves shown in Figure 2.8, it can be seenthat the force curves intersect at a value of dimensionless time (2)approximately equal to n; this is not true for low imoedance ratioswhere oscillations occur.This point of intersection can be used as aguide to the duration of the force pulse.For typical B coefficientsof 3 to 10, the duration of the force pulse can be represented bythe intersection point for all conditions of impedance ratio, Eli;;however, oscillations of the force pulse occur within the range ofthis intersection for low impedance ratios.

-. If the dimensionless duration is converted into real time forthe intersection point, then real duration, td, will be:It is of interest to note that t in Equation 2.12 is equivalent to onedhalf the real period of the ram and cushion. i .e. 2 n E .The duration given in Equation 2.12 is directly proportional to>-the square root of the ram weight and inversely proportional to thesquare root of the cushion stiffness.This means that by increasing theram mass by a factor of 2, the pulse length is increased by a factor of, or 1.1. Also, an increase in stiffness by a factor of 2 produces ndecrease in pulse length by a factor of E, or 1.111.The duration as a function of hammer and pile characteristicsis graphically shown in Figure 2.13. The pile impedances of Table 2.1are superimposed on the hammer characteristics for matched conditions.It is seen that for a given ram weight, the duration decreases with an-portionality to pile impedance, i.e. a 50% increase in pile impedanceincrease in pile impedance. Duration is approximately the inverse pro- 'results in an approximate 50% decrease in time duration.It should benoted that the aforementioned duration for low pile impedance relativeto hmer impedance does not include the total length of force pulsewith all the damped oscillating peaks, but only gives approximately theduration of the first oscillatory pulse cycle.The force pulse shape and the duration are independent of theram velocity at impact for a linear cushion.

Figure 2.13 TIME DURATION OF FDRm PUIf;E AS A FUNCTION OF HAMMER AND PILE CHARACITEI1ISTICS

2.4 - Bilinear CushionPile En-The effect of energy loss in a bilinear cushion will now be in-vestigated.First, it should be pointed out that inelastic behavior doesnot invalidate the concept of impedance match of hammer and pile; however,inelastic behavior is associated with energy losses within the cushion.-.The effect of the coefficient of restitution on the percentage of energyloss in the hammer cushion is shown in Table 2.3 for g coefficients of3, 5 and 20; = 5 is a typical ram to drivehead weight ratio. The coefficientsof restitution were varied between 1/3 and 1 (e - 1 is linearelastic), whereas pile impedance was varied from low to high relativeto the hammer.With reference to Table 2.3, it can be seen that the energy lossincreases as the coefficient of restitution decreases. As the coefficientincreases, the energy loss with respect to a particular coefficient-of restitution decreases for the impedance match and low pile impedancecondition. For the high pile impedance condition, the energy lossfor a particular coefficient of restitution is independent of B. Fortypical values ofthe energy loss in the cushion for coefficients ofrestitution of 1 to 314, which correspond to stiffer cushions such asaluminum-micarta, varies from 0 to 20%. For coefficients of restitutionof 112 to 1/3, which correspond to soft cushions such as wood, theenergy loss in the cushion, varies from 20 to 40%.

Table 2.3ENERGY LOSS OF BILINEAR CUSHIONCoefficientPercentage of Energy Loss in Cushionof High Pile Impedance Matched Impedance Low Pile ImpedanceRestitution* x = 10 E=3 F.=1CoefficientPercentage of Energy Loss in Cushiono f High Pile Impedance Matched Impedance Low Pile ImpedanceRestitution* ii = 10 x = 4 A = 1CoefficientofRestitution*Percentage of Enera Loss in CushionHigh Pile - Impedance Matched - Impedance Low Pile ImpedanceA = 40 A = 15 E = 4* See Figure 2.3

Pile ForceThe effect of a bilinear cushion will be investigated with respect-to peak pile force, force shape and duration.The variables are the same-considered in the discussion of energy losses.Inelastic behavior of the cushion has three distinct effects on:.the generated force pulse, namely:1) it lowers the peak force only:'cr- -$hethe low pile impedance conditions, 2) it attenuates the duration offorce pulse, and 3) it causes possible minor oscillation of the forcepulse for the matched and high pile impedance conditions.The effectsc,f varying the coefficient of restitution for 3 = 5 are considered typical;-t;ne results are presented in Figure 2.14.The effect of an inelastic cushion on peak pile force is tabulatedir?. Table 2.4 for differentcoefficients and the various coefficients0: restitution considered herein. The peak pile force is expressed as apercentage of the peak force generated with an elastic cushion (e = 1).1% is noted in Table 2.4 that peak pile force is independent of the de-gree of inelastic behavior for the impedance match and high pile impe-- daqce conditions. However, the peak force decreases with an increase ininelastic behavior (lower coefficient of restitution) for the low pileimpedance condition.With reference to Figure 2.14, it can be seen that a decrease inthe coefficient of' restitution results in a decrease in duration of the.. . force pulse. In Table 2.4, the duration is expressed in dimensionlesstime (2) which is directly proportional to real time.The dimensionlessduration of the force pulse is arbitrarily selected at a value of 10%

0,2Matched Pile0Dimensionless Time, zE = 5Dimensionless Time, zFigure 2.14 EFFECT OF BILINEAR CUSHIOM ON PILE FORCE

15=3 1tTable 2.4EFFl3CT OF BILIY3R9 CUSHION ON PEAK PILE RIRCE AND PULSE DURATIONPercentage of Peak Pile ForceGenerated with an Elastic CushionCoefficientImpeda~ceo f High Pile Impedance Match Low Pile ImpedanceRestitution ii = 10 z = 3 A=le=l(elastic) 100 100 100e=3/4 100 99 94e=1/2 100 97 86e=1/3 100 96 811( ~ = 5Percentage of Peak Pile ForceGenerated with an Elastic CushionCoefficientImpedanceof High Pile Impedance Xattch Low Pile ImpedanceRestitution ;1 = 10 z=4 x = le=l(elastic) 100 100 100e=3/4 100 99 9 3e=1/2 100 96 8 5e=1/3 100 94 801$=201CoefficientPercentage of Peak Pile ForceGenerated with an Elastic CushionImpedanceof High Pile Impedance Match Low Pile ImpedenceRestitution = 40 = 15 ii=4e=l(elastic) 100 100 100e=3/4 100 100 --e=l/2 100 100 --e=1/3 100 100 90*Denotes oscillating force pulse.**Dimer.sionless time taken at a load 10% of peek.ivDimensionless Time Pulse Duration**ImpedanceHigh Pile Impedance Match Low Pile Impedanceii = 10 A=3 I = l3.2 3.3 4.2*2.8 2.9 3.9"2.6 3.9* 3.3"2.1 3.5* 2.9'Dimensionless Time Pulse Duration*"ImpedanceHigh Pile Impedance Match Low Pile Impedancex = 10 A = 4 ii=13.2 3.3 >62.8 3.3" >62.5 3.9* >62.5" 4.0* >6Dimensionless Time Pulse Duration**ImpedanceHigh Pile Impedance Match Low Pile ImpedanceE = 40 A = 15 A=43.2 3.6 >5.0*2.9 3.6 --2.5 3.8* --2.4 4.0* >5.0*vlu

of the peak force.For a given pile impedance, duration decreases withan increase in the degree of inelasticity (decrease in coefficient ofrestitution) except for the special case of force pulse oscillations atthe impedance match condition.Small oscillations of the pile force for the impedance match condition(3 = 4) and low coefficients of restitution, as shown in Figure2.14, indicate discontinuity in oscillatory behavior. It is believedthat a relay in the analog computer system was responding erraticallyonly during unloading of the cushion; therefore, discontinuity of theforce pulse exists.In order to verify the results of this bilinearstudy, the linear cushion study was compared with the bilinear study forcoefficients of restitution equal to unity (elastic case).The comparisonshowed no difference in the generated force pulse; therefore, the generalconclusions based on the bilinear study are assumed to be unaffectedby the discontinu-ity in the force pulse oscillations.It should be notedthat the discontinuities occur long after the initial peak force.2.5 Nonlinear CushionScopeThe importance of the hammer cushion in determining peak pileforce and duration was demonstrated in the preceding sections.Thissection will further exemplify the effect of the hammer cushion by com-paring the behavior associated with typical soft and hard nonlinearcushions, namely, pine plywood and aluminum-micarta.The effect of softand hard nonlinear cushions will be investigated in two parts;1) com-

-parison of generated pile force peak, shape and duration, 2) comparisonof linear and nonlinear cushion behavior.Nonlinear cushions were investigated for typical hammer sizes, i.e.Vulcan 2 to Vulcan 010, and normal ram velocities ranging from 9 to15 ft/sec. The hemmer and cushion details investigated are tabulatedin Table 2.5.A drivehead weight of 1000 lbs was selected as typical for-the hammer range studied.Load-deformation characteristics for pine plywood cushions weretaken from the investigation by Hirsch, et al . (1966) as shown in Figure2.1%. This relationship can be approximated by a series of straightlines as shown in Figure 2.15b to obtain the assumed load-deformationcharacteristics utilized herein (Appendix B).The unloading slope is re-lated to the coefficient of restitution (e = 0.27 for the pine plywoodcushion). Similar approximate curves for other hammer sizes are shownin Fiyre 2.16.The load-deformation relationship for the aluminum-micartacushion was obtained from a static test. The static properties for-typical cushion materials agreed remarkably well with those determinedunder impact loads (Hirsch, et al. 1966). Both the real and assumedload-deformation characteristics are shown in Figure 2.17 and theapproximate loading curves for the hammer sizes considered herein arepresented in Figure 2.18.The aluminum-micarta cushion approaches anelastic cushion with a coefficient of restitution of 0.95.Before discussing the effects of pine plywood and aluminum-micarta cushions, their load-deformation relationships are cornpaced for

t I>Table 2.5TABULATION OF PROBE% INVESTIGATED FOR NONLINEAR CUSHIONSProblem Rm DriveheadRarnwt . wt . EVelocityNo. b e 13s. 13s. Coeff. Yo, ftlsecHammer Cushionh e Size"ACushionDataUsed1 Vulcan 010 10,000 1,000 10 9 Pine Plywood 13 1f2" d - 10" At. 314'' Pine Plywood2 Vulcan 010 10.000 1.000 10 12 Pine Plwwd 13 112" d 10" Ht. 9" . . d - 9" Ht.~vulcan 010Pine Plywood li 112" 4 - 10" Ht.Vulcan 08vulcan 08Vulcan 08vulcan 06vulcan 06vulcan 06vulcan 1vulcan 1vulcan 1Vulcan 2Vulcan 2vulcan 2Vulcan 010vulcan 010vulcan 01019 vacan08 8,000 1,000 8 9Pine PlywwdPine PlywoodPine PlywwdPine PlywoodPine PlywoodPine PlywwdPine PlywoodPine PlywoodPine PlywoodPine PlywoodPine PlywoodPine PlywoodAluminum-MicartaAluminum-Mi cart aAluminum-Micarta13 112" b 10" Ht.13 112" d 10" Ht.13 112" d - lo" Ht.li" d - 8" Ht.Dynamic BlwNo. 80e = 0.27Dynamic Test11" 6 - 8" Ht. (Hirsch et al., 19%)Y"4- 8"Ht.u" d - 8"Ht.11" d - 8"Ht.11" d - 8"Ht.lo" 4 - 8"Ht.lo" d - 8" ~t.10" d - 8"Ht.13 1/2" 6 - 10" Ht. Aluminum-Hcarta13 112" d 10" Ht. 13.4" d 4" d13 112" d - 10" Ht. Concentric Holes7.3" Ht.Aluminum-Micarta 13 112'' d - 10" Ht. 1,16,, Disc20 Vulcan 08 8,000 1,000 8 12 Aluminum-Micarta 13 112" d 10" At.21 Vulcan 08 8,000 1,000 815 Aluminum-Micarta 13 112" 8 - 10" Ht.22 ~ulcan 06 6,500 1,000 6.5 9 Aluminum-Micarta 11" d 8"Ht.23 Vulcan 06 6,500 1,000 6.5 12 Aluminum-Micarta 11" 4 - 8" ~ t.112" Alum. Disce = 0.95~ ~24 vdcan 06 6,500 1,000 6.5 15 Aluminum-Micarta 11" d - 8" Ht. Static Test25 Vulcan 1 5,000 1,000 5 9 Aluminum-Micarta 11" 6 - 8" Ht.26 vulcan 1 5,000 1,000 5 12 Alumin-Gn-Micarta 11"d- 8"Ht.27 Vulcan 1 5 ?OOO 1 ,.OOO 5 15 Aluninum-Micarta ll"6- 8"~t.

0 0.50 1.0 1.5Axial Deformation, inches(a) Real Curveo 0.50 1.00 1.50Axial Deformation, inches(b) Assumed CurveFigure 2.15 .REAL AND ASSUMED CURVES FOR PINE PLYWOOD CUSHION

mard. 1GIz200100.0 AiI+ . .. A. ..--+ .-C-.+-Vulcan 010 and 08-. . . ..+ .---. -.*. .-.1 I t -t------IiF .AIIII!II! !III+0 0.50 1.00 1.50 2.00 2.50Axial Deformation, inchesFigure 2.16 ASSUMED PINE PLYWOOD CUSHIONS FOR DIFFERENT HAMMERS

1 Axial Dcformstion, inches0 0.05 0.10 0.15Axid Dbformatlon, InchesFigure 2.17 REAL AND ASSUMED CVAVES FOR ALUMINUM-KSCARTA CUSHION

Axial Deformation, inchesFigure 2.18 ASSUMED ALUI4TNLR.I-MICARTA CUSHIONS FOR \DIFFERENT HAMMERS

a Vulcan No. 1 h mer (Figure 2.19).The comparison shows the markeddifference in stiffness between the cushions as well as the differencein the degree of inelasticity.These cushions represent the range ofproperties normally encountered in practice.Pile Force-Peak .?orce.The peak pile force was investigated for values of- impact velocity equal to 9, 12 and 15 ft/sec, which represents a typical-range in velocities.For comprtrison, the tabulated impact velocitiesfor several hammers along with the associated efficiencies are givenbelow: ,Impact Velocity, Vo , f t . /s ec .Iimer Drop Height, ft . e = 100%fVulcan 01.0 3.25Vulcan 08 3.25~ul.can 06 3.00Vulcan 1 3.00-Vulcan 2 2.50e = 75%fe = 50%fPile peak forces vary linearly with impact velocity; therefore,the peak forces can also represent typical values of hammer efficiencyfor the different hammers tabulated above.Pile peak force versus pileimpedance relationships for different hammers with pine plywood andaluminum-micarta cushions are shown in Figure 2.20.The relationshipsbetween pile force and impedance are expressed in terms of the usefulrange of hammer efficiencies, namely, 50 and 100%. Because peak force

0 0.25 0.50 0.75 1.00 1.25 1.50Axial Deformation, incheeFigure 2.19COMPARISON OF PINE PLYWOOD AND ALUMIRW-MICARTA CUSHIONSFOR WLCAN NO. 1 HAMMER

600500400300200100Hammer Efficiency = 50%A"o 2000 4000 6000 10,000Note:Pile Impedance, pcA,lbs-secin.1. Shaded areas represent maximum energy transmission2. Assume 1000 lbs. drivehead for all hammers.120010008006004002000Hmer Efficiency = 50%lbs-secPile Impedance, pcA, in.000Figure 2.20PEAK PILE FORCE FOR PINE PLYWOODAMD ALUMIIJUM-XICARTA CUSHIONS

and impact velocity arc linearly. related, peak force for other efficienciescan be readily determined by interpolation in terms of the square root ofhammer efficiency (Jef' ).With reference to Figure 2.20, it is shown that for a given hmerand efficiency the peak force increases with an increase in pile impedancefor both cushion materials.However, the increase is more pronounced for-the aluminum-micarta (hard) than for the pine plywood (soft) as the pileimpedance approaches high values.Also, the peak force generated in thepile with the aluminum-micarta cushion is approximately double that gene-rated with the pine plywood cushion.The optimum pile-hammer match for maximum endrgy transmitted tothe pile head is superimposed on Figure 2.20.It is seen, as expected,that the best match for the softer cushion (pine plywood) is the lowpile impedance range of 600 to 2600 lbs-sec/in. (equivalent steel area2of 4 to 18 in. ).The harder cushion (aluminum-micarta) is matched withhigh pile impedances, or equivalent steel areas of approximately 20 to280 in. .Shape and Duration.The pile force shape and duration is alsoaffected by differences in cushion material.Force pulses generated bya Vulcan hammer for the aluminum-micarta and pine plywood cushions arecompared in Figure 2.21 in term of the pile force coefficient, CFl.The Vulcan 1 hammer with different cushion materials and an impactvelocity of 12 ft/sec (ef = 71+.5%) was chosen as representative oftyoical hammer behavior.

For t'ne range in velocities investigated, 9 to 15 ft/sec, therewas a decrease in duration associated with the higher velocities; however,the variation was less than 10%. The pulse shape is associated with thecushion load-deformation characteristics.If the cushion loading curveis gradual and the unloading is abrupt, then the force pulse loading andunloading pattern is analogous in behavior.Comparison of the force-pulses in Figure 2.21 shows the more gradual loading and more abrupt un-loading of the pine plywood as opposed to the aluminum-micarta cushion.The abrugt unloading pattern is caused by increased cushion stiffnessupon unloading associated with the low coefficient of restitution of thepine plywood cushion (e = 0.27) 5s compdred to the aluminum-micartacushion (e = 0.95).The abrupt unloading of the pine plywood cushioncauses force pulse oscillations near the impedance match condition ofhammer and pile.This oscillatory force behavior for conditions of im-pedance match and low coefficients of restitution also occurred in thebilinear study.-The. pulse duration for the soft cushion (uine plywood) as com-pared to the hard cushion (aluminum-micarta) is larger by a factor of3 to 5. The real duration at 10% of peak force is tabulated below forthe Vulcan No. 1 hammer and various pile impedances.

Pulse Duration at 10% of Peak,- milliseconds Matched Pile Low PileHigh Pile Impedance Impedance ImpedanceVulcan 1 X=40 X=20 x=10 1=8 x = 6 A = 4 x = 2Pine Plywood 16 18 24 27 29 36 50For the impedance match of hammer and pile, the duration of thepulse for the pine plywood cushion is approximately 5 times longer thanthat for the aluminum-micarta cushion.The relationship is similer forother hammers as shown below:Vulcan 2Impedance Match Conditions Only- Time Pulse Duration at 10% PeakPine Plywood Aluminum-Mi cart a25-35 ms --Vulcan 1 - Vulcan 010 30-50 ms 6-12 ms.-The longer duration corresponds to the hammer with the heaviestram (Vulcan 010).The pronounced differences in behavior between a typical sortcushion (pine plywood) and a typical hard cushion (aluminum-micarta)point to the importance of the hammer cushion in pile driving.Pineand aluminum-micarta were chosen to encompass the potential range inbehavior of the generated force pulse.As a practical consideration,the hammer cushion can be readily changed.Thus, cushion stiffnessescan be chosen so as to attain the desired pile-hammer impedance match

or generated pile force pulse leading to maximum pile penetrationper blow.9--E uivalent Linear Cushion--Introduction.In this section, nonlinear and linear cushionbehavior are compared with respect to generated pile force pul.se, i.e.peak force and duration, for purposes of developing a method of repre---senting nonlinear cushions with equivalent linear cushions.The non-linear cushions considered are pine plywood and aluminwn-micarta.Thecomparisons of cushion behavior are made with respect to a range inhammer sizes, using the Vulcan 1 and Vulcan 010 hammers with a drive-head weight of 1000 lbs and an impact velocity of 12 f't/sec (ef = 74.5%).Peak Force.First, equivalent linear cushioris are selectedthat lead to the same generated peak pile force.The equivalent linearcushion stiffness refers to the loading stiffness only.As shown inthe bilinear cushion study, the unloading stiffness has a negligible.- pile impedances and low coefficients of restitution for the cushion.effect on the generated peak force except for the condition of very lowEven for extreme conditions, the unloading stiffness affects the peakforce by less than 20%.Equivalent linear stiffnesses for a range of pile impedances andthe pine plywood and aluminum-micarta cushions of the Vulcan 1 and 010hammers are tabulated in Table 2.6.The equivalent linear cushionstiffness increases with an increase in pile impedance for both hammersand both cushion types.It should be noted that all equivalent stiff-nesses are bounded by the lowest (kl) and highest (k ) loading stiffnesses3

Table 2.6EQUIVALENT LINEAR CUSHION FOR PEAK PILE FORCEL vulcnn I IArea ofEquivalent Linear CushionImpedance Pile SteelPine PlywoodAluminum-MicartaCondition Inpadance,* lb9-E6 6in.2 knx10 lbslin. Percent of kx knx10 lbslin. Percent of k,in . . - FLow 725 5 0.13 23 2.0 291450 10 0.27 46 4.1 58Medium 2900 20 0.41 -71 5.6 79Hi@ 5800 40 0.45 78 6.8 958700 60 0.47 81 7.1 100Note: Assumed nonlinear cuehion st ffnesses for Vulcan 1:Pine Plywood kl = 0.076~10 lbs/in. Aluminum-Micarta kl = 0.26~10~ lbs/in.k2 = 0.36~106 lbsfin. k2 = 4.0~10~ lbs/in.k3 = 0.58~10~ lbslin. k3 = 7.1~10~ lbslin.I vulcan 010 IArea ofEquivalent Linear CushionImpedance Pile lbs-sec Steel Pine PlywoodAluminum-Micarta7 Condition Impedance,* -- in.' k xl0 6 lbslin. Percent of k3 k xlO 6 lbslin. Percent of kin.P 3., ! Low 125 5 0.11 15 1.4 18- b1450 10 0.25 36 4.1 53Medium 2900 20 0.44 63 5.7 73. . Hiah 5800 40 0.51 73 6.4 828700 60 0.52 75 7.1 91-Note: Assumed nonlinear cushion stiffnesses for Vulcan 010:Pine Plwood kl = 0.092~106 lbs/in. Aluminum-Micarta kl = 0.28~106 ibs/in.k2 = 0.43~10~ lbslin.k, = 4.4~106 l>s/in.k3 = 0.70~106 lbs/in. k; = 7.8~10~ lbs/in.*Refer t o Table 2.1 for comparison of pile inpedances with dimensions of other piletvoe?. concrete and uoorl.

