Research Article Modeling Laterally Loaded Single Piles ...

Hindawi Publishing CorporationJournal of EngineeringVolume 2013 Article ID 243179 7 pageshttpdxdoiorg1011552013243179

Research ArticleModeling Laterally Loaded Single Piles Accounting forNonlinear Soil-Pile Interactions

MaryamMardfekri1 Paolo Gardoni2 and Jose M Roesset1

1 Zachry Department of Civil Engineering Texas AampM University College StationTX 77843-3136 USA

2Department of Civil and Environmental Engineering University of Illinois at Urbana-ChampaignIL 61801 USA

Correspondence should be addressed to Paolo Gardoni gardoniillinoisedu

Received 13 August 2012 Revised 4 December 2012 Accepted 18 December 2012

Academic Editor Sadhan C Jana

Copyright copy 2013 MaryamMardfekri et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

e nonlinear behavior of a laterally loaded monopile foundation is studied using the nite element method (FEM) to accountfor soil-pile interactions ree-dimensional (3D) nite element modeling is a convenient and reliable approach to account for thecontinuity of the soil mass and the nonlinearity of the soil-pile interactions Existing simple methods for predicting the deectionof laterally loaded single piles in sand and clay (eg beam on elastic foundation p-y method and SALLOP) are assessed usinglinear and nonlinear nite element analyses e results indicate that for the specic case considered here the p-ymethod providesa reasonable accuracy in spite of its simplicity in predicting the lateral deection of single piles A simplied linear nite element(FE) analysis of piles oen used in the literature is also investigated and the inuence of accounting for the pile diameter in thesimplied linear FEmodel is evaluated It is shown that modeling the pile as a line with beam-column elements results in a reducedcontribution of the surrounding soil to the lateral stiffness of the pile and an increase of up to 200 in the predicted maximumlateral displacement of the pile head

1 Introduction

Pile foundations are widely used to support laterally loadedstructures especially offshore e extensive growth of windfarms around the world has raised new concerns about theaccuracy of the analysis and design methods for laterally-loaded large-diameter monopiles (the most popular founda-tion structure for offshore wind turbines)

Common methods for the analysis of laterally loadedsingle piles can be generally classied into two categories(1) Winkler (elastic) foundation models and (2) continuousmodels accounting for the coupling of forces and displace-ments in the soil along the pile In each category the analysismay be static (monotonic or cyclic loading) or dynamic Alsothe behavior of the soil pile and soil-pile interaction may beconsidered as linear or nonlinear

Winkler foundation models are popular because of theirsimplicity and reasonable accuracyWhen the elastic stiffnessof the foundation can be considered constant with depth

one can even obtain simple closed form solutions for thepile head stiffness and exibility [1] e main differencebetween the different Winkler foundation models availableis in the selection of the foundation stiffness coefficients Fordynamic problemsNovak [2] has proposed the use ofWinklerfoundation coefficients based on Baranovrsquos equations [3]for in plane and out of plane vibrations of a disk ecorresponding horizontal 119896119896119909119909 and rotational 119896119896120593120593 springs perunit of length along the pile are functions of a dimensionlessfrequency 1198861198860 = Ω119877119877119877119877119877119904119904 where Ω = the frequency inradianssecond 119877119877 = the radius of the pile and 119877119877119904119904 = the shearwave velocity of the soil Unfortunately the horizontal termtends to zero at a zero frequency representing the static caseAs a result it is common to use the values corresponding to adimensionless frequency of 03 for smaller frequencies [1] Inthat case 119896119896119909119909 = 4119866119866 and 119896119896120593120593 = 266661198661198661198771198772 where119866119866 = the shearmodulus of the soil

For nonlinear analyses the p-y method is the mostcommonly used in this category It employs an elastic beam

2 Journal of Engineering

column member to model the pile and nonlinear horizontalsprings to represent the soil reactionse p-y curves describethe nonlinear behavior of the soil springs ey were devel-oped rst by atlock [4] for so clays under the water tableReese andWelch [5] and Reese et al [6] developed p-y curvesfor hard clays subjected to monotonic and cyclic loadingabove and under the water table respectively Analyzingthe results of the full scale tests conducted by Reese et al[6] Dewaikar et al [7] presented a modied approach toconstruct p-y curves in stiff clay In another study Kim andJeong [8] developed a framework based on 3D nite elementanalysis for determining a p-y curvee p-y curves for sandswere also developed by Reese et al [9] for monotonic andcyclic loading Briaud et al [10] developed an alternativemethod to obtain the p-y curves directly from pressuremetertests e method was reasonably accurate but complicatedand time consuming so Briaud [11] developed a simplerapproach called ldquosimple approach for lateral loads on pilesrdquoor SALLOP using the pressuremeter limit pressure and thepressuremeter modulus

