ML19044A772
| ML19044A772 | |
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| Site: | Seabrook  |
| Issue date: | 02/13/2019 |
| From: | C-10 Research & Education Foundation, Harmon, Curran, Harmon, Curran, Spielberg & Eisenberg, LLP |
| To: | NRC/SECY |
| SECY RAS | |
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| 50-443-LA-2, 50-443-LAR, ASLBP 17-953-02-LA-BD01, RAS 54795 | |
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ExperimentalandNumericalInvestigationofAlkaliSilicaReactioninNuclearReactorsGrantNo.:NRC-HQ-60-14-G-0010Oct.2014-Dec.2017($703,197)Final(Public)SummaryReport*December2017PrincipalInvestigatorVictorE.SaoumaUniversityofColorado,BoulderNRCTechnicalContactMadhumitaSircar*SynthesisofConfidentialReports:1-A:DesignofanAARProneConcreteMixforLargeScaleTesting1-B:AARExpansion;ctofReinforcement,SpecimenType,andTemperature1-C:ctofAARonShearStrengthofPanels2:Diagnosis&PrognosisofAARinExistingStructures3-a:RiskBasedAssessmentofthectofAARonShearWallsStrength3-b:ProbabilisticBasedNonlinearSeismicAnalysisofNuclearContainmentVesselStructureswithAAR NOTESThisreportprovidesasynthesisofthefollowingtialdocumentssubmittedtotheNRC:1-A:DesignofanAAR-ProneConcreteMixforLarge-ScaleTesting(93pages).1-B:AARExpansion;ofReinforcement,SpecimenType,andTemperature(123pages).1-C:EofAARontheShearStrengthofPanels(90pages).2:Diagnosis&PrognosisofAARinExistingStructures(191pages).3-A:Risk-BasedAssessmentofthetofAARonShearWallStrength(25pages).3-B:Probabilistic-BasedNonlinearSeismicAnalysisofNuclearContainmentVesselStructureswithAAR(216pages).Disclaimer:TheviewsandopinionsexpressedinthisreportarethoseoftheauthoranddonotnecessarilythepositionoftheNuclearRegulatoryCommission.Examplesofanalysisperformedwithinthisreportareonlyexamples.Theyshouldnotbeutilizedinreal-worldanalyticproductsastheyarebasedonlyonverylimitedanddatedopensourceinformation.2 Contents1Introduction51.1ObjectivesandMainConclusion..................................51.2Tasks.................................................51.3PICredentials.............................................52ResearchTasks62.1Task1:ShearStrengthDegradation................................62.1.1Task1-A:ConcreteMixDesign...............................62.1.2Task1-B:ExpansionMonitoring..............................72.1.3Task1-C*:ShearTests...................................92.2Task2:PrognosisforFutureExpansion/RILEM.........................132.3Task3:FiniteElementSimulations.................................142.3.1Task3-A:Risk-BasedAssessmentofShearWalls.....................142.3.2Task3-B:RiskAssessmentofanNCVSSubjectedtoAARandSeismicExcitation..163SynthesisandConclusion214RecommendationsforFutureWork21ListofFigures1Expansionofmortarbartests....................................6214"14"14"blockswithvariousreinforcements.......................73Storageofspecimens.........................................84Examplesofrecordedmeasurements................................85Exampleofanexpansionmeasurementanalysis..........................86ExperimentalSet-up.........................................97Interactionbetweenmodelandspecimens.............................108Compressivestrengthvs.tensilesplittingstrength........................109TestMatrix..............................................1010Experimentalandnumericalresults.................................1111FEAsimulations............................................1212Testset-upfortheshearwall....................................1413Structuralresponseofshearwallundercyclicdisplacement(withoutASR)..........1514Resultsofshearwallanalyses....................................1515Geometryandmodelidealization..................................1716LoadsimposedontheNCVSanalysis...............................1817ResponseofNPPunderanAARanalysis.............................1818ResponseofNCVSunderAARandseismic............................1919Principalstress-timehistoriesfromtheseismicanalysis......................1920Crackfromseismicanalysis.................................2021Dynamictesting...........................................233 