Nonlinear Seismic Ground Response Analysis: Protocols and … · 2009. 10. 15. · Stewart, J.P....

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,CityofSea@leI.M.Idriss,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.