Chapter 4 Earthquakes - OCDI 一般財団法人国際 …ocdi.or.jp/tec_st/tec_pdf/tech_235_270.pdfPART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 4 EARTHQUAKES – 237

PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 4 EARTHQUAKES

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Chapter 4 Earthquakes

Public NoticeEarthquake Ground Motions

Article 16 Level1earthquakegroundmotionsshallbeappropriatelysetintermsoftheprobabilistictimehistorywaveprofilesbasedonactualmeasurementsofearthquakegroundmotionsandbytakingintoconsiderationthehypocentercharacteristics,thepropagationpathcharacteristics,andthesitecharacteristics.2Level2earthquakegroundmotionsshallbeappropriatelysetintermsofthetimehistorywaveprofilesbased on actualmeasurements of the earthquake groundmotions, scenario parameters of earthquakehypocenters,and/orothers,andbytakingintoconsiderationthehypocentercharacteristics,thepropagationpathcharacteristics,andthesitecharacteristics.

[Technical Notes]1 Ground Motion1.1 GeneralThethreeimportantfactorsthataffectgroundmotionaretheeffectoftheruptureprocessonthefaultsurface,namelysourceeffects, theeffectof thepropagationpathfromthesource to theseismicbedrock,namelypropagationpatheffects,andtheeffectofthesedimentsontheseismicbedrock,namelysiteeffects(seeFig. 1.1.1).HeretheseismicbedrockisstratagenerallymadeofgranitehavinganSwavevelocityof3km/sormore. TheaccelerationFourierspectrumO(f )ofthegroundmotionmeasuredonthegroundsurfaceisgiveningeneralbytheproductofthesourceeffectsS(f ),thepropagationpatheffectsP(f ),andthesiteeffectsG(f ).

(1.1.1)

Herefisthefrequency.Also,thegroupdelaytimetgrO( f )measuredonthegroundsurfaceisgivenbythesumofthesourceeffectstgrS( f ),thepropagationpatheffectstgrP( f ),andthesiteeffectstgrG( f ).1)

(1.1.2)

Herethegroupdelaytimeis thederivativeof theFourierphasewithrespect totheangularfrequencyω =2π f,havingtheunitsoftime,andisapproximatelythearrivaltimeofthefrequencycomponentf.Inthiscasethearrivaltimeisthetimemeasuredfromthestartofthetimehistoryusedintheanalysis.Thesuperscriptsinequation(1.1.2)havethefollowingmeanings:Oistheactualmeasuredvalueonsite,Sisthesourceeffect,Pisthepropagationpatheffect,andGisthesiteeffect.TheexistenceofsedimentsaffectboththeFourieramplitudeandphaseofthegroundmotionasshownabove,butinthispartthetermusedfortheeffectontheFourieramplitude,inotherwordsG( f ),is“siteamplificationfactors”,andinthispartthetermusedfortheeffectonthegroundmotionoverallisthe“siteeffects”.

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TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN

Sourceeffects

Propagationpath effects

Locak soildepositLocak soildepositLocak soildeposit

Firm ground

Seismic bedrock

Amplificationof body wave

SiteGround surfaceTop of firm ground

SedimenntsVs>300m/s

Site characteristics

Generation andpropagation ofsurface waves

Vs>3000m/s

Fig. 1.1.1 Source Effects, Propagation Path Effects, and Site Effects

1.1.1 Source Effects

(1)ω-2Model(OmegaSquaredModel)Agenerallyacceptedmodelforthesourceeffectsofgroundmotionsistheω-2model.2)Intheω-2model,theaccelerationFourieramplitudespectrumoftheseismicwaveradiatingfromthesource,theaccelerationsourcespectrum,isexpressedbythefollowingequation

(1.1.3)

where M0 :seismicmoment fc :cornerfrequency ρ :densityofthemediumoftheseismicbedrock Vs :Swavevelocityintheseismicbedrock C :constant(seeequation(1.3.5)).

Fig. 1.1.2illustratessourcespectraofthedisplacement,velocity,andaccelerationinaccordancewiththeω-2model.Ascanbeunderstoodfromequation (1.1.3)andFig. 1.1.2,theaccelerationsourcespectrumdependingontheω-2modelisproportionaltothesquareofthefrequencyforfrequencieslowerthanfc,andisflatforfrequencieshigherthanfc.Thiscornerfrequencyfcisthefrequencycorrespondingtothebendinthesourcespectrum.TheseismicmomentM0isaphysicalmeasuretoexpressthesizeoftheearthquake,andisdefinedbythefollowingequation.3)

(1.1.4)

where µ :shearmodulusoftherockinthesourceregion A :areaofthesourcefault D0 :averagevalueofthefinalofsliponthefaultsurface

Onaverage thecorner frequency fc is inverselyproportional toM0 to thepowerof1/3. Therefore in theω-2model,theFourieramplitudespectrumoftheseismicwaveradiatingfromthesourceisproportionaltotheseismicmomentonthelongperiodside,andisproportionaltotheseismicmomenttothepowerof1/3ontheshortperiodside.EverytimetheMagnitudeisincreasedby1,M0increasesbyafactorofabout30,sothelongperiodcomponentofthegroundmotionradiatingfromthesource,thatisproportionaltoM0,becomesabout30timesandtheshortperiodcomponentthatisproportionaltoM0tothepowerof1/3,becomesabout3times.Inotherwords,asthemagnitudeoftheearthquakeincreases,thelongperiodcomponentincreasesmostofall.Whenanalyzinglongperiodstructures,suchashighrisebuildings,longspanbridges,oiltanks,baseisolatedstructures,etc.that


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areeasilyaffectedbythelongperiodcomponentofgroundmotions,itisparticularlynecessarytopayattentiontolargeMagnitudeearthquakes.

flat on the lowfrequency side.

Large M

Large M

Large M

Small M

Small M Small MSmall M

↑

↑

↑↑

↑

↑←

↓

↓

log

(dis

plac

emen

t Fou

rier s

pect

rum

)

log (frequency) log (frequency) log (frequency)

log

(vel

ocity

Fou

rier s

pect

rum

)

log

(acc

eler

atio

n Fo

urie

r spe

ctru

m)

On the high frequency side, it reduces inversely proportional to the square of the frequency. On log-log axes, a straight line with gradient -2.

The maximum value of the velocity source spectrum is near the corner frequency

On the low frequency side, it increases proportional to the frequency, with log-log axes, straight line with gradient 1.

On the low frequency side, it increases proportional to the square of the frequency, on log-log axes, a straight line with gradient2

On high frequency side, it reduces inversely proportional to frequency, with log-log axes, straight line with gradient -1.

Corner frequency, it depends on the magnitude of the earthquake. The difference of source spectrum with M is more prominent on the low frequency side.

Corner frequency, it depends on the magnitude of the earthquake. The difference of source spectrum with M is more prominent on the low frequency side.

flat on high frequency side.

Fig. 1.1.2 Displacement, Velocity, and Acceleration Source Spectra Depending on the ω-2 Model

(2)DirectivityThesourceofalargeearthquakeisnotasinglepoint,butisafaultsurfacehavingadefiniteextentofspread.Rupturestartsatapointonthefaultsurface,andspreadstothesurroundings.Atthistime,theSwavevelocityinthesourceregionandtherupturepropagationvelocityareaboutthesame,soataharborinthedirectionofpropagationoftherupture,theenergyoftheseismicwavessuccessivelyreleasedfromthefaultsurfacearriveataboutthesametime,sotheamplitudebecomeslarge.Thisphenomenonisreferredtoasthedirectivityofthegroundmotions. Associatedwiththis, it isknownthat in theareaswheretheamplitudeis largeasaresultof theeffectofdirectivity,ithasbeenreportedthattheoscillationsinthedirectionnormaltothedirectionofstrikeofthefaulttendtobestrong.5),6),7),8)

(3)AsperitiesItisknownthatthesliponthefaultsurfaceofalargeearthquakeisnotuniform,butnon-uniform.Theareaonthefaultsurfacewheretheslipisparticularlylargeisreferredtoasanasperity.Modelsthatexpressthenon-uniformdistributionofthefinalsliponthefaultsurfaceincludethevariableslipmodel,whichexpressesoffinalslipbyacontinuousfunction,andthecharacterizedsourcemodelwhicharrangesseveralrectangularasperitiesonthefaultsurface,andwithintheseasperitiestheamountofslipisuniform.

1.1.2 Propagation Path Effects

Theeffectofpropagationpathontheamplitudeofgroundmotionisfrequentlygivenbythecombinationofattenuation(1/r)asthewavespreadsfromthesourceinasphericalform,andinelasticdamping.Thefollowingexpressesthisintheformofanequation

(1.1.5)

where r :distancefromthesource Q :Qvalueonthepropagationpath.

TheQvalueisaquantityexpressingthemagnitudeofinelasticdampingcausedbyscatteringandconversiontoheatoftheseismicwaveonthepropagationpath.ThelargerthevalueofQ, thesmallertheinelasticdampingonthepropagationpath.ItisnecessarytobeawareofsituationswheregeometricattenuationintheformabovedoesnotapplyduetotheeffectofLgwaves,atypeofseismicwavepropagatedbyreflectionwithintheearth’scrustatadistancefromthesource.12)

1.1.3 Site Effects

Thesedimentsnearthegroundsurface,see Fig. 1.1.1,havealargeeffectontheamplitudeoftheseismicwaves,periodcharacteristics,duration,etc.Theeffectofthesedimentsisreferredtoasthesiteeffects.

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1.1.4 Nonlinear Behavior of Local Soil Deposit

Normallythepropertiesoflocalsoildepositvarywiththelevelofappliedstrain,andwhenstronggroundmotionsareacting,theshearmodulusreduces,andthedampingcoefficientincreases.Thisphenomenonisreferredtoasthenonlinearbehaviorofthelocalsoildeposit.

1.2 Level 1 Earthquake Ground Motions used in Performance Verification of FacilitiesTheLevel1earthquakegroundmotionisnormallysetusingaprobabilisticseismichazardanalysistakingintoconsiderationthesourceeffects,thepropagationpatheffects,andthesiteamplificationfactorsbetweentheseismicbedrockandthetopoffirmground.Thesetgroundmotionisawavewhoseamplitudeisdoublethatoftheseismicwaveincidentonthetopofthefirmgroundfrombelow(2Ewave).14)Intheprobabilisticseismichazardanalysis,ifaprobabilisticGreenfunctionmethodisusedtoevaluatethegroundmotionforeachexpectedearthquake,itisdesirablethatthesiteamplificationfactorsestimatedfromearthquakeobservationrecordsobtainedattheharbor,orseismicobservationrecordsobtainedfromK-NET,15)KiK-net,16)orotherseismicnetworks,neartheharbor,within2kmoftheharbor,areusedasthesiteamplificationfactors,afterconfirmingbymicrotremormeasurementsthatthegroundmotioncharacteristicsattheobservationpointdonotdiffergreatlyfromthoseatthelocationofthefacilities.Ifsuchsiteamplificationfactorscannotbeused,itisdesirablethatshorttermseismicobservationsaremadeattheharbor,seeANNEX 3 Evaluation of Site Amplification Factors (1),andthesiteamplificationfactorsareevaluatedusingthemethodstatedinANNEX 3 Evaluation of Site Amplification Factors (3).Iftheseseismicobservationscannotbemadeduetotheimminentconstructionperiod,etc.,thesiteamplificationfactorsoftheharbormaybeestimatedfromthesiteamplificationfactorsofnearbyobservationpoints,usingempiricalrelationships.However,itisnecessarytobeawarethattheevaluationaccuracyofthegroundmotioninthiscaseisgreatlyreducedcomparedwithestimatesbasedontheseismicobservations.

1.3 Level 2 Earthquake Ground Motions used in Performance Verification of Facilities1.3.1 Outline

TheLevel2earthquakegroundmotionismainlysettodeterminewhethertheseismicresistanceisatarationallevelfromtheviewpointofsafetyof thepublic,andis themustdamaginggroundmotionamongtheestimatedgroundmotionsatthesitefromscenarioearthquakes.TheLevel2earthquakegroundmotionisnormallysetbyastrongmotionevaluationtakingintoconsiderationthesourceeffects,thepropagationpatheffects,andthesiteamplificationfactorsbetweenseismicbedrockandtopoffirmground.Theterm“safetyofthepublic”usedhereisaconceptthatincludesmaintenanceof the functionof facilities thatarenecessary foremergencymeasuresafteranearthquake,andisabroaderconceptthan“safety”,whichisaconceptincontrastto“usability”or“reparability”.Thesetgroundmotionisasocalled2Ewavehavingdoubletheamplitudeoftheseismicwaveincidentonthetopofthefirmgroundfrom below.14) If probabilisticGreen functions are used in the strongmotion simulation, it is desirable that siteamplificationfactorsestimatedfromearthquakeobservationrecordsobtainedattheharbor,orearthquakeobservationrecordsobtainedfromobservationpointsneartheharbor,within2kmoftheharbor,suchasK-NET,15)KiK-net,16)orothernetworks,areusedasthesiteamplificationfactors,afterconfirmingusingmicrotremormeasurementsthatthegroundmotioncharacteristicsattheobservationpointsdonotdiffergreatlyfromthoseatthefacilitylocation.Ifthesesiteamplificationfactorscannotbeused,itisdesirablethatshorttermseismicobservation,seeANNEX 3 Evaluation of Site Amplification Factors (1),becarriedoutattheharbor,andthesiteamplificationfactorsareevaluatedbythemethoddescribedinANNEX 3 Evaluation of Site Amplification Factors (3). Ifseismicobservationscannotbecarriedoutduetotheimminentstartofconstruction,forexample,thesiteamplificationfactorsattheharbormaybeestimatedfromthesiteamplificationfactorsatnearbyobservationpoints,usingempiricalrelationships.However,inthiscaseitisnecessarytobeawarethattheevaluationaccuracyofthegroundmotionsisgreatlyreducedcomparedwith estimates based on the seismic observations. The procedure for calculating theLevel 2 earthquake groundmotionisshowninFig. 1.3.1. Theevaluationresultsof thegroundmotionfromthemethoddescribedbelowandtheevaluationresultsof thegroundmotionbyanotherorganizationassumingasimilarscenarioearthquakemaynotbethesame,butthisismainlycausedbydifferencesinthemethodofevaluatingthesiteeffects.Thefollowingmethodmaybeusedforcalculatingthegroundmotionforseismicperformanceevaluationofharborfacilities.


