Concept and methodology for evaluating core damage frequency considering failure correlation at multi units and sites and its application

The Tohoku earthquake (Mw9.0) occurred on March 11, 2011 and caused a large tsunami. The Fukushima Daiichi Nuclear Power Plant with six units were overwhelmed by the tsunami and core damage occurred. Authors proposed the concept and method for evaluating core damage frequency (CDF) considering failure correlation at the multi units and sites.

j o ur na l h o me p a g e:w w w e l s e v i e r c o m / l o c a t e / n u c e n g d e s

application

h i g h l i g h t s

•WedevelopamethodtoevaluateCDFconsideringfailurecorrelationatmultiunits

•Wedevelopaproceduretoevaluatecorrelationcoefficientbetweenmulticomponents

•WeevaluateCDFattwodifferentBWRunitsusingcorrelationcoefficients

•Weconfirmthevalidityofmethodandcorrelationcoefficientthroughtheevaluation

a r t i c l e i n f o

a b s t r a c t TheTohokuearthquake(Mw9.0)occurredonMarch11,2011andcausedalargetsunami.TheFukushima DaiichiNuclearPowerPlantwithsixunitswereoverwhelmedbythetsunamiandcoredamageoccurred Authorsproposedtheconceptandmethodforevaluatingcoredamagefrequency(CDF)considering fail-urecorrelationatthemultiunitsandsites.Basedontheabovemethod,oneofauthorsdevelopedthe procedureforevaluatingthefailurecorrelationcoefficientandresponsecorrelationcoefficientbetween themulticomponentsunderthestrongseismicmotion.Thesemethodandfailurecorrelationcoefficients wereappliedtotwodifferentBWRunitsandtheirCDFwasevaluatedbyseismicprobabilisticrisk assess-menttechnology.Throughthisquantitativeevaluation,thevalidityofthemethodandfailurecorrelation coefficientwasconfirmed

©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-ND

license(http://creativecommons.org/licenses/by-nc-nd/4.0/)

1 Introduction

TheTohokuearthquake(Mw9.0)occurredat14:46onMarch

11,2011andcausedalargetsunami.Thestrongseismicmotion

wasobservedattheFukushimaDaiichiNuclearPowerPlant

(F1-NPP)withsixunitsandreactorswereshutdownaftercontrolrods

hadbeeninserted.Whilethereactorswereshutdownnormally,

theywerethenoverwhelmedbythetsunamiabout46minafter

theearthquakeoccurred Thevarious componentsofthe water

intake system and emergency diesel generators were flooded

Externalpowersupplywasalsolostduetodamagebystrong

seis-micmotionsandthetsunami.Inthis situation,stationblackout

occurred.Asaconsequence,reactorcoolingsystemfunctionswere

lost,coredamageoccurredandradioactivematerialswerereleased

totheoff-sitearea(JapaneseGovernment,2011)

Regarding PRA methodology relating earthquake and earth-quakeinducedtsunami,implementationstandardsconsideringthe combinationoftheseeventsaretobedeveloped

However,inJapan,AESJatfirstpublishedSeismicPRA imple-mentationstandard(Hiranoetal.,2008;AtomicEnergySocietyof Japan,2009).ThentsunamiPRAimplementationstandard(Atomic EnergySocietyofJapan,2011)waspublished,referringresearch results(Ebisawaetal.,2012a)oftsunamiPRA

Conceptof considering combination of seismicand tsunami eventswasdevelopedbyoneofthispaperauthorsafterFukushima Daiichi (F1-NPP) accident (Ebisawa et al., 2012b) The concept was referred in revised seismic PRA implementation standard (Narumiyaetal.,2014)

And,thecurrentissuesrelatedtoseismicPRAandtsunamiPRA, basedonlessonslearnedfromtheFukushimaDaiichiaccidentare methodologyforevaluatingcoredamagefrequency(CDF)atmulti unitsandsites

http://dx.doi.org/10.1016/j.nucengdes.2015.01.002

Fig 1.Situation of tsunami (by Tokyo Elec Power Co., 2011).

Theconcerningpointsrelatedtotheseissues whichcrossing

overpluralunitsandsitesare;

(1)Correlationofdamagebetweenpluralcomponents

(2)Damageofsharedfacilities(seawatersupplysystem,electric

powersharing,offsitepowersupplier,etc.)