A number of recent studies have been conducted topredict the behavior of laterally loaded piles in different soilconditions Sanjaya Kumar et al [12] used ABAQUS andthe p-y method to study the behavior of laterally loaded pilefoundations in high marine clay with high potential to swellupon wetting and shrink upon drying Suleiman et al [13]conducted a test to measure the soil-pile interaction pressurefor small diameter piles in loose sand that the results can beused in developing the soil force-displacement relationship(ie the soil reaction or the p-y curve) An equivalent modelfor a laterally loaded linear pile-soil system was presented byChioui and Chenu [14] using articial lateral springs

Continuous modeling of the pile and the surroundingsoil are mostly done using nite element or boundary ele-ment models Both methods can provide rigorous solutionsaccounting for soil-pile interaction under static and dynamicloading For the linear case an accurate solutionwas proposedby Blaney et al [15] using the consistent boundary matrixdeveloped by Kausel [16] to reproduce the soil cavity occu-pied by the pile and adding then the pile enforcing compat-ibility of horizontal and vertical displacements between pileand soil along the pile An extensive number of studies werecarried out by Sanchez Salinero [1] comparing the results ofthis approach to those provided by a variety of othermethodsand proposing approximate formulas for the pile head stiff-ness is approach is only valid however in the linear elasticrange e nite element method is particularly convenientwhen desiring to account for nonlinear effects including thenonlinear behavior of the soil and of the soil-pile interface

A 3D nonlinear nite element analysis of a pile founda-tion in which both the soil and the pile are modeled with 3Dnite elements can be quite expensive and time consumingparticularly when incorporating nonlinear behavior As aresult some investigators have used nite elementmodels thatrepresent the pile by an elastic beam columnmember withouttransverse dimensions (only the centroidal axis) and only thesoil with 3D solid elements is method takes into accountthe continuity of the soil mass and is easy to use for linearstatic and dynamic analysis However the most important

limitation of this approach is that it does not take into accountthe dimension of the pile section

e work presented in this paper is part of a broaderresearch effort to assess the reliability of foundations for off-shore wind turbinesese are normally single large diameterhollow piles However many different methods have beenused and investigated by previous researchers for analysis oflaterally loaded piles most of previous studies are focusedon onshore pile foundations with diameters relatively smallerthan those in the offshore industry e rst objective of thispaper is to compare the results of different methods of analy-sis of laterally loaded piles and illustrate the possible variabil-ity of the results A second objective is to investigate how theconsideration of pile diameter affects the accuracy of simpli-ed models As a rst step the models used for the analysesof these foundations are validateden the model selected isimplemented in the computer program ABAQUS using 3Dbrick elements to discretize the soil around the pile and shellelements to model the hollow pile e results obtained withthis model for linear and nonlinear analyses are compared tothose provided by a variety of othermethods used in practice

In the following we rst examine four different modelsused for linear analysis of single pile foundations and evaluatethe inuence of accounting for the pile diameter in the sim-plied linear FE analyses In the next section we improve the3D nite element model by accounting for the nonlinearityof the soil and soil-pile interaction Two common simpliednonlinear models are then assessed using this model formono-piles in sand and clay

2 Linear Analyses

Analyses considering linear soil behavior and perfect bond-ing between the pile and the surrounding soil are conductedrst e pile selected for the study is hollow with a diameterof 4m and the properties listed in Table 1 Four differentmodels are studied

(1) e rst model is a 3D nite element model of boththe soil around the cavity occupied by the pile (solidelements) and for the pile with shell elements forhollow piles and brick elements for solid piles (shownin Figure 1)

(2) e second simpler model reproduces the soil withsolid elements lling the space without any cavitye pile is represented by the centroidal axis of a 1Dbeam column coinciding with the central axis of thesoil model enforcing only compatibility of horizontaldisplacements between the nodes of the pile and thoseof the soil along the axis

(3) e third model is the one proposed by Blaney et al[15] with the consistent boundary matrix with theradius of the cavity representing the soil and enforcingcompatibility of both horizontal and vertical displace-ments between the soil and the pile along its sides

(4) e fourth model is a beam on an elastic (Winkler)foundation with horizontal and rotational springsalong the side of the pile e constants selected forthe foundation are 119896119896119909119909 = 4119866119866 and 119896119896120593120593 = 266661198661198661198661198662

Journal of Engineering 3

T 1 Properties of the pile

Parameter Symbol ValuePenetration depth (m) 119871119871 210Diameter (m) 119863119863 400Wall thickness (m) 119905119905 005Modulus of elasticity (kPa) 119864119864119901119901 20119864119864119864Unit weight (kNm3) 120574120574119901119901 8700Poisson ratio 120584120584119901119901 030

