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3DEC建模.pdf

3DEC建模.pdf

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NON-LINEARSTATICANDDYNAMICANALYSISOFTHECUSHMANARCHDAMSUSINGDISTINCTELEMENTSD.D.Curtis1J.P.Aglawe2E.B.Kollgaard3D.E.Bowes4S.H.Fischer5ABSTRACTThepaperpresentsthedetailednon-linearstaticanddynamicanalysisoftheCushmanNo.1archdam.TheCushmanNo.1archdamisownedandoperatedbytheCityofTacoma,DepartmentofPublicUtilities.TheanalyseswereundertakenaspartoftheF.E.R.C.Part12investigations.Thestaticanddynamicanalysesareuniqueinthatopening,closing,andslidingalongjointsismodeledinconsiderabledetail.Thedistinctelementprogram3DECisusedinthenon-linearanalysisofthedamandfoundation.Webelievethatthesophisticatednon-linearanalysesthathavebeencarriedoutonthesedams’advancesthestate-of-the-artofdamassessmentunderseismicloading.Inthe3DECanalysis,allthedamcontractionjointsandthedam-foundationinterfacejointsareallowedtoopen,close,andslideunderstaticanddynamicloading.Inaddition,jointsinthefoundationrockaremodeledsuchthatstabilityanalysisofthedamandfoundationaremadewithinone3DECmodel.Thestaticanalysissimulatesdamconstruction,groutingofcontractionjoints,andreservoirimpoundment.Thestaticstabilityofthedamischeckedbygraduallyreducingthefrictionalstrengthofthejointsuntildisplacementsbecomeexcessive.Adetailednon-linearstaticanalysiswasundertakentoinvestigatesliponthedam-foundationinterface,particularlyattherightabutmentwherethecontactgeometryisadverselyslopeddownstream.Inthenon-linearseismicanalysis,thedamjointsanddam-foundationinterfaceopenandcloseduringtheearthquake.Atseveraltimeinstancesduringtheearthquake,theshearstrengthalongvariousjointsurfaceswasexceededandthiscausedrelativeshearslipdisplacements.Thepost-earthquakestabilityofthedamwasassessedbyincreasingupliftandgraduallyreducingthestrengthofthejoints.Bythismeansthedamwasfoundtobesafe._______________1SeniorCivilEngineer,AcresInternational,4342QueenSt.,P.O.Box1001,NiagaraFalls,OntarioCanada,L2E6W1,Tel:905-374-5200,Fax:905-374-1157,dcurtis@acres.com.2SeniorGeotechnicalEngineer,AcresInternational,4342QueenSt.,P.O.Box1001,NiagaraFalls,OntarioCanada,L2E6W1,Tel:905-374-5200,Fax:905-374-1157,jaglawe@acres.com.3ConsultingEngineer,4820EagleWay,Concord,CA,USA,94521,Tel:925-798-9475,Fax:925-689-3456,ebkollgaard@ca.astound.net.4ConsultingEngineer,292278thAve.Ct.N.W.,GigHarbor,WA,USA,98335,Tel:253-265-0811,Fax:253-265-0812,bowespe@halcyon.com.5SeniorPrincipalEngineer,TacomaPower,Generation,3628South35thStreet,Tacoma,WA,USA,98409,Tel:253-502-8316,Fax:253-502-8136,sfischer@ci.tacoma.wa.us.INTRODUCTIONTheCushmanDamsareonthelowerstretchoftheNorthForkoftheSkokomishRiveronthesoutheasternsideoftheOlympicpeninsulanearthesouthernendoftheHoodCanal.TheCityofTacomaownsboththedams.CushmanDam1isasinglecurvatureconcretearchdamwithanoverallheightof260ftabovethestreambed.The400ft-longcrestofthedamisatEl.741.5.ThereservoirnormalmaximumstoragelevelisEl.738.0.Thedamwascompletedandplacedintooperationin1926.TheCushman1dam/foundationcontactispoorlyshapedespeciallyattherightabutmentwhereitisslopedadverselyinthedownstreamdirection.Thisfactledtothequestionofabilityofthedamtowithstandthestronggroundmotionsassociatedwiththeseismicloading.Itwasrecommendedtoperformasophisticatednon-linearnumericalanalysistoascertaintheseriousnessoftheseismicresponseandevaluationofremedialmodifications.Thenon-linearstaticanddynamicanalyseswereperformedwith3DEC,athreedimensionaldistinctelementanalysisprogram.The3DECprogramwasusedtoperformanon-linearstaticanalysisofdamfollowedbyanon-lineardynamictimehistoryanalysis.The3DECprogramwasusedtoanalyzebothCushman1and2dams,butduetospacelimitations,themainresultsfromtheCushman1analysisarepresentedherein.MODELINGAPPROACHBriefDescriptionof3DECThe3DEC(3-DimensionalDistinctElementCode)programisthethree-dimensionalextensionofItasca'stwo-dimensionalcodeUDEC.Itisspecificallydesignedforsimulatingeitherthequasi-staticordynamicresponsetoloadingofrockmediacontainingmultiple,intersectingjointstructures.The3DECmodelisanassemblageofdiscretepolyhedrasrepresentingdiscontinuousmedium.Discontinuitiesaretreatedasboundaryconditionsbetweenblocks.Largedisplacementonthediscontinuitiessuchasslipandopeningissimulatedinadiscontinuousmedium.Relativemotionalongdiscontinuitiesisgovernedbylinearandnon-linearforce-displacementrelationsformovementinboththenormalandsheardirections.Theprogramusesanexplicitsolutionscheme,whichgivesastablesolutiontounstablephysicalprocesses.3DECisparticularlywellsuitedtosimulateblockystructures,suchasstonemasonryarches.Assessmentofthesafetyconditionsofoldmasonrybridges(Lemos,1997)andtheseismicbehaviorofstonemasonryarches(Lemos,1995)hasbeendoneusing3DEC.Ithasbeensuccessfullyemployedtosimulatethebehaviorofaconcretearchdamconstructedonajointedrockfoundation(Lemos,1996)andalsotoperformstabilityanalysisofundergroundpowerhousestation(DasguptaandLorig,1995,Dasgupta,etal.,1995).GeologicalSettingThebriefreviewoftheengineeringgeologyofCushmanDamNo1isgivenbyCoombs(1972).RecentgeologicalcompilationandreviewwasdonebyHamilton(2001)fortherightabutmentofCushmanDam1.ThebedrockintheareaofCushmanprojectsconsistsofthicksequenceofbasaltandandesiteflowswithlocalinterflowlayersoftuffandagglomerate,oftheEoceneageCrescentFormation.AtthedamsitetheCrescentFormationlayeringstrikesaboutNE-SW,crossingthecanyonatahighangleanddips45to60degreesSEdownstream.Variousjointsinthefoundationrockarepresent.StrikeanddipanglesforthevariousjointsaregiveninTable1.ThejointplaneA1intersectsnearthecontractionjointatstation3+64.79ofthedam.Figure1showsthejointplanesD,A1,A2andB.TherightabutmentwedgeisformedbyanassumedverticalplaneDontheupstream,rampfractureplaneBbelowthedam-foundationcontact,andthejointplanesA1andA2.Thesejointplanesformarightabutmentwedgewithatotalweightofabout30,000tons.Table1.OrientationsoftheDiscontinuitiesJointPlaneStrikeDipDN25WVerticalBN56E53NWA1N67E55SEA2N67E55SEModelDevelopment3DECmodelwasdevelopedasanassemblageofdiscreteblocksusingcommerciallyavailableprogramDISPLAY(EMRC,1997).Foundationrock,concretedam,andreservoirwaterelementswerediscretized.Anexplodedviewoffoundationrock,concretedam,andthereservoirisshowninFigure2.InFigure2,thereservoirisshownintheupperpartofthefigure,thedaminthemiddleandthereservoirinthelowerpartofthefigure.Thereservoirwasextendedmorethanthreetimesthedamheightintheupstreamdirection.Itisnotedthatthebulkofthemodelwascreatedusinga3DAutoCadmodel,whichwassuppliedbyTacomaPower.Inthefoundationrock,fourjointsetswereused.Intheconcretedam,thesevenverticalcontractionjointsandthedam/foundationcontactjointsweremodeled.VariousrockjointsformingarightabutmentwedgeareshowninFigure1.Figure3providesanillustrationofrightabutmentwedgealongwithdam.Rightabutmentgravitysectionsandthestartofthearchsectionofthedamarealsoshowntoobtainspatiallocationandorientationofthewedgewithrespecttothedam.Figure1.Dam-FoundationContact,ContractionJointsandFoundationRockMassDiscontinuitiesFigure2.ExplodedViewofFoundation,DamandReservoirFigure13DECmodelofCushmanArchDamNo.1Figure9a.Figure3.RightAbutmentWedgeGeometryandtheDam.TheRockWedgeAloneisshownintheInset.VariousFISHfunctionswerewrittentosimulatetheeffectofgroutingoftheindependentcantilevermonolithsatthecontractionjoints,theupliftpressuredistributionatthedam-foundationcontactandwaterpressureinthejointsontherightabutmentwedgesurfaces.FISHfunctionsprovideaprogrammingcapabilityin3DECthatallowstheusertoprogramsuchfeaturesasgroutingjoints,i.e.,closinggapsatthedamjoints.ModelingSequenceFigure4presentsvariousstagesduringthemodelingsequencetoestablishinitialstateofstress.Initialrockstresseswerecomputedusinggravityloading.Thedammonolithicblockswerethenconstructed.Groutingoftheindependentcantileverswassimulatedbyspecifyingaclosedgapbetweenthecontractionjointsaftergravityloadswereequilibrated.Thereservoirelementswereturnedontoloadthedamhydrostatically.Parametricstudieswereperformedtoexaminethesensitivityofthe3DECtoreducedfrictionalstrengthatthedam-foundationcontactandonthejointsformingtherightabutmentwedge.Finally,thedynamicanalysiswasperformedusingJuandeFucaandCascadiaseismicrecordsforMCEloading.PropertiesThejointsbetweenthedam-reservoirandreservoir-foundationareassumedtobeelastic.Contractionjointswithinthedamanddam-foundationcontactareassumedtohavezerocohesionand55degreesfrictionangle.Thedamfoundationwasquiterough,therefore,theassumedfrictionangleisconsideredconservative.Intherightabutmentwedgeanalysis,thecohesiononthejointplaneswassettozero.Theassumedtotalcombined(cohesiveandfrictional)shearstrengthonjointsB,D,A1andA2istakenas55degrees.RkItwasassessedthatthetotalshearstrengthofthejointplanesisatleastequivalenttothatwithacombinedfrictionangleof55degrees.Figure4ModelingMethodologyAdoptedforDynamicAnalysisofCushman-1ArchDamCreateDam+RockFoundation+ReservoirblocksfromSADSAPmodelExtendfar-fieldboundariesforrockfoundationandreservoirDiscretizemodelApplyboundaryconditionsRockonlyanalysisEquilibriaterockfoundationundergravityConstructarchdam+rightandleftwingwalldamsasmonolithswith7contractionjointsContractionjoint:coh=0psi,fric5degRockdamcontact:coh=300psi,fric55degEquilibriatethemodelGroutingClosethegapsonthecontractionjointsbetweentheconcretemonolithsContractionjoint:coh=0psi,fric55degActivatereservoirelementswaterel.741'(3ftaboveNormal)Elasticcontactbetweendam&reservoirreservoir&foundationReducestrengthparametersonRock-damcontactcoh=0psi,fric55degDynamicAnalysisReducestiffnessofjointsto5.588e4psi/inApplyviscousboudariestothesidesPerformTimeHistoryAnalysisIncludequietperiodatendoftimehistoryThebulkmodulusoftheelementsinthereservoirregionwassetto2.90x105psi.TheshearmoduluswascalculatedusingPoisson’sratioof0.495,i.e.,acompressiblefluid.DampingParametersandDiscretization:Thehydrodynamicinteractionbetweenthedamandthereservoirismodeledusingsolidelementsforthedamconcreteandreservoirwater.Thehighlyunevensurfacetopographyintheupstreamregionresultedincomplexgeometricalshapeforreservoirregion.Thedominantfrequencyrangefortheearthquakeanddamresponseisbetween0and5Hz.Themass-proportionalcomponentofRayleighdampingisemployed.Thefractionofcriticaldampingof4.35%wasobtainedasoperatingatthecenterfrequencyof3.43Hz.The3DECzone(element)sizewasadjustedtoensurethisfrequencywascapturedintheanalysis.STATICANALYSESInitialSetupTworeservoirelevationscorrespondingtousualloadingcase(738ft)andthePMFunusualloadingcase(745ft)wereconsidered.Theloadingduetoreservoirimpoundmentwassimulatedbyactivatingthereservoirelements.Acomparisonofresultswasmadeusingthereservoirmodeledwithsolidelementandmerelyapplyingthehydraulicloadsasnodalforces.Similarresponseofthedamwasobservedwhenthereservoirwassimulatedbyappliedhydraulicloadsontheupstreamfaceofthedam.Fortheusualloadconditionwithajointfrictionangleof55degrees,themaximumcomputedslipdisplacementattherightabutmentcontactwas0.06in.Whenthefrictionanglewasreducedto35degrees,themaximumcomputedjointsheardisplacementof0.129in.isobservedatthedamfoundationcontactasshowninFigure5.Thesheardisplacementisconcentratedontherightsideofthemid-cantilever,i.e.,wherethecontactisadverselyslopeddownstream.ItisnotedthatFigure5doesnotshowthedamelementsbutratherthegeometryasinputto3DEC.Themodelcontainsmorethan200,000elements.WedgeAnalysisThestaticnumericalanalysescarriedoutshowedthattherightabutmentwedgeattheCushmanDam1isstablewithfrictionanglesofreducedto25degreesonthediscontinuitieswithintherockmass.Theglobaldisplacementvectorpatternwithindamdidnotaltersignificantlyuntilthefrictionanglewasreducedto25degrees.However,evenforafrictionangleof25degrees,themaximumdisplacementsafterthereservoirimpoundingarelessthan0.3in.withinthedamandlesswithinthefoundation.Therefore,forbothusualandunusualloadingthefactorofsafetyagainstrightabutmentwedgefailureisgreaterthan3[i.e.,tan(55)/tan(25)isgreaterthan3].Asimilarconclusiononthewedgestabilitywasreachedusingamanualstabilityanalysis.Figure5.ShearDisplacementattheDam-FoundationContactSurface.DYNAMICANALYSESThedynamicloadingofthedamrepresentstheextremeloadingconditionforthedamstabilityassessment.TwocontrollingearthquakesgroundmotionsfortheCushmandamsitesaretheCascadia(inter-plate)andtheJuandeFuca(intra-plate)(Abrahamson,2001).Theanalyseswereperformedwithboththerecords.TheresultsfortheJuna-de-Fucaarediscussedinthispaper,althoughtheCascadiarecordgavesimilarresults.SeismicRecordThepeakaccelerationsinthehorizontalplaneare0.49g.Thepeakaccelerationintheverticalplaneis0.28g.Intheanalysis,thethreecomponentsoftheearthquakeareappliedsimultaneously.Aquietperiodoffivesecondswasusedtocheckthattherelativemovementtojointshadstoppedaftertheearthquake.Theinputaccelerationrecordwasintegratedtoobtainthevelocities.Thevelocitieswereusedastheprimaryseismicinputforthe3DECanalysis.ResultsofDynamicAnalysisTheresponseofanarchdamtoanearthquakeloadingisinfluencedtoagreatextentbyseismicinputcharacteristicsandthephysico-mechanicalpropertiesoftheintactconcrete,rockblocks,andthediscontinuitieswithinthem.Thestaticstateisaninitialconditionforthedynamicanalysis.Therelativedisplacementsofthecrowncantileverwerefoundandsnapshotsofstressesonthedamatthecriticaltimeswerestudiedtoexaminethestresseswithinthedambodyandshearingatthedam-foundationcontact.Thestateofstresswasalsoexaminedatthetimeofmaximumopeningofthecontractionjointswithinthedam.Itwasfoundthatthesevarioussnapshots,ofstress,thestressesremainedwithinacceptablelimits.3Dstressvectorplotonthedamsurface,beforeandaftertheseismicshakingonthedownstreamfaceareshowninFigures6and7respectively.Itcanbenotedthattheprincipalstressvectorsareorientednormaltothefoundationsurfaceandareparalleltothearchdirectionatthetopofthedam.Comparisonofstressvectorsbeforeandaftertheseismicshakingshowsthatsignificantstressredistributionwithintheconcretearchdamtakesplaceasaresultoftheseismicshaking.Forexample,asslipdisplacementsoccurattherightabutment,thenstressesaretransferredtotheleftabutmentbyarchaction.Figure6.StressDistributiononDownstreamFaceBeforeEarthquakeFigure7.StressDistributiononDownstreamFaceAfterEarthquakeThenon-linearanalysisperformedwith3DECoffersaninterestinginsightintovariousfailuremechanismsthatcandevelopastheblocksslide,slipandopenduringstaticanddynamicloading.The3DECresultswereusedintheDISPLAYprogramtoplotdeformedshapes.Figure8showstheexaggerateddeformedshapesofthedam.Itshouldbenotedthatthedisplacementsaregreatlyexaggerated;otherwiseitwouldbedifficulttoseethemovements.Figure9isazoomedviewofthedamblocksontherightside.Relativeseparationandrotationofthedamblockscanbeeasilyseeninthesefigures.Fromthesefigurestherelativemovementofvariousdamblockscanbeobserved.Figure8.ExaggeratedDeformedShapeoftheDamattheEndofEarthquakeRecordFigure9.ZoomedofExaggeratedDeformedShapeoftheDamattheEndofEarthquakeRecordThemaximumcomputedshearslipdisplacementwasintherangeof0.7to1.3in.Apost-earthquakeanalysiswasundertakenwiththedaminitsdisplacedconfigurationandtheupliftwasincreasedtofullreservoirheadontheupstreamhalfofthecontact.Asensitivityanalysisoffrictionalstrengthshowedthedamremainsstableinitspost-earthquakecondition.Itisinterestingtonotethatthedamwaslesssensitivetoreducedfrictionalstrengthinitspost-earthquakedeformedconditioncomparedtoresultsfromitspre-earthquakesensitivityanalysis.CONCLUSIONSThefollowingconclusionsaredrawn•Thedamisacceptablystableforthestatic,dynamicseismicandpost-earthquakeloadingconditions•Undersevereseismicloading,thedamwillexperiencepermanentmovementonthedamcontractionanddam/foundationjoints.Thecomputedmovementsareconsideredconservativebecausethedamshearkeysarenotmodeledandthecohesivestrengthoftheroughdam/foundationcontactisignoredintheanalysis.Themagnitudeofthemovementsisfoundtobeacceptable.•Modelingofmovementsonjointsasshownherein,allowsrealisticassessmentofdamsinstatic,dynamicandpost-earthquakeconditions.REFERENCESAbrahamson,N.,2001,TimeHistoriesforCushmanDam,ReporttoSteveFischer,January14,2001.Coombs,H.A.,1972,TheSkokomishRiverProjects,CushmanDamNo.1andCushmanDamNo.2,EngineeringGeologyinWashington,Volume1,WashingtonDivisionofGeologyandEarthResourcesBulletin,78,pp311-316.Dasgupta,B.andLorig,L.J,1995,NumericalModelingofUndergroundPowerhousesinIndia,inProceedingsoftheInternationalWorkshoponObservationalMethodofConstructionofLargeUndergroundCavernsinDifficultGroundConditions,(8thISRMInternationalCongressonRockMechanics,Tokyo,September1995,pp65-74,S.Sakurai,Ed.EMRC(EngineeringMechanicsResearchCorporation),DISPLAYIII,PreandPostProcessingProgram,Version7.0,February1997,Troy,Michigan,USA.Hamilton,D.H.,2001,EvaluationoftheEngineer

3DEC建模.pdf

3DEC建模.pdf

