GeotechnicalAnalysisExamplesTheintentionofthismoduleistodescribe thetypesofgeotechnicalproblemsthatcanbesimulatedusingOpenSees,andtodiscusstheessentialtoolsthatareneeded tocreatethetypesofmodelsusedingeotechnicalanalysis.
Becausemostgeotechnicalmodelsfilesarequitelargeincomparisontostructuralanalyses,thecurrentmodulewillalsopresentsomeadvancedgeotechnicalmodelstodemonstratewhatcanbedonewiththistool.
o OpenSeesgeotechnicalexamplescanbefoundat(amongotherplaces)
opensees.berkeley.edu/wiki/index.php/Examples
opensees.berkeley.edu/wiki/index.php/FluidSolidPorousMaterial
opensees.berkeley.edu/wiki/index.php/PressureDependMultiYield_Material
opensees.berkeley.edu/wiki/index.php/PressureIndependMultiYield_Material
GeotechnicalAnalysisExamplesTypesofgeotechnicalproblemsthatcanbesolvedwithOpenSees:
o StaticProblems:o Deformationanalyses(1D,2D,3D)o Consolidationproblems(diffusionproblems)o Soil-structureinteractionproblems
o Shallowfoundation(bearingcapacity,settlement)o Deepfoundations(verticalandlateralcapacity)
o DynamicProblemso Free-fieldanalysis(siteresponse)o Liquefactionandliquefaction-inducedphenomenao Soil-structureinteractionproblems
GeotechnicalAnalysisExamplesWhattoolswillweneed?
o 2Dand3Dsolidelementstocharacterizethesoildomain(continuum)o Appropriateboundaryconditionstoaccuratelyrepresent thesoildomainboundariesandnotsignificantlyaffect theareaofinterest
o Robustconstitutivemodelstocharacterize thestress-strain responseofthesoilundermonotonicandcyclicloadingconditions
o Interfaceelementsandmaterialstocapturetheinteractionbetweenthesoilandanyadjacentstructures
o Everythingelsewearediscussinginthisworkshop(howtocreatebeamelements,applyloads,boundaryconditions,recordresults,performanalyses,etc)
FiniteElementTools
Single-phaseformulationso Tocapturetheresponseofdrysoils(ortotalstressanalysis)o Onlyneedasinglephase
o Phase1:soilskeleton
Multi-phaseformulationso Tocapturetheresponseofsaturatedsoils(effective stressanalysis)o Nowneedtwophases
o Phase1:soilskeletono Phase2:porewater
Zero-Lengthelementso Tocaptureinterfaceresponsebetweensolidandbeamelements,andtoapplyabsorbentboundaryconditions
Contactelementso Tocaptureinterfaceresponsebetweendifferent bodies
SinglePhaseFormulations
Smalldeformationsolidelementso 2Dquadrilateralelements (quads)– typicallywith4nodeso 3Dhexahedralelements (bricks)– typicallywith8nodes
SinglePhaseFormulations
Single-phasequadelementsinOpenSeeso –ndm 2–ndf 2o Ingeotechnicalproblems,for2Danalysis,wenearlyalwaysareworkinginplanestrain,notplanestress
o Primarytools:quad,SSPquad,bbarQuad,enhancedQuado Exampleusageforquad element(allaresimilar)
elementquad$tag$n1$n2$n3$n4$thick$type$matTag <$press$rho$b1$b2>
where$thickisthethicknessintothescreen(often1.0),$typeisastringidentifying“PlaneStrain”or”PlainStress”,$matTag isthetagofthenDMaterial objectassociatedwiththeelement,$pressisanoptionalsurfacepressure(default0.0),$rhoisthemassdensity,and$b1and$b2arebodyforcesinthex- andy-directions
Counterclockwisenodeconnectivity!
SinglePhaseFormulations
Single-phasebrickelementsinOpenSeeso –ndm 3–ndf 3o Primarytools:stdBrick,SSPbrick,bbarBricko ExampleusageforstdBrick element(allaresimilar)
elementstdBrick $tag$n1$n2$n3$n4$n5$n6$n7$n8$matTag <$b1$b2$b3>
where$matTag isthetagofthenDMaterial objectassociatedwiththeelement,and$b1,$b2,$b3arebodyforcesinthex-,y-,andz-directions
Counterclockwisenodeconnectivity!
