Geotechnical Analysis Examples

QuakeCoRE OpenSees Training Workshop 2016

Geotechnical Analysis Examples

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


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!


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


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


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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Whatarethebenefitsoftheseelements?oNoshearlockinginbendingapplicationso Lesscomputationaldemandthanstandardelements

Executiontime: Quadelement =330sec SSPquad element =146sec

Siteresponseanalysistestproblem



Flexiblefootingloadtestproblem



unstabilized SSPquadUP stabilizedSSPquadUP9nodequadelement



Surfaceresponsespectrafromeffectivestresssiteresponseanalysis



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

ConstitutiveModels

ConstitutiveModels

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

GeotechnicalandSoilMechanicsExampleAnalyses

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.


Wewantouranalysistostartfromatrulyhydrostaticstateofstress, soweneedtousea3Dbrickelementanddefinethedomainwith3dimensions(-ndm 3).Wealsowantthetesttobeundrained,soweneedtouseau-pelementandasmallpermeability.Thisrequiresustouseadomainwith4dof (-ndf 4)astheporepressure isassignedtothe4th dof.


Thenodesarecreatedin3D(requires3coordinatespernode).Thesizeoftheelementdoesn’treallymatterforthisanalysis,a1.0unitcubeisused.

Duringtheinitialanalysisphase,wefixtheporepressuredof (dof 4)suchthatpressurecannotdevelop(analogoustohavingthevalveopen).

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ThePressureDependMultiYieldnDMaterial isusedhere.Theinputsandcapabilitiesofthismaterialmodelarediscussedat:http://opensees.berkeley.edu/wiki/index.php/PressureDependMultiYield_Material


TheSSPbrickUP element isused.Itrequiressomeinformationabouttheporefluid(waterinthiscase)andtheinitialvoidratioofthesoil.http://opensees.berkeley.edu/wiki/index.php/SSPbrickUP_Element


Notehowtheelementconnectivityisspecified inacounterclockwiseorder.Thisisnottheonlynodeorderingwecouldhaveused,butthenodenumberswerechosentomakeiteasytoinputintotheelement.

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quad/brickelementshaverecorders toeasilyoutputthestress/strainattheintegrationpointsoftheelementWeusethePenaltyconstraintsherebecauseduringtheshearingphase,alloftheporepressuredof willbefree.


Theconfinementpressure isappliedinaPlainloadPattern withtheimbeddedtimeSeries shownhere.Notethatwedividethedesiredmeanpressureby4whenapplyingnodalforces.

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ThisaTransientanalysis,sowemustspecifyananalysistimestep.Becausewewanttheshearingphasetostartfromessentiallystaticconditions,weuseverylargetimestepstoensure thatanywavescreatedbytheloadinghavedampedout.Thistechniqueonlyworksbecause thematerialiselasticduringthisphase!


Afterwearesatisfiedthathydrostaticstressconditionshavebeenappropriatelyapplied,weremovetheconstraintswespecifiedontheporepressuredof (4th dof)ofeachnodeto“closethedrainagevalves”.Thisisaccomplishedusingtheremovecommand

http://opensees.berkeley.edu/wiki/index.php/Remove_Command


ThenextstepistoinstructthenDMaterialobjecttoconsiderelastoplasticresponseusingtheupdateMaterialStage command.ThedefaultstateforthePressureDependMultiYield modelislinearelasticbehaviour.

http://opensees.berkeley.edu/wiki/index.php/UpdateMaterialStage


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)


Thematerialandgeometricparametersforthesoilcolumnareplacedinthebeginningofthefiletomakethingseasiertofindandchange.Thisexampleconsidersasingle40mthicklayerofsoil.Amodelfileforalayeredsoilprofilefollowstheexactsamesteps,itisjustmorecomplicated,soweareusingasimplercase.


Wealsodefinesomeanalysisparametershere, includingthegroundmotiondetails,theRayleighdampingterms,andNewmarkintegratorterms.

Wealsospecifysomeparametersthatwillbeusedtodetermine thesizeoftheelementsinthemodel.Herewehavespecified100Hzasthehighestfrequencywewantwellresolved (10elements inonewavelength).Theelementsizewillbedeterminedbasedonthisinformation.


Theelementsizedefinitionishere.Wesetatrialnumberofelementsbasedonthewavelengthcomputedpreviously,thenmakesureanintegernumberofelementswillbeinthemodel(can’thave2.34516elems).Thenumberofelems definestheverticalelementsizeandthenthenumberofnodes.


Thenodesforthesoilcolumnarecreatedinaloop.Takingadvantageoftcl scriptinglikethissavesatonoftime(andspaceinyourmodelfile).Forexample,inthiscasethereare160elementsinthemodel,whichcorresponds to322nodes.Enteringthosebyhandwouldnotbeveryfun.

TotalStressSiteResponseAnalysisThecomplianceoftheunderlyingmaterialisconsidered inthemodelusingadashpot(afterLysmer)andthegroundmotionapplicationtechniqueofJoynerandChen(1975).