(~igure 2.15 and 2.17) of the nonlinear cushioks (See Table 2.6).The equivalent linear cushion stiffness is shown in Table 2.6 asa percentage of the highest loading stiffness (k ).3impedances, 725 to 1450 lbs-sec/in.,The range of low pilecan be covered by a stiffness rangeof 20 to 60 % for both hammers and cushions investigated; the higherpercentage corresponds to the higher pile impeda~ce. !The interme'diate-pile impedance is covered by a range of 60 to 80%, whereas 75 to 100%aof the stiffest portion of the nonlinear cushion is required to coverthe higher pile impedances.The larger percentages correspond to thestiffer cushion, i .e. aluminum-micarta.Duration.The durations of the force pulses can be comparedin order to obtain an equivalent linear cushion, i.e., one giving thesame duration. The effect of the inelastic behavior (hysteresis) of-.the nonlinear cushion makes the analog/ with the linear rushi.on diffi-cult because of attenuation of the pulse duration caused by inelasticbehavior.Therefore, an equivalent linear cushion (linear and elastic)will be related to the nonlinear cushion (nonlinear and elastic) for thedetermination of durations.It is assumed that inelastic behavior(same coefficient of restitution) for both the bilinear and nonlinearcushions will attenuate the pulse durations in a similar mannerThe pulse duration is based on the point of intersection of thenonlinear and elastic force curves where dimensionless time z approximatelyequals n; therefore, the real duration is approximated by the relationship,td = n (same as Equation 2.12). Equivalent linear cushionstiffnesses for the approximated time pulse length for all pile impedancesare tabulated below:

Equivalent Linear Stiffness for Duration,6k x 10 lbs/in.Pine Plywood EquivalentAluminum-Mi cart a EquivalentVulcan 1 0.20 5.0Vulcan 010 0.40 5.0It is seen from the above tabulation that the equivalent linear loading-stiffness (k ) for the duration corresponds to the linear loading stifftdnesses (k ) for the peak pile force of the low to medium pile impedancesP(Figure 2.22b).This means that the equivalent linear stiffness isreasonably matched for both peak force and duration with respect to thelow to medium pile impedances.For the very low and the high pile impedances, equivalent linearcushions for duration and peak forces are not equal.For very low pileimpedances, the equivalent linear cushion (k ) for peak pile forcePrepresents the actual peak force, but the duration for this equivalent.-cushion is longer than the actual duration (Figure 2,228). The equivalentlinear cushion (kt&) for the duration represents the actual duration;however, the peak force as determined by this equivalent cushionis larger than the actual pcak force.For high pile impedances, theopposite effect exists wherein the shorter time pulse is associated withthe equivalent cushion (k ) for the peak force, and the lower peak forcePis associated with the equivalent cushion (k ) for the durationt d(~i~ure 2.22~).Recommended Secant Modulus.The equivalent linear cushion stiff-ness can also be obtained from recommended secant moduli values given

k = Equivalent Linear Loadinp Stiffness forPeak Pile Force.= Equivalent binear Loading Stiffness forTime Duration.DurationRe a1Time . ~DurationRealTimeDurationVery LowPileImpedance(8)Low and MediumPileHighPileImpedance(c)Figure 2.22 SCHEMATIC COMPARISON OF EQUIVALEFJT LINEAR CUSIiIONSTIFFNESS WITH RESPECT TO PEAK PILE FORCE ANDTIrn DURATION

y Lowery et al. (1969) which are supposed to be valid for predictingboth force pulse shape and magnitude.Equivalent linear stiffness ve.luescalculated from these recommended secant moduli will be evaluated onthe basis of the linear stiffness values determined previously for matchingpeak pile force and duration.The ca1.culated'values of linear loadingstiffness (k ) for the hammers and cushions considered in this sectionCare tabulated below:.Calculated Linear Cushion Stiffness,6k x 10 lbslin.cPine Plywood* Muminurn-?ticartaX* iVulcan 1 0.30 5.3Vdcan 010 0.36 6.4*E (secant) = 25,000 psi **E (secant) = 450,000 psiThe calculated values of thc linear stiffnesses (k ) correspondC.-to the peak force equivalent cushion (k ) given earlier for the inter-Pmediate range of pile irnpedanccs.The duration equivalent cushion(k ) given earlier is in general ngreement with the calculated cushiont dstiffness (kc).In general, it appears that the equivalent linear cushions ascalculated from recommended secant moduli given by Lowery et al. (SeeAppendix A) can give values in close agreement with the real behavior ofnonlinear cushions with certain exceptions as shown below.

Very Low Low and Medium HighPile Impedance Pile Impedance Pile Impedance-Peak Duration Peak Duration Peak DurationCalculated Too High Match Match Match TooLow MatchLinear Stiffness, (15-25%k(5-15%)'ou h",-1-m lowkcFor very low impedance, the peak forces or stresses calculated using. the secant modulus are larger than the real peak forces or stresses. At--the very low pile impedance, the maximum induced stresses are criticalbecause of the susceptibility of the pile to damage.By contrast, forhi@ impedance piles, actual induced stresses are normally low relative1to the yield point of the pile material; however, the real. peak forces orstresses are larger than the calculated values based on the recommendedsecant moduli.

CHAPTER 3PILE AND SOIL ESFONSE3.1 ----IntroductionPile penetration is accomplished only by generating a pile forcethat will overcome soil resistance at the pile tip.Therefore, emphasis-is placed on the pile and soil response at the pile tip. The investiga-tion of the soil and pile tip response includes a study of tip displace-ment, transmitted and reflectcd force pulses, end transmitted and re-flected energies.In addition, the effect of soil resistance along thepile length (skin friction resistance) will be qualitatively coniisideredwith respect to attenuation of the generated pile force as it approachesthe tip.The model of pile and soil tip used in this investigation isshown in Figure 3.1.Viscous damping (co), an elastic-plastic soil-spring (k , and a concentrated mass (m) are used to approximate thesrheological behavior of the soil under dynamic loading. Therefore, thesoil resistance takes into account: 1. elastic deformation, 2. perma-nent deformation, 3.static resistance, 4. viscous damping-strain rateeffect.Without the concentrated mass, the soil model is analogous tothe Kelvin-Voigt model and Smith's model (Smith, 1962).3.2 &namic - Behavior of SoilsThe main obstacle to predicting pile penetration response andstatic ultimate cavacity is simulating the soil mechanism during driving

FI= Generated Pile Force PulsePileConcentrated Soil Mass, rnsoil Spring, ks/Elastic, Elastic-Plastic or Non-Linear Inelastic+XViscous Damping, c0Figure 3.1PILE AND SOIL TIP MODEL

79with the proper dynamic characteristics of the soil. In an attempt todetermine the dynamic properties of the soil, a literature search wasmade for laboratory and field data that might lead to understanding thenature of dynamic soil resistance.The application-of lab results suchas triaxial unconfined compression, direct shear and model testsshould be considered only as indicative of the general nature of dynamicpile driving resistance.- Experimental ResultsAccording to Schimming et al. (1966), a French engineer, A.Collin, first recognized the time-dependent nature of soil strength in1846. For many years, only static strength and creep prohlerns of soilsreceived attention until the needs of protective structures required abetter understanding of dynamic soil behavior.Casagrnnde and Shannon(1948) initiated a test program to study the effects of the rate ofloading on soils such as clays, shales and dense dry sand.The testsresults indicated a significant increase in transient strength for co-hesive soils and only a slight effect on strength for dry sand.Seedand Lundgren (1954) studied the strain-rate effect on strength anddeformation characteristics of saturated sands.Whitman (1957) measuredthe increase in compressive strengths of cohesive soils. Since 1957,considerable attention has been devoted to dynamic soil properties.Aswmnary of soil dynamic test results is presented in Table 3.1.Thesummary is divided into two general soil classifications, cohesionlessand cohesive.The review of research shown in Table 3.1 indicates that boththe strength and modulus of the soil increase with an increase in strain

ate.However, the change in soil properties due to strain rate effectare more pronounced in cohesive soils than in cohesionless soils.For dry cohesionless soils there is a minimal difference betweendynamic and static behavior characteristics.The investigations on satu-rated cohesionless soils show a variation in strain rate effect fromminimal to significant and approaching that of the cohesive soils.This-variation can be attributed to the time dependency of excess pore pres-sures.Nhitman and Healy (1962) stated that since the friction angle isessentially independent of tine to failure, the strength of sand varieswith time to failure when excess pore pressures are time dependent.The time dependency of pore pressures and strain-rate effect ore a functionof the moisture content, grain size distribution, chemical composition,L-and density or compactness of the soil material.The possibility that cavitation may occur in some samples andnot in others might explain some of the variation of strain-rate effectin sands (Jones et al., 1966).According to Jones et al., cavitation,Pdeveloping at the expected reduced pressure of -1lipsi in sands, imposesa limit on increases in strength due to strain-rate effect, but thislimitation does not apply to clays in which cavitation does not normallyoccur during shear isho hop and Blight, 1963).The strain rate effect of cohesive soils is more definitivethan for cohesionless soils.This strain rate effect could be causedby a combination of factors such as a change in the inter-particlemechanism of yield in clay and a change in pore pressures due to nonuniformstress conditions.Whitman (1957) pointed out that the strain-rateeffect of cohesive soils is the result of viscous phenomena except whenfailure occurred by splitting.The dynamic properties of cohesive soils

are dependent upon moisture content or degree of saturation, structuralconfiguration, pore fluid type and degree of consolidation.The moisturecontent or degree of saturation appears to be the most pertinent soilproperty.Viscous characteristics are most pronounced above the optimumvater content and decrease to a negligible effect at no water content.Also, test results by Schimming et al. (1966) indicated that a pore-fluid viscosity radically different than that of water would produceradi cally different behavior.The preceding summary of dynamic soil behavior does not permitpostulating a failure mechanism during pile driving, but it indicates two'basic requirements for the model simulation of dynamic soil behavior,namely:1) under instantaneous applied load, the soil model should under-go instantaneous deformation and obtain a limiting value of capacity thatis equal to or in excess of the static value, 2) the soil model shouldindicate an increase in soil stiffness with an increase in loadinp, rate.The soil model shown in Figure 3.1 satisfies these two requirements.TheFsoil spring is normally assumed to be elastic-plastic and independentof time of loading whereas viscous damping and soil mass influence thestrain rate behavior.The static and dynamic load-deformation characteris-tics of the soil are shown in Figure 3.2.The strains at failure areshown to be ap;?roximately independent of strain-rate; this independencehas been proven by the test results previously summarized.Field ResultsSeveral investigators have attempted to correlate the wave equa-tion analysis using Smith's lumped-mass model (Appendix A) with pile load

Load--Resistance Due toDampingRU = Static Resistance1 p DeformationNet SetFigure 3.2LOIID-DEFORMATION CHARACTERISTICS OF SOIL MODEL

- tests. In a limited number of studies, attempts were made to determinethe dynamic properties of the soil model by trial and error procedures.This section will show the correlation with the field results and considerthe results of some model pile tests.First, however, the soil model used in Smith's wave equationanalysis is reviewed.The model js similar to that model shown inFigures 3.1 and 3.2 except that the soil mass is not included.The soil-A resistance equation proposed by Smith is shown below:R -dynamic(~+Jv) (3.1)Rstaticwhere R = dynamic soil resistance, R = static soil resisdynamicstatictance, J is a viscous damping factor and V is the instant,aneous velocityof the pile.This means that the real viscous damping constant c equn.7~0therefore, the J factor is related not only to velocity but alsoJRstatic7to static resistance.Rstaticequals k x ;here x is the elastic soilSdeformation. The yield point deformation is referred to as quake, Q.Smith proposed the same soil model for both the soils at the pile tipand along the sides; however, the soil dong the sides could act intension as well as compression whereas the 'soil at the tip did not havetension restraint.On the basis of a limited number of load test data, Smith (1960)proposed the following values for the soil parameters:Qside-%oint= 0.1 inch

Side damping was considered to be much less important than damping at thepile point because of the difference in the physical mechanism of thesoil failure.The side damping was arbitrarily taken as one-third ofthe demping at the pile point.Forehand and Reese (1964) correlated soil parameters used in thewave equation analysis with load test data.Three different types of-piles, concrete, steel pipe and steel 11-sections, were investigated forboth sand and clay soils.Becuase most of the hammer and pile variablescould be satisfactorily evaluated, the soil parameters could be variedand correlated with the load test data.Because of lack of knowledge,the side damping factor was assumed to be one-thrid of the point dampingin this study.The results of the correlation attempts for piles drivenin sand were consistent with Smith's recommended values.The range invalues of point and side quake was 0.05 to 0.15 in. and the range inpoint damping was 0.05 to 0.2 sec/ft.For piles driven into clay, the-correlation values of the soil parameters were much wider spread and notin accord with Smith's values. On the assumption that quake lies withinthe range of 0.1 to 0.2 inches, the range of the damping factors at thepoint was 0.5 to 1.0 sec/f% for Q = 0.1in. and 0.3 to 0.5 sec/ft forQ = 0.2 in.These damping factors for clsys are greater than Smith'srecommended values.Correlation of the wave equation analysis with field load testdata was also performed by Lowery et al. (1968).The pile-driving prob-lems in this study were investigated in three general locations, theTexas Gulf coast, the Arkansas River, and the sites of the Michigan Pile

Load Test programs.Nine different hammers were used to drive prestressedconcrete, steel H-sections, fluted-taper and pipe piles with lengths-~ranging from 30 to 180 feet.The soil conditions varied from sands in theArkansas River Project (Mansur et al., 1964) t o clays in the MichiganProgram (Michigan State Highway Commission, 1965) and combinations ofsands and clays in the Michigan Program and Texes Gulf Coast.According-+tothis correlation study, the soil quake ranged from 0.05 to 0.2 in.with 0.1 in. beirlg the most typical value for average driving conditions.The soil dmping factor, J . recommended for sands was 0.1 secjft;polnt 'for clays it is 0.3 secjft. The soil parameters for the combinations ofsand and clay were proportioned relative to the type and amount of ma-terial supporting the pile.The side damping factor was assumed one-third of the point damping.Pile load test results on the Arkansas River Project in mediumto fine silty sands below the water table indicated soil quake along theside of the pile equal to 0.1 to 0.2 inches (Coyle and Suiamin, 1967).- A study of load transfer of piles in clay indicated that the soil quakealong the pile variedwith depth; recommended values of quake wereequal to 0.15 inches to a depth of 20 feet and 0.07 inches for depthsgreater than 20 feet (coyle and Reese, 1966).Correlation studies between field data and soil model para-meters are somewhat limited; however, there %re some trends that can bededuced.First, the results for sands seem to be in genera1 agreementwith Smith's recommended values of soil parameters.Secondly, the clayproperties are more varied and damping factors for clay are higher than

Smith's values; however, the complexity of cohesive soils due to thixo-tropy and pore pressure effects with respect to time make an analysisduring driving very difficult.Because of this complexity wide varia-tions in clay properties are expected.The results of the lab strengthtests also agree with these general conclusions.Dynamic tri'axial test results by Coyle and Gibson (1970) indi-. cated that the damping factor (3) as defined by Smit;h is not a constant-for a particular soil but is a function of the loading velocity rate forboth sand and clay soils.This study shows the nonlinear relationshipbetween the ratio of dynamic to static resistance and loading velocity,and possibly helps explain some of the variation in the soil parameterstudies.For normal loading velocities of 2 to 12 fps, the dampingfactor for sands varies from 0.1 to 0.4 seclft; for clays it ranges from0.15 to 0.6 seclft. The lower damping factors corresponfi to the higherloading rates.Coyle and Gibson (1970) suggested the following modifi-cation of Smith's relationship to obtain a constant value of 3':R1 dynamicJ' = - ( - 1)SJ *staticAn acceptable constant, J', for saturated sands is derived if N is 0.20and for clays if N is 0.18.For the soils investigated, J' ranges from0.5 to 0.9 for sands, and 0.7 to 1.1 for clays. These soil dampingconstants are related to common soil properties of both sand and clay.The soil model chosen herein is representative of soil behaviorbased on research on dynamic soil properties in both the laboratory andthe field.At present, there are definite trends for the soil model

parameters with soil index properties.Of course, the correlation iscomplicated by the differences in soil behavior during and after piledriving.There is no attempt in this treatment to correlate soil para-meters with index properties; however, this study will investigate theeffect of the soil parameters with respect to generated force pulses inpile driving.-3.3 -- Basic EquationsThe equations of equilibrium of the pile and soil tip can bewritten for the soil model as previously Bescribed and shown in Figure3.3. The incident force pulse in the pile describes the velocity (VI).at a point in the pile as shown below:F = pcA VII(3.3)where pcA is pile impedance. Equation 3.3 is similar to Equation 2.1,Ibut subscripts I and R are required to distinguish between incident and- reflected waves.i'Then the incident wave encounters a discontinuity of materialand area such as the soil at the pile tip, the incident wave is trans-mitted to the soil and/or reflected back through the pile.to be satisfied at the pile and soil interface are the equality of1 both force and particle velocity (Figure 3.3);The conditions

F = IncidentI ForcePulseSoilSpring,ModelFree-Body DiagramFigure 3.3 FREE-BODY DIAGRAM OF PILE AND SOIL TIP MODZL

where VI and Y refer to the pile particle velocity of the incident andRreflected waves, m is the soil mass, c is the soil damping, and k is0 sthe soil spring stiffness which can be varied from elastic to nonlinearinelastic.Simultaneous solution of Equations 3.4 and 3.5 yields the fol-lowing expression between the incident force pulse and the soil tip-response :m~ + (co + pc~) i + k s x = 2 DCA v I (3.6)The solution of Equation 3.6 is used for the determination of tip dis-placement, transmitted and reflected force pulse, and transmitted andreflected energy.The reflected force pulse can be shown to beThe force reflections depend upon the following cases:1) If i matches VI, no reflections occur2) If < V compressive refl.ections occurI'- 3) If 2 > VI, tensile reflections occur.The transmitted enera, i.e. the energy transmitted to the soil,can be defined in terms of the incident and reflected energy as shownbelow:Energy (E~)Transmitted Energy (E ) = Incident Energy (E ) - ReflectedTI

The solutions of Equations 3.6, 3.7 and 3.8 were obtained withthe use of the analog computer as described in Appendix C.Attempts weremade to nondimensionalize these euqations; however, the restrictions ofthe initial and boundary conditions did not permit taking advantage ofthis approach.Therefore, particular problems were chosen and studiedindividually.3.4 TkResponse of Pile and Soil-- IntroductionThe response of the pile tip was investigated for varying pileimpedances, force pulse shapes and energies, and soil parameters.The.-pile impedances selected are 1000, 3000 and 6000 lbs-seclin., which representthin-wall pipe to a heavy-wall pipe, H-piles and mandrels. Theimpedances and equivalent section sizes for pile types such as steel,concrete and wood are shown in Table 3.2.. .These three impedances wereselected to represent the range of piling in comon use. The energylevels were varied from 6250 to 25,000 ft-lbs, which represent the commonrange of hammer energies after consideration of hammer efficiencies.The primary wave shape considered in this investigation is thesine wave, which corresponds to the impedance match condition describedin Chapter 2.Other wave shapes such as rectangular and triangular arealso included in order to determine the effect of wave shape on pile

Table 3.2PILE IMPEDANCE AND PILE TYPES FOR THE TIPMODEL INVESTIGATIONImpedance,lbs-secPCA, in.SteelConcreteWoodArea. Area. Diameter. Width Area. Diameter.2 2 (square)in in in.in.in 2 in.1000 6.9 32.4 6.4 5.7 113 12.0(Thin-wall Pipe)3000 20.7 9'7.2 11.1 9.9 339 20.0(Pipe or B-Pile)6000 41. .I+ 194.4 15.7 13.9 678 29.4(Mandrel.)

penetration (net set) and capacity.Considering the duration of theforce pulse for the matched condition of pile impedance and hammer,as shown in Figure 3.4 and described in Chapter 2, the peak forcefor the sine wave can be determined from the following relationship:- where pcA is impedance, E is the incident energy and t is the dura-I 1tion of the force pulse.The duration t was varied according to the1range in hammer weight and cushion stiffness for the matched conditionas shown in Figure 3.4; the corresponding peak forces used in thisstudy are referenced by case number as given in Table 3.3.The dura-tion and the corresponding peak force were varied with respect to aparticular energy level in order to investigate their effect on piletip response.These peak forces correspond to the peak values shown inFigure 2.10 (Chapter.2) determined on the basis of a three-foot hwnmerdrop.FIt is assmed that the incident force wave can fully developwithout interruption from the reflections at the pile head; therefore,the pulse length can be no longer than twice the pile length.The pulselength and corresponding pile length can be defined as follows:ct1 1 1- 2 2 1000Pile Length > - Pulse Length = - (-)ft.(3.10)where c is the velocity of wave propagation and t is the pulse dura-1tion in milliseconds.For steel, the velocity of wave propagation is

Table 3.3INCIDENT FORCE PULSE AND ENERGIES FOR TIP MODELPile ImpedanceEnergy, ft-lbslbs-secPCA, in. 6,250 12,500 25,000Case 1-1 Case 1-2 Case 1-3F = 141 112 kips F = 141 112 kips F = 141 112 kipsP P Ptl = 7 112 ms tl = 15 ms tl = 30 msCase 1-4 Case 1-5F = 100 kips F = 100 kips --Ptl = 15 msPtl = 30 msCase 1-6F = 70.7 kips --Ptl = 20 msCase' 3-1 Case 3-2 Case 3-3F = 425 kips ' F = 425 kips F = 425 kipsP P Ptl = 2 112 ms tl = 5 ms t = 10 ms1Case 3-A Case 3-B Case 3:CF = 300 kips F = 300 kips F = 300 kipsP P Pt =5ms tl = 10 ms tl = 20 ms1Case 3-4 Case 3-5F = 212 kips F = 212 kips --PPtl = 10 ms tl = 20 ms-case 6-1 Case 6-2 Case 6-3F = 850 kips F = 850 kips F = 850 kipsP P Ptl = 1 1/4 ms tl = 2 112 ms tl=5msCase 6-4 Case 6-A Case 6-BF = 600 kips F = 600 kips F = 600 kipsP P Ptl = 2 1/2 ms t1=5ms tl = 10 msNote:case 6-5 case 6-6 Case 6-7F = 425 kips F = 425 kips F = 425 kipsD u -PtA=5ms t =lOms t- = 20 ms1111. Force pulse is a sine wave with tl representing the timeduration and F representing the peak force.2. Soil mass (w/$ equals 1/4; equivalent soil weight is 97 lbs.3. Soil spring is elastic-plastic with a soil quake equal to 0.1 in.4. Soil damping is varied over a wide range.

about 16,600 ft/sec, whereas for both concrete and wood the propagationvelocity is approximately 12,000 ft/sec.The maximum duration of aforce pulse was chosen to be 30 milliseconds.Some of the ~ctual dura-tions for low pile impedances coupled with high energy levels exceededthis 30 millisecond criterion (~igure 3.4); they were not included inthis study because they represent impractical conditions.-The soil parameters include stiffness, mass and damping. Thesoil spring commonly employed is elastic-plastic in behavior with the un-loading parallel to the loading curve.The soil quake or soil yieldpoint deflection is varied; however, experimental and field results showthat a value of 0.1 in. is common.also investigated for comparison.A nonlinear inelastic spring wasThe soil mass was varied to representa soil weight (W) of 0 to 386 pounds.Thesoil dmping was varied overa wide range for each parameter study and individual problem.lbs-secdmping constant c was varied from 0 to 20,000 in. for the low pile0lbs-secimpedance and from 0 to 50,000 for the high pile impedance.in.Soil MassThe influence of soil mass on the dynamic behavior of the pileThetip is a mnction of the pile tip area arid the stress distribution.Thesoil mass is an additional resistance to pile motion or penetration.The soil mass was varied according to typical zones of influence of thestress distributions and investigated with respect to pile impedance.The problems investigated are shown in Table 3.4.The soil mass restraint is expected to be more influential forlow impedance piles than for piles with high impedances; therefore,

. . Table 3.4CASES INVESTIGATED FOR SOIL MASS EFFECTPile Impedance, Case Energy Peak Time Soil Mass, mlbs-secForce, Duration,ft-lbs kips mslbs-secPCA, in.w,lb sFNote:1. Sinusoidal Force Pulse2. Elastic-Plastic Soil Spring with Quake = 0.1 in.

