Numerical study on plate anchor stability in clay

Yu, L. et al. (2011). Géotechnique 61, No. 3, 235–246 [doi: 10.1680/geot.8.P.071]<strong>Numerical</strong> <strong>study</strong> on plate anchor stability in clayL. YU , J. LIU†, X.-J. KONG† and Y. HU‡Although the pullout capacity of plate anchors in clayhas been studied extensively, the results considering thecoupling effects of anchor inclination, clay non-homogeneityand self-weight are relatively rare. In the presentpaper, finite-element analyses are carried out to investigatethe coupling effects of these factors on the pulloutcapacity of strip plate anchors in clay. The numericalsolutions are presented in the familiar form of pulloutcapacity factors based on various anchor embedmentdepth, clay strength profile and clay self weight, and arealso compared with existing numerical and empiricalsolutions. A design procedure based on the data-fittingequations of the present finite-element solutions is alsopresented for the convenience of design engineers.KEYWORDS: anchors; bearing capacity; clays; offshore engineeringBien que la capacité d’arrachement des plaques d’ancragedans l’argile ait été l’objet d’un grand nombred’études, les résultats relatifs aux effets d’accouplementde l’inclinaison de l’ancrage, de la non homogénéité del’argile et du poids propre sont relativement rares. Dansla présente communication, on effectue une analyse auxéléments finis pour examiner les effets de l’accouplementde ces facteurs sur la capacité d’arrachement des plaquesd’ancrage dans l’argile. Les solutions numériques sontprésentées sous la forme familière de facteurs de capacitéd’arrachement basés sur différentes caractéristiques deprofondeur d’encastrement de l’ancrage, du profil derésistance de l’argile et du poids propre de l’argile, etsont comparées avec les solutions numériques et empiriquesexistantes. Une procédure d’étude, basée sur leséquations basées sur les données des solutions aux élémentsfinis actuelles, est également présentée, à l’intentiondes ingénieurs concepteurs.INTRODUCTIONThe design of many engineering structures requires thefoundation system to resist pullout forces. These types ofstructures, such as transmission towers and earth-retainingwalls, are commonly supported by soil anchors. Morerecently, plate anchors have been used widely in offshoreoil/gas exploration to provide a simple and economicalfoundation for mooring systems of offshore floating facilities(Merifield et al., 2001).Over the past four decades, considerable attention hasbeen paid to the pullout resistance of plate anchors undermonotonic loading conditions. Based on small-scale modeltests under 1g conditions, Das and co-workers (Das, 1980;Das et al., 1985a; Das et al., 1985b; Das & Puri, 1989)suggested procedures to estimate the ultimate pullout capacityof anchors in clay. However, the small-scale 1g conditioncannot take into account the effect of in situ overburdenpressure. To include the effect of overburden pressure, Rowe& Davis (1982) carried out a finite-element (FE) <strong>study</strong> ofanchors embedded in clay with both immediate breakawayand no breakaway interface between the anchor and the clayunderneath. Ultimate anchor capacity was not achieved intheir FE analyses. Instead, truncated capacities using elasticreasoning were reported. To investigate the effects of overburdenstress, anchor shape and anchor inclined pullout,Merifield and co-workers (Merifield et al., 2001; Merifield etal., 2003; Merifield et al., 2005) presented upper and lowerbound solutions of anchor pullout capacity using FE limitanalysis. The effects of anchor embedment depth, anchorinclination, clay unit weight, clay shear strength non-homogeneityand anchor shape on the pullout capacity factor havebeen studied. In addition, other researchers also investigatedthe pullout capacity of plate anchors in some particularsituations (Martin & Randolph, 2001; Wang, 2001; Thorneet al., 2004; Liu et al., 2006; Wang et al., 2006; Yu et al.,2007).DESIGN PROCEDURES IN THE PREVIOUS STUDIESA general layout of the anchor pullout capacity problemis shown in Fig. 1. The ultimate pullout capacity of a plateanchor in undrained clay is generally expressed as a functionof the undrained shear strength in the following formq u ¼ F uA ¼ s u N c (1)where A is the anchor plane area, s u is the undrained shearstrength of the clay, and the dimensionless factor N c iss u0s uManuscript received 19 May 2008; revised manuscript accepted 2February 2010. Published online ahead of print 31 August 2010.Discussion on this paper closes on 1 August 2011, for furtherdetails see p. ii. State Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology, Dalian, People’s Republic ofChina. Currently at the Centre for Offshore Foundation Systems,University of Western Australia, Crawley, Western Australia.† State Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology, Dalian, People’s Republic ofChina.‡ School of Civil and Resource Engineering, University of WesternAustralia, Crawley, Western Australia.su suh inHk uniform clay1βBAnchor embedment depth,where s s in NC clayuuhFig. 1. Model of strip plate anchors in NC clayzs uhsu su0 kzin NC clay235Delivered by ICEVirtualLibrary.com to:IP: 130.95.57.110On: Mon, 07 Mar 2011 03:15:09

