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Finite Element Analyses Applied in Design of Foundations and Anchors for Offshore Structures

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FiniteElementAnalysesAppliedinDesignofFoundations

andAnchorsforOffshoreStructures

LarsAndresen1;HansPetterJostad2;andKnutH.Andersen,M.ASCE3

Abstract:Offshorestructuresforoilandgasexploitationaredesignedtoaccommodatesevereenvironmentswithlargecyclicloads.Thesestructuresareeitherfoundeddirectlyontheseabed,ortheyaremooredtoanchorsinstalledintheseabedsoil.Thepermanentandcyclicloading,thefoundationoranchorgeometry,andthenonlinearsoilbehaviormaybeverycomplex,andmanyinterrelatedaspectsmustbeconsideredinthegeotechnicaldesignofthefoundations.Finite-elementanalyses(FEAs)areusedincreasinglytodealwiththesecomplex-itiesandofferthepotentialtoincreaseaccuracy,efficiency,andreliabilityandreducetheuncertaintyofthedesignprocess.Thispaperpresentsthemajorgeotechnicalaspectsinthedesignoffoundationsforoffshorestructuresandexamplesfromfinite-elementanalysescarriedoutattheNorwegianGeotechnicalInstitute(NGI)todealwiththeseaspects.AbriefreviewoftheprocedureusedatNGItoobtainsoilstress-strain-strengthrelationshipsfromcycliclaboratorytestsisincluded.ItisdemonstratedthatFEAoffersseveralbenefitsoverclassicalmethods,suchaslimitingequilibriumcalculations.DOI:10.1061/(ASCE)GM.1943-5622.0000020.©2011AmericanSocietyofCivilEngineers.

CEDatabasesubjectheadings:Finiteelementmethod;Offshorestructures;Foundations;Design;CyclicLoads.Authorkeywords:Finite-elementmethod;Offshorestructures;Foundationdesign;Cyclicloads.

Offshorestructuresforoilandgasexploitationmaybesubjectedtosevereenvironmentalloadsfromwaves,wind,current,andpos-sibly,iceandearthquakes.Strictrequirementsaresetfortheopti-mumperformanceoftheirfoundationsystems,andthefoundationdesignisakeyactivityintheoverallengineeringprocessofsuchstructures.Thefoundationsmustbedesignedfortheexpectedper-manentandcyclicloadhistory.Thebearingcapacityundercyclicloadingmaybehigherorlowerthanthebearingcapacityformonotonicloading,dependingonthecyclicdegradation,andlargecyclicandpermanentdisplacementsmaydevelop(seeFig.1).Varioustypesofstructuresandfoundationsystemsareused,suchaspiledjackets,jacketswithcaissons(skirtedfoundations),jack-uprigsonspud-cansormats,floatingstructuresmooredtodifferenttypesofanchors,andsteelorconcretegravitybasestruc-tures(GBSs)withorwithoutskirts.

Themajoraspectsingeotechnicalengineeringthataretypicallyconsideredinthedesignoffoundationsforoffshorestructuresare:1.Bearingcapacityandslidingresistance;2.Installationaspects;3.Foundationstiffness;

4.Consolidationandsettlements;

DivisionDirector,NorwegianGeotechnicalInst.,P.O.Box3930UllevaalStadion,N-0806Oslo,Norway(correspondingauthor).E-mail:Lars.Andresen@ngi.no2

ExpertAdvisor,NorwegianGeotechnicalInst.,P.O.Box3930UllevaalStadion,N-0806Oslo,Norway.E-mail:Hans.Petter.Jostad@ngi.no3

TechnicalDirector,NorwegianGeotechnicalInst.,P.O.Box3930UllevaalStadion,N-0806Oslo,Norway.E-mail:Knut.H.Andersen@ngi.no

Note.ThismanuscriptwassubmittedonJuly2,2009;approvedonMarch10,2010;publishedonlineonMarch19,2010.DiscussionperiodopenuntilMay1,2012;separatediscussionsmustbesubmittedforindi-vidualpapers.ThispaperispartoftheInternationalJournalofGeome-chanics,Vol.11,No.6,December1,2011.©ASCE,ISSN1532-31/2011/6-417–430/$25.00.

5.Soilreactionsagainstthestructure;and6.Soil-structureinteraction(SSI)

Theseaspects,whichmaybestronglyinterrelated,areshownschematicallyinFig.2.Eventhoughhandcalculationsandlimitequilibriummethods(LEM)havebeen,andstillarebeingused,finite-elementanalyses(FEAs)areusedincreasinglytodealwiththeaforementionedaspects.FEAshavemanyadvantages,includ-ingtheabilitytoincludecomplexgeometries,spatiallyvaryingsoilproperties,advancednonlinearandanisotropicconstitutivemodels,andpartialconsolidationunderlong-termloading,tonameafew.ThispaperpresentsexamplesofFEAsperformedattheNorwegianGeotechnicalInstitute(NGI)forallsixofthelistedaspectstypi-callyconsideredingeotechnicalfoundationdesign.ObjectivesaretodemonstratethatnumericalmodelingandFEAenabletheengi-neertosolveproblemsthatotherwisecan’tbesolved,toaidinde-velopingnewfoundationconcepts,tocontributetoamoreoptimaldesign,andtohelpreducetheuncertaintiesinthedesignprocess.However,theseexamplesalsoillustratethatgreatcaremustbetakenandthatspecializedknowledgeinFEAisrequired.Thepaperisorganizedinsixsectionsforthevariousdesignaspects.TheframeworkusedatNGItoaccountfortheeffectsofcyclicloadingonsoilbehaviorisbrieflyreviewedinthesectiononcyclicloadingandsoilproperties.ThereadershouldbeawarethatthispaperisnotacomprehensivereviewofFEAappliedtooffshorefoundationde-sign;rather,itisasummaryofworkperformedatNGI.

CyclicLoadingandSoilProperties

OffshorestructuresaresubjectedtomultidirectionalloadingF¼½Fx;Fy;Fz;Mx;My;Mz󰀁thatmaybeseparatedintoaverageloadsFa,e.g.,weightW0ofthestructureandthesustainedcomponentsofthestormlikewindsandcurrents,andcyclicloadsFcy,e.g.,wave,ice,andearthquakeactions.Thewaveactionwill,in

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dependingondrainageconditions,loadingrate,andsoildrainagecharacteristics.