Multi-PhaseFormulations
Fullycoupledu-pelementso 2Dquadrilateralelements (quads)– 4and9nodeso 3Dhexahedralelements (bricks)– 8and20nodes
Degreesoffreedomare:o Soliddisplacementsuono Porefluidpressurepon
Multi-PhaseFormulations
Multi-phasequadelementsinOpenSeeso –ndm 2–ndf 3o Primarytools:quadUP,SSPquadUP, bbarQuadUP,and9_4_QuadUP(thislastoneisaspecialcase)
o ExampleusageforquadUP elementelementquadUP$tag$n1$n2$n3$n4$thick$matTag $bulk$fmass $hPerm$vPerm <$b1$b2$t>
where$bulkisthecombinedbulkmodulusB=Bf/n,$fmass isthefluidmassdensity,$hPermand$vPerm arethehorizontalandverticalpermeabilities,$b1and$b2arebodyforcesinthex- andy-directions,and$t isasurfacetraction
Counterclockwisenodeconnectivity!
Multi-PhaseFormulationsThe9_4_QuadUPelementusesquadraticshapefunctionsfordisplacementandlinearforpressuretoavoidnumericalissues
o –ndm 2–ndf 3atthecornernodes, -ndf 2attheothers!Needtocreatetwomodeldomainstousethiselement.
o Exampleusagefor9_4_QuadUP elementelement9_4_QuadUP$tag$n1$n2$n3$n4$n5$n6$n7$n8$n9$thick$matTag$bulk$fmass $hPerm $vPerm <$b1$b2>
Nodes1,3,5,and7mustbecreatedwith3dof,whilenodes2,4,6,8,and9mustbecreatedwith2dof.Thisrequirestwoseparatedomains(i.e.needtospecifymodelBasicBuilder…twiceinthemodelfile)
Inalloftheu-pelements,duetothewayinwhichthesystemofequationsisformulated,thepressuredofareinthevelocityvector.Duetothis,theseelementscanonlybeusedinTransientanalysis,andrecordercallsforpressureusevel
ReducedIntegrationElements
Stabilizedsingle-point(SSP)solidelementso SSPquad,SSPquadUP,SSPbrick,and SSPbrickUPoUsestabilizedsingle-pointintegrationwithanenhancedstrainfieldtoremovevolumetricandshearlocking
oWhyaren’tallelements formulated inthismanner?o Thereareissueswhichmustbeovercomeinordertousesinglepointintegration.Thestiffnessmatrixbecomesrankdeficient,leadingtospuriousdeformationmodes
o Stabilizationtechniquesareusedtoovercometherankdeficiency
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ReducedIntegrationElements
Whatarethebenefitsoftheseelements?oNoshearlockinginbendingapplicationso Lesscomputationaldemandthanstandardelements
Executiontime: Quadelement =330sec SSPquad element =146sec
Siteresponseanalysistestproblem
ReducedIntegrationElements
Whatarethebenefitsoftheseelements?oNoshearlockinginbendingapplicationso Lesscomputationaldemandthanstandardelements
Flexiblefootingloadtestproblem
ReducedIntegrationElements
Whatarethebenefitsoftheseelements?oNoshearlockinginbendingapplicationso Lesscomputationaldemandthanstandardelements
unstabilized SSPquadUP stabilizedSSPquadUP9nodequadelement
ReducedIntegrationElements
Whatarethebenefitsoftheseelements?oNoshearlockinginbendingapplicationso Lesscomputationaldemandthanstandardelements
Surfaceresponsespectrafromeffectivestresssiteresponseanalysis
ReducedIntegrationElements
Whatarethebenefitsoftheseelements?oNoshearlockinginbendingapplicationso Lesscomputationaldemandthanstandardelements
SSPquadUP element
9_4_QuadUPelement
ConstitutiveModels
In2Dand3D,weneedtousematerialmodelsthatcancapturemulti-dimensionalresponse
o ForthisreasonnDMaterial objectswillbeourprimarytoolsforgeotechnicalmodelinginOpenSees
o Therearemanyavailableoptionso GeneralnDMaterials (e.g.ElasticIsotropic,J2Plasticity)o SoilnDMaterials (forbothtotalandeffective stressanalysis)o nDMaterials formodelingconcretewalls
oWewillalsoneedtomakeuseofuniaxialMaterials forthingslikeimplementingabsorbingboundariesandsoil-structureinteractionproblems.