236 YU, LIU, KONG AND HUusually referred to as the breakout/pullout capacity factor, ratio. However, the present <strong>study</strong> shows that the N cvalue ofwhich can be calculated froma shallowly embedded anchor is much lower than that ofanchor roughness. Most of the available publications providedthe N vertical sides. The soil domain was defined in horizontal andc value of an anchor with very large embedment vertical dimensions as 20B for the cases of H/B ¼ 10 butN c ¼ F deeply embedded anchor. Moreover, the anchor inclinationu(2) and clay non-homogeneity also have significant effects onAs uN c value of shallowly embedded anchors. The ultimateFollowing the terminology of Rowe & Davis (1982), the bearing factor of a very deep anchor is referred in theanalysis of anchor behaviour may be divided into two present paper as the maximum ultimate bearing capacitydistinct categories, namely as ‘immediate breakaway – factor, N c,max .vented’ and ‘no breakaway – attached’ respectively. In the Step 4: for a non-homogeneous clay profile, Merifield et‘immediate breakaway’ case the clay–anchor interface separatesimmediately upon pullout action, so that a gap is freeto develop behind the anchor. This represents the case whereal. (2001) presented equations with the similar form to thefollowing equations to calculate the weightless and ultimatepullout capacity factorsthere is no adhesion or suction between the clay and anchor.NIn the ‘no breakaway’ case, the opposite is assumed, withc0,k6¼0 ¼ s k N c0,k¼0 (6)the clay–anchor interface sustaining adequate tension to N c,k6¼0 ¼ s k N c,k¼0(7)ensure the anchor remains in contact with the clay at alltimes. In reality, it is likely that the true breakaway state of where s k and s k are defined in this paper as the soil nonhomogeneityfactors to the anchor capacity factor in weight-an anchor will fall somewhere between the extremities ofthe immediate breakaway and no breakaway cases. The less uniform clay and to the ultimate anchor capacity factoranchor pullout capacity of the immediate breakaway case is in uniform clay respectively. Both s k and s kare functions ofalways applied for practical design because it is more embedment ratio (H/B) and degree of clay non-homogeneity.conservative when compared with the no breakaway case. In the <strong>study</strong> by Merifield et al. (2001) kB=s u0 was taken asFor a non-homogeneous clay profile, the change in clay the degree of non-homogeneity in the range ofshear strength with depth is assumed to vary linearly as kB=s u0 ¼ 0 . 1–1 . 0. However, for a practical clay strengths u ¼ s u0 þ kz (3)profile, as shown in Fig. 2(a), the upper bound and lowerbound of the clay shear strength are about s u ¼ 2 . 0+1 . 5zwhere s u0 is the undrained shear strength at the mud line, zis the depth below the mud line and k ¼ ds u =dz is thegradient of strength increasing with depth.Overall, the pullout capacity factor of a plate anchor inand 0 . 0+1 . 3z respectively. The clay non-homogeneity ofthis practical case exceeds the <strong>study</strong> range of Merifield et al.(2001). For example, for a large anchor with 5 m anchorwidth, the clay strength at surface s u0 would be very low inthe immediate breakaway case in clay, N c , is the function of offshore engineering. Thus kB=s u0 could be very large.anchor depth, anchor inclination, clay unit weight and theclay non-homogeneity. A similar procedure was suggested inmost of the existing publications to obtain the pulloutcapacity of a plate anchor in clay. That procedure and theFurthermore, the anchor pullout capacity is determined bythe clay in the vicinity of the anchor rather than the clayclose to the surface, especially for deeply embedded anchors.Therefore, it could be more straightforward to take anotherattempts to improve it by the current FE <strong>study</strong> are described dimensionless factor, kB=s uh , to describe the clay nonhomogeneity,belowwhere s uh is the undrained shear strength ofStep 1: calculate the pullout capacity factor of the plateanchor in weightless uniform clay, N c0,k¼0 . The representativethe clay at the anchor embedment depth.Therefore, the motivations of the present paper aresolutions of N c0,k¼0 were provided by Das (1980) using(a) to investigate the effect of anchor inclination andsmall-scale model tests, by Rowe & Davis (1982) using FEembedment depth on the ultimate pullout capacityanalyses and by Merifield et al. (2001) using numerical limitfactor, Nanalyses. The FE solutions of N c0,k¼0 will be presented andc(b) to investigate the effect of clay non-homogeneity oncompared with the previous results in this paper.NStep 2: for inclined anchors in weightless clay, the pulloutc0 and N c .capacity factor can be derived fromN c0, â6¼0 ¼ N c0, â¼08 þ ðN c0, â¼908The dimensionless ratio of kB=s uh is taken as the clay nonhomogeneityfactor in the present paper. Approximate equa- 2âN c0, â¼08 Þ(4) tions are presented to fit the FE results of pullout capacity908factors for various cases. Thus a design procedure based onthe fitting equations is proposed to estimate the pulloutwhere â is the anchor inclination angle, as shown in Fig. 1.This equation was proposed by Das & Puri (1989) and wasverified by Merifield et al. (2005). The current FE resultscapacity factor of a plate anchor with given depth, inclination,clay self-weight and clay strength profile in uniformand normally consolidated (NC) clay.will show that equation (4) is valid for pullout capacityfactors of vented plate anchors in weightless soils, but notfor the cases when soil weight is included, nor for the casesof attached plate anchors.Step 3: with the assumption that the effects of clay unitweight and shear strength are independent of each other andmay be superimposed, the pullout capacity factor consideringclay unit weight can be calculated fromFINITE-ELEMENT MODELSThe present numerical analyses were conducted by theAfena FE package (Carter & Balaam, 1995). The clay wassimulated by elasto-plastic model with Tresca failure criterion.Poisson ratio í ¼ 0 . 49 and friction and dilation anglesj ¼ ł ¼ 0 were set to simulate the undrained condition.N c ¼ N c0 þ ªH < N All of the FE calculations were based on six-nodedc(5) triangular elements with a three-point Gauss integration rules uhwhere N to calculate the element stiffness matrices. The analysescis the limit/ultimate pullout capacity factor forattached anchors. The limiting value of N assumed a perfectly rigid plate anchor, progressively displacedalong the pullout direction. A full fixity was appliedc for deeplyembedded anchors is a function of the anchor geometry and at the base of the soil domain and roller conditions at itsDelivered by ICEVirtualLibrary.com to:IP: 130.95.57.110On: Mon, 07 Mar 2011 03:15:09