CyclicSoilProperties

Asoilelementsubjectedtocyclicloadingwilldevelopaverageuaandcyclicucyexcessporepressure,andaverageγaandcyclicγcyshearstrainsthatincreasewithtimeorincreasingnumberofcycles,asillustratedinFig.4.Ultimately,thestrainswillbecomeverylarge(γaand/orγcy>15%)andthesoilelementisconsideredtohavereachedfailure.

Thedevelopmentofporepressureandshearstrainwilldependonthecombinationofaverageτaandcyclicτcyshearstresses.Byrunningseverallaboratorytestswithdifferentcombinationsofτaandτcy,diagramsofthetypeshowninFig.5areestablished.ThediagramsshowthestrainresponseafterN¼100cyclesforasoilelementindirectsimpleshear(DSS),triaxialcompression,andex-tensionmodeofloading.Itisseenthattheresponsedependsonthestresspathandtheaverageshearstressτa.Similardiagramsmaybeestablishedforvariousnumbersofcycles,e.g.,N¼1,10,or1,000.Thecyclicshearstrengthisthemaximumshearstressthatcanbemobilized,i.e.,thesumofaverageandcyclicshearstressesτfcy¼τa;fþτcy;fatfailure(i.e.,15%strain).Cyclicstrengthde-pendsonthenumberofcyclesN,theaverageshearstressτa,andthestresspath,i.e.,triaxialcompression(TXC),triaxialextension(TXE),orDSS,andcanbedeterminedfromdiagramsofthetypeshowninFig.5.Ageneralstresspathmaybedefinedbytheangleαbetweenthemajorprincipalstressσ1andthevertical,andthecyclicstrengthτfcyðN;τa;;αÞmaybeobtainedbyinterpolationbe-tweenresultsobtainedforTXC(α¼0°),DSS(α∼30°),andTXE(α∼90°).ThediagramsinFig.5alsogiveinformationaboutthecyclicandaverageshearstress-shearstrainrelationshipasafunc-tionofthecyclicshearstress;examplesaregiveninFig.6.

ThediagramsinFigs.5and6givethesoilbehaviorforacyclicloadhistorywithNcyclesofconstantcyclicshearstress.Inastorm,however,thecyclicshearstressislikelytovaryfromonecycletothenext,similartothatshownintheloadtableinFig.3(c).TheequivalentnumberofcyclesNeqvofthemaximumcyclicshearstressis,therefore,defined.Neq(lessthanN)isthenumberofcyclesofthemaximumloadthatwouldgivethesameeffectas

addition,causecyclicpressurevariationsΔpw;cyontheseabedoutsidethestructure(Fig.3).

Therealirregularcyclicloadhistoryis,fordesignpurposes,normallysimplifiedintoadesignstormcompositionofacertainduration,e.g.,a100-yearreturn-periodstormwithan18-hbuild-upand6-hpeakperiod.Cyclicloadingisgroupedintoseveral(i…n)loadpackageswithacertainnumberofwavesNiatdifferentloadlevelsfcy;i.Ni=numberofcycles;andfcy;i¼Fcy=Fcy;max=loadlevelforloadpackagei.ThecyclicloadperiodTpistypically10–15sforwaveloadingandapproximately1sforearthquakeloading.

Fig.3showsthegeometry,theloading,andasimplifiedillus-trationoftheshearstressesalongapotentialfailuresurfaceforanoffshoregravitybasestructure.Theaverageshearstressτaiscomposedoftheinitialshearstressτ0¼1=2σ0v0ð1ÀK0ÞfromtheanisotropicinsituconsolidationstressesandanadditionalshearstressΔτa¼fðFaÞinducedbytheaverageloading.Thecyclicshearstressτcy¼fðFcyÞisinducedbythecyclicloading.Theini-tialshearstressτ0hasbeenactingunderfullydrainedconditions,whereastheadditionalaverageshearstressΔτaandthecyclicshearstressτcymay,ingeneral,actunderpartlydrainedconditions,

Fig.2.Majorgeotechnicalaspectsconsideredindesignoffoundationsforoffshorestructures

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Downloaded from ascelibrary.org by Nanjing University Of on 11/23/12. Copyright ASCE. For personal use only; all rights reserved.Fig.3.Loadingandsoilresponseforanoffshoregravitybasestructure:(a)planviewoffoundationandloading;(b)crosssectionwithsimplifiedsoilstressconditions;(c)designloadparcels;(d)definitionofaverageFaandcyclicFcyloadcomponents

followingthecyclicloadhistorywithvaryingloadintensity.Forclays,i.e.,undrainedconditions,Neqvmaybedeterminedbykeep-ingtrackofthecyclicshearstrainduringthecyclicloadhistorybythe“strainaccumulation”procedure(Andersenetal.1992).Forsandsorconditionswithdrainage,Neqvcanbedeterminedbykeep-ingtrackofthepermanentporepressureaccumulatedduringthecyclicloadhistory(Jostadetal.1997;Andersenetal.1994).Thereasonforusingtheporepressureaccumulationprocedureforsandisthatsomedrainageislikelytooccurduringtheloadhistoryinsand.Itisassumed,however,thatdrainagedoesnothavetimetooccurwithineachcycle.Toaccountfordrainage,itisnecessarytokeeptrackoftheaccumulatedporepressure.

Theaccumulationproceduresusestrainorporepressurecon-tourdiagramsofthetypepresentedinFig.7andstormloadcompositionsofthetypepresentedinFig.3(c).ThediagramsinFig.7wereestablishedbasedonthesamelaboratorytestsastheonesusedtoestablishthediagramsinFig.5.

Inprinciple,aconstitutivemodelcouldbeformulatedthatfol-lowseachindividualcycleandusedinatimedomainFEanalysiswiththecompleteloadhistory.Atthepresent,NGIdoesnothavesuchamodelforthatpurposethatissufficientlyrobustandfitslaboratorydataaccuratelyenough.Instead,therelationshipsgiveninFigs.5–7areusedintheconstitutivemodelsthatareimple-mentedintotheFEprogramsusedforoffshorefoundationdesignatNGI.Becausetheaverageshearstressandthecyclicstrengtharefunctionsofthecyclicshearstress,itisnecessarytoknowthecyclicshearstresswhenenteringthediagramsinFigs.5–7.ThisisdonebycalculatingtheshearstressesinthesoilasfunctionsofthecyclicloadsFcy.InFEA,iterationsareperformedtoupdateτa¼τaðτcyÞastheτcydistributionchanges(JostadandAndresen2009).