. -the soil mass effect was initiated for a pile with low impedance, namely,lbs-sec1000 . . This study (Table 3.4) included a sine force pulse withIn.an energy of 16,680 ft-lbs. and soil masses (~/g) of 0, l/4 and 1, whichare equivalent to soil weights, 0, 97 and 386 lbs, respectively.TheIeffect of soil mass on the net set of the pile tip for the above de-scribed conditions is negligible as shown in Figure 3.5.-It should be noted that the soil mass was assumed attached tothe pile tip. Consequently, the mass undergoes both penetration mdi1 rebound. In the real case, the pile can separate from the mass duringrebound or during impact when the mass is driven faster than the pilettip motion.However, because the mass had a negligible effect. on piletip penetration (Figure 3.5); it was assumed that the effect of massis also negligible if the pile -tip cm separate from the soil mass.lbs-secTransmitted energy for the low pile impedance, 1000---i-n ,was also compared for different mass constants and the differences werefound to be negligible.However, the mass caused a delayed response of*the net transmitted energy; similar behavior occurred for the reflectedforce pulse.This delayed response can be seen by comparing the reflectedforce for the different mass constants (Figure 3.6).As shown in Figure3.6, the larger soil mass has an instantaneous resistance effect forlow damping values and thereby delays the peak reflected tensile forceand changes the reflected force shape.With an increase in resistance,lbs-sece .g. damping (co) of 2000 --- , the mass effect becomes negligiblein.with respect to the response pattern.The response pattern was shownfor no soil spring resistance; however, the behavior characteristics

. . .. .ForceKips01bs-secin.Time, msForceKipsTime, msForceKipsFigure 3.6Time, msNote: 1. Pile Impedance =1000 lbs-secin.2. Energy =16,680 ft-lbs3. Simsoidal ForcePulse4. No SpringResistanceCOMPARISON OF REELECTED FORCE PULSE RESPONSEFOR DTFFERENT SOIL MASSES

were the same with different spring forces as evidenced by the negligibleeffect of soil mass on the net set of pile tip for different soil springresistances (Figure 3.5).The other cases listed in Table 3.4 resultedin similar conclusions.Because the range in soil mass investigated did not have a significanteffect on pile tip response, a soil mass of 1/4 or an equivalentweight of 97 lbs. was used for the following parameter study as a standardallowance.Incident Force PulseIn the most efficient pile driving technique, the incident forceis effective against the soil resistance in such a way that maximumpenetration (net set) or minimum driving time occurs along with the de-sired pile performance.The effectiveness of the incident force pulse isinvestigated by varying the energy, peak force and duration of a sinu-soidal wave, and by varying the wave shape.The effects of a sinusoidal incident force wave with differentFenergies and different durations for the same energy will be investigated.The cases investigated are summarized in Table 3.3; however, thelbs-secbehavior pattern for a pile impedance of 3000in.is representativeof dl cases and, hence, is the only data presented. The net set re-sponse of the pile tip for different ultimate soil spring resistances(RU) and energy levels are shown in Figure 3.7.The soil spring iselastic-plastic with a quake value of 0.1 in., and soil damping is varied.It should be noted that for a given soil damping value the net set increaseswith an increase of input energy providing the peak force ismore than one-half of the ultimate spring force.

Damping Constant, c x 1000,0lbs-secin.Note:Soil Spring Elwtio-Plastic and Quake = 0.1 in.Figwe 3.7 NET SET RESPONSE OF THE PILE TIP FOR PILElbs-secIMPEDANCE OF 3000 in.

. -The force pulses with longer durations for a given enerrg levelare more efficient for pile penetration provided the peak pile force isequal to or greater than the ultimate soil spring resistance.For ex-ample, compare the conditions where the soil spring ultimate equals 100and 300 kips as shown in Figure 3.7.The different force pulses workingagainst a soil spring resistance of 100 kips clearly show that maximumnet set occurs with an increase in force duration for the same enerrg-level. However, all the peak pile forces considered are greater thanthe 100 kips.For the condition of 300 kips resistance, the caseswherein the peak forces equal or exceed the spring resistance are moreefficient for pile penetration than the longer time pulses'with peakforces lower than the ultimate spring resistance.The condition of400 kips resistance further exemplifies the influence of the generatedpeak force versus time pulse length.Also, the pile tip deformation iscompletely elastic if twice the peak pile force is equal to or less thanthe ultimate spring resistance.Based on the previous example, and theanalogous behavior of the other pile impedances investigated, theFfollowing conditions can be summarized for a given enera input:1. For the conditionF(pile peak force)Ru(soil spring ultimate)+ , maximumpile penetration occurs with no soil resistance.2. For the conditionF(pile peak force)Ru(soil spring ultimate), l, maximmpenetration increases with an increase in duration and isinfluenced little by the peak force.

3. %r the condition'(pile peak force) < ,R u(sol1 . . spring ultimate)maximum pile penetration is pr-imarily dependent on the peakforce and is influenced little by the duration.peak force)4. For the condition - -Ru(soil spring ultimate)< 1/2, no net pilepenetration occurs; the deformations are purely elastic.-An investigation was also made of the effect of force pulse shape.The wave shapes--triangular, sine and square--are compared for a constantincident energy of 12,500 ft-lbs and a constant peak force for a particu-lar value of pile impedance; therefore, the duration is different foreach wave shape.The triangular pulse is symmetric in shape as shown inTable 3.5.The cases compared for the effect of wave shape are tabulatedin Table 3.5; however, the behavior pattern for a pile impedance of 3000lbs-sec .is representative of all cases and, hence, is the only data prein.sented.The effect of wave shape on pile penetration is shown inFigure 3.8..- lbs-secFor the pile impedance of 3000 , the longer pulse (triin.angular wave) is the most efficient for pile penetration provided thepile peak force is greater than the soil spring resistance as shown inFigure 3.8 for a soil spring ultimate (R ) equal to 100 kips.uThis be-havior indicates that the efficiency order of the wave shape is triangu-lar (most efficient), sine and square (least efficient) for the condi-tion of the peak pile force greater than R . As the peak pile forceUapproaches and becomes less than the soil spring resistance (R ), theuorder of efficiency reverses with the square wave being the most effi-

Table 3.5CASES INVESTIGATED FOR WAVE SWE EFFECTPile Imnedance. Case Wave Energv Peak TimeShape Force, Durationlbs-secPCA, in.ft-lbs kips tl, ms-Wave1-13 Spiked 12,500 141 1/2 22 112 '" kips2 Sine 12,500 141 1/2 15 r\ lL 1/2 kips1-14 Square 12,500 141 1/2 7 1/27 1/2 ms141 1/2 kips3-12 Spiked 12,500 300 153-B Sine 12,500 300 10 n15 ms300 kips10 ms6-9 Spiked 12,500 600 7 1/26000 6-A Sine 12,500 600 56-10 Square 12,500 600 2 1/25 ms2 1/2 ms600 kips600 kipsNote:1) Elastic-plastic spring with Quake = 0.1 in.2) Soil Mass, u / = ~ 114

a,z o 4 8 12 16 20: , RU = 200k+ '. ... ----': -' 1.20.8.- ....... ...L .......a -- ..+ . -. . - . -. . . . --- Sine.... -- + -.--. .-- . . . .... ..-.- ------ Square '"'...0.4 With Quake = 0.1 in.0- ' - -....Legend:lbs-secDamping Constant, c x 1000, in.0TriangularSoil Spring is Elastic-PlasticFigure 3.8 EFFECT OF WAVE SHAPE ON PILE PFNETRATION FORlbs-secPILE IMPEDANCE OF 3000 in--'""

- - cient and the triangular wave the least efficient, as shown in Figure3.8 for the condition of RU equal to 400 kips. This behavior indicatesthat duration near the peak pile force is significant for the conditionof peak pile force less than the soil spring resistance.Based on the previous example, and the analogous behavior ofthe other pile impedances investigated, the following conditions can besummarized for different wave shapes with a particular energy:- F (pile peak force)1. For the condition of -t -, maximumF(soil spring ultimate)pile penetration occurs with no soil resistance.2. For the condition ofF(pile peakFsoil spring ultimate)> 1, maximumpile penetration occurs for the force pulse shape withthe longest duration.3. For the condition ofF(nile peak force),< and >sol1 spring ultimate)maximum pile penetration occurs for the force pulse shapewith the longest duration near the peak gile force.4. For the condition ofF(pile peak force) < no net-F(soil spring ultimate)pile penetration (only elastic deformation) occurs;therefore, wave shape is not pertinent.It is believed that the foregoing behavior is generally validfor other wave shapes, pile impedances and energy levels.

Soil PropertiesThe soil properties are represented by the soil spring, dampingand mass resistance.The soil mass effect has been previously discussedand will not be included in this section; however, the effects of bothdamping and the soil spring on pile tip response will be discussed herein.Before the numerical results are considered, the response be--havior of a pile tip with respect to the soil restraint will be dis-cussed qualitatively.For damping restraint only with no soil spring re-sistance (free-end condition) the incident compressive wave is re-flected as a tensile wave with the same penk force and shape at zerodamping, and no transmitted wave exists.As the damping restraint isincreased, the reflected wave passes from a tensile to a compressivewave with no reflections occurring when the pile impedance and thedamping constant are equal.A compressive wave reflection equal to theincident wave corresponds to a fixed-end condition.The no-reflection-condition represents the optimum match between pile and soil for maxi-mizing transmitted energy.When a soil spring is included along with damping, the dampingconstant required for maximum energy transmission decreases with in-creases in spring resistance.Soil damping and the soil spring con-trol both the reflected force wave and transmitted energy.With re-spect to the efficiency of pile driving, the set (penetration) efficiencyis more significant than energy efficiency; however, the conceptof transmitted energy efficiency can be used as a reference frameworkfor discussing the behavior characteristics of the pile tip.

The foregoing brief qualitative behavior of pile tip responsecan best be exemplified by consideration of a particular problem, namely,lbs-secCase 3-B with a pile impedance of 3000 . The reflected forcein.wave for this case due to an incident sinusoidal wave is shown inFigure 3.9. The set shown by the curves for a spring force equal tozero clearly shows the transition of tensile to compressive reflection;no reflection occurs at a damping constant of 3000 lbs-sec which equalsin.- the pile impedance.With the addition of the elastic-plastic soil spring, the waveshape for low damping values is controlled by the springs, whereas forhigh damping values the reflected wave is dominated by the damping re-straint.The first break in the low damping value reflections as shownin Figure 3.9 (R = 100 kips) signifies the beginning of plastic springubehavior, and the cross-point of the reflected waves (Figure 3.9 andRU= 100 kips) signifies the unloading of the spring. Thebeginning ofthe plastic behavior ofthe soil spring occurs more rapidly with thesmaller soil spring resistances (R ), whereas the unloading conditionu-occurs more rapidly with the higher soil spring resistance (R ).It can be seen by the reflected forces (Figure 3.9) that as thesoil spring ultimate (R ) increases the damping constant decreases fromU3000 Ibs-sec to zero for the condition of least reflection; therefore,in.this condi.tion also applies to the maximum transmitted energy of theUsoil.The soil damping values at maximum transmitted energy and thecorresponding transmitted energy efficiencies (percentage of trans-mitted to incident energy) have been tabulated for the cases of the

,r . c = Damping constant,olbs-secin.Incident Wave:Figure 3.90.r( -&-~ * .----------..-.-----20 Time , ms 14Sine Wave F = 300 kips tl = 10ms. EI = 12,500 ft-lbsPREFLECTED FORCE PULSES FOR CASE 3-B WITHPILE IMPEDANCE OF 3000 lbs-secin.

asic parameter study listed in Table 3.3 as well as the Case 3-B presentedherein (Table 3.6).As seen from Table 3.6, soil damping values atmaximum transmitted energy for different pile impedances and soil springresistances (R ) correspond to the general behavior as previously de-Uscribed.The transmitted energy efficiciency has a value of 100% at zerosoil spring resistance and reduces to a minimum value of approximately 70%-as the soil spring resistance approaches the value of the pile peakforce.With a soil spring force in excess of the peak force in the pile,the efficiency of the transmitted energy reduces markedly.This reductionin energy transmission is indicative of the pile penetration, i.e., pilepenetration decreases with a decrease in transmitted enera. However,it should be noted that maximum energy transmission does not guaranteemaximum pile penetration.Maximum pile penetration is also dependent onthe force pulse shape with respect to the soil resistance as describedpreviously.The relected force pulses shown in Fi.gure 3.9 are representativeFof the behavior of the other cases studied.The reflected wave corres-ponds to the incident wave form, i.e. a longer and lower peak incidentwave produces a corresponding reflected wave.Also, the reflected waveshape corresponds to the incident wave as shown by the exanples used forthe triangdar and square wave investigation.The effect of damping on pile penetration is clearly definedby the condition that any additional restraint impedes penetration;therefore, an increase in either the damping constant or spring ulti-mate reduces the pile tip set for a given problem.This fact is readily

. . Table 3.6SOIL DiiMPlNC AT OPTIMD( ENERGY TWINSMISSIONI rile Ir!pdancr = 1000Ia m " l n"ere, i imnsm,srlon. r v c . e ibs-in/.l... i u e VTransmlrted Energy Erflciency, $ ''Energy Per& TlmeInput Force, hiatlo",R = 0 Ru = 50' Ru = look Ru = 200kC,brc rt-lbs. kips m ~ .1-1 6.250 141 1/2 1 1/2 100G1000 8 500 222 2521-4 6.250 100 151-6 6,250 70.1 301-2 12,500 111 112 151-5 1?,500 100 30100 93 92 L6- 10000 ..100881000-1000 s ,100 4 . g2% - 0loo 98 95 551000 s %..100 931000 -- -. 0100 %55I-? 25,000 141 112 30I i'llc impedance = 3000- I"lulplng value e nx,mun rner rsnsm2ssion I.," $PCEnergy YeR* Time Tr:n%rtFd Zrriciency. P+lUInput Force. Durerion.ClS" rt-lbs. kipsR = ok R = 108 nu = 200k nu = 300k R" = book n = 600k".5- 1 6.250 425 2 1/23-A 6.250 300 53-h 6.250 212 103000 3000 & 2000 2000 2000 k 1000 6000100 96 90 83 17 -173000- 0 a000%'3%'100 $ 50 zr7m 76--100 911 81--0000 2000 k 1000 2 0 60003000 3000 k 2000 2000 & 1000 .- 0 3 ,3-2 12.500 425 5loo 98 93 90 83 513-8 12,500 300 10 - 3000 - 2000 - 10000 - 020100 91 92 59ii;3000 3000 6 1000 2 =20,000 - 03-5 12,500 212 20..100 97 90 55 93-3 25,000 425 10 30003000 k 2000 2000 S 1000 I000 0 - 0-133 DT553000 Tic0 -..- 0 0 ..100 99 95 853-C 25,000 300 10 - - 6T[ File Impeesnce = 6000 - Iin.DrnDl"R value et naximwn Eneipy Trsnsmi.sia,,, c , Ibb-ii/s"c~ ~ ~ r gpeak y ~ime Transmitted enera Errieiency. $Input Force, nwation,Case rr-lbr. kipsR = O R" = look R" = 200k A" = 300k nu = i200k n = sooh n = OOG"".56000 6000 - 6000 - 60006 k 10~000 6 & 10,0006-1 6,250 850 1. l/b100 100 95 90 %? 19 7160006-Li 6,250 600 2 1/2 - - 6000 6 6 3000 6 s 3000 .. ?!20?6000100 92 7- 18 55@g - 6000 3000 y$? -- 3 k 1000 A?&!? ..6 5 6,250 1425 5100 99 92 116000 @ - 6000 3ooo6-2 12,500 850 2 1/2-- 3000F'6000G-n- 6000 3000 - 3000 -I000 k 0 -. 012,500 600 5100 98 93 92 85 - 73 506ooo - 6000 - 3000 - 10006 6 12,500 1125 10 ..100 99 91 82 G60005- +' 6000 - 3000 lo00 1000 L 06-3 25.000 850100 99 .95 89 hi6-9 25.000 600 10 6ooo @g - 3000 - 3000 0 0100 98 97 95 91 8i t66000 - 3000 6 - 06-1 25,500 b21 20--100 100 53-- loo 99 95 91 89 loBi

.. -shown in the results of the investigation such as the particular casepreviously discussed and shown in Figure 3.7.Soil spring quake and spring force-deflection shape will now beinvestigated.The cases investigated for the quake and spring shapeeffect are shown in Table 3.7.The soil quake effect was investigatedwith respect to an elastic-plastic soil spring and a sine force pulse-(0 to 0.40 in.) covered both stiff soils to soft soils. Effects ofwith an energy level of 12,500 ft. lbs.The range in quake valuesthe soil quake on the net penetration are shown in Figures 3.10, 3.11lbs-secand 3.12 for pile impedances of 1000, 3000, and 6000 , rein.spectively. All plots show a decrease in net penetration with an in-crease in soil quake.This decrease in net penetration with a softersoil spring can be attributed to the larger elastic strain enerey requiredto reach the yield point, Q.The problems previously discussed have been associated with anelastic-plastic soil spring; however, the behavior of a different force-deformation shape will also be considered herein.-vestigation with respect to the spring force shape is li-sted in TableThe range of the in-3.7. The incident force pulses and pile impedances are the same as forthe quake study.The nonlinear and inelastic spring can be compared tothe elastic-plastic spring for the effect of penetration (Figure 3.13);soil quake at the break in spring load-deformation curve was held con-stant (0.1 in.).The stiffer nonlinear spring increases the soil re-sistance; therefore, the nonlinear spring will reduce penetration asshown in Figure 3.13.It should be noted that at high damping constants

Table 3.7CASES ASSOCIATED WITH SOIL SPRING QUAKEAND SPRING FORCE DEFLECTION SHAPEEPFECT OF SOIL QUAKE*Pile Case Input Peak ForceImpedance, Energy Force, Timelbs-secDuration,ft-lbs kips m6in.in.EFFECT OF,SPRING FORCE SHAPE*" 1Pile Case Input Peak Force Soil Spring TypeImpedance, Energy Force, Timelbs-secDuration,- in.ft-lbs kips msR - .1-2 12,500 141 1/2 15 elastic-plastic "YE7 a1000 1-8 12,500 141 112 15 nonlinear and inelastic1-9 12,500 141 112 15 elasticR -3-8 12,500 300 10 elastic-plastic "0AQ=0.1"3000 3-7 12,500 300 10 nonlinear and inelastic3-8 12.500 300 10 elastic6-A 12,500 600 5 elastic-plastic AsQ=o. 1"6000 6-14 12,500 600 5 nonlinear and inelastic6-15 12,500 600 5 elasticQ=0.lM1. Elastic-plastic soil spring2. Sinwoidal force pulse** Sinusoidal force pulse

Damping Constant, cx 1000, lbs-scc/in.0Incident Force Wave: Sine Wave with Fp = 141 1/2 kips a d15 ms. EI 12.500 ft-lbs11" = 200 ktl =-Figure 3.10EFFECT OF SOIL QUAKE ON PENETRATION FOR PILE IMPEDANCE OF 1000 lbs-secin .'

1- .. a-. .. 4-4 .Damping Constant. cox 1000, lbs-secin.Incident Force Wave:Sine Wave with F 1300 kips t -10 ms. E =12,500 ft-lbsP 1 IFigure 3.11EFFECT OF SOIL QUAKE ON PENETRATION FORPILE IMPEDANCE OF 3000 lbs-sec/fn.

k. 0.8 ; ,--;NO+; I1 : Different Scale IVertical--- ,Curve (inches)Incident Force Wave:Ngure 3.120 4 8 12 16 20Damping Constant, c x 1000,olbs-secin.- Sine Wave F 600 kips tl = 5ms EI = 12.500 +t-lbsPEFFECT OF SOIL QUAKE ON PENETRATIO!I FOR PILEIMPEDANCE OF 6000 lbe-sec/in.

ertical ScaleU0 4 8 12 16 20Damping Constant cox 1000, lbs-secin.Figure 3.13 EFW%CT OF SOIL SPRING FORCE SHAPE ON PILE PEN'ETRATION

' penetration is not influenced by the spring force shape.The reflectedforce also changes little for different spring force shapes with highdamping.This study has indicated the influence on pile penetration ofthe parameters of the incident force wave with respect to the soil re-sistance properties.The investigation of pile response was devoted tothe pile tip only; the effect of soil resistance along the pile (skin- friction) was not included.3.5 Effect of Soil Resistance Along Pile LengthIntroductionThe purpose of this section is to investigate qualitativelythe effect of the side soil resistance (skin friction) on the attenuationand shape of the incident force pulse.It is the attenuated forcepulse that reaches the pile tip and causes penetration.-In order to study attenuation of the incident force pulsean illustrative problem with selected hammer, pile and soil characteristicswill be solved with the use of Smith's lumped-mass and spring model(see Appendix A).The problem shown in Figure 3.14 considers a 150 ftlbs-seclong pile with an impedance of 3000 in. driven with a hammer withan energy delivery at impact of 12,500 ft-lbs.The soil skin frictionresistance is considered uniformly distributed along the pile; however,values of the soil resistance parameters will be varied.The soil re-sistance distribution includes a variation in the relative amounts oftotal skin friction and point bearing.The soil resistance is repre-

Enerey at Impact = 12,500 ft-lbs.HmerCushion6k = 1x10 lbs/in. and e = 1.0W2 = 1000 lbsSide Soil Resistance - UniformVaried from 0 to 100%Q = 0.05 to 0.20 in. Normally 0.10 in.ssecsecJ =Oto0.15, Normally 0.05 -Sftlbs-secPile: Impedance = 3000 in.Area of Steel = 20.7 in. 2Length = 150 ftPile Model:Lumped-Masses and SpringsSegment Length = $ ft?.rt - 6 ibs- 353 lbs Kseg=lOx10Se&- Tip Soil Resistance-Varied from 0 to 100%0.10 in. J 0.15 sec/ftPtNote:Total Soil Resistance Equals 100 kipsfigure 3.14 EXAMPLE PROBLEM FOR THE EFFECT OF SOIL RESISTANCE ALONG PILE

-.sented by an elastic-plastic spring and damping. Details of the example,problem are shown in Figure 3.14.Distribution of Soil Resistance ..The attenuation of the incident force pulse at the pile headwas investigated with respect to a range in uniform soil resistance alongthe pile length of 0% (point-bearing) to 100% (friction) utilizing thesoil parameters recommended by Smith (1960). From this study, thegenerated peak force pulse was attenuated by approximately one-half thetotal of the side friction load.The total side friction load is proba-bly a limit of attenuation.The effect of attenuation by frictional soil resistance is notas critical to pile penetration as the effect of the tip resistance be-cause of the physical nature of the soil resistance distribution.Soilresistance along the pile is distributed in parts, i.e. a percentageof resistance at each lumped mass segment; therefore, the effect of thetotal soil spring resistance for all segments is smaller for a givenquake value than if the same resistance occurred at one segment (~iletip).Also, the tip resistance damping is assumed higher than theside resistance damping because of the physical mechanism of the soilfailure; hence, resistance to penetration is greater at the pile tip.Therefore, driving a point bearing pile would be the more difficult(less set per blow) and driving a frictlon pile would be the less dif-ficult (more set per blow).Other pile driving conditions are inter-mediate between those of pure friction and point bearing piles.