ListofTables1Standardsusedforaggregateandconcretetestingprograms...................72Statisticalanalysisofresults.....................................124 1Introduction1.1ObjectivesandMainConclusion1Thisprojecthasaddressedthetwomostimportantquestionsraisedbyanuclearcontainmentvesselstructure(NCVS)subjectedtoAlkali-AggregateReaction(AAR):1.Howfastwillthereactionevolve,andwhatistheanticipatedmaximumexpansion?2.Istheresilience(i.e.abilitytosafelywithstandanearthquake)and,ifso,byhowmuch?Thosearecriticalquestionthebeyond60possiblelifeextensionofNCVS.2Itwillbeshownhereinthatbasedonthetests(\high"expansionof0.6%)andanalyses("moderate"expansionof0.3%)performed,a20%degradationislikelytooccurinbothcases.1.2Tasks3Inrecognitionofthefactthatthisisacomplexcoupledproblemrequiringexpertiseinbothmaterials(understanding,testing)andstructures(abilitytoconductcredibleanalyses),aholisticapproachhasbeenimplementedtocompletethefollowingtasks:Task1:Twosubtasksaresummarizedinthereports:1-A:MixDesignDesignaconcretemix(withlocallyavailableaggregates)thatwillexpandbyapproximately0.5%in6months,hasacompressivestrengthofaround4,500psi,a3"slumpandlowaircontent.1-BExpansionMonitoring:Castnotonly16shearspecimensbutmanyothersaswell1(suchasspecimenswithvariousuniaxial,biaxialortriaxialreinforcements),curethemundercontrolledconditionsandassessbothexpansionandcrackindices.1-CSheartests*:assessshearstrengthdegradationofplainandstructuralconcretesubjectedtoAAR.Task2*:Developadiagnosisandprognosistoolbasedontheacceleratedtestinordertoassessresidualexpansionovertime.Morespa)Diagnosistoestimatethedegreeofreactioninconcretealongwiththecorrespondingexpansion;b)PrognosistopredictfutureandultimateASRexpansion;andc)provideresultsinaformatsuitableforproperelementsimulation.Task3:NumericalsimulationsusingourMerliniteelementcodeanditsconstitutivemodelforAAR,whichhasbeenadoptedbymanyresearchersandpractitioners.Twosubtasksareincluded:3-A:Risk-BasedAssessmentofashearwallsubjectedtoareversecyclicloadandtestedattheUniversityofToronto.ThesestepswerecarriedoutwithinthescopeofanASCETroundrobin.3-BImpactofAARonSeismicResponse*ofanNCVS.Eachofthesetaskswillbesummarizedseparately.Thoseidenbyan*directlyaddressthescopeoftheproject,othersaresupportivetasks.1.3PICredentials4VictorSaoumaisaProfessorofCivilEngineeringattheUniversityofColoradoinBoulder;ChairofRILEM'sCommitteeonthePrognosisofdeteriorationandlossofserviceabilityinstructuresbyalkali-silicareactions;pastPresidentofFraMCoS(FractureMechanicsofConcrete);conductedAARrelatedresearchfortheSwissfederaldamsafetyagency,theTokyoElectricPowerCompany(TEPCO),theOak1Note:Thecontractcalledfor8specimens,withnomonitoringofadditionalspecimens.5 RidgeNationalLaboratory;MemberoftheMaterialsAgingandDegradation(MAaD)ExternalReviewCommittee(ORNL,LightWaterReactorSustainabilityR&DProgram);pastmemberoftheExpandedProactiveMaterialsDegradationAnalysisExpertPanel(PMDA)forconcreteinnuclearreactors;RevieweroftheFrenchresearchprogramMACENA(associatedwithVeRCoRs);recentlypublishedanEPRIreportonthenumericalmodelingofNCVS;isabouttolaunchamajor3-yearresearchprogramonAARfortheBureauofReclamation;publishedabookonNumericalModelingofAAR;haspublishedover30papersonAAR,chloridedSeismicAnalysisandStochasticAnalyses(hispaperonanAARconstitutivemodelisprobablythemostwidelycopiedandcited);haspioneereddynamictesting(real-timehybridsimulation);isalsotheManagingPartnerofarecentlyformedconsultingcompanyX-Elastica.2ResearchTasks2.1Task1:ShearStrengthDegradation2.1.1Task1-A:ConcreteMixDesign5AssessmentoftheimpactofAARthroughalaboratorytestingcampaignhingesonourabilitytoreplicateamixdesignthatisrepresentativeoftheoneusedinNCVS.Forstarters,reactiveaggregateshadtobeideninColorado,thentheconcretemixdesignhadtobedeveloped.6Twosourcesofaggregateswereidenandexpansionmortartestswereperformedonvariously-sizedaggregates,Fig.1.Bothsourcesyieldedhighlyreactiveaggregates,andonewasselected.Figure1:Expansionofmortarbartests7Followingtheselectionofanaggregatesource,aconcretemixdesignwith:aminimumcompressivestrengthof4,000psi[27.6MPa],aslump2of5in.