Fig.4.Shearstress,shearstrain,andporepressureduringcyclicloading

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Downloaded from ascelibrary.org by Nanjing University Of on 11/23/12. Copyright ASCE. For personal use only; all rights reserved.Fig.5.ContoursofaccumulatedaverageshearstrainγaandcyclicshearstrainamplitudesγcyforcombinationsofaverageandcyclicshearstressesfornormallyconsolidatedDrammenclayafterN¼100cycles:(a)DSSloading;(b)triaxialcompressionandextensionloading

Fig.6.Averageshearstress–shearstrainrelationshipsasfunctionofcyclicshearstressamplitude:(a)DSSloading;(b)triaxialcompressionandextensionloading

BearingCapacity

Bearingcapacityandhorizontalslidingstabilityareprobablythemostimportantaspectsoffoundationdesign.Calculationsareper-formedtocheckthatthefoundationcancarrythedesignloadswithadequatesafetyagainstfailureorexcessivedeformations.Usuallyalimit-statedesignisused,anddifferentultimate-limit-statesareconsidered,suchasthestormloadwitha100-yearreturnperiod.Traditionally,thelimitequilibriummethodhasbeenusedinsuchcalculations;however,FEAisincreasinglyusedandhastheadvan-tagesthatmorecomplexgeometriesandloadingmaybeaccountedfor,itismorerigorous,andthegoverningfailuremechanismisidentifiedautomaticallybythemethod,i.e.,thereisnoneedforasearchthroughpossiblegoverningmechanisms.Examplesfrombearingcapacityanalysesforaconcretegravitybaseplatform,theholdingcapacityofasuctionanchor,andthecapacityofajacketplatformfoundedonskirtedfoundationsaregiveninthissection.BearingCapacityofaGravityBasePlatform

ThebearingcapacityoftheoffshorestructureshowninFig.3wasanalyzedusing3DFEA,andtheanalysesaredocumentedinmoredetailinAndresenetal.(2007).Thisplatformisusedforstorageandprocessingofliquidnaturalgas(LNG)andis200mlong,100mwide,and60mhigh.Thewaterdepthis25m.Thefoun-dationconsistsofaflatbasethatisgroutedinfullcontactwiththe

seabedandhasseveralrowsofcorrugatedsteelskirtspenetrating1mintothesoil.Theskirtsareforscourprotectionandtopreventslidingalongtheweakertopsoil.Thesubmergedon-bottomweightW0ofthestructureinoperationis2,000MN,includedaddedballastthatprovidesincreasedmeaneffectivestressesandthusincreasedshearstrengthoftheunderlyingsoil.

Trialanalyseswereruntoidentifythegoverningfailuremecha-nismandthesufficientmodeldimensions.Itwasimportanttomin-imizethemodeldimensionstoobtainafinemeshdiscretizationwithareasonablecomputationtime(overnight).ThePlaxis3DFoundationprogram(Plaxis3DFoundation2.1)wasusedwith9,00015-nodedwedgeelementsdiscretizingthesoilandthefoun-dationbaseslab.

Thesoilconsistsofmediumstiffclayto5mdepthandthenmediumdensefinesandbelowtheclaytogreatdepths.TheeffectsofconsolidationfromtheplatformweightW0andtheporepressurebuildupandpartialdrainageduringthestormareaccountedforwhenassessingthestrength.Thestrengthswereassessedonthebasisofsite-specificcycliclaboratorytestsandthestormcompo-sitionshowninFig.3(c),usingtheaccumulationproceduresfromAndersenetal.(1994).Onlythewaveswithloadlevelhigherthan

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Downloaded from ascelibrary.org by Nanjing University Of on 11/23/12. Copyright ASCE. For personal use only; all rights reserved.Fig.7.ContourdiagramsforsoilresponseinaDSStestasfunctionofnumberofcyclesandcyclicshearstresslevel:(a)cyclicshearstrainresponse;(b)accumulatedporepressureresponse

30%ofthemaximumwaveswereusedbecausealowerloadwasfoundtohavenodegradingeffectonthestrength.ThisresultedinNeqv¼10andtheshearstrengthprofilesthatareshowninFig.8(b).Thefigureshowsthecyclicshearstrengthforτa¼0fortheclaylayer(layerII)andthesandlayer(layerIII)belowtheplatformandoutsidetheplatform.Thewaveloadingistwo-waysymmetricalwithFa¼0,whichresultsinτa¼0onthehorizontalplanethatconstitutesnearly90%ofthefailuremecha-nism.Thestrengthbelowtheplatformishigherthanoutsidetheplatformfootprintbecauseoftheincreasedeffectivestressesfromtheplatformweight.Theeffectoftheplatformweightloadspread(distributionofΔσ0vbelowtheplatform)isaccountedforbyanapproximatedsimple1∶3rule,asshownonFig.8(a).

TheresultingfailuremechanismisshowninFig.9andconsistsmainlyofslidinginthey-directionalongthetopoftheweakerlayerat5mdepth.Passiveandactiveearthpressureresistancedevelopalongthe200-m-wideand5-m-deepwindwardandleewardplanes.Sidesheardevelopsalongthe100-m-wideand5-m-deepsideplanes.Thischaracterizesthegeometryofthemainfailuremecha-nism;however,torsion,overturningmoments,andtheunevendistributionofseabedpressurealsoaffectthemechanism.Fig.9(a)showsthatthetorsioncausessomerotationofthefoundation.DiscretizationError

CapacitycalculationscarriedoutbyFEAwillalwayscontaindis-cretizationerrors,i.e.,therewillbeanovershootinthecalculatedultimatecapacity.ThiserrorisaresultofthesimplificationdoneinFEA,wherethecontinuousdisplacementfieldisrepresentedbyafinitenumberofelementinterpolations.Thediscretizationerrorcanbereducedbyusingafinermesh,withthepenaltyofanincreasedcomputationalcost.Itisnotpossibletoquantifytheerrorfromtheresultofoneanalysiswithonlyonemeshrealization,andoftenonemustthenrelyonexperiencefromsimilarproblemstojudgeifthediscretizationerrorisacceptable.

Fortheproblempresentedinthesectiononthebearingcapacityofagravitybaseplatform,thediscretizationerrorwasquantifiedbycalculatingthehorizontalloadcapacitywiththesameFEmodel

Fig.8.FEcalculationsforbearingcapacityofagravitybaseplatform:(a)elementdiscretizationandmateriallayeringbelowandoutsideoffoundation;(b)cyclicshearstrengthτf;cyprofilesfortriaxialcompres-sion(TXC),directsimpleshear(DSS),andtriaxialextension(TXE)

butwithdifferentmesheswithvaryingnumbersofelements.TheresultsareshowninFig.10.Itisseenthat,byincreasingthenumberofelements[reducingtheaverageelementsize(AES)],thecalculatedcapacityisreduced.ItispossibletofitacurvetotheresultsthatcanbeextrapolatedtoAES¼0(infinitenumberofelements),wherethediscretizationerrorvanishes.