上传者: zhangqiang2025
46次下载 0人收藏 暂无简介 简介 2012-05-14 举报

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NON-LINEARSTATICANDDYNAMICANALYSISOFTHECUSHMANARCHDAMSUSINGDISTINCTELEMENTSD.D.Curtis1J.P.Aglawe2E.B.Kollgaard3D.E.Bowes4S.H.Fischer5ABSTRACTThepaperpresentsthedetailednon-linearstaticanddynamicanalysisoftheCushmanNo.1archdam.TheCushmanNo.1archdamisownedandoperatedbytheCityofTacoma,DepartmentofPublicUtilities.TheanalyseswereundertakenaspartoftheF.E.R.C.Part12investigations.Thestaticanddynamicanalysesareuniqueinthatopening,closing,andslidingalongjointsismodeledinconsiderabledetail.Thedistinctelementprogram3DECisusedinthenon-linearanalysisofthedamandfoundation.Webelievethatthesophisticatednon-linearanalysesthathavebeencarriedoutonthesedams’advancesthestate-of-the-artofdamassessmentunderseismicloading.Inthe3DECanalysis,allthedamcontractionjointsandthedam-foundationinterfacejointsareallowedtoopen,close,andslideunderstaticanddynamicloading.Inaddition,jointsinthefoundationrockaremodeledsuchthatstabilityanalysisofthedamandfoundationaremadewithinone3DECmodel.Thestaticanalysissimulatesdamconstruction,groutingofcontractionjoints,andreservoirimpoundment.Thestaticstabilityofthedamischeckedbygraduallyreducingthefrictionalstrengthofthejointsuntildisplacementsbecomeexcessive.Adetailednon-linearstaticanalysiswasundertakentoinvestigatesliponthedam-foundationinterface,particularlyattherightabutmentwherethecontactgeometryisadverselyslopeddownstream.Inthenon-linearseismicanalysis,thedamjointsanddam-foundationinterfaceopenandcloseduringtheearthquake.Atseveraltimeinstancesduringtheearthquake,theshearstrengthalongvariousjointsurfaceswasexceededandthiscausedrelativeshearslipdisplacements.Thepost-earthquakestabilityofthedamwasassessedbyincreasingupliftandgraduallyreducingthestrengthofthejoints.Bythismeansthedamwasfoundtobesafe._______________1SeniorCivilEngineer,AcresInternational,4342QueenSt.,P.O.Box1001,NiagaraFalls,OntarioCanada,L2E6W1,Tel:905-374-5200,Fax:905-374-1157,dcurtis@acres.com.2SeniorGeotechnicalEngineer,AcresInternational,4342QueenSt.,P.O.Box1001,NiagaraFalls,OntarioCanada,L2E6W1,Tel:905-374-5200,Fax:905-374-1157,jaglawe@acres.com.3ConsultingEngineer,4820EagleWay,Concord,CA,USA,94521,Tel:925-798-9475,Fax:925-689-3456,ebkollgaard@ca.astound.net.4ConsultingEngineer,292278thAve.Ct.N.W.,GigHarbor,WA,USA,98335,Tel:253-265-0811,Fax:253-265-0812,bowespe@halcyon.com.5SeniorPrincipalEngineer,TacomaPower,Generation,3628South35thStreet,Tacoma,WA,USA,98409,Tel:253-502-8316,Fax:253-502-8136,sfischer@ci.tacoma.wa.us.INTRODUCTIONTheCushmanDamsareonthelowerstretchoftheNorthForkoftheSkokomishRiveronthesoutheasternsideoftheOlympicpeninsulanearthesouthernendoftheHoodCanal.TheCityofTacomaownsboththedams.CushmanDam1isasinglecurvatureconcretearchdamwithanoverallheightof260ftabovethestreambed.The400ft-longcrestofthedamisatEl.741.5.ThereservoirnormalmaximumstoragelevelisEl.738.0.Thedamwascompletedandplacedintooperationin1926.TheCushman1dam/foundationcontactispoorlyshapedespeciallyattherightabutmentwhereitisslopedadverselyinthedownstreamdirection.Thisfactledtothequestionofabilityofthedamtowithstandthestronggroundmotionsassociatedwiththeseismicloading.Itwasrecommendedtoperformasophisticatednon-linearnumericalanalysistoascertaintheseriousnessoftheseismicresponseandevaluationofremedialmodifications.Thenon-linearstaticanddynamicanalyseswereperformedwith3DEC,athreedimensionaldistinctelementanalysisprogram.The3DECprogramwasusedtoperformanon-linearstaticanalysisofdamfollowedbyanon-lineardynamictimehistoryanalysis.The3DECprogramwasusedtoanalyzebothCushman1and2dams,butduetospacelimitations,themainresultsfromtheCushman1analysisarepresentedherein.MODELINGAPPROACHBriefDescriptionof3DECThe3DEC(3-DimensionalDistinctElementCode)programisthethree-dimensionalextensionofItasca'stwo-dimensionalcodeUDEC.Itisspecificallydesignedforsimulatingeitherthequasi-staticordynamicresponsetoloadingofrockmediacontainingmultiple,intersectingjointstructures.The3DECmodelisanassemblageofdiscretepolyhedrasrepresentingdiscontinuousmedium.Discontinuitiesaretreatedasboundaryconditionsbetweenblocks