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If records of earthquake motion at the harbor have been obtained and site amplification factor has been evaluated

I f r eco rds o f ea r thquake motion at the harbor have been obtained but site amplification has not been evaluated

If records of earthquake motion at the harbor have not been obtained

Evaluation of Site amplification factor(1.2.2 (3))

Site amplification factor

Select scenario earthquakes(1.3.2)

Set source parameters(1.3.3)

Calculate strong ground motion(1.3.5)

Level 2 seismic motion

Seismic observatios from 1 to several years(1.2.2 (1))

If seismic observations cannot be carried outdue to imminent construction period etc.(1.2.2 (4))

Fig. 1.3.1 Procedure for Calculating the Level 2 Earthquake Ground Motion

1.3.2 Scenario Earthquakes for the Level 2 Ground Motion

Itisnecessarytoselectthescenarioearthquakeforthelevel2groundmotioncomprehensivelytakingintoconsiderationinformationonpastearthquakesandinformationonactivefaults.Inparticular,atthetimeofperformanceverification,theactivefaultsshouldbebasedonthelatestsurveyresults.Regardingpastearthquakes,references53)and54)arecomprehensive documents. Reference 35) is a document that summarizes the fault parameters for themain pastearthquakes. References33) and34) are comprehensivedocuments regardingactive faults. In addition to these,afterthe1995Hyogo-kenNambuEarthquake,activefaultsweresurveyed,andtheresultsweremadepublicbytheHeadquartersforEarthquakeResearchPromotionandlocalgovernments.Byreferringtotheabovedocuments,thefollowingshouldbeconsidered:

(a) Therecurrenceofearthquakesthathavecausedsignificantdamageinthepast

(b)Earthquakesduetotheactivityofactivefaults

(c) Otherearthquakesforwhichthereisaconcernoveroccurrencefromaseismologicalorgeologicalviewpoint

(d)Earthquakespostulatedbythenationalorganizationssuchas theCentralDisasterPreventionCouncilandtheHeadquartersforEarthquakeResearchPromotion

(e) Earthquakespostulatedinthelocaldisasterplans

(f)M6.5earthquakes55)Theremaybesomeduplicationwithin(a)to(f).Fromthese,scenarioearthquakeforthelevel2groundmotionshouldbeselectedas theearthquakecapableof inducing themostdamaginggroundmotionat theharbor. Itcanbedifficulttodecidewhichofthepostulatedearthquakesin(a)to(f)abovecaninducethemostdamaginggroundmotionattheharbor.Forexample,decidingwhichofanearbycomparativelysmallearthquakeoradistantcomparatively largeearthquakecan induce themostdamaginggroundmotionat theharbor isnotnecessarilyeasy.Also,groundmotionshavevariousaspects,suchasamplitude,frequencycharacteristics,durationetc.,sodeterminingwhichearthquakehasthelargesteffectonafacilityissometimesonlyknownafterfirstevaluatingthegroundmotions,andthencarryingoutseismicresponseanalysis.Therefore,itisnotnecessaryatthisstagetomakegreateffortstoshortlistthescenarioearthquakestoasingleearthquake,butseveralcandidateearthquakesshouldbeselected.Inthiscase,thegroundmotionthathasthegreatesteffectonthefacilitybasedontheresults

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oftheseismicresponseanalysiswillultimatelybecomethelevel2earthquake.Whenthenumberofearthquakestobeconsideredislarge,onemethodistocarryoutinadvanceasimpleevaluationofthegroundmotionsusingattenuationequations,andeliminateearthquakeswhoseeffectisclearlysmall.Fortheearthquakespostulatedin(d),refertothefollowinghomepages:CentralDisasterPreventionCouncil:http://www.bousai.go.jp/jishin/chubou/index.html HeadquartersforEarthquakeResearchPromotion:http://www.jishin.go.jp/main/p_hyoka02.htm ThereasonsforconsideringM6.5rightbelowearthquakesareasfollows.55)Anactivefaultisthetraceofanearthquakefault,referredtoasasurfacefaulttrace,thathasappearedinthegroundsurfaceduetoalargeearthquakeinthepast.However,inthecaseofcomparativelysmallscaleearthquakes,surfacefaulttracedonotappear,soeveninlocationswherethereisnoactivefault,thereisthepossibilityofoccurrenceofacomparativelysmallscaleearthquake.Takemuraetal.56)investigatedtherelationshipbetweenthescaleofanearthquakeandtheprobabilityofappearanceofsurfacefaulttrace,andtherelationshipbetweenthescaleofanearthquakeandtheextentofdamage,32)seeFig. 1.3.2,forearthquakeswithintheearth’scrustofM>5.8occurringinJapanbetween1885and1995.Accordingtotheirresults,earthquakesofM<6.5haveaverylowprobabilityofappearanceofsurfacefault trace,butearthquakesofM≥6.8haveaprobabilityofappearanceofsurfacefault traceofnearly100%.Also,focusingonthefactthatearthquakesofM=6.6and6.7areveryfew,itisinferredthatthisisbecausetheearthquakefaultpenetratestothegroundsurface.ThereforeitisconsideredappropriatethatthescaleoftheearthquakepostulatedatlocationswherethereisnoactivefaultshouldbeaboutM6.5.

Fig. 1.3.2 Relationship between Scale of Earthquakes and Probability of Appearance of Surface Faults 56)

Amongharbor facilities, therearesomeforwhich it is required thata tsunamibeexpectedfollowing thegroundmotion,andtheperformancein thesecircumstances isprescribed. In thiscase, thegroundmotiontobecombinedwith the tsunamidoesnotnecessarilyhave tobe themostdamaginggroundmotion, i.e.,Level2earthquakegroundmotion,expectedfortheharbor.Forexample,atacertainharbor,bothanearthquakeatanactive faulton landandansubduction-zoneearthquakemaybeexpected,and itmaybeexpected that theearthquakeattheactivefaultonlandwillbringthemostdamagingseismicmotion.Inthiscase,atsunamidoesnotaccompanytheearthquakeat theactivefaultonland,soit isnotrationaltoexpectthat immediatelyafterthegroundmotionoftheearthquakeattheactivefaultonland,atsunamiwillattach,andthiswouldresultinexcessiveinvestment.Therefore,theremaybesituationswhereitisnecessarytoevaluatethegroundmotionsthatprecedeatsunami,apartfromthelevel2earthquakemotion.Inthiscasethemethodofevaluatingthegroundmotionsmaybetosimplychangetheearthquakefromthatforthelevel2earthquakemotiontotheearthquakethatisthecauseofthetsunami,andapplythefollowingevaluationmethodasitis.

1.3.3 Setting the Source Parameters

ThesourceparametersnecessaryforevaluatingtheLevel2earthquakegroundmotionincludemacroscopichypocenterparameters,suchaspositionofthebasepoint,strike,dip,length,width,areaandseismicmoment,microscopicsourceparameters,suchasnumberofasperities,areaofasperities,seismicmomentofasperitiesandrisetime,etc.,andotherparameters, such as rupture startingpoint, rupturevelocity and rupturepropagation type. Themeaningof theseparameters isshowninFig. 1.3.3. Thesourceparametersmaybeset inaccordancewith thestandardmethodofsettingtheparametersshownbelow,ortheymaybesetbycarryingoutaseparatedetailedsurvey.


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Final slip D0

slip

Rise time Tr Time

Dip δ

Ground surface

Strike North

Final slip D0

Fault surface

Rake angle λ Width W

Up

Length L

(a) Explanation of fault parameters (1) (b) Explanation of fault parameters (2)

φ

Fig. 1.3.3 Meaning of Source Parameters

(1) WhentheRecurrenceofanEarthquakethathasCausedSignificantDamageinthePastisExpectedIftherecurrenceofanearthquakethathascausedsignificantdamageinthepastispostulated,suchastheTonankaiandNankaiearthquakes,itisdesirablethatdocumentsconcerningtheearthquakesthathaveactuallyoccurredinthepast,referredtoaspastevents,beusedasmuchaspossible. Regardingthemacroscopicsourceparameters,ifparametersofthepasteventsareknown,thoseparametersmaybeused. Themacroscopic sourceparametersofmanypast earthquakesarecontained inReference35).Whenonlyoneof the seismicmomentM0 and the fault areaS isgivenand theothermustbeestimated, thefollowing equation 57), 58)maybeused. By combining equation (1.3.1) andEsherby’s equation for a circularcrack,59)theaveragestressdropfortheentirefaultsurfaceis3MPa.

(1.3.1)

Regardingthemicroscopicsourceparameterssuchasasperitylocation,etc.,anappropriateapproachshouldbetakendependingonthevolumeofdataforthepastevents.Firstly,ifthemicroscopicsourceparametersforthepasteventshavebeeninvestigatedwellusingwaveprofiledata,etc.,thoseparametersmaybeused.Forexample,thisisthecasewhenconsideringtherecurrenceofthe1923KantoEarthquake,60)recurrenceofthe1968TokachiOkiEarthquake,44)orrecurrenceofthe1978MiyagiKenOkiEarthquake.44)Next,ifwaveprofiledatafromthepasteventisnotavailable,andiftheearthquakeintensitydistributionisknownfromhistoricaldocuments,microscopicsourceparameterssettobeconsistentwiththisearthquakeintensityinformationmaybeused.Forexample,thisisthecasewhenconsideringtherecurrenceoftheHoeiEarthquake,theAnseiTokaiEarthquake,ortheAnseiNankaiEarthquake.Asanexampleofthemicroscopicsourceparametersdefinedsoastobecompatiblewiththeearthquakeintensitydistribution,therearethemicroscopicsourceparametersfortheexpectedTonankaiandNankaiearthquakestheCentralDisasterPreventionCouncil,seeFig. 1.3.4. Theotherparameterssuchasrupturestartpointetc.aredealtwithinthesamewayasthemicroscopicsourceparameters.Inthecaseofanearthquakeoccurringatanactivefault, theaverageintervalbetweenactivities is long,soinalmostallcasesitisnotpossibletorefertothepastevents.However,asanexception,ifexpectingarecurrenceofthe1995Hyogo-kenNambuEarthquakeorsimilar,theaboveconsiderationmaybeused,withoutusing(2) When an Earthquake is Expected to Occur at an Active Fault.

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Tonankai earthquake

Nankai earthquake

Fig. 1.3.4 Source Model of the Tonankai and Nankai Earthquakes Expected by the Central Disaster Prevention Council 61)

(2) WhenanEarthquakeisExpectedtoOccuratanActiveFaultThemacroscopic source parameters for an earthquake occurring at an active faultmay be set in accordancewiththefollowingconcepts. First, thestrike anddipangleδofthefaultareobtainedbasedontheresultsof geological, topographical, and geographical surveys. Also, the total length of fault segmentswith a highpossibilityofsimultaneousoccurrenceissetasthefaultlengthL.Ifthedipangleδisunknown,incaseofastrikeslipfault,itmaybeassumed90°,incaseofahighanglereversefault,itmaybeassumed60°,incaseofalowanglereversefault,itmaybeassumed30°,andincaseofareversefaultthatisneitherhighanglenorlowangle,itmaybeassumed45°.ThefaultwidthWofanearthquakeoccurringatanactivefaultislimitedbythethicknessHoftheseismogeniclayerintheupperearth’scrust,sowhenL<H/sinδ,W=L,andwhenL>H/sinδ,W=H/sinδmaybeassumed.58),62)WhenthethicknessHoftheseismogeniclayerisunknown,20kmmaybeassumed.ThefaultareaSisobtainedfromtheestimatedfaultlengthLandfaultwidthW.TheseismicmomentM0maybeobtainedfromthefaultareaSusingthefollowingempiricalequation.63)

(1.3.2)

Themicroscopicsourceparametersforanearthquakeoccurringatanactivefaultmaybedefinedasfollows.First,thetotalareaofasperitiesasapercentageofthetotalfaultareaisassumedtobe22%.58),62),63),64),65)Thenumberofasperitiesisassumedtobe1or2.58)IfthemagnitudeofthepostulatedearthquakeisM7orlarger,thenumberofasperitiesisassumedtobe2.Whenthenumberofasperitiesisassumedtobe2,thelargeroneisassumedtobe16%ofthetotalfaultarea,andthesmalleroneisassumedtobe6%.58),64)Theshapeoftheasperitiesaretakentoberectangularasmuchaspossible.58),63)Theseismicmomentoftheasperityisassumedtobe44%ofthetotalseismicmoment.58),63),64)Whentherearetwoasperities,theseismicmomentofthelargeroneisassumedtobe36%ofthetotalseismicmoment,andtheseismicmomentofthesmalleroneisassumedtobe8%.58),64)TherisetimeτoftheasperityisdefinedfromthewidthWaoftheasperityandtherupturevelocityVrusingthefollowingequation.58)

(1.3.3)

Thelayoutof theasperity isarrangedinrelationshipto therupturestrongpoint,whichisdiscussedlater,sothattheruptureofoneoftheasperitiespropagatestowardstheharbor.Thisisbecauseduetotheeffectofdirectivity,aparticularlystronggroundmotionisgeneratedinthedirectionofpropagationoftheruptureoftheasperity,andastronggroundmotiongeneratedinthiswayresultedindevastatingdamageinthe1995Hyogo-kenNambuEarthquake.4)Specifically,theasperityisarrangedasshowninFig. 1.3.5.Thedepthofthecenteroftheasperityistakentobe10km. Oftheotherparameters,therupturestartingpointislocatedasshowninFig. 1.3.5inrelationtothelocationoftheasperity.Therupturevelocityisassumedtobe80%oftheSwavevelocityinthesourceregion.58)Theruptureisassumedtopropagateradially.


