Copyright2012byBentleySystems,Inc.Version7.0Revision1
1.0INTRODUCTION
1.1OVERVIEW
PSI,PileStructureInteraction,analyzesthebehaviorofapilesupportedstructuresubjecttooneormorestaticloadconditions.Finitedeflectionofthepiles("Pdelta"effect)andnonlinearsoilbehaviorbothalongandtransversetothepileaxisareaccountedfor.Theprogramusesafinitedifferencesolutiontosolvethepilemodelwhichisrepresentedbyabeamcolumnonanonlinearelasticfoundation.Thestructurerestingonthepilesisrepresentedasalinearelasticmodel.
PSIfirstobtainsthepileaxialsolution,thenusestheresultinginternalaxialforcestoobtainthelateralsolutionofthepiles.Ingeneral,soilsexhibitnonlinearbehaviorforbothaxialandtransverseloads,thereforeaniterativeprocedureisusedtofindthepileinfluenceonthedeflectionofthestructure.
1.2PROGRAMFEATURES
PSIisdesignedtousepileandsoildata,specifiedinaninputfile,inconjunctionwithlinearstructuraldataproducedbytheSACSIVprogram.AmongthefeaturesofPSIarethefollowing:
1. TubularandHpilecrosssectionssupported.
2. Pilemayhavevaryingpropertiesalongitslength.
3. Soilaxialbehaviormayberepresentedbyadhesiondata,nonlinearTZdata,orasalinearspring.
4. Endbearingeffectsmaybeaccountedfor.
5. SoillateralbehaviorrepresentedbynonlinearPYcurves.
6. BasicsoilpropertiesmaybeusedtogeneratethesoilaxialpropertiesintheformofTZcurvesoradhesiondata,endbearingTZdataand/orlateralsoilpropertiesintheformofPYcurves,basedonAPIRP2Arecommendations.
7. Soilstratificationmaybemodeled.
8. Mudslideconditionsimulationcapabilities.
9. Completesoilpropertyplotcapabilities,includingPY,TZandadhesiondata.
10. Analysisresultsplotcapabilities,includingdeflections,rotations,loads,reactions(soilandpile),andunitycheckratiosplottedalongthepilelength.
11. Createsuptotwoequivalentlinearizedfoundationsuperelementstobeusedbydynamicanalysesinlieuofpilestubs.
12. ImplementationofAPIRP2A20Editionsoiladhesion,TZandPYdatagenerationbasedonbasicsoilproperties.
13. Createsfoundationsolutionfilecontainingpilestressestobeusedforfatigueanalysis.
14. Allowstheusertodesignateloadcasestobeusedforpilecapacityandcodecheckcalculations.
ThePileandPile3Dprograms,whicharesubprogramsofPSI,maybeexecutedalonetocalculatethebehaviorofasinglepile.Inadditiontothefeaturesoutlinedabove,thePileprogramhasthefollowingfeatures:
1. Determinesanequivalentpilestubthatyieldsthesamedeflectionsandrotationsasthesoil/pilesystem.
2. AllowstheapplicationofforcesandmomentsobtainedfromSACSanalysestocreateapostfiletobeusedforasubsequentfatigueanalysis.
2.0CREATINGPSIINPUTThenonlinearfoundationmodel,includingthepileandthesoilproperties,isspecifiedseparatefromthemodelinformationinaPSIinputfile.
TheinterfacejointsbetweenthelinearstructureandthenonlinearfoundationmustbedesignatedintheSACSmodelbyspecifyingthesupportconditionPILEHDontheappropriateJOINTinputline.TheanalysisoptionPImustbespecifiedeitheronthemodelOPTIONSlineordesignatedintheExecutive.
2.1DEFININGANALYSISOPTIONS
Pile/SoilinteractionoptionsareinputonthePSIOPTline.
2.1.1GeneralOptions
Generaloptionssuchastheupwardverticalaxisandtheunitsarespecifiedincolumns89and1012,respectively.CEmaybespecifiedincolumns1718tohavetheprogramcontinuetheanalysisregardlessoferrorsencounteredintheiterationprocedure.
2.1.2AnalysisOptions
Thefinalpilestressanalysisoptionisdesignatedincolumns2324.Thepile/structurecoupledinteractionanalysismaybeskippedbyspecifyingSKincolumns1920.Likewise,thesolutionfinetuningproceduremaybeskippedbyenteringNAincolumns2122.
2.1.3ConvergenceandToleranceCriteria
Thedisplacement,rotationandforceconvergencetolerancesaredesignatedincolumns2532,3340and6772,respectively.Themaximumnumberofiterationsforapilehead,if
otherthan20,maybespecifiedincolumns4143.Solutioniterationcontinuesuntileachdegreeoffreedomatthepileheadhasconvergedtowithinthespecifiedtolerancesoruntilthemaximumnumberofiterationshasbeenexceeded.Enter'N'incolumn15ifequilibriumrelaxationisnottobeused.Equilibriumrelaxationimprovesthechancesofconvergence.
2.1.4PileOptions
Thepileunitweightmaybedesignatedincolumns7380iftheeffectofthepileweightistobeincludedintheanalysis.Thenumberofincrementsthatthepileistodividedintomaybeoverriddenincolumns6264.
2.1.5OutputOptions
Thepilestiffnesstables,reducedstiffnessmatrixofthelinearstructureandthereducedforcevectormaybeprintedbyspecifyingPTincolumns4445,4647or4849,respectively.IntermediateiterationresultsandinputdatamaybeprintedbyspecifyingPTincolumns5051and5253,respectively.
AsampleofthePSIOPTlinespecifyingEnglishunitsandadensityof490follows:
2.1.5.1CreatingaPileSolutionFile
Asolutionfilecontainingpileinternalloadsandstressesateachincrementalongthepilemaybecreated.EnteredPPincolumns5455ontheOPTIONSlinetocreateasolutionfiletobereadbytheFatigueprogram.TheinlineSCFoptionusedtofactorstressesmaybespecifiedincolumns5658ontheOPTIONSline.
Note:TheFTGoptionshouldbespecifiedincolumns5658ifstressesaretobeunfactoredsothatoneoftheinlineSCFoptionsavailableinFatiguemaybeused.
ThefollowingPSIOPTlineindicatesthatafatiguesolutionfileistobeused.ThestressesarenottobefactoredbecausetheywillbefactoredbytheinlineSCFdesignatedintheFatigueinputfile.
AnauxiliarydetailpilefilemaybegeneratedbyenteringPFincolumns5455.
2.1.6DesignatingLoadCasesforPileCapacityandCodeCheck
Bydefault,allloadcasessolvedinthePSIexecutionareusedtocodecheckandcalculatepilecapacitysafetyfactors.TheusermaydesignatewhichloadcasesaretobeincludedorexcludedforthepurposeofpilecheckandcapacityusingtheLCSELline.
DesignatewhethertheloadcaseslistedaretobeincludedorexcludedbyenteringINorEX,respectively.Forexample,thefollowingspecifiesthatloadcasesOP08,OP09andEQ01aretobeexcluded.
2.2DEFININGPLOTOPTIONS
PlotoptionsaredesignatedonthePLTRQ,PLTPL,PLTLCandPLTSZinputlines.
2.2.1PlotData
DatatobeplottedisdesignatedonthePLTRQinputline.Soilinputdata,axialdeflection,axialload,axialsoilreactions,requiredpilethicknessandunitycheckratiomaybeplottedversuspilepenetration.Lateraldeflection,lateralrotation,bendingmoment,shearloadandlateralsoilreactionalongoraboutthepilelocalYandlocalZaxesmaybeplottedversuspenetrationinadditiontotheresultant.
Bydefault,foranyoftheresultplotoptions,foreachloadcaseaseparateplotisgeneratedforeachpile.PilestobeplottedmaybedesignatedonthePLTPLlinewhileloadcasestoplotmaybedesignatedonthePLTLCline.Alternatively,aplotenvelopeshowingthecriticalvalueforallloadcasesselectedmaybeplottedinsteadbyspecifyinganE(forenvelope)afterthedesiredoption.Plotappearanceoptionssuchasgridlinesandcrosshatchingmaybedesignatedalso.
Thefollowingrequestssoildataplotsalongwithlateralandaxialdisplacement,pileunitycheckandpileredesignplots:
2.2.2DesignatingPilestoPlot
Bydefault,plotsaregeneratedforeachpiledefinedinthePSIinputfile.PilestobeplottedmaybedesignatedonthePLTPLlinebespecifyingthepileheadjointnamesofthepilestobeincludedforplotting.Thefollowingdesignatesthatonlypilesdefinedbypileheadjoints4and8aretobeincludedinplots.
2.2.3DesignatingLoadCasestoPlot
Bydefault,allloadcasesareincludedforplotgeneration.IfloadcasesarespecifiedonthePLTLCinputline,thenonlyloadcasesspecifiedwillbeincludedforplottingpurposes.ThefollowingdesignatesthatonlyloadcasesOP00andST90aretobeplotted.
2.2.4OverridingPlotSize
Thedefaultplotpapersize,charactersize,crosshatchingspacingandnumberofcolorsmaybeoverriddenusingthePLTSZline.
2.3DEFININGTHEPILE
Thegeometryandcharacteristicsofpilesandconductorsbelowthepileheads,includingsectionandmaterialproperties,pilebatter,pilechordangle,weightperunitlengthandseveraldimensionoverridesareincludedinthePSIinputfile.
2.3.1PileSectionProperties
SectionpropertiesfortubularsectionscanbecalculateddirectlyfromtheoutsidediameterandwallthicknessinputonthePLGRUPlineorcanbedefinedonthePLSECTline.Nontubularsectionsand/ortubularsectionswithuserdefinedstiffnesspropertiesaredefinedusingPLSECTlines.
WhenasectionlabelisspecifiedonthePLGRUPline,thepropertiesaredeterminedfromtheinputonthecorrespondingPLSECTline.Fortubularsections,thesectionlabelfieldshouldbeleftblankwhensectionpropertiesaretobedeterminedfromtheoutsidediameterandwallthicknessspecifiedonthePLGRUPline.
WhendefiningsectionpropertiesusingaPLSECTline,theuniquecrosssectionlabelreferencedbyasubsequentPLGRUPlineandthecrosssectiontypearerequiredincolumns814and1618,respectively.Thecrosssectiondimensionsmustbespecifiedincolumns5174.
ThePSIprogramcalculatesthecrosssectionstiffnesspropertiesbasedonthecrosssectiondimensionsinput.Thecalculatedstiffnesspropertiesmaybeoverriddenincolumns1948.Likewise,theunitweightspecifiedonthePSIOPTmaybeoverriddenincolumns7580.
ThefollowingdefinesthepilesectionnamedH47asanHsection:
2.3.2PileGroupProperties
Pilegrouppropertiessuchasmodulusofelasticity,shearmodulus,andyieldstressarespecifiedontheappropriatePLGRUPline.ThegrouptowhichapileisassignedisdesignatedonthePILEline.
2.3.2.1PileGroupEndBearingArea
TheeffectiveendbearingareaisspecifiedonthePLGRUPlineincolumns7580.Theusermayspecifyendbearingareaforeachpilesegmenttomodelasteppedpile.NormallyonlythePLGRUPlinecorrespondingtothebottomsegmentofthepilewillhaveendbearingareaspecified.
2.3.2.2SegmentedPileGroups
AseriesofPLGRUPlineswiththesamegrouplabelareusedtodefinethepropertygroupofasegmentedpile.Eachinputlinecorrespondstooneofthesegmentsofthatpilegroup.Materialpropertiesofthesegmentinadditiontothesegmentlengtharerequired.
Forexample,thefollowingdefinesa200foottubularpilegroupnamedPL1consistingoftwosegments.Thefirstsegmenthasawallthicknessof1.5andyieldof50.0whilethesecondhasawallthicknessof0.75andayieldof36.0.Thelengthofthefirstsegmentis50feetwhilethesecondis150feetlong.Endbearingareaisdefinedforthesecondsegmentonly.
Note:Thelengthofeachsegmentmustbespecified.Also,althoughthelocalXaxisofthepileisupfromthepileheadjointtowardthereferencejoint,segmentpropertiesareassignedfromthepileheadjointdownalongthepile.Intheaboveexample,thefirst50feetfromthepileheaddownisdefinedas60x1.5.
2.3.2.3PileGroupSurfaceDimensionOverrides
Bydefault,theactualdimensionsofthepileareusedtocalculatesoilresistance.Thesurfacedimensionofapilegroup,usedforsoilresistancecalculations,maybeoverriddenonthePLGRUPlineincolumns5869.Fortubularpiles,theODandwallthicknessarerequired,whiletheeffectivewidthanddepthareinputforHsections.