- Soil ParametersThe effect of soil parameters, quake and damping, along the pilelength will now be investigated.This soil parameter study makes use ofthe illustrative problem (Figure 3.14) with a uniform soil skin frictiondistribution amounting to 50% of total pile load capacity.Soil quakeand soil damping along the pile length were varied.The soil properties-at the tip were held constant.In order to compare the effects of soil parameters, the totalforce response (incident and reflected added together) at the pile tipwere compared for the variations in soil parameters.It is assumed thatany! changes in the soil parameters along the pile,would produce a changein the total force response at the pile tip.The side soil quake was varied between 0.05 and 0.20 in. as shownin Figure 3.15, and the difference in total force response was found tobe negligible.-Also shown in Figure 3.15 is the effect of side soil damping,which was varied between limits of 0 and 0.15 sec/ft. The change inresponse for the sidedamping is slightly more noticeable than theeffect of quake; however, the force pulse is still not particularlysensitive to the side damping term.The relative percentage of total resistance at the pile tipand along the pile length is significant for evaluation of pile penetra-tion.Pile penetration behavior is not particularly sensitive to soilparameters along the pile length; therefore, these parameters are not ofmajor importance to the evaluation of pile penetration.

Time After Ram Impact, miLlisecondsNote: Refer to Figure 3.14 for Pile and Soil Data R = 50%tipFigure 3.15EFFECT OF QUAKE AND DAMPING ALONG THE PILE ON PILE TIP FORCE

CHAPTER :rCHARACTERISTICS OF HAMMER-PILE-SOIL SYSTEMAFFECTING PILE DRIVING BEHAVIORI4.1 IntroductionIIThe purpose of this chapter is to 8ummarize the effects of thevariables affecting pile driving behavior by looking at the hammer-pile-soil system as a whole. The variables of the hammer, pile and soil willI -be summarized and explained with the use of parameter studies (chaptersI1 2 and 3) and illustrative examples from field case histories. A corres-1Iponding analysis using the wave equation (Smith's lumped mass-spring model)will also be shown for each field case history.Field studies with dieselhammers will be included where the variable under consideration is inde-pendent of combustion force uncertainties.Comparison of wave equation1 . analyses with field case histories will illustrate the power of this ana-II.-lytical tool, and lend further validity to the use of wave propagationtheory in pile driving.Dynamic enera formulas will be compared to thewave equation analysis, and the limitations of energy formulas will bedelineated.4.2 Pile HammerEnergyThe pile hammer is an enera source used to generate a force pulsein the pile in order to oliercome soil resistance and achieve penetration.The potential energy of the hammer is a function of the ram weight andstroke, or equivalent stroke at impact.Hammer potential enera has two

sources of losses, namely, energy loss during ram fall and loss in trans-mission through the cushion and drivehead to the pile.Energy losses priorto impact include mechanical losses such as friction, preadmission ofsteam or air etc., whereas the transmitted energy losses include the inelasticbehavior of the hammer cushion and contacts, and ram rebound.It should be noted that it is not only necessary to transmit energyin order to achieve maximum penetration and load capacity, but it is also-necessary that the shape of the generated force-time pulse be proper. Inthis section transmitted energy will be considered first and the effect offorce pulse shape will follow.Considering transmitted energy only, pile penetration and loadcapacity increase with an increase in transmitted energy for a given pileprovided the peak force generated is greater than one-half the ultimatesoil spring resistance at the pile tip.The effect of energy on the re-sponse of piles with impedances of 1000, 3000 and 6000 lbs-sec (equivain.lent pile types and sizes are shown in Table 3.2) is shown in Figure 4.1.The pile response is taken from some of the cases investigated in Chapter3 for a sinusoidal incident wave acting against a viscous damping factor,J = 0.15 sec/ft, and soil quake,- ptassumed in wave equation analyses.&pt = 0.10 in., which are commonlyl'he soil spring is elastic-plasticwith a variable ultimate resistance (nu). The curves on Figure 4.1were obtained by selecting the pile net set (Chapter 3) for various ultimatespring resistances (R ) and the damping value related to the Jufactor; the number of hammer blows per unit set is the reciprocal ofpile net set.As shown in Figure 4.1, pile penetration and capacity increasewith an increase in transmitted energy for a given pile impedance.Fur-

-. -ther, ultimate pile capacity increases, with an increase in energy, at agreater rate for higher pile impedances.In order to compare the effect of transmitted energy on pile im-pedance (Figure 4.1), the ultimate pile resistance was determined at tenblows per inch, which was arbitrarily selected as a practical limit todriving resistance.With the energy input doubled, ultimate pile capacityincreased more significantly for the high pile impedance than for the lowimpedance. For example, the ultimate capacity for the pile impedance of- 6000 lbs-secincreases approximately 180 percent when the input energyin.doubles (6250 to 12,700 ft lbs); whereas, the ultimate capacity increaseslbs-secapproximately 40 and 15 percent for impedances of 3000 and 1000in. ,respectively.Increasing tde energy from 12,500 to 25,000 ft lbs increasesthe ultimate capacity approximately 50 percent for an impedance of6000 lbs-sec lbs-sec, and 25 percent for an impedance of 3000in.in. , .It was noted in Chapter 3 that a finite tip displacement was ob-served for the condition of zero ultimate pile capacity.This occurred-because only one pass of the force pulse was considered. In reality,larger tip displacements would occur because of reflections and translationof the pile; at zero damping the displacement would be infinite (Kolsky,1963). Therefore, in plots of hammer blows per inch versus ultimate pilecapacity, as shown in Figure 4.1, the curve starts at the origin.Thisalso explains the reverse curvature near the origin.The pile tip model (Chapter 3) is used to investigate the effectof the first cycle of the force pulse.Displacement of the pile tip witha free-end condition due to the incident and reflected pulse can be readilydetermined by the expression:6 = 2 ImpulseP cA

-. .where 6 is the maximum free-tip displacement.For the sine force pulsesused in Figure 4.1, the displacement of the free-end tip can be written:where 6Sis the maximum free-tip displacement, F is peak force and tlPis pulse duration.As seen from Equation 4.2, the tip displacement for the high-associated with lower pile impedances cause a larger net set, or apile impedance is smaller than for low pile impedance.Longer durationssmaller number of hammer blows.Therefore, more reverse curvature nearthe origin is noted for high pile impedance than low pile impedance.The calculated tip displacements (Equation 4.2) matched the displacementsdetermined in Chapter 3 quati ti on 3.6).The effect of energy losses such as mechanical and transmitted isimportant to the pile response.The determination of the mechanicallosses and the corresponding energy at impact were previously discussed.More information is needed on hmer efficiencies for the purpose of im-proving input data to wave equation analyses-The transmitted energy is a function of the impedance ratio,--'A , and the coefficient of restitution of the hammer cushion. Fornormal drivehead weights the condition of maximum energy transmissionoccurs when I equals 0.6 to 1.1. For high impedance ratios, transmittedRenergy is reduced because of ram rebound, whereas the low impedance ratiocauses a slower rate of energy transmission.Energy losses increase witha decrease in the coefficient of restitution of the cushion material.Coefficients of restitution ranging from 1 to 3/4 (equivalent to analuminum-micarta cushion) yield energy losses of 0 to 20%, respectively,

whereas coefficients of 112 to 113 (equivalent to a wood cushion) yield* .energy losses of 20 to 40%, respectively.Lost energy can not drive piles, but losses can be minimized byensuring proper hammer operation and proper match of the hammer and pileThe hammer cushion plays a vital role in energy transfer; an ideal cushionwould have a coefficient of restitution equal to unity (no hysteresis).All present cushion materials exhibit hysteresis; soft materials such as-wood lead to the highest energy losses.A more efficient low-stiffnesscushion than wood could be obtained by the use of a longer aluminum-micarta stack, or possibly by the use of other materials.Field Study 1. This field investigation exemplifies the improve-ment of driving efficiency with greater hammer energy.0; course, this.-greater hammer energy should not cause pile damageThe soil profile consists of 10 ft of alluvium, dense sand andgravel, underlain by a very dense sand with thin layers of silty clay.The piles were 14BP89, 90 ft long. Soroe were driven with a Vulcan 08and some with a Vulcan 014 hammer. Both hammers had a standard aluminum-micarta cushion.Test drives with the two hammers were made 15 ft apart.The driving records are shown in Figure 4.2.The Vulcan 014 hammer hasa rated energy approximately 60% greater than the Vulcan 08, and thedriving records indicate an improved driving efficiency for the Vulcan014 approximately proportional to the difference in the rated energies.Results of a wave equation analysis shown in Figure 4.2 are inaccord with the driving records and the effects of greater input energy.On the basis of the final driving resistance at an elevation of 206 ft,the wave equation analysis predicts a capacity of 250 tons for the piledriven with the Vulcan 014 hammer and 210 tons for the pile driven with

250 -.Gr. Elev. (Vulcan 014)Gr. Elev. (Vulcan 08)----DrivingRecordr Driven with Vulcan 014Driven with Vulcan 08I210200 '0 50 100 150 200 250 300Hmer Blows Per Foot0 5 10 15 20 25 30Hammer Blows Per InchFigure 4.2 FIELD STUDY 1-EFFECT OF INPUT ENERGY ON PILE RESPONSE

131the Vulcan 08.(This discrepancy may be accounted for by variations insoil profile; no load tests were per;'ormed.)Thus, the wave equationanalysis has the ability to treat properly major changes in the variables.Generated Force PulseEnergy is not the only consideration for the determination of piledriving behavior; the form of the generated force pulse can be variablefor a given energy input.The relative shape of the force pulse, whether-- a high peak value with short duration or a low peak with long duration,has an important influence in overcoming the soil resistance and achievingpile penetration.As determined in the parameter study of Chapter 3, the forcepulse with a longer duration for a given energy level is more efficientfor penetration (more set per blow) when the peak pile force is equal toor greater than the soil spring resistance.When the peak pile force isless than the soil spring resistance, penetration efficiency is larger forthe largest peak forces; duration is not critical in this case.Thepenetration will be completely elastic when the peak force is equal to- or less than one-half the soil spring resistance.The behavior pattern of a point bearing pile driven with variousforce pulses is illustrated by the example in Figure 4.3.This exampleIbs-secassumes a pile impedance of 3000 and an energy level of 12,500in.ft-lbs.The generated force pulse with the longer pulse length andsmaller peak force is more efficient for driving at low soil spring re-sistances; however, maximum pile capacity can be obtained with thelarger peak force.This example points out the improvement in drivingefficiency with high peak forces at high soil resistances

Hammer Blow Per InchSinusoidal Inciaent Force PulsePeak Pile Forcetl Time Pulse DurationJmgure 4.3 EFFECT OF GENKRATED FORCE PULSE ON PILE RFSPONSEFOR A GIVEN ENERGY LEVEL

- .An extreme example of the foregoing behavior pattern is shown inFigure 4.4 for a pile impedance of 6000 lbs-sec in. and an energy of 6,250ft-lbs.This example typifies the behavior pattern when the input enerais too low for practical driving.At driving resistances beyond thepractical limit (10 to 20 blows/inch), efficiency is higher for the forcepulse with the longer duration.However, the pulse with the higher peakforce still becomes the most efficient, eventually, but only at extremely-high driving resistances.Thus, as a general rule, for easy driving thepulse length is important, whereas for hard driving the peak force is im-portant for driving efficiency provided sufficient input energy isavailable.The force pulse can be varied by varying hammer parameters (seeChapter 2).Energy at impact can be written in the following form:1 2Energy @ Impact = -2 ml vo(4.3)-where y is ram mass and V is the ram velocity at impact. For the same0input energy, an increase in ram mass by a factor a results in a decreasein ram velocity by a factor 14; therefore, both ram weight and velocityare variables that should be investigated in relation to the generatedpile force pulse.Ram velocity is directly proportional to pile peakforce provided the pile behaves elastically; however, the duration ofthe pulse is independent of ram velocity (Chapter 2).The ram weight affects both peak force and pulse duration.Thepulse length can be approximated by the expression t = nd2.17, therefore, an increase in ram weight by a factor of 2 causes anincrease in pulse length by a factor of 1.41.For the same height offall or impact velocity the heavier ram increases the peak pile force

Hammer Blows Per InchSinusoidal Incident Force Pulae F P = Peak Pile Force tl = Time Pulse DurationFigure 4.4LACK OF PILE ENERGY TO PRODUCE EFFICIENT DRIVING FORHIGH PILE PEAK FORCES

- .(J?igure 2.10); however, this increase in peak force is minimized at lowpile impedance. For example, consider the study of the nonlinear and in-elastic cushions (Chapter 2) for the Vulcan 1 and Vulcan 010 hammers withram weights of 5,000 and 10,000 lbs, respectively.The peak force in-creases approximately 10% with the increase in ram weight at a low pilelbs-secimpedance of 725 in.peak pile force increases approximately 25%.lbs-sec. At a high impedance of 8700 in. , the-The hammer cushion is a transmitting element; however, the cushionproperties can be readily changed in order to shape the force pulse aswell as to achieve an impedance match of pile and hammer.As a practicalmatter, the hammer cushion is one of the most important items in piledriving because it can be easily changed in order to achieve the desireddriving force pulse.An increase in cushion stiffness causes an increasein pile peak force; however, there is a limit beyond which peak force isnot significantly improved (Figure 2.10).This stiffness limit increasesas the pile impedance increases, and decreases with an increase in ramweight (See Table 2.2).- The pulse length is inversely proportional to the square root ofthe cushion stiffness as shown in Equation 2.12.This means that an in-crease in cushion stiffness by a factor of 2 decreases the pulse lengthby a value of 1.41.Also, inelastic behavior of the cushion causes adecrease in pulse duration; this trend increases with an increase indegree of cushion inelasticity (Table 2.3).The effect of cushion in-elasticity on peak force is minimal except for the condition of low p5.leimpedance and coefficients of restitution less than 0.5.For typical drivehead weights, equal to 1/3 to 1/10 of ram weight,the peak force is approximately independent of drivehead weight; however,

-. the pulse duration is larger with a decrease in drivehead weight for thematched and low pile impedance conditions.Field Study 2.This field investigation points out the importanceof shaping the generated force pulse with respect to a given hammer energyinput.In this case history, the change in the force pulse was accomplishedIby changing the hammer cushion material.A pile job was being successfully accomplished with precast con--crete piles (design load of 75 bons) driven with a Link Belt 520 hmer.The 50 ft concrete piles had a 16 in. square butt and 10 in. square tipand were driven into 10 to 20 ft of silty clay underlain by silty sandand gravels.Two pile load tests were performed and the desired ultimatecapacity of 150 tons obtained at an embedded length of 50 ft. The LinkBelt 520 hammer with a standard aluminum-micarta cushion plus a pilecushion consisting of e 2 inch oak block with rubber belting drove eachpile in 15 to 20 minutes.However, the Link Belt hammer broke down andwas replaced with a Vulcan 1 hammer.Pile driving was continued with the Vulcan 1 hammer and a standard- wood cushion (oak) during repair of the Link Belt hammer. Driving wasaccomplished to the desired penetration depth of 50 fi; however, thedriving time, on the order of 60 to 80 minutes, was excessive.Uponchanging to an aluminum-micarta cushion assembly, the driving timedecreased 30 to 40 minutes per pile.The results of the wave equationanalysis for the Vulcan 1 hammer with aluminum-micarta cushion assemblynnd a wood cushion assembly are shown in Figure 4.5.The wave equationanalysis readily shows the effect of the different cushion materials.me stiffer cushion (aluminum-micarta) results in higher generated peakforces as well as higher efficiency of enera transmission to the pile;

0 5 10 15 20 25 30Hammer Blows Per InchFigure 4.5 rFIELD STUDY 2 - EFFECT OF KAMMER CUSHION ON PILE DRIVING

therefore, faster and easier driving is to be expected.If it is assumedthat the pile has a certain ultimate capacity at 50 ft of penetration, itcan be seen from Figure 4.5 that such capacity will always be obtained withfewer blows/inch with the aluminum-micarta cushion.The field drivingrecords Mly supported the analytical results; driving times with thealuminum-micarta cushion were approximately one-half that for the woodcushion.-4.3 PileIn addition to its static load carrying function, the pile mustalso transmit an incident force pulse whfch is capable of overcoming thesoil resistance.The capability of the pile to transmit the force pulserequired to achieve the desired penetration is a function of pile impedanceor area.Factors that influence impedance such as structural damage ora change in the pile cross-section must also be considered.Boundaryconditions due to the finite length of real piles will be considered in-this discussion.Impedance or AreaThe impedance match of hammer and pile for maximum energy transmissionhas been previously discussed and will not be repeated here; however,the effect of pile impedance on the force pulse will be evaluated.For given hammer conditions, an increase in pile impedance causes an increasein peak force (See Figure 2.10). This behavior means that a 'higher impedance pile is capable of transmitting a higher peak force.The limit on the peak force would be governed by the dynamic yield propertiesof the pile material, and pile damage would ensue if the yield

139stress is exceeded.Damage can sigcificantly alter driving characteristics;this effect will be discussed later in this section.In the followingdiscussion it is assumed that the pile behaves elastically.The force pulse length is inversely proportional to pile impedance,i.e. pulse length decreases with an increase in pile impedance.Longtime pulses and low peak forces are associated with smaller pile impedances,whereas short pulses and high peaks prevail for larger pile impedances.-This behavior suggests (Chapter 3) that the low impedance pile is moreefficient (more set per blow) for driving at low soil resistance becauseof the longer pulse length.However, the high impedance pile is morecapable of being driven to a high load capacity because of its ability toform and transmit high peak forces.The effects of pile impedance on theability to drive to a given ultimate load capacity is shown in Figure4.6 for the cases investigated in Chapter 3. The pile response shownin Figure 4.6 indicates the efficiency of the low impedance pile at lowsoil resistances, and the capability of the high impedance pile to-achieve a high load capacity.The importance of pile impedance can not be overemphasized. Anoptimum pile design involves a delicate balance; insufficient impedanceor area prevents achieving the desired pile performance, whereas toomuch pile impedance or area leads to an uneconomical design.The effectof pile impedance on pile driving will be illustrated by the followingfield studies.Field Study 3.The soil profile consists of 10 ft of alluvium,dense sand and gravel, underlain by a very dense sand with thin layersof silty clay.Two steel piles with different areas were driven witha Vulcan 08 hammer and a standard aluminum-micarta cushion.One pile

12,500 ft. lbs.&mmer Blows Per InchSinusoidd Incident Force PulsepcA in units of lbs-aeclin.Figure 4.6EFFECT OF PILE IMPEDANCE ON DRIVINGCAPABILITY AT DIFFERENT ENERGY LEVELS

141was a pipe 90 ft long of 14 in. OD by 0.375 in. wall thickness driven2closed-end; the area of steel was 16.0 in. . The other pile was a214 BP 89, 90 ft long with an area of 26.2 in. . The wave equation analysisshown in Figure 4.7 compares the behavior of the two piles.From theanalysis, the pile with the greater area of steel has the ability toachieve a higher capacity and, therefore, greater depth of penetration.Driving records of these two piles, at a distance of 10 ft apart, indi--cate that the pipe pile achieved maximum penetration at an elevation of224 ft and a depth of 24 ft, whereas the BP section was driven to a depthof 40 ft (~igure 4.7). The driving records and analysis are in generalagreement.No load tests were performed.Field Study 4.This field study covers two case histories thatwill show how an increase of pile impedance after the piles were drivenmade it possible to obtain the desired ultimate load capacity.In bothcases, pipe piles were driven to high resistances, but were unable toobtain the desired load capacity.Greater penetration and thus higher-load capacity were obtained by redriving the piles after concreting.Pile impedance is increased by concreting.In the first case history, the soil profile consists of 107 ftof medium cloy underlain by sand.Pipe piles 8 518 in. by 0.250 in.with closed ends, 110 ft long, were driven with a Vulcan 06 harmner anda standard wood cushion block.The piles were designed for ah ultimatecapacity of 100 tons, and were driven to 4.5 blows per inch.The waveequation analysis shown in Figure 4.8 predicts a capacity of 70 tonsat 4.5 blows per inch, and indicates that the required 100 tons couldnot be achieved with the pile selected.Several load tests failed at80 tons, or 20 tons less than required. Driving the piles deeper into

300-Hammer Blows Per Foot2Wave EquationAnalysis2--= 16.0 in., 0 x03u"z~------200 PQC~.!L -Q//./ rc-10 15 20 25 - 30~Hammer Blows Per InchFigure 4.7FIELD STUDY 3 - EFFECT OF PILE AREAON DRIVING CAPABILITY

Figure 4,8FIELD STUDY 4 - CONCRETING PIPE PILESTO IMPROVE IEPEDANCE AND ACHIEVE THEDESIRED CAPACITY

the sand was the most desirable solution.This could be accomplished byconcreting to improve pile impedance before redriving.The piles wereconcreted and redriven with a Vulcan 06 hammer to the required depthand ultimate capacity.A comparison of the pipe pile with and withoutconcrete as shown in Figure 4.8 clearly shows the benefit of the improvedimpedance.In the other case history, the soil profile consists of 25 ft ofclayey silt underlain by 60 ft of medium sand and 10 ft of dense sand and-gravel overlying interbedded layers of limestone and shales with possiblecley seams.The piles were pipe 105 ft long with 12 314 in. OD x 0.219 in.wall thickness designed for an ultimate capacity of 200 tons.All pileswere driven with a Bodine Resonant Driver.The piles driven to soundbedrock satisfied the load capacity requirement; however, the desiredcapacity could not be achieved in the weathered bedrock zones.In orderto obtain the high peak forces necessary for further penetration a Link-Belt 520 diesel hammer was chosen.Driving on the pipe pile alone pro-duced only elastic defonation with no penetration.However, after con--creting, the pipe piles were successfully driven to the desired capacity.The wave equation analysis of the pipe with and without concrete, asshown in Figure 4.8, clearly indicate the greater ability of concretedpiles with respect to achieving penetration and load capacity.Field Study 5.This field study will show how the wave equationanalysis was used to explain inconsistencies in a mandrel driven pile.A mandrel driven pile consists of a thin-wall pipe or shell driven witha heavy wall pipe core; the core is commonly referred to as a mandrel.After driving, the mandrel is removed and the thin-wall pipe or shelllef't in the ground for concreting.Therefore, use of a mandrel is an

effective means of obtaining the impedance required during driving, whereasa minimum amount of steel (and money) can be left in theground afterdriving by removing the mandrel core.The soil profile consists of 17 ft of silt size ash underlain by30 ft of sand and gravel grading from medium to dense. The sand and gravelare underlain by 10 ft of layered silt and clay and 45 ft of very dense ,sand and gravel overlying shale.Thin-wall pipe piles 12 in. OD by0.141 in. wall thickness were driven with a 115 plf mandrel 49 ft long.-The hammer was a Link Belt Model 440 with a standard aluminum-micartacushion.The desired ultimate capacity was 180 tons, and the designload was 75 tons.A test pile was driven to a depth of 34 ft at a resistance of43 blows per inch. The load test was unsatisfactory; failure occurredat 125 tons.The effect of driving the pipe pile with and without theuse of the mandrel was determined by using the wave equation analysisshown in Figure 4.9.The analysis clearly shows that the mandrel wasnot effective in transmitting the pile force; therefore, the thin-wallpipe was transmitting the pulse because the mandrel probably was notFin contact with the pile tip.To be effective, it is necessary that the,mandrel simultaneously engages both top and tip of the pile so that themandrel and tip will. drive together...In order to prove whether or not the mandrel was being effectivelyused, comparative drives were made with and without a 3/4 inch spacerplate at the pile tip.The drive without the plate penetrated to a depthof 38 ft and a resistance of 12 blows per inch.The pile driven with the3/4 inch plate penetrated to a depth of 46 ft at a driving resistance of9 blows per inch. Gross set was measured during driving; a set 0.56 in.