[12.7cm],anaircontentsetat3%,and,mostimportantly,theexpansiontargetforreactivesamplessetatarelativelyhigh0.5%(tobereachedwithinapproximately6monthsunder95%RHand38Ctemperature)hadtobedesigned.8Inordertoenhancethereaction,cementwithahighnaturalalkalinitywasselectedandthenthealkalinitywasfurtherraisedbyaddingsodiumhydroxide.9Controlspecimensusedthesamereactiveaggregates3;however,theywere(successfully)enrichedwithlithium,whichinhibitedthereaction.10Throughoutthistask,ASTMstandardswerestrictlyrespected,Table1.2Theslumpvalueisslightlyhigherthannormal;however,mostspecimenshadtoreceiveclosely-spacedreinforcementsandmoreovernosuperplasticizerwasusedsoasnottointerferewitheitherthesodiumhydroxideorlithium,whichwereintroducedtoenhanceorinhibittheAARreaction.3ItistheP.I.convictionthatusingatnon-reactiveaggregate,orash,canbeverymisleadingwheninterpretingresults.6 Table1:StandardsusedforaggregateandconcretetestingprogramsAggregateTestsStandardConcreteTestStandardCoarseaggregaterelativedensityASTMC127SlumpASTMC173FineaggregaterelativedensityASTMC128UnitWeightASTMC138CoarseaggregatebulkdensityASTMC29AirContentASTMC231Finenessmodulus/gradationASTMC136TemperatureASTMC1064MoisturecontentASTMC566CompressiveStrengthASTMC39ASRExpansionMoASTMC129311ApetrographicanalysisoftheconcreteprismandtwomortarbarswasconductedtoverifythattheexpansionobservedwasindeedaresultofexpansivegelsduetoASR.Thereactiveaggregateswereidenasareactivemixofporousandsemi-poroust-likegrains,metamorphic,sedimentaryandmagmaticrocktypes.12AverageexpansionsofthecastconcreteareshownbelowinFig.4(a)forspecimensstoredinthefogroom(averageRH95%,T=38C)2.1.2Task1-B:ExpansionMonitoring1316concretepanelsweretobecastfortestingoncetexpansionhadoccurred.Itwasthusdecidedtopouratotalof37additionalspecimensinordertomonitorexpansionunderntconditions(106x6x14",124x4x16"prisms,and1514x14x14"blocks).Thesevariousspecimenswerestoredunderttemperatures,andsomewerewithstrainandtemperaturegages.14Inanattempttofurtherelucidatetheimpactofisotropicoranisotropicreinforcementonexpansion,the14"x14"x14"blockswereassignedtreinforcementratiosusing#3or#4steelreinforcement,Fig.2.Figure2:14"14"14"blockswithvariousreinforcements15Thefogroomarrangementforspecimensstoredat95Fand90%RHwascarefullyplanned(duetolimitedsize),Fig.3(a).16Theleaching(causedbyainalkalinitybetweenspecimenandambientair)ofalkalinityfromtheconcretewasamajorpotentialproblem.Itwasaddressedbywrappingspecimensinburlapandcontinuouslywettingthemwitha1Maqueoussodiumhydroxide(NaOH)solution,Fig.3(b).17Atotalof147expansionreadingswererecordedperiodically,storedinadatabaseandthenanalyzed.Theexpansionreadingswerecontinuouslyrecorded,Fig.4(a).7 (a)Installationofreactiveandnon-reactiveshearspecimens,blocks,prismsandcylindersinthefogroom(b)Sprinklersystemwettingtheburlap-wrappedshearspecimenFigure3:Storageofspecimens18Likewise,some160crackindexreadingswererecordedatage520days(with0.005"resolution),Fig.4(b).(a)Expansionsofall6614-inchprisms(P14)(b)CrackIndicesforCubesFigure4:Examplesofrecordedmeasurements19Theextensive(multi-variable)databasewasthenanalyzedandvariouswerequanFig.5.