2.3.3DefiningPileElements
PileelementsarespecifiedonPILElinesfollowingthePILEheaderinputline.Thepileelementisnamedbythepileheadjointinthemodeltowhichitisattached.Thepileheadjointtowhichthepileisattachedisspecifiedincolumns710.Thepilegrouptowhichthepileisassignedisspecifiedincolumns1618.
Note:PileheadjointsmustbedesignatedassuchintheSACSmodelfilebyPILEHDincolumns5560onthecorrespondingJOINTline.
ThesoilIDdefiningpile/soilinteractionpropertiesinthelocalXZplaneisdesignatedincolumns6972.IfthesoiltableforlocalXYplaneinteractionisdifferentfromthatoftheXZplane,theapplicablesoilIDmustbespecifiedincolumns7477.
Thefollowingdefinesapileconnectedtopileheadjoint2.ThepileisassignedtopilegroupPL1andusessoiltableSOL1.
2.3.3.1PileBatter
Thepilebatterisdefinedbyeitherabatterdefinitionjointspecifiedincolumns1114orbatterdefinitioncoordinatesspecifiedincolumns2150onthePILEline.Thebatterofthepiledesignatedbelowisdefinedusingthepileheadjointandjoint201.
Note:Whenspecifyingabatterdefinitionjoint,thebatterdefinitionjointmustbeabovethepileheadjoint.Thepilewillbeorientedsuchthatthepileaxisliesonthelinethroughthebatterdefinitionjointandthepileheadjoint.
Batterdefinitioncoordinatesareusedtodeterminethepilebatterifnobatterdefinitionjointisspecified.TheglobalX,YandZdistancesfromthepileheadtoanypointaboveitlyingonthepileaxisshouldbeinputincolumns2130,3140and4150,respectively.Forexample,todefineapilebattered1:8intheglobalXZplaneandverticalintheglobalYZplane,battercoordinatevaluesofX=1.0,Y=0.0andZ=8.0shouldbeentered.
2.3.3.2PileLocalCoordinateSystem
ThepiledefaultlocalcoordinatesystemisdefinedwiththelocalXaxispointingupwardfromthepileheadjointalongthepileaxisdefinedbythepilebatterjointorbattercoordinates.
Bydefault,thelocalYandZaxisorientationsareloadcasedependent.Foreachloadcase,thelocalYaxisisautomaticallyorientedsuchthatitcoincideswiththedirectionofmaximumpileheaddeflection.Thefigureontherightillustratesthedefaultlocalcoordinatesystemofthepile.
TheorientationofthelocalYandZaxesmaybeoverriddenbytheuserbyspecifyingtherotationangleaboutthelocalXaxisincolumns5156onthePILEline.Inthiscase,thelocalYaxiswillnotbealignedinthedirectionofmaximumpileheaddeflectionbutwillbedefinedbytherotationangleasshowninthefigurebelow.
Note:ThepileanalysisisdoneinthelocalXZandXYplanes.Formudslidecases,apilerotationangleshouldbeusedinordertoorienteitherthepilelocalXZorXYplaneinthedirectionofthemudslide.
2.3.4PileClusters
Pilesdrivenincloseproximitytootherpilescanhaveadifferentcapacityfromasinglepileactingindependently.
Figure1a.showsapairofpilesincloseproximitytoeachother.Thereisatendencyforpilestoactasaunitinthedirectionofthelinejoiningthecentersofthetwopiles.Therefore,thecombinedresistanceforthetwopilesinthisdirection,islessthandoubletheresistanceofasinglepile.Intheotherdirection,however,thereisnosuchinteractionandthetwopilesbehaveindependently.
Figure1b.showsaclusteroffourpiles.Inthiscaseallfourpileswillhavereducedresistanceinbothdirections.
ThebehaviorofsuchclusterscanbemodeledbyreducingthePYcurvesinputforthedirectionswherethepilesactasasystemratherthanindependentpiles.
2.4MODELINGSOILPROPERTIES
2.4.1Overview
PSIallowstheusertospecifythepile/soilresponsetoaxial,lateral,andtorsionalloadsappliedatthepileheadthroughnonlinearloaddeflectioncurves(PYandTZcurves).Axialresistancecanalsobespecifiedintermsoflinearspringratesandsoiladhesionvalues.Inaddition,axialbearingcapacitymaybespecifiedatthepiletipandatarbitrarypointsalongthepile,whenmodelingpileswithvaryingdiameter.Inlieuofpilecapacitycurvesoradhesiondata,thecharacteristicsofthesoilmayalsobespecifiedintermsofbasicsoilproperties(unitweight,shearstrength,etc.),thattheprogramcanusetodevelopthepile/soilresponsebasedonAPIRP2Arecommendations.
ThePSIprogramrequiresthatthesoilpropertiesbedefinedinaspecificorder,namelyaxialresistance,bearingcapacity,torsionalresistancefollowedbylateralcapacity.Foraxial,bearingandlateralcapacity,thesoilcapacityorpropertiesmaybedefinedatvariouselevationsorsoilstratum.
Note:Whenmultiplesoilsaretobedefined,allpropertiesofthefirstsoilmustbedefinedbeforeanypropertiesofthenextsoilmaybespecified.
2.4.2SpecifyingElevationsforSoilResistanceCurves
Withinasoilstratum,thePSIprogramconnectstheinputPYorTZpointswithstraightlinestofullydefinethepile/soilinteractioncurveforarbitrarydisplacementsinthatstratum.Atdepthsbetweenspecifiedsoilstrata,PSIhastheabilitytolinearlyinterpolatebetweencurvesortouseaconstantTZcurve.
Whenthesoilpropertiesaretobeassumedconstantthroughoutthedepthofasoilstrata,thedistancesfromthepileheadtothetopandbottomofthestratashouldbothbespecified.Thecurvegeneratedisusedfortheentiredepthofthestrata.Whensoilpropertiesspecifiedapplyonlytoaspecificelevation,onlythedistancetothetopofthestratashouldbespecified.Thesoilcurvegeneratedappliesonlythespecificelevationdesignated.
Soilpropertiesatelevationswithoutresistancecurvesdefinedareobtainedbyinterpolatingbetweenthecurvesdefinedimmediatelyaboveandbelow.Forexample,thefirstSOILAPIAXLlineinthesamplebelow,specifiesthataxialsoilpropertiesfromelevation0.0to30.0areconstant.ThesecondSOILAPIAXLlinestipulatesthattheTZcurvesgenerateddefinessoilpropertiesatelevation60.0.Therefore,axialsoilpropertiesatelevationsbetween30and60willbedeterminedthroughlinearinterpolationbetweenthetwocurves.
2.4.3SoilAxialResistance
Foranysoil,thefirstpropertythatmustbedefinedistheaxialresistanceorcapacity.Axialloadsareresistedbydistributedlongitudinalsurfaceshearforcesalongthelengthofthepileandbyendbearingforcesattheendandatintermediatepointswherethepilesouterdiameterchanges.Axialresistanceforaparticularsolimaybespecifiedintermsofeitheralinearaxialspring,adhesion(skinfriction),oraxialloaddeflectioncurves(TZcurves).
2.4.3.1LinearAxialSpring
PileheadaxialbehaviormadebemodeledasalinearaxialspringatthepileheadusingtheSOILAXIALHEADinputline.ThesoilIDandthelinearstiffnessofthespringmustbespecifiedincolumns4144and3140,respectively.
Whenusingapileheadaxialspring,theaxialforceinthepileisassumedtolinearlydissipatefromthepileheadaxialforcetozeroattheendofthepile.Nootheraxialcapacitydataorbearingcapacitydatamaybespecifiedwhenassigninganaxialspringtoapilehead.
2.4.3.2GeneratingAdhesion&BearingCapacityperAPIRP2A
PSIcanautomaticallygeneratethepileaxialadhesionorskinfrictionandbearingcapacitybasedonAPIguidelinesfrombasicsoilcharacteristicsinputbytheuser.
TheSOILAXIALHEADlineisrequiredtogenerateskinfrictionandbearingcapacitiesfrombasicsoilcharacteristics.ThenumberofsoilstratatobedefinedandthesoilIDornamemustbespecifiedincolumns1820and4144,respectively.
Thepropertiesofeachstratamakingupthesoilarespecifiedimmediatelyfollowingtheheaderlineusingeitherthesand,clayorrocksoilaxialstratalinedesignatedbySOILAPIAXLincolumns112.TheAPIversionisinputincolumn13andthestratalocationlabelSLOCincolumns1417isrequired.Theverticaldistancefromthepileheadtothetopandbottomofthestrataarespecifiedincolumns1924and2530,respectively.Thesoiltypeandthesoilcharacteristicsareinputincolumns3277.
Note:Eitherasand,clayorrocksoilaxialstratalineisrequiredforeachsoilstratatobedefined.
Axialadhesioncapacityiscalculatedforeachsoilstratuminput.Beginningatthetopstrata,thelengthoverwhichtheadhesionmustacttodissipatetheaxialloadiscomputed.Ifthislengthislessthanthestratathickness,theaxialloadiscompletelydissipatedinthecurrentstrata.Iftherequiredlengthisgreaterthanthestratathickness,theexcesspileloadintothenextstratabelow.Theprocedureisrepeateduntilallofthepileloadisdissipatedoruntilallstratumhavereachedcapacity.Ifthetotalpileloadhasnotbeendissipated,theexcessloadistransferredbyendbearinguntiltheendbearingcapacityisreached.Ifthetotalaxialloadhasnotbeendissipated,thepilefails.
Note:Becauseendbearingdataisautomaticallygenerated,noendbearingdatashouldbespecifiedwhengeneratingaxialcapacityautomatically.
2.4.3.3UserDefinedAdhesionandBearingCapacityData
AdhesionandbearingcapacitydatamaydirectlyinputbytheuserusingtheSoilAxialAdhesionheaderline(namedSOILAXIALHEAD)andspecifyingthenumberofsoilstratum,theendbearingcapacityandthesoilID/nameincolumns1810,2130and4144,respectively.
ThedistancebetweenthepileheadandthetopandbottomofeachofthesoilstratummustbespecifiedontheSOILSLOCline(s)immediatelyfollowingtheheaderline.ThesoiladhesiondataforeachstrataisdefinedonthefollowingSoilAxialAdhesionCapacityline(s).
2.4.3.4GeneratingTZCurves&BearingCapacityperAPIRP2A
PSIcanautomaticallygenerateaxialloaddeflectioncurves(TZcurves)andbearingloaddeflectioncurves(QZcurves)basedonAPIguidelinesfrombasicsoilcharacteristicsinputbytheuser.
TheSOILTZAPIHEADlineisrequiredtogenerateTZandQZcurvesfrombasicsoilcharacteristics.ThenumberofsoilstratatobedefinedandthesoilIDornamemustbespecifiedincolumns1820and4144,respectively.
Thepropertiesofeachstratamakingupthesoilarespecifiedimmediatelyfollowingtheheaderlineusingeitherthesand,clayorrocksoilaxialstratalinedesignatedbySOILAPI
AXLincolumns112.TheAPIversionisinputincolumn13andthestratalocationlabelSLOCincolumns1417isrequired.Theverticaldistancefromthepileheadtothetopofthestrataisspecifiedincolumns1924.Thedistancefromthepileheadtothebottomofthestratamaybeoptionallyinputincolumns2530.Thesoiltypeandthesoilcharacteristicsarerequiredincolumns3277.
Note:Becauseendbearingdataisalsoautomaticallygenerated,noendbearingdatashouldbespecifiedwhengeneratingaxialcapacityautomatically.
2.4.3.5GeneratingTZCurvesUsingCPTBasedMethods
PSIcanautomaticallygenerateTZandQZcurvesbasedononeofthefourAPIrecommendedCPTbasedmethods,namelySimplifiedICP05,OffshoreUWA05,Fugro05andNGI05.ThechosenmethodisinvokedbyspecifyingoneofICP,UWA,FUGandNGIinColumns6264oftheSOILTZAPIHEADline.ACPTtooldiametershouldalsobespecifiedinColumns6672.ThesubsequentstrataaredefinedusingtheSOILAPIAXLlineswithCPTenteredinColumns3234.Inadditiontothedatarequiredforthedefinitionofthestratumlocationandtype,thefollowingsoilpropertiesaredefinedforeachCPTstratum(i)theconetipresistanceinColumns4247,(ii)theconstantvolumeinterfacefrictionangleinColumns5459and(iii)thesubmergedmassdensityinColumns4853.ThecoefficientoflateralearthpressuremaybespecifiedoptionallyforusagewiththeSimplifiedICPmethodinordertocalculatethesandrelativedensityusingtheTicinoSandrelationship.Ifthecoefficientoflateralearthpressureisnotspecified,thesandrelativedensityiscalculatedusingtheLunneandChristoffersonformula.
