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JonathanP.Stewart,Ph.D.,PEUniversityofCalifornia,LosAngeles
AnnieO.Kwok,Ph.D.PraadGeotechnical,LosAngeles,CA
NonlinearSeismicGroundResponseAnalysis:ProtocolsandVerificaBon
AgainstArrayData
Contributors
ProjectTeam: YoussefHashash,U.IllinoisUrbana‐Champaign
NevenMatasovic,GeosyntecConsultants,Hun;ngtonBeach,CARobertPyke,Consultant,Lafaye@e,CA
ZhiliangWang,GeomatrixConsultants,Oakland,CAZhaohuiYang,URSCorpora;on,Oakland,CA
Contributors
ProjectAdvisors: YousefBozorgnia,PEER
SusanChang,[email protected],Univ.ofCalifornia,Davis
SteveKramer,Univ.ofWashington
FaizMakdisi,GeomatrixConsult.
GeoffMarRn,Univ.SouthernCal.
LelioMejia,URSCorp.TomShantz,Caltrans,Sacramento
WalterSilva,PacificEngineeringandAnalysisJosephSun,PacificGasandElectricCo.
Outline
• ProblemdefiniBonandobjecBves• ParameterselecBonandcodeusageprotocols
• ValidaBonstudies• Equivalent‐linear(EL)&non‐linear(NL)modelcomparisons
ProblemDefiniBon
GroundmoBondefiniBoninCh.11ofASCE7‐05USGSMCEMapsandNEHRPSiteCoefficients
Ss,S1,TL Fa,Fv
ProblemDefiniBon
• Site‐specificPSHA/DSHA• ReplacesUSGSMaps• Why?
– LocaBon‐specific– Improvedtreatmentofsite
effects
– Improveddis‐agg.
• Site‐specificgroundresponse
• ReplacescodeFaandFv• Why?
– Codefactorso^enconservaBve
– Site‐specific“signature”ongroundmoBon
– Characterizesubsurfacedemand
“Sitespecificanalysis”inASCE‐7
USGS Map Changes 2002-2007
Ground Motion Specification
• Previous: response spectral acceleration – peak response of sdof oscillator in one horizontal direction
• 2010 NEHRP Provisions: peak response of sdof oscillator in two horizontal directions
ProblemDefiniBon
HowdoweaccountforsiteeffectsonIM?
ProblemDefiniBon
• SitefactorinGMPE
How do we account for site effects on IM?
ProblemDefiniBon
• SitefactorinGMPE
• Site‐specificanalysisV s
Input Rock Att.
G/GMax
D
γ
Output
How do we account for site effects on IM?
ProblemDefiniBon
• Equivalent‐linearmethods(68%ofusers)
• Nonlinear(32%)
Howdoweperformsite‐specificanalysis?
V s
Input Rock Att.
G/GMax
D
γ
Output
KramerandPaulson,2004
ProblemDefiniBon
Whyisnonlinearnotusedmore?
• PoorlydocumentedandunderstoodparameterselecBonprotocols
• Effectsofparametricvariabilityunknown
• NLbenefitsrelaBvetoELareunclear
ProjectObjecBves
“De‐mysBfy”theapplicaBonofNLcodes:• Provideclearandwelldocumentedcodeusageprotocols
• ValidateperformanceagainstverBcalarraydata
• IdenBfycriBcalsourcesofvariability• ExamineNL/ELdifferences
AlributesofNLCodes
• Discretelumpedmassesorfiniteelement/diff.