NUMERICAL STUDY ON PLATE ANCHOR STABILITY IN CLAY 237s u : kPas u : kPa0 5 10 15 20 100 0 020 30 4012 4s u,CAUEDepth: m34su 0 1·3z8su 2 1·5z5Approximatelinear relationshipDepth: m6 12s u,CAUCs u,DSS7Vane 13Vane 358 16Vane 429 AverageApproximatelinear relationship10 (a)20Fig. 2. Undrained shear strength of the clay from Gulf of Guinea (from NGI/COFS (2006)):(a) in situ vane tests; (b) laboratory test (CAUE, triaxial extension; CAUC, triaxial compression;DSS, simple shear)(b)10B for all the other cases. Calculations for a larger meshdomain indicated that extending the boundaries farther awayfrom the plate anchor did not influence the calculated limitresistance force. A typical model for a horizontal plateanchor embedded at H/B ¼ 1.5 is shown in Fig. 3.The mesh close to the plate anchor is refined. The meshdensity (h min ) and the displacement increment size (d i ) werechosen by the following criteria given by Hu & Randolph(1998)h minB ¼ 0 :01 (8) 0 : 8d i E kB¼ 0:17 (9)B s u s uhNodes ofplate anchorNodes ofsoil elementsNormal springFig. 4. Sketch of nodal joint elementsShear sliderShearspringA numerical test shows that with further halving h min and d igiven by equations (8) and (9) can only achieve a furtherconvergence of not more than 0 . 2%, when the effectiveanchor breadth is extended by half of the size of theadjacent element to the anchor edge.Elasto-plastic nodal joint elements, which follow Herrmann’sprinciple (Herrmann, 1978), were used to simulatethe soil–structure interaction. As shown in Fig. 4, a pair ofnodes is placed at the same initial geometric location(separated in the figure for clarity). One stands for the rigidMesh refine zoneplate anchor and the other is the corresponding node of theadjacent soil element. The node pair is linked with a normalspring and a shear spring. The stiffness of the normal springwas set up with a very large value relative to the soilstiffness to avoid the penetration of the soil node into theplate. For the vented (immediate breakaway) condition, thenormal force of every nodal joint element will be checkedafter every calculation step. If tension force occurs, thestiffness of the normal spring and the maximum shear forceof the slider are both set to zero and this is maintained forall the following calculation steps. The maximum shearstrength of the shear slider, ô max , can be taken as ô max ¼ 0for smooth anchors and ô max ¼ s u for rough anchors, wheres u is the undrained shear strength of the adjacent soil.Smooth anchors were analysed in this paper to provideconservative solutions. The effect of roughness on theanchor pullout capacity will be discussed briefly later.Fig. 3. Mesh detailsDisplacements applied onthese nodesNUMERICAL RESULTS AND DISCUSSIONDefinition of failureFigure 5 shows the responses of the anchor pulloutcapacity factor plotted against its displacement for variouscases in weightless uniform clays. For the cases withDelivered by ICEVirtualLibrary.com to:IP: 130.95.57.110On: Mon, 07 Mar 2011 03:15:09

238 YU, LIU, KONG AND HU1412 β N cH/B 10, β 90°, vented10H/B 10, β 0°, vented86H/B 6, β 90°, ventedH/B 6, β 0°, vented42H/B 1, β 90°, ventedH/B 1, β 0°, vented00 200 400 600 800 1000 1200d E / BsFig. 5. Typical N c –pullout displacement curvestvented interface, only shallowly embedded anchors (H/B < 6) can reach limit pullout resistance before d t E/Bs u ¼ 100, where d t is the total displacement of theanchor. For the cases of H/B ¼ 10 (vented), N c cannotreach the limit value until d t E/Bs u ¼ 1000, where the clayfailure mechanisms have just reached the clay surface, asshown in Fig. 6(b). For these deeply embedded anchors inweightless clays, the deformation due to plastic flowbefore failure is so great that, for practical purposes,failure would be deemed to have occurred at a load wellbelow the collapse load. That is why Rowe & Davis(1982) defined the failure load as the load that would giverise to a displacement four times that predicted by anelastic analysis. However, for most deeply embedded anchorsin offshore engineering, the surcharge due to clayweight is quite large compared with the clay shearstrength (Wilde et al., 2001). This always ensures a fullylocalised clay flow mechanism and ‘attached’ conditionbetween anchor and clay when soil weight is relativelylarge (ª’H/s u . 6 . 4 for strip footing, Song et al. (2008)).Whereas for attached cases, N c can reach the limit valuevery quickly for all the embedment ratios with any pulloutangles (only H/B ¼ 10, â ¼ 08 was plotted in Fig. 5). Inthis paper, the pullout capacity factors of weightless claysare supposed to provide N c0 values (pullout capacity factorin weightless clay) for equation (5). Since soil weightcannot be ignored in most offshore practices owing to thelarge anchor size and deep embedment, the ultimate valuesin the N c –displacement curves were selected as the breakoutfactors. Furthermore, this can ensure fully developedsoil failure mechanisms.The pullout capacity factors of strip anchors in weightlessuniform clayThe pullout capacity factors of strip anchors in uniformclay (s u ¼ 20 kPa, ª ¼ 0) are calculated first and the resultsare presented in Fig. 7. The FE results of Rowe & Davis(1982) and the numerical limit solutions of Merifield et al.(2001) are also presented for comparison. It can be seen thatfor the cases with attached bases (no breakaway), N c of bothhorizontal and vertical plate anchors agree well with theresults of Rowe & Davis (1982). The current N c of ahorizontal plate anchor reaches the limit value ofN c,max ¼ 11 .59 when H/B > 3, which is very close to thesolution of N c,max ¼ 11. 42 by Rowe & Davis (1982).For the cases with vented bases (immediate breakaway),the current N c0 values fall favourably in the range of theupper and lower bound solutions from H/B ¼ 1–10. Noteu7γ 8 2·5, 5, 7·5 and 10 10(a)7γ 8 2·5, 5, 7·5 and 10 10(b)Fig. 6. Soil collapse mechanisms as depicted by arrows of nodaldisplacement increments and contours of the octahedral shearstrain increment (ª 8 ) for H/B 10 in uniform weightless soil:(a) d t E=Bs u 100; (b) d t E=Bs u 1000that the current FE results are a little lower than the upperbound solutions when the anchor is deeply embedded. Thismight be because of the much denser mesh (h min /B , 0 . 