(a)Normalizedexpansionsforvariousreinforcementratios(b)ofTemperatureonPrismsFigure5:Exampleofanexpansionmeasurementanalysis8 2.1.3Task1-C*:ShearTests20Thisisoneofthetwomostimportanttasks:theexperimentalassessmentoftheimpactofAARontheshearstrengthofbothplainandreinforcedconcrete.Theformerisamaterialcharacterization,whilethelatterinvolvesastructuralcharacterization.21Theshearstrengthassessmentshouldnotbe\corrupted"bystresses4.Ontheotherhand,perfectsheartestsaremechanicallyimpossible,yettheymaybecloselyapproximatedthroughacomplexset-up.22ThetestconceptisillustratedinFig.6(a).A10x30x40-inchconcreteblock(plainorreinforced)istplacedinsideacage,or\shearbox"(showninblue)andisthensubjectedto:a)aconstantlateraltforce(simulatingtheverticalstressatthesimulatedlocation);andb)twoopposingverticalforcesappliedthrougheccentricallyplacedpads(showninblack),thustheverticalforcesareultimatelyimposingshearforces.Asaresult,adiagonalcrackwilldevelopwithinthe(red)band.Finally,theshearboxisplacedwithintheofaonemillion-pound(previouslycalibrated)MTStestingmachine,Fig.6(b).(a)Concretepanelinsidetheshearbox.(b)ShearboxinsidethetestingmachineFigure6:ExperimentalSet-up23Forthestructuralassessment,thepanelsmustbecorrelatedwithanactualNCVSwithinthelimitsoftestingconstraints.Conceptuallyspeaking,themodelmaybeviewedas\extracted"fromtheNCVS,rotated90degreesandtheninsertedintotheloadframefortesting,Fig.7.24Itisimportanttonotethatthecircumferentialreinforcement(showninblue)correspondstotheshorttransversesteelrodsinthespecimen,whilethevertical(red)rodscorrespondtotheaxialreinforcementsinthespecimen.25Priortotesting,the28-daycompressivestrengthwascorrelatedwiththeone-yeartensilesplittingstrength,revealingnoticeabledeteriorationinthelatterforthereactiveconcrete,Fig.8.26Sixgroupsofspecimens(labeledAthroughH)weretested,Fig.9.Mostspecimenswheresubjectedtoa4Forthisreason,shearstrengthcannotreliablybeassessedusingbeams.9 Figure7:InteractionbetweenmodelandspecimensFigure8:Compressivestrengthvs.tensilesplittingstrength\baseline"force(basedontheconcreteweightabovethelevelconsidered),whileothersweretestedatlowerorhighervaluestoassesstheirimpactonstrength.Thetestmatrixcanbebettervisualized(andunderstood)bymeansofFig.9.Figure9:TestMatrix27Forthepreviouslytestmatrix,the7followingquestionswereinvestigated:ofAARonmaterialandstructuralresponses:1.A-FWhatistheofAARonreinforcedconcrete(structure)subjectedtoabasenement?10 2.D-GWhatistheofAARonplainconcrete(material)subjectedtoabaset?3.E-HWhatistheofAARonplainconcrete(material)subjectedtohighement?oftsundervariousscenarios.Thiswillnullify(tosomeextent)theimpactoftheselectedbaselinenormaltractionandmoreovertheresultofwhetherahighercontyieldsahigherfailureshearforce:4.B-AWhatistheoflowtonreinforcedconcretewithAAR?5.C-AWhatistheofhightonreinforcedconcretewithAAR?6.E-DWhatistheofhightonplainconcretewithAAR?7.H-GWhatistheofhightonplainconcretewithoutAAR?28Atthetimeoftesting,theAARexpansionwasabout0.6%,Fig.4(a).29Fig.10(a)summarizesallofthe16individualexperimentalandnumerical(tobediscussedfurtherbelow)resultsinasinglediagram.Inabsolutevalueterms,theseresultsarerelativelyt,astheywouldneedtobenormalized(asdictatedbythequestionsraisedabove).Fig.10(b)showsthenormalizedmeans(whenmorethanonedatapointexists)withrespecttothereferencemeans(asindicatedinFig.9).(a)Rawresults(b)NormalizedexperimentalandnumericalresultsFigure10:Experimentalandnumericalresults11 30AstatisticalsummaryofthesetestresultsisprovidedinTable2,alongwithanattemptatnormalizingshearforceswithpf0c,f0candf0t(let'srecallhereinthattheACIshearstrengthequationisafunctionofpf0c).Table2:StatisticalanalysisofresultsP1P2P3P4Exp.PmaxP1=pf0cP1=f0cP1=ftA,B,C,D,ECumulativeMean202.6491.1141.15549.20std/Mean16%16%19%22%F,G,HCumulativeMean247.65103.7343.45364.19std/Mean18%18%18%18%31AelementsimulationofthetestswasperformedusingthecodenamedMerlin.Thenumericallycomputedload-displacementcurvesareshowninFigs.11(a)and11(b),whilethecorrespondingexperimentalresultsaresimplypresentedasanasymptotichorizontalpeakvalue5.Fig.11(c)showstheextentofinternalcracking,correspondingtovariouspointsalongtheload-displacementcurve.