ConstitutiveModels
ListofnDMaterials inOpenSees
http://opensees.berkeley.edu/wiki/index.php/NDMaterial_Command
ConstitutiveModels
ListofnDMaterials inOpenSees
http://opensees.berkeley.edu/wiki/index.php/NDMaterial_Command
ConstitutiveModels
Forgeotechnicalanalysis,itiscritical thatweachievetheproperinitialstateofstressinthesoilbeforewestartapplyingexternalloads
o Thisistypicallydoneusingastagedanalysiswheresettingsand/orpropertiesofthesoilmaterialsarechangedfromthemodelfileaftercompletingdifferentanalysisstages
o Someadditionalcommandsthatmakethispossible:
o updateMaterialStage –material$matTag –stage$stageNum
o setParameter –value$pVal –eleRange $e1$eN $paramName
oDocumentationwilldiscusswhatoptionsareavailableforagivennDMaterial object
ConstitutiveModels
Forsoil-structureinteractionproblems,weneedawaytocapturetheinterfaceresponsebetweensolidelements(soil)andbeamelements(pile)
WecanusePy,Tz,andQzuniaxialMaterials andzeroLength elements forthispurpose.
o PySimple1o TzSimple1o QzSimple1
o PyLiq1o TzLiq1
ConstitutiveModels
PySimple uniaxialMaterial formodelinglateralsoil-pileinteractionresponse
o uniaxialMaterial PySimple1$tag$soilType $pult $y50$Cd<$c>
o $soilType à 1=clay(Matlock),2=sand(API)o $pultà ultimatecapacityofp-ymaterialo $y50à displacement at50%ofpulto $Cdà dragresistance(1=nogap,<1=gap)o $cà viscousdamping
ConstitutiveModels
PyLiq1uniaxialMaterial forlateralsoil-pileinteractionresponsewithconsiderationforstrengthreductionwithbuild-upofexcessporepressure
o uniaxialMaterial PyLiq1$tag$soilType $pult $y50$Cd$c$pRes$solidElem1$solidElem2
o $soilType à 1=clay(Matlock),2=sand(API)o $pultà ultimatecapacityofp-ymaterialo $y50à displacement at50%ofpulto $Cdà dragresistance(1=nogap,<1=gap)o $cà viscousdampingo $pResà residualp-yresistanceforru =1.0o $solidElem1and$solidElem2à solidelements fromwhichthePyLiq1objectwillobtainmeaneffectivestressesandporepressures
ConstitutiveModels
PyLiq1uniaxialMaterial forlateralsoil-pileinteractionresponsewithconsiderationforstrengthreductionwithbuild-upofexcessporepressure
BoundaryConditions
PeriodicboundaryconditionscanbeimplementedusingtheequalDOF command(whichwehaveseenbefore)
o equalDOF $retainedNode $constrainedNode $dof1$dof2…
o $retainedNodeà tagoftheretainednode(masternode)o $constrainedNodeà tagoftheconstrainednode(slavenode)o $dof1$dof2...à constraineddof
BoundaryConditions
Absorbingboundariescanalsobeimplementedusingtoolsandtechniquesthatwe’veseenalready
Single-ElementTestingItisoftenusefultotest,verify,andcalibratesoilconstitutivemodels(nDMaterials)usingsingleelementteststhatputmaterialsthroughthesamestresspathsaslaboratorytestsforsoils.
Forexample,aconventionaltriaxial compression(CTC)testcanbemodeledusingasingleelementasshowninthisschematic.
SingleElementTesting
We’llquicklywalkthroughthesingleelementCTCtestfile.Thefirsttaskistodefinesomegeneraltermsthatwillbeusedintheanalysis.