.Largedisplacementonthediscontinuitiessuchasslipandopeningissimulatedinadiscontinuousmedium.Relativemotionalongdiscontinuitiesisgovernedbylinearandnon-linearforce-displacementrelationsformovementinboththenormalandsheardirections.Theprogramusesanexplicitsolutionscheme,whichgivesastablesolutiontounstablephysicalprocesses.3DECisparticularlywellsuitedtosimulateblockystructures,suchasstonemasonryarches.Assessmentofthesafetyconditionsofoldmasonrybridges(Lemos,1997)andtheseismicbehaviorofstonemasonryarches(Lemos,1995)hasbeendoneusing3DEC.Ithasbeensuccessfullyemployedtosimulatethebehaviorofaconcretearchdamconstructedonajointedrockfoundation(Lemos,1996)andalsotoperformstabilityanalysisofundergroundpowerhousestation(DasguptaandLorig,1995,Dasgupta,etal.,1995).GeologicalSettingThebriefreviewoftheengineeringgeologyofCushmanDamNo1isgivenbyCoombs(1972).RecentgeologicalcompilationandreviewwasdonebyHamilton(2001)fortherightabutmentofCushmanDam1.ThebedrockintheareaofCushmanprojectsconsistsofthicksequenceofbasaltandandesiteflowswithlocalinterflowlayersoftuffandagglomerate,oftheEoceneageCrescentFormation.AtthedamsitetheCrescentFormationlayeringstrikesaboutNE-SW,crossingthecanyonatahighangleanddips45to60degreesSEdownstream.Variousjointsinthefoundationrockarepresent.StrikeanddipanglesforthevariousjointsaregiveninTable1.ThejointplaneA1intersectsnearthecontractionjointatstation3+64.79ofthedam.Figure1showsthejointplanesD,A1,A2andB.TherightabutmentwedgeisformedbyanassumedverticalplaneDontheupstream,rampfractureplaneBbelowthedam-foundationcontact,andthejointplanesA1andA2.Thesejointplanesformarightabutmentwedgewithatotalweightofabout30,000tons.Table1.OrientationsoftheDiscontinuitiesJointPlaneStrikeDipDN25WVerticalBN56E53NWA1N67E55SEA2N67E55SEModelDevelopment3DECmodelwasdevelopedasanassemblageofdiscreteblocksusingcommerciallyavailableprogramDISPLAY(EMRC,1997).Foundationrock,concretedam,andreservoirwaterelementswerediscretized.Anexplodedviewoffoundationrock,concretedam,andthereservoirisshowninFigure2.InFigure2,thereservoirisshownintheupperpartofthefigure,thedaminthemiddleandthereservoirinthelowerpartofthefigure.Thereservoirwasextendedmorethanthreetimesthedamheightintheupstreamdirection.Itisnotedthatthebulkofthemodelwascreatedusinga3DAutoCadmodel,whichwassuppliedbyTacomaPower.Inthefoundationrock,fourjointsetswereused.Intheconcretedam,thesevenverticalcontractionjointsandthedam/foundationcontactjointsweremodeled.VariousrockjointsformingarightabutmentwedgeareshowninFigure1.Figure3providesanillustrationofrightabutmentwedgealongwithdam.Rightabutmentgravitysectionsandthestartofthearchsectionofthedamarealsoshowntoobtainspatiallocationandorientationofthewedgewithrespecttothedam.Figure1.Dam-FoundationContact,ContractionJointsandFoundationRockMassDiscontinuitiesFigure2.ExplodedViewofFoundation,DamandReservoirFigure13DECmodelofCushmanArchDamNo.1Figure9a.Figure3.RightAbutmentWedgeGeometryandtheDam.TheRockWedgeAloneisshownintheInset.VariousFISHfunctionswerewrittentosimulatetheeffectofgroutingoftheindependentcantilevermonolithsatthecontractionjoints,theupliftpressuredistributionatthedam-foundationcontactandwaterpressureinthejointsontherightabutmentwedgesurfaces.FISHfunctionsprovideaprogrammingcapabilityin3DECthatallowstheusertoprogramsuchfeaturesasgroutingjoints,i.e.,closinggapsatthedamjoints.ModelingSequenceFigure4presentsvariousstagesduringthemodelingsequencetoestablishinitialstateofstress.Initialrockstresseswerecomputedusinggravityloading.Thedammonolithicblockswerethenconstructed.Groutingoftheindependentcantileverswassimulatedbyspecifyingaclosedgapbetweenthecontractionjointsaftergravityloadswereequilibrated.Thereservoirelementswereturnedontoloadthedamhydrostatically.Parametricstudieswereperformedtoexaminethesensitivityofthe3DECtoreducedfrictionalstrengthatthedam-foundationcontactandonthejointsformingtherightabutmentwedge.Finally,thedynamicanalysiswasperformedusingJuandeFucaandCascadiaseismicrecordsforMCEloading.PropertiesThejointsbetweenthedam-reservoirandreservoir-foundationareassumedtobeelastic.Contractionjointswithinthedamanddam-foundationcontactareassumedtohavezerocohesionand55degreesfrictionangle.Thedamfoundationwasquiterough,therefore,theassumedfrictionangleisconsideredconservative.Intherightabutmentwedgeanalysis,thecohesiononthejointplaneswassettozero.Theassumedtotalcombined(cohesiveandfrictional)shearstrengthonjointsB,D,A1andA2istakenas55degrees.RkItwasassessedthatthetotalshearstrengthofthejointplanesisatleastequivalenttothatwithacombinedfrictionangleof55degrees.Figure4ModelingMethodologyAdoptedforDynamicAnalysisofCushman-1ArchDamCreateDam+RockFoundation+ReservoirblocksfromSADSAPmodelExtendfar-fieldboundariesforrockfoundationandreservoirDiscretizemodelApplyboundaryconditionsRockonlyanalysisEquilibriaterockfoundationundergravityConstructarchdam+rightandleftwingwalldamsasmonolithswith7contractionjointsContractionjoint:coh=0psi,fric5degRockdamcontact:coh=300psi,fric55degEquilibriatethemodelGroutingClosethegapsonthecontractionjointsbetweentheconcretemonolithsContractionjoint:coh=0psi,fric55degActivatereservoirelementswaterel.741'(3ftaboveNormal)Elasticcontactbetweendam&reservoirreservoir&foundationReducestrengthparametersonRock-damcontactcoh=0psi,fric55degDynamicAnalysisReducestiffnessofjointsto5.588e4psi/inApplyviscousboudariestothesidesPerformTimeHistoryAnalysisIncludequietperiodatendoftimehistoryThebulkmodulusoftheelementsinthereservoirregionwassetto2.90x105psi.TheshearmoduluswascalculatedusingPoisson’sratioof0.495,i.e.,acompressiblefluid.DampingParametersandDiscretization:Thehydrodynamicinteractionbetweenthedamandthereservoirismodeledusingsolidelementsforthedamconcreteandreservoirwater.Thehighlyunevensurfacetopographyintheupstreamregionresultedincomplexgeometricalshapeforreservoirregion.Thedominantfrequencyrangefortheearthquakeanddamresponseisbetween0and5Hz.Themass-proportionalcomponentofRayleighdampingisemployed.Thefractionofcriticaldampingof4.35%wasobtainedasoperatingatthecenterfrequencyof3.43Hz.The3DECzone(element)sizewasadjustedtoensurethisfrequencywascapturedintheanalysis.STATICANALYSESInitialSetupTworeservoirelevationscorrespondingtousualloadingcase(738ft)andthePMFunusualloadingcase(745ft)wereconsidered.Theloadingduetoreservoirimpoundmentwassimulatedbyactivatingthereservoirelements.Acomparisonofresultswasmadeusingthereservoirmodeledwithsolidelementandmerelyapplyingthehydraulicloadsasnodalforces.Similarresponseofthedamwasobservedwhenthereservoirwassimulatedbyappliedhydraulicloadsontheupstreamfaceofthedam.Fortheusualloadconditionwithajointfrictionangleof55degrees,themaximumcomputedslipdisplacementattherightabutmentcontactwas0.06in.Whenthefrictionanglewasreducedto35degrees,themaximumcomputedjointsheardisplacementof0.129in.isobservedatthedamfoundationcontactasshowninFigure5.Thesheardisplacementisconcentratedontherightsideofthemid-cantilever,i.e.,wherethecontactisadverselyslopeddownstream.ItisnotedthatFigure5doesnotshowthedamelementsbutratherthegeometryasinputto3DEC.Themodelcontainsmorethan200,000elements.WedgeAnalysisThestaticnumericalanalysescarriedoutshowedthattherightabutmentwedgeattheCushmanDam1isstablewithfrictionanglesofreducedto25degreesonthediscontinuitieswithintherockmass.Theglobaldisplacementvectorpatternwithindamdidnotaltersignificantlyuntilthefrictionanglewasreducedto25degrees.However,evenforafrictionangleof25degrees,themaximumdisplacementsafterthereservoirimpoundingarelessthan0.3in.withinthedamandlesswithinthefoundation.Therefore,forbothusualandunusualloadingthefactorofsafetyagainstrightabutmentwedgefailureisgreaterthan3[i.e.,tan(55)/tan(25)isgreaterthan3].Asimilarconclusiononthewedgestabilitywasreachedusingamanualstabilityanalysis.Figure5.ShearDisplacementattheDam-FoundationContactSurface.DYNAMICANALYSESThedynamicloadingofthedamrepresentstheextremeloadingconditionforthedamstabilityassessment.TwocontrollingearthquakesgroundmotionsfortheCushmandamsitesaretheCascadia(inter-plate)andtheJuandeFuca(intra-plate)(Abrahamson,2001).Theanalyseswereperformedwithboththerecords.TheresultsfortheJuna-de-Fucaarediscussedinthispaper,althoughtheCascadiarecordgavesimilarresults.SeismicRecordThepeakaccelerationsinthehorizontalplaneare0.49g.Thepeakaccelerationintheverticalplaneis