F 1 3D nite element model of the pile foundation

e pile is subjected at the head to a vertical load of5000 kN a horizontal load of 2503 kN and a momentof 84983 kNm ese are values obtained considering theextreme forces on an offshore wind turbine For the linearanalyses the soil is assumed to have a Youngrsquos modulus 119864119864119904119904 =50 000 kPa a Poissonrsquos ratio 120584120584119904119904 = 03 and a unit weight120574120574119904119904 = 20 kNm3

e predicted deections at the pile head by the fourmodels are 209mm for the 3D FE pile model 683mm forthe 1D FE pile model 205mm for the consistent boundarymatrix and 243mm for the Winkler foundation e defor-mation of the soil with the 3D nite element model is shownin Figure 2 while Figure 3 shows the corresponding defor-mations with the 1D model of the pile e results obtainedusing the 3D nite element model are in good agreementwith the approach that employs consistent boundary matrix(less than 2 off)e agreement with the results of theWin-kler foundation is not quite as good but still acceptable (about20 off) e model without the cavity and with the pile as a1D linear element yields deections that are 200 too large

To understand better the reasons for this large discrep-ancy it was decided to conduct studies for other pile sizesClearly the results of the 1D model are only a function of thesoil properties and of the product EI of the Youngrsquos modulusof the pile by the moment of inertia of the cross sectionbut not explicitly of the pile diameter For a hollow pile themoment of inertia is not uniquely related to the diameter andtherefore in this case the actual size of the cavity has no effect

F 2 Deformation of the soil with the 3D model of the pile


on the results of the model if the moment of inertia is keptconstantiswould also be the case for aWinkler foundationmodel with only horizontal springs

Table 2 shows the results of the four models for hollowpiles with the same EI value of 2421E + 8 kN-m2 butdiameters of 1 2 and 4m e agreement between the 3Dnite element model and the boundary matrix method isgood in all three cases (about 3 off in average) As expectedthe results for the 1D pile model do not change e resultsfor the Winkler model vary slightly because of the rotationalsprings but the variation is still very small and the accuracydeteriorates as the diameter of the pile decreases To see whenthe results of the 1Dmodel would become similar to those ofthe more accurate solutions the boundary matrix model wasrun for a larger number of diameters going down to 002mFigure 4 shows the variation of the head displacement withthe pile diameter in semi-log scale e deection predictedby the boundary matrix model for a pile with a diameter of002m is 685mmnow in good agreementwith the predictionof the 1Dmodel It is interesting to observe that the variation


T 2 Variation of pile head displacement versus pile diameter in different linear analysis methods with constant EI for the pile

Pile diameter (m) Pile head deection (mm)3D pile FEM 1D pile FEM Consistent boundary matrix Winkler foundation

100 325 683 (110) 340 (5) 252 (23)200 276 683 (148) 275 (1) 250 (10)400 209 683 (227) 205 (2) 243 (17)

0

10

20

30

40

50

60

70

80

02 2

Pil

e h

ead

defl

ecti

on

(m

m)

002

Pile diameter (m)

Consistent boundary matrix

Winkler foundation3D pile FEM

1D pile FEM

F 4 Variation of pile head displacement versus pile diameterin linear analyses with constant EI for the pile

of the displacement for this hollow pile is approximatelyinversely proportional to the radius to the power 026 Itis noteworthy that while clearly the piles with very smalldiameter and large value of EI are unrealistic it is desiredto cover a wide range of values of the diameter to see moreclearly the trend It must also be remembered that whenusing a 1D beam-column to represent the pile with a niteelement soil mesh that does not include a cylindrical cavityone is assuming a zero diameter that is not just unrealistic butphysically impossible

3 Nonlinear Analyses

reedifferentmodels are used to conduct nonlinear analysesas follows

(1) e 3D nite element model of the previous runsIn this case however the soil and the soil-pile interface arenonlinear e nite element model using ABAQUS has thecapability of taking into account the initial state of stressesin the soil mass e initial conditions of stress are appliedbefore the pile is installed and as a rst step the effective bodyforces are calculated to account for geostatic equilibriumeextreme static loads due to the performance of the turbine andwave and wind loading are applied then

A 22m long pile with a diameter of 4m is modeledas a steel pipe using 4-node quadrilateral shell elementswith reduced integration A 1m long segment of the pile isconsidered to be above ground level to avoid the soil goingover the pile Linear elastic behavior is assumed for the pile