(3)Humanreliability,etc

Intheseissuesrelatedtothemultiunitsandsites,thereare

manystudies(Fleming,1999;Jung,2003;Fleming,2005;Hakata,

2006;Schroer,2012;Kawamura,2014)

Inthesestudies,Fleming(2005)referredabouttheideaofsite

risk metrics instead of thetypical CDF and large early release

frequency(LERF)characterization.Thisideaisnosimplewayto

manipulate thesingle-unit PRAtocapture riskfrom multi-unit

plant.Schroer(2012)describedaboutathoroughclassificationof

multi-unitriskinteractionsanddependencies,alongwiththe

appli-cationofsuchcategoriestotheexistingmethodsformulti-unitCDF

evaluation

Kawamura(2014)pickeduptheissueofhumanreliabilitybased

onexperienceinFukushimaDainiNPPattheTohokuearthquake

andpointeduptheimportanceofclosecollaborationbetween

soft-wareandhardware

Ontheotherhand,authorsproposedtheconceptandmethod

forevaluatingCDFconsideringfailurecorrelationatthemultiunits

andsites(Ebisawaetal.,2012c).Basedontheabovemethod,oneof authorsdevelopedtheprocedureforevaluatingthefailure corre-lationcoefficientandresponsecorrelationcoefficientbetweenthe multicomponentsunderthestrongseismicmotion(Ebisawaetal., 2012c).Theseprocedureandfailurecorrelationcoefficientswere appliedtotwodifferentBWRunitsandtheirCDFwasevaluated Throughthisquantitativeevaluation,thevalidityofthemethod andfailurecorrelationcoefficientwasconfirmed

This paper describes the overview of the F1-NPP accident Thepaperhighlightstheconceptandmethodologyforevaluating CDFconsideringfailurecorrelationatmultiunitsandsites Fur-thermore,thepaperalsoreferstheevaluationresultsthatthese procedureandfailurecorrelationcoefficientswereappliedtotwo differentBWRunits

2 Overview of Fukushima NPP accident and lessons learned from the accident

2.1 OverviewofF1-NPPaccidentatTohokuearthquake/tsunami F1-NPPwasoverwhelmedbyatsunamiabout46minafterthe earthquakeasshowninFig.1.Thetsunamiheightwassohighthat theexpertsestimatedittobemorethan10mfromaphotograph showingtheoverflowstatusoftsunamiseawall(10m)inFig.1 (JapaneseGovernment,2011;Ebisawaetal.,2012c;Kameda,2012)

Fig 3.Procedure of seismic PRA.

Asto the sea water pump facilities for component cooling,

allunits were flooded by thetsunami as shown in Fig 2 The

EmergencyDieselGenerators and switchboardsinstalled inthe

basement floor of the reactor and the turbine buildings were

floodedexceptforUnit6,andtheemergencypowersource

sup-plywaslost(JapaneseGovernment,2011;Ebisawaetal.,2012c;

Kameda,2012)

Ontheotherhand,operatorsucceededtostartRCICand

oper-atecontrollingresidualheatwell,however,RCICstoppedtowork

aftertwo days.CoolingsystemsinFLotherthan RCICwerenot

operatedduetoalossofACpower.Failureofreactorcorecooling

resultedincoredamageinabout5or6h.Temperatureand

pres-sureintheprimarycontainmentvesselroseup,andradioactive

materialswerereleasedthroughsealsintothepowerplantand

thenthesurroundingarea.Consequently,awideareawas

contam-inatedbytheradioactivematerials(JapaneseGovernment,2011;

Ebisawaetal.,2012c;Kameda,2012)

2.2 LessonslearnedfromtheF1-NPPaccident The current issues of seismic engineering based on lessons learnedfromF1-NPPaccidentarereferredasfollows(Ebisawaetal., 2012c);

(i)Occurrenceofgiganticmainearthquakeandtsunami,a com-binationofseismichazardandtsunamihazard,

(ii)Considerationofgiganticaftershockandtriggeredearthquake, (iii)Coredamageoverashortperiodoftimebasedonfunctional failureofsupportsystems(seawatersupply,powersupplyand signalsystems),

(iv)Commoncausefailureofmultistructuresandcomponents, (v)Dependencyamongneighboringunits,

(vi)Externaleventsriskevaluationatmultiunitsandsitesand (vii)Combinedemergencyofbothnaturaldisasterandthenuclear accident

Fig 5. Accident sequence evaluation.