ItshouldbenotedthattheunitskinfrictionsthataregeneratedusingCPTbasedmethodsaredependentonpilegeometry.Furthermore,theunitskinfrictionsgenerallydifferintensionandcompression.
InaccordancewithAPIrecommendation,theunitendbearingisassumedtobefullymobilizedatz/D=0.1.Theunitskinfrictionisassumedtobemobilizedat0.1inches,consistentwithpreviousAPIrecommendationsforcohesionlessstrata.AzfactormaybespecifiedforusagewithCPTbasedmethodsusingColumns3440oftheSOILTZAPIHEADline.
Thefollowing(metric)exampleillustratestwoCPTstrata,thelatterofwhichhasdefinedaconetipresistanceof5.0MPaandaconstantvolumeinterfacefrictionangleof28degrees.TheCPTtooldiameteris3.56cmandtheaxialresistancecurvesaretobeconstructedusingtheSimplifiedICP05method.
2.4.3.6ApplyingAPIGeneralScourRecommendations
TheAPIguidelinesdefinegeneralscourasseabederosionduetowaveandcurrentaction.Generalscourcanaffectboththeaxialandlateralsoilresistance,duetodecreasesinconetipresistanceandverticaleffectivestress.
APIrecommendationspresenttwomethodsfortakinggeneralscourintoaccountwhencalculatingaxialresistance.Twomethodsarepresented,henceforthreferredtoastheNNIandFugromethods.Bothmethodsinvolvethedeterminationofascourreductionfactor,,whichfactorstheoriginalconetipresistancetogiveafinalconetipresistance:
TheNNImethod,specifiesthatthescourreductionfactoristheratioofthefinalverticaleffectivestresstotheoriginalverticaleffectivestress.TheFugromethodprovidesamorecomplicatedformulafor,andisrecommendedforhighgeneralscourdepthsandnormallyconsolidatedsands.
TherearealsoAPIrecommendationsfortakinggeneralscourintoaccountwhencalculatinglateralresistance.Thescourbringsaboutareductioninlateralsupportdueto(i)adecreasedverticaleffectivestressand(ii)adecreasedinitialmodulusofsubgradereaction(ES).
TheSCOURlineprovidesameanstospecifyadepthforgeneralscour.ThegeneralscourdepthisappliedtoallpilesinthemodelandisspecifiedinColumns914oftheSCOURline.TheaxialsoilresistanceisreducedbygeneralscouronlyforsoilsthathavebeendefinedusingCPTdata.Bydefault,theNNImethodisused,althoughtheFugromethodmaybeusedbyspecifyinganFinColumn7oftheSCOURline.ThelateralsoilresistanceisreducedforallcurvesgeneratedusingAPIrecommendations.Scourrecommendationsshouldonlybeappliedtocohesionlessstrata.Forthisreason,thegeneralscourdepthislimitedbythetopdepthofthefirstclaystratumoftherelevantlateralsoiltable.
UsergeneratedTZ,QZandPYcurvesareunaffectedbythegeneralscourspecification.
2.4.3.7UserDefinedTZCurves
TZcurvesdefiningthesoilaxialresistancemaybeinputdirectlybytheuser.TheSOILTZAXIALheaderlinedesignatingthenumberofsoilstratum,themaximumnumberofpointsonanycurveandthesoilIDornamemustinitiatetheTZcurveinput.
Foreachsoilstrata,thestratalocationlineandtheTZcurvedatafollow.Thestratatopandoptionallythebottomelevationareinputincolumns2530and3136oftheSOILSLOCline.ThenumberofpointsdefiningthecurveandtheTfactorusedtoscaletheforcevalueofallpointsspecifiedaredesignatedincolumns2223and3944,respectively.Ifthecurvehasthesameshapewhetherthepileisintensionorcompression,enterSMincolumns1819.
TheTandZdataforeachpointonthecurveareenteredontheSOILTZlineimmediatelyfollowingthesoilstratalocationline.Thenumberofdatapointsenteredmustcorrespondtothevaluespecifiedonthestratalocationline.
Note:Whenusingthesymmetricoption,onlypositivevaluesforTandZmaybeinputandtheorigin,T=0andP=0mustbethefirstdatapoint.
2.4.3.8UserDefinedBearingCapacityCurves
TZorQZcurvesdefiningthepileendbearingcapacitymaybeinputdirectlybytheuser.TheSOILBEARINGheaderlinedesignatingthenumberofstratumatwhichcapacitycurveswillbedefined,themaximumnumberofpointsonanycurveandthesoilIDornamemustinitiatetheendbearingcurveinput.
Foreachstratathatbearingcapacityistobedefined,thestratalocationlineandtheTZ/QZcurvedatafollow.Thestratatopandoptionallythebottomelevationareinputincolumns2530and3136oftheSOILSLOCline.ThenumberofpointsdefiningthecurveandtheTfactorusedtoscaletheforcevalueofallpointsspecifiedaredesignatedincolumns2223and3944,respectively.
TheTandZdataforeachpointonthecurveareenteredontheSOILTZlineimmediatelyfollowingthesoilstratalocationline.Thenumberofdatapointsenteredmustcorrespondtothevaluespecifiedonthestratalocationline.
Note:Bothpositive(endbearing)andnegative(suction)valuesmaybeentered.Userdefinedendbearingdatashouldnotbedefinedifsoilaxialresistancedataisgeneratedautomatically.
2.4.5SoilTorsionalResistance
Torsionalloadsareresistedbyadhesionvalues(skinfriction)alongthelengthofthepileorbyalinearspringvalue.Theresultingshearsactinthecircumferentialdirectionaroundtheperimeterofthepile.Torsionalresistancemustbespecifiedfollowingsoilbearingproperties.Ifthesoiltorsionalresistanceisnotspecified,thetorsionalstiffnessdefaultstoavalueequaltoGJ/L,whereListhelengthofthepile,GisthemodulusofrigidityofthepileatthepileheadandJisthetorsionconstantofthepilecrosssectionatthepilehead.Inaddition,awarningmessageisissued.
2.4.5.1LinearTorsionalSpring
Thetorsionalresistancemayberepresentedbyalineartorsionalspringatthepilehead.Thetorsionalspringstiffnessisspecifiedincolumns3140oftheSOILTORSIONHEADline.ThesoilIDornameisspecifiedincolumns4144.
Note:Whenspecifyingatorsionalspringstiffness,torsionaladhesiondatamaynotbespecified.
2.4.5.2SoilTorsionAdhesion
Thepilesoiltorsionaladhesionresistancedatamaybeinputdirectlybytheuser.TheSOILTORSIONHEADlinewiththenumberofstratumandthesoilIDornamedesignatedincolumns1820and4144,respectively,mustbespecified.
ThedistancefromthepileheadtothetopandthebottomofeachsoilstrataisspecifiedontheSOILSLOCline(s)immediatelyfollowingtheheader.Thetorsionadhesioncapacityatthetopandthebottomofeachstratadefined,isspecifiedontheSOILlineimmediatelyfollowingthestratalocationline.
2.4.6SoilLateralResistance
Pileheadlateralloadsareresistedbydistributednormalforcestransversetothepileaxisalongitslength.TheseresistancesmaybespecifiedintermsoftherelationshipbetweenlateralloadanddeflectionrepresentedbyPYcurves.PYcurvescanbegeneratedautomaticallyfrombasicsoilpropertiesorspecifiedbytheuser.
2.4.6.1GeneratingPYCurvesperAPIRP2A
PSIcanautomaticallygeneratelateralloaddeflectioncurves(PYcurves)basedonAPIguidelinesfrombasicsoilcharacteristicsinputbytheuser.
TheSOILLATERALHEADlineisrequiredtogeneratePYcurvesfrombasicsoilcharacteristics.ThenumberofsoilstratatobedefinedandthesoilIDornamemustbespecifiedincolumns1820and4144,respectively.Thereferencepilediameterforwhichthecurvesaregeneratedshouldbeenteredincolumns2833ifthePvaluesofthecurvesaretobemultipliedbytheratioofthepilediametertothereferencediameter.BoththePandYvaluesmaybescaledbytheratioofthepilediametertothereferencediameterbyspecifyingYEXPincolumns2427.
ThepropertiesofeachstratamakingupthesoilarespecifiedimmediatelyfollowingtheheaderlineusingeitherthesandorclayorsoillateralstratalinedesignatedbySOILAPILATincolumns112.ThestratalocationlabelSLOCincolumns1417isrequired.Theverticaldistancefromthepileheadtothetopofthestrataisspecifiedincolumns2530.Thedistancefromthepileheadtothebottomofthestratamaybeoptionallyinputincolumns3136.Thesoiltypeandthesoilcharacteristicsarerequiredincolumns1922and4568,respectively.
Foreachstrata,PYdatamaybedesignatedaseitherstaticorcyclicbyspecifyingSorCincolumn23.Forsandstratum,therelativelocationofthewatertableisdesignatedincolumn24.ThePvaluesforaparticularstratamaybefactoredbythenumberinputincolumns3740.Additionally,thePYcurvemaybeshiftedbydesignatingtheamounttobe
addedtogeneratedYvaluesincolumns4144.Ahighprecision"P"factorforthisPYcurvecanbespecifiedincolumns7076.
2.4.6.2UserDefinedPYCurves
PYcurvesdefiningthesoillateralresistanceforasmanysoilstrataasdesiredmaybeinputdirectlybytheuserasdiscretePYpairsateachsoilstratum.Theonlyrestrictionwhenspecifyingpointsonthecurve,isthatthelateralforceP,mustbeasinglevaluefunctionofthedisplacementY.Shifted,flatandhumpedPYcurvesarepermitted.
TheSOILLATERALheaderlinedesignatingthenumberofsoilstratum,themaximumnumberofpointsonanycurveandthesoilIDornamemustinitiatethePYcurveinput.
Thereferencepilediameterforwhichthecurvedataapplies,shouldbeenteredincolumns2833.ThePvaluesofthecurvesaremultipliedbytheratioofthepilediametertothereferencediameter.BoththePandYvaluesmaybescaledbytheratioofthepilediametertothereferencediameterbyspecifyingYEXPincolumns2427.AYfactortobeappliedtoallYvaluesinputmaybespecifiedincolumns3440.
Note:AlthoughthePYcurvesmaybefactoredbytheratioofthepilediametertothereferencediameter,onlytheoriginalinputcurveisreportedinthelistingfile.
Foreachsoilstrata,thestratalocationlineandthePYcurvedatafollow.Thestratatopandoptionallythebottomelevationareinputincolumns2530and3136oftheSOILSLOCline.ThenumberofpointsdefiningthecurveandthePfactorusedtoscaletheforcevalueofallpointsspecifiedaredesignatedincolumns2223and3740,respectively.ThePYcurvemaybeshiftedalongthedeflectionaxisbyspecifyingaYshiftvalueincolumns4144.Ifthecurvehasthesameshapewhetherthepileisintensionorcompression,enterSMincolumns1819.Ahighprecision"P"factorforthisPYcurvecanbespecifiedincolumns7076.
ThePandYdataforeachpointonthecurveareenteredontheSOILPYlineimmediatelyfollowingthesoilstratalocationline.Thenumberofdatapointsenteredmustcorrespondtothevaluespecifiedonthestratalocationline.
Note:Whenusingthesymmetricoption,onlypositivevaluesforPandYmaybeinputandtheorigin,P=0andY=0mustbethefirstdatapoint.
Note:Withinasoilstratum,thePSIprogramconnectstheinputPYpointswithstraightlinestofullydefinethepile/soilinteractioncurveforarbitrarydisplacementsinthatstratum.Atdepthsbetweenspecifiedsoilstrata,PSIhastheabilitytolinearlyinterpolatebetweenPYcurvesortouseaconstantPYcurve.
2.4.7SoilLiquefactionPotential
SACScancalculatetheliquefactionpotentialofasoillayerforagivenearthquakeloadingandchangethesoilstiffnesspropertiesaccordinglybeforeconductingthepilesoilinteractionanalysis.ThisfunctionalityisavailableinCollapse,PileandPSIprogramsinSACS.
ForeachsoildefinedinaPSIorPileinputfile,usercanspecifythesoilliquefactiondata.OneSOILLIQUEFYHEADlinefollowedbyanumberofSOILLIQUFYSLOClines,oneforeachstratum,isrequiredtocompletelydescribetheliquefactiondataforthesoil.
SOILLIQUEFYHEADlinedescription:ThenumberofsoilstratatobedefinedandthesoilIDornamemustbespecifiedincolumns1820and4144,respectively.Seismicloadingmustbespecifiedbyprovidingthevaluesoftheearthquakemagnitudeandthepeakgroundacceleration(asaratioofgravity)incolumns3436and3740,respectively.Thereisalsoanoptiontomaketheestimationofliquefactionpotentialmore(orless)conservativebychangingthevaluesof%horizontalshiftinCRRcurveand%verticalshiftinCRRcurveincolumns2126and2732,respectively.Also,theeffectofliquefactiononsoilstiffnesspropertiescanbemodulatedbychangingtheliquefactionmultiplierfactorincolumns4550.