T 3 Elastic-plastic properties of soil

Parameter Symbol ValueSand Clay

Modulus of elasticity (kPa) 119864119864119904119904 50119864119864119864 1198645119864119864119864Unit weight (kNm3) 120574120574119904119904 2000 2000Poisson ratio 120584120584119904119904 030 030Angle of internal friction (∘) 120601120601 euro400 mdashUndrained shear strength (kPa) 119878119878119906119906 mdash 1500

For an actual soil prole it would be necessary to selectthe most appropriate nonlinear constitutive model and todetermine the values of the required parameters dening themodel from laboratory tests For the purposes of this workand considering two hypothetical soils a sand and a clay avery simple Mohr Coulomb model as implemented in theprogram ABAQUS is used with the properties presented inTable 3e nite elementmesh of the 1198640mtimes10mtimes1198641m soilmass is generated using isoparametric brick elements withreduced integration for the soil

e nonlinear behavior of the soil-pile contact ismodeledusing ldquocontact pairrdquo in ABAQUS Tangential movementbetween the two parts pile and surrounding soil is allowedwith a friction coefficient of 067 In the radial direction aldquono separationrdquo contact behavior is assumed e pile outersurface is chosen as the ldquomaster surfacerdquo and the surface ofthe soil mass which is in contact with the pile is considered tobe the ldquoslave surfacerdquo e ldquosmall slidingrdquo tracking approachis employed for the contact of the two bodies assumingthat even if the two bodies undergo large motions there isrelatively little sliding of one surface along the other Anelastic-plastic Coulomb model is also used to describe thenonlinear behavior of the soil-pile contact Figure 5 shows thedeformation of soil with 3D nonlinear nite element modelof pile foundation

(2) A model using the p-y curves is implemented specif-ically for this work As indicated in the introduction sectionthe p-y curves were originally proposed by Matlock [4] forso clays under the water table and models for hard claysand sands were shortly aer introduced by Reese et al [6]In this work the sand and the hard clay model are usede clay model requires the specication of a parameter 12057612057650that has to be determined from experiments Since the soilconsidered was not a real one on which experiments couldbe performed a value of 0005 as recommended by Reeseet al [6] is used In the linear elastic range for very smalldisplacements the initial stiffness of the springs representingthe p-y curves normally varies with depth In this case


F 5 Deformed mesh of the pile foundation in 3D nonlinearanalysis

however to be consistent with the nite element model theinitial stiffness value is considered to be constant with thedepth and equal to 4119866119866 as for the linear analyses with theWinkler foundation Since the p-y curves are in fact a form ofthe Winkler foundation model with only horizontal springsthe solution in the elastic range would be only a functionof the EI of the pile and independent of the diameter fora given moment of inertia e nonlinear variation of thestiffness is on the other hand affected by the pile diameterIt should also be noticed that with the p-y method thereare nonlinear springs attached to the side of the pile butnot at the bottom One must decide therefore whether thepile tip is free hinged or xed For long piles the differencebetween these three cases when considering the pile headdisplacement is negligible However in the present case theparameter 1198971198970 = (4119864119864119901119901119868119868119901119901119870119870119870

14 with119864119864119901119901 =modulus of elasticityfor the pile (kPa) 119868119868119901119901 = moment of inertia for the pile (m4)and 119870119870 = soil-spring constant (kPa) which is the ratio of thesoil resistance 119875119875 (kNm) at a depth 119911119911 to the horizontal piledisplacement 119910119910 (m) at the same depth is of the order of 10mso the displacements for a hinged tipmay be 25 smaller thanfor a free tip For a linear analysis the assumption of a hingedtip where the displacement of the pile tip is assumed to beconstrained and equal to that of the soil mass at the bottomwhile the rotation is allowed freely may be more realistic butfor the nonlinear one it is considered that the free end whereboth the tip displacement and rotation are allowed would bemore appropriate For the sake of comparison and to see theeffects of such assumption the results are presented for bothboundary conditions

(3) Amodel implementing the simple approach for lateralloads on piles (SALLOP) proposed by Briaud [11] It isa semitheoretical or semiempirical method in which theframework is theoretical but the factors in the theoreticalequations are adjusted by comparison to some full-scale loadtests SALLOP uses two different theoretical solutions forinnitely long (exible) piles and for short rigid piles in a

Winkler uniform soil Dening a transfer length 1198971198970 that is thetypical parameter associated with the solution of a beam onelastic foundation as done earlier the pile head displacement1199101199100 for long exible piles (119871119871 119871 1198711198971198970) under a combined loadingof a horizontal force and a moment at its head is [17]

1199101199100 =211986711986701198971198970119870119870

+21198721198720

11989711989720119870119870 (1)

where 1198671198670 = horizontal force applied at the pile head (kN)1198721198720 = moment applied at the pile head (kNm) and thesoil-spring constant 119870119870 is dened empirically by optimizingthe comparison between the predicted deection and themeasured deections