Theseissuesareconnectedasthefollowingperspectivesbased

ontheabove2.1.2damageofF1-NPP

-Weaksiteprotectiondespitetheevidenceonthechanceof

simul-taneoustsunamiandearthquakeiscorrespondedtotheabove(i)

and(ii)

-Flooddamagetosafetyrelatedswitchgearsandemergency

gen-eratingdiesels,whichwerelocatedinthebasementofturbine

buildingsas thekeycauseof StationBlackouttounits1–4is

correspondedtothe(iii)

-Inadequateuseofplant-specificandinternalfloodPRAtoidentify

andimprovesafetyvulnerabilitiesiscorrespondedtothe(iii)

-Inadequate knowledge and awareness about the multi-unit

dependenciesandinteractionsiscorrespondedtothe(iv)–(vi)

-Insufficientaccidentmanagementandplanningonalltheplant

units,aswellasgovernmentagenciesiscorrespondedtothe(vi)

and(vii)

Thecontentsrelatedtotheissue(iii),(v),(vi)and(vii)arefoundin chapters4and5

3 Outline of seismic PRA

3.1 SeismicPSAProcedure(AtomicEnergySocietyofJapan,

2009) TheprocedureofseismicPRAconsistsoffivestepsasshownin Fig.3

-Step1:Collectionofinformationrelatedtoearthquakesandthe settingofaccidentscenarios

-Step2:Seismichazardevaluation

-Step3:Fragilityevaluation

-Step4:Accidentsequenceevaluation

-Step5:Documentation

Intheaboveprocedure,coredamagefrequency(CDF)is evalu-atedbythefollowingEq.(1)

CDF=

0



−dH(∝)

d∝



whereH(˛)isseismichazard,P(˛)iscoredamageprobability,˛is peakgroundaccelerationatbedrock

3.2 Collectionofinformationrelatedtoearthquakeandsettingof accidentscenario(AtomicEnergySocietyofJapan,2009) Thecollectionofinformation relatedtoearthquakesand the settingofaccidentscenariosisshowninFig.3.First,relevant infor-mationshouldbegathered.Then,a“plantwalk-down”basedonthe gatheredinformationshouldbeconducted.Finally,various acci-dentscenariosbasedongatheredrelevantinformationandresults

ofthe“plantwalk-down”shouldbeset

3.3 Seismichazardevaluation(AtomicEnergySocietyofJapan,

2009) The evaluation of the seismic hazard should be considered

“aleatory uncertainty” and “epistemic uncertainty” The former derivesfromphenomenologyand thelatterderivesfromalack

ofrecognitionandinformation.Theepistemicuncertaintiesexist

inthesourcemodelsandpropagationmodelsofseismicmotionas describedabove.Evaluationofepistemicuncertaintyisconducted

byusingalogictree(LT)withthisepistemicuncertaintyasatarget

asshowninFig.4

Fig 7.Concept of evaluation of response correlation.

3.4 Fragilityevaluation(AtomicEnergySocietyofJapan,2009)

ThefragilityF(˛)ofcomponentisevaluatedbythefollowingEq

(2)

F(˛)=

0

fR(˛,xR)

 xR

0 fC(x)dx



wherefR(˛,xR)isrealisticresponseofcomponentrepresented

as logarithmic normal distribution (median MR(˛), logarithmic

standarddeviationˇR)bythefollowingEq.(3).fR(˛,xR)is

capac-ityofcomponentrepresentedaslogarithmicnormaldistribution

(medianMC,logarithmicstandarddeviationˇC)bythefollowing

Eq.(4).˛ispeakgroundaccelerationofseismicmotionatbedrock

fR(˛,xR)=√ 1

2ˇRxexp



−12



ln(x/MR(˛)) ˇR

2

(3)

fC(x)=√ 1

2ˇCxexp



−12



ln (x/MC) ˇC

2

(4)