• MDOFresponsecomputedforspecifiedbasemoBon
• Time‐domainsoluBon
CodesConsidered
• DEEPSOIL(Y.Hashash)• D‐MOD_2(N.Matasovic)
• OpenSees(Z.Yang)• SUMDES(Z.Wang)
• TESS(R.Pyke)
Outline
• ProblemdefiniBonandobjecBves• ParameterselecBonandcodeusageprotocols
• ValidaBonstudies• Equivalent‐linear(EL)&non‐linear(NL)modelcomparisons
IssuesforCodeApplicaBon
• SpecificaBonofinputmoBon
SoilOutcroppingMoBon
RockOutcroppingMoBon
RockWithinMoBon
IssuesforCodeApplicaBon
• SpecificaBonofinputmoBon
• Viscousdampingparameters
IssuesforCodeApplicaBon
• SpecificaBonofinputmoBon
• Viscousdampingparameters
• ParameterizaBonofnonlinearmaterialbehavior
IssuesforCodeApplicaBon
• SpecificaBonofinputmoBon
• Viscousdampingparameters
• ParameterizaBonofnonlinearmaterialbehavior
Backbone curve
IssuesforCodeApplicaBon
• SpecificaBonofinputmoBon
• Viscousdampingparameters
• ParameterizaBonofnonlinearmaterialbehavior
Unload/reload rules; damping
InputMoBonSpecificaBon
QuesBons:1. ApplyinputmoBonasoutcroppingorwithin?2. RigidorelasBcbase?
Vs‐Halfspace=?
SoilOutcroppingMoBon
RockOutcroppingMoBon
RockWithinMoBon
SiteCondiBon30m Vs=300m/s
ElasBcSoil
Half‐space:Vs=600m/s
InputMoBonSpecificaBon
D=5%
SiteCondiBon30m Vs=300m/s
ElasRcSoil
Half‐space:Vs=600m/s
InputMoBonSpecificaBon
D=5%
FrequencyDomainmethodsprovideexactsoluBon
SiteCondiBon30m Vs=300m/s
ElasBcSoil
Half‐space:Vs=600m/s
InputMoBonSpecificaBon
D=5%
Control(Outcropping)MoBon
InputMoBonSpecificaBon
InputMoBonSpecificaBon
InputMoBonSpecificaBon
InputMoBonSpecificaBon
InputMoBonSpecificaBon
InputMoBonSpecificaBon
RecommendaRon:• Mo;onrecordedasoutcropping:useas‐recorded
outcroppingmoBon+elasBcbase
• Mo;onrecordedwithin(baseofver;calarray):useas‐recordedwithinmoBon+rigidbase
ViscousDampingParameters
• Soildamping(D)ishystereBc
• Occursatsmallandlargestrains
ViscousDampingParameters
• Soildamping(D)ishystereBc
• Occursatsmallandlargestrains
• Nonlinearmodel– HandleslargestrainD– Dmin=0
Dmin=0
ViscousDampingParameters
• Soildamping(D)ishystereBc
• Occursatsmallandlargestrains
• Nonlinearmodel– HandleslargestrainD– Dmin=0
• Challenge:representnonzeroDminwithRaleighdamping
Dmin>0
ViscousDampingParameters
• Why needed?
Dmin>0
Viscous Damping Parameters
• Why needed? • Three formulations
Viscous Damping Parameters
• Why needed? • Three formulations • Issues:
– Which formulation?
Viscous Damping Parameters
• Why needed? • Three formulations • Issues:
– Which formulation? – Target damping?
Viscous Damping Parameters
• Why needed? • Three formulations • Issues:
– Which formulation? – Target damping? – Matching
frequencies?
Viscous Damping Parameters
Approach: • FD provides exact
sol’n for linear case
• Find parameters that optimize match of NL to FD
?