(a)Controlspecimens(b)AAR(c)Computedinternalcracking,intermsoftheload-displacementcurveFigure11:FEAsimulations.32Basedontheabove,thefollowingobservationscanbeproposed:1.Testresultsareremarkablyclosewithinagivengroup.ThenormalizedstandarddeviationsforseriesA,DandF(wheremorethanonetestisavailable)are5.0,2.0and0.58percent,respectively.Thisreinforcesthereliabilityofourtestprogram.5Experimentallyspeaking,themeasuredactuatorstrokeincludedsubstantialelasticdeformationofthebluecagehousingthespecimen,Fig.6(a).12 2.Theelementsimulationsaccuratelyreplicatedtheexperimentalresults.Hence,asimilarsimula-tioncouldassesswithgoodreliabilitythesheardegradationcorrespondingtotlevelsofAARexpansion.3.TheAARcausesa20%reductioninshearstrengthforreinforcedconcretespecimens(i.e.structuralunderbaset;A/F.4.TheAARcausesa20%reductioninshearstrengthfornon-reinforcedconcretespecimens(i.e.ma-terialunderbaseement;D/G.5.TheAARcausesa20%reductioninshearstrengthfornon-reinforcedconcretespecimens(i.e.ma-terialunderhighment;E/H.6.AreductionintforreinforcedconcretepanelswithAARresultedina20%reductioninshearstrength;B/A.7.AnincreaseincontforreinforcedconcretepanelswithAARresultedina10%increaseinshearstrength;C/A.Thisisnotaccuratelyreplicatednumerically.8.Anincreaseintfornon-reinforcedconcretepanelswithAARresultedinan10%increaseinshearstrengthof;E/D.9.Anincreaseinctfornon-reinforcedconcretepanelswithoutAARresultedina20%increaseinshearstrength;H/G.10.WhenexperimentalshearstrengthP1isnormalizedwithrespecttopf0c,f0candft(P2,P3,andP4,respectively)foralltestseries,seeTable2,thelowestnormalizedstandarddeviationsareassociatedwithP1andP2.Non-reactiveconcreteexhibitsslightlyhighervalues(18%vs.16%);however,thismaybeduetothelimitednumberofdatapoints(4insteadof12).11.Theshearstrengthdegradationof20%islessthanthesplittingtensilestrengthdecrease(50%),Fig.8.33Alltheseresultshadbeenanticipatedbut,priortothispresentresearchprogram,werenotyetquan2.2Task2:PrognosisforFutureExpansion/RILEM34ARILEMCommitteechairedbytheP.I.isdedicatedtothistask.Theroughly36-membercommitteecontainsalltherenownedleadersinthisspeldofconcern.35WorkingGroups:WG1:-DiagnosisandprognosisofAASinexistingstructuresPrognosisThereportwilladdress:1)Diagnosesbasedonpetrographicandmicroscopicinterpretationtoestimatethedegreeofpastex-pansion;2)Acceleratedresidualtestingtopredictfutureultimateexpansionsthatcanbeachievedinlaboratoryconditions;3)Proceduretousetheaboveasinputdataforaelementsimulation;and4)Samplereportsforeachmethod.Part1hasbeencompleted,andPart2isnearlycompleted6.Parts3and4havejustgottenunderway.WG-2:NumericalBenchmark/Round-RobinAnalysesListsabout12simpleproblems(relatedtobothmaterialsandstructures)tobeanalyzedbyFEAcodesfor\validation".Thisreportiscompleteand,tothebestofourunderstanding,theP.I.istheonlytohavecompletedallanalyses.WG3:-FieldAssessmentandMonitoringThetpart,dealingwithNDEandwrittenbyGiannini,JacobsandRivard,isnowcomplete.Currently,CourtoisandGrimal(ElectricitedeFrance)willbe6Contributors:Canada-Laval-Fournier,Canada-Ottawa-Sanchez,France-IFSTTAR-LCPC-Martin,France-Toulouse-Sellier,Japan-Katayama,Spain-Torroja-Menendez,Switzerland-EMPA-Leeman,UK-Wood.13 revisingandupgradingthedocumenttoaddressassessments.WG4:ImpactsofASRonHydraulicStructuresandNuclearPowerPlantsProblemsandResearchNeeds.TheinitialversionwaswrittenbyAmberg(Lombardi,Switzerland)andGocevski(HydroQue-bec)forthehydroandnuclearrespectively.ThisdocumentwillberevisedandeditedbyGrimmal(ElectricitedeFrance).36OurnextannualmeetingwillbeheldMay21-22attheBureauofReclamationinDenver(NRCisherebyinvited).37Thecommitteeshouldwrapupitsworkin2019.2.3Task3:FiniteElementSimulations2.3.1Task3-A:Risk-BasedAssessmentofShearWalls38OECD/NEA/CSNIhasreleasedabenchmarkproblemcenteredonashearwallstestedattheUniversityofToronto.Shearwalls,Fig.12,withandwithoutAARweretested.Results(loaddisplacementcurve)aftera260daysexpansionweremadeavailable,andparticipantswererequestedtopredictresponseat1,000days.Bygeneralconsensus,thedataprovidedbytheUniversityofTorontowereincompleteandquestionable.39CUBoulderneverthelessparticipatedinthisexerciseandspentasubstantial(andunallocated)amountoftimecompletingtheexercise.Theoriginalityoftheanalysiswasitsprobabilisticbasisembeddedintoacomprehensivereport.Allotherreportsweredeterministic.Figure12:Testset-upfortheshearwall40ApreliminarydeterministicanalysisyieldedtheresultsshowninFig.13.41Priortoconductingaprobabilisticanalysis,asensitivityanalysiswasperformed.15potentialvariableswereselected,eachoneassignedaprobabilitydistributionfunction,and31analyseswerethenperformed.Sensitivitieswerethensorted,andtheseresultsareshownintheformatofaso-calledTornadoDiagram,Fig.14(a).ThecorrespondingpredictionisdisplayedinFig.14(b)42Followingthesensitivityanalysis,ofthe15potentialvariables,only5wereselected,andaMonteCarlo-basedsimulationwithLatin-Hypercubesamplingwascarriedout.43Thisstepwasachievedthroughaspecialsoftwaredevelopedin-housethatstartswithaspreadsheetcontainingthevariablesandtheirdistributions,thenproceedstogeneratetheelementmeshes,runstheanalyses,\data-mines"theoutputandultimatelyproducethedesiredresults.44Atotalof100analyseswereperformed,andthe16%and84%fractile(correspondingtomeanminusandmeanplusonestandarddeviation)capacitycurveswereextracted,Fig.14.Experimentalresultsdidindeed14 (a)Load-displacementundercyclicload(b)Deformedshapes;Contoursshowthemaximumprincipalstrains(c)CrackpropagationinwebandcolumnsFigure13:Structuralresponseofshearwallundercyclicdisplacement(withoutASR)fallwithinthenarrowlimits.45Thisanalysishasprovidedtheframeworkallowingforsubsequentrisk-basedassessments,similartothisone,tobeeasilyperformed.(a)Tornadodiagram(b)Capacitycurves(c)SW(d)SW-1000Figure14:Resultsofshearwallanalyses15 2.3.2Task3-B:RiskAssessmentofanNCVSSubjectedtoAARandSeismicExcitation46OnepremiseofthisanalysisisthatAARbyitselfwillnotjeopardizethestructuralintegrityofanNCVS,atmostitsserviceability(throughdeteriorationofthesteel-concretebondinterface).Ontheotherhand,AARwilldegradeshearstrengthandthusmaytheresilienceofthestructurewhensubjectedtolateralload(i.e.seismicexcitation),especiallysincemanyNCVSarenotwithshearreinforcement.47Thereportassociatedwiththistaskiscomposedoftwoparts:1.Averyextensivecoverageofthetheoriesrelatedto:AAR,nonlineartransientelementanalysis,seismichazardanalysis,andprobabilistic-basedanalyses.Tothebestofourknowledge,thiscoverageisbyfaronethemostextensive(moresothanNUREG-1150).2.Detailed3DtransientanalysisofanNCVSsubjectedto40yearsofAARexpansion(upto0.3%)andthensubjectedtoseismicexcitation..Followingisasummaryoftheanalysis.48TheNCVSselectedforourcasestudyisheavilybytheoneillustratedinNUREG-6706andisschematicallyshowninFig.15(a).49Notethat56'ofthetotal122'-highcylindricalpartisbelowgradeandonlytheconcreteunderneathitwillbesubjectedtoAAR(asaresultofthehighRHlikelytobepresentinthesurroundingfoundation).Areinforcementratioof0.5%wasassumedforboththeverticalandhorizontaldirections.50FortheseismicstudyoftheNCVStobeproperlyperformed,radiationmustbedampedandtheofrockingmitigated.51RadiationdampingwasmitigatedbyplacingLysmerdashpots(alsoknownas\silent"boundarycondi-tions)attheendofthefoundation.52Rockingiscausedbytheeccentricityofthecenterofmass,whichissubjectedtothelateralinertialforce.Rocking(seldomaddressedinpublishedreports)thesoil-structureinteractionbypotentiallyupliftingthebasefromtherock(especiallyifverticalexcitationhasbeentakenintoaccount)andopeningagapbetweenthestructureandtheadjacentrock.Thisphenomenonwasmitigatedbyinsertingzero-thicknessjointelementsaroundthecontainer(andbelowit).53Anotherparasiticofrockingisthe\hammering"ofthebase,whichoccursalongwitha(nearly)linearupliftingofthefoundationbase.Thisctwasmitigatedbyperformingastaticanalysiswithrigidverticalsupportsatthebaseandthen(withtheinternalstrains/stresses\lockedin")restartinginitiationofthetransientanalysis.Inthissecondanalysishowever,thesupportsareremovedandthereactionsaresubstitutedbycorrespondingverticalforces(equaltothereactions).Thusthestructurehasnosupportwhatsoever(onlypossibleindynamicanalyses).54AnanalysiswasperformedusingtheMerlinelementcode,withthemodelsshowninFigure15(b).TheNCVSis37mhigh,hasabasemat3.0mthickandaninternalradiusof19.0m.PotentialseparationduetorockingisshowninFig.15(c),andthefoundationdimensionsaregiveninFig.15(d).Alsodisplayedinthesearethe15tcolor-codedmaterialgroupsdescribedinthenextsection.55Essentially,thisanalysisseekstosimulate40yearsofslowAARexpansion,followedbyafewsec-ondsofintenseseismiclateralexcitation,Fig.16(a).TheimposedAARwasamoderate0.3%volumetric16 