Similarly the pile head displacement for short rigid piles(119871119871 119871 1198971198970) is Should we change

1199101199100 =2 1007649100764921198671198670119871119871 + 119871119872119872010076651007665

1198701198701198711198712 (2)

For the SALLOP calculations a linear interpolationbetween two values will be used if the pile length is between 1198971198970and 1198711198971198970More details on SALLOPare presented at Briaud [17]

For the pile with a diameter of 4m the 3D nite elementmodel predicts a displacement of 40mm in sand and 251mmin clay e corresponding results with the p-y curves are382mmand 375mmwith a free tip (285mmwith a hinge atthe bottom) with the SALLOP method 360 and 45mmethreemethods provide results in good agreement for the sandbut there are larger differences for the clay particularly for theSALLOP approach and with a free tip for the p-y curves

e effect of the pile diameter with a constant value ofthe EI of the pile was again investigated for the nonlinearcase Table 4 and Figure 6 present the results of the threemethods for diameters of 1 2 and 4m Again since theSALLOP method is based purely on a Winkler foundationwith horizontal springs the results are independent of thediameter for a xed EI e p-y curves give results that varywith the diameter but less signicantly than the 3D solutionIt is interesting to notice that for the sand the best agreementis obtained for a diameter of 4m For the 1m diameter theprediction of the SALLOP method would be about 40 ofthe FEM result with the p-y curve it would be about 62For the clay on the other hand the best agreement betweenthe threemethods is obtained for the diameter of 1m (almostexactly the same results) whereas the discrepancy increasesas the diameter increases e prediction with the SALLOPmethod is about 80 too large whereas that with the p-y curves assuming a free tip is about 50 off for the 4mdiameter

It seems also that given the lack of a spring acting on thebottom face of the pile in the p-ymodel for the larger diame-ter pile the assumption of a hinged tipmight bemore realisticwhereas for the smaller diameters it is better to consider afree tip Considering the fact that the characteristics of thesoils are not actually determined from laboratory tests butsome of the parameters are chosen purely as logical valuesand that a very simple nonlinear soil model was used ndingan exact agreement between the three methods would havebeen surprising e fact that they provide results with the


T 4 Variation of pile head displacement versus pile diameter in different nonlinear analysis methods with constant EI for the pile

Pile diameter (m)

Pile deection at the ground level (mm)Sand Clay

3D FEM p-y SALLOP 3D FEM p-y SALLOPFree tip Hinged tip

100 910 570 (35) 360 (60) 455 453 (1) 312 (32) 450 (1)200 606 435 (29) 360 (41) 339 405 (20) 300 (12) 450 (33)400 400 382 (5) 360 (10) 251 375 (50) 285 (14) 450 (80)

1

10

100

0 1 2 3 4 5

FEM

SALLOP

Pil

e h

ead

defl

ecti

on

(m

m)

Pile diameter (m)

(a)

1

10

100

0 1 2 3 4 5P

ile

hea

d d

eflec

tio

n (

mm

)

Pile diameter (m)

FEM

SALLOP

(b)

F 6 Variation of pile head displacement versus pile diameter in nonlinear analyses for (a) sand and (b) clay with constant EI for thepile

same order of magnitude for the range of pile diametersconsidered is encouraging On the other hand it is importantto notice the effect of the pile diameter on the foundationstiffness beyond the value of the EI something that wouldoccur irrespective of the constitutive model used Obtaininga very good agreement for a given pile diameter with amore rened selection of the nonlinear soil model and of thesoil parameters will not guarantee similar accuracy for othervalues of the diameter and the same soil

4 Summary and Conclusions

is study for the rst time provides a comprehensivecomparison of common techniques for analysis of laterallyloaded single piles in different soil types and for a wide rangeof pile dimensionse effect of the pile diameter on its lateralbehavior in the linear elastic range was studied using variousanalysis procedures assuming a constant pile stiffness (EI)and different pile diameters for hollow piles a 3D ABAQUSnite element model a model with the soil reproduced with3D elements but the pile represented by a line a modelusing a consistent boundarymatrix and aWinkler foundationmodel e results show that the pile head lateral deectionis not only a function of EI but also of the pile diameter Itdecreases considerably as the pile diameter increases whileEI is maintained constant Modeling a pile as a 1D line withbeam-column elements as done sometimes in the literature

results in a smaller contribution of the surrounding soil to thelateral stiffness of the pile and an increase of up to 200 in themaximum displacement of the pile head