iHammer B~OUS Per InchFigure 4.9FIELD STUDY 5 - E F~CT OFMANDREL ON PILE DRIVING

was observed for the pile driven wit:iout the 314 inch plate, and 0.28 in.with the plate, both in accordance with predictions from the wave equationanalysis.Thus, the wave equation analysis fully predicted the differencesbetween the two driving systems.This field study and analysis alsoclearly shows that the capability of the pile to transmit the force pulserequired to achieve the desired penetration is a function of pile im-pedance.Cushioning Effect-A change in the pile cross-section will affect the pile impedanceand can produce a cushioning effect.For example, compare the waveequation analysis of a 125 ft pipe pile with and without a change in thepile tip section (Figure 4.10).The pipe is 14 in. OD by 0.500 in. wallthickness and the tip section is 30 ft long of 14 in. OD by 0.188 in.wall thickness.The pile with the smaller tip cross-section has theeffect of lowering the pile impedance; therefore, a cushioning effectexists.The analytical comparison clearly shows that greater penetrationand higher load capacity is achieved with the higher pile impedance (with-out smaller cross-sectional area of tip section).-Also, pile damage caused by driving has the effect of loweringpile impedance in the damaged zone; this will be referred to herein asa cushioning effect.The damaged zone or smaller impedance section ofthe pile controls transmission of the force pulse.The field problemdiscussed herein will exemplify the cushioning effect caused by piledamage.Field Study 6.The soil profile consists of 13 to 24 ft of fillincluding silt, clay, bricks, etc., underlain by stiff clay.The bedrockis at an average depth of 30 ft and consists of soft shale and lime-

Hammer Blows Per InchFigure 4.10 EFFECT OF DIFFEmNTPILE IMPEDANCE WITHINPILE LENGTH

stone. The piles were 10 BP 42 with a design load of 75 tons; they were-.driven with a Delmag Dl2 using a standard oak cushion. Pile load testsfailed on piles driven to less than 40 blows per inch; however, the waveequation analysis indicated that the required resistance (150 tons)could be reached at 11 blows per inch (Figure 4.11).The foregoing discrepancy between theory and test indicated thata cushioning effect could have resulted from pile damage since the tips-were not reinforced and the piles were encountering bricks, etc. Theeffects of damage can be estimated by the wave equation analysis; forthis purpose the lower pile segment was assumed to have 10 percent of itsoriginal stiffness.The comparison of predicted behavior for the damagedand the undamaged pile section clearly shows that the damaged pile couldnot achieve the required 150 ton ultimate load capacity (Figure 4.10).Several piles were pulled and revealed damage such as warping, bending,etc., as expected and foreseen by reference to wave propagation analysis..LengthPile length affects the generated force pulse shape with respect'to reflections from the pile tip. Reflections can support or interferewith the incident force pulse.The pile length required for freedom fromreflection interference is directly proportional to the pulse duration,which is a function of hammer weight, cushion stiffness and pile impedance.The pulse duration increases with larger ram weight and decreases withlarger cushion stiffness and pile impedance.A longer pile has a betterchance of transmitting a generated Force pulse without interference thana short pile; however, the effect of reflections can aid or retard pilepenetration depending on the relative impedance of the pile and the soilresistance.

Figure 4.11FIELD STUDY 6 - EFFECT OFDAJUGE ON PILE DRIVING

For high pile impedance, the force pulse duration is short; there-.. fore, reflections will not significantly alter the generated force pulseeven for short piles.This behavior of high pile impedance indicates thedriving resistance will probably not be significantly different for ashort or long pile.However, the pulse length duration is long for lowpile impedances and the effect of length can aid or retard the generatedforce pulse.For the short pile and low pile impedance, the reflectionswill likely be compressive and add to the generated force pulse.For; the long pile, the effect of reflections will be a separate pulse andwill not add directly to the generated force pulse.This behavior ofthe low pile impedance indicates the short pile will probably drive moreefficiently than the long pile.The behavior of pile length for high and low pile impedances canbe shown by a particular example.2of 5 and 40 in.driven with a Vulcan No. 1 hammer.Consider variable steel pile areas(725 and 5800 lbs-sec pile impedances, respectively),in.The pile lengths are 20 and 160 ft,and the soil resistance is considered at the pile tip only.The waveequation analysis of the combination of impedances and lengths are shown- in Figure 4.12. The behavior of the piles as shown in Figure 4.12 indi-cates slightly more efficient driving for the longer pile than theshorter pile with high impedance;however, the difference in driving be-havior between the two lengths is not significant.For the low pile im-pedance, the shorter pile drives much more efficiently than the longerpile.The difference in driving efficiency of the long and short pilecan be illustrated by the force-time relationship, both generated andreflected, at the head of the pile.For the high pile impedance, con-

WAVE EQUATION ANALYSIS,Do:o;o!.ocPI,. .-PII.rollo".' -.,.,m.---Dot* a--*r.o 5 20 L 160 it~.~.th 2O b 160 ftAte0- L."QI~--..?FernI Enere), 15.000 ft-lbs,, -.-?!- core FWW -1000 lbs A ~ V -- ~ I - --Alum.-Micarts ,'l~10~lbs/i~;. OO4.Qo,,,OtlQ-,,,,&.Q- 0.10 0.15.-b e Oeo,,,, -- Jpnt -~.$me! in,w. M I:.,m,on tnornn.rl .C.shton SO>~@Icumrn.rt. ..-. ---"Hommar Blows ParInchFigure 4.12EFFECT OF PILE LENGTH ON DRIVING

sider the force pulse at the pile head for a soil spring resistance of- 300 kips (Figure 4.13~3). Comparison of the force pulses for the long andshort pile indicate that only small differences exist when the force levelis greater than the soil spring estimate resistance.However, the forcepulse peak for the shorter pile was attenuated somewhat.This attenua-tion, as a result of tension reflection at the beginning part of the re-flected pulse causes less efficient driving for the shorter pile.-_For the low pile impedance and a soil spring resistance of 150kips, the force pulse of the shorter pile has a hi&er peak and a longtime duration above the level of the soil spring resistance (Figure 4.13).The shorter pile has compressive reflections that add to the generatedforce pulse; whereas, the compressive reflections of the longer pile areseparate and do not add the generated force pulse.This effect of reflec-tions produces more efficient driving for the shorter pile than thelonger pile at low impedances.Mosley and Raamot (1970) presented wave equation analysesillustrating pile length behavior.Their results indicate a typicalpattern of driving efficiency as shown in the example above; however,- the'difference in driving behavior was presented without explanation.With the assumption of the same relative distribution of soilresistance along the sides and tip, irrespective of pile length, thefollowing general conditions can be indicated:11. For high pile im-pedances, driving efficiency between longer and shorter piles is notsignificantly different; however, longer piles will probably be slightlymore efficient. 2. For low pile impedances, shorter piles will bemore efficient than longer piles.

600 . + . .Time, millisecondsa) High Pile Lmpedmce. I i I. Long File0 1601Time, mllllsecondsb) Law Pile ImpedanceFigure 4.13 EFFECT OF PILE LWGTX OE FORCE PULSE

The behavior pattern based on pile length only is difficult be-155cause the real soil resistance distribution changes with depth.Realsoil profiles are quite variable and the soil distribution as well aspile length must be considered for each individual case.4.4 Soil ResistanceThe soil provides the resistance which must be overcome by theincident force pulse in order to achieve penetration.The effect of theincident force pulse with respect to assumed resistance has been pre-viously discussed; however, the effects of the soil characteristics interms of the hammer-pile-soilsystem w ill be considered in this discussion.These soil charac'teristics include the effect of soil distribution, quakeand damping, and freeze or relaxation.Soil Resistance DistributionSoil resistance distribution refers to the relative amounts ofultimate soil resistance at the pile tip and along the length of the pile.-The soil resistance along the pile length attenuates the generated forcepulse, and thereby decreases the effectiveness of the force pulse whenit arrives at the pile tip. Iiowever, it should be recognized that thelarger the percentage of side resistance, the smaller is the resistanceat the point for a given total resistance.For example, a friction pile derives almost all of its supportfrom side friction; therefore, there is practically no resistance at thepoint and only a small pile tip force is necessary to cause penetration.By contrast, in a point bearing pile the generated force pulse is workingagainst the total resistance at the pile point.Because of differences

in the physical mechanisms of soil failure along the pile and at the tip,- the point resistance is assumed to possess higher damping than the sideresistance; therefore, damping alone could cause more resistance topenetration at the pile point.The differences in physical behavior between point bearing andskin friction can be explained very easily.If the frictional resistanceacting on a given pile segment (increment of length) is examined, it isseen that the pile force pulse peak greatly exceeds the soil resistance.G Thus, the force pulse can pass through many segments without seriousattenuation.However, if all soil resistance is concentrated at the piletip the large disparity between pile tip force and total soil resistancedis;appears, and efficiency of pile penetration diminishes (Chapter 3).It is difficult to compare the driving resistance and load capacityin two different soil profiles, such as those wherein frictionpiles or point bearing piles are found; however, a field study coupledwith a wave equation analysis can be presented to show the effect ofdriving through a soft layer to a point bearing layer.- clay underlain py sand. Pipe piles 8 5/8 in. by 0.250 in. were drivenField Study 7.The soil profile consists of 107 ft of mediumclosed-end with a Vulcan 06 hmer and a wood cushion.Driving re-sistance in the clay varied from 6 to 9 blows/ft, but final drivinginto the sand was at 3 to 5 blows/in.The wave equation analyses fordriving in clay (10% point bearing) and into sand (70% point bearing)can be compared, as shown in Figure 4.14; 10% point bearing indicatesthat 10% of total soil resistance is assumed to occur at the pile tip.The comparative analysis shows the improvement of the driving efficiencyfor the friction pile (10% point bearing).

IHsmmer B l m Per InchFigure 4.14FIELD STUDY 7 - EFFECT OF THE PERCENTAGEOF POINT BEARING RESISTANCE

Also, the amount of friction can be estimated with the use of- wave equation analysis. The friction amounts to 25 to 35 tons at a re-sistance of 6 to 9 blowslft with an estimated total capacity of 70 tonsat final driving.Quake and DampingAn increase in both soil quake and soil damping decreases theeffectiveness of a given pile force pulse.The effects of quake and-damping have been discussed previously in Chapter 3; however, the effectsat the pile tip will be briefly summarized herein with respect to theentire hammer-pile-soilsystem.The soil quakes investigated previously with respect to an elastic-Ipiastic soil spring cover the range of behavior for stiff and dense soilsto soft or 'loose soils.The values of quake considered are 0.20 in.,0.10 in. and 0.05 in.; the higher quake values represent soft or loosesoils, whereas the lower values represent stiff or dense soils.Severalstudies of field conditions indicate that a quake of 0.10 in. is a good-average value. . An investigation of the soil quake parmeter is shownin Figure 4.15 for three different pile impedances, an input energy of12,500 I%-lbs, and a damping constant, J equal to 0.15 sec/ft.pt'Figure 4.15 clearly indicates the loss of driving capability and capa-city with a corresponding increase in soil quake.Also, the effect ofsoil quake is more pronounced for higher pile impedances.For example,the difference in behavior with respect to quake for loose and densesoils is not significant at a pile impedance of 1000 lbs-sec/in.How-ever, the difference is marked for a pile impedance of 6000 lbs-sec/in.It-~ ~Field correlation of pile load tests with wave propagation analy-ses plus laboratory test results indicate that damping factors for clays

-0 5 10 15 20 25 30Hemmer Blare Per InchSinusoidal Incident Force Pulse100% Point Bearing - J = 0.15 sec/rtPtFigure 4.15EFTECT OF SOIL QUAKEON PILE RESPONSE

are higher than for sands.A common average damping factor, J pt, for the- pile tip is assumed to be 0.15 sec/f%. The investigation of damping shownin Figure 4.16 covers the range of one-half to twice the normal value.Field correlations indicate that the results for sands are in good agreementwith the normally assumed value of 0.15 sec/ft; however, in claysdamping values are higher, but pore pressure effects with respect to timemake the analysis difficult.The effects of soil damping shown in Figure-4.16 were evaluated for three different pile impedances, an input energyof 12,500 ft-lbs, an3 a soil quake of 0.10 in. An increase in the dampingfactor decreases driving ability for all pile impedances, not just thehigher impedances as is the case for soil quake.Freeze and RelaxatiohA wave propagation analysis considers the relationship betweendriving resistance and capacity at the time of driving; however, differencesin soil properties often occur after driving and cause a dis-crepancy between static and dynamic pile load capacities.Increases in-soil strength (set-up or freeze) occur in soils such as soft clays orloose cohesionless deposits. For soft and loose soil deposits, the gainin strength is a result of pore pressure dissipation. Thixotropiceffects are prevalent in cohesive soils, whereas densification andstrengthening due to adjacent pile driving can also occur in cohesionlesssoils.Relaxation, or loss in soil strength after driving, can possiblyoccur in stiff or dense deposits.In this case, dissipation of negativepore pressures or a loosening effect due to adjacent pile driving invery dense materials may cause a loss in capacity.The engineer's ability to predict freeze or relaxation is neces-sary in order to achieve a technically sound and economical job.Useflil

200100= 12,500 ft. lbs.'0 5 10 15 20 25 30Sinusoidal Incident Force Pulse100% Point Bearin84 ~0.10 in.PtFigure 4 .l6 EFFECT OF SOIL DAMPINGON PILZ RESPONSE

information on the magnitude of freeze or relaxation can be obtained- from redriving piles. After the pile is driven and final hammer resis-tance in blows/in. is recorded, the pile is allowed to stand for a periodof time before redriving.Redriving gives the hammer resistance in blows/in. for the first several hammer blows.This hammer resistance duringredriving can be used to obtain an ultimate pile capacity from the waveequation analysis.Pile capacity as determined from redrive data can becompared with the initial driving capacity; the difference in load capa---cities will approximate the magnitude of relaxation or freeze. If theredriving resistance is greater than driving resistance, then freeze isexhibited.Redrive data is difficult to obtain because the first few ham-me,r blows are critical and the hammer must be properly warmed-up inorder to function at full energy during the first few hammer blows.An accumulation of information on load tests correlated with thewave analysis as a reference framework can be achieved for various typesof soils exhibiting freeze or relaxation.Freeze is a normal occurrencebecause of the type of soil profiles that dictate the use of piles.The- with a knowledge of freeze can be effectively used in pile foundationfollowing field study will show how the wave equation analysis coupleddesign.Field Study 8.The soil profile consists of 30 fY of sand and60 ft of soft to medium varved clay overlying hardpan. The piles are12 3/4 in. by 0.250 in. pipe 95 fY long with closed-ends. The piles,driven with a Link-Belt 520, are designed for 110 tons working load.Analysis of this combination of pile, hammer and soil by use of thewave equation as shown in Figure 4.17 indicates that the pile can notachieve the required ultimate capacity of 220 tons (factor of safety =2.0) without freeze. The effect of freeze was considered for the varved

0 5 10 15 20 25 30Hammer Blows Per InchFigure 4.17 F'IELD STUDY 8 - USE OF WAVE EQUATIONANALYSIS IN DESIGN FOR SOIL EXHIBJBINGlmlzFA

clay; however, the magnitude of freeze was not known.Pile driving and- - redriving data from a project in the same soil deposit was analyzed withthe use of the wave equation and it was found that 50 to 100 tons perpile could be attributed to freeze. The project was designed for a 165ton ultimate (factor of safety = 1.5) at a recommended driving resis-tance of 10 blows/in. as shown by the wave equation analysis.Theeffect of freeze was expected to provide a factor of safety of 2.Twoload tests were performed as shown in Figure 4.17 and the tests indicated80 to 90 tons of freeze as expected.4.5 Design ToolThe dynamics of driving piles with impact hammers has been ampli-fied by independent idealized studies of the parameters controlling thegenerated force pulse in the head of the pile and the soil resistanceparameters at the pile tip.The results of the parameter study not onlyindicate relative effects of the parameters controlling pile driving, butcan be used as a design tool.For example, consider a proposed 12 WF 106 pile (impedance of-lbs-sec4500 ) and a design load of 150 tons with a factor of safety ofin.2 (ultimate capacity 300 tons). The pile is 95 f't long and embedmentis 45 rt. The Vulcan 010 hammer is being considered.For 70% hammerefficiency, the velocity at impact is approximately 12 ft/sec (Figure2.11). The standard cushion size for a Vulcan 010 hammer is 13 1/2 in.in diameter and 10 in. height.The cushion material can be selectedfor maximum energy transmission or peak pile force; the criteria maynot lead to the same cushion requirements.The cushion should be

selected such that the peak pile force exceeds the ultimate capacity of- the pile; it should in addition be as efficient as possible in transmitting5enera.For maximum energy transmission, the impedance ratio relation-ship (Equation 2.4) can be used to calculate the desired hammer cushion.6The range in calculated cushion stiffnesses is 0.6 to 2.2 x 10 lbs/in.The desired cushion would be a short oak wood or asbestos stack (5 in.height), or a long aluminum-micarta stack (20 in. height).An adapter-would be required in order to obtain a stack height greater than 10inches.The generated weak force with the cushion for maximum energytransmission can be obtained in Figure 2.10.The range in peak forces is400 to 480 kips. This range can be determined by interpolation betweenlbs-sec.impedances 2900 and 5800 in.For an ultimate capacity of 300 tonsor 600 kips, a greater cushion stiffness than the stiffness for maximumenergy transmission is desired.In order to achieve a peak force greater than the ultimate pile6capacity, a cushion stiffness of approximately 10 x 10 lbs/in. isselected (~i~ure 2.10). By interpolation, the peak force is found to beabout 660 kips; therefore, the desired cushion material would be aluminum-Imicarta with a stack height of 7 in.The maximum driving stresses equal22 ksi. The '(-inch cushion is stiffer th~n that for maximum energy trans-mission but is required to achieve efficient penetration.The wave equation analysis (Smith's lumped mass-spring model)of the particular example was also performed with the results shown inFigure 4.18. The cushion selected was aluminum-micarta. As seen fromFigure 4.18, the driving resistance of approximately 10 blows/in. willachieve the ultimate capacity of 300 tons.Ten hmer blows per inch is

WAVE EQUATION ANALYSIS~ e b - Dot. - - J --_-Lotol.on -- -- - P,,. 12 WF 106 A..O u ~ n - L.-OV"-L ~woner.1 A:.@ - - ~*nolnF.,t40..~ At.0 Leno'h"0mm.r Vulcan 010 E ~ 32.500 . ~ ft-lbs, ~ ~ .LL.Q%,- Comb To.

a practical limit for driving resistance.This correlation of the idealized- studies of parameters and the wave equation analysis indicates that theidealized studces can be used as a preliminary design tool.The advantageof this design tool is that no computer analysis is necessary and onlysimple calculations along with the results incorporated herein are required.4.6 Wave Equation Analysis Versus Enerm Formulas-In the last century, energy formulas have been widely used to pre-diet the bearing capacity and driving characteristics of an individualpile.Energy formulas are based on conservation of energy where therated hammer energy is equated to the energy required for pile penetrationplus energy losses, i.e. nonuseful energy for pile peneiration.E = R s + lossesr u(1t.4)where s is the net set of the pile per hammer blow.Authors of energy1formulas have attempted to incorporate these losses by empiricism and/or-Newtonian impact.two free and massive bodies.Newtonian impact denotes the efficiency of impact ofThe bodies in the pile analysis are theram (W1) and the pile (W ). Also, the efficiency (e ) of the hammer isPfoften included to take account of losses prior to impact.Energy formu-las then take the following form:where n is the coefficient of restitution for inelastic behavior at im-pact and e is a temporary set .representing losses such as temporarycompression, plastic deformation, etc.The e value takes many forms; it

is usually based on empiricism or simplified calculations... , - wl + n%accounts for the efficiency of Newtonian impact.w, + w PIn reality, the pile is a distributed mass, not a concentratedme expressionmass, and is 'also restrained by the soil; these facts violate Newton'simpact theory.These limitations and deficiencies of energy formulas arewidely recognized, but no effective method was available to replace themuntil recently.- The impact resulting when a pile hammer strikes a pile is apractical illustration of longitudinal impact in elastic rods.The wavepropagtition analysis attempts to describe the force pulses generated andreflected along the pile's length. The relationship between the generatedpulse and the soil resistance di.ctates the pile's response to driving.Correlations of wave equation analyses with field case histories illustrateithe power of this analytical tool.It is a significant step forward inthe art of pile foundation design.The wave equation analysis and energy formulas are both mathe-matical tools used to achieve the same goal; i-e. the use of a dynamic'- analysis to predict driving capability and static load capacity at thetime of driving.Therefore, the wave equation analysis fulfills thefunction of the dynamic energy formulas in a more accurate and comprehensivemanner.With the wave equation analysis established as the proper dynamictheoretical framework, the deficiencies of energy formulas can now beinvestigated with respect to the hammer-pile-soil system. Nineteendifferent and widely accepted energy formulas have been arbikrarilyselected for this investigation as shown in Table A.l, Appendix A. The

variables of the hammer-pile-soilsystem included in the energy formulas- discussed herein, are listed in Table 4.1.Many of the energy formulas indicate that for piles driven to thesame set or number of blows/in., the capacity is independent of pile areaor impedance.The importance of pile impedance or area for transmittingthe force pulse and developing load capacity has been exemplified byfield studies and wave equation analyses (unmarked as shown in Table 4.1).Where pile impedance or other variables are taken into account in energy2 formulas they will be marked with an X in Table 4.1. The letter U isused to denote that the variable has been treated unsatisfactorily, whereasa blank indicates that the variable is ignored.Some of the energy formulas attempt to account for the effect ;of pile impedance or area by meds of pile weipat; however, the energyformulation penalizes the heavier pile. For the same driving resistance,W +n2W1the expressionW.', which represents Newtonian impact efficiency,+ W1 Pdecreases with an increase in pile weight; therefore, the calculatedultimate pile capacities decrease with increase in pile weight (Equation4.5). In reality, ultimate pile capacities increase with an increase- in pile impedance (and weight) because of the improved ability to trans-mit force.A closer examination of the energy formulas and the wave equationanalysis shows that the two approaches are often in complete disagreementon the basis of driving resistance alone.For instance, compare a lightand a heavy pile for the same soil condition, available hammer energy,pile length and embedment depth.In this problem, there is no reasonto suspect any difference in the pile capacity between the light andheavy pile; however, the driving characteristics will be different.The wave

-Table 4.1COMPARIGON OF WAVE EQUATION AAALYGIS AND WERGY FORMULABVari able8Energy Formula Pile Hammer Pile 6011 Hammer Ram DriveheadImpedance Cushion Cushioning Resistance Energy Velocity Weightor Area Effect Distribution1. Engineering Nsvs X2. Nodified Engineering News U3. Cov U4. V ~ C M Iron work^U3. Bureau of Yarde and Docks6. Rankine7. Dutch8. Ritter9. Eytelvein10. navy-McKw11. Ganders12. Gate813. Daniah14. Janbu15. Hiley16. Redtenbacker17. Pacific Cmat UniformBullding Code18. Canadian NationalBuilding Code X X X19. Olson and Fleste XWave Equation Analysis X X X X X X XLegend: Bl& Space - variable not accounted forU - variable unsatisfactorily accounted forX - variable accounted for

equation analysis clearly indicates tbat the heavy pile is a better trans-- mitter of the generated force pulse; therefore, the driving resistancewould be lower at a given ultimate capacity than for the light pile.Energy formulas erroneously predict a higher capacity for the higherdriving resistance, i.e. for the light pile in this instance.The hmer cushion is instrumental in shaping the generated forcepulse; however, it is probably the most overlooked consideration in piledriving.The reason for this neglect can probably be attributed to the- fact that most energy formulas completely ignore cushion stiffness. Thereare attempts to account for energy losses in a cushion, but not for theeffects of stiffness.A pile cushioning effect due to damage, or a composite section,can not be accounted for in energy formulas; however, the wave equationanalysis can readily account for damage or composite section at any locationalong the pile's length.Soil resistance distribution is generally not accounted for inenera formulas; however, there are attempts to account for frictionversus point bearing piles in some of the formulas.The amount of hmer energy in terms of ram weight and velocityis taken into account for all energy formulas; however, the effects ofthe enera components (ram velocity and ram weight) are not consideredon an individual basis. As shown in the previous discussion, generatedpeak pile force is directly proportional to ram velocity; therefore,ram velocity is instrumental in shaping the force pulse.The forcepulse shape, as shown in Chapter 3, is critical for achieving the requiredpile penetration and load capacity.The effect of drivehead weight onshaping the pile force pulse also is not considered in any of the energyformulas .