0.28g.Intheanalysis,thethreecomponentsoftheearthquakeareappliedsimultaneously.Aquietperiodoffivesecondswasusedtocheckthattherelativemovementtojointshadstoppedaftertheearthquake.Theinputaccelerationrecordwasintegratedtoobtainthevelocities.Thevelocitieswereusedastheprimaryseismicinputforthe3DECanalysis.ResultsofDynamicAnalysisTheresponseofanarchdamtoanearthquakeloadingisinfluencedtoagreatextentbyseismicinputcharacteristicsandthephysico-mechanicalpropertiesoftheintactconcrete,rockblocks,andthediscontinuitieswithinthem.Thestaticstateisaninitialconditionforthedynamicanalysis.Therelativedisplacementsofthecrowncantileverwerefoundandsnapshotsofstressesonthedamatthecriticaltimeswerestudiedtoexaminethestresseswithinthedambodyandshearingatthedam-foundationcontact.Thestateofstresswasalsoexaminedatthetimeofmaximumopeningofthecontractionjointswithinthedam.Itwasfoundthatthesevarioussnapshots,ofstress,thestressesremainedwithinacceptablelimits.3Dstressvectorplotonthedamsurface,beforeandaftertheseismicshakingonthedownstreamfaceareshowninFigures6and7respectively.Itcanbenotedthattheprincipalstressvectorsareorientednormaltothefoundationsurfaceandareparalleltothearchdirectionatthetopofthedam.Comparisonofstressvectorsbeforeandaftertheseismicshakingshowsthatsignificantstressredistributionwithintheconcretearchdamtakesplaceasaresultoftheseismicshaking.Forexample,asslipdisplacementsoccurattherightabutment,thenstressesaretransferredtotheleftabutmentbyarchaction.Figure6.StressDistributiononDownstreamFaceBeforeEarthquakeFigure7.StressDistributiononDownstreamFaceAfterEarthquakeThenon-linearanalysisperformedwith3DECoffersaninterestinginsightintovariousfailuremechanismsthatcandevelopastheblocksslide,slipandopenduringstaticanddynamicloading.The3DECresultswereusedintheDISPLAYprogramtoplotdeformedshapes.Figure8showstheexaggerateddeformedshapesofthedam.Itshouldbenotedthatthedisplacementsaregreatlyexaggerated;otherwiseitwouldbedifficulttoseethemovements.Figure9isazoomedviewofthedamblocksontherightside.Relativeseparationandrotationofthedamblockscanbeeasilyseeninthesefigures.Fromthesefigurestherelativemovementofvariousdamblockscanbeobserved.Figure8.ExaggeratedDeformedShapeoftheDamattheEndofEarthquakeRecordFigure9.ZoomedofExaggeratedDeformedShapeoftheDamattheEndofEarthquakeRecordThemaximumcomputedshearslipdisplacementwasintherangeof0.7to1.3in.Apost-earthquakeanalysiswasundertakenwiththedaminitsdisplacedconfigurationandtheupliftwasincreasedtofullreservoirheadontheupstreamhalfofthecontact.Asensitivityanalysisoffrictionalstrengthshowedthedamremainsstableinitspost-earthquakecondition.Itisinterestingtonotethatthedamwaslesssensitivetoreducedfrictionalstrengthinitspost-earthquakedeformedconditioncomparedtoresultsfromitspre-earthquakesensitivityanalysis.CONCLUSIONSThefollowingconclusionsaredrawn•Thedamisacceptablystableforthestatic,dynamicseismicandpost-earthquakeloadingconditions•Undersevereseismicloading,thedamwillexperiencepermanentmovementonthedamcontractionanddam/foundationjoints.Thecomputedmovementsareconsideredconservativebecausethedamshearkeysarenotmodeledandthecohesivestrengthoftheroughdam/foundationcontactisignoredintheanalysis.Themagnitudeofthemovementsisfoundtobeacceptable.•Modelingofmovementsonjointsasshownherein,allowsrealisticassessmentofdamsinstatic,dynamicandpost-earthquakeconditions.REFERENCESAbrahamson,N.,2001,TimeHistoriesforCushmanDam,ReporttoSteveFischer,January14,2001.Coombs,H.A.,1972,TheSkokomishRiverProjects,CushmanDamNo.1andCushmanDamNo.2,EngineeringGeologyinWashington,Volume1,WashingtonDivisionofGeologyandEarthResourcesBulletin,78,pp311-316.Dasgupta,B.andLorig,L.J,1995,NumericalModelingofUndergroundPowerhousesinIndia,inProceedingsoftheInternationalWorkshoponObservationalMethodofConstructionofLargeUndergroundCavernsinDifficultGroundConditions,(8thISRMInternationalCongressonRockMechanics,Tokyo,September1995,pp65-74,S.Sakurai,Ed.EMRC(EngineeringMechanicsResearchCorporation),DISPLAYIII,PreandPostProcessingProgram,Version7.0,February1997,Troy,Michigan,USA.Hamilton,D.H.,2001,EvaluationoftheEngineer
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