Broadband synthetic input; Range of site conditions
ViscousDampingParameters
Approach: • FD provides exact
sol’n for linear case
• Find parameters that optimize match of NL to EL
ViscousDampingParameters
Approach: • FD provides exact
sol’n for linear case
• Find parameters that optimize match of NL to EL
ViscousDampingParameters
Approach:
• FDprovidesexactsol’nforlinearcase
• FindparametersthatopBmizematchofNLtoELRecommendaRons:1. FullRDpreferredtosimplifiedRD2. Target=smallstraindamping3. IteratetoopBmizematchingfrequencies,or4.f1=fsite;f2=5×fsite
NonlinearMaterialBehavior
Backboneparameters• Gmaxok
NonlinearMaterialBehavior
Backboneparameters• Gmax• τlim;o^enunavailable,notin
equaBon
NonlinearMaterialBehavior
Backboneparameters• Gmax
• τlim• γr:pseudo‐referencestrain
(empirical)
Truereferencestrain,γref=τff/Gmaxτff=shearstrength
NonlinearMaterialBehavior
Backboneparameters• Gmax• τlim• γr• a,β:empirical
NonlinearMaterialBehavior
Backboneparameters
• Empiricalmodel– validforγ<∼0.5%
Darendeli(2001)Zhang‐Andrus‐Juang(2005)
NonlinearMaterialBehavior
Backboneparameters
• Empiricalmodel– validforγ<∼0.5%– γr=f(σ’,PI,OCR)– fixedvaluesofa,β γr
Darendeli(2001)Zhang‐Andrus‐Juang(2005)
NonlinearMaterialBehavior
Backboneparameters
• Empiricalmodel• Biasatlargestrainwithγr
NonlinearMaterialBehavior
Backboneparameters
• Empiricalmodel• Biasatlargestrainwithγr
for γr=γref=τff/Gmax (true ref. strain) τ→τff at large strain
NonlinearMaterialBehavior
Backboneparameters
• Empiricalmodel• Biasatlargestrainwithγr• Biasatsmallstrainwithγref
NonlinearMaterialBehavior
• Backbonecurveparameters
• Empiricalsource• Biasatlargestrainwithγr• Biasatsmallstrainwithγref
• SoluBon:transiBonfuncBon
G/Gmaxmatch
τffmatch
NonlinearMaterialBehavior
Backboneparameters
• Empiricalsource• Biasatlargestrainwithgr• Biasatsmallstrainwithgref• SoluBon:transiBonfuncBon• “Actual”vs“target”
NonlinearMaterialBehavior
Soildamping
• ParameterizaBon– Notdirectlyspecified– Productofunload‐reloadrules(Masing)
NonlinearMaterialBehavior
Soildamping
• ParameterizaBon• CharacterisBcs
– D→0atsmallstrain
NonlinearMaterialBehavior
Soildamping
• ParameterizaBon• CharacterisBcs
– D→0atsmallstrain
– Dlargeatlargestrain
NonlinearMaterialBehavior
Soildamping
• ParameterizaBon• CharacterisBcs• Issues
– Labastarget?– Importanceofmisfit
NonlinearMaterialBehavior
Soildamping
• ParameterizaBon• CharacterisBcs• Issues• Strategiesformanagingmisfit– Matchbackboneandaccept
misfit
NonlinearMaterialBehavior
Soildamping
• ParameterizaBon• CharacterisBcs• Issues• Strategiesformanagingmisfit– Matchbackboneandaccept
misfit
– OpBmizeG/GmaxandDcurvefits
NonlinearMaterialBehavior
Soildamping
• ParameterizaBon• CharacterisBcs• Issues• Strategiesformanagingmisfit– Matchbackboneandaccept
misfit
– OpBmizeG/GmaxandDcurvefits
– ModifyMasingtomatchboth
NonlinearMaterialBehavior
Soil damping • Parameterization • Characteristics • Issues • Strategies for
managing misfit • Significant?
NonlinearMaterialBehavior
Soildamping
• ParameterizaBon• CharacterisBcs• Issues• Strategiesformanagingmisfit
• Significant?