Wedefinethedesiredconfiningstress, theapplieddeviatoricdisplacement,andthepermeabilityofthesoil(forundrainedconditions,setthistosomethingverysmall)Wealsodefine theRayleighdampingparametersatthebeginningofthefilesotheyareeasytofindifwewanttochangethem.TheRayleighcommandiscalledlater,oncewe’vedefinedthedomain.
SingleElementTesting
Wewantouranalysistostartfromatrulyhydrostaticstateofstress, soweneedtousea3Dbrickelementanddefinethedomainwith3dimensions(-ndm 3).Wealsowantthetesttobeundrained,soweneedtouseau-pelementandasmallpermeability.Thisrequiresustouseadomainwith4dof (-ndf 4)astheporepressure isassignedtothe4th dof.
SingleElementTesting
Thenodesarecreatedin3D(requires3coordinatespernode).Thesizeoftheelementdoesn’treallymatterforthisanalysis,a1.0unitcubeisused.
Duringtheinitialanalysisphase,wefixtheporepressuredof (dof 4)suchthatpressurecannotdevelop(analogoustohavingthevalveopen).
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SingleElementTesting
Thenodesarecreatedin3D(requires3coordinatespernode).Thesizeoftheelementdoesn’treallymatterforthisanalysis,a1.0unitcubeisused.
Duringtheinitialanalysisphase,wefixtheporepressuredof (dof 4)suchthatpressurecannotdevelop(analogoustohavingthevalveopen).
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SingleElementTesting
Thenodesarecreatedin3D(requires3coordinatespernode).Thesizeoftheelementdoesn’treallymatterforthisanalysis,a1.0unitcubeisused.
Duringtheinitialanalysisphase,wefixtheporepressuredof (dof 4)suchthatpressurecannotdevelop(analogoustohavingthevalveopen).
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SingleElementTesting
Thenodesarecreatedin3D(requires3coordinatespernode).Thesizeoftheelementdoesn’treallymatterforthisanalysis,a1.0unitcubeisused.
Duringtheinitialanalysisphase,wefixtheporepressuredof (dof 4)suchthatpressurecannotdevelop(analogoustohavingthevalveopen).
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SingleElementTesting
ThePressureDependMultiYieldnDMaterial isusedhere.Theinputsandcapabilitiesofthismaterialmodelarediscussedat:http://opensees.berkeley.edu/wiki/index.php/PressureDependMultiYield_Material
SingleElementTesting
TheSSPbrickUP element isused.Itrequiressomeinformationabouttheporefluid(waterinthiscase)andtheinitialvoidratioofthesoil.http://opensees.berkeley.edu/wiki/index.php/SSPbrickUP_Element
SingleElementTesting
Notehowtheelementconnectivityisspecified inacounterclockwiseorder.Thisisnottheonlynodeorderingwecouldhaveused,butthenodenumberswerechosentomakeiteasytoinputintotheelement.
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SingleElementTesting
quad/brickelementshaverecorders toeasilyoutputthestress/strainattheintegrationpointsoftheelementWeusethePenaltyconstraintsherebecauseduringtheshearingphase,alloftheporepressuredof willbefree.
SingleElementTesting
Theconfinementpressure isappliedinaPlainloadPattern withtheimbeddedtimeSeries shownhere.Notethatwedividethedesiredmeanpressureby4whenapplyingnodalforces.
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SingleElementTesting
ThisaTransientanalysis,sowemustspecifyananalysistimestep.Becausewewanttheshearingphasetostartfromessentiallystaticconditions,weuseverylargetimestepstoensure thatanywavescreatedbytheloadinghavedampedout.Thistechniqueonlyworksbecause thematerialiselasticduringthisphase!
SingleElementTesting
Afterwearesatisfiedthathydrostaticstressconditionshavebeenappropriatelyapplied,weremovetheconstraintswespecifiedontheporepressuredof (4th dof)ofeachnodeto“closethedrainagevalves”.Thisisaccomplishedusingtheremovecommand
http://opensees.berkeley.edu/wiki/index.php/Remove_Command
SingleElementTesting
ThenextstepistoinstructthenDMaterialobjecttoconsiderelastoplasticresponseusingtheupdateMaterialStage command.ThedefaultstateforthePressureDependMultiYield modelislinearelasticbehaviour.
http://opensees.berkeley.edu/wiki/index.php/UpdateMaterialStage
SingleElementTesting
Theshearingphaseisthelastpartoftheanalysis.ThedeviatorstressisappliedunderstraincontrolinthisexamplebyspecifyingthedisplacementsoftheuppernodesintheloadPattern usingthesp commandhttp://opensees.berkeley.edu/wiki/index.php/Sp_Command
Single-ElementTestingFromtherecordedstresses, wecancreateaplotofthestresspathforthissingleelementsimulatedCTCtestasshownbelow.