SOILLIQUEFYSLOClinedescription:Liquefactionstratalinesshouldfollowtheliquefactionheaderline.Thelocationofthestratumwithrespecttothewatertableshouldbespecifiedincolumn18.Theverticaldistancesfromthepileheadtothetopandthebottomofthestratumarespecifiedarespecifiedincolumns1924and2530,respectively.TheconetipresistancevalueandthesleevefrictionvalueobtainedfromtheCPTtestsarespecifiedincolumns4550and5156,respectively.Submergedunitweightofthesoilisspecifiedincolumns5762.Ifliquefactioneffectsaretobeignoredforastratum,calculationmethodincolumns3133shouldbespecifiedasN.Ifsoiltypeisknown,itcanbespecifiedincolumns3437.
IfthesoiltypeforaparticularlayerisdescribedasCLAYorifthesoiltypeisnotspecifiedandSACSdetermines(basedontheCPTdata)thatthesoiltypeislikelytobeclay,orifcalculationmethodisspecifiedasN,thenitisassumedthatthislayerisnotpronetoliquefactionandstiffnessvaluesforthislayerarenotchanged.Inallothercases,SACScalculatesthefactorofsafetyforliquefactionduetotheseismicloadingspecifiedbytheuser.Ifthefactorofsafetyiscalculatedtobegreaterthanorequalto1.0,thenthereisnochangeinthesoilstiffness.Ifthefactorofsafetyiscalculatedtobelessthan1.0,thenthelayerisconsideredasliquefiedandafactorcalledliquefactionmultiplieriscalculated.Ifthecalculatedvalueoftheliquefactionmultiplierislessthan1.0,thensoilskinfrictionresistance(Tz),bearingresistance(Qz),andlateralresistance(Py)aremultipliedwithliquefactionmultipliertocalculatethestiffnessoftheliquefiedsoillayer.
Note1:Liquefactionrelatedcalculationsareconductedatthemiddepthofeachliquefactionstratumspecifiedbytheuser.Therefore,itisadvisabletouseseveralsoilliquefactionstratathroughthepiledepthforabetterestimationoftheliquefactionpotential.
Note2:liquefactioneffectontheaxialbehaviorisignoredifsoilaxialresistanceisdefinedasadhesionorlinearaxialspringatthepilehead.
Note3:Both"from"and"to"informationforeachliquefactionstratumisrequired.Thestratashouldbecontinuousandshouldcoveratleasttheentirelengthofthepile.
2.5CREATINGFOUNDATIONSUPERELEMENTS
UptotwolinearizedfoundationstiffnessmatrixmaybegeneratedateachpileheadtobeusedbytheSACSdynamicsmodulesinlieuofapilestub,pilespringetc.Theprogramcreatesacoupledthreedimensionalstiffnessmatrixforaparticularpilegroupthathaslateralstiffnesspropertiesinbothlateraldirectionsalongwithaxialstiffnessproperties.Thestiffnesspropertiesarederivedfromeithertheaveragedisplacementofallpilesofthepilegrouporthemaximumpiledisplacementsfortheloadcasesdesignatedbytheuser.
Note:Asuperelementiscreatedforeachpilegroup.Thesuperelementisappliedtoeachpileheadconnectedtoapileassignedtothepilegroupinquestion.
2.5.1FoundationSuperElementOptions
LinearizedfoundationsuperelementsorstiffnessmatricesarecreatedateachpileheadautomaticallybythePSIprogramifthePILSUPinputlineisspecified.
Themethodusedtocalculatedthepilestiffness,AVGorMAX,foraparticularpilegroupisspecifiedincolumns810.Uptofourloadconditions,specifiedincolumns2124,2932,3740and4548,maybechosentocalculatethepilestiffnessintheglobalXdirection.IfdifferentloadcasesaretobeusedtocalculatestiffnessintheglobalYdirection,theymaybespecifiedincolumns2528,3336,4144and4952,respectively.
AsecondfoundationsuperelementmaybegeneratedbyspecifyingasecondPILSUPline.Inthesamplebelow,thefirstsuperelementistobeusedforFatigueanalysisandiscreatedusingloadcases8and9,whilethesecondsuperelementistobeusedforearthquakeanalysisandiscreatedusingloadcasesDEDXandDEDY.
Note:StiffnessiscalculatedindependentlyintheXandYdirections.
2.6SIMULATINGMUDSLIDES
MudslidesagainstthejacketabovethepileheadcanbemodeledinSeastate.MudslidesagainstthepilesaremodeledinPSIorPileusingflatand/orshiftedPYcurves.InPSI,oneofthepilelocalcoordinatedirectionsisorientedtocorrespondtothedirectionofthemudslidebyspecifyingapilerotationangleonthePILEline.Separatesoiltables(axial,bearing,torsion,lateral)aredefinedforthelocalXYandXZplanesofthepile.
Note:Normallytheaxial,bearingandtorsionlineswillbethesameforthetwodirectionswithonlythelaterallinesbeingdifferent.
Inthedirectionofthemudslide,thePYdatacanbethesameasintheotherdirectionexceptthatashiftisspecifiedincolumns4144ontheSOILSLOCline.Conversely,aflatPYcurvethathasconstantvalueofPforallYvalues,maybespecifiedforthemudslidedirection.Ineithercase,forceisexertedbythesoilagainstthepileevenwhenthereisnodisplacement.Thiscorrespondstoanactivesoilexertingathrustonthepileasopposedtotheusualproblemofpassivesoilresistingathrustexertedbythepile.
IfaninitiallysymmetricalPYcurveisgivenapositiveYshift,asshowninthefigurebelow,thenforanypiledisplacementlessthantheshiftamount,anegativeforceisexertedonthesoil(PYdataisforthesoil,notthepile).Thisinturnresultsinaforceonthepileinapositivedirection.ThustomodelamudslideinthepositiveYdirection(pilecoordinates)apositiveshiftshouldbeused.InthesamemannerifaflatPYcurveisusedtomodelamudslideinthepositiveYdirectionthentheconstantvalueforPmustbenegative.
ThefigureabovealsoshowsthatforvaluesofYbeyondthelimitsoftheinputdata,theprogramextendsthecurveasflat.Forthisfiguretobevalid,theusermustinputthedirectionforthepilelocalcoordinatessothatthepilelocalYorZaxisisalignedwiththemudslide.ThisisdoneonthePILElineincolumns50to56.
ThefollowingillustratesshiftedPYdataforsoiltableSOL2.Thecurvesforeachstrataaresymmetricandareshifted7.0and4.25,respectively.
Note:Sincethepilelocalcoordinatesaredefinedbythedirectionofthemudslide,ifanysignificantlateralloads(suchaswaves,currentorwind)areactingonthejacketinadirectiondifferentfromthatofthemudslide,theusershouldcheckthefinalpileheadloadsinthePileheadComparisonreporttomakesurethatproperconvergencehasbeenachieved.
2.7INPUTTINGPILEHEADSTIFFNESSTABLES
Becausethepile/soilfoundationexhibitsnonlinearbehavior,thepileheadstiffnessmatrixvariesforeachiterationofeachpileforeachloadcase.Normallythiswouldrequirethereformulationofthepilestiffnessmatrixateachiteration,thusrequiringagreatdealofcomputationtime.PSIeliminatesthisrequirementbyinitiallyformingatableofpileheadstiffnesscoefficientsforarangeofvaluesexpectedinthesolution.Thepileheadstiffnessusedforanyiterationisfoundbylinearlyinterpolatingbetweentablecoefficientvalues.Iterationsarecontinueduntilanapproximatesolution(within5percent)isfound.PSIthenproceedsusingafinetuneprocedurewhichrecalculatestheindividualpilestiffnessforeachiteration.
2.7.1OptionalUserDefinedPileheadStiffnessTables
Ingeneralnormalconvergenceforpileheadloadsis0.5percent.Forsomesituationshowever,thepileheadstiffnesstablesgeneratedautomaticallybyPSImaynotbeadequatetoobtainthisconvergenceorsufficientprogramaccuracy.Inthesecases,auserspecifiedpileheadstiffnesstablemayberequired.
Asdiscussedabove,beforetheiterativesolutiontothelateraldeformationproblemsbegins,PSIfirstdoesanumberofpilesolutionsforallcombinationsofuserinputofaxialloadordisplacement,pileheadlateraldisplacement,andpileheadrotation.Theiterativesolutionwillproducevaluesforpileheadaxialload,ordisplacement,lateraldisplacement,androtation.Thesevaluesshouldbewithintherangesspannedbytheuserspecifiedinputvalues.Thisisparticularlyimportantifthefinalvaluesareinahighlynonlinearregionofthecorrespondingloaddeformationsurface.
Note:Tablerangesforalldegreesoffreedommustbespecifiedifanyareincludedintheinputfile.
2.7.1.1GuidelinesforAxialRanges
TheusershouldselecttheinputTABRvaluesbasedonpriorexperiencewithsimilarstructuresandsoilconditionsaswellasPSIanalyses.Thefollowingisofferedasaguide.
First,thecapacityofthepileincompressionandtensionshouldbefound.IftheaxialsoildataisintermsofTZdata,thecapacitycanbefoundusingthePileprogramwithalargeinputvalueofpileheadaxialdisplacement,largeenoughsothattheZvalueofanypointonthepileisontheflatpartoftheTZcurve.Tenortwentyinchesisusuallysufficient.IftheactualsoildataisexpressedintermsofadhesiondataoriftheAPIsoiloptionisselected,thepilecapacitycanbefoundbyrunningPilewithavalueofaxialloadmuchlargerthanthepilecapacity,inwhichcasetheoutputwillincludeareporttotheeffectthattheappliedloadexceedsthecapacityandthecapacitywillbereported.Avalueof100,000kipsshouldbesufficientinmostcases.
Aftertheaxialcapacitiesintensionandcompressionarefound,thesevaluesaredividedbyafactorofsafetytogetthemaximumworkingvaluesforaxialload.Thentheintervalbetweenthesetwovaluesissubdividedintoapproximatelyequalsubdivisions,thesetwopointsarethenusedasthevaluesontheaxialTABRlines,thepoint0.0shouldbeamongtheinputvalues.Usuallynomorethanatotalofsevenvalueswillberequired.
Note:Ifthesoilexhibitshighlynonlinearproperties(suchashumpedTZcurves)andifthepilewillbeoperatingunderconditionsthatplacethedeflectionsalongthelengthofthepileinthehighlynonlinearregion(e.g.pastthehump),thenthepileheadforcedisplacementcurveswillalsobehighlynonlinearandtheaboveguidelinesmaynotbeadequate.MoreTABRvaluesmaybeneededanditmaybenecessarytomakespacingbetweenvaluesmuchclosertogetherforpointswheretheslopeofthecurveischangingrapidlythanfortheregionswheretheslopeischanginglessrapidlysothattheshapesofthepileheadloadvs.
2.7.1.2GuidelinesforLateralRanges
NormallyPYsoilpropertiesaresymmetrical,theprincipalexceptionbeingforshiftedPYcurves.TABRvaluesshouldbeenteredforseveralvaluesfromzerotoabout1.5timesthelargestexpectedlateraldeflection.Normallysixorsevenvalueswillbesufficient.IfthePYdataisnotsymmetricalthenseveralvaluesfromabout1.5timesthemaximumexpectednegativedefectionto1.5timesthemaximumexpectedpositivedeflectionshouldbeentered.Thezerodeflectionpointshouldbeoneoftheentries
Note:Ifthemaximumpileheadlateraldeflectionissmallenoughsuchthatthepileheadlateralloadvs.deflectioncurveisapproximatelylinearforallvaluesofdisplacementuptothemaximumthenmanyfewerthansevenpointsmaybeused.