Theexamplefromthesectiononthebearingcapacityofagravitybaseplatformdemonstratesthat3DFEAsaresuitedforcalculatingbearingcapacitiesofoffshorefoundationswithmulti-directionalloadingandcomplexgeometries,suchasskirtedbases.However,oneshouldbeawarethattheremaybeaneedforaveryfinemeshdiscretizationtoavoidovershooting.Furthermore,careshouldbetakenbecauselittleexperienceandonlylimitedvalidationexamplesexistfortheapplicationof3DFEAstosuchproblems.

HoldingCapacityofSuctionAnchors

Anindustrysponsoredstudyonthedesignandanalysisofdeepwateranchorsinsoftclaywascompletedin2003,inwhichNGIparticipatedwiththeOffshoreTechnologyResearchCenter(OTRC)intheUnitedStatesandtheCenterforOffshoreFounda-tionSystems(COFS)inAustralia.ThestudyisdocumentedinAndersenetal.(2005).Independent3DfiniteelementanalysesforseveralhypotheticalcaseswereperformedbyNGI,COFS,andOTRC.

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Downloaded from ascelibrary.org by Nanjing University Of on 11/23/12. Copyright ASCE. For personal use only; all rights reserved.Fig.9.Failuremechanismplottedascontourshadingsofdisplace-mentsatfailure:(a)topviewshowingrotationaldisplacementscausedbytorsionmoment(displacementvectorsaretangentialtocontourlines);(b)shortsidecrosssection

Fig.11.Holdingcapacitiesofasuctionanchorcalculatedby3DFEA:(a)capacitiescalculatedforvariouscombinationsofhorizontal(H)andvertical(V)loads;(b)deformedmeshandcontourshadingsofdispla-cementsillustratingfailuremechanismfor45°loadingangle

Fig.10.TheeffectofmeshrefinementinFEA:Horizontalloadcapa-cityversusaverageelementsize(numberofelements);dottedcurverepresentsproposedextrapolationtowardsAES¼0

Thecase,C2,consistedofanopencylindricalanchorwithweightW0¼300kN,diameterB¼5m,anddepthD¼7:5m,givingadepth-to-diameterratioofD=B¼1:5.Thesoilcyclicshear

DSS

strength(τfcy¼su)datawas:sDSS¼1:25×z,sCuu¼1:2×su,

DSSandwithssEu¼0:8×suualongtheoutsideskirtwall=DSS

0:65×su.Fig.11(a)showsholdingcapacitiesforthiscasecalcu-latedbythethreegroups(NGI,UWA,andOTRC)forvariousloadanglesfrompurehorizontaltopureverticalloading.Ineachcasetheloadisattachedtotheanchorattheoptimalattachmentpointsuchthattheanchorispreventedfromrotating.

Fig.11(b)showsthefailuremechanismforaloadangleof45°calculatedbyNGIusingtheprogramBIFURC3D(NGI1999).

Itcanbeseenthattheanchorisnotrotatingandthatthemechanisminvolvessomeofthesoilunderneaththeskirttiplevel.

Theoverallconclusionfromthisstudywasthatthe3DFEAresultswereingoodagreement.Thedifferenceincapacitycalcu-latedbythedifferentgroupswasgenerallylessthan3%,andthecapacitieswereapproximately10%higherthantheresultsNGIob-tainedbyusinglimitingequilibriummethods.Hence,itwasdem-onstratedthatby3DFEA,reliableresultswereobtainedthatwerelessconservativethantheresultsobtainedbylimitingequilibriumcalculation.Fromthisandotherstudies,ithasbeenfoundthatitisimportanttomodeltheanisotropyoftheundrainedshearstrengthandthereducedundrainedshearstrengthalongtheoutsideskirtwalladequately.Ithasalsoproventobeveryefficienttousespecialzero-thicknessinterfaceelementsalongtheskirtoutsideandunder-neaththeskirttip.Ifsuchelementsarenotused,itmaybeneces-sarytouseanextremelyfinemeshdiscretizationintheseareastoallowforapossiblefullslipbetweentheanchorandthesoil.CapacityofSkirtedFoundationsonaSteelJacketPlatform

TheDraupner-Eplatformisasteeljacketlocated160kmoff-shorefromNorwayatawaterdepthof70m.ThestructureandtheexperienceofinstallationofthejacketaredocumentedbyTjelta(1995).Unlikemostjacketplatforms,whicharesupported

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Downloaded from ascelibrary.org by Nanjing University Of on 11/23/12. Copyright ASCE. For personal use only; all rights reserved.Fig.13.Idealizedcyclicverticalloadhistoryandcalculatedverticaldisplacementsofleewardlegofajacketduringa6-hpeakstormperiod

Fig.12.(a)Draupnerjacketbeingliftedontoabarge(ImagecourtesyofLeifBerge,Statoil);(b)upliftcapacityofskirtedfoundationversusverticaldisplacementsfordifferentloadingratescalculatedbyfullycoupledFEA

bypiles,Draupnerisfoundedonsteelbucketfoundations(seeFig.12(a)).

Thefourcylindricalfoundations,each12mindiameter,areequippedwith40-mm-thicksteelskirtsthatpenetrate6mintotheseabedbyappliedsuction.ThesoilconditionsconsistofverydensesandwitharelativedensityDrintherange90–100%inthetop23m.

Whereasclaygenerallyisundrainedduringatypicalstormhis-tory,sandmayrespondfullydrainedduringchangesintheaverageloadand,atthesametime,respondundrainedtotheshort-termloadingfromsinglewavecycles.Thelong-termdrainedverticalupliftcapacityofthesefoundationsis,therefore,quitelowandcon-sistsonlyofdrainedinsideandoutsidewallfriction.However,thecapacityfortheshort-duration(Tp∼11s)waveloadwithatypicalrateof0:2MN=sismuchhigher,asillustratedinFig.12(b).NGIhasimplementedaspecialconstitutivemodelfortheanaly-sisofsuchjacketswithskirtedfoundationsinsandinthein-housefiniteelementprogramBIFURC(NGI1999).Themainparameterinthismodelistheaccumulatedporepressureuaasafunctionofthecyclicshear-stressamplitudeτcyandnumberofcyclesN.ThesoilresponsefortheaverageloadFaiscalculatedusingthemobilizedfrictionmodel(Nordaletal.19).Theaccumulatedporepressureiscalculatedbasedonthecyclicshear-stressampli-tudeτcy,calculatedfromthecyclicloadsFcyinaseparateanalysis,withinputoftheactualequivalentnumberofcyclesineachinte-grationpointNeq.Theτcymaybecalculatedbyanonlinearelasticconstitutivemodelexpressingtherelationshipbetweenτcyandγcy,showninFig.5.TheequivalentnumberofcyclesisfoundfromporepressurecontourdiagramsofthetypeshowninFig.7(b).