Single-ElementTestingWecansimulateotherlaboratorytestsusingsingleelementmodelsandasimilarapproachtowhatwejustsaw.
Forexample,adirectsheartestcanbemodeledusingasingleelementasshowninthisschematic.Themodelfileforacyclicdirectsheartesthasbeenmadeavailablethroughthisworkshop.
TotalStressSiteResponseAnalysis
Alayeredorhomogenoussoilprofileismodeledin2Dusingnodeswith2DOF.
ThisexampledescribeshowtorunatotalstresssiteresponseanalysisinOpenSees.
Soilconstitutivemodelsinclude:PressureDependMultiYieldPressureIndependMultiYield
Periodicboundaryconditionsareenforcedinhoriz.directionusingtheequalDOFcommand
AcompliantbaseisconsideredusingaviscousdashpotmodeledusingazeroLength elementandtheviscousuniaxialMaterial .
AdetaileddiscussionisavailableontheOpenSeespracticalexamplespageat:http://opensees.berkeley.edu/wiki/index.php/Site_Response_Analysis_of_a_Layered_Soil_Column_(Total_Stress_Analysis)
TotalStressSiteResponseAnalysis
Thematerialandgeometricparametersforthesoilcolumnareplacedinthebeginningofthefiletomakethingseasiertofindandchange.Thisexampleconsidersasingle40mthicklayerofsoil.Amodelfileforalayeredsoilprofilefollowstheexactsamesteps,itisjustmorecomplicated,soweareusingasimplercase.
TotalStressSiteResponseAnalysis
Wealsodefinesomeanalysisparametershere, includingthegroundmotiondetails,theRayleighdampingterms,andNewmarkintegratorterms.
Wealsospecifysomeparametersthatwillbeusedtodetermine thesizeoftheelementsinthemodel.Herewehavespecified100Hzasthehighestfrequencywewantwellresolved (10elements inonewavelength).Theelementsizewillbedeterminedbasedonthisinformation.
TotalStressSiteResponseAnalysis
Theelementsizedefinitionishere.Wesetatrialnumberofelementsbasedonthewavelengthcomputedpreviously,thenmakesureanintegernumberofelementswillbeinthemodel(can’thave2.34516elems).Thenumberofelems definestheverticalelementsizeandthenthenumberofnodes.
TotalStressSiteResponseAnalysis
Thenodesforthesoilcolumnarecreatedinaloop.Takingadvantageoftcl scriptinglikethissavesatonoftime(andspaceinyourmodelfile).Forexample,inthiscasethereare160elementsinthemodel,whichcorresponds to322nodes.Enteringthosebyhandwouldnotbeveryfun.
TotalStressSiteResponseAnalysisThecomplianceoftheunderlyingmaterialisconsidered inthemodelusingadashpot(afterLysmer)andthegroundmotionapplicationtechniqueofJoynerandChen(1975).
Forthismodelingapproach,aviscousdashpotisplacedatthebaseofthesoilcolumn.
HerewealsoimplementtheperiodicboundaryconditionsusingtheequalDOF command.
TotalStressSiteResponseAnalysis
ThenDMaterial andelementsaredefinedhere.Theelementsaredefinedinaloopaswell.Settingthisupinitiallytakesabitofthought,butitdefinitelypaysoff.
TotalStressSiteResponseAnalysis
TheviscousuniaxialMaterial isusedwithazeroLength elementtodefinethedashpotatthebaseofthesoilcolumn.Recordersforthegravitystageoftheanalysisarealsodefinedhere.
TotalStressSiteResponseAnalysis
Thegravityanalysisphase(thatensures thereisaproperinitialstateofstress inthesoilbeforegroundmotionapplication)isdefinedhere.