Themaximumexpectedlateraldeflectioncanbeestimatedasfollows:NormallySeastatewillhavebeenruntoproducetheloadsonthestructure.Theresultingbaseshearcanbedistributedequallytothepiles,thesepileheadshearswillthenbemultipliedbyafactorofabout1.5togetworkingpileheadshears.ThePileprogramcanberunwiththispileheadshearactinginconjunctionwiththeworkingpileheadaxialload(describedabove).Apileheadrotationalspringhavingstiffnessapproximatingthatofthestructureatthepileheadjointcanbeusedtoaccountfortherestraininginfluenceofthestructureonthepile.ThepileheaddisplacementandrotationcanthenbeusedasthemaximumTABRvalues.TABRvaluesforpileheaddisplacementshouldbeenteredinradiansfromthemaximumnegativetothemaximumpositivevalues.ItisimportantthatbothpositiveandnegativevaluesbeenteredevenifthesoilhassymmetricalPYdatabecausethesignificanceofthesignofthepileheadrotationisthattherotationeitheraugments(positive)thedeflectioncausedbythepileheadshearordiminishesit(negative).Againnormallysevenapproximatelyequallyspacedvalueswillsuffice.InmanycasesthefollowingsetofTABRvaluesforpileheadrotationwillbeadequate:
Note:Ifthesoilexhibitshighlynonlinearproperties(suchashumpedPYcurves)andifthepilewillbeoperatingunderconditionsthatplacethedeflectionsalongthelengthofthepileinthehighlynonlinearregion(e.g.pastthehump),thenthepileheadforcedisplacementcurveswillalsobehighlynonlinearandtheaboveguidelinesmaynotbeadequate.MoreTABRvaluesmaybeneededanditmaybenecessarytomakespacingbetweenvaluesmuchclosertogetherforpointswheretheslopeofthecurveischangingrapidlythanfortheregionswheretheslopeischanginglessrapidlysothattheshapesofthepileheadloadvs.displacementcurvesareadequatelyapproximatedbythepiecewiselinearcurvesthatareusedtorepresentthem.
2.7.1.3GuidelinesforTorsionalRanges
Whiletorsionalloadsonthepileheadsarealmostneververylarge,atorsionTABRlineisalwaysrequired.Thereisnointeractionoftorsionwithanyoftheotherloads(axial,lateral,andbending).Inmostcasestwopoints(e.g.0.0and100.0)willbesufficient.
3.0CREATINGPILEINPUT
3.1OVERVIEW
PileandPile3DaresubprogramsofPSIthatcanruninstandalonemodefortheanalysisofapilesubjecttoknownpileheadforcesordisplacements.TheyaremainlyusedtoperformsingleorisolatedpileanalysesandutilizethesameinputfileasthePSIprogramwithminormodifications(seeSection5.2fordetails).PileandPile3DcanbeusedtoplotsoildatapriortoexecutingaPSIanalysis.TheycanalsocreateapostfileforusebytheFatigueprograminordertoevaluatethepilefatiguelife.
Ingeneral,thePSIinputlinesmaybeusedinthePileorPile3Dinputfiletodescribethepileandsoilmodelexceptwherenotedinthefollowingsections.Thefollowingappliestoexecutionofsinglepileanalysisor3Dsinglepileanalysis,generatingequivalentlinearizedfoundationandpilefatigueusingPileorPile3D.WhenusingPileorPile3Dtogenerateplotsofsoildata,thePSIinputfilemaybeusedwithoutmodification.
ThedifferencebetweenPileandPile3Disnotedinsubsequentsections.Basically,thedifferenceliesintwoandthreedimensionalpileanalysis.Pile3DoffersanextendedsetofoptionsforsinglepileanalysisoverthatwhichissupportedbyPile.OptionssupportedonlybyPile3Daremarkedassuchinthetext.
3.2DEFININGANALYSISOPTIONS
ThePileprogramrequirestheuseofthePLOPTlinetodesignateanalysisoptions.
Theinputandoutputunitsarespecifiedincolumns78and1112,respectively.Thenumberofpileincrements,themaximumnumberofiterationsandthelateraldeflectionconvergencetolerancearedesignatedincolumns1315,1820and2130,respectively.Thepileunitweightmaybedesignatedincolumns3140.
Thesoildataplotsand/orsoilreactionsmaybeoutputbyspecifyingPTincolumns4344and6162,respectively.
ThefollowingshowsaPLOPTlinedesignatingEnglishunits,thelatestAPIcodeand490.materialweight.
ThecouplingofaxialandtorsionalloadingonapilemaybeachievedusingthecurrentPLOPTlinewiththePile3Dprogram.TheoptionisinputasTTZincolumns4547ofthePLOPTline.Withthisoptionchosenanytorsionalsoildatawillberemovedfromtheinputdatafile.Thisdatawillbecomputedinternally.ThisoptionwiththePile3Dloadingfeaturesisparticularlyusefulforcaissonlikestructureswithfoundationswhicharetorsionsensitive.
Aspecificationofaxialandtorsionalloadcouplingisshown.TheexamplespecifiesAPIWSD20theditionunitycheckswithEnglishinputandoutputunits.Tenpilelengthincrementsareusedforthefinitedifferencesolution.Pileselfweightisincludedintheanalysiswithpiledensityof490.0lb/ft.Aninputechoistobeprinted,allTZplotswillbeproducedononeplot,andaxialandtorsionalloadsaretobecoupled,withsoilreactionsreportedalongeachstationofthepile.
3.3SPECIFYINGPLOTOPTIONS
AsinPSI,plotoptionsaredesignatedonthePLTRQ,PLTLCandPLTSZinputlines.Inaddition,sincethePileprogramonlyallowsonepiletobedefined,thePLTPLinputlinethatallowsspecificationofwhichpilestoplot,isnotapplicable.
3.3.1PlotData
DatatobeplottedisdesignatedonthePLTRQinputline.Soilinputdata,axialdeflection,axialload,axialsoilreactions,requiredpilethicknessandunitycheckratiomaybeplottedversuspilepenetration.Lateraldeflection,lateralrotation,bendingmoment,shearloadandlateralsoilreactionalongoraboutthepilelocalYandlocalZaxesmaybeplottedversuspenetrationinadditiontotheresultant.
Bydefault,foranyoftheresultplotoptions,loadcasestoplotmaybedesignatedonthePLTLCline.Plotappearanceoptionssuchasgridlinesandcrosshatchingmaybedesignatedalso.
Thefollowingrequestssoildataplots,lateralandaxialdisplacementalongwithunitycheckplots:
Note:EnvelopeoptionsonthePLTRQlinearenotavailableinthePileprogram
3.3.2DesignatingLoadCasestoPlot
Bydefault,allloadcasesareincludedforplotgeneration.IfloadcasesarespecifiedonthePLTLCinputline,thenonlyloadcasesspecifiedwillbeincludedforplottingpurposes.
3.3.3OverridingPlotSize
Thedefaultplotpapersize,charactersize,crosshatchingspacingandnumberofcolorsmaybeoverriddenusingthePLTSZline.
3.3.4PlottingSoilDatafromPSIInput
ThePileprogrammaybeusedtoplotsoildatasothatitmaybecheckedpriortoPSIexecution.WhenusingthePileprogramtogenerateplotsofthesoildata,thePSIinputfilemaybeusedwithoutmodification.
3.4DEFININGTHEPILE
Ingeneral,thepileisdefinedusingthesameinputasrequiredbythePSIprogram.Exceptionsarenotedinthefollowingsections.
3.4.1PileSectionProperties
SectionpropertiesaredefinedusingthePLSECTandPLGRUPlinesusedinthePSIinputfile.
3.4.2PileGroupProperties
Pilegrouppropertiessuchasmodulusofelasticity,shearmodulus,andyieldstressarespecifiedontheappropriatePLGRUPlineasinPSI.
3.4.3DefiningPileElements
PileelementsarespecifiedonPILElinesfollowingthePILEheaderinputline.Thepileelementisnamedbytheoptionalpileheadjointnamespecifiedincolumns710.Thepilegrouptowhichthepileisassignedisspecifiedincolumns1618.
ThesoilIDdefiningpile/soilinteractionpropertiesinthelocalXZplaneisdesignatedincolumns6972.
Note:BecausethePileisatwodimensionalanalysis,onlysoiltablefortheXZplaneisrequired.
ThefollowingdefinesapileassignedtopilegroupPL1andusessoiltableSOL1.Apileheadjointwasdesignatedforreferencepurposes.
PileBatter
ThepilebattermustbedefinedbybatterdefinitioncoordinatesspecifiedonthePILEline.TheglobalX,YandZdistancesfromthepileheadtoanypointaboveitlyingonthepileaxisshouldbeinputincolumns2130,3140and4150,respectively.Forexample,thefollowingdefinesapilebattered1:8intheglobalXZplaneandverticalintheglobalYZplane.
Note:Pilebattercoordinatesmaybespecifiedregardlessofwhethertherisevalueofthebatteristhesameforbothplanes.Forexample,apilebattered1:8intheglobalXZplaneas1:10intheglobalXYplanemaybedefinedusingtheX,YandZbattercoordinatesof10.0,8.0and80.0.
PileHeadHeight
WiththePile3Dprogram,thepileheadheightrelativetothemudlinemaybeadjustedwiththePILEline.Pileheadheightisspecifiedincolumns5764ofthisline,withpositiveheightslyingabovemudlineandnegativeheightslyingbelowmudline.PilesegmentlengthsandpileheadloadsspecifiedonthePLOD3Dlinearebaseduponthispileheadheight.
ThefollowingsamplespecifiesapilebatterintheglobalXZplaneof1:10andverticalintheglobalYZplane.Thepileheadlies10.0unitsabovethemudline.ThepilegroupisPL1andthesoiltableisSOL1.
3.4.4PileLocalCoordinateSystem
ThepilelocalcoordinatesystemusedinthePileprogramisdefinedasfollows:
ThepilelocalXaxisextendsfromthepileheaddownthepilealongthepilecenterline.ThelocalZaxisisperpendiculartothepilelocalXaxisandisassumedtobedirectedtotherightofthepile.Usingtherighthandrule,thelocalYaxisisnormaltothepileandpointsintothepage.
PositiveaxialdeflectionisassumedtobedeflectiondownalongthepileaxiswhilepositivelateraldeflectionisalongthepositiveZaxis.PositiverotationisassumedabouttheYaxisandisintothepaperusingtherighthandrule.
ThePileprogramreportspileinternalloadingsuchthatpositiveinternalaxialloadistensionandapositiveinternalZshearloadactsalongthelocalZaxis.ApositiveinternalYmomentactsaboutthelocalYaxisandresultsinacompressivestressontherightsideofthepile.Internalstressesarereportedsuchthatapositiveaxialstressistensileandpositiveshearstressresultsfromapositiveshearload.PositivebendingstresscorrespondstoapositivemomentaboutthelocalYaxis.
3.4.5PileheadSpring
UnlikePSI,thePileprogramdoesnotincludetheeffectsofthestiffnessofthestructureconnectedabovethepilehead.Bydefaultthetopofthepileisassumedtobefreetorotateandtranslate.
However,thestiffnesseffectsofastructureconnectedatthetopofthepilemaybeincorporatedbyspecifyingelasticboundaryconditionsatthetopofthepileusingthePLSPRGline.Alateraland/orrotational(bending)springmaybedefinedbyspecifyingthespringtypeandthespringconstant.Thefollowingdefinesalateralandarotationalspring:
3.5MODELINGSOILPROPERTIES
3.5.1Overview
Ingeneral,soilresistanceisdescribedusingthelinesavailableforuseinPSIinputexceptwherenotedinthefollowingsections.
3.5.2SoilAxialResistance
TheaxialcapacityofthesoilmaybedescribedusingthesameinputlinesavailableinthePSIprogram.
3.5.2.1InputtingAxialLoadDistribution
Ifaxialsoildatainunavailable,theusermayinputtheaxialloaddistributioninthepileusingtheAXLOADline,thusallowingPiletobypasstheaxialsolution.
Thenumberofpointsalongthepilethataxialloadwillbespecifiedisdesignatedincolumns1416.Foreachofthesepoints,theaxialforceandthedistancefromthepileheadmustbespecified.Pileusestheseinputvaluesinperformingthelateralsolution.Thefollowingdefinestheaxialloadinthepileateightpoints:
Note:Compressiveforceshouldbeenteredaspositivevalues.Thefirstvalueenteredshouldbetheaxialloadatthepilehead(0.0incolumns2429).Thisvalueisusedastheaxialloadinthepile.AnyadditionalaxialloadspecifiedusingPLLOADlinesisignored.
3.5.3SoilTorsionalResistance
TorsionalresistanceofthesoilisnotconsideredbythePileprogram.AnySOILTORSIONinputlinesareignored.
3.5.4SoilLateralResistance
SoillateralcapacityismodeledusingthesametechniquesasthePSIprogrammodule.
3.5.5SoilLiquefactionPotential
SoilliquefactionpotentialiscalculatedusingthesametechniquesasthePSIprogrammodule.
3.6INPUTTINGPILEHEADSTIFFNESSTABLES
Pileheadstiffnesstabledataisnotrequired.AnypileheadstiffnessdatainputisignoredbythePileprogram.
3.7SPECIFYINGLOADINGFORISOLATEDPILEANALYSIS
Theloadingatthetopofthepilemustbedescribedwhenexecutinganisolatedpileanalysis.Ifcodecheckistoperformed,thecodemustbedesignatedincolumns910onthePLOPTline.