Byusingthisconstitutivemodeltogetherwithacoupledstressequilibriumandporewaterflow(consolidation)finite-elementfor-mulation,itispossibletoanalyzeporepressureaccumulationanddissipationproblems.TheprocedureisdescribedinmoredetailinJostadetal.(1997).Asavalidationoftheprocedure,theresponseofabucketfoundationresemblingtheonesfortheDraupnerplat-formwascalculated.Theaverageverticalloadoneachfoundationpriortothestormloadingwas10MN.Fig.13showstheidealizedcyclicloadhistory,withincreasingaverageVaandcyclicVcyver-ticalload,andthecalculatedverticaldisplacements(maximum,minimum,andpermanent)duringa6-hpeakdesignstormperiod.Theresultsarefortheskirtedfoundationthatexperiencesincreasedaverageverticalloadduringthestorm(leewardleg).Thehorizontalloadcomponentisassumedtobetakenbythelessmobilizedfoun-dations.Itcanbeseenthatthefailuremodeisthedevelopmentoflargeverticalsettlements.

Installation

Suctionanchorsandskirtedgravitybasefoundationshavesteelorconcreteskirtsthatprotrudeintothesoilduringinstallation.Theskirtspenetratedownintothesoilasaresultoftheweightofthestructureoracombinationoftheself-weightandanappliedunder-pressureunderthebase.Theinstallationmethodandprocessaffectimportantaspectsofthedesignsuchasthepenetrationresistance,thedistributionofcontactstressesbetweenthefoundationstructureandthesoil,andtheshearstrengthalongtheskirts(frictioncapac-ityoftheskirts).

Numericalanalysisofinstallationprocessessuchasthepenetra-tionofasteelskirtintotheseabedisextremelychallenging.Ideally,theanalysisshouldaccountforalargedeformation,acontinuouslychangingcontactarea,andremoldingofthesoil.MethodsthathandlelargedeformationssuchastheupdatedLagrangian(UL)orthematerialpointmethod(MPM)(Coetzeeetal.2005;Beuthetal.2007)arepromisingbutstillunderdevelopmentandnotused

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regularlyindesignpractice.ThearbitraryLagrangianEulerian(ALE)andthediscreteelementmethod(DEM)arealsoworthmentioningandhavebeenusedtomodellargedeformations,e.g.,Liuetal.(1998)andCundallandStrack(1979).Inthissec-tion,resultsarepresentedfromastudywheresmall-andlarge-deformationFEAswerecarriedouttostudyhowthesoildisplacedbyapenetratingskirtmayaffectthehorizontalstressesalongtheoutsideskirtwall.

Set-UpEffectalongBucketAnchorOutsideSkirtWallAnimportantpartofbucketanchordesigninclayisthedetermi-nationoftheshearstrengthalongtheoutsideskirtwallintheopera-tionalcondition.Thisshearstrengthisaffectedbythehorizontalstressincreaseresultingfromsoilbeingdisplacedoutwardfromtheadvancingskirttipduringinstallation.Thestrengthisalsohighlyaffectedbythesensitivityoftheclay,thedissipationofexcessporepressureswithtime,andthixotropy,asshownbyAndersenandJostad(2002).Strengthincreaseswithtime,andthiseffectisoftenreferredtoasset-up.

Duringself-weightpenetration,asignificantpartofthesoildis-placedbytheskirtwillmoveoutsidetheskirtwall,asfordrivenpiles.Whenunderpressureisapplied,however,mostoftheclaydisplacedbytheskirtisexpectedtomoveintotheanchor.Theout-wardsoilmovementduringweightpenetrationwillcauseasignifi-cantincreaseinthehorizontalstressoutsidetheskirtwall,whereasthemovementofsoilintotheanchorduringunderpressurepenetra-tionmaygivesignificantlysmallerhorizontalstressbuilduporevenstressreduction.

ThesoilmovementsandhorizontalstressbuildupwerestudiedbyasmalldeformationstepwisegeometryupdatedFEAprocedureforbothaflatandataperedskirttipbyAndersenetal.(2004),usingthePlaxisprogram.Later,thisprocesswasstudiedinmoredetailatNGIbylarge-deformationFEanalyseswiththeAbaqusandPlaxisprograms,usingtheupdatedLagrangianmethod.AnexampleofaFEmodelfromthesestudiesisshowninFig.14(a).TheanchorhasadiameterD¼5:5m,skirtthicknesst¼0:05m,penetrationdepthZ¼16m,andataperedtip.Interfaceelementswereusedtomodelthedisturbedzoneofclaybetweenthe“intact”clayandsteelskirtandintheinterfacesbetweentheclayandtheskirttip.Anundrainedshear-strengthprofilesu¼2:0þ1:25·depth(kPa)wasmodeled.

Tomodelaccuratelyboththein-andoutsideskirtfrictionandtheskirttipbearingcapacity,afiniteelementmeshwithextremelocalrefinementintheskirttipregionandwithinterfaceelementsaroundtheskirttipwasused.ForthemeshshowninFig.14(a),theratiobetweenthemodelwidth(20m)andtheskirtthickness(0.05m)is~400.Theratiobetweenthedimensionsofthelargestandsmallestelementinthemeshisaboutthesame.

Fig.14(b)showsvectorsofhorizontaldisplacementsaroundthetaperedskirttipduringpenetrationat14mdepth.Itisseenthatthesoilalongthetaperedpartoftheskirtmovesoutsidetheskirtwall.However,theunderpressurecausesaportionofthesoiltomoveinsidetheskirtatsomedepthbelowtheadvancingskirttip.Thesoilbeingcontinuouslymovedoutsideoftheadvancingtipduringpenetrationiscausingastressbuildupalongtheskirtoutsidewall.Fig.15(a)showscontoursofaddedhorizontalstressinthevicinityoftheskirttipforacasewithself-weightpenetration.