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HarborHarbor Fault line on active fault mapGround surface

Top surface of seismogenic layer(depth of about 3-4km)

Asperity width W

Asperity length LRupture starting point

Diagram viewed from this directionCross-sectiondiagram

Bottom surface of seismogenic layer (depth of about 20km)

Depth of center ofasperity 10km

Asperity

↓δ

Fig. 1.3.5 Arrangement of Asperity and Rupture Starting Point

(3) WhenM6.5EarthquakeisExpectedtoOccurjustBeneaththeSiteTheseismicmomentM0canbecalculatedfromtheMagnitudeusingthefollowingequation.66)

(1.3.4)

Therefore,thefaultareaSmaybeobtainedfromequation (1.3.2).Thedipangleδ maybeassumedtobe90°.Whatfollowsisthesameasin(2) When an Earthquake is Expected to Occur at an Active Fault.Thenumberofasperitiesistakentobe1.

1.3.4 Evaluation of Site Amplification Factors

ThesiteamplificationfactorscanbeevaluatedinaccordancewithANNEX 4 Analysis of Seismic MotionfortheLevel1earthquakegroundmotions.

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2 Seismic Action2.1 Modeling and Seismic Action of the Ground - Structure SystemThegroundmotionsdescribedinSection 1 Ground Motionaregroundmotionsthatareindependentofthefacilities,anddonotdependonthetypeofthefacilitiesoranalysismethod.Thisisreferredtoasa“referencegroundmotion”inISO23469.1)Incontrast,theseismicaction,thetermusedinISO23469,necessaryforperformanceverificationofportfacilitiesisdefineddifferentlydependingonthefacilityoranalysismethodasstatedbelow.Whensettingtheseismicactionforseismicperformanceverification,firstlythegroundmotionisevaluatedbySection 1 Ground Motionforthecasewherethefacilitiesdonotexist,andnexttheseismicactionisevaluatedcorrespondingtothetypeoffacilitiesoranalysismethod. Normally, the analysismethods used in seismic performance verification of port facilities can be classified asequivalentstaticanalysisanddynamicanalysis.Also,theanalysismethodscanbeclassifiedassimpleanalysisordetailed analysis depending onwhether ground-structure interaction is taken into consideration. As a result theanalysismethodsusedinseismicperformanceverificationcanbeclassifiedinto2×2=4categories.Here,simplifiedanalysisfocusesonapartoftheground–structuresystem,andanalyzesitsbehavior,andtheseismicactionisdefinedastheeffectonthepartunderconsiderationfromoutsideitsboundary.Ontheotherhand,indetailedanalysis,thetotalbehavioroftheground–structuresystem,forexamplethegraypartinFig. 2.1.1(b),isanalyzed,andinthiscasetheseismicactionisdefinedasthegroundmotioninputtothebottomendoftheanalysisdomain.Forexample,inasimplifiedequivalentstaticanalysis,namelyseismiccoefficientmethod,ofacaissontypequaywall,asindicatedingrayinFig. 2.1.1(a),thepartofthewholeonwhichthefocusisappliedisthewall,andanalysisofitsbehavioriscarriedout. Inthiscasetheseismicactionistheinertiaforces,earthpressureandhydrodynamicpressureduringtheearthquakeactingonthewallfromtheexternaldomain.Inadetaileddynamicanalysis,mainlyeffectivestressanalysis,ofthecaissontypequaywall,asindicatedingrayinFig. 2.1.1(b),thefocusisontheentiresystemcomprisingthecaisson,thebackfill,theseawater,andthefoundationgroundsbelowthecaisson,anditsbehaviorisanalyzed.Inthiscasetheseismicactionisthegroundmotioninputtothebottomendoftheanalysisdomain.Indetaileddynamicanalysis,theearthpressureandhydrodynamicpressureduringtheearthquakeactingonthecaissonwallareproducedastheresponseanalysisresults,andarenotsetasanaction. Thetypesofanalysismethodusedforseismicperformanceverificationofportfacilitiesandthemethodofdefiningtheseismicactioninaccordancewiththeanalysismethodarediscussedbelow.

Film groundSeismic motion

Sea bottom

SeaCaisson

(b) Detailed dynamic analysis (effective stress analysis)

(a) Simplified Equivalent static analysis (seismic coefficient method)

Film ground

Sea bottom

SeaCaisson

Earth pressureInertia forceHydrodynamic pressure

Fig. 2.1.1 Seismic Action in the Seismic Coefficient Method and Effective Stress Analysis (Example of a Caisson Type Quaywall)

2.2 Seismic Action in the Seismic Coefficient Method 2)

AsshowninFig. 2.2.1,thismethodisconsideredwhenarigidobjectisonarigidground.Assumethemassoftheobjectism,anditsweightisW.Ifthegroundmovestotherightwithanaccelerationα,aninertiaforceαmactsontheobjecttotheleft.Atthistimeafrictionforceofαmmustactonthebottomsurfaceoftheobject,inorderthatitwillnotslide.Ifthestaticfrictioncoefficientonthebottomsurfaceisnotsufficientlylarge,theobjectwillslide,andinmostcases,dependingonthechangesoftheaccelerationforceafterwards,aresidualdisplacementwilloccur.Atthistime,whencheckingwhetherslidingwilloccur,itispossibletoapplyastaticforceαmtotheobject.Thisisthefundamentalideaoftheseismiccoefficientmethod. Thefollowingequationshowsthemagnitudeoftheinertiaforceactingintheseismiccoefficientmethod.

(2.2.1)

Ifkhiswritteninsteadofα/g,thefollowingequationisobtained.

(2.2.2)


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Inotherwords,theinertiaforceduetothegroundmotionsisobtainedbymultiplyingtheweightofthefacilitybythecoefficientkh. Thiskhisreferredtoastheseismiccoefficient.Theseismiccoefficientsetforperformanceverificationisreferredtoastheseismiccoefficientforverification.

Fig. 2.2.1 Concept of the Seismic Coefficient Method

Intheclassificationofanalysismethodsgivenin2.1 Modeling and Seismic Action of the Ground - Structure System,Theseismiccoefficientmethodisasimplifiedequivalentstaticanalysis.Problemsofthestabilityoffacilitiesin an earthquake can be converted into static equilibriumproblems and conveniently analyzed, so themethod isusedwidely,notonlyforports.Inthefieldofports,thismethodisusedfortheperformanceverificationofgravityquaywalls,sheetpilequaywalls,andcelltypequaywallssubjecttotheLevel1earthquakegroundmotions.Whenappliedtogravitytypequaywalls,itisnecessarytoconsidertheinertiaforcesactingonthewall,aswellastheearthpressureandhydrodynamicpressureduringtheearthquake,asshowninFig. 2.1.1(a). Forthelevel1earthquakemotion,whencarryingoutseismicperformanceverificationusingtheseismiccoefficientmethod, it isnotnecessary to take thevalueof theexpectedmaximumaccelerationof thegrounddividedby theaccelerationofgravityastheseismiccoefficientforverificationtobeappliedtothestructure.Forexample,substitutingα=215Galintoequation(2.2.1)givesk=0.22.However,itisknownfromexperience2),4)thatwhenagroundmotionwithamaximumaccelerationexceeding215Galactsonaquaywallwithaseismiccoefficientforverificationof0.22,aresidualdeformationdoesnotnecessarilyoccur.Thereasonsforthishavenotbeenphenomenologicallyexplainedsufficiently,but it isconsidered thatoneof thereasons is thateven ifa215Galaccelerationactson thequaywall,iftheactionisinstantaneous,itisdifficulttocauseavisibleresidualdeformationtothequaywall.ThemethodofconvertingtheaccelerationtimehistoryofthescenarioLevel1earthquakegroundmotionstotheseismiccoefficientforverificationvariesdependingonthestructuralformofthemooringfacility.ForgravityquaywallsrefertoPart III Chapter 5, 2.2.2 Actions,andforsheetpilesquaywallsrefertoPart III Chapter 5, 2.3.2 Actions. When carryingout a seismicperformanceverificationusing the seismic coefficientmethod, the earthpressureduring the earthquake and the foundation ground properties are as discussed later. However, with the seismiccoefficientmethodnormally it isassumedthat liquefactiondoesnotoccur in thegroundbehind thewallor in thefoundations, and the earthpressureduring the earthquakeand foundationgroundproperties are setbasedon thisassumption.Therefore,whencarryingoutseismicperformanceverificationbytheseismiccoefficientmethodfortheLevel1earthquakegroundmotion,ananalysistopredictwhetherliquefactionwilloccurinthegroundbehindthewallorinthefoundationsiscarriedout,andifitisdeterminedthatliquefactionmayoccur,itisnecessarytotakemeasuresagainstit. As can be understood from its principle, the seismic coefficientmethod is amethod for determiningwhetherdeformationwilloccurinspecificmodes,suchassliding,overturning,insufficientbearingcapacityofthefoundationgroundetc.,basedonstaticequilibriumofforces.Ifdeformationdoesoccur,itisnotpossibletocalculatebytheseismiccoefficientmethodhowmuchresidualdeformationiscaused.Thisisalimitationoftheseismiccoefficientmethod,andbecauseof this limitation it isnotpractical toapply theseismiccoefficientmethodto theLevel2earthquakegroundmotion.Normally,forverystronggroundmotions,suchasLevel2earthquakegroundmotions,itisassumedthatthefacilitywillsuffersomedamage,anditisnecessarytoinvestigatetheprocessofthisdamagewhencarryingouttheseismicperformanceverification.5),6) Thesameappliestoportfacilitiessuchasmooringfacilitiesetc., inwhichitisassumedthatdeformationwillbecausedbytheLevel2earthquakegroundmotion,anditisrequiredtocarryoutthedesigntolimitthedeformationtobeequaltoorlessthantheallowableamount.Inordertomeetthisrequirement,itisnecessarytocarryoutaseismicresponseanalysisoftheground–structuresystem,asdescribedlater,nottheanalysisbytheseismiccoefficientmethod.

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2.3 Seismic Action in the Modified Seismic Coefficient Method 2)

Inthecaseoftheseismiccoefficientmethod,theaccelerationactingonthefacilityisequaltotheaccelerationactingontheground.Incontrast,inthecaseofaflexiblestructureasshowninFig. 2.3.1,theaccelerationα' actingonthefacilityisnotthesameastheaccelerationα actingontheground.Inthiscase,ifthedynamiccharacteristicsofthefacility,suchasthenaturalperiods,etc.,andthetimehistoryofthegroundaccelerationaregiven,itispossibletocalculatetheresponseaccelerationofthefacility.Byapplyingtothefacilitytheequivalentstaticforceobtainedbymultiplyingthemaximumvalueoftheresponseaccelerationofthefacilitybyitsmassm,itispossibletoreplacetheactualphenomenonwithstaticequilibriumofforcestocarryouttheseismicdesign.Whenthescopeoftheseismiccoefficientmethodisexpandedinthiswaytostructureswithflexibility,itiscalledthemodifiedseismiccoefficientmethod.Usingthetimehistoryoftheexpectedgroundacceleration,ifaresponsecalculationiscarriedoutinadvanceforfacilitieswithvariousnaturalperiods,andif themaximumvalueoftheresponseaccelerationofthefacilityisarrangedasafunctionofthenaturalperiod,theresultisreferredtoasanaccelerationresponsespectrum.

Fig. 2.3.1 Concept of the Modified Seismic Coefficient Method

Themodifiedseismiccoefficientmethodisclassifiedasasimplifiedequivalentstaticmethodintheclassificationofanalysismethodsin2.1 Modeling and Seismic Action of the Ground - Structure System. Forobtainingtheresponse acceleration of the facility in themodified seismic coefficientmethod, it is frequently assumed that therestoringforcecharacteristicsofthefacilityarelinear.However,whenaverystrongearthquakeactsonthestructure,therestoringforcecharacteristicofthefacilityactuallybecomesnonlinear,asaresultofplasticityinthestructuralmembers. Therefore, the responseaccelerationobtainedunder theassumptionof linearitybecomesmeaningless.Thereforethemodifiedseismiccoefficientmethodisunsuitableforverystronggroundmotions,suchastheLevel2earthquakegroundmotion.

2.4 Seismic Action in the Seismic Deformation Method 2)

Inextended, longfacilitiessuchasburiedpipelinesor immersedtunnels,etc.,wheretheapparentweightperunitvolumeandstiffnessarecomparativelysmall,theaccelerationappliedtothefacilityisseldomaproblem.Theweightandstiffnessofthesefacilitiesissmall,sotheeffectoftheexistenceofthesefacilitiesonthesurroundinggroundissmall,andthedisplacementsinthefacilitytendtobegovernedbythedisplacementsinthesurroundingground.Whenthedisplacementinthesurroundinggroundisnotuniform,strainiscausedinthefacility.Thisisaproblemforseismicdesign. Intheseismicdeformationmethod,firstthedisplacementofthegroundforthecasewherethefacilitydoesnotexistthereisobtained,andnextthedisplacementandstressinthefacilityisobtainedbasedontheassumptionthatthedisplacementof the facility is thesameas thedisplacementof theground. Inotherwords, incontrast to theseismiccoefficientmethodinwhichtheequivalentstaticloadisappliedtothefacilityastheseismicaction,intheseismicdeformationmethodthedisplacementofthegroundisappliedtothefacilityastheseismicaction.Incaseswherethestiffnessofthesubsurfacestructureisquitehigh,andtheerrorintheassumptionthatthefacilitydeformsexactlythesameasthegroundislarge,thedisplacementofthegroundcanactonthefacilityviasprings.Theseismicdeformationmethod isclassifiedasasimplifiedequivalentstaticanalysis in theclassificationofanalysismethodsgivenin2.1 Modeling and Seismic Action of the Ground - Structure System.