01here but h min /B ¼ 0 . 125 in Merifield et al. (2001)) used inthe current paper.For vented anchors with small embedment ratios (H/B , 3), all results by current FE analysis, Rowe & Davis(1982) and Merifield et al. (2001) stay closely together.However, for the vented anchors with large embedmentratios (H/B . 3), the solutions of Rowe & Davis (1982)appear much lower than the other results. This might bemainly due to the truncation criterion applied in Rowe andDavis’ analysis, whereas the ultimate failure capacity wasselected in the current FE analysis. The current FE resultsagree well with the solutions by Merifield et al. (2001),since the limit analysis provides the ultimate capacities ofthe anchors by using rigid plasticity.The effect of anchor inclination on the pullout capacityfactors of vented anchors in weightless clayFigure 8 shows the pullout capacity factors of vented plateanchors with various inclinations in weightless uniformDelivered by ICEVirtualLibrary.com to:IP: 130.95.57.110On: Mon, 07 Mar 2011 03:15:09

N cN c14121086420114121086420122334455H/B(a)H/B(b)66Attached, current FE <strong>study</strong>Attached, FE (Rowe & Davis, 1982)Vented, current FE <strong>study</strong>Vented, UB (Merifield et al., 2001)Vented, LB (Merifield et al., 2001)Vented, FE (Rowe & Davis, 1982)77HB8N* c,max 11·598B9910N*c,max 11·59Fig. 7. Comparison of the bearing capacity factors for plateanchors in weightless uniform clay: (a) horizontal anchor;(b) vertical anchorN c09876543210NUMERICAL STUDY ON PLATE ANCHOR STABILITY IN CLAY 239β 90° (vertical), 67·5 ° , 45°,22·5° and 0° (horizontal)1 2 3 4 5 6 7 8 9 10H/BFig. 8. Effect of inclination on N c of vented anchors in uniformweightless claysH10clays. At all embedment ratios, the pullout capacity factorN c0 is the highest for the vertical anchor and lowest for thehorizontal anchor. The soil displacement increments atH=B ¼ 1 are shown in Fig. 9. The dashed lines, which wereformed according to the contours of the maximum shearstrain in the octahedral plane, show the approximate shearslip planes. The shear contours are not plotted for clarity. Itcan be seen that shear failure occurs only in front of theplate anchor but not behind, owing to the vented condition.For the horizontal anchor, the clay failure develops verticallyfrom both anchor edges to the surface (Fig. 9(a)). For thevertical anchor, the length of total clay shear failure planesis obviously greater than that for the horizontal anchor. Thisresults in the N c0 of the vertical anchor being higher thanthat of the horizontal anchor at H/B ¼ 1 in weightless uniformclay. The soil flow mechanisms for rough anchors arealso depicted in Fig. 9. The effect of anchor roughness willbe discussed later.A simple relationship to estimate the capacity of inclinedanchors, as shown in equation (4), has been proposed byDas & Puri (1989) and confirmed by Merifield et al.(2005). This equation is also valid for the current FEresults.The values of the pullout capacity factors of horizontaland vertical plate anchors in weightless uniform clay can beapproximated by the following equationsN c0, â¼08,k¼0 ¼ 2:483ln ðH=BÞþ 1:974R 2 ¼ 0:9999N c0, â¼908,k¼0 ¼ 2:174ln ðH=BÞþ 3:391R 2 ¼ 0:9999(10)Thus, the pullout capacity factor of a strip plate anchorembedded at any depth and any inclination in weightlessuniform clay can be calculated by equations (10) and (4).The effect of overburden pressureThe existing publications (Rowe & Davis, 1982;Merifield et al., 2001) show that the N c of a plate anchorincreases linearly with the dimensionless overburden pressure,ªH=s u , but remains not larger than the ultimatepullout capacity factor N c , as shown in equation (5). Bothof the publications gave only a limit value of N c foranchors at very deep embedment ratios. In expanding theirresults, the effects of clay self-weight on plate anchors bothin uniform and in NC clays are calculated in this paper.Only the cases in NC clay are presented in Fig. 10. Thecurrent FE results show that the assumption of superimpositionof the overburden pressure is also valid in NC clay;however, the ultimate limit pullout capacity factor N cvaries severely with anchor embedment ratios and inclinationsin NC clay.Once the clay self-weight is included in the anchor analysis,the soil flow around the anchor becomes localised at arather shallow embedment. At the same time, the soiladjacent to the anchor base is attached to the anchor withouta gap forming beneath it. This is due to the overburdenpressure generated from the soil weight and acting at theanchor base. The current FE results show that, for plateanchors at any embedment ratio with any inclination angle,the ultimate pullout capacity factors of vented anchors withvery large overburden stress ratios of ªH=s uh are almostidentical to those of attached anchors, only with a minimaldifference of less than 0.5% due to computer round-offerrors. For attached plate anchors, the clay weight (or overburdenstress) has no effect on the pullout capacity, sinceDelivered by ICEVirtualLibrary.com to:IP: 130.95.57.110On: Mon, 07 Mar 2011 03:15:09