InFig.15(b),thepermanentstresschange,afterfinalpenetration,outsidetheskirtwallisshown.Thereisasignificantpermanentstressincreaseoutsidetheskirtwallforself-weightpenetration,whereasthereisastressreductionforpenetrationbyunderpressure.Usingataperedskirttipgivesonlyaslightlydifferentstressre-sponse.Theresultsfromthesmall-strainstepwiseupdatedgeometry

Downloaded from ascelibrary.org by Nanjing University Of on 11/23/12. Copyright ASCE. For personal use only; all rights reserved.Fig.14.Finiteelementanalysisofsuctionanchorinstallation:(a)FEmodel;(b)horizontaldisplacementsfield(vectors)aroundtaperedskirttipduringpenetrationbyunderpressure

procedure(Andersenetal.2004)agreedverywellwithresultsobtainedwithlarge-deformationupdatedLagrangiananalyses.

FoundationStiffness

Theassessmentofthefoundationstiffnessandthecyclicdisplace-mentsareimportanttopicsinthedesignoffoundationsforoffshorestructures.Themaximumcyclicdisplacementamplitudesinastormmaybeofinterestfor,e.g.,thedesignofpipelinesconnectedtothefoundation,andthefoundationstiffnessmaybeusedinthedynamicanalysescarriedoutforthestructuraldesignoftheplat-formsuperstructure(shaftsorlegsandtopside).RotationalStiffnessoftheTroll-APlatform

TheTroll-AplatformisahugeconcretegravitybasestructurelocatedintheNorwegiantrenchatawaterdepthof305m.Theplatformwasinstalledin1995.ThefoundationdesignperformedbyNGIisdescribedinHansenetal.(1992).

ThefoundationrotationalstiffnessandcyclicdisplacementsduringastormhavebeencalculatedusingtheNGIin-houseFEcodeINFIDEL(NGI1991)andtheAbaqusFEprogram.Theplat-formandtheFEmodelofitsfoundationareshowninFig.16.Symmetryandantisymmetrywereutilizedandaone-quartermodel

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Downloaded from ascelibrary.org by Nanjing University Of on 11/23/12. Copyright ASCE. For personal use only; all rights reserved.Fig.16.Troll-AplatformwithitsconcretegravitybasestructureandAbaqusmodelforcalculationoftherotationalstiffnessoffoundation

Fig.15.Resultsfromsuctionanchorskirtpenetration:(a)build-upofhorizontalstressesoutsidetaperedskirttipduringself-weightpenetra-tion;(b)meanstressdistributioninhorizontalcrosssectionat13.7mdepthforsituationwhereskirtisbeingpenetratedtoitsfinaldepthof16m

ofthefoundation,includingthefourshafts,the19concretecais-sons,andthe36-m-deepconcreteskirtsprotrudingintothesubsoil,wasestablished.Thesoillayeringisshownwithdifferentcolorsdownto100m.Infiniteboundaryelementswithinitialstiffness(notshown)areusedaroundthemodelperiphery.TheFEone-quartermodelhas1.3milliondegreesoffreedom.

Thestiffnessiscalculatedforvariousstagesofcyclicloading,i.e.,onecycleofthemaximumwave(N¼1),or300cyclesofthemaximumwave(N¼300).Fig.17(a)showsthecalculatednor-malizedplatformrotationasafunctionofthenormalizedoverturn-ingmoment,andFig.17(b)showsthesecantrotational(rocking)stiffnessduringthemomentloading.Notethattherotationalstiff-nessrepresentsthecyclicdisplacementamplitudeduringthemaxi-mumwaveasafunctionofthemaximumwaveloadamplitudeandis,thus,nottheload-displacementbehaviorinindividualcycles.Becausethesoilisdegradedduringrepeatedcyclicloading,thestiffnessislowerforthe100-yeardesignstorm(N¼300)thanduringtheapplicationofonecycle(N¼1).Nonlinearstress-strain

Fig.17.RotationalstiffnessofTroll-Aplatform,duringinstallation(N¼1)andfor100-yeardesignstorm(N¼300)fromAbaqus3DFEA:(a)overturningmomentamplitudesversusrotation;(b)secantrotationalstiffnessversusoverturningmoment

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Downloaded from ascelibrary.org by Nanjing University Of on 11/23/12. Copyright ASCE. For personal use only; all rights reserved.Fig.18.DeformedmeshandcontourshadingsofdeformationduringapplicationofmaximumwaveloadingfromAbaqusmodelofTroll-Aplatform;maximumdisplacementatshaftlevel110maboveseabedis~10cm

relationshipsofthetypesshowninFig.6fortherelevantNandτawereusedtoobtaintheseresults.

Insomecases,thefoundationmayberegardedasrigidcomparedtothesoilstiffness;thosecasesdonotrequireanysophisticatedmodelingofthestructure.However,inothercases,theremaybeconsiderableflexibilityinthestructureandinitsfoundations.Inthesecases,itmaybenecessarytoperformamoresophisticatedsoil-structureinteractionanalysiswithrealisticrepresentationofthestructuregeometryandstiffness.Fig.18showsanexampleinwhichtheflexibilityofthestructurerelativetothesoilissignificantandonwhichafullSSIanalysishasbeenperformed.Thefigureshowstherotationandcontourshadingsofdeformationduringapplicationofthemaximumwavemoment.

RotationalStiffnessoftheShahDeniz“Jack-Up”Foundations

TheShahDenizplatformisapermanentsteeljack-upunit(TPG500conceptfromTechnip)locatedintheCaspianSeaatawaterdepthof~100m.Thejack-uplegsarefoundedonlargesteelbucketfoundations,asshowninFig.19.Thethreefoundationsare30mindiameterandequippedwithcorrugatedsteelskirtsthatarepenetrated9mintotheseabed.Thesoilconditionsaremainlysanddownto18mdepthandclayunderneath.

Theloaddistributionbetweenthelegsandthemaximumleg-momentduringastormishighlydependentontherotationalstiff-ness(fixity)ofthefoundations.Anincreasedfixityreducestheleg-momentandalsothelateraldisplacementofthetopside.Thedynamicloadamplificationisalsodependentonthedynamicfoun-dationstiffness.Theassessmentofthestaticanddynamicfounda-tionstiffnesswas,therefore,akeyactivityinthedesignofboththeplatformanditsfoundations.Acomplicatingfactorwasthatthelarge-diameterfoundations,andinparticular,thetopplates,werequiteflexiblerelativetothesoil.