Forthismodelingapproach,aviscousdashpotisplacedatthebaseofthesoilcolumn.

HerewealsoimplementtheperiodicboundaryconditionsusingtheequalDOF command.


ThenDMaterial andelementsaredefinedhere.Theelementsaredefinedinaloopaswell.Settingthisupinitiallytakesabitofthought,butitdefinitelypaysoff.


TheviscousuniaxialMaterial isusedwithazeroLength elementtodefinethedashpotatthebaseofthesoilcolumn.Recordersforthegravitystageoftheanalysisarealsodefinedhere.


Thegravityanalysisphase(thatensures thereisaproperinitialstateofstress inthesoilbeforegroundmotionapplication)isdefinedhere.

Weapply10stepswithelasticresponse inthematerial,updatethematerialstagetoconsiderplasticresponse, thenapply40moresteps.Largetimestepsareusedtodampoutthewavesgeneratedbyloading.


ThesetTime commandisusedtoresettheanalysistimebackto0.0,theloadsfromthegravityphaseremaininplace,thisjuststartstheclockbacktothestartfortheshakingphase.

ThewipeAnalysis commandremovesallofthepreviousanalysisobjectsfromthemodel.Wewilldefineanewsetforthenextstage.


AfterthemethodofJoynerandChen(1975),thegroundmotionisappliedtothebaseofthesoilcolumnasaforcetimehistoryThisforceisproportionaltotheproductofthedensityandshearwavevelocityoftheunderlyingmaterial(assumedtoberock)andthevelocitytimehistoryofthegroundmotionrecord.APlainloadPattern isusedforthispurpose.


Beforeconductingtheanalysisusingtheanalysisobjectsshownhere,weusetheCourant–Friedrichs–Lewy(CFL)conditiontofindastableanalysistimestepbasedonthesizeandstiffnessoftheelements.Thetimestepofthegroundmotionwillbeusedunlessitisfoundthatasmallertimestepisneeded forstability.


surfaceacceleration

surfaceresponsespectra

EffectiveStressSiteResponse

Theapproachissimilartothetotalstressanalysis.Alayeredsoilprofileismodeled in2Dwithperiodicdisplacement boundaryconditionsenforcedusingtheequalDOFcommandandacompliantbaseisconsideredusingaviscousdashpotmodeledusingazeroLength element andtheviscousuniaxialMaterial.

The9_4_QuadUPelement isusedtomodel thesoil.Thiselement considerstheinteractionbetweentheporefluidandthesolidsoilskeleton,allowingforphenomenasuchasliquefactiontobemodeled.

ThePressureDependMultiYield02 constitutivemodelisusedforthesoil.

SiteResponseAnalysis

summaryofsoilbehavioratthreedepthswithinthesoilprofile

SiteResponseAnalysis

displacement ofsoilcolumnduringanalysiswithcontoursofexcessporepressureratio

EffectiveStressSlopeAnalysis

Modelproblem:

Thisexamplepresentsa2Deffectivestressanalysisofaslopesubjecttoanearthquakegroundmotion.

Theelements andconstitutivemodelsmatchthoseusedinthesiteresponseanalysisexamples.

Thefree-fieldsoilresponseisappliedtothemodelusingfree-fieldcolumnswhicharemuchmoremassivethantheadjacentsoil.


Modelproblem:

Thisexamplepresentsa2Deffectivestressanalysisofaslopesubjecttoanearthquakegroundmotion.

Theelements andconstitutivemodelsmatchthoseusedinthesiteresponseanalysisexamples.

Thefree-fieldsoilresponseisappliedtothemodelusingfree-fieldcolumnswhicharemuchmoremassivethantheadjacentsoil.

Finiteelementmesh:


excessporepressureratio

shearstress-strain

lateraldisplacement

excessporepressureratiocontoursnearslope


displacement offullmeshduringanalysisshowingpropagationofshearstresswaves


displacement neartheslopewithcontoursofexcessporepressureratio(redisru =1.0)

ProgressiveExcavationAnalysis

ThisexamplepresentsasimulatedexcavationsupportedbyasheetpilewallusingOpenSees.

TheInitialStateAnalysis featureisusedtocreatethegravitationalstateofstress inthemodelwithoutaccompanyingdisplacements.

Theplanestrainformulationofthequadelement isusedforthesoilwiththePressureDependMultiYield nDMaterial forconstitutivebehavior.

ThesheetpilewallismodeledusingthedispBeamColumnelement withanelasticfibersectionforlinearelastic constitutivebehavior.

Soilelements totherightofthewallareprogressivelyremovedtosimulateanexcavation.

Thesoil-wall interfaceismodeledusingtheBeamContact2Delement.


shearandmoment inthewall wall-soilcontactforces

verticalstresscontours shearstresscontours


Nodaldisplacementmagnitudeduringtheexcavationanalysis


shearandmoment inthewallduringtheexcavationanalysis

SFSIofCompleteBridgeSystem






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Geotechnical Analysis Examples

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