240 YU, LIU, KONG AND HUβ 0°β 45°(a)β 90°β 0°β 45°(b)β 90°Fig. 9. Flow mechanisms of the soil around the plate anchors with vented bases in weightless uniform clay (H/B 1):(a) smooth interface; (b) rough interface12108N c 61:1N c 642H/B 1, 3, 1000 1 2 3 4 5 6 7γH/s uh(a)121084200121:1H/B 1, 3, 4, 6, 10345γH/s uh(b)Fig. 10. Effect of overburden pressure (s u 1+2z kPa): (a) â 08;(b) â 90867HB88B9H91010the clay weight does not change the soil flow mechanismaround the anchor. Thus there are two ways to obtain theultimate pullout capacity factor N c : vented anchor with alarge overburden stress ratio of ªH=s uh , or, attached anchorwith or without clay weight. Under these two scenarios, theclays are both attached to the anchor bases and the N cvalues should be identical.The ultimate pullout capacity factors (N c ) of plate anchorsat various embedment ratios in uniform and NC claysare plotted in Fig. 11. A vented base was assumed here andthe overburden stress ratio was taken as ªH=s uh ¼ 10, whichwas large enough to ensure a fully localised clay flowmechanism. It can be seen from Fig. 11(a) that all of thepullout capacity factors reach a limit value of 11 . 59 at theembedment ratio of H/B > 3. This limit value was definedas the maximum ultimate pullout capacity factor (N c,max )inthis paper. Exact solutions for deeply embedded (infinitelythin) circular plates range from 12 . 42 for a smooth interfaceto 13 . 11 for a rough interface (Martin & Randolph, 2001).The corresponding solution for a smooth strip anchor is11.42 for the FE result by Rowe & Davis (1982), 11.16 forlower bound and 11 . 86 for upper bound by Merifield et al.(2001). The N c,max ¼ 11 .59 by the current FE analysis fallswithin the range of existing solutions.It can also be seen from Fig. 11(a) that the N cvalues ofshallowly embedded anchors (H/B , 3) increase with increasingembedment ratio H/B and decrease with increasinganchor inclination angle â. These variations have similartrends and become more profound in NC clay, as shown inFig. 11(b). For vertical plate anchors in NC clay (â ¼ 908 inFig. 11(b)), the ultimate pullout capacity factor varies fromN c ¼ 4. 88 at H/B ¼ 1 to N c ¼ 11. 01 at H/B ¼ 10. Themaximum ultimate pullout capacity factor in this NC clay(s u ¼ 0 . 1+3z kPa) is also N c,max ¼ 11. 59.The values of the ultimate pullout capacity factors of plateanchors in uniform clays can be fitted by the followingexpressionsDelivered by ICEVirtualLibrary.com to:IP: 130.95.57.110On: Mon, 07 Mar 2011 03:15:09

1412108N * c642011412108N * c6422N* c,max 11·59β 0° (horizontal), 22·5°, 45°, 67·5°, 90° (vertical)34NUMERICAL STUDY ON PLATE ANCHOR STABILITY IN CLAY 2415H/B(a)6N* c,max 11·59 for β 0°N*c 11·01 for H / B 10, β 90°β 0° (horizontal), 22·5°, 45°, 67·5°, 90° (vertical)78910Note that equation (12) is different from equation (4) on theright-hand side.In both uniform and NC clays, the ultimate anchor pulloutcapacity factor N cis the highest for a horizontal plateand lowest for a vertical plate. This trend is opposite to theresults in weightless clay presented above (Fig. 8). The soilflow mechanisms of shallow plate anchors (H/B ¼ 1) inuniform clay with ªH=s uh ¼ 10 are shown in Fig. 12. Itcan be seen that the soil failure planes of a horizontalanchor (Fig. 12(a)) develop deeply into the clay and thelength of failure planes is longer than those of a verticalanchor (Fig. 12(b)). This is why the ultimate pulloutcapacity factor of a horizontal anchor is larger than that ofa vertical anchor.The soil flow mechanisms of deeply embedded anchorswith attached bases are depicted by the octahedral shearstrain increments in Fig. 13. In uniform clay, the flowmechanism of â ¼ 08 (Fig. 13(a)) is almost identical withthat of â ¼ 908 (Fig. 13(b)), except rotated by 908. Thisconfirms that the ultimate pullout capacity factors are thesame for horizontal and vertical plate anchors with H/B > 3in uniform clay, as shown in Fig. 11(a). Whereas, in NCclay, the flow mechanism of â ¼ 08 is almost the same asthat in uniform clay. However, for an anchor with â ¼ 908 inNC clay, although the flow mechanism is still localised(without reaching the soil surface), it is obviously asymmetricalto the anchor pullout direction and concentrates on theupper side of the plate anchor, since the soil is weaker atshallower depth. This is why the N cvalue for an anchorwith â ¼ 08 is higher than that for an anchor with â ¼ 908in NC clay, as shown in Fig. 11(b).0123N c, â¼08,k¼0 ¼ 2 :90ðH=BÞþ 6:02 < N c,max ¼ 11 :59R 2 ¼ 0:9999N c, â¼908,k¼0 ¼ 2 :72ðH=BÞþ 4:02 < N c,max ¼ 11 :59R 2 ¼ 0:999745H/B(b)Fig. 11. Ultimate pullout capacity factors N cin clay: (a) inuniform clay; (b) in NC clay (s u 0.1 +3z kPa)(11)The N c of an inclined plate anchor can be calculated fromN c, â ¼ N c, â¼908 þ N c, â¼08N 2908 âc, â¼908908(12)678910The effect of clay non-homogeneity on the anchor pulloutcapacity factorAs discussed in the introduction, the dimensionless ratioof kB=s uh is taken in this paper as the degree of clay nonhomogeneity,where s uh is the undrained shear strength ofclay at the anchor embedment depth, as shown in Fig. 1.When <strong>study</strong>ing the effect of clay non-homogeneity, s uh waskept constant. The increase in kB=s uh was realised by increasingthe gradient of soil strength k. The range of theclay non-homogeneity kB=s uh is from uniform clay to NCclay of s u ¼ 0 . 1+3z kPa, which covers the practical range ingeotechnical design.The effect of kB/s uh on N c0 . Starting from uniform clay, theincrease of clay non-homogeneity, kB=s uh , will enlarge thereduction of the shear strength of the clay above the anchorembedment depth and also enlarge the increment of the shearstrength of the clay below the anchor embedment depth. Inweightless clay, only the clay in front of the plate anchor failsand flows plastically. The clay failure planes develop from theanchor edges to the clay surface, as shown in Fig. 9.Therefore, it is expected that the clay non-homogeneitywould decrease the pullout capacity factor of a vented plateAnchor embedmentdepth level(a)Anchor embedmentdepth level(b)Fig. 12. Soil flow mechanisms of shallowly embedded plate anchors with attached bases (H/B 1):(a) â 08; (b) â 908Delivered by ICEVirtualLibrary.com to:IP: 130.95.57.110On: Mon, 07 Mar 2011 03:15:09