Thefoundationstiffnesswascalculatedby3DFEAusingtheBIFURC3D(NGI1999)in-houseprogram.Nonlinearelasticstress-strainrelationshipsofthetypesshowninFig.6wereusedforboththeaverageMaandthecyclicMcymomentloading.Fig.19(b)showsthe3DFEmodel.Thefoundationwasmodeledwithshellelements,withinterfaceelementsbelowthetopplate

Fig.19.(a)TPG500jack-upplatform;(b)FEmodelof30-m-diameterskirtedanchor

andalongthein-andoutsideoftheskirtwalls.Prescribeddis-placementswereappliedoverthetopplate.Becauseofthehighlynonlinearbehavior,aniterativeprocedurewasusedwherethedeflectionpatternuðx;yÞofthefoundationtopplatewascalculatedbytheTechnipstructuralengineers,basedonsoilspringscalcu-latedbyNGI.

ConsolidationSettlements

Foundationdesigngenerallyinvolvesestablishingthetime-settlementrelationshipduringthelifetimeofthestructure.Thisbecomesespeciallyimportantforgravitybaseplatformsonclaywherethelargeweightcancausesubstantialsettlementsandthelowpermeabilitymaycausetheconsolidationprocesstolastsev-eralyears.

Time-SettlementforaGravityBasePlatform

Inthissection,anexampleisgivenfortheFEanalysisofthetime-settlementrelationshipforagravitybaseplatformandforthe

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Downloaded from ascelibrary.org by Nanjing University Of on 11/23/12. Copyright ASCE. For personal use only; all rights reserved.Fig.21.IllustrationofredistributionofaveragestressfromaskirtedGBSfoundationduringcyclicloading:(a)FEmodel;(b)concentrationofaverageshearstressunderthetipafterapplicationofweightloadingW0;(c)reductionofaveragestresses(weight)underskirttip;(d)in-creaseofaveragestresses(weight)underneathbaseduringcombinationofweightW0andcyclicloadingVcy

SoilReactionDistributions

Fig.20.(a)Cam-claytypeofstress-strainrelationship;(b)1styearloadinghistoryandverticalsettlementsforgravitybaseplatform(GBS)andnearbyseabed,calculatedbyFEA

seabedinthevicinityoftheplatform.Thesettlementoftheseabedwasusedasinputinthedesignofapipelineconnectiontotheplatform.

Theinputdatafortheanalysisarethegeometry,soillayering,soilpermeabilityandstiffness,drainageconditions,andtheloadhistory.Thepermeabilityandstiffnessarebothstress-dependent.Cam-clay-typemodelsliketheoneshowninFig.20(a)arewell-suitedforrepresentingstress-dependentstiffnessandhavememorythataccountsforpreconsolidationstress.

Fig.20(b)showsthefirstyearloadhistoryandcalculatedset-tlementsforthegravitybaseplatformandforpointsontheseabed5,10,15,and20mofftheplatform.Thefullycoupledporepres-suredissipationandequilibriumanalyseswereperformedusingthePlaxisFEprogramwithacam-clay-typematerialmodel.Theloadhistoryreflectsthegraduallyincreasingballastweightduringthefirst90daysafterinstallation.Onecycleofon-andoff-loadingrepresentsthesituationwheretheplatformisfilledtomaximumweightwithliquidnaturalgasandthenoff-loadedtotheaverageweight.Itcanbeseenthattheplatformsettles~80cmduringthefirstyear,whereasthesurroundingseabedgenerallysettles10–20cm.Thepipelineconnectionwasthendesignedforarelativesettlementof70cmoverthenearest20mfromtheplatform.Otherimportantcomponentscontributingtothetotalsettlementofoff-shorefoundations,likeimmediatesettlements,creep,andeffectsofcyclicloading,arenotconsideredhere.

Forthestructuraldesignofthefoundations,thedistributionofreactionstressesonthefoundationforthedifferentloadingcondi-tionsmustbeknown.Aspectsthatareofparticularinterestmaybethedistributionofcontactstressunderneaththebaseandhowmuchoftheloadiscarriedbytheskirtwallandskirttipcomparedtothebase.Normally,soilreactionsareprovidedtothestructuralengi-neersintheformofanumberofpossibledistributiondiagramsforasetofunitloadcases.Thereareaspectssuchasunevenseabed,installationeffects,andredistributionwithtimethatmakeitverydifficulttoaccuratelycalculatereliabledistributions.Thereactionsare,therefore,inmostcases,basedonengineeringjudgmentandconservativeestimatestoprovidearobuststructuraldesign.FEAmay,however,providevaluableinsightintothemechanismsofloadtransferbetweenthefoundationandthesoil.ForskirtedgravitybasefoundationssuchastheoneshowninFig.21(a),themaininterestistoassessthefractionofthesubmergedweightcarriedbybasecontactstresses,skirtfriction,andskirttipresistance,respectively.AreasonableestimatemaybeprovidedbyapplyingthesubmergedweightW0toaFEmodelsuchastheoneshowninFig.21(a)forthesubsoilandthefoundationwithbaseandskirts.

RedistributionduringCyclicLoading

Theloadswill,however,redistributewithtime.Duringcyclicload-ing,therewillbeatendencyforredistributingweightfromtheskirtstothebase.Thisisaresultofthedegradationofstrengthandstiffnessforcombinationsofaveragestress(causedbytheweight)andcyclicstress.AconstitutivemodelforcyclicloadinghasbeendevelopedatNGIinwhichtheinputisdiagramsofthetypeshowninFig.6.ThismodelhasbeenusedinFEAofthisloadtransfermechanismfromskirttobase.ThemechanismisillustratedinFig.21(b).Thesoilbelowtheskirttipishighlymobilizedasa

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resultofweightloadingandhastoreducetheaveragestresses(weight)whenthecyclicstressesincrease.Otherpartsofthefoun-dation,suchasthebase,arelessmobilizedbyweightloadingandmayincreaseboththecyclicandtheaveragestresses,i.e.,carrymoreoftheweight.

Soil-StructureInteraction

Structuraldesignofoffshoreplatformsisoftenbasedonhighlysimplified,uncoupledfoundationbehavior.Inreality,theremaybealargedegreeofinteractionbetweenthebehaviorofthesoil,thefoundations,andthesuperstructure.Insomecases,andinparticular,forquiteflexiblestructuressuchasjack-ups,thereisapotentialbenefitofaccountingforthisinteraction.Inthissection,anexampleisgivenofafullSSIanalysisofajack-upplatformusingFEA.