Weapply10stepswithelasticresponse inthematerial,updatethematerialstagetoconsiderplasticresponse, thenapply40moresteps.Largetimestepsareusedtodampoutthewavesgeneratedbyloading.
TotalStressSiteResponseAnalysis
ThesetTime commandisusedtoresettheanalysistimebackto0.0,theloadsfromthegravityphaseremaininplace,thisjuststartstheclockbacktothestartfortheshakingphase.
ThewipeAnalysis commandremovesallofthepreviousanalysisobjectsfromthemodel.Wewilldefineanewsetforthenextstage.
TotalStressSiteResponseAnalysis
AfterthemethodofJoynerandChen(1975),thegroundmotionisappliedtothebaseofthesoilcolumnasaforcetimehistoryThisforceisproportionaltotheproductofthedensityandshearwavevelocityoftheunderlyingmaterial(assumedtoberock)andthevelocitytimehistoryofthegroundmotionrecord.APlainloadPattern isusedforthispurpose.
TotalStressSiteResponseAnalysis
Beforeconductingtheanalysisusingtheanalysisobjectsshownhere,weusetheCourant–Friedrichs–Lewy(CFL)conditiontofindastableanalysistimestepbasedonthesizeandstiffnessoftheelements.Thetimestepofthegroundmotionwillbeusedunlessitisfoundthatasmallertimestepisneeded forstability.
EffectiveStressSiteResponse
Theapproachissimilartothetotalstressanalysis.Alayeredsoilprofileismodeled in2Dwithperiodicdisplacement boundaryconditionsenforcedusingtheequalDOFcommandandacompliantbaseisconsideredusingaviscousdashpotmodeledusingazeroLength element andtheviscousuniaxialMaterial.
The9_4_QuadUPelement isusedtomodel thesoil.Thiselement considerstheinteractionbetweentheporefluidandthesolidsoilskeleton,allowingforphenomenasuchasliquefactiontobemodeled.
ThePressureDependMultiYield02 constitutivemodelisusedforthesoil.
EffectiveStressSlopeAnalysis
Modelproblem:
Thisexamplepresentsa2Deffectivestressanalysisofaslopesubjecttoanearthquakegroundmotion.
Theelements andconstitutivemodelsmatchthoseusedinthesiteresponseanalysisexamples.
Thefree-fieldsoilresponseisappliedtothemodelusingfree-fieldcolumnswhicharemuchmoremassivethantheadjacentsoil.
EffectiveStressSlopeAnalysis
Modelproblem:
Thisexamplepresentsa2Deffectivestressanalysisofaslopesubjecttoanearthquakegroundmotion.
Theelements andconstitutivemodelsmatchthoseusedinthesiteresponseanalysisexamples.
Thefree-fieldsoilresponseisappliedtothemodelusingfree-fieldcolumnswhicharemuchmoremassivethantheadjacentsoil.
Finiteelementmesh:
EffectiveStressSlopeAnalysis
excessporepressureratio
shearstress-strain
lateraldisplacement
excessporepressureratiocontoursnearslope
EffectiveStressSlopeAnalysis
displacement offullmeshduringanalysisshowingpropagationofshearstresswaves
EffectiveStressSlopeAnalysis
displacement neartheslopewithcontoursofexcessporepressureratio(redisru =1.0)
ProgressiveExcavationAnalysis
ThisexamplepresentsasimulatedexcavationsupportedbyasheetpilewallusingOpenSees.
TheInitialStateAnalysis featureisusedtocreatethegravitationalstateofstress inthemodelwithoutaccompanyingdisplacements.
Theplanestrainformulationofthequadelement isusedforthesoilwiththePressureDependMultiYield nDMaterial forconstitutivebehavior.
ThesheetpilewallismodeledusingthedispBeamColumnelement withanelasticfibersectionforlinearelastic constitutivebehavior.
Soilelements totherightofthewallareprogressivelyremovedtosimulateanexcavation.
Thesoil-wall interfaceismodeledusingtheBeamContact2Delement.
ProgressiveExcavationAnalysis
shearandmoment inthewall wall-soilcontactforces
verticalstresscontours shearstresscontours