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2.5 Seismic Action in the Seismic Response Analysis of Ground - Structure Systems

Eachofthemethodsdescribedsofarsimplifytheactualphenomena,butseismicresponseanalysisthatmoretruelyreproduces the overall ground - structure systembehavior can also be carried out. This is classified as detaileddynamicanalysisintheclassificationofanalysismethodsgivenin2.1 Modeling and Seismic Action of the Ground - Structure System.Seismicresponseanalysisofground-structuresystemsisfrequentlybasedonthefiniteelementmethod,inparticulartheeffectivestressmethod,asshowninFig. 2.5.1.Inthiscasetheseismicactionisthegroundmotioninputatthebottomendoftheanalysisdomain. Ingeneral,thegroundmotionatthebottomendoftheanalysisdomainisthesumofanupcomingwaveEandadowngoingwave(F).MethodsofapplyingtheinputgroundmotionstothebottomendoftheanalysisdomainincludethemethodinwhichtheactualseismicwavemotionsE+Fareappliedtothebottomendoftheanalysisarea,andthemethodinwhichanseismicwavehavinganamplitudetwicethatoftheseismicwaveincidentfrombelowisappliedtothebottomendoftheanalysisdomain,namely2Ewaveinputmethod.Whencarryingoutacalculationtoreproducedamageactuallyincurred,orwhencarryingoutasimulationofashaketablerest,theremaybemeasurementsofthegroundmotionsatthebottomendoftheanalysisdomain,includingtheupcomingwaveandthedowngoingwave,andinthesecasestheE+Fwaveinputmethodcanbeused.However,forseismicresponseanalysisofgroundstructuresystemscarriedoutforseismicperformanceverificationthe2Ewaveinputmethodisused.Inthiscase,ifdirectlybelowtheanalysisdomainthereisgroundthatcanbeconsideredtobefirmground,thegroundmotionatthefirmgroundobtainedinSection 1 Ground Motionmaybeusedasitis.However,ifdirectlybelowtheanalysisdomainthereisgroundthatcannotbeconsideredtobethefirmground,itisnecessarythatthegroundmotiondefinedatthefirmgroundbeconvertedtoa2Ewavedirectlybelowtheanalysisdomainbyaseismicresponseanalysisforthelocalsoildeposit,andthis2Ewaveistheninputted.

Horizontal displacement3.5m

Inclination angle4.1°

+4.0m

-36.0m

Vertical displacement 1.5m

Fig. 2.5.1 Example of Residual Displacement of a Gravity Quaywall Calculated by Effective Stress Analysis

References

1) InternationalOrganizationforStandardization:ISO23469,Basesfordesignofstructures-Seismicactionsfordesignnggeotechnicalworks,2005

2) Tsuchida,H.andS.Iai:EarthquakeEngineeringforconstructionengineers,Sankai-doPublishing3) Sano,T.:Structuraltheoryofhouses(Vol.I&II),Disasterpreventionsurveycommittee,Vol.83,19164) Noda,S.,T.UwabeandT.Chiba:Relationbetweenseismiccoefficientandgroundaccelerationforgravityquaywalls,Rept.

ofPHRIVol.l4No4,19755) JSCE:Proposalsoncriteriaofearthquakeresistance,JSCE,19966) JSCE:Thethirdproposalandcommentaryonseismicdesignofcivilengineeringstructures,JSCE,2000

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ANNEX 3 Evaluation of Site Amplification Factors1 Evaluation of Site Amplification Factors

Thefollowing isanexplanationof thefundamentalmethodofevaluationof thesiteamplificationfactorbasedonseismicobservationrecords,forthecasethatthereisanobservationpointontherockthatcanberegardedastheseismicbedrocknear theharbor,basedonFig. A-3.1. ThesiteamplificationfactorbetweenseismicbedrockandgroundsurfaceattheobservationpointattheharborcanbeobtainedfromtheratiooftheFourieramplitudespectraattheobservationpointattheharborandanobservationpointonthenearbyrock.Whenthesiteamplificationfactorsbetweenseismicbedrockandthetopoffirmgroundarenecessarytheamplificationfactorsfromthetopoffirmgroundtothegroundsurfaceareevaluatedbylinearmultiplereflectiontheory,14),17)basedongrounddataattheobservationpointintheharbor.Thenbydividingthesiteamplificationfactorsbetweenseismicbedrockandgroundsurfacebytheamplificationfactorsfromthetopoffirmgroundtothegroundsurface,thesiteamplificationfactorsbetweenseismicbedrockandtopofthefirmgroundcanbeobtained.Inthiscasethedampingfactormaybetakentobe3%. However,normallythereisnoobservationpointontherockthatcanbeconsideredtobetheseismicbedrockneartheharbor,sonormallytheamplificationfactorsfromtheseismicbedrocktothegroundsurfaceisevaluatedusingtechniquessuchasspectralinversiontechniques,asdescribedlater.

Sourceeffects

Propagation patheffects

Amplification ofbody wave

Observation point at harborObservation point at harborO1 ( f )

G( f ) =O1 ( f ) / O2 ( f )

Observation point on rock O2 ( f )

Ground surface

Top of firm groundSediments

Site characteristics

Generation and propagation ofsurface waves

Seismic bedrockVs>3000m/s

Firm groundVs>300m/s

Local soildepositLocal soildepositLocal soildeposit

Fig. A-3.1 Fundamental Concept Regarding Evaluation of Site Amplification Factors

(1)SeismicObservationforEvaluationofSiteAmplificationFactorsItisdesirablethatthesiteamplificationfactorsbeevaluatedbasedonseismicobservationrecordsfortheharbor.ObservationofstrongseismicmotioniscarriedoutatthemajorharborsinJapan,seeFig. A-3.2,andthesiteeffectscanbeevaluatedbyusingtheserecords.Observationofstronggroundmotionisatypeofseismicobservationwhichusesequipmentthatwillwithstandverystrongmotionfromdamagingearthquakes.ObservationrecordsofstrongmotionearthquakeobservationinJapaneseharborareascanbedownloadedfromtheNationalInstituteforLandandInfrastructureManagementhomepage(http://www.eq.ysk.nilim.go.jp). If the harbors are not subject to designated strong ground motion observation points and if no seismicobservation records can be obtained in nearby points within 2km of the harbor in advance of performanceverificationofanimportantfacility,itisdesirablethatseismicobservationrecordsbeobtainedforevaluationofsiteeffectsbycarryingoutseismicobservations.Inthiscase,itisdesirabletoconfirmthatthegroundmotioncharacteristicsattheobservationpointdonotdiffergreatlyfromthoseatthefacilitiesinstallationlocation,bymicrotremormeasurementcarriedoutinadvance.Thetimeperiodnecessaryforseismicobservationsdependsontheseismicityofthatarea,butingeneralinJapan’scase,iffromonetoseveralyears’observationiscarriedout,itispossibletoobtainsufficientrecordsofmediumandsmallearthquakesordistantlargeearthquakesinorder toevaluatethesiteeffects. Inorder toobtainmanyrecordsinashortobservationperiod,normallythetrigger level, the level of vibration that initiates the seismometer observation, is set lower than that normallyusedforobservationofstrongearthquakes. Inordertoavoidtheeffectofextraneousvibrationsfromnearby,onemethod is touseamechanisminwhich the trigger isoperatedwhen thevelocityexceedsacertain level,nottheacceleration.Anothermethodistocarryoutcontinuousmeasurementregardlessofwhetherthereisanearthquakeornot,andtoextractthedatalaterafteranearthquakehasoccurred.


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Kagoshima

Oita

Hiroshima

Sakiaminato

AmagasakinishinomiyaashiyaOsakaTsuruga

Kanazawa

Fushikitoyama

NiigataSakata

Akita

Aomori

HakodateOkushiri

Setana

Otaru

Rumoi

Mombetsu

NemuroKushiro

TokachiUrakawa

Tomakomai

Hachinohe

MiyakoKamaishiOfunato

SendaiSoma

Onahama

HitachinakaKashima

TokyoChibaKawasaki

YokohamaYokosuka

TagonouraShimoda

ShimizuOmaezaki

MikawaKinuuraNagoyaYokkaichi

WakayamaKomatsushimaKochi

MatsuyamaHososhimaMiyazaki

Shibushi

Muroran

Abashiri

Kobe

Nakagusuku

HiraraIshigaki

Naha

Fig. A-3.2 Strong Motion Earthquake Observation in Japanese Harbor Areas

(2) SpectralInversionAssumingthatMearthquakeshavebeenobservedatNobservationpoints,theFourieramplitudespectrumofthe observation records can be expressed by the following equation as the product of the source effects, thepropagationpatheffects,andthesiteeffects.18)

(A-3.1)

where Si ( f ) :sourceeffectsoftheithearthquake

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Pij( f ):propagationpatheffectsfromthehypocenteroftheithearthquaketotheseismicbedrockofthejthobservationpoint

Gj ( f ):siteamplificationfactorsofthejthpoint

ThepropagationpatheffectsPij( f )canbeexpressedby thefollowingequation, taking intoconsiderationgeometricattenuation,1/r,ofthewavespreadinginsphericalformfromthehypocenterandinelasticdamping.

(A-3.2)

where rij :distancefromthehypocenteroftheithearthquaketothejthobservationpoint Q :Qvalueonthepropagationpath

Substitutingequation (A-3.2)intotherighthandsideofequation (A-3.1),andtakingcommonlogarithmsofbothsides,thefollowingequationisobtained.

(A-3.3)

Inorder to simplify the expression shownhere, the fwhich indicatesdependenceon frequencyhasbeenomitted. Equation (A-3.3) includes M+N+1 number of unknowns, including the source effects Si, the siteamplificationfactorsGj,andtheQvalue.Therefore,iftherearemoreequations,namelythenumberofrecordsthatcanbeused,thanthenumberofunknowns,itispossibletoobtainthecombinationofunknownsforeachfrequencyf,bythemethodofleastsquaressothattheresidualerrorofequation (A-3.3)isminimized.Theaboveisthebasicconceptofspectralinversion.ItisalsopossibletohavetheQvalueasaknownquantity,andobtainM+Nnumberofunknownquantities. However,thereisatrade-offrelationshipbetweenthesourceeffectsSiandthesiteamplificationfactorsGjinequation (A-3.3).Forexample,assumingthatacertaincombinationofSiandGjisasolution,thecombinationSi/2and2Gjisalsoasolution.Asamethodforavoidingthis,thereisthemethodofassumingthatthesiteamplificationfactorsare1atarockobservationpoint,referredtoasthestandardobservationpoint,selectedinadvance.Atthistimeitisnecessarytocarefullyconsidertheselectionofthereferencepoint.Thefollowingpoints19areusefulforselectingthereferencepoint.Firstly,selectthepointwiththesmallestsiteamplificationcharacteristicsforeachfrequencyasthereferencepointbasedontheresultsofpreliminaryanalysis.However,astheamplificationinthehighfrequencyrangeinweakgroundsissmall,thepointselectedasthereferencepointshouldbelimitedtopointswithsufficientlylargeSwavevelocities.Specifically,thereferencepointshouldbeselectedfrompointsforwhichtheaverageSwavevelocityfromthegroundsurfacetothedepthof10mis400m/sorhigher.Also,inorder toavoid thecharacteristicsofeach individual recordgreatlyaffecting the results, the referencepointshouldbelimitedtothosepointsforwhichrecordsofseveral,about5earthquakes,measurementrecordshavebeenobtained.Besidesbasingtheselectionofthereferencepointontheabovecriteria,itisnecessarytomakethedecisionbasedonanexaminationofwhetherthelowfrequencypartofthesourceeffectsSiobtainedfromtheactualinversionresultsiscompatiblewithCentroidMomentTensor,CMT,solution20）,forexample,thatoftheF-netoftheNationalResearchInstituteforEarthScienceandDisasterPrevention. Inaddition,thepointstonotewhenactuallycarryingoutthespectralinversionareasfollows: Inspectralinversionitisnormallyassumedthatthereisgeometricattenuation,1/r,ofthewavespreadinginsphericalformfromthehypocenter.However,atdistantobservationpoints,geometricattenuationintheformabove becomes inapplicable as a result of the effect ofLgwaves transmitted by reflectionwithin the earth’scrust.12)Inordertoavoidthis,itisnecessarytoexcluderecordsofearthquakesthatoccurfaraway,about150-200kmorfarther. TherecordsofsmallscaleearthquakesfrequentlydonothavegoodS/Nratiointhelowfrequencyrange.Whenconsideringharborfacilities,therearetimeswhenitisnecessarytoensureaccuracydownto0.2Hzonthelowfrequencyrange,soitisnecessarytouserecordsofM4.5orlarger.Also,itisdesirabletochecktheS/Nratioonthelowfrequencyrangeofeachoftherecordsusedintheanalysis.21)Ontheotherhand,therecordsoflargescaleearthquakesareaffectedbytheruptureprocessofthefault,soitbecomesinappropriatetoconsiderasinglesourceeffectS i,unaffectedbydirection.Therefore,itisdesirabletoavoidrecordsforM6.0orlarger.Asaresultoftheabove,earthquakesintherangeM4.5–M6.0arefrequentlyusedinspectralinversion. Inordertoavoidnonlinearbehaviorofthelocalsoildeposit,itisdesirabletoavoidtheuseofrecordswithlargeamplitude.Itisalsonecessarytopayattentiontothelengthoftherecordsusedintheanalysis.Itisalsopossibletoextractbysomemethodthe“Swavepart”oftheobservedgroundmotion,anduseitsFourierspectrumintheanalysis.However,whenconsideringharborfacilities,itisnecessarytoobtaintheamplificationfactorsoftheFourierspectrumincludinglaterphasesbyanalyzingnotonlytheSwave,butalsosurfacewaves. NozuandNagao22)appliedspectralinversiontoadatasetthatcontainedstrongmotionearthquakerecordsinJapaneseharborareasaswellasK-NET,KiK-net,andotherstronggroundmotionrecords,andobtainedthesite