MomentFixityofaJack-UpPlatform

Three-leggedjack-upunitsfoundedonspud-cansarewidelyusedoffshoreasmobiledrillingunits.Intheconventionaldesign,thespud-canreactionforcesareobtainedfromastructuralanalysiswithpinnedfootingconditions.Thereisapotentialbenefitinaccountingfortherotationalstiffnessofthefootingsbecauseanincreasedrotationalstiffnesswillreducethemaximumbendingmoment,hulldisplacement,anddynamicloadamplification.Ac-countingforverticalandhorizontalflexibilityofthefootingswill,ontheotherhand,havetheoppositeeffect.

InJostadetal.(1994)aFEAprocedureispresentedforanintegratedanalysisofajack-upplatformanditssoilfoundationsystemwherethenonlinearrelationshipbetweenthespud-candisplacementsandreactionforcesisincorporated.Redistributionofthereactionforcesbetweenthespud-cansisalloweduntiltheoverallbearingcapacityofthejack-upplatformisreached.Theprocedureisbasedonthefollowing:

1.Thecyclicforcedisplacementcharacteristicsofthespud-canarecalculatedbyFEAusingthe3DcodeINFIDEL(NGI1991)andstress-strainrelationshipsofthetypeshowninFig.6orFig.22(b).

2.The3Dbearingcapacityenvelopes(V,H,M)areestablishedbyalimitingequilibriumanalysisasproposedbyAndersenandLauritzen(1988).

3.ThecyclicforcedisplacementcurvesandthebearingcapacityenvelopesareimplementedintoanonlinearstructuralFEprogramforthesoil-structureinteractionanalysisofthejack-up.

Thepotentialbenefitoftheprocedurewasdemonstratedbyanexamplecalculation(JostadandAndersen2006)ofathree-leggedjack-uprigoftheGorillaClass,installedinastiffclaysiteatawaterdepthof94m.Therighasalongitudinallegspacingof56mandatransverselegspacingofm.Theavailableleglengthbelowthehullis132m.Theweightoftheplatformduringoper-ationis204MN,whichgivesanaveragelegloadof68MN.Thegeometryofthespud-can,includingtheproposedskirtconfigura-tion,isshowninFig.22(a).Themomentfixitywasincreasedbyequippingthefootingswithskirtsthatpenetrateintothesoil.Theinnerandoutercircularskirtsarestiffenedby12radialsteelplates,withthicknessof10mm,connectedtothespud-cantip.

Thedesignstormisa6-hstormwitha50-yearreturnperiod.Theequivalentmaximumlumpedcharacteristicenvironmentalloadcausedbywaves,wind,andcurrentis33.5MN.Theloadaccountsfordynamicamplificationassumingpinnedfootings.Thestiffclayprofilehasanaverageundrainedshearstrengthsavuof60kPathatisconstantwithdepth.Theoverconsolidationratiois40inthe

Downloaded from ascelibrary.org by Nanjing University Of on 11/23/12. Copyright ASCE. For personal use only; all rights reserved.Fig.22.(a)20-m-diameterskirtedspud-canfootingforjack-upplatform;(b)normalizedcyclicshearstressversusshearstraincurvesforclay

top5mand4below5mindepth.Bythestrainaccumulationpro-cedure,itisfoundthattheequivalentnumberofcyclesNeqvis~10fortheupperclaywithOCR¼40and~7fortheclaybelow5mdepthwithOCR¼4.Thecorrespondingnormalizedcyclicstress-strainrelationshipsareshowninFig.22(b).

Thecyclicload-displacementrelationshipsfortheindividualfoundationsarecomputedbythe3Dfinite-elementprogram,INFIDEL.Becausetheloadsontheindividualfootingsdependonboththestiffnessofthestructureandtheloadpath-dependentnonlinearstiffnessoftheindividualfootings,theanalysesareperformedbyintegratedSSIanalysesasdescribedinJostadetal.(1994).

ThemainresultsfromtheseSSIanalysesarethemaximumhorizontalcyclicdisplacementcomponentofthehull,thecriticalmomentintheleg,andtheglobalbearingcapacityofthejack-upplatform,asfunctionsoftheloadfactorpmultipliedbythecharacteristicenvironmentalload.Theanalysesgive,inaddition,displacementsandrotationoftheindividualfootingsandthecor-respondingreactionforces.ResultsforthewindwardandleewardlegsareshowninFigs.23(a)and23(b).

FromFig.23(a),itcanbeseenthattheloadfactorp,wherethemomentinthelowerlegguidebecomescritical(i.e.,equalto1GNm),isincreasedbyapproximately16%byequippingthespud-canswithskirts.Theresultswithoutskirtsare,inthiscase,aboutthesameasforpinnedfootings.Furthermore,itwasfoundthat,byusingskirts,theglobalbearingcapacityofthejack-upplat-formwasincreasedby~60%.

Thistypeofanalysisinvolvingloadpath-dependentnonlinearanalysesofembeddedcircularfoundationsinalayeredsoilforallloadlevels,includingthecombinationoftheaverageverticalloadandthecyclicloadsthatcausefailure(largedisplacements)oftheindividualfoundation,ispracticallyimpossiblewithoutusingthefinite-elementmethod.

Int. J. Geomech. 2011.11:417-430.

properties.Thisframeworkisvalidatedbycomparisonstofieldandlaboratorymodeltestsandprototypestructures(e.g.,Andersenetal.19,1993)andhasbeenusedsuccessfullyincombinationwithlimitingequilibriumandfinite-elementanalysesinfoundationdesignfornumerousoffshorestructuressafelyoperatingallovertheworld.

Thefinite-elementmethodisincreasinglyused,offeringseveralbenefitsoverthelimitingequilibriummethod.Inthispaper,exam-plesarepresentedwhereFEAshaveprovedtobefavorable.

Acknowledgments

Downloaded from ascelibrary.org by Nanjing University Of on 11/23/12. Copyright ASCE. For personal use only; all rights reserved.Thispaperisarevisedversionofapaperoriginallypresentedatthe12thIACMAGconferencein2008.Thewriterswouldliketothankallcolleagueswhocontributedtothiswork.Wethankourcolleague,Mr.KristofferSkau,whocarriedouttheAbaqusanaly-sisfortherotationalstiffnessoftheTrollplatform.

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SummaryandConclusions

Inthispaper,variousaspectsofthedesignoffoundationsandan-chorsforoffshorestructuresusedinoilandgasexploitationhavebeenpresented.Themaindifferencebetweenonshoreandoffshorefoundationdesignisthattheoffshorefoundationsarealwayssub-jectedtocyclicloadingwhichmaycausesoilstrengthandstiffnessdegradation.Inoffshoregeotechnics,wearealsomostlydealingwithsaturatedsoil.

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