242 YU, LIU, KONG AND HU1·1γ 81·0(a)0·00050·00040·0003s k N ckN c00·90·80·70·6H/B 1, 1·5, 2, 3, 4, 6, 10HB0·50·400·20·40·60·81·0kB/s uh(a)1·11·0H/B 1, 1·5, 2, 3, 4, 6, 100·9H(b)(c)s k N ckN c00·8BFig. 13. Soil flow mechanisms of deeply embedded plate anchorswith attached bases (H/B 6, depicted by the shear strainincrement in the octahedral plane, ª 8 ): (a) â 08, kB/s uh 0 (orkB/s uh 0.17); (b) â 908, kB/s uh 0; (c) â 908, kB/s uh 0.17anchor in weightless clay. Here a non-homogeneity factor, s k ,is defined to express the effect of clay non-homogeneity onthe anchor pullout capacity factor in weightless clay0·70·600·20·4 0·6kB/s uh(b)Fig. 14. Effect of soil non-homogeneity on the bearing capacityfactors of plate anchors in weightless soil: (a) horizontalanchor; (b) vertical anchor0·81·0s k ¼ N c0,k6¼0(13)kBN c0,k¼0s k, â¼908 ¼ 1 f 90s uhfwhere N c0 is the pullout capacity factor of the plate anchor90 ¼ 0:68H 0 : 50:41 when H BB , 4 (15)in weightless clay.Figure 14 shows the relationship between s k and kB=s uh f 90 ¼ 0:153 H for horizontal and vertical plate anchors at various embedmentratios. It can be seen that for the horizontal anchor atB þ 0 :341 when H B > 4where the maximum difference between sany embedment ratios (Fig. 14(a)), s k decreases linearly withk, â¼908 by thisequation and that by the FE analysis is also less than 1increasing kB=s uh . The gradient of the linear relationship is. 4%.a function of anchor embedment ratio, H/B. The clay nonhomogeneityfactor of a horizontal plate anchor in weightlessclay, s k, â¼08 , can be approximately expressed by theuh on N c . Similar to the definition of s kThe effect of kB/sdescribed above, a non-homogeneity factor of the ultimatefollowing equationspullout capacity factor is defined askBs k, â¼08 ¼ 1 f 0ss uhk ¼ N c,k6¼0N (16)c,k¼0f 0 ¼ 1:77H 0 : 31:289 when H BB , 4 (14) where N cis the ultimate pullout capacity factor.For the cases with high overburden stress ratios, the clayf 0 ¼ 0:192 H B þ 0 :644 when H behind the vented plate anchors would flow together with theB > 4 anchor similar to the cases of attached anchors. Thus clays onboth sides of the anchor contribute to the anchor pulloutcapacity. Whether s k is less or more than 1 . 0 depends onwhere the maximum difference between the s k, â¼08 solution which part of the clay (over or under the anchor embedmentby this equation and that by the FE analysis is less than depth) contributes more to the pullout capacity. For a shallowly1.4%.embedded horizontal plate anchor, for example H/B ¼ 1 withFor a vertical anchor, the relationship between s k,â¼908 â ¼ 08, the total length of the clay failure planes below theand kB=s uh is shown in Fig. 14(b). By applying linear anchor embedment depth is longer than that above the anchorfunctions, the following equation can be used to calculate embedment depth (Fig. 12(a)). This means, for this case, thes k, â¼908 clay non-homogeneity would have a positive effect on theDelivered by ICEVirtualLibrary.com to:IP: 130.95.57.110On: Mon, 07 Mar 2011 03:15:09

******NUMERICAL STUDY ON PLATE ANCHOR STABILITY IN CLAY 243ultimate pullout capacity factor. The FE results of s kareshown in Fig. 15(a). As expected, s where the maximum error between equation predictions andk . 1. 0 for H/B ¼ 1 and the FE results is less than 2 . 1%. For vertical anchors1.5 with â ¼ 08. For the case of H/B ¼ 2, the increase ofkB=s uh has little effect on N c before kB=s uh ¼ 0 . 2, but has anobvious negative effect when kB=s uh . 0 . s k,â¼908 ¼ 1 f kB902. For horizontals uhanchors with deeper embedment (H/B > 3), the fully localised f 90clay flow mechanisms are mobilised, as shown in Fig. 13(a),¼ 0 :267 H when Hthus the effect of kB=s uh on N BB < 3(18)c of a deep horizontal anchor isfminimal (as shown in Fig. 15(a)). 90 ¼ 0 :60 when H B . 3For all vertical anchors in NC clay, kB=s uh has a negativeeffect and leads to approximately linear reduction on N c where the maximum error between equation predictions andvalue, as shown in Fig. 15(b). With increasing anchor the FE results is less than 3 . 0%.embedment ratios from H/B ¼ 1 to H/B ¼ 3, the negativegradient of the s For both horizontal and vertical anchors, the effect of claykto kB=s uh increases gradually. When non-homogeneity tends to have less effect on either N c0 oranchor embedment ratio becomes higher (H/B > 4), fully N c values with increasing anchor embedment ratio.localised clay flow mechanisms are mobilised, for exampleH/B ¼ 6 with â ¼ 908 in Fig. 13(b) and (c), so the gradientof s kto kB=s uh does not change much when the embedment The effect of anchor roughnessratio varies from H/B ¼ 4 to 10.Smooth anchor–clay interfaces were assumed in the aboveEfforts have also been made to obtain fitting equations ofs analyses to provide lower bound solutions for anchor pulloutk for horizontal anchors. Although it is difficult to achieve capacity. Some selected cases with rough interfaces wereperfect agreement with simple equations, the following equationsare proposed. For horizontal anchorseffect of anchor roughness. The percentage increases on N c0also carried out to provide an overall demonstration on thes k, â¼08 ¼ 1 þ 0 :8 0:3 H kB0:383 kB 1 : 36 and N cin both uniform and NC clays (s u ¼ 0 . 1+3z kPa)are presented in Fig. 16. The comparison of the clay flowB s uh s uhmechanisms of shallow plate anchors between smooth andwhen H rough interfaces are presented in Fig. 9.B < 2(17) For horizontal plate anchors, the weightless pullout capacityfactor, N c0 , is not noticeably affected by the anchors k, â¼08 ¼ 1 :0 when H B . 2 roughness both in uniform clay and in NC clay (as shown inFig. 16). This is because the symmetry of the soil flowmechanism prevents the development of significant shear1·15N c0s k N cksN k N ckc01·101·051·000·950·9001·11·00·90·80·7H/B 3~10H/B 6H/B 40·2H/B 10H/B 3H/B 1·5H/B 20·4 0·6kB/s uh(a)H/B 2H/B 1BH0·8H/B 1·5BHH/B 11·0N * c,rough N * c,smooth 100%: %N* c,smoothN c0,rough N c0,smooth 100%: %N c0,smooth302520151050130252015105234su 0·1 3zkPa, β 90°su 0·1 3zkPa, β 0°Uniform clay, β 90°Uniform clay, β 0°5H/B(a)67su 0·1 3zkPa, β 90°su 0·1 3zkPa, β 0°8Uniform clay, β 90°Uniform clay, β 0°9100·600·20·4kB/s uh(b)0·60·81·0012345H/B(b)678910Fig. 15. Effect of soil non-homogeneity on the limit bearingcapacity factors of plate anchors: (a) horizontal anchor (â 08);(b) vertical anchor (â 908)Fig. 16. Effect of anchor roughness on anchor capacity factors:(a) anchor in weightless clay (ª 0); (b) anchor in clay withenough weight (ªH=s uh >8)Delivered by ICEVirtualLibrary.com to:IP: 130.95.57.110On: Mon, 07 Mar 2011 03:15:09

244 YU, LIU, KONG AND HUstresses at the anchor–clay interface. The clay flow mechanismsof â ¼ 08 smooth and â ¼ 08 rough shown in Fig. 9 arealmost identical. This