ANALYSIS OF PILED RAFT SYSTEMS IN LAYERED SOILS

INTERNATIONALJOURNALFORNUMERICALANDANALYTICALMETHODSINGEOMECHANICS.VOL.20,57-72(1996)ANALYSISOFPILEDRAFTSYSTEMSINLAYEREDSOILSL.D.TAANDJ.C.SMALLSchoolofCivilandMiningEngineering,UniwrsiwofSydney.NSW2006.AutraliaSUMMARYThispaperpresentsamethodofanalysisforpiledraftsystemsconstructedinlayeredsoils.Themethodpresentedtakesaccountoftheinteractionsoftheraft,pilesandsoilwithoutthecostofafullthree-dimensionalrigorousanalysis.Thisisdonebytheuseoffinitelayermethodsfortheanalysisofthesoilandfiniteelementmethodsfortheraft.Examplesareprovidedinthepaperforpiledraftsconstructedonlayeredsoils,andresultsarepresentedforbendingmomentsintheraftandloadsinthepiles.KEYWORDS:piledraftsystems;raft-pile-soilinteraction;finitelayermethods;foundationsINTRODUCTIONPiledraftfoundationsarecommonlyusedtosupportthesuperstructuresofbridges,buildingsandheavyindustrialplant.Foundationengineersneedtoknowhowthestructuralloadistransmittedtothesupportingsoilandhowthestructuralloadistransferredtothepilesandsoilbeneath.Theyalsoneedtobeabletocomputethedifferentialdisplacementsandmomentsintheraft.Severalmethodshavebeenproposedforanalysingpiledraftsystems.EarlyworkwascarriedoutbyDavisandPoulos.'Theirmethodwasbasedonpiletopileandpiletosoilsurfaceinteractionsanduiceuersa.ButterfieldandBaneqee'analysedpilecapswithcompressiblepilesusingasimilarmethod.Thesemethodsarelimitedhowever,torigidraftsonly.BrownandWeisner3analysedastripfootingunderauniformlydistributedloadandassumedthatthesoilwasanisotropichomogeneouselastichalf-space.Later,WeisnerandBrown4analysedapiledstripfootingsubjecttoconcentratedloads.HainandLee5usedthefiniteelementmethodtoanalysetheraft,andpilegroupinteractionfactorstoanalysethepilebehaviour.Poulos6proposedthefinitedifferencemethodforanalysisoftheraftinapiledraftsystem.ThispaperextendsthemethodofanalysisforpilegroupsinlayeredsoilwhichwasdescribedbyTaandSmall,'wherethesoilismodelledusingthefinitelayerTheraftismodelledusingthefiniteelementmethodandtreatedasathinelasticplate,andthereforethepresentmethodcanbeusedtoanalysearaftwithanygeometryandanystiffness.Thesoilcanbeconsideredtobeanisotropicorcross-anisotropichorizontallylayeredmaterialandthepilesmayberandomlydistributedbeneaththeraft.METHODOFANALYSISTheraftisassumedtobeathinelasticplateandthefiniteelementmethoddescribedbyBognerelal.isusedtoanalyseit.Theraftisdividedintoanumberofrectangularelements(seeFigurel(a)),eachelementhavingfournodesand16degreesoffreedom.Thecontactloadpressuresbetweentheraftandthesoilsurfaceandbetweentheraftandthepileheadsareassumedtobeuniformblocksofpressurewhichactovereachelementintheraft.DisplacementsatthecentreofCCC03639061/96/010057-1601996byJohnWiley&Sons,Ltd.ReceivedI7MarchI995RevisedISJune199558L.D.TAANDJ.C.SMALLfa)PiledraftsystemIPabi(b)AxialloadsonpilesFigure1.Forcesconsideredtoactonthepilesandonthesoil(c)loadsonthesoileachraftelementcanbeexpressedas''or=[IrlQr+a6+be,+COY+op0(1)where[Ir]istheinfluencematrixofthepinnedraft,thecolumnsofwhicharethedeflectionsatthecentersofallraftelementsduetoaunituniformloadplacedoneachraftelementinturn,Qrthecontactloadpressuresontheraft,oqothevectorofdeflectionsatthecentreofeachraftelementforthecaseofthepinnedraftactingundertheappliedloads,a=(1,1,...,l)T,6theverticaltranslationoftheraftatthepin,8,thex-rotationoftheraftrelativetothepinand8,they-rotationoftheraftrelativetothepin,if(x,,y,)arethexandyco-ordinatesofthepinand(xi,yi)aretheco-ordinatesofthecentreofeachraftelement,thentheleverarmvectorsbandccanbewrittenasfollows:Tb=(YI-~p,y2-yp,**.9yi-yp,.*.vyn-Y,)c=(XI-X,,x2-x,,...,xi-x,,...,X-xp)TTheraftmustberestrainedfromfreebodyrotationsandtranslationstoallowtheinfluencematrixtobeassembled,andsoitmustbe'pinned'atonenode.ANALYSISOFPILEDRAFTSYSTEMSINLAYEREDSOILS59Thepilesareassumedtohaveasolidcircularcross-sectionandeachpileisdividedintoanumberofelements.Theload-displacementrelationshipofthegroupofpilesmaybewrittenasfollows:Qp+Pp+Ppb=CKpIwp(2)where[K,]isthestiffnessesofallpilesinthegroup,wpthevectorofdisplacementsattheendsofeachpileelement,Qpthevectorofloadsactingonthepileheads,PpthevectorofloadsactingalongthepileshaftsandPpbthevectorofloadsactingatthepilebases.Thesoilisdividedintoanumberoflayers.Theloadsonthesoilcanbeconsideredastwodifferenttypes.Thefirstistheloadwhichistransmitteddirectlyfromtherafttothesoilsurface,calledthecontactload,Q,.Thesecondistheloadthatistransmittedfromtherafttothesoilthroughthepileshafts,referredtoasfrictionloads,P,,andthebaseloads,P,b.TheloadP,isconsideredtobeaseriesofringloadsalongthepileshaftsandPubisconsideredtobeauniformpressureatthebases.Hence,thesoildisplacementrelationshipcanbewrittenasfollows:QsPsPsb=CKsIOs(3)where[K,]isthesoilstiffnessmatrixanda,thevectorofsoildisplacementsforalltheelementsatthetopsurface,alongthepileshaftsandthepilebases.Equations(2)and(3)canbecombinedandwrittenasfollows:Qp+Qs+PpPs+pbpPsb=CKpIOpCKsIOs(4)Theequilibriumoftheinteractionatthepile-soilinterfacerequiresthatandPP=-P,Ppb=-Psbandassumingthereisnoslipalongtheshaftsthentheverticaldisplacementsatthepile-soilinterfaceswillbethe