expansionaccumulatedover40years,Fig.16(b).Lastly,asyntheticgroundmotionoflinearlyincreasingintensitywasapplied,Fig.16(c)(sixtaccelerogramswereactuallyapplied).56ThetechniqueofapplyingrelativelyfewlinearlyincreasingaccelerationsisknownasEnduranceTimeAnalysisFunctions(ETAF).57Apreliminaryanalysis(asdescribedabove)wasperformedundertheassumptionoftheabsenceofAAR.Resultswillbecontrastedwiththisbaseline.58ThestructuralresponseoftheNCVSsubjectedtoAARonly(Static+AAR)isshowninFig.17.Notetheimpactofusingjointelementsatthebaseandaroundthevesseltoallowforpotential(hidden)\delamination"betweenthebasematandfoundation.59TheimpactofAARonthestructuralresponseofanNCVScannowbeascertainedbycomparingStatic+SeismicandStatic+AAR+Seismicfor:Displacements:Theabsolutevaluesofthe(horizontal)displacementscorrespondingtopeaksin(thesix)(a)Cross-sectionandgeometry(b)Detailedgeometry(c)Potentialrockingandensuingseparationofcontainerfromfoun-dation(d)ModelandaccompanyingmaterialgroupsFigure15:Geometryandmodelidealization17 (a)Schematicrepresentationoftheanalysis(b)ImposedAARexpansionmodel(c)ETAFaccelerogramFigure16:LoadsimposedontheNCVSanalysis(a)Swellingofthecontaminatedzone(b)Evolutionofjointopening/slidingduetoAAR(c)InternalcrackingFigure17:ResponseofNPPunderanAARanalysisETAFcasesareshowninFig.18(a).Thisisarampingcurvesincethegroundaccelerationisindeedaslinearlyincreasing(Fig.16(c)).Threesetsofresultsareindicated,namely:1.GroundmotionwithoutAAR2.AARwithaccompanyingmaterialdegradationfollowedbygroundmotion.3.AARwithoutmaterialdegradationfollowedbygroundmotion.TobetterdeterminetheimpactofAAR,theresponseshavebeennormalizedwithrespecttotheanalysiswithoutAAR(i.e.groundmotiononly),Fig.18(b).ItshouldbenotedthatthedisplacementsareallplottedasETAfunctions(expressionofthemaximumabsolutevaluesofEDPduringthetimeintervalfrom0tot,intermsoftime).Hence,anETAfunctionincreasesovertimeinanengineeringdemandparameter(EDP-timecoordinatesystem).Failureinthisfunctioncorrespondstoa(semi-)verticallineatt=tfailure.StressesThehistogramsofmaximumprincipalstressesareshowninFig.19forvariouslocations.ResultsarepresentedforgroundmotiononlywithoutAAR(inblue),andAAR(withdegradation)followed18 (a)Displacementatthetop(b)NormalizeddisplacementsandmeanFigure18:ResponseofNCVSunderAARandseismicbygroundmotion.(a)Base(b)Gradeelevation(c)Mid-heightaboveground(d)DomebaseFigure19:Principalstress-timehistoriesfromtheseismicanalysisCrackingofthestructureisshowninFig.20.60Fromtheprevioussummarizingresults,thefollowingobservationscanbe1.AAR(withmaterialdegradation)willsoftentheconcrete,thusresultinginsmallerlateraldisplace-ments.2.Ifmaterialdegradationisignored(whichisanerroneousabstraction),displacementswillstillbe19 Figure20:CrackfromseismicanalysissmallerthancaseswithoutAAR,butlargerthanAARwithdegradation.NotethatthediscrepancywithrespecttothecasewithoutAARstartsataround9sec(i.e.untilthispoint,theAARhadlittleimpactondeformation).3.TheimpactofAAR(withandwithoutdegradation)istime-dependentduetothecomplexitiesoftheinternalstressstatesinducedbyAARorresultingfromtheseismicexcitation,Fig.18(b).Onaverageandforthiscasestudy,AARwithdegradationresultsina20%change,whereasthecasewithoutdegradationonlyyieldsan8%variationwithrespecttothe\GM"model.4.Theprincipalmaximumstresshistoryatvariouslocations,Fig.19,revealsthatadditionaldamagewillbeinducedbyAAR(withinternaldamagebeingtakenintoaccount).