3.5 Accidentsequenceevaluation(AtomicEnergySocietyof Japan,2009)

In cases of needing to evaluate accident sequences, the sequencesarerepresentedbyusinganeventtree(ET)basedon var-iousaccidentscenarios.Thedevelopedfaulttrees(FTs)thatconsist

ofeacheventtreeareshowninFig.5 Coredamageprobabilities(CDPs)areevaluatedbyusingETs, FTsandby examiningthefragilities ofcomponents.TheCDFis estimatedbymultiplyingtheseismichazardcurveperGalbyCDP curve,whichthencorrespondstoasemicircularshapeareathatis calculatedbytheintegrationofseismicmotionacceleration(Gal) 3.6 CalculationcodeforseismicPRAandtsunamiPRA

JNESdeveloped thecodeforevaluatingseismicandtsunami marginsbasedonseismicPRAandtsunamiPRAtechnologiesand calledasthecalculationcodeSANMARG(JNES,2014a,b).SANMARG hasthefollowingmainfunctions

(1)FunctionofseismicPRAfromtheabove3.2to3.5 (2)FunctionoftsunamiPRAasthesameprocedurefromtheabove 3.2to3.5

Fig 9.Target buildings and components.

(3)Functionconsideringfailurecorrelation

(4)Functionofbothsingleunitandmultiunits

(5)FunctionofbothET/FTanalysisandlargeFTanalysis

4 Concept and methodology regarding failure correlation

of at multi units and sites

4.1 Characteristicsofmultiunitsandsites(Ebisawaetal.,2012c)

Seismicgroundmotioninfluenceontheregionisabout150km

inradiusontheseismichazardofJapan.Therearemultiunitsand

sitesintheregionsuchasWakasaregionwith14unitsandfive

sitesinJapanasshowninFig.6

ThestandardizationoftheplantseismicdesigninJapanhasbeen advanced.However,understrongseismicmotion,itisverylikely thatvariousstructuresandcomponentsatmultiunitsandsites wouldfailatthesametime

4.2 Conceptregardingfailurecorrelationatmultiunitsandsites (Ebisawaetal.,2012c)

JNEShasbeenstudyingfromtheviewpointof“Correlated Seis-micMotionMethodology”,“Correlationofcomponent’responsein thebuildingsatthesamesite”and“multi-unitandsiteevaluation methodology”asshowninFig.7

Fig 11.Floor response spectra and logarithmic standard deviation.

Inaddition,itisnecessarytodeterminethe“SafetyGoal”and

“PerformanceGoal”

ConceptsregardinginfluenceonCDPoffailurecorrelationare

showninFig.8.Failurecorrelationisdefinedasthecorrelation

coefficient␳Fj,FkbetweenperformancefunctionFjofcomponent

jinunitJandthatofFkofcomponentkinunitK.FjandFkare representedasfollows

Fj=ln



fRj fCj



=lnfRj−lnfCj

Fk=ln



fRk fCk



=lnfRk−lnfCk wherefRjandfCjareresponseandcapacityofcomponentj, respec-tively.fRkandfCkarethoseofcomponentk.InFig.8,CDPJandCDPK areCDPofunitJandK,respectively.CDPJisbiggerthanCDPK.CDPJK

isoverlapareaofCDPJandCDPK.CDPisCDPconsideredfailure correlationcoefficientbetweenunitJandK

Therightcaseisdependence(Inclusion)andis1(Complete subordination).CDPK is involved inCDPJ CDP is CDPJ in rela-tionship of union betweenJ and K (ORcase) CDP is CDPK in relationshipofintersectionbetweenJandK(ANDcase).Theleft case isdependence (Exclusion)and is−1(Mutualexclusion) CDPKisnotinvolvedinCDPJ.CDPisCDPJ+CDPKinORcase.CDP

is0inANDcase.Thecentercaseisindependenceand␳is0 (Com-pleteindependence).CDPisCDPJ+CDPK−CDPJKinORcase.CDP

isCDPJKinANDcase

Anexampleoftheaboveleftcaseisrelationshipbetween com-ponentwithseismicisolationandthatwithoutseismicisolation Sinceeachnaturalperiodislargeseparated,response character-isticsoftheircomponentsareverydifferent.Inthecomponents withoutseismicisolation,sincetheirresponsecharacteristicsare roughlysimilar,themostrealisticcaseissubordinationand␳isthe rangebetween0and1.Inthiscase,therearethefollowingthree eventcauses(Fleming,2005)

(1)Eventcausesinitiatingevent(IE)onunitJ:consequentialcore damage(CD)onunitJ

(2)Eventcausesinitiatingevent(IE)onunitK:consequentialCD

onunitJ

Fig 13.Response coefficients between the different damping factors and periods at the different lumped mass in the different buildings.