NonlinearMaterialBehavior
Recap:• Targetbackbonecurve
– Considershearstrengthforlargestrainproblems
– Retainsmallerstrainalributes
• Targetdampingcurve
• ModulusreducBon&dampingmatchstrategies
Outline
• ProblemdefiniBonandobjecBves• ParameterselecBonandcodeusageprotocols
• ValidaBonstudies• Equivalent‐linear(EL)&non‐linear(NL)modelcomparisons
ValidaBon
• ObjecBves:testNLcodesimplementedwithusageprotocols
• VerBcalarraysitesconsidered:– TurkeyFlat,CA– LaCienega,CA– Kiknet,Japan(SiteKGWH02)– Lotung,Taiwan
ValidaBonOverview
BaselineGeotech.Model(Bestest.Vsprofile,Materialcurves,UnitWeight)
SHAKE04DEEPSOILD‐MOD_2OPENSEESSUMDESTESS
PredictedSoilMoBons
ResidualsbyComparingtoData
VariabilityDuetoModels
RecordedDownholeMoBon
ValidaBonOverview
AlternaBveGeotech.Models
(Unc.inVsprofile&materialcurves)
SHAKE04DEEPSOILD‐MOD_2OPENSEESSUMDESTESS
PredictedSoilMoBons
ResidualsbyComparingtoData
VariabilityDuetoMaterialProperBes
RecordedDownholeMoBon
• BaselineVsfrommeasurements
• BaselineG/GmaxandDcurvesfrommaterial‐specificlabtesBng
• StandarddeviaBons– Vs:Toro(1997)– G/GmaxandD:Darendeli(2001)
• FOSM
LaCienegaResults
Baseline conditions
LaCienegaResults
Baseline conditions
LaCienegaResults
Analysisofvariability
• Codetocode• Velocity• Materialcurves
• Overall(uncorrelatederrors)
OtherSites/InterpretaBon
MedianResults:• ModestunderpredicBonatshortperiodsfor3of4sites
• Noresultsforhighlynon‐linearsoil(yet)
OtherSites/InterpretaBon
Variability:
• σG:relatedtosoildepth;lowTonly
MaterialCurvesσG
OtherSites/InterpretaBon
Variability:
• σG:relatedtosoildepth;lowTonly
• σV:importantatT1ifI.C.
Vsprofileσv
OtherSites/InterpretaBon
Variability:
• σG:relatedtosoildepth;lowTonly
• σV:importantatT1ifI.C.
• σm:importantatlowT
ComputaBonalModelσm
Outline
• ProblemdefiniBonandobjecBves• ParameterselecBonandcodeusageprotocols
• ValidaBonstudies• Equivalent‐linear(EL)&non‐linear(NL)modelcomparisons
EL/NLComparison
• LargeamplitudesyntheBc
• EL:flatspectrumatlowT
• NL:realisBcshape
ConcludingRemarks
• Whenusegroundresponseanalysis?
• When/whyuseNLgroundresponseanalysis?
• ParameterselecBon:principaldifferencesfromEL:– Shearstrength– Viscousdamping
Summary&Conclusions
• When/whyuseNL?– Whenlargestrainsresponseexpected– ProducesdifferentPGAandspectralshapefromEL(assumedto
bemorerealisBc)
• InputmoBon– As‐recordedmoBons(w/compliantbaseifoutcropping)
• Viscousdamping– AvoidsimplifiedRD– Target=Dmin
– CarefulselecBonofmatchingfrequencies
Summary&Conclusions
• BackbonecurveparameterizaBon– BiggestdifferencefromELisconsideraBonofτff– Rateeffectonshearstrength– CyclicdegradaBoneffects
• Casehistoriesindicatepossibleoverdamping.Causeunknown.
• NLcodesnowpracBcalandconvenientforuse
ReferencesandAcknowledgementsStewart,J.P.andKwok,A.O.(2008).“Nonlinearseismicgroundresponseanalysis:codeusageprotocolsandverificaBonagainstverBcalarraydata,”inGeotechnicalEngineeringandSoilDynamicsIV,May18‐22,2008,Sacramento,CA,ASCEGeotechnicalSpecialPublicaBonNo.181,D.Zeng,M.T.Manzari,andD.R.Hiltunen(eds.),24pages(electronicfile).
Stewart,J.P.,Kwok,A.O.,Hashash,Y.M.A.,Matasovic,N.,Pyke,R.,Wang,Z.,andYang,Z.(2008).“Benchmarkingofnonlineargeotechnicalgroundresponseanalysisprocedures,”ReportPEER2008/04,PacificEarthquakeEngineeringResearchCenter,UniversityofCalifornia,Berkeley.
Kwok,A.O.,Stewart,J.P.,Hashash,Y.M.A.,Matasovic,N.,Pyke,R.,Wang,Z.,andYang,Z.(2007).“UseofexactsoluBonsofwavepropagaBonproblemstoguideimplementaBonofnonlinearseismicgroundresponseanalysisprocedures,”J.Geotech.&Geoenv.Engrg.,ASCE,133(11),1385‐1398.