Nonlinear analyses were next conducted using the threedimensional nite element models of the soil and pileemploying ABAQUS for a sand and a clay e static (mono-tonic) calculationswere conducted for an extreme lateral loadand bending moment A Mohr-Coulomb constitutive modelwas used for the generic soilse nonlinear contact betweenthe pile and the soil were accounted for using some of thetools available in ABAQUS e results were compared tothose provided by the use of p-y curves for sand and hardclay and with the SALLOPmethod suggested by Briaud [11]Both the p-ymodel for sand and the SALLOPmethod providereasonable answers for the pile with a diameter of 4m but theaccuracy deteriorates for smaller diameters particularly forthe SALLOPmethodwhere the results are independent of thediameter for a xed value of EI For the clay the p-y curvesassuming a free tip and the SALLOP predictions are good forthe smaller diameter pile (diameter of 1m) but deteriorate forlarger diameters It appears that for these cases with the p-ymethod the assumption of a pile hinged at the bottom wouldprovide better results

e study conducted uses the 3D nonlinear nite elementmodel as an accurate model for the pile sizes of interest inrelation to the foundations of offshore wind turbines to assessother simpler models It indicates that when using common


simple models and particularly if the pile is modeled as aline neglecting the size of the soil cavity the results may beinaccurate

References

[1] I Sanchez Salinero ldquoStatic and dynamic stiffnesses of singlepilesrdquo Geotechnical Engineering Report GR82-31 e Univer-sity of Texas at Austin 1982

[2] M Novak ldquoDynamic stiffness and damping of pilesrdquo CanadianGeotechnical Journal vol 11 no 5 pp 574ndash698 1975

[3] V A Baranov ldquoOn the calculation of excited vibrations of anembedded foundationrdquo Voprosy Dynamiki Prochnocti vol 14pp 195ndash209 1967 (Russian)

[4] H Matlock ldquoCorrelations for design of laterally loaded piles inso clayrdquo in Proceedings of the 2nd Annual Offshore TechnologyConference vol 1 pp 577ndash588 1970 Paper 1204

[5] L C Reese and R C Welch ldquoLateral loading of deep foun-dations in stiff clayrdquo Journal of the Geotechnical EngineeringDivision vol 101 no 7 pp 633ndash649 1975

[6] L C Reese W R Cox and F D Koop ldquoField testing andanalysis of laterally loaded pilein stiff clayrdquo in Proceedings of the7th Annual Offshore Technology Conference vol 2 pp 671ndash6901975 Paper 2312

[7] D M Deaikar R S Salimath and V A Saant ldquoA modiedP-Y curve for the analysis of a laterally loaded pile in stiff clayrdquoAustralian Geomechanics Journal vol 44 no 3 pp 91ndash1002009

[8] Y Kim and S Jeong ldquoAnalysis of soil resistance on laterallyloaded piles based on 3D soil-pile interactionrdquo Computers andGeotechnics vol 38 no 2 pp 248ndash257 2011

[9] L C Reese W R Cox and F D Koop ldquoAnalysis of laterallyloaded piles in sandrdquo in Proceedings of the 6th Annual OffshoreTechnology Conference vol 2 pp 473ndash483 1974 Paper 2080

[10] J L Briaud T D Smith and L M Tucker ldquoA pressuremetermethod for laterally loaded pilesrdquo in Proceedings of the 11thInternational Conference on Soil Mechanics and FoundationEngineering vol 3 pp 1353ndash1356 AA Balkema Rotterdame Netherlands 1985

[11] J L Briaud ldquoSALLOP simple approach for lateral loads onpilesrdquo Journal of Geotechnical and Geoenvironmental Engineer-ing vol 123 no 10 pp 958ndash964 1997

[12] V Sanjaya Kumar K G Sharma and A VaradarajanldquoBehaviour of a laterally loaded pilerdquo in Proceedings of the 10thInternational Symposium onNumericalModels in Geomechanics(NUMOG rsquo07) pp 447ndash452 April 2007

[13] M T Suleiman A Raich T W Polson W J Kingston andM Roth ldquoMeasured soil-pile interaction pressures for small-diameter laterally loaded pile in loose sandrdquo in GeoFloridaAdvances in Analysis Modeling and Design Conference pp1498ndash1506 February 2010 Geotechnical Special PublicationPaper 199

[14] J S Chioui and C H Chenu ldquoExact equivalent model for alaterally-loaded linear pile-soil systemrdquo Soils and Foundationsvol 47 no 6 pp 1053ndash1061 2007

[15] G W Blaney E Kausel and J M Roesset ldquoDynamic stiffnessof pilesrdquo in Proceedings of the 2nd International Conference onNumerical Methods in Geomechanics pp 1001ndash1012 1976

[16] E Kausel ldquoForced vibrations of circular foundations on layeredmediardquo Research Report R 74-11 Civil Engineering Depart-ment MIT 1974

[17] J L Briaude Pressuremeter A A Balkema Rotterdam eNetherlands 1992

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column member to model the pile and nonlinear horizontalsprings to represent the soil reactionse p-y curves describethe nonlinear behavior of the soil springs ey were devel-oped rst by atlock [4] for so clays under the water tableReese andWelch [5] and Reese et al [6] developed p-y curvesfor hard clays subjected to monotonic and cyclic loadingabove and under the water table respectively Analyzingthe results of the full scale tests conducted by Reese et al[6] Dewaikar et al [7] presented a modied approach toconstruct p-y curves in stiff clay In another study Kim andJeong [8] developed a framework based on 3D nite elementanalysis for determining a p-y curvee p-y curves for sandswere also developed by Reese et al [9] for monotonic andcyclic loading Briaud et al [10] developed an alternativemethod to obtain the p-y curves directly from pressuremetertests e method was reasonably accurate but complicatedand time consuming so Briaud [11] developed a simplerapproach called ldquosimple approach for lateral loads on pilesrdquoor SALLOP using the pressuremeter limit pressure and thepressuremeter modulus

A number of recent studies have been conducted topredict the behavior of laterally loaded piles in different soilconditions Sanjaya Kumar et al [12] used ABAQUS andthe p-y method to study the behavior of laterally loaded pilefoundations in high marine clay with high potential to swellupon wetting and shrink upon drying Suleiman et al [13]conducted a test to measure the soil-pile interaction pressurefor small diameter piles in loose sand that the results can beused in developing the soil force-displacement relationship(ie the soil reaction or the p-y curve) An equivalent modelfor a laterally loaded linear pile-soil system was presented byChioui and Chenu [14] using articial lateral springs

Continuous modeling of the pile and the surroundingsoil are mostly done using nite element or boundary ele-ment models Both methods can provide rigorous solutionsaccounting for soil-pile interaction under static and dynamicloading For the linear case an accurate solutionwas proposedby Blaney et al [15] using the consistent boundary matrixdeveloped by Kausel [16] to reproduce the soil cavity occu-pied by the pile and adding then the pile enforcing compat-ibility of horizontal and vertical displacements between pileand soil along the pile An extensive number of studies werecarried out by Sanchez Salinero [1] comparing the results ofthis approach to those provided by a variety of othermethodsand proposing approximate formulas for the pile head stiff-ness is approach is only valid however in the linear elasticrange e nite element method is particularly convenientwhen desiring to account for nonlinear effects including thenonlinear behavior of the soil and of the soil-pile interface

A 3D nonlinear nite element analysis of a pile founda-tion in which both the soil and the pile are modeled with 3Dnite elements can be quite expensive and time consumingparticularly when incorporating nonlinear behavior As aresult some investigators have used nite elementmodels thatrepresent the pile by an elastic beam columnmember withouttransverse dimensions (only the centroidal axis) and only thesoil with 3D solid elements is method takes into accountthe continuity of the soil mass and is easy to use for linearstatic and dynamic analysis However the most important

limitation of this approach is that it does not take into accountthe dimension of the pile section

e work presented in this paper is part of a broaderresearch effort to assess the reliability of foundations for off-shore wind turbinesese are normally single large diameterhollow piles However many different methods have beenused and investigated by previous researchers for analysis oflaterally loaded piles most of previous studies are focusedon onshore pile foundations with diameters relatively smallerthan those in the offshore industry e rst objective of thispaper is to compare the results of different methods of analy-sis of laterally loaded piles and illustrate the possible variabil-ity of the results A second objective is to investigate how theconsideration of pile diameter affects the accuracy of simpli-ed models As a rst step the models used for the analysesof these foundations are validateden the model selected isimplemented in the computer program ABAQUS using 3Dbrick elements to discretize the soil around the pile and shellelements to model the hollow pile e results obtained withthis model for linear and nonlinear analyses are compared tothose provided by a variety of othermethods used in practice

In the following we rst examine four different modelsused for linear analysis of single pile foundations and evaluatethe inuence of accounting for the pile diameter in the sim-plied linear FE analyses In the next section we improve the3D nite element model by accounting for the nonlinearityof the soil and soil-pile interaction Two common simpliednonlinear models are then assessed using this model formono-piles in sand and clay

2 Linear Analyses

Analyses considering linear soil behavior and perfect bond-ing between the pile and the surrounding soil are conductedrst e pile selected for the study is hollow with a diameterof 4m and the properties listed in Table 1 Four differentmodels are studied

(1) e rst model is a 3D nite element model of boththe soil around the cavity occupied by the pile (solidelements) and for the pile with shell elements forhollow piles and brick elements for solid piles (shownin Figure 1)