(3)MultiunitsIEonunitJandunitK:consequentialCDonunitJ

andunitK

4.3 MethodologyforevaluatingCDFconsideringfailure

correlationatmultiunitsandsites

The CDF considering failure correlation at multi units is

expressedbythefollowingequation.Inthisreport,TheCDF

rep-resentstargetunitsastwo-units(unitjandunitk)

CDF=

0

−dH(∝)

where CDF (1/siteyear) is CDF considering failure correlation

betweenunitjandk.H(˛)isseismichazard(1/year).Pjk(˛)isCDP

consideringfailurecorrelationcoefficientbetweenunitjandk.˛

ismaximumaccelerationatbedrock(Gal)

Pjk(˛)isevaluatedbythefollowingequation(AtomicEnergy

SocietyofJapan,2009)

Pjk(˛)=(2)−1(|V|)−1/2

 uj

−∞

 uk

−∞

exp

−12X(˛)·V−1·X(˛) dxj

X(˛) ·V−1·X(˛) = [x j (˛)x k (˛)]



1

=



1



(7)

whereX(˛)ishorizontalmatrixofresponse(Xj(˛))andk(Xk(˛)).

X(˛)isverticalmatrixof(xj(˛)andxk(˛)).ujandukaremaximum

valueofintegralintervalwhichiscalculatedbythemedianand

logarithmicstandarddeviationoftheresponseandcapacity.j,kis

failurecorrelationcoefficientbetweenunitjandk.Viscorrelation

matrixcalculatedbyjk.V−1isreversematrixofV

ThejkobtainsthefollowingEq.(8)(AtomicEnergySocietyof

Japan,2009;Bohnetal.,1983).Intheequation,thefirstitemis

correlationofplantresponse.Theseconditemiscorrelationofplant capacity

j,k= ˇRj·ˇRk

ˇ2

Rj+ˇ2

Sj·

ˇ2

Rk+ˇ2 Sk

·Rj,Rk

ˇ2

Rj+ˇ2

Sj·

ˇ2

Rk+ˇ2 Sk

whereRj,Rkisthecorrelationcoefficientofresponsebetweenunit

j and k ˇRj and ˇRk are the logarithmic standard deviation of responseofunitjandunitk,respectively.Sj,Skisthecorrelation coefficientofcapacitybetweenunitjandunitk.ˇSjandˇSkarethe logarithmicstandarddeviationofcapacity

4.4 Procedureforevaluatingresponsecorrelationcoefficientand itsevaluationexample

4.4.1 Definitionofresponsecorrelation(Ebisawaetal.,2012c) Responsecorrelationisdefinedascorrelationofsympathetic vibrationbehaviordependingonthefrequencycharacteristicsof inputseismicmotionsandthevibrationcharacteristicsof compo-nentsandstructures

4.4.2 Evaluationprocedureofresponsecorrelationcoefficient (Ebisawaetal.,2012c)

Theevaluationprocedureandconditionsofresponsecorrelation coefficient(CC)areasfollows

(1)Frequencyandphasecharacteristicsofinputseismicmotions:

30seismicmotionsaretobesetupinvariousphaseand fre-quencycharacteristics

(2)Level of maximum acceleration of input seismic motions:

300Galforlinearresponseregionand2000Galfornon-linear responseregion

(3)Target buildingsand components: Asshownin Fig.9, reac-torbuildingandheatexchangebuildinginwhichseawater

Table 1

supplysysteminstalled.Majortargetcomponentsareindicated

inFig.9

(4)Buildingfloormodeling.Buildingflooronwhichtarget

com-ponentsandstructuresareinstalledaremodeledas8massin

lumpedmassvibrationmodelasshowninFig.10

(5)Dampingfactorsofcomponentsandstructures:4value;1%,2%,

3%,5%

(6)Evaluationrangesofresponsespectra:5rangesdividedby0.02,

0.05,0.10,0.15,0.50s,asshowninFig.11,foreachdamping

factor

(7)EstimationequationofCC(Ri,Rk):estimationequationofCC

(Ri,Rk)isEq.(9)

Ri,Rk=Cov(Xi(˛),Xk(˛))

whereXj(˛)andXk(˛)arerandomvariablesofresponsesofplantj

andkresponse.jandkarestandarddeviationsofXj(˛)andXk(˛).