172-The aforementioned variables represent limiting factors of thehammer-pile-soil system affecting pile penetration and load capacity.However, it should be emphasized that the weak link in the hammer-pile-soilsystem will control driving behavior, irrespective of other variablechanges.If several parameters represent equally weak links, then allsuch parameters would have to be changed simultaneously in order toachieve a significant change in driving capability.As discussed herein,-the wave equation analysis has the ability to account for all the signi-; ficant variables in the hammer-pile-soil system, whereas energy formulaspossess inherent limitations.Limitations of the energy formulas clearly revolve around thetransmitting elements of the generated force pulse, i.e. pile impedance!or area pnd hammer cushion, as well as soil considerations (See Table 4.1).These limitations do not mean that energj formulas can not be a valuabletool if they are properly used.Energy formulas are readily usable andcan be a Galuable tool if they are empirically adjusted for a particulardriving condition, i.e. some given soil condition, pile type and drivingequipment.Load tests must be used as a basis for adjusting the par-ticular energy formula used.Althoua energy formulas can be useful ona jobto job basis, a proper theoretical fremework is necessary toconsolidate and evaluate pile driving experience for the purpose of advancingthe state of the art. Wave propagation analyses are the propertheoretical treatment; there is, however, a need for more refined inputdata for hammer, pile and soil parameters.

CHAPTER 5CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH5.1 - ConclusionsConclusions of a general nature are presented below.Detailsof these conclusions have been given at the appropriate places in indi--vidual chapters.1. In order to achieve maximum pile penetration and capacityfor a given available energy, the shape of the force-time pulse is significant.2. For a given pile, penetration and capacity increase withan increase in transmitted energy provided the generatedpeak force is greater than one-half the ultimate soil re-sistance (R~). The effect of the increase in transmittedenergy is greater for high than for low pile impedances,as measured by pcA.3. For a given hammer, maximum energy can be transmitted tothe pile head by a proper match between pile impedanceand hammer impedance; the Impedance Ratio, p~~/Jmlk', shouldfall between 0.6 and 1.1.4. Lost energy accomplishes no pile driving. Energy lossesincrease with an increase in the inelastic behavior of thecushion material (low coefficient of restitution); there-fore, the ideal cushion is one that possesses a coefficientof restitution of unity (linear elastic).

5. For high pile impedances relative to hammer impedance, thegenerated pile force pulses are nearly sinusoidal.As thepile impedance approaches that for the best match of hammerand pile (providing maximum transmitted energr), the forcepulses have a damped sinusoidal shape.Oscillatory forcesare present during the unloading portion of the force pulsefor lor1 pile impedances.6. The relationships for maximum pile penetration or maximumset per hemmer blow with respect to the shape and durationof the tip force pulse are summarized below for a givenendrgy input:a) Fori' (pile peek force)+ -, maximum pileRu(ultimate soil spring force)penetration occurs with no soil resistance.b) ForF($ile peak force)Ru(ultirnate soil spring force)> 1, pile penetra-tion increases with an increase in time duration, andis influenced relatively little by peak force.F (pile penk force)c) For < 1, and > 1/2,Ru(ultimate soil spring force)pile penetration is primarily dependent on peak force,and is influenced relatively little by duration.F (pile peak force)d) For - < 1/2, no netRu(ultimate soil spring force)pile penetration and only elastic deformations occur.

7. Peak pile force is directly proportional to ram velocityat impact provided the pile behaves elastically.Durationof the force pulse is independent of the ram velocity.Thepeak force data presented herein for different hammer andpile properties can be used as a guide for structural designof the pile to withstand driving.8. Ram weight affects both peak pile force and pulse duration.If the ram weight is doubled, the peak pile force is slightlyincreased (less than 25%); the maximum increase occursfor high pile impedances.Pulse duration is approximatelyproportional to the square root of thd ram weight.9. Hammer cushion properties can be conveniently selected inorder to control the shape of the force pulse as well asto match pile and hammer characteristics.The peak forcegenerated in a pile with an aluminum-micarta cushion (stiff)is approximately double that generated with a pine plywoodcushion (soft).Pulse durations for the sort cushions arelarger, by a factor of 3 to 5, than the pulse length generatedby stiff cushions.10. In general, equivalent linear hammer cushions derived fromappropriate secant moduli and used in analysis are in closeagreement with the real behavior of nonlinear cushions.11. Inelastic behavior of hammer cushions leads to attenuationof peak pile forces only for low pile impedances.Inelasticbehavior causes attenuation of duration of the force pulse

for all pile impedances; therefore, the pulse lengthdecreases with an increase in the degree of cushion inelasticity.12. For given hammer conditions, generated peak pile force increasesapproximately in proportion to the pile impedance(or area) for low impedances.The proportion decreasesfor high pile impedances.Pulse duration is approximatelyinversely proportional to pile impedance.13. Low impedance piles are more efficient with respect todriving (more set per blow) at low driving resistancesbecause the force pulse is longer.Ifowever, high impe-dance piles are more capable of being driven to a highload capacity because of their ability to form andtransmit high peak forces.14. Greater penetration and higher load capacity can be ob-tained by redriving pipe piles after concreting.Pileimpedance is increased by concreting.15. A mandrel or drive core is an effective means of obtainingthe impedance required for driving.16. Pile damage caused by pile driving has the effect oflowering pile impedance in the damaged zone; therefore,the driving capability of a damaged pile is lower than foran equivalent undamaged pile.17. Length of the pile affects interference with the generatedforce pulse by reflections from the pile tip.Reflections

can aid or retard pile penetration.Shorter piles arelikely to be more efficient and achieve higher capacityfor low pile impedances.For high pile impedances, pilelength does not significantly alter either driving efficiencyor load capacity.18. Pile penetration behavior may not be particularly sensitiveto soil parameters (quake and damping) along the sideof piles.19. If the frictional resistance acting on a given pile segment(increment of length) is examined, the pile peak force ingeneral greatly exceeds the soil resistance.Thus, theforce pulse can pass through many segments without seriousattenuation.However, if all soil resistance is concen-tratcd at the pile tip, the disparity between pile tipforce and total resistance is not large and efficiencyof pile penetration diminishes.20. An increase in both soil quake and soil damping at thepile tip decreases the effectiveness of a given pile forcepulse.The difference in behavior with respect to changesin quake are not significant for low pile impedances;however, the differences are marked for high pile impe-dances.An increase in the damping factor decreasesdriving ability for all pile impedances.21. All dynamic analyses, including both the wave equationand enera formulae, consider the relationship between

driving resistance and load capacity at the time ofdriving; however, differences in soil properties often occurafter driving and cause a discrepancy between static anddynamic pile load capacity.soil freeze or relaxation.This discrepancy can be termed.An accumulation of informationon load tests and redriving data correlated with waveequation analyses as a reference framework providesempirical data on freeze and relaxation that can be effectivelyused in pi1.e foundation design.22. With the aid of wave propagation analysis and field casehistories, limiting factors to pile penetration and loadcapacity are summarized below in the order they are likelyto be encountered in practice:1) Pile - Insufficient impedance or cross-sectional area.2) IIammer Cushion - Too soft.3) Pile Cushioning Effect - Pile damage or a change inpile cross-section.4) Soil Resistance - Too much point bearing, or soilrelaxation.5) Hammer Energy - Insufficient.23. It should be emphasized that the weak link in the hammerpile-soilsystem will control driving behavior, irrespectiveof other parameters.If several parameters are equallyweak, then all the weak parameters would have to be changedsimultaneously in order to achieve any effective change indriving capability.

24. For pile driving, the wave equation analysis and energyformulas are mathematical tools used to achieve the samegoal, namely, the use of a dynamic analysis to predictdriving capability and static load capacity.However, thelimitations of energy formdas include failure to takeinto account properly the transmitting elements (pileimpedance or area, hammer cushion, drivehead) and ramvelocity as they affect the generated fdrce pulse.Energyformulas also do not account for soil considerations (distribution,yield criterion and damping), and they do notprovide a stress analysis in the pile.25. Correlations of wave equation analyses with field casehistories illustrate the power of this analytical tool.It is a significant step forward in the art of pilefoundation design.-5.2 Suggestions for Future ResearchThe ultimate goal in pile foundation design is a general understandingof both pile-soil interaction during installation, and the in-teraction of superstructure, piles and soil after construction.fore, a better understanding of pile group behavior is needed.There-Becauseof the difficulty in obtaining data on the behavior of pile groups, thefollowing suggestions will be directed towards achieving a better understandingof single-pile behavior, which is a desirable starting pointin pile foundation design.

180In an effort to predict pile performance in a variable soilprofile, pile drivers are placed in a rather unique dual role, namely,a contractor's driving tool and an engineer's measuring instrument.Thedriving resistance to pile penetration in terms of hammer blows per unitset is a measure of the pile's ability to support load. With the inherentvariability of soil profiles, attainment of a prescribed driving resistanceis an assurance that the desired pile capacity is achieved; there--fore, dynamic analysis of single-pile behavior is of great practical im-portance.Though the wave propagation analysis is quite useful, morefield data must be gathered and analyzed to establish more accuratelythe input parameters.Better input information is required for hamme?properties such as the effect of combustion in diesel hammers, impactvelocity (hammer efficiency) and hammer cushion stress-strain data.More accurate soil information is needed on damping, quake,, and dynamicversus static properties.-The complexity of diesel hammers as force generators is characterizedby the almost simultaneous occurrences of combustion and impartforces. Information on the occurrence of the combustion with respect toimpact and combustion gas forces are lacking.Hammer instrumentationis required for investigation of the interaction of ram impact and com-bustion in order to determine components of the generated force pulse.t40re hammer input data on ram velocity at impact and cushionproperties are needed.Ram velocity at impact for different hammersshould be measured during field driving and correlated with hammerparameters such as speed, stroke, position etc., in order to develop

more reliable relationships with hammer efficiency.Ram velocity isimportant in shaping the generated force pulse.Hmer cushion data isavailable for common materials such as wood and aluminum-micarta; however,data is needed for other materials such as wire rope, wood chips, ropeetc.Also, there is a need to find more efficient materials for hammercushions.The capability of changing cushion behavior during driving; would be desirable. For easy driving, a soft cushion is desirable,whereas a stiff cushion is needed for hard driving in order to achievehigh peak forces.Analysis of field measurements of generated pile forcps shouldbe directed towards determination of the soil resistance both at the piletip and along the side.Quake and damping can be varied in the waveequation analysis; the analysis can be forced to match pile forcemeasurements in order to deduce the proper soil parameters.Soil para-meters should be correlated with index properties of the soil.Also,soil data must be accumulated along with load test data for development- of procedures that allow the magnitude of freeze (set-up) or relaxationto be predicted.The effects of pile length and soil distribution on soil responseneed investigation on a hndamental basis.Different boundary condi-tions of pile length cause force reflections to change the pile forcepulse.The effect of reflections coupled with attenuation due to soildistribution need investigation with respect to the force pulse shape(peak and duration).The pile head and soil tip model were studiedseparately herein; however, future research should involve coupling the

two systems together to study the pile length and soil distribution effect.It is hoped that this will lead to approximate methods of predicting peakcompressive and tensile forces in the pile without resorting to a fullwave equation analysis.This in turn- will allow. rational structural designof the pile to resist driving.

REFERENCESAirhart, T. P., T. J. Hirsch and H. M. Coyle, (19671, "Pile-SoilSystem Response in Clay as a Function of Excess Pore Water Pressureand Other Soil Properties," Texas Transportation Institute, ResearchReport 33-8, Texas A & M University, September.Bender, C. H., Jr., C. G. Lyons and L. L. Lowery, Jr., (19691, "Applicationsof Wave-Equation Analysis to Offshore Pile Foundations," OffshoreTechnology Conference, Houston, Texas, May 19-21.Bishop, A. W.and C. E. Blight, (1963), "Some Aspects of Effective Stressin Saturated and Partly Saturated Soils ," Geotechnique, Vol. 13,-pp- 177-197.Casagrande, A. , and W. L. Shannon, 8 "Strength of Soils Under DynamicLoads," Proceedings ASCE, Vol. 74, No. 4, pp. 591-608.Chan, P. C., T. J. Hirsch and H. M. Coyle, (1967), "A Laboratory Study ofDynamic Load-Deformation and Damping Properties of Sands Concernedwith a pile-Soil System," Texas Transportation Institute, ResearchReport Texas A & M University, January.Chellis, R. D., (1961), Pile Foundation,Second Edition, McGraw-Hill, NewYork, 704 p.Coyle, H. M. , and L. C. Reese, (1966), "Load Transfer for Axially LoadedPiles in Clay," Journal of the Soil Mechanics and Foundations Division,ASCE, Vol. 92 No. SM2, Proc. Paper 4702, pp. 1-26.Coyle, H. M., and G. C. Gibson, (1970), "Empirical Damping Constants forSands and Clays," Journal of the Soils Mechanics and FoundationsDivision, ASCE, Vol. 96, No. SM3, Proc. Paper 7296, pp. 949-965. .- Cuwnings, A. E., (1940), "Dynamic Pile Driving Formulas," Contributionsto Soil Mechanics.1925-1940, Boston Society of Civil Engineers,Boston, pp. 392-413.Cunny, R. W. and R. C. Sloan, (1962), "Dynamic Loading Machine and Resultsof Preliminary Small-Scale Footing Tests," Symposium on Soil Dynamics,ASTM Special Technical Publication No. 305, pp. 65-77.Davisson, M.T., (1969), Personal Comunication.1)Davisson, M. T., (1970), "Design Pile Capacity, Conference on Designand Installation of Pile Foundations and Cellular Structures, LehighUniversity, April 13-15.

(1Davisson, M. T., and V. J. McDonald, (1969), Energy Measurementsfor a Diesel Harmner," Performance of Deep Foundations, ASTM STP 444,PP. 295-337.Donnell, L. H., (19301, "Longitudinal Wave Transmission and Impact,"Transactions, ASME, Vol. 52, Paper APM-52-14.Edwards, T. C., (1967), "Piling Analysis Wave Equation Computer ProgramUtilization Manual," Texas Transportation Institute, ResearchReport 33-11, Texas A & M University, August, 40 p.Eiber, R. J., (1958), "A Preliminary Laboratory Investigation of thePrediction of Static Pile Resistance in Sand," Master's Thesis,Case Institute of Technology.Feld, J., (1957), i is cuss ion in Session 6-piling and Piled Foundations,"Proceedings of the Fourth International Conference on SoilMechanics and Foundation Engineering, London, Vol. 3, pp. 180-101.Forehand, P. W. and 3. L. Reese, Jr., (1963), "Pile Driving Analysis11Using the Wave Equation, M.S. Thesis, Princeton University,Princeton, New Jersey.Forehand, P. W. and J. L. Reese, Jr., (1964), "Prediction of PileCapacity by the Wave Equation," Journal of the Soil Mechanicsand Foundations Division, RSCE, Vol. 90, No. SM2, Proc. Paper3820, March, pp. 1-25.Fox, E. N., (1932), "stress Phenomena Occurring in Pile ~riving,"Engineering, London, Vol. 134, pp. 263-265.Gibson, G. C. and H. M. Coyle, (1968), "Soil Damping Constants Relatedto Common Soil Properties in Sands and Clays," Texas TransportatationInstitute, Research Report 125-1, Texas A & M University,September, 28 p.Glanville, W. H., G. Grime, E. N. Fox and W. W. Davies, (1938), "An i/"Investigation of the Stresses in Reinforced Concrete Piles duringDriving," British Building Research Board Technical Paper No. 20,D. S. I. R.Goble, G. G., R. H. Scmlan and J. J. Tomko, (1967), "Dynamic Studieson the Bearing Capacity of Piles," Presented to the IlighwayResearch Board Annual Meeting January 18, Case Institute ofTechnolofg, 63 p.

Goble, G. G., J. J. Tomko, F. Rausche and P. M, Green, (1968), "DynamicStudies on the Bearing Capacity of Piles," Vol. 1 and Vol. 2, ReportNo. 31, Case Western Reserve University, July.Goldsmith, W., (1961.1, Impact, The Theory and Physical Behaviour ofColliding Soilds , Arnold LTD. , London, 379 p.Graff, C. R., (1965), "The Wave Equation and Pile Driving," FoundationFacts, Vol. I, No. 2, p. 8.Hagerty, D. J., (1969), "Some Heave Phenomena Associated with Pile Driving,"Ph.D. Thesis, University of Illinois, Urhana, Illinois.Healy, K. A., (1962), "The Response of Soils to Dynamic Loadings, Report 11:I Triaxial Tests upon Saturated Fine Silty Sand ," U. S. Army Engrs . ,-Waterways Experiment Sta., Vickshurg, Miss.IHeising, W. P . , (1955 ) , Discussion, "Impact and Longitudinal Wave Transmission, "Transactions ASME, August, pp. 971-972.Hirsch, T. J., (1966), "Fundamental Design and Driving Considerations for 4,'. 1 :'IConcrete Piles," Highway Researc? Record, Number 147, Highway Research Ji t?" I.. . Board, pp. 24-34.iHirsch, T. J. and C. H. Samson, Jr.., (1966), "Driving Practices forPrestressed Concrete Piles," Texas Transportation Institute,Research Report 33-3, Texas A & M University, April, 6 p.BHirsch, T. J. and T. C. Edwards, (1966), "Impact Load-Deformation Propertiesof Pile Cushioning Materials," Texas Transportation ~nstitute, ResearchReport 33-11, Texas A & M University, May, 12 p.Housel, W. S., (1965). "Michigan Study of Pile Driving Hammers," Journalof the Soil Mechanics and Foundations Division, ASCE, Vol. 91, No.SM5, Proc. Paper 4483, pp. 37-64.#Ireland, H. O., (1957), "Pulling Tests on Piles in Sand," Proceedings ofthe Fourth International Conference on Soil Mechanics and FoundationEngineering, London, Vol. 2, pp. 43-45.Ireland, H. O., (1966), "The Conduct and Interpretation of Pile LoadingTests," Seminar Sponsored by Foundation and Soil Mechanics Group,Metropolitan Section, ASCE, New York, April 12-13, Mey 10-11.Isaacs, D. V., (1931), "Reinforced Concrete Pile Formulae," Journal of the //Institution of Engineers Australia, Transactions, Vol. 12, pp. 305-323.Johnson, C. L., (1956), Analog Computer Techniques, McGraw-Hill Book Company,Inc., New York.

Jones, R., N. W. Lister and E. N. Thrower, (1966), "The Dynamic Behaviorof Soils and Foundations," Proceedings of Symposium on Vibration inCivil Engineering, Imperial College, London, pp. 121-140.Kane, H., Davisson, M. T., R. E. Olson and G. K. Sinnamon, (1964), "A Studyof the Behavior of a Clay under Rapid and Dynamic Loading in the One-Dimensional and Triaxial Tests," Report No. RTD TDR-63-3116, Air ForceWeapons Lab.Kerisel, J., (1961), "Fondations Profondes en Milieu Sableux," Proceedingsof the Fifth International Conference on Soil Mechanics and FoundationEngineering, Montreal, Vol. 2, pp. 73-83.Kerisel, J., (1964), "Deep Foundations, Basic Experimental Facts ," Proceedingsof North American Conference on Deep Foundations, Mexico City.Kolsky, H., (1963), Stress Waves in Solids, Dover, New York, 213 p.Korb, K. W. and H. M. Coyle, (1969), "Dynamic and Static Field Tests on aSmall Instrumented Pile," Texas Transportation Institute, ResearchReport 33-12, Texas A & M University, February, 24 p.Korn, G. A. and T. M. Korn, (1956), Electronic Analog Computers, 2nd. Ed.,McGraw-Hill Company, Inc., New York.Lee, L. L., Jr., T. C. Edwards and T. J. Hirsch, (1968), "Use of the WaveEquation to Predict Soil Resistance on a Pile During Driving,"Texas Transportation Institute, Research Report 33-10, Texas A & MUniversity, August, 32 p.Lowery, L. L., Jr., T. J. Hirsch and C. H. Samson, Jr., (1967), "PileDriving Analysis - Simulation of Hmers , Cushions, Piles, andSoil ," Texas Transportation Institute, Research Report 33-9, TexasA & M University, August, 81 p.Lowery, L. L., Jr., J. R. Finley, Jr. and T. J. Hirsch, (1968), "A- son of Dynamic Pile Driving Formulas with Wave Equation," TexasTransportation Institute, Research Report 33-12, Texas A & MUniversity, August, 16 p.Compuri-Lowery, L. L., Jr., T. J. Hirsch, T. C. Edwards, H. M. Coyle end C. H. Samson,Jr., (1969), "pile Driving Analysis - State of the Art," Texas TransportationInstitute, Research Report 33-13, Texas A & M University,January, 79 P .Lowery, L. L., Jr., T. C. Edwards and J. R. Finley, Jr., (1969), "Increasingthe Ability to Drive Long Off-Shore Piles," Offshore Technology Conference,Houston, Texas, Msy 15-21.Mansur, C. I., A. H. Hunter and M. T. Davisson, (1964), "Pile Driving andLoading Tests, Lock and Dam No. 4, .&kansas River and Tributaries,"U. S. Army Engineer District, Little Rock, 82 p.Meyerhof, G. H., (19511, "The Ultimate Bearing Capacity of Foundations,"Geotechnique, Vol. 2, pp. 301-332.