(2) e second simpler model reproduces the soil withsolid elements lling the space without any cavitye pile is represented by the centroidal axis of a 1Dbeam column coinciding with the central axis of thesoil model enforcing only compatibility of horizontaldisplacements between the nodes of the pile and thoseof the soil along the axis

(3) e third model is the one proposed by Blaney et al[15] with the consistent boundary matrix with theradius of the cavity representing the soil and enforcingcompatibility of both horizontal and vertical displace-ments between the soil and the pile along its sides

(4) e fourth model is a beam on an elastic (Winkler)foundation with horizontal and rotational springsalong the side of the pile e constants selected forthe foundation are 119896119896119909119909 = 4119866119866 and 119896119896120593120593 = 266661198661198661198661198662















100 325 683 (110) 340 (5) 252 (23)200 276 683 (148) 275 (1) 250 (10)400 209 683 (227) 205 (2) 243 (17)

0

10

20

30

40

50

60

70

80

02 2

Pil

e h

ead

defl

ecti

on

(m

m)

002

Pile diameter (m)



1D pile FEM



















1199101199100 =211986711986701198971198970119870119870

+21198721198720

11989711989720119870119870 (1)



1199101199100 =2 1007649100764921198671198670119871119871 + 119871119872119872010076651007665

1198701198701198711198712 (2)







Pile diameter (m)



100 910 570 (35) 360 (60) 455 453 (1) 312 (32) 450 (1)200 606 435 (29) 360 (41) 339 405 (20) 300 (12) 450 (33)400 400 382 (5) 360 (10) 251 375 (50) 285 (14) 450 (80)

1

10

100

0 1 2 3 4 5

FEM

SALLOP

Pil

e h

ead

defl

ecti

on

(m

m)

Pile diameter (m)

(a)

1

10

100

0 1 2 3 4 5P

ile

hea

d d

eflec

tio

n (

mm

)

Pile diameter (m)

FEM

SALLOP

(b)










References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























100 325 683 (110) 340 (5) 252 (23)200 276 683 (148) 275 (1) 250 (10)400 209 683 (227) 205 (2) 243 (17)

0

10

20

30

40

50

60

70

80

02 2

Pil

e h

ead

defl

ecti

on

(m

m)

002

Pile diameter (m)



1D pile FEM



















1199101199100 =211986711986701198971198970119870119870

+21198721198720

11989711989720119870119870 (1)



1199101199100 =2 1007649100764921198671198670119871119871 + 119871119872119872010076651007665

1198701198701198711198712 (2)







Pile diameter (m)



100 910 570 (35) 360 (60) 455 453 (1) 312 (32) 450 (1)200 606 435 (29) 360 (41) 339 405 (20) 300 (12) 450 (33)400 400 382 (5) 360 (10) 251 375 (50) 285 (14) 450 (80)

1

10

100

0 1 2 3 4 5

FEM

SALLOP

Pil

e h

ead

defl

ecti

on

(m

m)

Pile diameter (m)

(a)

1

10

100

0 1 2 3 4 5P

ile

hea

d d

eflec

tio

n (

mm

)

Pile diameter (m)

FEM

SALLOP

(b)










References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















1199101199100 =211986711986701198971198970119870119870

+21198721198720

11989711989720119870119870 (1)



1199101199100 =2 1007649100764921198671198670119871119871 + 119871119872119872010076651007665

1198701198701198711198712 (2)







Pile diameter (m)



100 910 570 (35) 360 (60) 455 453 (1) 312 (32) 450 (1)200 606 435 (29) 360 (41) 339 405 (20) 300 (12) 450 (33)400 400 382 (5) 360 (10) 251 375 (50) 285 (14) 450 (80)

1

10

100

0 1 2 3 4 5

FEM

SALLOP

Pil

e h

ead

defl

ecti

on

(m

m)

Pile diameter (m)

(a)

1

10

100

0 1 2 3 4 5P

ile

hea

d d

eflec

tio

n (

mm

)

Pile diameter (m)

FEM

SALLOP

(b)










References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Pile diameter (m)



100 910 570 (35) 360 (60) 455 453 (1) 312 (32) 450 (1)200 606 435 (29) 360 (41) 339 405 (20) 300 (12) 450 (33)400 400 382 (5) 360 (10) 251 375 (50) 285 (14) 450 (80)

1

10

100

0 1 2 3 4 5

FEM

SALLOP

Pil

e h

ead

defl

ecti

on

(m

m)

Pile diameter (m)

(a)

1

10

100

0 1 2 3 4 5P

ile

hea

d d

eflec

tio

n (

mm

)

Pile diameter (m)

FEM

SALLOP

(b)










References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Modeling Laterally Loaded Single Piles ...

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