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amplificationfactorsbetweenseismicbedrockandgroundsurfaceofthestronggroundmotionobservationpointsineacharea,inparticularharbors.TheresultsareavailableonCD-ROM.22)

(3)Method of Evaluating the Site Amplification Factors from Simultaneous Records from the Harbor and itsSurroundingsIfrecordshavebeenobtainedforthesameearthquakeattheharborandanearbyobservationpoint,andifthesiteamplificationfactorshavealreadybeenevaluatedatthenearbyobservationpoint,thesiteamplificationfactorsattheharborcanbeevaluatedbythefollowingmethod.Firstly,inordertobeabletoexplaintherecordatthenearbyobservationpoint,thesourceeffectsoftheearthquakeunderconsiderationareappropriatelyset.Next,itispossibletoobtainthesiteamplificationfactorsattheharborbydividingtheFourieramplitudespectrumattheharborbythesourceeffectsandbythepropagationpatheffects.23)Itisnecessarytobeawarethatiftheharborandthenearbyobservationpointareinfairlydifferentdirectionsfromthehypocenter,thenitispossiblethattheaccuracyoftheevaluationwillbereducedbythedependenceondirectionofthesourceeffectsoftheearthquake. Iftheearthquakehasoccurredsufficientlyfaraway,thesourceeffectsandthepropagationpatheffectsoftheharborandthenearbymeasurementpointcanbeconsideredtobecommon,soevaluationofthesourceeffectsmaybeomitted,andthesiteamplificationfactorsoftheharbormaybeevaluatedbytakingtheratioofthespectraofthetwopoints.Therecordsoflargeearthquakesthathaveoccurredparticularlyfarawayarenotsuitableforspectralinversion,buttheS/Nratioisfrequentlygooddowntothelowfrequencyrange,sotheycanfrequentlybeused in thismanner. Fig. A-3.3 showsacomparisonof theratioof thesiteamplificationfactorsobtainedfromSZO013,K-NETShimizu,andSZO014,K-NETShizuoka,fromtherecordsof theKiiHantoNantoOkiEarthquakeswithM7.1andM7.4,whichoccurredon5thSeptember2004,andtheratioofthesiteamplificationfactorsbasedonspectralinversion.Itcanbeseenthattheratiosofthesiteamplificationfactorsobtainedbythetwomethodsagreewell.

Ratio of G( f )2004/9/5 W7.1

Frequency (Hz)

SZ00

13/S

Z001

4

SZ00

13/S

Z001

4

Frequency (Hz)

Ratio of G( f )2004/9/5 W7.4

Fig. A-3.3 Comparison of the Ratio of Site Amplification Factors Evaluated by Two Methods

(4) EvaluationoftheSiteAmplificationFactorswhenSeismicObservationRecordshavebeenObtainedatSeveralLocationsNeartheHarbor Ifgroundmotionrecordscanbeobtainedatseverallocationsneartheharbor,itispossibletoobtainseveralsiteamplificationfactors.Inthiscase,itisnecessarytocarryoutzoningontheseveralsiteamplificationfactors.Incoastalareas,suddenchangesaresometimesseeninthebedrockdepths,duetothebasinstructure,soitisnecessarytobeawarethatifzoningiscarriedoutaccordingtowhetherthephysicaldistanceislongorshort,itispossibletomaketheevaluationonthedangerousside.Theuseofmicrotremorscanbeconsideredasameansofcarryingoutsimplezoning.Therearemanyexamplesofresearchintotheuseofmicrotremorstodeterminethesubsurfacestructure.Amongthemisresearchfocusedontheratioofthespectraofthehorizontalcomponentandtheverticalcomponent,hereafterreferredtoastheH/Vspectrum,obtainedbymeasurementofthreecomponentsofmicrotremors,26)andresearchfocusedontheaverageSwavevelocityobtainedfromarraymeasurements,27)howeverthesearemainlyforinvestigatingtheshallowsubsurfacestructure.Also,researchexamplesfocusedonthedeepsubsurfacestructureusingmicrotremorsfrequentlyusephasevelocitybyarraymeasurement.28)TherearecomparativelyfewexamplesofresearchonthedeepsubsurfacestructureusingtheH/Vspectrumfrom3componentmeasurements,butforSatoetal.29)haveindicatedthatthemicrotremorspectralpeakappearingintherangewithperiodequaltoorgreaterthan1secondcanbeexplainedbytheH/VspectralpeakintheRayleighwavedowntotheseismicbedrock,basedonmeasurementrecordsatSendai. Itisconsideredthatofthemicrotremormeasurements,3-componentmeasurementissuitableforinvestigating

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thesubsurfacestructurebecauseofthesimplicityofthemeasurements.Forthedeepsubsurfacestructure,itisalsopossibletoconsiderzoningbyfocusingonthepeakinthelongperiodsideofthemicrotremorH/Vspectrum.

2 Probabilistic Seismic Hazard Analysis

TheuniformhazardFourierspectrumatthetopoffirmgroundandthecorrespondingtimehistorycanbecalculatedinaccordancewiththeprocedureshowninFig. A-3.4.31)Thefollowingisanexplanationoftheflow.

Earthquake catalog data (earthquakes whose sources are difficult to specify in advance)

Fault model data(earthquakes whose sources can be specified)

Probabilistic design ground motion (uniform hazard waveprofile)

Earthquake generation model: Poisson processEarthquake magnitude: random (Gutenberg-Richter equation)Distance: random

Active fault data(earthquakes whose sources can be specified)

Logic tree

Uniform hazard Fourier amplitude spectrum Group delay time (Fourier phase spectrum)

Amplitication due to deep subsurface structure: by spectral inversionPhase delay: source with highest contribution + phase delay due to site effects

Earthquake generation model: For example, Poisson processEarthquake magnitude: fault specificDistance: fault specific

Extent of fault: probabilistic Greens function method

Attenuation relation: theoretical seismic motion for point source (seismic wave from a subfault)Attenuation relation: theoretical

seismic motion for point source (Fourier amplitude spectrum)

Fig. A-3.4 Method of Calculating the Uniform Hazard Fourier Spectrum and the Corresponding Time History 31)

Firstly,thesourcesofearthquakesthatcouldoccurinthefutureneartheharborareclassifiedintothosethatcannotbeeasilydefinedandthosethatcanbedefined,andeachofthesourcesaremodeled.Heremodelingthesourcesmeanssettingthepositionandsizeofthesources.Tomodeltheformer,earthquakecatalogdata32)thatrecordsearthquakesthat have occurred near the site in the past are used. Tomodel the latter, active fault data 33), 34) obtained fromtopographicalandgeologicalsurveysandfaultmodeldataforpastearthquakes35)areused.Forsourcesthatcannotbeeasilydefinedinadvance,thesourcesmaybeequallyspreadoveranareathatappearstobeseismicallyactive,hereafterreferredtoasaseismicarea,orsourcesmayberandomlysetwithintheseismicarea,seeFig. A-3.5(a).Ontheotherhand,forthesourcesthatcanbedefined,thepositionandsizeofthesourceisset,seeFig. A-3.5(b). Aftermodeling thesources, theearthquakeMagnitudes thatcouldoccurat thesesources in the futureand thefrequencyoftheiroccurrenceareevaluated.Inthecaseofsourcesthataredifficulttodefineinadvance,themodeloftheGutenberg-Richterequation,namelybvaluemodel,seeFig. A-3.6(a),isassumedinwhichspecifiesrelationshipbetweenthelogarithmofthefrequencyofoccurrenceofanearthquake,N,andtheMagnitude,M.TheearthquakeMagnitudes are the Magnitude values obtained from the earthquake Magnitude-frequency relations. Also, thefrequencyofoccurrencewithintheseismicareacanbeobtainedfromthenumberofoccurrencesofearthquakesintheearthquakecatalogdataandtheirtimeofmeasurement.Inthecaseofsourcesthatcanbedefined,themaximumMagnitudemodel,maximummomentmodel, seeFig. A-3.6(b), inwhich themagnitude of the earthquakes thatoccur isconstant is frequentlyused. TheMagnitudeandfrequencyofearthquakesoccurringonactivefaultsarefrequentlycalculatedfrominformationonthelengthoftheactivefault,theaveragesliprate,andothertopographicalandgeologicalinformation.


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(a) Earthquakes for which the sources are difficult to define in advance

M1M2

M3

X1

X2

X3

Evaluation ground point

(b) Earthquakes for which the sources can be defined

M

X1

X2 X3

Evaluation ground point

Fig. A-3.5 Modeling of Sources

Foreachof thepostulatedearthquakes, theFourieramplitudespectrumat the topoffirmground iscalculatedtakingintoconsiderationthesourceeffects,thepropagationpatheffects,andthesiteamplificationfactorsbetweenseismicbedrockandtopoffirmground.Forsourcesthatcanbedefined,itisdesirablethattheFourieramplitudespectrumiscalculatedbyamethodcapableoftakingintoaccountthefinitenessofthefault,suchastheprobabilisticGreenfunctionmethod.Forsourcesthatcannotbeeasilydefinedinadvance,itcanbeassumedthatthesourceeffectsoftheearthquakesfollowtheω-2model. Asaresultoftheabove,manyFourieramplitudespectraareevaluatedwithprobabilities,seetopfiguresof Fig. A-3.7. Therefore, thesecanbearrangedso that the relationshipbetween theFourieramplitudespectrumand theannual probability of exceedancehazard curve, canbeobtained for each frequency, seeFig. A-3.7. When theseareoverlayedthehazardsurfaceisobtained,seeFig. A-3.7,sothatfocusingonaparticularannualprobabilityofexceedanceauniformhazardFourieramplitudespectrumisobtained,seeFig. A-3.7. Thereare4samples in thetopfiguresofFig. A-3.7. Thismeans thatalthough theseareearthquakes fromthesamesource, theirmannerofoccurrenceisnotthesame. Inordertoinvestigatetheextentofuncertaintyintheevaluationresultsduetotheselectionofassumptionsandmodelsusedintheaboveevaluationprocess,alogictreemaybeused.Inalogictree,thecombinationsofmodelandparametervaluesareappropriatelyset,andanalysisiscarriedout,andthereliabilityisevaluatedfromthevariationintheanalysisresults. ToobtainthetimehistorycorrespondingtoauniformhazardFourieramplitude,informationregardingFourierphaseisnecessary.InthiscaseitisdesirablethattheFourierphasebedefinedtakingintoconsiderationthecharacteristicsfoFourierphaseattheevaluationpoint.

(a) Earthquakes for which the sources are difficult to define in advance

(b) Earthquakes for which the sources can be defined

b value model

Magnitude (M)

Freq

uenc

y of

occ

uren

ce (

log(N

))

M

Maximum Magnitude model

Magnitude (M)

Occ

urre

nce

freq

uenc

y (l

og(N

))

Fig. A-3.6 Evaluation of Magnitude of Earthquake and Frequency of Occurrence

–254–


Four

ier a

mpl

itude

spec

trum

f5f4f3f2f1

Accumulated values for all earthquakes

Hazard curve foreach frequency

Fourier amplitude spectrum

Ann

ual f

requ

ency

of o

ccur

ence

Uniform hazard Fourier amplitudespectrum for hazard level p0

p 0 A

nnua

l pro

babi

lity

of e

xcee

denc

e

Frequency

Sample 1Sample 2

Sample 3Sample 4

f1

Earthquake 2

Frequency

Four

ier a

mpl

itude

spec

trum

Sample 1Sample 2

Sample 3Sample 4

Frequencyf1

Four

ier a

mpl

itude

spec

trum Earthquake 3Earthquake 1

Sample 1Sample 2

Sample 3Sample 4

Frequencyf1

Four

ier a

mpl

itude

spec

trum

Frequency f = f1

f = f1

f = f2

f = f3

f = f4

f = f5

Hazard surface

Fourier amplitude spectrum

Earthquake 3Earthquake 3

Earthquake 2Earthquake 1

Fig. A-3.7 Procedure for Calculating the Uniform Hazard Fourier Amplitude Spectra


–255–

ANNEX 4 Analysis of Seismic Motion1 Seismic Response Analysis of Local Soil Deposit

NormallytheLevel1earthquakegroundmotionissetastheincidentwave,2Ewaves,onthetopofthefirmground.However,whentheacceleration,velocity,displacement,shearstress,shearstrain,etc.,areneededatotherdepthsofthelocalsoildeposit,theycanbeobtainedbyaseismicresponseanalysisofthelocalsoildeposit. Thefollowingis adescriptionof the seismic responseanalysis for thispurpose. For seismic responseanalysis forperformanceverificationofseismic-resistant,seePart III, Chapter 5 Mooring Facilities. Normallyseismicresponseanalysisofthelocalsoildepositiscarriedoutbymodelingthelocalsoildepositabovethefirmground.However,therangeinSwavevelocityofthefirmgroundcanbeconsiderable,soitisnecessarytoconfirmthattheSwavevelocityofthefirmgroundconsideredwhensettingtheLevel1earthquakegroundmotionandtheSwavevelocityofthefirmgroundconsideredfortheseismicresponseanalysisareconsistenttoacertainextent.Also,whencarryingoutseismicresponseanalysisforthepurposeofpredictingliquefaction,conventionallythewavewasconvertedtocorrespondtoSMAC-B2beforeinputting.However,henceforththisconversionisnotnecessary.Conventionallyawaveprofileofpaststrongmotionrecordswasinputwithamplitudeadjustment,andinthiscasethereferencemaximumaccelerationwasequivalenttoSMAC-B2,sothewaveprofilewasconvertedtocorrespondtoSMAC-B2.