Ideyerhof, G. G., (1959), "Compaction of Sands and Bearing Capacity of Piles,Proceedings ASCE, Vol. 85, No. SM6, pp. 1-29.Michigan State Highway Commission, (19651, "A Performance Investigation,tof Pile Driving Hammers and Piles, Research Project 61 F-60, Lansing.Mosley, E. T., (1967), "Wave Equation Analysis," Foundation Facts, Vol. 3,No. 2, pp. 15-17.Mosley, E. T. and T. Raamot, (1970), "Pile Driving Formulas," Paper presentedat Highway Research Board Annual Meeting, January.Nordlund, R. L., (1963), "Bearing Capacity of Piles in Cohesionless soils,"Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 89,No. SM3, Proc. Paper 3506, pp. 1-35.-Olson, R. E. and J. F. Parola, (1967), "Dynamic Shearing Properties of Compacted,,11Clay, Proceedings of International Symposium on Wave Propagation andDynamic Properties of Earth Materials, Albuquerque, New Mexico,pp. 173-182.Olson, R. E. and K. S. Flaate, (1967), "Pile-Driving Formulas for FrictionPiles in Sand," Journal of the Soil Mechanics and Foundations Division,ASCE, Vol. 93, No. SM~, Proc. Paper 5604, pp. 279-296.Parsons, J. D., (1966), "piling Difficulties in the New York Area," Journalof the Soil Mechanics and Foundations Division, ASCE, Vol. 92, No.Sm, Proc. Paper 4617, pp. 43-64.Peck, R. B., (1958), "A Study of the Comparative Behavior of kriction Piles,"Highway Research Board, Special Report 36, 72 p.Raamot, T., (1967), "Analysis of Pile Driving by the Wave Equation," FoundationFacts, Vol. 3, No. 1, pp. 10-12.- Raamot, T. (1967), "Wave Equation Approach to Pile Driving," The MunicipalEngineers Journal, Vol. 53, First Quarterly Issue, pp. 11-19.Rakhmatulin, Kh. A. and Yu. A. Dem'yanov, (1961), Strength Under HighTransient Loads, a translation of ~rochnostpri IntensivnykhKratkovremennykh Nagruzkakh, Israel Program for Scientific Trans-Lations, Jerusalem, 1966, 342 p.Reeves, G. N., H. M. Coyle and T. J. Iiirsch, (1967), "Investigation ofSands Subjected to Dynamic Loading," Texas Transportation Institute,Research Report 33-7A, Texas A & M University, December, 9 p.Saint-Venant, (~efore 1900), "Th6orie de lt61asticit6 des corps solids,"Clebsch. Reference referred to by Timoshenko and Goodier, (1951),Theory of Elasticity, pp. 446.

.-Smson, C. H., Jr., T. J. Hirsch and L. L. Lowery, Jr., (1963),"Computer Study of Dynamic Behavior of Piling," Journal of theStructural Division, AXE, Vol. 89, No. ST^, Proc. Paper 3608,August, pp. 413-449.Scanlan, R. H. and J. J. Tomko, (1969), "Dynamic Prediction of PileStatic Bearing Capacity," Journal of the Soil Mechanics andFoundations Division, ASCE, Vol. 95, No. SM2, Proc. Paper6468, pp. 583-604.Schimming, B. B., H. J. Haas and H. C. Saxe, (1966), "Study of Dynamicand Static Failure Envelopes," Journal of the Soil-Mechanicsand Foundations Division, ASCE, Vol. 92, No. SM3, Proc. Paper 4735,pp. 105-124.-Seed, H. B. and R. Lundgren, (1954)~ "Investigation of the Effect ofTransient Loading on the Strength and Defomtion Characteristicsof Saturated Sands," Proceedings ASTM, Vol. 54, pp. 1288-1306.Smart, J. D., (1969), "Vibratory Pile Driving," Ph.D. Thesis, Universityof Illinois, Urbana, Illinois.Smith, E. A. L.. (1950), "Pile Driving Impact ," Industrial ComputationSeminar, International Bus5ness Machines Corp., New York.Smith, E. A. L., (1955,), "Impact and Longitudinal Wave Transmission,"Transactions ASME, August, pp. 963-973.Smith, E. A. L. , (1957), "The Wave Equation Applied to Pile 'Driving,"Raymond Concrete Pile Co.Smith, E. A. L., (19581, "Pile Calculations by the Wave Equation,"Concrete and Constructional Engineer, London.-Smith, E. A. L:, (1960), "Pile-Driving Analysis by the Wave Equation,"Journal of Soil Mechanics and Foundations Division, ASCE, Proc.Paper 2574, August.Smith, E. A. L., (1962), "Pile-Driving Analysis by the Wave Equation,"Transactions ASCE, Vol. 127, Part I, pp. 1145-1171.Szechy, C., (i960), "A New Pile Bearing Formula for Friction Piles inCohesionless Sand," Symposium on Pile Foundations, InternationalCongress of the International Association for Bridge and StructuralEngineers, Stockholm, pp. 73-76.

Taylor, D. W., (1948), Fundamentals of Soil Mechanics, John Wiley andSons, New York, 700 p.Terzaghi, K. and R. B. Peck, (1967), Soil Mechanics in EngineeringPractice, 2nd. Edition, John Wiley and Sons, New York, 729 p.Timoshenko, S. and J. N. Goodier, (1951), Theory of Elasticity, 2nd.Edition, McGraw-Hill Co., New York, pp. 438-459.Tomko, J. J., (1968), "Dynamic Studies on Predicting the Static BearingCapacity of Piles," Ph.D. Thesis, Case Western Reserve University.Tomlinson, M. J., (1957), "The Adhesion of Pile Driven in Clay Soils,"Proceedings of the Fourth International Conference on SoilMechanics and Foundation Engineering, London, Vol. 2, pp. 66-71.Vesi6, A. S., (1964), "Investigations of Bearing Capacity of Piles inSand," Proceedings of North hericen Conference on Deep Foundations,Mexico City.Vesi6, A. S. ,i (1967), "Ultimate Loads and Settlements of Deep Foundationsin Sand;" Proceedings of a Symposium or Bearing Capacity andSettlement of Foundations, Duke University, pp. 53-68.Vulcan Iron Works, (19271, "Pile Driving Machinery," Catalogue No. 53,80 p.Whitman, R. V. (1957), "The Behavior of Soils Under Transient Loadings,"Proceedings of the Fourth International Conference on Soil Mechanicsand Foundation Engineering, London, Vol. I, pp. 207-212.Whitman, R. V. and K. A. Healy, 6 "The Response of Soils to DynamicLoadings, Report 9: Shearing Resistance of Sands During Rapid-Loadings," U. S. Amy Engrs., Waterways Experiment Sta., Vicksburg,Miss.Whitman, R. V., A. M. '~ichardson, Jr. and N. M. Nasim, (1962), "TheResponse of Soils to Dynamic Loadings, Report 10: Strength ofSaturated Fat Clay," U. S. ArnIy Engrs., Waterways Experiment Sta.,Vicksburg, Miss.Yang, N. C., (19561, "Redriving Characteristics of Piles," Journal of theSoil Mechanics and Foundations Division, ASCE, Vol. 82, No. SM3,Proc. Paper 1026.Yang, N. C., (1970), "Relaxation of PIles in Sand and Inorganic Silt,"Journal of the Soil Mechanics and Foundations Division, ASCE, Vol.96, No. SM2, Proc. Paper 7123, pp. 395-409.

APPENDIX ARFVlEW OF SINGLE-PILE ANALYSISIt is the purpose of this appendix to present the methods available.for the analysis of a single pile.Current means of analyzing a single-pile may be classified either as static or dynamic.Dynamic methods of-analysis include:1) dynamic energy formulas; 2) wave equation analysis;3) pile force and acceleration field measurements.In order to validate design assumptions, pile load tests are gen-erally performed.However, the interpretation of pile load test data isnot unique; differences of opinion among engineers on the same test datamake correlations difficult. Ireland (1966) summarized various methodsof interpretation of pile load test data as well as information on proceduresfor pile load testing.A.2 Static Pile Formulas-Nl the static pile formulas may be expressed by the followingbasic equation:where R is the ultimate pile capacity, R is the load carried by friction,u falong the pile perimeter, and R is the load carried by point resistance.PVariations in answers from Equation A.1 are due to the methods used toevaluate the friction and point-bearing portions of ultimate pile capacity.Driving a pile into granular soil will cause the soil in the zone aroundthe pile to displace laterally; therefore, a change in densification andhorizontal stresses is expected.In order to calculate the skin friction

191resistance of a pile, the horizontal stresses acting on the pile surfaceas well as the coefficient of friction of the pile and soil must beevaluated. A number of investigations (j.deyerhof, 1951, Ireland, 1957;Szechy, 1960; Vesic, 1964; Nordlund, 1963) have been made to determine themagnitude an8 distribution of the horizontal stress acting on the pilesurface after driving.Experimental studies by Kerisel (1964) and Vesic(1964) help indicate the behavior of the point resistance with respect todepth.. Vesic (1967) evaluated various theories of static pile capacity-. .and concluded that no theory could be recommended to the foundation engineerwithout reservations.. .A review of various studies indicates that the stateof stress around a driven pile in sand is very complex; therefore, staticpile formulas for sand are still speculative.It is commonly assumed that the capacity of a single pile in clay isdue to skin friction.Several studies, such as by Tomlinson (1957) andPeck (1958), indicated that the adhesion between the pile and the claycould be related to the undisturbed strength of clay.For soft to mediumclays, the adhesion is essentially equal to the undrained shear strength ofthe undisturbed clay.However, piles driven in stiff clay do not developthe full strength of the soil in skin friction.One possible explanationfor low friction is the separation of pile and soil because of lateral pilemovement.The separation can be maintained because of the clay's strength.When piles are driven in clays the soil in the vicinity of the pile isremolded; therefore, a loss in shear strength occurs.With time arterdriving, the soil regains strength by both consolidation' and thixotropy;therefore, the relations between skin friction and time are complex andss yet are not predictable.

Limitations of static thearies in sand can be summarized in twoparts, namely, skin friction and tip resistance.First, the skin frictionis strongly a function of pile material and construction technique, butstatic theory does not take into account construction technique.Second,the actual behavior of pile tips in sand is not in accord with commontheories (~esic, 1964). Static analysis does, however, give a more repre--sentative simulation of the static loading condition being investigated.Static theories take .variations in the soil profile into accountStatic analysis is a useful tool in pile design; however, itshould be recognized that it alone can not be relied upon.Real soil pro-files are quite variable; therefore, the desired pile length or depth ofpenetration to achieve the required load capacity is also variable.Loadcapacity as measured by driving resistance (blows/inch] is a useful indi-cator for an individual pile that allows appropriate adjustme~ts to bemade at the time of driving.A.3 Eneray Formulas-In the last century, engineers have attempted to predict the driv-ing characteristics and bearing capacity of piles by use of dynamic energyformulas.Dynamic energy formulas are based on the simple energy rela-tionship:Energy Input = Energy Used + Energy Lost(A.2)where energy input is available hammer energy at impact, energy used isthat actually used in driving the pile, and energy lost is returned tohammer (rebound) or simply lost, i.e. non-useful energy for pile penetration.Non-usefliL energy may include: hammer efficiency; ram rebound;plastic behavior at the contacts between the ram, cushion and pile; tempo-

193rary elastic compression of the pile and soil; heat losses in the cushionblock. and soil5 radiation losses related to soil vibrations due to generatedstress waves; and friction losses due to the pile slipping with re-spect to the soil.A great number of pile driving formulas have beenderived that incorporate these energy losses and attempt to predict theenergy transmitted to the pile.These losses have been estimated byassuming that pile driving is a problem in Newtonian impact.In reality,-the pile is a distributed mass, not a concentrated mass, and it is alsorestrained by the soil; these facts violate Newton's impact theory(Cummings, 1940).However, it should be pointed out that energy formulasare still in common use today and can be a valuable tool if they are em-pirically adjusted for a part$cular driving condition, i.e. some givensoil condition, pile type and driving equipment.Load tests must be usedas a basis for adjusting the particular dynamic formula used.There are many dynamic energy formulas available todoy (over four-hundred according to Smith, 1960) derived from the simple energy relation--ship previously described; however, they can be divided into two majorgroups. One group is strictly empirical in which the energy losses &epredicted from field data, and the other group can be classified as semi-theoretical in which the determination of losses is based on Newtonianimpact.Eighteen different and widely used pile formulas plus the statis-tical adjustment of Gates formula by Olson and Flaate (1967) have beenselected for this investigation.The enera formulas discussed are shownin Table A.l along with a list of notation.It is beyond the scope of this investigation to derive or discuss indetail the basis for the driving formulas in Table A.1;however, derivationsand concepts can be readily found in Isaacs (19311, Cummings (1940), Taylor

Table A.1TABULATION OF PILE ENERGY FORMLIT,&12 E1. Engineering News: R = - ru S + P12 E W1 + n%2. Modified Engineering News: R = - r.u s+e W1+WPP12 ef Er3. Gow: R =u s + e(w /WP 1)120 E4. Vulcan Iron Works: R = r- u 10s + 112 Wlh5. Bureau of Yards and Docks: R =u s + 0.36. Rankine: Ru z [/ T I12 E8. Ritter: RW1=I1 S W1 + W +W1+Wp.9. Eytelwein: R = ru s + 0.1 W /W Single-Acting HammersP 1e12 (E + A P)R =ru s + 0.1 W /WP 112 E10. Navy-Mckay: R = ru s(l+O.3W/W)P 112 E11. Sanders: R = - ru SPDouble-Acting Hammers

Table A.l (continued)12. Gates: RU = 990 log (10/s)e E13. Danish: R = f r12 E14. Janbu: R = - ru kU s12 ef E~ w1 + n2W15. Hiley: R =u s + 1/2(c1 + C + Cw1 + W2 3)P16. Redtenbacker: =-Rn 12 L1 P10. Canadian National Building Code:12 ef el Er-RU - s + s/2W, + niie 1 = W1+WPFriction Piles

Table A.l (continued)2W + 0.511 W.=11 w, + wPPoint Bearing Piles19, Statistical Adjustments of Gates Formula (0lson and Flaate, 1967):Key: Ru ultimate pile capacity (lbs)rated hammer energy (ft-lbs)set (in.)temporary set representing losses (in.)weight of the pile (lbs)weight of the ram (lbs)height of ram fall (ft)cross-sectional area of pile (ins2)Young's modulus of pile (psi)length of pile (ft)length of pile, measured-from head to center of driving resistanceresistance (ft)hammer efficiency (%)effective area of piston cine2)mean pressure of steam or air (.psi)

Table A.l (continued)ncoefficient of restitutionrecoverable deformation of drivehead and pile head (in.)C2recoverable deformation of pile (in.)C 3recoverable deformation of soil (in.)c 4C 5slope of a regression line (dimensionless)intercept of a regression line (lbs)

198(1948), Chellis (19611, Terzaghi and Peck (1967), Olson and Flaate (1967)and other publications concerned with foundation engineering.A.4 Vlave-Equation AnalysisIntroductionIn recent years, impact and longitudinal wave transmission theoryhas been given considerable attention because it is a better simulation ofthe pile driving operation than is the theory of Newtonian impact.A com-parison of the Newtonian impact model and longitudinal wave model is shownin Figure A.1.The impact resulting when a pile hammer strikes a pile is a practi-cal illustration of longitudinal impact in elastic rods.Wave propagationanalysis attempts to describe the travel of the impulse up and down thepile as the pile is being driven.soil system shown in Figure A.2.Consider qualitatively the hammer-pile-During ram impact, the ram, driveheadand pile are assumed to deform elastically.The hammer cushion is inelas-tic; therefore, energy losses are inherent in the cushion.- Previous experience has shown that a hammer cushion is required inorder to protect the hammer from damage.Of course, the cushion materialalso affects the stresses induced in the pile.A prerequisite for the cu-shion is that it be an expendable material; therefore, wood is commonly usedwhereas alternating thin discs of aluminum and micarta have become promi-nent in recent years.There are other types of cushion materials employedin practice today; however, aluminum-micarta and wood cushions represent theextremes in load-deformation characteristics.The aluminum-micarta assemblyapproaches an elastic condition whereas the wood cushion represents inelastic

ImpactVelocity1 Drivehead ] m 2ImpactVelocityIPile.-- PCAt FrictionI Point BearingNewtonian ModelLongitudinal Wave ModelFigure A.lIMPACT MODELS

201behavior.The cushion material and its effects are discussed later indetail.The elastic compression of both the ram and drivehead may be neglec-ted since these members are infinitely rigid.The elastic compressionof the pile is appreciable, and does not occur instantaneously throughoutthe entire length of the pile.As ram impact occurs, a force pulse isdeveloped in the pile that travels downward toward the pile tip at a-constant velocity, c, which depends on properties of the pile material(Figure A.2b).When the force pulse propagates within the embedded portion of thepile, it is attenuated by soil frictional resistance along the pileasshown in Figure A.2c.untii the stress wave reaches the tip, the maximumstress in the pile is independent of driving resistance.When the forcepulse reaches the pile tip, a reflected force pulse, governed by the soilresistance at the tip, is generated.For the case of a pile driven torefusal, the incident compression wave is reflected as a compressive wavetravelling up the pile with velocity, c, and identical in shape to thewincident wave.The extreme opposite to driving refusal is a pile with afree-end.In this case, the soil offers negligible resistance to driving;therefore, the incident compressive wave is reflected as a tension wavetravelling up the pile with velocity, c, and is identical. in shape to theincident wave.In practice, pile driving is somewhere in between theextreme case of a fixed and a free tip condition; therefore, the reflectedwave will also be a function of the soil response at the pile tip.Some of the variables that will affect the generated force pulseshape along the pile will now be considered.Ram weight and velocity cancharacterize the pulse shape for a given enera input.For the same energy,

. a light ram and resulting high velocity will produce high peak stressesover a short time duration, whereas a heavier ram will cause lower peakstresses with a relatively long time duration.The cushion block is veryimportant in shaping the force pulse; therefore, special emphasis shouldbe placed on its effects.The stiff cushion will produce high peakstresses and short time duration, whereas the soft cushion will producea longer duration pulse with lower peak stresses.A schematic represen-- tation of the variable pulses that can be produced by a hammer with a-given energy rating is shown in Fiyre A.3.HistoryHistorically, St. Venant Ad Boussinesq are believed to have firstdeveloped the theory of longitudinal impact of a rod struck longitudinallyat one end.The development of this theory occurred within the period1867 to 1883, and according to Timoshinko and Goodier (1951) a history ofthe problem can be found in the reference by St. Venant.The basis forthe analysis is the classical one-dimensional wave equationin which x is the direction of the longitudinal axis; u is the longitudi-nal displacement of the bar in the x direction; t denotes time; c repre-sents the velocity of propagation of stress or strain wave along the bar,c = m; E is the modulus of elasticity of the bar; and p is the massper unit volume of material. Equation (~.3) is based onthe conditionthat lateral strains (distortion waves) are negligible so that plane trans-

Pulse A - associatedwith light ram, highram velocity & stiffcushion. 1Pulse B - associated withheavy ram, low ram velocity& soFt cushion.$.Pile LengthFigure A.3 VARIABLE FORCE W EGIVEN ElSERGY IIOPUTFOR A

.verse sections are not distoited. The assumption that plane sections re-main plane is acceptable for stress pulses with lengths that are large (atleast 10 times) compared to the lateral dimensions of the rod or bar(Kolsky, 1963).The general solution of Eq. (A.3) isu = f (ct-x) + g (ct +x)(n.4)where f and g are arbitrary functions representing waves travelling upand down the bar.The problem consists of determining the functions f and-g for various time intervals after the start of impact.The application of one-dimensional wave equation to problems oflongitudinal wave transmission can be readily found in references byKolsky (1963), Timoshinko and Goodier (1951), Donne11 (1930), Rakhmatulinand Dem'yanov (1966), and Goldsmith (1960).Isaacs (1931) is believed to be the first to apply wave analysis topile driving.Isaacs simplified the boundary conditions by placing onlyan elastic spring between the hmer ram and pile.These simplifiedboundary conditions include zero frictional resistance along the pile, and-a plastic soil resistance acting at the pile tip. Pox (1932) used the pilemodel proposed by Isaacs; however, Fox chose a boundary condition for thecushion that is more representative of actual cushion behavior. Thecushion is represented by a visco-elastic spring throu@out the range ofcompressive stresses.An investigation of the stresses induced in reinforced concretepiles during driving was performed by Glanville et al. (1938).Fox'stheoretical treatment was used, but it was necessary to simplify theboundary conditions in order to express the solutions in terms of quantitiesmeasurable in practice.!Che modified boundary conditions included elastic

cushion and soil resistance behavior.Cmings (1940) pointed out thateven for these modified assumptions the complete solution involves longand complicated mathematical. expressions that precludes its use forpractical problems.Considering the boundary conditions of a real pile-driving problem,i.e. soil resistance along the pile, realistic parameters for the cushion,soil, and other pile-hammer details, a rigorous solution by use of the-wave equation is not known. Smith (1950) proposed a mathematical model,based on a lumped-mass and spring system, that accounts for the effectsof the boundary conditions of a real pile driving problem.According toLowery et al. (1967), Smith continued to develop his method (Smith 1955,1957, 1958), but his method of analysis did not become popular until thepaper (Smith, 1960) i n which a number of parameters were recommended toaccount for the dynamic behavior of soil, pile and cushion.The availa-bility of the computer made Smith's approach more attractilre, and con-siderable effort has been done in this area, for example:Bender, etal. (1969); Davisson (1970); Graff (1965); Hirsch (1966); Korb and Coyle- (1969); Lowery, et al. (1968); Lowery, et al. (1969); Mosley (1967) ;Raamot (1967); in addition to those mentioned elsewhere herein.Smith's ModelConcept. Smith's mathematical model of the hammer-pile-soil sys-tem is shown in Figure A.4.The ram, hammer cushion, drivehead, pilecushion, and pile are represented by appropriate discrete weights andsprings.Spring constants for the various types of cushion material canbe obtained from test results, whereas those of the pile segment can bereadily calculated.Soil characteristics, both along the sides and at thepile tip, are represented by a combination of elastic-plastic springs to