agrees with the findings of Rowe &Davis (1982). However, the soil failure mechanism of verticalanchors is asymmetric and shear stresses can be developedalong a rough anchor–clay interface. From the cases ofâ ¼ 908 in Fig. 9, it can be seen that the clay flow mechanismof the rough anchor is obviously more extended thanthat of the smooth anchor. From the zoom-in figures aroundthe top edge of the anchors it can be seen that, for thesmooth anchor, the clay adjacent to the front face of theanchor moves freely upwards while the nodes stand forthe rigid anchor moving horizontally. However, for the roughanchor, only the two nodes nearest to the anchor top edgemove upwards a little bit, all the other nodes move togetherwith the anchor nodes. The pullout capacity factor of avertical rough plate anchor at H/B ¼ 1 is about 8% higherthan that of a vertical smooth plate anchor in the current FEanalysis. This value is smaller than the 22% increase givenby the lower bound solutions (Merifield et al., 2001) for thesame case (H/B ¼ 1, â ¼ 908) and also smaller than the 30%increase given by Rowe & Davis (1982). However, therewere no detailed discussions on the effect of anchor roughnessby Rowe & Davis (1982) and Merifield et al. (2001).Therefore, the reason for such a large difference is not clear.The effect of anchor roughness on the ultimate pulloutcapacity factor, N c , is similar to that on the anchor pulloutcapacity factor in weightless clay, N c0 . Anchor roughnesshas very little effect on a deep anchor and a horizontalanchor.It can also be seen from Fig. 16 that the roughness effectis much larger in NC clay than in uniform clay. The increasefor a shallow vertical anchor in NC clay with s u ¼0.1+3.0z kPa can be more than 20%, for either N c0 or N c .This is because the increasing shear strength gradient increasesthe degree of asymmetry, which is displayed in Fig.13(c), where a vertical anchor is deeply embedded at H/B ¼ 6. Thus, a non-horizontal anchor would have a nonsymmetricalsoil failure mechanism, which would in turngenerate shear force on the plate. This is why a 5% increasein the ultimate pullout capacity factor was still obtained fora deeply embedded vertical anchor in NC clay.Suggested procedure for estimating the anchor pulloutcapacityThe pullout capacity factor of a strip plate anchor inuniform or NC clay, N c , can be calculated by the followingprocedure, and the flow chart for design is summarised inFig. 17.(a) Determine representative values of the soil parameterss uh (s uh ¼ s u0 þ kH in NC clay), ª and kB=s uh , theanchor size B , inclination angle â and embedmentdepth H.(b) Calculate the weightless pullout capacity factor ofhorizontal and vertical anchors in uniform clay,N c0, â¼08,k¼0 and N c0, â¼908,k¼0 using equation (10).(c) Calculate the clay non-homogeneity factors of theweightless pullout capacity factor, s k , for horizontaland vertical anchors by equations (14) and (15). Thus,the pullout capacity factors of horizontal and verticalanchors in weightless NC clay, N c0, â¼08,k6¼0 andN c0, â¼908,k6¼0 , can be obtained by equation (6).(d) Calculate the pullout capacity factor of an inclinedplate anchor in weightless NC clay, N c0 , using equation(4).(e) Obtain the ultimate pullout capacity factor of horizontaland vertical anchors, N c, â¼08,k¼0 and N c, â¼908,k¼0 , fromequation (11).( f ) Calculate the non-homogeneity factors of the ultimatepullout capacity factors of horizontal and verticalanchors, s k , using equations (17) and (18). Thus theultimate pullout capacity factors of horizontal andvertical plate anchors in NC clay, N c, â¼08,k6¼0andN c, â¼908,k6¼0, can be obtained by equation (7).(g) Predict the ultimate pullout capacity factor of aninclined plate anchor, N c, using equation (12).(h) Superpose the overburden pressure; the final pulloutcapacity factor N c can be calculated from equation (5).CONCLUSIONSAn FE <strong>study</strong> into the pullout capacity of strip plateanchors in uniform and NC clays has been presented. Considerationhas been given to the coupling effects of anchorembedment ratios, anchor inclination, clay self-weight andclay non-homogeneity. The results have been presented aspullout capacity factors in both graphical and numericalform to facilitate their use in solving practical designproblems. A systematic design procedure has also beenproposed.The following conclusions can be drawn from the resultspresented in this paper.(a) The anchor inclination has two distinct effects on theanchor pullout capacity factor. In weightless clay,N c0, â¼908 of the vertical vented anchor is the highestand N c0, â¼08 of the horizontal vented anchor is thelowest at a given embedment ratio. On the other hand,when ªH=s uh is large enough, or with attachedanchor–clay interfaces, N c, â¼08of the horizontal anchoris the highest and N c, â¼908of the vertical anchor is thelowest.(b) The assumption of superimposition of the overburdenpressure is valid for vented plate anchors in bothuniform and NC clays. The ultimate pullout capacityfactor, N c, decreases with increasing anchor inclinationangle, â, and increases with increasing anchor embedmentratio, H/B, until the maximum pullout capacityfactor, N c,max , is reached. The effect of anchorinclination on N cin NC clay is greater than that inuniform clay.(c) The pullout capacity factors of attached anchors are thesame as those of vented anchors with large soiloverburden stress ratio, ªH=s uh , which is the ultimatepullout capacity factor, N c .(d) The degree of soil non-homogeneity, kB=s uh , has anapproximately linear negative effect on anchor pulloutcapacity in weightless clay. The reduction was up to50% for horizontal anchors and 30% for verticalanchors.(e) For horizontal anchors, the increase in the degree ofclay non-homogeneity, kB=s uh , will increase the valueof the ultimate pullout capacity factor, N c, for shallowanchors (H/B < 1 . 5), but decrease N c value for deeperanchors (H/B > 2). The change in N cvalue due to claynon-homogeneity for horizontal anchors is less than15%. For vertical anchors, the increase in the degree ofclay non-homogeneity, kB=s uh , decreases N c value foranchors at any embedment ratios. The reduction in N cvalue is up to 30% for shallow anchors. The reductionbecomes less with increasing anchor embedment ratio.( f ) The anchor roughness has an obvious positive effect onanchor pullout capacity where an asymmetrical soilflow mechanism is formed. Because of this, the anchorroughness has more effect on a vertical anchor than onDelivered by ICEVirtualLibrary.com to:IP: 130.95.57.110On: Mon, 07 Mar 2011 03:15:09

