ProbabilisticProbabilistic SeismicSeismic HazardHazard AssessmentAssessment SeismicSeismic FailureFailure ModesModes SlidingSliding failurefailure throughthrough weakweak liftlift lineline HorizontalHorizontal crackingcracking LiquefactionLiquefaction ofof damdam oror foundationfoundation CrackingCracking fromfrom severesevere shakingshaking SurfaceSurface faultfault displacementdisplacement throughthrough thethe foundationfoundation OvertoppingOvertopping fromfrom landslidelandslide failurefailure intointo reservoirreservoir Liquefaction induced flow slide from M 6.6 event @ ~ 14 km; 0.5 g Fault surface rupture – Chelongpu fault M 7.6 Chi-Chi earthquake, Taiwan PSHA “Probabilistic seismic hazard analysis (PSHA) is a methodology that estimates the likelihood that various levels of earthquake-caused ground motions will be exceeded at a given location in a given future time period. The results of such an analysis are expressed as estimated probabilities per year or estimated annual frequencies.” Senior Seismic Hazard Analysis Committee (SSHAC) PSHA “While there is considerable information on earthquake ground motions and potential future locations of earthquakes, there is also considerable uncertainty in the inputs to the analysis.” PSHA Project for the Mid-Columbia Dams PSHA “Recognizing the need to identify and address these uncertainties as part of a PSHA, the Senior Seismic Hazard Analysis Committee (SSHAC, 1997) established the goal for all PSHA’s to quantitatively assess these uncertainties and to represent the distribution of the informed technical community of alternative models and parameter values.” PSHA Project for the Mid-Columbia Dams PSHA Considers the contribution from all potential sources of earthquake shaking collectively Considers the likelihood of those events Uncertainty is treated explicitly Annual probability of exceeding specified ground motions is computed Steps in PSHA Basic Components of a PSHA & All Seismic Hazard Analyses I Seismic source characterization II Development of hazard curves III Development of uniform hazard spectra (UHS) IV Development of acceleration time histories SEISMIC SOURCE CHARACTERIZATION Known faults Areal or Background sources (i.e., random seismicity) Logic Tree SEISMICSEISMIC HAZARDHAZARD CURVESCURVES ProducedProduced fromfrom severalseveral availableavailable computercomputer codescodes IncorporateIncorporate uncertaintiesuncertainties inin slipslip rate,rate, magnitude,magnitude, faultsfaults lengthslengths UseUse groundground motionmotion attenuationattenuation relationshipsrelationships thatthat relaterelate PGAPGA andand SASA toto distancedistance betweenbetween sourcesource andand sitesite andand earthquakeearthquake magnitudemagnitude -- NGANGA NextNext GenerationGeneration AttenuationAttenuation modelsmodels SiteSite conditionsconditions veryvery important;important; i.e.,i.e., ““soilsoil”” versusversus ““rockrock”” MeanMean HazardHazard CurvesCurves byby SourceSource MeanMean && FractileFractile CurvesCurves forfor PHAPHA SiteSite ResponseResponse PeriodPeriod ofof structurestructure-- ConcreteConcrete (sensitive(sensitive toto shortshort period,period, 0.20.2--0.40.4--secsec SA)SA) versesverses EmbankmentEmbankment (sensitive(sensitive toto longlong period,period, 11--secsec SA)SA) SiteSite conditionsconditions-- SoilSoil versesverses rockrock ShearShear wavewave velocityvelocity (V(VS30)30) –– ShearShear wavewave velocityvelocity inin upperupper 100100 ftft -- Important,Important, becausebecause mostmost NGANGA relationshipsrelationships nownow incorporateincorporate this)this) UNIFORMUNIFORM HAZARDHAZARD SPECTRASPECTRA UniformUniform hazardhazard spectraspectra (UHS)(UHS) areare computedcomputed oror developeddeveloped fromfrom thethe seismicseismic hazardhazard curves.curves. ThisThis isis donedone byby developingdeveloping hazardhazard curvescurves (i.e.(i.e. spectralspectral accelerationacceleration vs.vs. exceedanceexceedance probability)probability) forfor severalseveral vibrationvibration periodsperiods toto definedefine thethe responseresponse spectra.spectra. Then,Then, forfor aa givengiven exceedanceexceedance probabilityprobability oror returnreturn period,period, thethe ordinatesordinates areare takentaken fromfrom thethe hazardhazard curvescurves forfor eacheach spectralspectral acceleration,acceleration, andand anan ““equalequal hazardhazard”” responseresponse spectrumspectrum isis generated.generated. TIMETIME HISTORIESHISTORIES ForFor higherhigher levellevel studies,studies, accelerograms,accelerograms, oror accelerationacceleration timetime histories,histories, areare developeddeveloped forfor thethe sitesite thatthat representsrepresents thethe seismicseismic hazardhazard atat thethe returnreturn periodsperiods ofof interest.interest. TheThe suitessuites ofof motionsmotions atat eacheach returnreturn periodperiod areare usuallyusually selectedselected toto spanspan thethe likelylikely variabilityvariability inin spectraspectra responsesresponses atat differentdifferent periods,periods, andand toto accountaccount forfor differencesdifferences inin distance,distance, magnitude,magnitude, andand sitesite conditions.conditions. TheThe selectedselected groundground motionsmotions areare thenthen usedused forfor dynamicdynamic analysesanalyses usingusing programsprograms suchsuch FLACFLAC,, SHAKE,SHAKE, oror LSLS-- DYNADYNA TimeTime HistoriesHistories (10K)(10K) ScaledScaled toto MeanMean UHSUHS New Zealand, M 6.6 Northridge, M 6.7 Cascadia, M 9 FaultFault DisplacementDisplacement HazardHazard AnalysisAnalysis (PFDHA)(PFDHA) SomeSome sitessites itit maymay bebe aa majormajor concernconcern (i.e.,(i.e., LauroLauro && TerminalTerminal Dams,Dams, CA;CA; HelenaHelena ValleyValley Dam,Dam, MT)MT) HazardsHazards calculationscalculations areare analogousanalogous toto probabilisticprobabilistic groundground motionmotion methodologymethodology MethodologyMethodology originallyoriginally setset forthforth byby SteppStepp andand othersothers (2001)(2001) forfor YuccaYucca MtnMtn LauroLauro DamDam FaultFault InvestigationsInvestigations RuptureRupture LengthLength vsvs DisplacementDisplacement 2 SRL=15 SRL=39 1.5 SRL=57 1 Pdf 0.5 0 0 100 200 300 400 500 600 700 800 Displacement, cm Exceedence (All) 1.E-02 16% Median 1.E-03 84% 1.E-04 1.E-05 0 100 200 300 400 500 Displacement, cm Sheffield Dam - 1925 QUESTIONS?QUESTIONS? .