(1) TypesofSeismicResponseAnalysisforLocalSoilDeposit

(a) ClassificationaccordingtothedimensionsconsideredinthecalculationDepending on the dimensions considered in the calculation, seismic response analysis may range from1-dimensional to3-dimensional. Normallywhen investigating theseismic responseof thegroundonly, fornatural grounds or artificial groundswith a horizontally layered structure, 1-dimensional seismic responseanalysisisfrequentlycarriedout.Incoastalareasitisfrequentlypossibletoassumethathorizontalstratificationispredominant. Inthesecases,it isconsideredthatcalculationresultswithsufficientaccuracyforpracticalpurposescanbeobtainedfroma1-dimensionalmodel. Also,relatedtothis,frequentlythetypeofseismicwaveusedinthecalculationistheSwavethatispropagatedvertically.Normallyincoastalareas,theSwavevelocityinthegroundnearthesurfaceislow,sotherayoftheseismicwavenearthesurfacebecomesalmostvertical,seeFig. 1.1.1.Also,thesametendencycanbeseeninthecaseofsurfacewaves.Althoughthisisaslightlydetaileddiscussion,surfacewavescanbeconsideredtobeasuperpositionofPwavesandSwaveswithinthelocalsoildeposit.AtthistimetheraysofthePwaveandSwavealsoapproachtheverticalnearthesurface.Therefore,byconsideringanSwavetransmittingvertically,itisconsideredthatthecalculationwillhavesufficientaccuracyforpracticalpurposes.

(b)Classificationaccordingtomodelingofthesoilstress-strainrelationshipSeismicresponseanalysisoflocalsoildepositisclassifiedintoequivalentlinearanalysisandnonlinearanalysis,fromtheviewpointofmodelingofthesoilstress-strainrelationship.Equivalentlinearanalysistakesaccountofthedependenceoftheshearmodulusandthedampingfactorofthesoilontheamplitude,strictlyspeakingthestrainof thesoil,of thegroundmotion,seeChapter 3, 2.4.1 Dynamic Modulus of Deformation, Fig. 2.4.2.However,inthiscalculationmethoditisassumedthatduringthetimeoftheearthquaketheirvaluesareconstant.Ofcoursethisassumptionisdifferentfromthereality,butatthetimethatequivalentlinearanalysiswasdeveloped,theperformanceofcomputerswasnotashighastoday,sotheseassumptionsweremadefortheconvenienceofthecalculation.Incontrasttothis,innonlinearanalysisthecalculationtakesintoconsiderationthattheshearmodulusetc.ofthesoilvariesthroughoutthetimeofthegroundmotion.Iftheintentionistobeascloseaspossibletotheactualphenomenathenitisnecessarytocarryoutnonlinearanalysis,butifthestraininthesoilisnottoolarge,itisconsideredthatequivalentlinearanalysiscanprovideresponseanalysisresultsthatareclosetotheactualphenomenatoacertainextent.Thelevelofstrainatwhichequivalentlinearanalysiscanbeapplieddependsonthemethod,butisabout0.5to1.0%orless.36),37)Therefore,ifasaresultofcarryingoutequivalentlinearanalysisitisfoundthatthestrainobtainedexceedsthisamount,itisnecessarytochangetheanalysismethodtononlinearanalysis. Inequivalentlinearanalysisthefollowingrepeatedcalculationsarecarriedout. First,theeffectiveshearstrainisobtainedfromthemaximumshearstrainforeachlayer,incaseof2-dimensionsorhigher,foreachelement,calculatedataparticularstep,fromthefollowingequation.

(A-4.1)

where γmax :maximumshearstrain γeff :effectiveshearstrain α :coefficient(normally0.65)

–256–


Next, fromtheeffectiveshearstrain, theshearmodulusandthedampingfactoraremodifiedtaking intoconsiderationthestraindependenceofFig. 2.4.2ofChapter 3, 2.4.1 Dynamic Modulus of Deformation,andtheroutineproceedstothenextstep.Thisoperationisrepeateduntiltheshearmodulusconverges.Theearliestequivalent-linerseismicresponseanalysisprogramisSHAKE.38)WhenSHAKEwasfirstdeveloped,therewerenoothercompetingprograms,anditwaswidelyusedindesignpractice.Also,FLUSH,39)the2-dimensionalversionofSHAKE,iswidelyused.However,inrecentyearstheproblemswithSHAKEhavegraduallybecomeapparent,asaresultofcomparisonofSHAKEcalculationresultswithactualseismicobservationrecords.40)Oneoftheseproblemsisthatthehighfrequencycomponentsareunder-estimated.Whentryingtoestimatetheincidentwavesonthefirmgroundbasedontheseismicwaveobservedatthesurface,thehighfrequencycomponent is over-estimated). FDEL, 41)DYNEQ, 42) andother programs that are improvedoverSHAKEinthisrespecthavebeenproposed. Intheseprogramstheproblemofunder-orover-estimationofthehighfrequencycomponentissolvedbyusingfrequencydependentshearstrain,insteadoftheeffectiveshearstrainobtainedfromequation (A-4.1). Nonlinearanalysisisananalysismethodthatcanbeappliedwhenthestraininthegroundislarge,about0.5–1.0%orlarger.However,whetherthenonlinearanalysisgivesthecorrectresultornotnaturallydependson the constitutive equation used andwhether the soil constants are appropriate or not. There are varioustypesofanalysisprogramfornonlinearanalysis,usingvariousconstitutivemodels.Itisimportanttouseananalysisprogramthathassuccessfullyreproducedverticalarrayobservationrecordsobtainedundersimilarconditions, soil properties and strain levels, in the past with good accuracy.36) Nonlinear analysis can beclassifiedintoeffectivestressanalysisandtotalstressanalysis.Whenexcessporewaterpressureappearsinaground,theeffectivestressisreduced.Asaresult,thestressstateofthesoilchanges,sothesoilrestoringforcecharacteristicsanddampingcharacteristicsarechanged,sotheresponsecharacteristicsofthegroundarealsochanged.Effectivestressanalysisiscapableofexpressingthistypeofsituation,andisamethodthatiscapableofdirectlyobtainingtheexcessporewaterpressuregeneratedinagroundbycalculation.Ontheotherhand,intotalstressanalysis,theexcessporewaterpressureisnotcalculatedinthecalculationprocess,soitisnotpossibletotakeaccountofthechangeinseismicresponseduetothechangeineffectivestress.Ifexcessporewaterpressureisgeneratedmorethanacertainlevel,about0.5orhigherintheeffectivestressratio,thereisalargepossibilitythatthetotalstressanalysisresultswillsignificantlydifferfromtheactualseismicresponse.Therefore,iftheintentionistoanalyzetheactualphenomenatruely,itisnecessarytocarryoutaneffectivestressanalysis. One of the analysis programs for effective stress analysis is FLIP.43) Fig. A-4.1 shows the results of acalculation44)usingFLIPver.3.3toreproducetheverticalarrayrecordsobtainedatPortIslandinKobePortduringthe1995Hyogo-kenNambuEarthquake.PortIslandrecordswereobtainedatthefourdepths:GL-83m,GL-32m,GL-16m,andgroundlevel.HeretheNScomponentwaveobservedatGL-83mwasusedastheinputwave,andthewavesattheotherlevels,GL-32m,GL-16m,andgroundlevel,werecalculatedandcomparedwiththeobservedwaves.Thecapabilitytoreproducetheobservedwaveswasverygood.Fromthisresult,analysisresultsforthe1993KushiroOkiEarthquake,45)andothers,itisjudgedthatFLIPisananalysisprogramthatcangiveaccurateresults,providedthesoilconstantsareappropriatelyset.However,ineachindividualcase,whethertheFLIPresultsarecorrectornotdependsonwhetherthesoilconstantshavebeenproperlysetornot.

50

0

-50

0 10 20 30 40 50

50

0

-50

0 10 20 30 40 50

50

0

-50

0 10 20 30 40 50

50

0

-50

0 10 20 30 40 50

velo

city

(cm

/s)

Time (s)

Port Island GL-0m(NS)

Ovserbed waveFLIP

velo

city

(cm

/s)

Time (s)


Ovserbed waveFLIP

velo

city

(cm

/s)

Time (s)


Ovserbed waveFLIP

velo

city

(cm

/s)

Time (s)


Ovserbed wave(Imput wave to the FLIP)

Fig. A-4.1 Reproduction of the Vertical Array Records at Port Island during the 1995Hyogoken Nambu Earthquake using FLIP 44)


–257–

(c) ClassificationaccordingtotypeofnumericalsolutionmethodSeismicresponseanalysisoflocalsoildepositcanbeclassifiedaccordingtonumericalsolutionmethodintomultireflectiontheoryandthefiniteelementmethod.AsshowninFig. A-4.2,multireflectiontheoryisamethodthatconsidersahorizontallylayeredground,anditisassumedthatashearwaveincidentonthegroundpropagetesupwards,andattheboundaryofeachlayerreflectionandtransmissionrepeatedlyoccurs,andthecoefficientsoftheanalyticalsolutionaredeterminedateachlayer,sothattheboundaryconditionsaresatisfied.Theformulationisdescribedin,forexample,Reference17),inaneasytounderstandmanner.Inmultireflectiontheory,normallythesoilstress-strainrelationshipislimitedtolinearorequivalentlineartype.Thecalculationisnormallycarriedoutinthefrequencydomain.SHAKE,38)FDEL,41)DYNEQ,42)usemultireflectiontheoryasthenumericalsolutionmethod.

Time (s)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

20

0

40

60

Dep

th (m

)

Thic

knes

s (m

)

Sym

bol

(a) Soil boring log (b) Time sequence of reflection and transmission

Soil

type

Wei

ght p

er u

nit v

olum

e(k

N/m

3 )

Vs (m

/s)

Sand

Sand

Siltyclay

Siltysand

Sandyclay

Sand

Sandygravel

6

14

12

14

14

12

19.8

16.1

10.7

18.5

20.6

19.3

23.5

120

200

150

220

220

310

630a1

a2

a3

a4

a5

a6a7a7

a9

a10

a11

a12

b3b3

b4b4

b2

b1

a8a8

Fig. A-4.2 Multireflection Theory 14)

AsshowninFig. A-4.3,thefiniteelementmethodisamethodinwhichthegroundisdividedintoafinitenumberofelements,andthedifferentialequationsgoverningthesystemisconvertedintoalgebraicequationsintermsoftheresponseofthesystematthenodesandthensolved.Thefiniteelementmethodisusednotonlyforgrounds,butisusedinawiderangeoffields.Thecharacteristicofthismethodisthatitiscapableofdealingwiththe2-dimentionaland3-dimentionalchangesinsoilpropertiesandlayerthickness.FLUSH39),FLIP43),andothersusethefiniteelementmethodasthenumericalsolutionmethod.Thecalculationsareconductedinthedomainsoffrequencyandtime.

(b) Cross-section on left divided into elements(a) Ground cross-section

RockClay

Fig. A-4.3 Finite Element Method

(2) GroundModelingforSeismicResponseAnalysisofLocalsoildepositThefollowingisanexplanationofthemodelingofthegroundandmethodofdeterminingtheparametersnecessaryforobtainingasolutionforaseismicresponseanalysisforthelocalsoildeposit,focusingon1-dimension.

① OutlineTocarryoutaseismicresponseanalysisforthelocalsoildeposit,thegroundattheobjectivepointismodeledbydividingitintoseverallayers.Foreachlayer,thelayerthickness,density,andshearmodulusundersmallstrainarenecessaryparametersregardlessofthesolutionmethod.Inaddition,inthecaseofequivalentlinearanalysis,thestraindependenceoftheshearmodulusandthedampingfactorarenecessary.Theparametersnecessaryfornonlinearanalysisdependonthemethodofmodelingthestress-strainrelationshipofthesoil,butinthecaseofFLIP,inadditiontotheaboveparameters,themodulusofvolume,angleofshearresistance,theupperlimitvalueofhystereticdampingfactor,andparameters todefineliquefactionarenecessarycharacteristics.Ofthese,theparameterstodefineliquefactioncharacteristicsarenecessaryonlyforcarryingoutaneffectivestressanalysis.

–258–


②ModelingprocedureTheengineeringbedrockissettakingtheresultsofthesoilinvestigationintoaccount.AtthistimetheSwavevelocityofthegroundselectedastheengineeringbedrockmustnotdiffersignificantlyfromtheSwavevelocityofthegroundselectedastheengineeringbedrockwhensettingthegroundmotion.Thegroundisdividedintolayerscorrespondingtothechangesinthesoilproperties.Inthiscase,evenifthesoilclassificationisthesame,ifSwavevelocity,Nvalue,orquvaluedifferssignificantly,theyareconsideredtobeseparatelayers.Eachgroundisclassifiedintoeithersandysoil,clay,orgravel.Inanactualground,itisrareforasoiltocomprisesandorclayonly,andusuallygravel,sand,silt,andclayaremixedinvariousproportions.Heresoilwithafine,particlesize75µmorless,contentof20%orlessisconsideredtobesandysoil,andothersareconsideredtobecohesivesoils.Rubblestonesusedinmoundsandbackfillingisconsideredtobegravel. Asforsoildensityofeachlayerforwhichundisturbedsamplingofasoilhasbeencarriedout,thedensityofthesoilismeasuredfromthesoiltestsample,andthisvalueisused.However,ifthedensityhasnotbeenmeasured,thevaluesshowninTable A-4.1maybeusedforconvenience.ThestandardvaluesshowninTable A-4.1arestandardvaluesforseismicresponseanalysis,anditisnecessarytobeawarethattheymaynotbeusedforotheranalysesinwhichdensityisagoverningfactor.