TheloadingordisplacementsforwhichtoanalyzethepilearedesignatedonthePLLOADline(s).Thelateralforceordisplacementisinputincolumns2130,whilemomentorrotationisinputincolumns3140.Eitheraxialforceoraxialdisplacementbutnotboth,mustbespecifiedincolumns4150or5160,respectively.
Note:Enterpositiveaxialloadforcompressionorpositiveaxialdisplacementfordisplacementdownalongthepile.
Theallowablestressmodifierormaterialfactormaybespecifiedincolumns7175.
AsmanyPLLOADlinesasdesiredmaybeinput.Bydefault,eachPLLOADlineisconsideredtobeaseparateloadconditionunlesstheStartfromprevioussolutionflagisset.Ifthisflagisset,theloadingspecifiedpriortothepresentPLLOADlineisassumedtobetheinitialpositionforthepresentanalysistobegin.Thefollowingdesignatespileloadingwiththesecondlinecontinuingfromtheprevioussolution:
Note:WhenthePileprogramisrunusingaPSIinputfile(withthePSIOPTlinereplacedbyaPLOPTline),apileanalysiswillbeperformedoneachpileforeachpileloadcase,evenifallpilesareidenticalandareinstalledinthesamesoil.Toavoidthisduplication,itissuggestedthatredundantPILElinesberemovedfromthePileinputfile.
3.7.13DPileHeadLoad
ThefirststepincreatingthreedimensionalpileheadloadinginPile3DisspecifyingthepileheadheightonthePILEline.Afterspecifyingthepileheadheight,loadingisappliedtothepileviathePLOD3Dline.Threedimensionalloads(forcesandmoments)orthreedimensionaldisplacements(translationandrotation)maybeappliedtothepileattheheightspecifiedinthepreviousPILEline.ForcesFordisplacementsDarespecifiedincolumns1134momentsMorrotationsRarespecifiedincolumns3558.AllquantitiesspecifiedonthePLOD3Dlinearespecifiedinthepilelocalcoordinatesystem.
Thefollowingsamplespecifiespileforcesof100.0intheaxialdirection,8.0inthelocalYdirectionandatorsionalmomentof10.0.Thepileitselfhasabatterof1:10intheglobalXZplaneandapileheadheightof10.0.Allforces/momentsareappliedatthisheightabovethemudline.
3.7.2SpecifyingPileLoadAtDepth
Anewfeatureofthreedimensionalsinglepileanalysisistheabilitytospecifypileloadingatplacesalongthepileotherthanthepilehead.ThisfeatureiscontainedinthelineDEPLOD.Loads(forcesandmoments)arespecifiedatagivenverticaldepthrelativetothemudline.Verticaldepthisspecifiedincolumns814.Forcesarespecifiedincolumns1636withmomentsspecifiedincolumns3757.EachDEPLODlinecreatesasinglepileanalysis.AllquantitiesspecifiedontheDEPLODlinearespecifiedintheglobalcoordinatesystem.Assuch,inordertoeffectivelyusetheDEPLODlinethemodelmusthavethepositiveglobalZaxisintheverticalupwarddirection.
Thefollowingsamplespecifiesglobalpileforcesof8.0intheglobalXdirection,0.0intheglobalYdirection,and100.0intheglobalZdirection.Globalpilemomentsof0.0abouttheglobalX,0.0abouttheglobalY,and10.0abouttheglobalZarespecified.Thepileloadingisspecifiedat10.0unitsbelowthemudline.
3.8CREATINGAPILEFATIGUESOLUTIONFILE
ThePileprogramcanbeusedtocreateapilesolutionfileforusebysubsequentfatigueanalysis.TheSCFoptionshouldbespecifiedonthePLOPTlineincolumns6365.
TheforcesandmomentstobeappliedtothepilearedesignatedontheLOADinputline.TheforcesalongX,YandZaxesareenteredincolumns1723,2430and3137,respectivelyalongwiththemomentsabouttheX,YandZaxesspecifiedincolumns3844,4652and5359,respectively.
Bydefault,theloadsspecifiedareassumedtobeinthepilelocalcoordinatesystem(shownonright).Ifontheotherhand,thepileloadsweretakendirectlyfromamemberinternalloadsreportorarespecifiedusingtheTimoshenkosignconvention,MEMBandINTLmustbespecifiedincolumns6164and6669,respectively.
AsmanyLOADlinesasrequiredmaybespecified.Aloadcondition,withresults,willbecreatedinthesolutionforeachLOADlinespecified.
3.9CREATINGAPILESTUB
Itisoftendesirableornecessarytoreplacethenonlinearpilesoilsystemwithanapproximatelyequivalentlinearpilestubbeamelement.Staticanalysisofthelinearizedsystemforinstance,maybesufficientlyaccurateforpreliminarydesignpurposes.Fordynamicanalysis,itisnecessarytolinearizethefoundation.
ThePileprogramoffersanautomatedequivalentpilestubdesignfacilityinwhichtheprogramcalculatesanequivalentpilestubandoutputsinputlinescontainingthepilestubpropertiesincludingmemberlength,memberoffsetsandprismaticsectionproperties.
3.9.1PileStubLoading
TheloadingordisplacementsusedtocalculatetheequivalentlinearizedfoundationelementarespecifiedonthePLSTUBline.ThelateralandbendingstiffnessmaybedeterminedusingforcesandmomentsordisplacementandrotationbyenteringForDincolumn10,respectively.Ifdeflectionsaredesignated,thelateraldeflectionandrotationareenteredincolumns2130and3140.Otherwise,lateralshearforceandmomentshouldbeentered.Eitheranaxialloadoraxialdisplacement,butnotboth,maybespecifiedincolumns4150or5160.
Note:Theloadsspecifiedatthepileheadshouldbespecifiedinthepilelocalcoordinatesystem.ForamoredetaileddiscussiononthetheoryandderivationoftheequivalentpilestubprocedureusedbyPile,seetheCommentary.Sampleproblem2illustratestheprocedureindetail.
3.10CREATINGALOAD/DEFLECTIONCURVEFORSOILS
ThePileprogramcanbeusedtocreatetheloadversusdeflectioncurvesforagivenpilehead.Thisisusefulforthevisualizationofspecificstaticload/deflectioncharacteristicsinthespecifiedpilehead.Pileheadcapacitymayoftenbeeasilydeterminedbyexaminingthepeakofthepileheadload/deflectioncurve.
Thecreationofaload/deflectioncurveisaccomplishedbymeansoftheLODFLline.Thislineisusedtocalculatetheaxialcompressionandtensionpileheadversusdeflection.Thenumberofdeflectionincrementsisenteredincolumns710.Themaximumaxialdeflectionisenteredincolumns1120.Thedeflectionrangefromzerotothemaximumaxialdeflectionisdividedevenlybythenumberofdeflectionincrements.Apileheadloadiscalculatedforeachaxialdeflection.IftheunitsspecifiedwereSI,thefollowinglinedefinesaload/deflectioncurvewithfiftypointsandamaximumaxialdeflectionof15.0centimeters.
Note:theLODFLlineisonlyusedinsinglepileanalysis.
Usingtheaboveloaddeflectionline,thepileprogramwillproduceaneutralpicturefilewiththeload/deflectioncurveplottedwiththegivennumberofpointsandmaximumaxialdeflection.Anexampleoftheoutputproducedisshown.TheLODFLoptionsusedtocreatethefigurewerethoseshownaboveintheexampleline.
4.0COMMENTARY
4.1INTRODUCTION
PSI,(PileStructureInteraction),analyzesthebehaviorofapilesupportedstructuresubjecttooneormorestaticloadconditions.Finitedeflectionofthepileisaccountedfor(thePdeltaeffect)andthesoilmayexhibitnonlinearforcedeformationbehaviorbothalongandtransversetothepileaxis.
Becauseofthenonlinearbehaviorofthepilesoilsystem,theoverallstiffnessofthestructurefoundationsystemisafunctionofdisplacement.Inalinearanalysisthestructuralstiffnessmatrixisformedbasedontheundeformedstructureanddoesnotchangeasthestructuredeforms.Whenthereissignificantnonlinearity,however,thestiffnessmatrixforthedeformedshapecannotbedetermineduntilthedeformedshapeisobtained.Thedeformedshape,inturn,cannotbefounduntilthestiffnessmatrixisfound.
Iterativemethodshaveproventobeusefulforsolvingproblemsofthistype.Onestartswithaninitialassumptionforthedisplacementsandsolvesforthestiffnessmatrix.Newdisplacementsarefoundusingthisstiffnessmatrix,thenanupdatedstiffnessmatrixisformed.Theprocessisrepeateduntilthecalculateddisplacementsforaniterationarewithinaspecifiedtoleranceofthosefromthepreviousiteration.
Thetechniquedescribedaboveisnotpracticalforstructureswithmanydegreesoffreedomwithoutfirstintroducingthenotionofcondensationofthestructuralstiffnessmatrix.
Thestructureisdividedintotwoparts,withtheinterfaceatthepileheadjointsatornearthemudline,asshowninFigure1below.
Thepilesbelowthepileheadjointsarenonlinearelementswhilethestructureabovethepileheadjointsislinear.Thestructureabovethepileheadjointsservesthefollowingroles:
1. Connectthepilestoeachotherwithamediumhavingcertainwelldefinedlinearstiffnessproperties.2. Introduceloadstothepileheads.
Theprocessofcondensationinvolvesreducingthelinearstructureabovethepileheadjointsandloadstoanequivalentlinearstiffnessmatrixinvolvingonlythepileheaddegreesoffreedomandasetofforcesappliedtothosedegreesoffreedom.Forexample,afourpilejacketmayhaveseveralhundreddegreesoffreedombutthenonlinearpartofthestiffnessmatrixwillonlyhave24degreesoffreedom(i.e.4pileheadjointswith6degreesoffreedomperpile).
4.2DERIVATIONOFINTERACTIONEQUATIONS
Toderivetheinteractionequation,firstconsiderasinglepileasillustratedinthefigurebelow.
Assumethatthedeflectedshapeofthepileisverynearlyinaplanecontainingtheaxisofthepile.Thisassumptionisvalidif:
1. Thepileheadtorquedoesnotinfluencethelateraldeflection.2. Theresultantpileheadbendingmomentisaboutanaxisperpendiculartothedirectionoftheresultantpileheadlateralforce.
Note:Thereasonsforthisassumptionwillbeaddressedlaterinthediscussion.
Thefirstoftheseconditionsmaybeacceptedbasedontheusualsmalldisplacementrestrictionofstructuralanalysis.Theusualconditionsunderwhichoffshorestructures(andindeedmostotherstructures)operateproduceresultantpileheadbendingmomentsandlateralforcesthatnearlysatisfycondition2.Notethatitisnotassumedthatallofthepilesdeforminthesameplane,butonlythateachpiledeformsinaplane.Thatplane,however,maybedifferentfrompiletopile.
Plotscanbedevelopedrelatinganypileheadforce(ormoment)componenttoanypileheaddisplacement(orrotation)componentforfixedvaluesofaxialloadandtheotherdisplacementorrotationcomponents.AtypicalplotmayhavethegeneralappearanceofFigure3.TheslopeofthecurveatapointsuchasA,isdefinedasthestiffnesscoefficientrelatingtheforceormomenttothedisplacementorrotationatthatpointA.Itisafunctionofdisplacement,rotation,oraxialload.
TheequationoftheFvs.curvemaybewrittenintheform:
(1)
whereKandFOarefunctionsof,,andP.Theseconsiderationsaregeneralizedto6pileheaddegreesoffreedomandtheresultswritteninmatrixform:
(2)
where{F},{},and{FO}are61matrices(columnvectors)and[K]isa66matrix.Inaddition,[K]and{FO}arefunctionsof,,andP.
Figure4isaschematicsketchofajacketsupportedbypiles.Thenonlinearpilesaresymbolicallyrepresentedbythespringlikeelementsatthepileheadjoints.Externalforcesareappliedoverthejacketincluding,perhaps,atthepileheadjoints.Thejacketconsistsofthepileinterfacedegreesoffreedom(designatedbysubscriptI)andthefreedegreesoffreedom(designatedbythesubscriptF).TheForceDisplacementrelationshipforthejacketpilecombinationcanbewritteninpartitionedmatrixnotationas:
(3)
Inequation3,thetermsFFandFIaretheexternalforcevectorsappliedtothestructureatthefreeandinterfacedegreesoffreedomrespectivelyandDFandDIarethecorrespondingdisplacementvectors.KPistheassemblednonlinearstiffnessmatrixofthepilesattheinterfacedegreesoffreedom,andFOisthecolumnvectorofthepileinterceptforces.Asdiscussedpreviously,bothKPandFOdependontheinterfacedisplacementvectorDI.Allotherstiffnesscoefficientsareindependentofthedisplacementsandcanbeevaluatedonceatthestartoftheproblem.