-Pile CushioNote:K representsKt representssoil springs.Soil ResistanceActual.ModelFigure A. 4SMITH'S MATHEMATICAL MODEL

simulate static resistance and dashpots to account for the dynamic responseof the soil. Actual situations may deviate somewhat from those in Figure~.4. For example, a pile cushion might not be used, or an anvil may beplaced between ram and hmer cushion, or a follower used; such cases arereadily accommodated in Smith's analysis.The numerical method used to describe force transmission in thismathematical model is illustrated in Figure A.5.This figure illustrates-ram has an initial velocity (V ) and acceleration that can be converted into0a displacement (D ) for a given time interval (~t) by the equation D1=Vo1(~t). For this time interval ( t = tl), the compression of the hammerthe force build-up in the pile during the initial stages of impact.The-cushion can be readily determined; therefore, the force in the hammercushion (F1) can be calculated by the equation F1=KID1 as shown in Figure A. 5.The force build-up in the hmer cushion induces a drivehead accelerationwhich can be evaluated by the equilibrium equation F=ma, where m isthe mass, s. is acceleration, and F is the summation of forces acting on thedrivehead.From this acceleration, a change in vel.ocity can be readilycalculated on the assumption that the drivehead is uniformly acceleratedin rectilinear motion for the time interval ( t) between times t and t2.1The resulting velocity of the drivehead can be converted into a displace-ment.The displacement compresses the first pile spring causing a forceF on the first segment of the pile, K D Also during time t2-t1 the ram2 2 2-has travelled an additional distance which can be calculated by the deter-mination of a new velocity of the ram for the time interval.The differencein displacement between the ram and drivehead during time t -t represents2 1the compression of the hammer cushion, which is used to calculate a new cu-shion force.This procedure can be repeated for successive time intervals,and

forces in the pile system can be traced for any desired length of time.Asthe generated force pulse is traced along the embedded portion of the pile,the mathematical procedure has to account also for the soil resistance.When using the lumped-mass and spring model as described above, caremust be exercised in the selection of the time interval At.Each spring andmass unit has a "critical" time interval, which is the time required for astress wave to traverse the particular spring and associated mass.- selected time interval for computations must never be greater than thist,critical" time interval; otherwise, the numerical results will be meaning-less because the calculation will not progress as fast as the actual stressThewave.However, an unnecessarily small time interval involves a great dealof extra work with little or no increase in accuracy.Basic Equations.The following equations are used for the solutionof Smith's pile model:where m is the mass number; t denotes time interval number; At is the timeinterval, in seconds; D(m,t) is the displacement of mass m in time intervalit, in inches; V(m,t) is the velocity of mass m in time interval t, in feetper second; ~(m,t) represents compression of spring m during time interval t,

in inches; ~(m) is the spring rate of mass m, in pounds per inch; ~(m,t) isthe force in internal spring m in time interval t, in pounds;~(m,t) is thetotal soil resistance on mass m,in pounds per inch; D1(m,t) is the plasticdisplacement of the soil spring m in time interval t, in inches; K' (m) isthe spring constant associated with the soil spring acting on mass m, inpounds per inch; ~ ( m ) is a constant that accounts for the dynamic responseof the soil acting on mass m, in seconds per feet; and g is gravitational2acceleration, in feet per second . These basic equations can be readily- programmed for solution by means of a digital computer.Smith's Model versus Classical Wave Equation.The classical one-dimensional wave equation (Eq. A.3) can be readily converted into a differenceequation for solution by successive approximation.Xeising (1955) pointedout that the difference equation is an exact solution of the partial differ-ential equation whenwhere AL is the segment length. For other values of A t the solutions are-approximate. Smith (1960) and Forehand and Reese (1963) showed that thedifference equation could also be obtained by combining Smith's basic equa-tions (Equations A.5 to A.9) into a single equation.Thus, Smith's basicequations are equivalent to the wave equation for purposes of numericalComparison of a (generated pile force pulse from the rigorous analysisof Chapter 2 and from the wave equation analysis (Smith's model) was madefor a particular hammer and pile condition, as shown in Figure A.6.Therewas no soil resistance along the pile lengthand the pile was assumed longenough to avoid interference by reflection from the pile tip.The pile and

hammer characteristics are typical of current pile specifications.Theinduced pile forces as determined by the rigorous analysis and by the waveequation analysis are in close agreement, thus verifying Smith's model.Input and Output.The basic equations (Equations A.5 to A.9) areprogrammed into a digital computer for solution.Several programs areavailable (lowery et al., 1967 and Edwards, 1967) . The various inputparameters and output data are summarized in Table A.2.The initial condition is the impact velocity of the ram, which can-be calculated fron the energy of the hammer at impact, i .e. energy at im-pact = E x e where E is rated hammer energy and e is the hammer effirf r fciency.Hammer efficiencies (Chapter 1) are only valid when the hammer isoperating at dl capacity.If the hammer is not operating properly, ef-ficiency can be considerably less' than the recommended values.Efficiencycan be checked in the field by obtaining a measured ram velocity at im-pact and comparing this to the rated velocity as shown in the equation be-low:-v measurede = ()2 x 100% (A.11).f vtheoreticalThe measured field velocity can be obtained by high speed photographyor a radar unit; however, this type of field control is difficult and costly.Fortunately, hammer speed may be indicative of efficiency.For example,consider the relationship between hammer efficiency and hammer speed ob-tained with radar equipment as shown in Figure A.7 (Davisson, 1969).Theoperating efficiency was 70% at the rated hmer speed of 60 blows perminute.This efficiency is less than the commonly recommended value of75 to 85% for single acting hammers. Also, efficiency drops off quitesharply with a reduction in speed, e.g. e = 50% at 50 blows per minute.f

Table A.2INPUT AND OUTPUT - WAVE EQUATION ANALYSISWeight of RamImpact VelocityEnera at Impact, Er+ eCushion Stiffness and Coefficient of Restitution(Same for Extra cushions)Drive Head Weight (Anvil Also for ~iesels)Combustion Force for DieselsPile Length during Driving, Area, & Stiffness, Material(Same for Mandrels)Soil Resistance: % R in Friction and Its~isvribution% Ru at TipQuake, Q and DampingFactors, JAnalyze RoringsFollower Length, Area, & StiffnessJoints (with or without tension)Stresses and Deflections at any Point vs. TimeUltimate Pile Capacity, Ru,Blows/Inchat Time of Driving vs.

100I . IVulcln 1 Hammer70 EP Boiler & 140 psi0-5 Raymond Mandrel - 8 Stops80 -6040/70% e ,Prnted speed,fl'/*////P0 /20O303040 50Hammer Speed, blows /min .60(After Dnvisson, 1969)Mgure A.7RELOTIOmIP BETWZEZ HAMMERmc1ENCY m SPKED

It is clear that more information on hammer efficiency is needed, based onactual field measurements.The spring constants for various types of hamper cuqhions are obtainedfrom test results.A typical shape of the dynamic stress-strain curve fora cushion along with the idealized shape used for the wave equation analysisis shown in Figure 2.3 (Chapter 2).According to Lowery et a1 (1969), itwas found that the wave equation accurately predicted both the shape andmagnitude of the stress wave induced in a pile when the idealized stress--strain curve is used.The idealized shape can be used as long as the loadingportion is based on a secant modulus for the material, and the unloadingportion of the curve is based on the actual dynamic coefficient of restitu-tion.This coefficient of restitution accounts for the energy loss in thecushion material.Typical values of secant moduli of elasticity and coeffi-cients of restitutions for various materials are presented below:(Loweryet al, 1969)Cushion MaterialE (secant)CpsiMicarta Plastic 450,000Oak reen en)45 ,0OOXAsbestos Discs 45,000Fir Plywood35 ,OOOXPine Plywood 25,000"Gum30 ,OOOX* Load applied perpendicular to wood grain.Input hammer parameters such as rated energy, hammer efficiency, ramweight, drive head weight, anvil weight, cushion properties, and combustionforce for diesel hammers are summarized in Table A.3.The interaction ofram impact and combustion in a diesel hmer is not readily determinable;

Teble A.31I?WW DATA FOR DIESEL IIAIWZRSKhDrive HeadKC -Optional--RatedEnergyStiffnessDriveHammer RR~I Anvil HeadHammerRam CushionEfficiency Wei~ht Wt. !.it .lbs~n x 10Type Hammer ft-lbs . f lbs. 1'0s. lbs. T-~n x lo6 ibSMKT DE-20 16,000 1.00!.KT DE-30 22,400?KT DE-40 32,000CombustionForcelbs .Delmag D5 9,040Delmag D12 22,600Delmag D22 39,800Delmag D44 80, 000Link Belt180 8,130Link Belt 312 15,000Link Belt 440 18,200Link Belt 520-26,300Note:1. The hm~ner ~ n d pile cushion innut depend on materi~l properties

houever, an idealized force-time curve can be assumed (Figure ~.8). Themagnitudes of explosive pressures in Table A.3 were obtained from Lowery,The complexity of the diesel hammer is best characterized by con-sidering the details of one complete ram cycle starting with descent of theram.As the ram descends, it passes the intake-exhaust port and traps airin the combusion chamber.With further ram descent, the ram is working-against an air spring and the ram velocity is thereby decreased.Fuel in-jection is initiated prior to impact, and combusion occurs with peak gasforce and impact force occurring almost simultaneously.During impact, thecombusion force continues and eventually returns the ram to the top ofits! stroke.It is obvious that hammer instrumentation is required to studyram impact and velocity, and combustion forces.At present, informationon the occurrence of combustion with respect to impact, combustion burntime, and peak gas forces is lacking.A study by Davisson and McDonald(1969) giving measurements of pile force of a long concrete-filled pipe-pile driven with a diesel hammer indicated peak Eas forces of approximately280 kips. More research on diesel hammer input is required.Pile input parameters include material type, length during drivingcross-sectional area and modulus of elasticity.In general, piles arebroken into segments not to exceed approximately 10 feet, but no fewer thanfive segments are used.The stiffness and weight of each pile segment canbe easily calculated, and the selection of the proper time interval is in-cluded within the program to avoid instability with respect to the "critical"time interval (discussed previously).The program has provisions for hand-ling joints in the' pile-hammer system, i.e. mechanical joints which prohibitthe transmission of tensile stresses or transmit tensile stresses only after a

Impact Force caused byFalling RamIdealized DieselExplosion Force-Time, ms(~fter Lowery, et nl 1969)Figure A. 8 IDEALIZED FORCE-TIMEM)R A DIESEL HAMMERCURVE

specified movement of the joint.219Inp'~t properties for mandrels or followers'are analogous to those for the pile.The load-deformation characteristics assumed for soil in Smith'snumerical solution are shown in Figure 3.2 (Chapter 3).The soil locatedalong the side' of the pile is assumed to resist rebound as well as downwardmotion.sion.However, the soil at the tip of the pile will only resist compres-Based on a limited number of comparisons with load test data, Smith(1960) proposed the following values for the soil parameters:-Qside = Q (along side of pile) = 0.1 in.&p .olntJ .sldeJ .polnt= Q (at pile tip) = 0.1 in.= J (along side of pile) = 0.05 sec/ft= J (kt pile tip) = 0.15 sec/?tA limited amount of work has been done on soil input data.Fore-hand and Reese (1964) investigated the soil parameters used in the waveequation by correlating with load test data.Correlation attempts forpiles driven in sand were consistent with Smith's recommended values, where-as there was a lack of correlation for piles driven in clay.More recent- (1967), have been directed towards obtaining better soil input data byinvestigations, Chan et al. (1967), Reeves, et al. (1967), Airhart, et 'al.performing laboratory dynamic and static tests on saturated sands and afull scale instrumented pile in clay.The studies showed that the soilparameters are a function of the loading velocity. Gibson and Coyle (1968)related soil damping constants with common soil properties for both sandand clay.More detailed discussion of soil response with respect todynamic loading is considered in Chapter 3.The soil resistance distribution must be included in the analysis.Soil resistance distribution includes the percent resistance at the

pile tip compared to the percent resistance along the sides of the pile.'Aiso, the frictional resistance distribution must be incorporated.Thesoil resistance distribution can not be predicted in an exact manner, butanalysis of borings can give reasonable limiting values for this distribution.The maximum displacement of the pile tip is found during the numericalanalysis of a single impact, and this displacement (set) can be convertedinto hammer blows per inch (reciprocal of set) for a particular ultimaterssistance.With consideration of various ultimate soil resistances andthe corresponding pile response, results of the wave analysis can be pre-sented as shown in Figure A.9.The relationship between ultimate pileload capacity at the time of driving and driving resistance in blows perinch is of primary interest.Also, compressive and tensile stresses and de-flections at any point with respect to time can be obtained.A tracingof the stresses can easily produce the maximum stresses that are obtainedto determine whether or not the pile will be damaged during driving.Forexample, in Figure A.9 the maximum compressive stresses are shown versusdriving resistance.-A.5 Pile Force and Acceleration Field Measurement AnalysisA method of predicting the static bearing capacity of both full-scale and reduced-scale piles from dynamic measurements taken in the fieldduring pile driving is presented by Tomko (1968). Several other reportsassociated with Tomko's work also present this method of analysis (Gableet al., 1967; Goble et al., 1968; Scanlan and Tomko, 1969).The dynamicfield measurements consist of force and acceleration measured as a func-tion of time at the pile head during driving.A brief review of the pro-posed method will be presented.

WAVE EQUATION ANALYSISJ O ~ ~ ~ June ~ 1969 ~ 1 3 J -Boston AreaLocolion14" OD x 0.312 PipePil., 13.44 in.' Lenpth 60 ft- - -F01low.r Arm LenglhHornm*~ VUlcUl 010 Energy 32r500 ft.l.b3m, 70% Comb. Force -kl~l&.z.H.lm.1 Idrir. heodl 1300 lb Anvil -Cushion I h0rnm.r)in.0.15-Cmhion (pile1 k - I -Closure is 14" $ x 1 114" PlateComm.nlsO,,d,0'10" ~,,~0.05*EHomrner Blows PerInchFigure A.9TYPICAL RESULTS OF TH3 WAVE EQUATION ANALYSIS

The pile is as-sumed to he a rigid 'odystruck by a time varying hammerforce F(t) as shown in Figure A.lO.Applying Plewton's law to this assumedmodel, the following expression is obtained:where F(t) is hammer force varying with times, g(t) is the total soilresistance force with respect to time, a(t) is the pile acceleration withrespect to time, and M is the mass of the pile only. From this simplified--theory, the predicted ultimate strength of the pile is given bywhere F(to) is the force acting at the top of pile and i(to) is theacceleration at the top of pile both measured at time t when the velocity0of the top of the pile first reaches zero after a hmer blow.The relation-ship of Equation A.13 is based on the following assumed soil resistanceforce,-where ii is the velocity of the assumed rigid body pile and Ro is the staticresistance.According to Tomko (1968), the general feasibility of theproposed method was determined by Eiber (1958).Predicted static resistance (Equation A.13) can be readily obtainedfrom force and acceleration measurements; velocity is obtained by integrationof the acceleration record.The measuring and recording equipment has beenset up to apply this technique in the field.Correlation between neasuredand predicted pile capacity shows promise; however, there are same questionsabout the validity of the analysis of long piles as compared to short piles.

F(t) - Hammer Force in Pile Head(Force and AccelerationMeasurement at Pile Head)Pile - Assumed to be RigidMIR(t) - Total Soil ResistanceFigure A.10SIMPLIFIED PILE MODEL

The entire length of a short pile would be influenced by the generatedforce pulse, thereby approaching the rigid condition. As pile lengthincreases, the ratio of generated force pulse length to pile lengthdecreases, making it necessary to consider wave propagation in the pile.This method for determining pile capacity has the advantage of using actualmeasurements on each pile; however, a disadvantage is that predeterminationof driving capability is not possible.

APPENDIX BANALOG COMPUTER PROGRAM FOR FORCE GENERATORB.l-- Linear and Bilinear CushionThe analog computer program was designed to solve the differentialequations in nondimensional form for the force generator modeldxmlB and % = - ordz m 2in which X = -, X = x, z = t/T, T =- W1 . Details of this derivation is shown in Chapter 2. In particular,W2Equations B.2 were solved:..5 = - (X - X2) + gT 21- Figure B.l illustrates the analog computer program for thegeneral case of a force generator (pile hammer) applying a force pulseat the pile head. Integrators 1, 5, 18 and 20 and amplifiers 4, 11, 21and 9 represent the basic circuitused in the solution.All appropriategains are indicated on the amplifiers and integrators.integrator 1 are the components of X....The inputs toand inputs to amplifier 4 are the1..components of X in Equation B.2. The term X is integrated two times,2 I..through integrators 1 and 18 or 20, to produce X The term X is inte-1' 2grated two times, through integrators 5 and. 18 or 20, to produce X 2'

The loading portion of the cushion spring displacement (X - x2)1is controlled by integrator 18; whereas, the unloading of the cushionIspring displacement is controlled by integrator 20 and potentiometer 31.Potentionmeter 31 is used to control the unloading slope of the bilinearcushion, and relay 4 is used to switch the loading to the unloading portion.The diode function generator is used for the nonlinear cushion; discussionwill be reserved for the section on nonlinear cushions.For the linearand bilinear cushion, the loading slope of the spring force (amplifier 8)-and deflection (amplifier 21) is set for the same output with the diodefunction generator. The spring force (amplifier 8) and the initial con-..dition are fed into integrator 1 to produce X.Initial conditions are the ram weight term g ~ 2 (~otentiometer 10)and the ram velocity at impact VXlo0expressed in nondimensional terms= V T (potentiometer 7). These initial conditions are fed into in-0tegrator 1. Let x represent the voltage for the initial condition0X10 = V T. The desired outputs can be readily determined from this in-0put voltage as will be shown in the following disucssion.The input2 . 2term gT is usually so small compared to V T, that input of gT can0-normally be neglected.determined -The pile force F, output voltage of x7at Glifier 7, can be10 xwhere C = -Fl X 0P 7pamplifier 7, can be determined7. The peak pile force F , peak voltage output x at

where C = 2 =1lo xi,R XoThe cushion spring force F output voltage of x at amplifier 8,s' 8can be determined. . 1' *:,I11 . ..J::I'1..... IX8where CFS x0x= - . The spring displacement (x - x2),at amplifier 21, can be determined21-- (xl- x 2 ) = V o T [Cs]-X21where C = - .s x 01output voltage ofThe ram displacement (X ) and pile head displacement (X ) have1 2a voltage ouiput of xP3 at amplifier 23 and x24spectively.The displacements can be determinedx = V T LCp]l owhere C = x /x and C = x /x .R 23 o P 24 oat amplifier 24, re-(B.7)The energy transmitted to the pile can be determined by multi-plying the pile force and the velocity (servo M) and the product is shownin amplifier 12.The product is integrated (integrator 13) and theresults of voltage output (x ) can be used to deterinine the energy as13follows :1 2Energy = - m V2 l o 'It should be noted that the circuit involving the desired outputof the amplifiers as previously shown could be replaced by a curve-following x-y recorder.Any amplifier's output could be plotted versustime. Time is controlled by potentiometer 28 and amplifier 15. All

-.possible input parameters, ram velocity and ram weight effect, may be con-229sidered as well as any combination of ram mass, hammer cushion, driveheadmass and pile impedance.B.2 Nonlinear Cushion-For the nonlinear cushions, the nondimensional equations as shownfor the linear and bilinear cushions were used to solve a particular case.A particular case includes a ram and drivehead wei&t, ram velocity, andcushion spring force and deformation relationship as approximated by aseries of straight lines (Figure 2.15).The diode fbnction generator isused to obtain the desired spqing force and deformation relationship.The voltage output x21 at amplifier 21 is used for the desired deforma-tion (~~uation ~ . 6 ) and voltage output x8 at amplifier 8 is used to ob-tain the desired spring force (~~uation B.5).The diode function genera-tor controls the slopes and the break points of the loading curve.The-hyteresis potentiometer 31 controls the slope of the unloading wave.The desired spring force shape is set up prior to the solutionwith the use of an oscillatory; the diode system is cut loose from thepile system in order to set up the spring force shape efficiently.The voltage output representing the cushion spring properties(amplifier 8 and 21) is determined by arbitrarily assuming the loading i !stiffness as some function of k . The stiffness k is selected within0 0 Ithe range of upper and lower stiffnesses for a particular hammer andcushion material.For example, problem number 11 is shown in Table2.5 (Vulcan 1 with ram velocity of 12 ft/sec and pine plywood cushion).The selected k for this problem was 200 x lo3 lbs/in. This value of k0 0

can now be used to determine X = V T in terms of inches; a voltage x10 0 0represents this initial condition. All other hammer parameters (ml, m2,Vo'T) are now known and the pile characteristics (x) can be varied toobtain a series of solutionsAfter the desired cushion spring shape is set up, the analogcomputer program is initiated and the solution obtained.The conversionof analog output for the nonlinear cushion is identical with that shownfor the linear and bilinear cushions.--

APPENDIX CANALOG COMPUTER PROGRAM FUR PILE TIPThe analog computer program was designed to solve the differentialequation for the pile tip modelsolved:mK + (co + pcA)i + k x = 2 pcA Vs I (c.1)In particular, Equation C.2 (machine equation) was scaled andin which the time sealing factor is 1/1000 sec. i.e. real time = 1/1000machine time. References by Johnson (1956) and Korn and Korn (1956)indicate analog computer techniques.Figure C.l illustrates the analog computer program for the generalcase of a force pulse applied at the pile tip.Amplifier 2, integrators4, 7 and 13, and amplifiers 8, 14 and 9 represent the basic circuit usedin the solution.All appropirate gains are indicated on the amplifiers.The inputs to amplifier 2 are the components of X in Equation C.2.Theterm 2 is integrated two times, through integrators 4 and 7 or 13, to- k Sproduce the spring force term x which is fed back to amplifier 2.10The loading portion of the soil spring is controlled by integrator 7 andamplifiers 8 and 11. The initial break in the soil spring is controlled byxpotentiometer 37 and the second slope in the soil spring is controlledby potentiometer 54.The unloading portion of the soil spring is con-trolled by integrator 13 and amplifier 41.Relay 1 is used to switchfrom the loading to unloading portion.The term 2 is multiplied byC- 0(potentiometer 44) and by (servo 1) before being fed back to1000amplifier 2 t o produce Z. The mass coefficient g/W (l/m) is controlled bypotentiometer 43. Potentiometer 40 controls the magnitude of servo 1.

VITAJerry Frank Parola was born at Hillsboro, Illinois, on7 September 1939. He attended public schools in Taylor Springs andHillsboro, Illinois, and graduated from Hillsboro High School in 1957.He attended the University of Illinois at Urbana-Champaign and receivedhis Bachelor of Science Degree in Civil Engineering in 1962 and thedegree of Master of Science in Civil Engineering in 1963.lie has been on the staff of the Civil Engineering Department ,of the University of Illinois as both a teaching and a research assistant.IIe has been a research assistant in both structures and soil mechanics.During his education he worked as a private consultant and for privateconsultants in foundation engineering.He is a member of Chi Epsilon, Phi Eta Sigma, and Sigma Xi,an Associate Member of the American Society of Civil Engineers, and aMember of the International Society of Soil Mechanics an2 FoundationEngineering.