(a)Atthebase,Fig.19(a),maximumprincipalstressesareindeedpositiveandattenuatewithtime.AtstressesarelowerinthepresenceofAARexpansion,butthensuddenlyincreasewithalocalizeddamageattime17sec.(b)Atthegradeelevation,stressesaremuchhigherwithoutAAR,andthengraduallydecreasewithnoindicationoffailure.Notethatthetensilestrengthequals3.1MPa.Ontheotherhand,inthepresenceofpriorAARexpansion,thestressesarenegative,andasuddenlocalizedfailureappearsatt=14sec.20 (c)Forapointabovegrade,stressesarehigherintheabsenceofAAR,andthereisanindicationoflocalizedfailureatt=15sec.InthepresenceofAAR,thisfailureisdelayedtoabout17sec.(d)Atthebaseofthedome,theAARstressesaresubstantiallyhigherthanwithstressesabsent,andlocalizedfailureoccursaround17sec.5.Forthiscase,AARhasreducedstressesatthebasebutsubstantiallyincreasedthematthebaseofthedome.6.ThepreviousobservationsarequalitativelybythecrackshowninFig.20.Indeed,thedamageindex(DI),i.e.theratioofcrackedcross-sectionstototalarea,ishighestwhenAAR(withdamage)hasprecededtheseismicexpansion.7.TheAARhasamuchgreaterimpactontheportionofNCVSbelowgradethanonthatabovegrade(wherenoAARhasbeenmodeled).3SynthesisandConclusion61Tothebestofourknowledge,thisstudyisthemostcomprehensiveontheofAARontheshearstrengthofconcrete.6216largespecimenswerecarefullypreparedandtestedusingauniqueapparatusdesignedforsheartesting.Itwasdeterminedthata0.6%expansionreducesstrengthby20%.63Forthisparticularstudy,AAR(arelativelylow0.3%)reducedtheresilienceofanNCVSsubjectedtoseismicexcitationbyapproximately20%.64Itshouldalsobenotedthatthisreduction,associatedwitha0.3%localizeduniformexpansion,isroughlyequaltothereductioninshearstrengthexperimentallyobservedforexpansionsofabout0.665Ourresultsimplythatamaterialshearstrengthdegradationofx%willhavealargerpercentualimpactonthedisplacementsandstresseswhenusedinthenonlinearseismicanalysisofaNCVS.Inourstudythematerialdegradationwas20%correspondingtoanAARof0.6%,whereastheiteanalysishada20%degradationforanAARof0.3%.66Throughthevalidatedelementcode,parametricstudiesfortcombinationscouldbecon-ductedwithareasonablelevelof4RecommendationsforFutureWork67Whensuchanextensiveinvestigationisperformed,invariablysomepointsarefoundtorequirefurtherThesefallintotwocategories:desirableandcritical.Desirabletopicsinclude:NumericalRepeattheelementanalysis:1.IncludearandomdistributionoftheAAR-contaminatedconcretesoastobetteranactualcase.2.Includedeconvolution,andpossiblyfrattenuationoftheexcitationrecord.3.StochasticanalysisresultinginfragilitycurvesExperimentalteststoinclude:1.Amoredetailedexperimenttostudytheoftemperature,sizeandreinforcementonASRexpansioninconcrete.21 2.Studyofthetransitionfromacceleratedlaboratorytests(underconstanthightemperatureandrelativehumidity)toanactualstructuresubjectedto(typicallylower)variabletemper-atureandrelativehumidity.3.FurtherstudysizeagreaternumberofspecimensgraduallyincreasinginsizewouldbeneededtoderiveamoreestatementregardingitsCriticalBasedontheP.I.'spastexperiencewithdynamictesting7,Fig.21(c),concreteexhibitsastrengthincreasewhensubjectedtoadynamicload.TheP.I.,inusingarelativelyuniquefacilityattheUniversityofColorado(asetofthreedynamicactuatorscontrolledbycustomsoftware),Fig.21(a)showedthatforthecolumnstested,a30%increaseinstrengthwasachieved.Accordingly,thetestset-uplaidoutinFig.21(b)ishighlyrecommended,butonlyifseekingto(partially)circumventthedeleteriousofAARontheshearstrengthofanNCVSsubjectedtoseismicexcitation(careful,asthefailuremodemayshiftwithastrongerconcrete).7Nottobeconfusedwithslowreversecyclicloadingthatsome,veryerroneously,labelasaseismicload.22 (a)Experimentalset-up:constantverticalforce,zerotoprotation,dynamiclateraldisplacement(b)Proposedtestset-up(c)DynamictestsperformedbytheP.I..Toactivatevideo:1.Clickonimage;2.WhenpromptedbyOptions,selectTrustthisdocumentalways;3.ClickagainontheimageFigure21:Dynamictesting23