Figure5(above)showsthefreebodiesofthejacketandpiles.Theforcesactinginthesebodiesincludetheequalandoppositeinterfaceforcevector,FI.Theforcedisplacementrelationshipsforthepilesandjacketrespectivelyare:
(4)
(5)
Equations4and5aresimplyabreakdownofequation3intothecontributionfromthenonlinearpileandlinearstructurerespectively.Combiningthesetwoequationsyieldsequation3.Equation5canbeexpanded,resultingin:
(6)
(7)
Equation6issolvedforDFandtheresultissubstitutedintoequation7,whichisthenrearrangedtogive:
(8)
Equation8isamatrixequationwhoseorderisequaltothenumberofinterfacedegreesoffreedomofequation4.AddingthesetwoequationseliminatestheinternalinterfacevectorFI.
(9)
ThetermsinthisequationcanbegroupedintothosethatdependonDIandthosethatdonot.Theliketermsarecollectedandtheequationarerearrangedresultingin:
(10)
where:
Equations4and10arethebasisfortheiterativesolution.Onecandoananalysisofeachpileusingthecurrentpileheaddisplacementvectorasitsboundarycondition.Thepileheadforceandmomentarecalculated,thenasecondpileanalysisisdonewithanincrementaddedtothedisplacements,resultinginnewforcesandmoments.Thestiffnesscoefficientsthenaretheratiosofeachofthepileheadforce(ormoment)incrementstoeachofthedisplacement(orrotation)increments.Thepileheadinterceptforce(ormoment)componentsarethencalculatedusingequation4.
Thisprocesscanberepeatedforeachiterationateachpileheadandforeachloadcase.Thisapproach,althoughtheoreticallysound,canrequirealargenumberofpileanalyses.
ThePSIprogramusesamoreefficientapproach.Insteadofdoingpileanalysesateachpileforeachiterationofeachloadcase,anumberofpileanalysesaredoneattheoutsettoproduceasetofpileheadforcevs.displacementcurvessimilartoFigure3.Valuesforpileheadaxialload(ordeflection),lateraldeflection,androtationthatspantherangeofvaluesexpectedinthefinalsolutionareused.Theprogramperformsapileanalysisforeachcombinationoftheseloadsandrotationsandstorestheresults.Foreachiteration,thepileheaddisplacementsareusedtodeterminetheresultingpileheadstiffnesscoefficientandinterceptforcesfromthecurves.Thisprocedureiscontinueduntilapreliminaryconvergenceismet.Uponconverging,PSIcontinuesiteratingbutnowperformsacompletepilestiffnessanalysisforeachiteration.Thisfinetuningprocedurecontinuesuntiltheforcetoleranceormaximumnumberofiterationsismet.
4.3ALIGNINGTUBULARPILELOCALCOORDINATES
ThePYdataforthetypeofproblemscommonlyencounteredintheoffshoreapplicationscanbehighlynonlinearforarangeofdisplacementsoverwhichthepilemayhavetofunction.Thisresultsinpileheadlateralforcedisplacementcurvesthatarelikewisenonlinear.Becauseofthis,inordertogetmoreaccurateresults,PSIperformsitsiterationsintheplaneoftheresultantpileheadlateraldisplacementfortubularpiles.
Inactuality,thefinalresultsmayhaveasmallcomponentofdisplacementoutoftheanalysisplane.Thisisbecause,foreachpile,theplaneisfoundinthefirstiterationandthatplaneisusedforallfurtheriterations.ThechordangleusedinthefirstiterationisreportedintheInitialDeflectionsreportforeachloadcaseundertheheaderBeta.
Toillustratethenecessityfortheapproachtaken,considerapilehavingthepileheadforcedisplacementcurveshowninfigure8(b).Furthermorethepileisloadedinadirectionmakinganangleof45degreeswiththecoordinatesusedforanalysis.ThetrueresultantforceonthepileheadisF,thecorrespondingtrueresultingdisplacementis.ThetrueXandYcomponentsofthepileheadforceareeach0.707(F).Ifthepilewereanalyzedinthesecomponentdirectionsthedisplacementswouldbeequaltoeachotherandhavethevalue0.707,asshowninfigure8(b).Thevectorsumofthesedisplacementswouldbewhichisfarlessthanthetruedisplacement.Thusinordertoinsureanaccurateresultitisseenthattheiterativeanalysisshouldbedoneintheplaneofthepiledeformation.
Thereforeaccuracyislostifalargecomponentofpileheadbendingmomentexistsinthedirectionoftheresultantpileheadlateralload.Ontheotherhand,ifthiscomponentofmomentissmallthenonlyanegligibleerrorismadebyvectoriallycombiningtheanalysesinthetwoplanes.
4.4APIRP2APILERESISTANCE
PSIallowstheusertospecifythepile/soilresponsetoaxial,lateral,andtorsionalloadsappliedatthepilehead.Inlieuofthisinformation,theusermayspecifygeneralsoilpropertieswithwhichthePileprogramwillusetodevelopthepile/soilresponsebasedonAPIRP2Arecommendations.
4.4.1AxialResistance
4.4.2UltimatePileCapacity
Section6.4ofthetwentietheditionofAPIRP2Asuggestthatthepilecapacity,Qd,maybedeterminedfrom:
(6.41.11)
wheref=unitskinfrictioncapacity,As=sidesurfaceareaofpile,q=unitendbearingcapacityandAp=grossendareaofpile.
4.4.3SkinFrictionandEndBearing
Forpipepilesincohesivesoils,theunitskinfriction,f,atanypointalongthepile,canbecalculatedfromthefollowing:
wherecistheundrainedshearstrengthandisadimensionlessfactorthatmaybetakenas:
where=c/po'andpo'istheeffectiveoverburdenpressure.Theunitendbearingqforpilesincohesivesoilsistakenas9*c.
Forpipepilesincohesionlesssoil,theunitskinfrictionandunitendbearingarecalculatedfrom:
(6.4.31)
(6.4.32)
whereK=coefficientoflateralearthpressure,pO=effectiveoverburdenpressure,=angleofsoilfrictiononpilewallandNq=bearingcapacityfactor.
Note:Unitskinfrictionandunitendbearingforcohesionlesssoilsdonotincreaselinearlywiththeoverburdenpressureindefinitely.Thevaluesarelimitedtothemaximumvalueslistedinthetablebelow.
Theusermayentervaluesfortheseparametersoruseprogramdefaults.Thecoefficientforlateralearthpressure,K,maybebetween0.5and1.0assuggestedbyAPI,andhasadefaultvalueof1.0.Atanydepththeprogramusestheweightofthesoilabovethelevelastheeffectiveoverburdenpressure,PO.Thisweightiscalculatedusingthesubmergedunitweightofthesoil,whichtheusermustinput.Thedefaultvaluesforfrictionangle,,andbearingcapacityfactor,Nq,dependonthesoiltypeandarelistedalongwithfmaxandqmaxbelow:
SoilType Nq fmax qmaxGravel 350 50 2.4 250
CleanSand 300 40 2.0 200
SiltySand 250 20 1.7 100
SandySilt 200 12 1.4 60
Silt 150 8 1.0 40
Note:Forrocktheusermustinputvaluesfortheskinfrictioncapacity,f,andtheunitbearingcapacity,q.
4.4.4SoilAxialLoadTransferCurves
Axialloadtransferandpiledisplacementcurves,TZcurves,areconstructedbasedonAPIRP2Arecommendations.TheTZcurvesaregeneratedbasedonthefollowingtableswherezisthelocalpiledeflection,Disthepilediameter,tisthemobilizedsoiladhesionandtmaxisthemaximumsoilpileadhesionorunitskinfriction.
Clay Sandz/D t/tmax z t/tmax0.00 0.00 0.00 0.00
0.0016 0.30 0.10 1.000.0031 0.50 1.000.0057 0.75 0.0080 0.90 0.0100 1.0 0.0200 0.700.90 0.700.90
4.4.5TipLoadDisplacementCurves
TheendbearingortiploadcapacitycanbegeneratedintheformofendbearingTZ(orQZ)curvesbasedonAPIRP2Arecommendationsasfollows:
z/D 0.002 0.013 0.042 0.073 0.100 t/tp 0.25 0.50 0.75 0.90 1.00 1.00
wherezistheaxialtipdeflection,Disthepilediameter,tisthemobilizedendbearingcapacityandtpisthetotalendbearing.
4.4.6LateralResistanceforSoftClays
PYcurvesforlateralresistancearegeneratedbasedonthesuggestionsinsection6.8ofthetwentietheditionofRP2A.Forsoftclaystheultimateresistingpressure,pu,isgivenby:
forXXR
(6.8.22)
where:
c=undrainedshearstrengthofundisturbedclaysampleD=pilediameter=effectiveunitweightofthesoilJ=dimensionlessconstantbetween0.25and0.5X=depthbelowsoilsurfaceXR=depthtobottomofthezoneofreducedresistance.
Note:XRisthevalueofXforwhichequations6.8.21and6.8.22produceequalvaluesforpu.
OncetheultimateresistanceisknownthePYcurveisconstructedasaseriesofstraightlines.Twocasesarise:staticandcyclicloadconditions.ForthestaticcasethefollowingpointsdefinethePYcurve:
wherep=lateralresistance,y=lateraldeflection,yc=2.5ecDandec=strainatonehalfthemaximumstressforundrainedcompressiontestforundisturbedsamples.
ForcyclicloadingthepointsdefiningthePYcurvesare:
4.4.7LateralResistanceforSand
RP2Agivestheultimatebearingcapacityforsandasthesmallervalueof:
wherepu=ultimateresistance(subsciptsforshallow,dfordeep),=effectiveunitweightofsoil,H=depth,D=pilediameterandC1,C2,C3=coefficientsfromfigure6.8.61inAPIRP2A(using'=angleofinternalfrictionforsand).
Theloaddeflection(PY)curvesarenonlinearandareapproximatedbythefollowingexpression:
wherepu=ultimatebearingcapacityatdepthH,k=initialmodulusofsubgradereaction,y=lateraldeflection,H=depth,A=0.9forcyclicloadingor3.00.8H/D0.9forstaticloading.
4.5EQUIVALENTPILESTUB
Thefollowingisthederivationofthemethodusedtolinearizethesoil/pilesystemintoanequivalentpilestub.
Throughoutthisdiscussion,thefollowingdefinitionsapply:
RigidLinkRelationships:
GoverningEquationsMatrixNotation
ElasticStub
RigidLink
(B2)
(B3)
or
(B3')
Substituting3'into1theninto2thefollowingequationresults.
(B4)
(CombinedStiffness)Theelasticstubstiffnessmatrixcanberewrittenasfollowsfrombeamtheory.
Invertingthematrixyields:
therefore,fortheelasticstub:
(B5)
(B6)
(B7)
Substitutethesevaluesintoequation4todeterminecombinedstiffnessterms.
SolvingforI,LoandLyields:
(B8)
(B9)
(B10)
Inaddition,theaxialstiffnessofthepileismodeledbygivingthepileacrosssectionalareasuchthat:
or
wherethelength,L,isfromequation(B10).
4.5.1RulesforModelingaPileStub
Pilestubsmaybemodeledsuchthatthestubrunsdownfromthepileheadtothepilestubtiporfromthepilestubtipuptothepileheadjoint.Ineithercase,thedistancefromthepileheadtothepiletipisrepresentedbyL+Lo,whereListheactuallengthofthepilestubelementandLoiseitherapositiveornegativeoffset.
ThePileprogramreportsthepilestubpropertiesassumingthatthepilestubismodeledfromthepileheaddowntothepilestubtip.Therefore,positiveoffsetsreportedbytheprogramrefertoanoffsetdownfromthepileheadjointthatshortensthestubmember(seeFigureA).Conversely,offsetsreportedasnegativenumberselongatethepilestubabovethepileheadjoint(seeFigureB).
Whenaddingpilestubstoamodel,thefollowingrulesshouldbeadheredto:
1. UsePrismaticcrosssectionPRIfortheelasticstubmodel.Useshearareastentimeslargerthantheaxialareatoeliminatesheardeflection.
2. Uselocalmemberoffsets.
3. Fixthetipofthepilestubtoground.
5.0TROUBLESHOOTINGCOMMONPROBLEMS
PSIisaniterativesolutionapproachtoahighlycomplicatedproblemandassuchrequiresacertaindegreeofcareonthepartoftheuser.ThefollowingsectiondiscussesmeansofavoidingandcorrectingproblemsthatmayariseduringexecutionofPSI.
1. Whenapilecannotcompletelydissipatetheaxialload,itmayexperiencesoilpunchthrough.Usuallypilesexhibitingthisproblemmustberedesignedwithincreasedpilepenetration,thusprovidingmorepilelengthavailabletodissipatetheload
ThisproblemmayalsooccurifuserspecifiedTABRvaluesexceedthepilesaxialcapacity.Ifthefinalaxialloadsaremuchsmallerthantheuserinputvalues,thevaluesshouldbedecreasedsothattheaxialbehaviorisadequatelydefinedintherangeofthesolutionvalueandtheuserspecifiedloadsdonotcausepunchthrough.Alternatively,theusercanspecifyaxialdeflectionvaluesinsteadofloadvalues.