NUMERICAL STUDY ON PLATE ANCHOR STABILITY IN CLAY 245Input design parameters ( s uh s u0 kH , γ, H , B , β, kB/s uh )Nc0, β0°, k 0 2·483 ln( H/B ) 1·974N c0, β90°, k 0 2·174 ln( H/B ) 3·391Eq. (10)N * c, β0°, k 0 2·90( H/B ) 6·02 N * c,max 11·59N * c, β90°, k 0 2·72( H/B ) 4·02 N * c,max 11·59Eq. (11)sk, β 0° 1 f0f 0 1·77⎛H⎞⎜⎝⎟B ⎠0.3−Hf 0 0·192 0·644BkBEq. (14)skBuh sk, β 90° 1 f901.289whenwhenHBHB 4 4f 90 0·68⎛H⎞⎜⎝⎟B ⎠0.5s uh−0.41Hf 90 0·153 0·341BEq. (15)whenwhenHBHB 4 4s* k, β 0° 1 s* k, β 0° 1·0s*k, β 90° 1 f * 90⎛ H⎞kB⎜0.8 −0.3⎟ ⋅⎝ B⎠ suhkBs uhf * 90 0·267f * 90 0·601.36⎛ kB ⎞ 0·383 ⎜⎝s⎟ when⎠HBwhenwhenuhHBHB 3 3whenHBHB 2 2Eq. (18)k k ·N sc0, β0°, 0 , β0° N c0, β 0°, k 0Nc0, β90°, k0 sk, β9 0 ° · N c0, β 90°, k 0Eq. (6)N* s*c, β0°, k0 k, β0° · N* s*·N* c, β0°, 0k kk c, β90°, 0 , β90°N* c, β90°, k 0Nc0 N c0, β 0° ( Nc0, β90° Nc0, β 0° ) ·2⎛ β ⎞⎛90°− β ⎞⎜⎝⎟Eq. (4)N*c N* c, β 90° ) ⎜ ⎟90 ⎠ N*c, β 90° ( N* c, β 0° ·⎝ 90° ⎠°2Eq. (12)Final result,Nc N*Eq. (5) Nc0 γH s uhc Fig. 17. Design flow chartEq. (17)Eq. (7)Delivered by ICEVirtualLibrary.com to:IP: 130.95.57.110On: Mon, 07 Mar 2011 03:15:09

246 YU, LIU, KONG AND HUa horizontal anchor. At the same time, it has moreeffect on the anchors in NC clay than those in uniformclay.ACKNOWLEDGEMENTThe research presented here is supported by the NationalNatural Science Foundation of China (50978045, 90815024).This support is gratefully acknowledged.NOTATIONA plane area of the plate anchord i displacement increment applied to the anchord t total displacement applied to the plate anchorF u pullout force on the plate anchorH embedment depth of a plate anchor (as the anchorcentre)k soil strength gradientkB=s uh degree of soil non-homogeneityN c anchor pullout capacity factorN c0 anchor pullout capacity factor in weightless clay withvented baseN cultimate anchor pullout capacity factorN c,maxmaximum anchor pullout capacity factor with deepembedmentq u average anchor pullout pressures k non-homogeneity factor for anchor in weightless soilwith vented bases k non-homogeneity factor for anchor ultimate pulloutcapacitys u clay undrained shear strengths uh clay undrained shear strength at the anchor embedmentdepths u0 undrained shear strength at the clay surfacez soil depthâ anchor inclination angleª unit weight of the clayªH=s uh overburden stress ratioª 8 shear strain increment in the octahedral planeREFERENCESCarter, J. P. & Balaam, N. P. (1995). AFENA users manual. Sydney,Australia: Geotechnical Research Center, University of Sydney.Das, B. M. (1980). A procedure for estimation of ultimate capacityof foundations in clay. Soils Found. 20, No. 1, 77–82.Das, B. M., Moreno, R. & Dallo, K. F. (1985a). Ultimate pulloutcapacity of shallow vertical anchors in clay. Soils Found. 25,No. 2, 148–152.Das, B. M., Tarquin, A. J. & Moreno, R. (1985b). Model tests forpullout resistance of vertical anchors in clay. Civ. Engng PracticingDes. Engrs 4, No. 2, 191–209.Das, B. M. & Puri, V. K. (1989). Holding capacity of inclinedsquare plate anchors in clay. Soils Found. 29, No. 3, 138–144.Herrmann, L. R. (1978). Finite element analysis of contact problems.J. Engng Mech., ASCE 104, No. 5, 1043–1057.Hu, Y. & Randolph, M. F. (1998). H-adaptive FE analysis of elastoplasticnon-homogeneous soil with large deformation. Comput.Geotech. 23, No. 1–2, 61–83.Liu, J., Wu, L. & Hu, Y. (2006). Pullout capacity of circular plateanchors in NC clay. J. Dalian Univ. Technol. 46, No. 5, 712–719.Martin, C. M. & Randolph, M. F. (2001). Application of the lowerbound and the upper bound theorems of plasticity to collapse ofcircular foundations. Proc. 10th Int. Conf. Comp. Methods Adv.Geol., Tucson 2, 1417–1428.Merifield, R. S., Sloan, S. W. & Yu, H. S. (2001). Stability of plateanchors in undrained clay. Géotechnique 51, No. 2, 141–153,doi: 10.1680/geot.2001.51.2.141.Merifield, R. S., Lyamin, A. V., Sloan, S. W. & Yu, H. S. (2003).Three-dimensional lower bound solutions for stability of plateanchors in clay. J. Geotech. Geoenviron. Engng, ASCE 129, No.3, 243–253.Merifield, R. S., Lyamin, A. V. & Sloan, S. W. (2005). Stability ofinclined strip anchors in purely cohesive soil. J. Geotech.Geoenviron. Engng, ASCE 131, No. 6, 792–799.NGI/COFS (2006). Shear strength parameters determined by in situtests for deep water soft soils, NGI Report 20041618. NorwegianGeotechnical Institute/Centre for Offshore FoundationSystems.Rowe, R. K. & Davis, E. H. (1982). The behaviour of anchor platesin clay. Géotechnique 32, No. 1, 9–23, doi: 10.1680/geot.1982.32.1.9.Song, Z., Hu, Y. & Randolph, M. F. (2008). <strong>Numerical</strong> simulationof vertical pullout of plate anchors in clay. J. Geotech. Geoenviron.Engng, ASCE 134, No. 6, 866–875.Thorne, C. P., Wang, C. X. & Carter, J. P. (2004). Pullout capacityof rapidly loaded strip anchors in uniform strength clay. Géotechnique54, No. 8, 507–517, doi: 10.1680/geot.2004.54.8.507.Wang, C. X. (2001). Large deformation and non-tension analysis ofselected problems in soil mechanics. PhD thesis, University ofSydney, Australia.Wang, D., Hu, Y. & Jin, X. (2006). Two-dimensional large deformationfinite element analysis for the pulling-up of plate anchor.Chin. Ocean Engng 20, No. 2, 269–278.Wilde, B., Treu, H. & Fulton, T. (2001). Field testing of suctionembedded plate anchors. Proc. 11th Int. Offshore Polar EngngConf., Stavanger 2, 544–551.Yu, L., Liu, J. & Kong, X.-J. (2007). Stability of plate anchors inNC clay. Rock Soil Mech. 28, No. 7, 1427–1434.Delivered by ICEVirtualLibrary.com to:IP: 130.95.57.110On: Mon, 07 Mar 2011 03:15:09