Cov(Xj(˛),Xk(˛))iscovarianceofXj(˛)andXk(˛).

4.4.3 Evaluationexamplesofresponsecorrelationcoefficient

(1)ExampleofresponseCCsbetweenthedifferentdampingfactors

andperiodsatthesamelumpedmassinthesameR/B

TheexampleofresponseCCsbetweenthedifferentdamping

factorsandperiodsatthesamelumpedmassinthesamereactor

buildingisillustratedinFig.12.Inthisfigure,thetargetlumped

massnumberistheexampleofNo.2.Therearevariousdamping

factorsandperiods.Theresponsecorrelationcoefficientsareshown

asthecolorvalues.TheCCsinthecaseofthesamelumpedmass,

dampingfactorandperiodare1.0andredvaluesinthediagonal

lines

(2)ExampleofresponseCCsbetweenthedifferentdamping

fac-torsandperiodsatthedifferentlumpedmassinthedifferent

building

TheexampleofresponseCCsbetweenthedifferentdamping

factorsandperiodsatthedifferentlumpedmassinthedifferent

buildingisillustratedinFig.13.TheresponseCCbetweenthe

dif-ferentdampingfactorsandperiodsatthesamebuildingareorange

colorareabout0.7.Ontheotherhand,thoseatthedifferent

build-ingshowsgreencollarareabout0.3

(3)Resultsofresponsecorrelationcoefficient

Table1summarizestheCCfocusedonthedifferenceoffloor

levelsandnaturalperiods.Whentwomasspointsareinstalled

onthesamelevelandhavethesamenaturalperiod,CCsare1.0 Whentwomasspointsareinstalledonthedifferentleveland havethedifferentnaturalperiod,CCsare0.5–0.6

Asforthechangeofthecorrelationcoefficient,afew ten-dencies wereseen in thesame period thoughthedamping changed

4.5 ProcedureforevaluatingCDFconsideringfailurecorrelation

atmultiunitsandsites TheprocedureforevaluatingCDFatmultiunitsandsites con-sistsoftwosteps.FirststepistoevaluatetheCDFatasingleunit consideringfailurecorrelation.Secondstepistoevaluateatmulti unitsandsitesbasedonthesingleunitevaluationresult

(1)Singleunit TheproceduretoestimatetheCDFofasingleunitconsidering failurecorrelationisasfollows

(1) In thecase of complete independence, identifythe sig-nificant components which influence the CDF in F-V importanceanalysis

(2) Outofalltheidentifiedcomponents,select3or4

(3) Identifyresponsecorrelationcoefficient

(4) UsethemtocarryoutCDFevaluationconsideringthefailure correlation

Intheabove(2),criterionofcut-offvalueforselecting3

or4componentsisoveraboutF-Vvalue0.2

(2)Twoormoreunits TheproceduretoestimatetheCDFofamulti-unitsite consid-eringfailurecorrelationisasfollows

(1) Accordingtothefailurecorrelationtreatmenttargetingtwo units,treatmentofmorethantwounitsissimilartothatof twounits

Table 2

Fig 15.Example of fragility evaluation of emergency diesel generator.

Fig 16.Example of fragility evaluation of RCW piping supports.

atmultiunitsandsites TheprocedureforevaluatingCDFatmultiunitsandsites con-sistsoftwosteps.FirststepistoevaluatetheCDFatasingleunit consideringfailurecorrelation.Secondstepistoevaluateatmulti...

(2)Twoormoreunits TheproceduretoestimatetheCDFofamulti-unitsite consid-eringfailurecorrelationisasfollows

(1) Accordingtothefailurecorrelationtreatmenttargetingtwo units, treatmentofmorethantwounitsissimilartothatof... consideringfailurecorrelation.Secondstepistoevaluateatmulti unitsandsitesbasedonthesingleunitevaluationresult

(1)Singleunit TheproceduretoestimatetheCDFofasingleunitconsidering failurecorrelationisasfollows