2. Theiterativepilesolution(eitheraxialorlateral)mayfailtoconverge.Theprogramwillproduceamessagetotheeffectthatthesolutiondidnotconvergefortheparticularsetofconditionsinvolved.
ThisusuallyoccursfortheaxialsolutionwhentheTZcurveshaveasharpslopediscontinuityforthesamevalueofdisplacementoverthelengthofthepile.Iftheaxialloadissuchthatthepiledisplacesbythisamount,theiterationproceduremaycyclebackandforthfromoneportionoftheTZcurvetoanotherwithoutconverging.TheproblemcanbecorrectedbyeitherreplacingtheTZcurvesbyoneswithamoregradualtransitionfromoneportiontoanotherorbychangingtheTABRvalue(ifspecified)byasmallamount(perhaps5or10percent)sothatthepilesolutionwillberemovedfromthepointofslopediscontinuity.Similarbehaviormayoccurforthelateralsolution,butislesscommonsinceforlateralloadstheentirepiledoesnotdisplacebyapproximatelythesameamountasisthecaseforaxialloads.LackofconvergenceforlateralloadsmaybesimilarlycorrectedbymodifyingthePYcurvestosmoothouttheslopediscontinuitiesorbychangingtheoptionallateralTABRdeflectionvalues.
3. Thenumberofiterationsallowedperloadcasemaybeexceededif:
a.toofewiterationsarerequested(columns4143ofthePSIoptionsline).b.theconvergencetolerancesaretoosmall(columns2540ofthePSIoptionsline).c.unusualsoilconditions,suchasaverystiffstratum(rock)sandwichedbetweentwoverysoftstrata,arepresent.
Theproblemcanusuallyberesolvedbyincreasingthenumberofiterations.
4. Thecombinedreducedstructuralstiffnessmatrixandpileheadstiffnessmatrixisnonpositivedefinite.Thecombinedstructuralandpilestiffnessmatrixmaybesingular.Thisisusuallytheresultofajointinthestructurebeingimproperlyconstrained.Oneverycommoninstanceofthisiswhenaconductorisreleasedforallthreerotationsatallofitsnodes,includingthetopone.Thiscausestheconductortohavenotorsionalstiffness,whichresultsinthesingularstiffnessmatrix.ThecorrectionistoremovethereleaseforrotationaboutthelocalXaxisatanynodeornodes.
6.0SAMPLEPROBLEMS
ThestructureshowninthefigurewasusedtoillustratethevariouscapabilitiesofthePSIprogram.Threeseparaterunsareillustrated:
1. ThefirstproblemisatypicalPSIanalysiswhereaxialandlateralsoilpropertiesaredescribedbyTZandPYcurvesrespectively.Inaddition,numerousplotsweregeneratedincludingthesoildata,axialandlateraldeflectionsandpileunitycheck.ThepileheadstiffnesstablesweregeneratedautomaticallyinPSI.
2. SampleProblem2isasinglepileanalysisusedtodeterminetheequivalentpilestubofthesoil/pilefoundation.Inlieuofcurvestodefinethesoilloaddisplacementrelationships,generalsoilpropertieswereinput.PileusedthisinformationtoformthesoilloaddisplacementrelationshipperAPIRP2Arecommendations.
3. SampleProblem3illustratesamudslidecaseintheglobalXdirection.Userdefinedpileheadstiffnesstableswereused.
SAMPLEPROBLEM1
ThefollowingisanexampleofatypicalPSIanalysiswhereTZandPYcurvesareusedtodefinetheloaddisplacementrelationshipofthesoil/pilefoundationintheaxialandlateraldirectionsrespectively.
Thestructureshowninthefigurestandsin82.02ft.ofwater.Themodelcontainsoneuserdefinedloadcondition(LC1),whichrepresentsa150psfliveloadonthedeck.Loadconditions2and3containenvironmentalloadingincludingwind,wave,currentandgravity.Windarea,marinegrowth,coefficientofdragandmassoverrides,andmemberandgroupoverridesarespecified.Loadconditions4and5arecombinationsofloadcases1and2,and1and3respectively.Onlytheloadcombinations(LC4andLC5)arepassedtoPSIforanalysis.
ThefollowingisaportionoftheSACSinputfilecontainingtheinputlines.Forclarity,somemodeldatanotspecifictoPSIhasbeenomitted.Themodelinputfilespecifiesthefollowing:
A. TheOPTIONSlinespecifiesaPSIanalysis(col.1920)withnocodecheckforthemainstructure(col.2526).B. TheLCSELlinespecifiesthatonlyloadcases4and5aretobepassedtoPSIforanalysis.C. Joints2,4,6and8arespecifiedaspileheadjointsbyPILEHDincolumns5560ontheJOINTline.
ThefollowingisthePSIinputfileusedinSampleProblem1,followedbyadetaileddiscussionoftheinputlines.
A. ThePSIOPTlinespecifiesEnglishunits(col.1012)andthatafinalpileanalysisistoexecutedwithsummarizedoutputreports.
B. ThePLTRQlinerequestthatsoildata,axialdeflection,lateraldeflectionandunitycheckplotsbegenerated.
C. ThePLGRUPlinesdesignatepilegroupPL1asa28inchdiametersegmentedmember1.5inchwalland50ksi,forthefirst50feetand0.75inchwall36ksifortheremaining175feet.
D. Pileheadjoints2,4,6and8areassignedreferencejoints201,203,205and207respectively.AllpileshavememberpropertiesdefinedbygroupPL1andusesoilpropertiesdefinedbysoilgroupSOL1.
E. TheSOILTZAXIALHEADlineindicatesthattwosoillayerswillbedefinedbyTZcurvesforsoilgroupSOL1.
F. Theelevationofthesoillayer,thenumberofpointsdefiningthecurveforthatlayerandthefactortowhichmultiplyTby,aredesignatedontheSOILSLOCline.
G. TheTZcurveforthesoillayerspecified,isdefinedbythepointsspecifiedontheSOILTZline.
H. Atorsionalspringwithstiffnessvalueof277910.0inkip/radianforsoilgroupSOL1isdesignatedontheSOILTORSIONHEADline.
I. TheSOILLATERALHEADlinespecifiesthatfivesoilstrata,withamaximumof13pointsdefiningthePYcurve,willbeusedtodefinethelateralloaddeflectionrelationshipofthesoil/pilesystem.Thereferencediameteris28.0inches.
J. ThePYcurveforthesoillayerattheelevationspecifiedonthepreviousSLOCline,isdefinedbythepointsspecifiedontheSOILPYline.
ThefollowingarethePSIoutputplotsandaportionofthelistingfileforSampleProblem1.
SAMPLEPROBLEM2
SampleProblem2isasinglepileanalysisusedtodeterminetheequivalentpilestubofthesoil/pilefoundation.Inlieuofcurvestodefinethesoilloaddisplacementrelationships,generalsoilpropertieswereinput.PileusedthisinformationtoformthesoilloaddisplacementrelationshipperAPIRP2Arecommendations.
Thefollowingistheinputfileusedfortheequivalentpilestubanalysisalongwithadescriptionoftheinputlines:
A. ThePILOPTlinespecifiesEnglishunits(col.1012)andthatapilecodecheckistoexecuted.
B. ThePLTRQlinerequestthatsoildataplotsbegenerated.
C. ThePLGRUPlinesdesignatepilegroupPL1asa28inchdiametersegmentedmember1.5inchwalland50ksi,forthefirst50feetand0.75inchwall36ksifortheremaining175feet.
D. Pileheadjoint2isassignedmemberpropertiesdefinedbygroupPL1andusesoilpropertiesdefinedbysoilgroupSOL1forthepilelocalXZandXYplanes.
E. TheSOILAXIALHEADlineindicatesthatthesoilaxialpropertieswillbedescribedforeightsoilstrata.TheprogramwillgenerateskinfrictionandbearingbasedonAPIRP2Arecommendations.ThesesoilpropertiesareassignedtosoilgroupSOL1.
F. Theelevationofeachsoillayer,thetypeofsoilandthecharacteristicsofthesoillayerarespecifiedontheSOILAPIAXLSLOCline.
G. Atorsionalspringwithstiffnessvalueof1000.0inkip/radianforsoilgroupSOL1isdesignatedontheSOILTORSIONHEADline.
H. TheSOILLATERALHEADlinespecifiesthatsixsoilstratawillbeusedtodefinethelateralloaddeflectionrelationshipofthesoil/pilesystem.Thepilereferencediameteris28.0inches.
I. TheSOILAPILATSLOClinesspecifythesoilpropertiestobeusedtodevelopPYcurvesbasedonAPIRP2Arecommendations.Thesoiltype,elevationandsoilpropertiesforeachsoillayerarespecified.
J. ThePLSTUBinputlinedesignatestheloadsordeformationsthataretobeusedtodetermineanequivalentpilestub.Inthissample,theDincolumn10designatesthatpileheaddisplacementswillbeinput.Areferencejointname1002incolumns11to14isdesignatedandalateraldisplacementof2.2802inchesandarotationof0.01306radiansarespecified.Thecorrespondingaxialloadof625.4isalsospecified.
ThefollowingistheneutralpicturefileandaportionofthePileoutputlistingforSampleProblem2.
SAMPLEPROBLEM3
SampleProblem3isthesameasSampleProblem1exceptthatamudslideintheglobalXdirectionwasisspecifiedinthePYdata.Also,userdefinedpileheadstiffnesstablesarespecifiedintheinputfile.ThefollowingisthePSIinputfile,followedbyadescriptionofthelines.
A. ThePSIOPTlinespecifiesEnglishunits(col.1012)andthatafinalpileanalysisistoexecutedwithsummarizedoutputreports.Theweightofthepileistobeincluded,andcalculatedusingadensityof490lbs/cu.ft.
B. ThePLTRQlinerequestthatsoildata,lateraldeflectionandunitycheckplotsbegenerated.
C. ThePLGRUPlinesdesignatepilegroupPL1asa28inchdiametersegmentedmember1.5inchwalland50ksi,forthefirst50feetand0.75inchwall36ksifortheremaining175feet.
D. Pileheadjoints2,4,6and8areassignedreferencejoints201,203,205and207respectively.AllpileshavememberpropertiesdefinedbygroupPL1andusesoilpropertiesinthelocalXZandXYplanesdefinedbysoilgroupsSOL1andSOL2respectively.Also,pilechordanglesof225,135,45and315degreesforpileheadjoints2,4,6,and8respectively,havebeenassignedinordertoalignthepileXYplanewiththeglobalXZplane.
E. TheSOILTZAXIALHEADlineindicatesthattwosoillayerswillbedefinedbyTZcurvesforsoilgroupSOL1.
F. Theelevationofthesoillayer,thenumberofpointsdefiningthecurveforthatlayerandthefactortowhichmultiplyTby,aredesignatedontheSOILSLOCline.
G. TheTZcurveforthesoillayerspecified,isdefinedbythepointsspecifiedontheSOILTZline.
H. Atorsionalspringwithstiffnessvalueof277910.0inkip/radianforsoilgroupSOL1isdesignatedontheSOILTORSIONHEADline.
I. TheSOILLATERALHEADlinespecifiesthatfivesoilstrata,withamaximumof13pointsdefiningthePYcurve,willbeusedtodefinethelateralloaddeflectionrelationshipofthesoil/pilesystem.Thereferencediameteris28.0inches.
J. ThePYcurveforthesoillayerattheelevationspecifiedonthepreviousSLOCline,isdefinedbythepointsspecifiedontheSOILPYline.
K. ThesecondSOILTZAXIALHEADlineindicatesthattwosoillayerswillbedefinedbyTZcurvesforsoilgroupSOL2.TheprocedureforTZcurvesforSOL2isthesameusedforSOL1.
L. TheSOILLATERALHEADlinespecifiesthattwosoilstrata,willbeusedtodefinethemudslidelateralloaddeflectionrelationshipofthesoil/pilesystem.Thereferencediameteris28.0inches.
M. ThePYcurveforthesoillayerattheelevationspecifiedonthepreviousSLOCline,isdefinedbythepointsspecifiedontheSOILPYline.
N. Thepileheadstiffnesstablesforaxialdeflection,lateraldeflection,rotationandtorsionarespecifiedforpilegroupPL1andeachsoilgroupSOL1,andSOL2bytheTABRlines.
ThefollowingarethreeoftheplotfilescreatedinSampleProblem3.AportionofthePSIlistingfilefollowsonthesubsequentpages.