Table A-4.1 Standard Values of Soil Density 46)

Soiltype Condition Density(g/cm3)

CohesivesoilWatercontent≥60% 1.5

Watercontent≥60% 1.7

SandysoilHigherthangroundwater

level 1.8

Belowgroundwaterlevel 2.0

Rubblestonesbackfilling 2.0

The shearmodulusunder small soil strain, shear strain about10-6, used in the response analysis canbecalculatedfromtheSwavevelocityobtainedbyin-situinvestigation.

(A-4.2)

where G0 :elasticshearmodulusundersmallsoilstrain ρ :density VS :Swavevelocity

IftheSwavevelocityhasnotbeenobtainedbyin-situinvestigationforasandysoil,theshearmoduluscanbeestimatedfromtheNvalueusingthefollowingequation.

(A-4.3)

However,thisequationshowstheaveragevalueobtainedfromnumberofactualdata,soitisnecessarytobeawarethattherewasasignificantamountofvariation47).Fordetails,refertoChapter 3, 2.4.1 (6) Simple Estimation of Shear Modulus and Damping Factors.If theunconfinedcompressive strength (qu)of cohesive soilshasbeenobtained, the shearmodulusmaybeestimatedfromthefollowingequation48).

(A-4.4)

WhentheSwavevelocityshallbeestimatedusingtheNvalue,iftheNvaluepriortoconstructionisonlyavailable,suchasforthegroundsunderneathawall,theNvalueafterconstructionshallbeestimated,takingintoconsiderationtheeffectoftheeffectiveoverburdenpressureduetothewalloramound.Thefollowingequationmaybeusedintheestimation.

(A-4.5)


–259–

where N :Nvalueafterconstruction N0 :Nvaluebeforeconstruction σν' :effectiveoverburdenpressureafterconstruction(kN/m2) σν0' :effectiveoverburdenpressurebeforeconstruction(kN/m2)

Wherethegroundconditionschangebeforeandaftertheconstruction,andwhenPSloggingiscarriedoutonlybeforeconstruction,theSwavevelocityafterconstructionmaybeestimatedfromthefollowingequation,whichtakesintoaccounttheeffectofthechangeineffectiveoverburdenpressure,andusestheSwavevelocitymeasuredbeforetheconstruction.

(A-4.6)

where VS :Swavevelocityafterconstruction VS0 :Swavevelocitybeforeconstruction σν' :effectiveoverburdenpressureafterconstruction(kN/m2) σν0' :effectiveoverburdenpressurebeforeconstruction(kN/m2)

Bis0.25inthecaseofasandysoiloracohesivesoilwithaplasticityindexIp=30orless,andis0.5inthecaseofacohesivesoilwithplasticityindexIp=30orhigher.ThemeasurementoftheSwavevelocityofrubblemoundandbackfillisdifficult,butforrubblemoundandbackfilltolargequaywallsatawaterdepthofabout-10m,thefollowingvaluesofSwavevelocityobtainedfromthecalculationequation49)derivedfromtheresultsofseismicobservationsonacompositebreakwatermaybeused.

Swavevelocityoftherubblemound:VS =300m/sSwavevelocityofthebackfill :VS =225m/s

Also,thereisanexample50)inwhichthevalueoftheSwavevelocityforboththerubblemoundandthebackfillis300m/sforareferencemeaneffectiveconfiningpressureof98kN/m2.Whenacaissonisconsideredasakindofground,thefollowingvaluesmaybeusedastheSwavevelocityofthecaisson.

Swavevelocityofcaisson :VS =2000m/s

It is known that the shearmodulus under small soil strain is proportional to the power of the effectiveconfiningpressure.Equation (A-4.2)showsarelationshipbetweentheshearmodulusandtheSwavevelocity,soitmaybeinferredthattheSwavevelocityisproportionaltothepoweroftheeffectiveconfiningpressure.Thisrelationshipisobtainedasfollowsfrompastelementtests.48),51)

(a) TheshearmodulusforacohesivesoilwithplasticityindexofIp=30orhigherisproportionaltotheeffectiveconfiningpressuretothepowerof1.

(b)TheshearmodulusforasandysoiloracohesivesoilwithplasticityindexofIp=30orlessisproportionaltotheeffectiveconfiningpressuretothepowerof0.5. On theother hand,Fig. A-4.4 shows a graphof the averageSwavevelocity forToyoura standard sandobtainedbycentrifugalmodeltestscorrespondingtotheconfiningpressureatthemiddleofsandground.ThesolidlineinthegraphisthecorrelationcurveVS =K(σc')a.TheaveragevalueoftheSwavevelocityofasandgroundincreasesasthecentrifugalaccelerationincreases,whichdemonstratesthesignificantdependenceontheconfiningpressure.Fig. A-4.5showsthedistributionoftheSwavevelocitywithdepthdeterminedforthesametestsample.ThebrokenlineinthegraphisthecurveofthecasewheretheSwavevelocityisproportionalto theconfiningpressure to thepowerof0.25,and thiscurvewasobtainedusing theSwaveat themiddleinthesandgroundasreference.InbothcasestheSwavevelocityincreasesasthedepthincreases,andthechangewithrespecttodepthisapproximatelyproportionaltothepowerof0.25.Theseresultswereobtainedbyapplyingcentrifugalaccelerationvaryingfrom10Gto50Gtoa24cmthicklayerofsoiltoartificiallyvarytheeffectiveconfiningpressure.52)

–260–


Ave

rage

she

ar w

ave

velo

city

of s

and

grou

nd (m

/s)

Confining pressure at middle of sand ground σc' (KN/m2)

Vs =100.6 (σc')0.341

Vs =167.3 (σc')0.341

Case 2 (Dr = 50%)

0 10 20 30 40 50 60

200

250

300

350

400

450

Case 1 (Dr = 48%)

Fig. A-4.4 Relationship between the Average S Wave Velocity of a Sand Ground and the Confining Pressure 52)

Shear wave velocity (m/s) Shear wave velocity(m/s)

Dep

th (m

/s)

Dep

th (m

/s)

Case 1 Case 2-12

-8

-4

0

-8

-4

0 500

-12

Fig. A-4.5 Distribution of S Wave Velocity in a Sand Ground 52)

(c) StraindependenceofshearmodulusanddampingfactorNormallywhentheshearstrain issmall, theshearmodulus is largeandthedampingfactor issmall,butasthestrainincreases,theformerreducesandthelatterincreases,seeChapter 3, 2.4.1 Dynamic Modulus of Deformation, Fig. 2.4.2.Thestraindependencecharacteristicsoftheshearmodulusandthedampingfactorvarywiththeconfiningpressureandthesoilpropertiesofeachstratumetc.Therefore,theshearmodulusanddampingfactorvaluesusedshouldbeobtainedfromsoilstestscorrespondingtotheshearstrainlevel,asmuchaspossible.

(d)ParametersnecessaryfornonlinearanalysisTheparametersnecessaryfornonlinearanalysismaybesetbasedonPart III, Chapter 5, 2.2.3 Performance verification (9) Performance Verification for Ground Motions (detailed method).


–261–

ANNEX 5 Evaluation of Ground Motion1 Evaluation of Strong Ground Motion

(1)OutlineMethodsforevaluatingstronggroundmotionstakingintoconsiderationthesourceeffects,thepropagationpatheffects,andthesiteamplificationfactorsincludetheoreticalmethodsandsemi-empiricalmethods.Thetheoreticalmethodsmodelthemediumfromthesourcetotheharborasanelasticbody,andevaluatethegroundmotionsattheharborbasedonthetheoryofelastodynamics. Amongthesemi-empiricalmethods,theempiricalGreen’sfunctionmethodisamethodinwhichthemeasuredgroundmotionfromamediumorsmallearthquake,whosemechanismandpropagationpathiscommonwithalargeearthquake,isconsideredtobeaGreenfunction,andthegroundmotionforthelargeearthquakeissynthesizedbysuperposition.67),68),69)Atthistime,ifasuitablemediumorsmallearthquakerecordisnotavailabletobeused,thestochasticGreen’sfunctionmethodhasbeenproposedinwhichanartificialmediumorsmallearthquakerecordiscreated,andthensuperposed,70)andthismaybealsoclassifiedasasemi-empiricalmethod.Inadditiontherearebroadbandhybridmethodsinwhichthelongperiodcomponentsofthegroundmotionsarecalculatedbytheoreticalmethods,theshortperiodcomponentsarecalculatedusingsemi-empiricalmethods,andthetwoaresuperposed.71)Ineachoftheabovemethods,itisknownthatiftheoreticalmethodsareappliedtoareaswithcomparativelywell-knownsubsurfacestructurestoperiodslongerthanabout1second,observedgroundmotionscanbereproducedwithgoodaccuracy.72)However,althoughinformationonthesubsurfacestructurehasbeencollectedactivity,73)atpresenttheareasforwhichthesubsurfacestructureissufficientlywellknowntoenabletheoreticalmethodstobeappliedareverylimited.Ontheotherhand,ofthesemi-empiricalmethods,intheempiricalGreen’sfunctionmethod,theeffectofthesubsurfacestructureincludedintherecordsofmediumandsmallearthquakesisdirectlyreflectedinthepredictionresults.Also,intheprobabilisticGreenfunctionmethod,whichislikewiseclassifiedasasemi-empiricalmethod,itispossibletoutilizethesiteamplificationfactorsevaluatedfromspectralinversion18)orsimilarlybasedonstrongmotionrecordsatthesite.74)Basedontheabove,atharborsforwhichtherearecomparativelyplentifulstrongmotionrecords,itisdesirablethatsemi-empiricalmethodsareusedinevaluatingthedesigngroundmotion.Inareaswherethesubsurfacestructure iscomparativelywellknown, it ispossible tousetheoreticalmethodsorbroadbandhybridmethods, but in this case the appropriatenessof the subsurface structuremodel shouldbeverifiedinadvancefromtheviewpointofconsistencywiththestrongmotionrecords. Determiningwhethertheresultsofastrongmotionevaluationarevalidornotshould,asarule,becarriedoutfromtheviewpointofwhetherthecalculationconditionsandcalculationprocedureareinaccordancewiththecontentsofthissection.However,comparisonofthecalculationresultswithstrongmotionrecordsobtainedundersimilarconditionsisuseful.Forexample,onecanrefertostrongmotionrecordsinthenearsourceregionof the1995Hyogo-kenNambuEarthquakeor the2004Niigata-kenChuetsuEarthquake. However,normallythegroundmotionsdependgreatlyonthesourceeffectsandthesiteeffects,sobecauseof theseconditions itispossiblefortheamplitudeofthecalculatedgroundmotionstodiffergreatlyfromtheexistingstrongmotionrecords.Ifacalculatedresultwhoseamplitudediffersgreatlyfromtheexistingstrongmotionrecordsisobtained,itshouldbeinvestigatedwhetheritispossibletorationallyexplainthedifferencebythedifferenceinthesourceeffects,suchasdifferencesinthesizeoftheearthquakeorthesiteeffects,andifitispossibletorationallyexplainthedifference in thisway, theresultscanbeaccepted. Ifarationalexplanation isdifficult, thereshouldbeacheckforerrors in inputsetc. In thisway,comparisonwith theexistingstrongmotionrecords isuseful fromtheviewpointofpreventing simple errors. Whencarryingout a comparisonwith the existing strongmotionrecords,comparisonofthemaximumaccelerationshouldbeavoided.Thisisbecausenormallythemaximumaccelerationofagroundmotioniseasilyaffectedbythehighfrequencycomponentat2Hzorhigher.However,thehighfrequencycomponentat2Hzorhigherdoesnothavemucheffectonharborfacilities,soeventhoughthemaximumaccelerationsarecompared,thisdoesnotverifythecalculationresultsinthefrequencyrangethathasalargeeffectontheharborfacilities.Normallythemaximumvelocityisabetterindexthanthemaximumacceleration. Incidentally, themaximum velocity of the groundmotions observed at the ground surface onsedimentsinthenearsourceregionofthe1995HyogokenNambuEarthquakeandthe2004Niigata-kenChuetsuEarthquakewasabout100to150cm/s.

(2)ProbabilisticGreenFunctionMethodTheprobabilisticGreenfunctionmethodisamethodinwhichfirstgroundmotionsatthesiteareevaluatedforasmallearthquake,whicharethensuperposedtoobtainthemotionsforalargeearthquake.Thespecificprocedureisasfollows.

–262–


L

W1~N

1~N

1~N1~Nijij

subfault ij

large event

small event

rrr

w

ij0

ξξ

Fig. A-5.1 Probabilistic Green Function Method

First,focusingononeoftheasperities,namelylargeeventin Fig. A-5.1fortheexpectedearthquake,theasperityisdividedintoN×N. Thenasmallearthquakehavingthesameareaaseachsub-faultoftheasperity,namelysmalleventinFig. A-5.1,isconsidered.TheFourieramplitudeofthegroundmotionfromthesmalleventatseismicbedrockwhichisequivalenttotheprobabilisticGreenfunctionatseismicbedrock,isdefinedastheproductofthesourcespectrumofthesmallearthquakeequation (A-5.1)andthepropagationpatheffectsequation(A-5.2).75)

(A-5.1)

(A-5.2)

where M0e : seismicmomentofsmallearthquake fc : cornerfrequencyofsmallearthquake ρ : densityattheseismicbedrock VS : Swavevelocityattheseismicbedrock R : radiationcoefficient FS : amplificationeffectduetothefreesurface(=2) PRTITN : effectofpartitionofthegroundenergyintotwohorizontalcomponents

r : hypocentraldistanceofthesmallearthquake Q : Qvalueofthemediumonthepropagationpath

Whenconsideringanearthquakeoccurringatanactivefault,ρ =2.7g/cm3andVS =3.5km/smaybeassumed.Anaveragevalueinalldirectionsof0.63maybeusedforR .Whenestimatingthegroundmotionnearthefaultofanearthquakeoccurringatanactivefaultwithinabout10kmfromthefault,PRTITN=0.85forthecomponentnormaltothestrikedirection,and0.53forthecomponentparalleltothestrikedirection.Thesevaluesaredefinedtakingintoconsiderationthatinthenearsourceregionofanearthquakeoccurringatanactivefault,theFourieramplitudeofthecomponentnormaltothestrikedirectionisabout1.6times8)thatofthecomponentparalleltothestrikedirection.Whenevaluatingthegroundmotionsfarfromanearthquakeoccurringatanactivefault,andwhenevaluatingthegroundmotionsduetootherearthquakes,PRTITN =0.71maybeusedassumingthattheenergyofthegroundmotionisequallydistributedtothetwohorizontalcomponents.Inanycase,itisnecessarytosetPRTITNsothatthesumofsquaresofthetwohorizontalcomponentsis1.Table A-5.1showsthestandardvaluesofPRTITN.

Table A-5.1 Standard Values of PRTITN

Nearthefault Exceptnearthefault

Subduction-zoneearthquake 0.71 0.71

Inlandactivefaultearthquake 0.85(componentnormaltostrike)0.53(componentparalleltostrike) 0.71

M6.5earthquakejustbeneaththesite 0.71 0.71


–263–

Theseismicmomentof thesmallearthquakeM0ecanbeobtainedbydividing theseismicmomentof theasperitybyN 3.ThecornerfrequencyfcofthesmallearthquakecanbeobtainedfromthefollowingequationbyBrune.76),77)

(A-5.3)

where Se :ruptureareaofthesmallearthquake

Equation (A-5.3)is“Brune’sequation(36)”76)asitis.Bycombiningequation (A-5.3)andEsherby’sequationforacircularcrack,59)itispossibletoderivethewell-knownequationthatexpressesthecornerfrequencyasafunctionoftheseismicmomentandthestressdrop.Inequation (A-5.2),anappropriateregionalQvalueshouldbeused. ThewaveprofilethatsatisfiestheFourieramplitudesattheseismicbedrockdefinedasaboveisobtainedbyBoore’smethod75)orbyNozuandSugano’smethod,44)andthisistakentobethestochasticGreen’sfunctionattheseismicbedrock. Next, the groundmotion from the small event, the stochasticGreen’s function, at the ground surface isobtained.InthiscasetheeffectofthesedimentsonboththeFourieramplitudeandphaseofthegroundmotion,namelythesiteeffects,istakenintoaccount.Specifically,itcanbecalculatedbythefollowingmethod.74)Asstatedpreviously,normally theFourier amplitudeof thegroundmotion isgivenby theproductof the sourceeffects,thepropagationpatheffects,andthesiteeffects,andthegroupdelaytimeofthegroundmotionisgivenbythesumofthesourceeffects,thepropagationpatheffects,andthesiteeffects.1)

(see1.1.1)

(see1.1.2)

Nowifanearthquakewhosesizeandhypocentraldistancearesufficientlysmallisobservedatthesiteunderconsideration,itisconsideredthatexpectfortheshiftalongtimeaxis,thegroupdelaytimeintherecordpracticallyexpresses thethirdtermontherightsideofequation(1.1.2), inotherwordsthesiteeffects. Therefore, if theFourier transformof thestochasticGreen’s functionpreviouslyobtainedfor theseismicbedrock ismultipliedbyG( f ),andtheFouriertransformoftherecordsatisfyingtheaboveconditionsafteradjustingitsamplitudeinthefrequencydomainto1,thenitsinverseFouriertransformgivesthestochasticGreen’sfunctionatthegroundsurface.Expressingthisprocessintheformofaspecificequationgivesthefollowing.

(A-5.4)

where A( f ) :Fourier transform of the stochastic: C Green’s function at the ground surface (complex

number) Ab( f ):Fouriertransformofthestochastic:CGreen’sfunctionatseismicbedrock(complexnumber) G( f ) :siteamplificationfactorsbetweenseismicbedrockandgroundsurface(realnumber) OS( f ):Fourier transform of medium or small earthquake record obtained at the site (complex

number)

Itisdesirablethatthemediumorsmallearthquakerecordforthesiteusedatthistimeshouldhaveanincidentangletothesiteassimilartothatofthescenarioearthquakeunderconsiderationaspossible.Thisisbecauseinthiswayitispossibletomoreappropriatelytakeintoconsiderationtheeffectofthesedimentsontheriserphaseofthegroundmotions. WhenevaluatingthestochasticGreen’sfunctionatthegroundsurfacebythismethod,itisnecessarythatthesiteamplificationfactorsG( f )beevaluatedinadvance.Forevaluatingthesiteamplificationfactors,therearetwomainapproaches.OneapproachistoextracttheSwavecomponentfromthegroundmotionbysomekindofmethod,andobtainitsamplificationfactors.18)TheotherapproachistoincludenotjusttheSwavecomponentbutalsothesurfacewavescomponentintheanalysis,andtoobtaintheamplificationfactorsoftheFourierspectrumincluding later phases.23) Which approach is taken depends on the objectives, butwhen carrying out strongmotionpredictiontakingthecontributionnotonlyoftheSwavesbutalsothesurfacewavesintoaccount,thelatterapproachisnecessary.Inparticular,ifthemethoddescribedaboveisused,thecontributionoftheSwaveandthecontributionofthesurfacewavesareblendedtogetherinthegroupdelaytimeofthemediumorsmallearthquakerecordobtainedatthesite,soitisnecessarytoconsiderthecontributionofbothtotheamplitudealso. ThegroundsurfaceforthegroundmotionfromtheasperitycanbecalculatedbysuperposingtheGreen’s

–264–


functionatthegroundsurfaceusingthefollowingequations,81)seeFig. A-5.1.Bycarryingoutthissuperposition,thedirectivityeffectinthedirectionofrupturepropagationistakenintoaccount.

(A-5.5)

(A-5.6)

(A-5.7)

where U (t) :groundmotionfromasperity u (t) :stochasticGreen’sfunctionatthegroundsurface f (t) :functiontocorrectforthedifferenceintheslipvelocitytimefunctionbetweenalargeearthquake

andasmallearthquake r :hypocentraldistanceofsmallearthquake rij :distancefromelementijtothesiteofinterest N :numberofsub-divisions(Fig. A-5.1) τ :risetime n' :integerforremovingtheapparentperiodicitythatappearswhensuperposingthewaves r0 :distancefromtherupturestartingpointoftheasperitytothesiteofinterest ξij :distancefromtherupturestartingpointtotheijthelement VS :Swavevelocityoftheseismicbedrock Vr :rupturevelocity

Whenthereareseveralasperities,thesameprocedureisfollowedforeachasperity,andthelinearLevel2earthquakegroundmotionat thegroundsurface iscalculatedbyaddingthecontributionsfromeachasperity.Finally,theLevel2earthquakegroundmotion,2Ewave,atthetopofthefirmgroundiscalculatedbyseismicresponseanalysisofthelocalsoildeposit. Thecontributionofthebackgroundareascannormallybeignoredwithoutproblemforthepurposeofperformanceverificationofportfacilities. Intheabovecalculationprocess,thelinearLevel2earthquakegroundmotionatthegroundsurfaceiscalculatedatonce,butthisdoesnotincludethenonlinearbehaviorofthelocalsoildepositduringalargeearthquake,soitisnecessarytobeawarethatthisnormallyresultsinanoverestimation.InordertocalculatemorerealisticLevel2earthquakegroundmotionatthegroundsurface,normallytheLevel2earthquakegroundmotionatthetopofthefirmgroundisobtainedatonce,thenaseismicresponseanalysisiscarriedoutagaintakingintoaccountthenonlinearbehaviorofthelocalsoildeposit. ExamplesoftheapplicationofthemethoddescribedheretopastearthquakesareintroducedinReference44).Also,acalculationprogramforthemethoddescribedhereisavailableonCD-ROM.44)

(3)EmpiricalGreenFunctionMethodTheempiricalGreenfunctionmethodisamethodforevaluatingthegroundmotionsatthesiteofinterestduetoalargeearthquakeforthecasewheretherecordsofsmallearthquakesthathaveoccurrednearthelargeearthquakeunderconsiderationhavebeenobtainedatthesiteofinterest,bysuperposingtheserecords.ThesmallearthquakerecordsusedforsuperpositionatthistimearereferredtoasempiricalGreen’sfunctions.Therecordsobtainedatthesiteofinterestnaturallyincludetheeffectofthepropagationpatheffectsandthesiteeffects,soamajorfeatureofthismethodisthatthegroundmotionsduetoalargeearthquakecanbeevaluatedwithgoodaccuracywithoutevaluatingthesepropagationpatheffectsandthesiteeffects.However,thismethodcannotbeappliedifitisnotpossibletoobtainsuitablesmallearthquakerecordsatthesiteofinterest.Also,asstatedbelow,therearesomeitemsthatrequireratherspecializedconsideration. Forsuperpositionofthewaveprofiles,equations (A-5.5)to(A-5.7)ofthestochasticGreen’sfunctionmethodcanbeappliedvirtuallyas theyare. However,forequation (A-5.5) it isnecessarytosubstitute thefollowingequationwhichcontainsacorrectioncoefficientC,inorderthatthesmallearthquakebeappropriatelyreflected.81)

(A-5.9)

TheparametersNandCassociatedwiththesuperpositionaredefinedsoastosatisfythefollowingequation.


–265–

(A-5.10)

where M0a :seismicmomentoftheasperity M0e :seismicmomentofthesmallearthquake Sa :areaoftheasperity Se :ruptureareaofthesmallearthquake

Ascanbeunderstoodfromtheabove,whenapplyingtheempiricalGreenfunctionmethod,itisnecessaryto appropriately estimate the parameters of the small earthquake. For the seismicmomentM0e of the smallearthquake,itispossibletorefertoCMTsolutions,20)forexample,oftheF-netbytheNationalResearchInstituteforEarthScienceandDisasterPrevention.TheruptureareaSeofthesmallearthquakecanbeobtainedfromthecornerfrequencyfcusingequation (A-5.3).Toobtainthecornerfrequencyofthesmallearthquake,themethod82)ofobtainingtheratioofthespectraofearthquakeswithdifferentmagnitudesthatoccurrednearbymaybeused. Otherpoints tonotewhenapplying theempiricalGreenfunctionmethodinclude theradiationcoefficientproblem.Theradiationcoefficientoftheseismicwavefromthesourcehasdirectiondependenceaccordingtotheory,20),83)anddependingonthemechanismofthesmallearthquakesuchasstrike,dipandrakeangle,and,bychance,thesiteofinterestmaycorrespondtoatroughintheradiationcoefficient.Inthatcase,iftherecordsaresuperposedastheyare,itispossiblethatthelargeearthquakegroundmotionswillbeunderestimated.Therefore,itisnecessarytopaysufficientattentiontothemechanismsofthesmallearthquakesused. Asdescribedabove,evaluationofgroundmotionsbytheempiricalGreenfunctionmethodrequiresseveralspecialisttypejudgments,soitisnecessarytopayattentiontothesepoints.

2 Seismic Response Analysis of Local Soil Deposit

SeismicresponseanalysisoflocalsoildepositmaybecarriedoutinaccordancewiththedescriptioninANNEX 4, 1 Seismic Response Analysis of Local Soil Deposit.However,whentheLevel2earthquakegroundmotionisacting,thestrainlevelinthelocalsoildeposittendstobecomeparticularlylarge,soitisnecessarytopayparticularattentiontotheanalysismethod.

3 Spatial Variations in the Ground Motion Considered in Performance Verification of Facilities

Ifthegroundissignificantlynon-uniforminthehorizontaldirectionwithintheareaoccupiedbyastructure,spatialvariationinthegroundmotionmaybebroughtaboutasaresult.Therefore,itisdesirablethatthenon-uniformityinthehorizontaldirectionofthegroundconditionswithintheareaoccupiedbythestructurebeevaluated,andifthenon-uniformityissignificant,thespatialvariationinthegroundmotionshouldbeevaluatedtakingtheeffectofthenon-uniformityintoaccount.Forthis,itisalsodesirabletotakeintoconsiderationtheeffectofthenon-uniformityinthehorizontaldirectionofthegroundbelowthetopofthefirmground.Ifthenon-uniformityofthegroundinthehorizontaldirectionissignificant, themosteffectivespecificmethodforevaluatingthespatialvariationofthegroundmotionisthemethodofevaluatingthegroundmotionatseveralpointsusingthemethodstatedinANNEX 5, 1 Evaluation of Strong Ground Motion (2) and (3),basedon the recordsofseismometers installedatseveralpoints.Anothermethodwhenthesubsurfacestructureissufficientlywell-knownistocarryoutanevaluationusinganappropriatenumericalanalysismethodsuchasthefiniteelementmethodorthefinitedifferencemethod.Thisisaratherspecialistdiscussion,butwhenapplyingthemethoddescribedinANNEX 5, 1 Evaluation of Strong Ground Motion (2) ,itisnecessarytopaysufficientattentiontoensurethatthephysicalmeaningofthephasedifferencesinthegroundmotionsevaluatedattheseveralpointsisnotlost.ThephysicalmeaningofthephasedifferencesinthegroundmotionsevaluatedbythemethoddescribedinANNEX 5, 1 Evaluation of Strong Ground Motion (2) canbelostifthestochasticGreen’sfunctionsattheseismicbedrockofseveralpointsareseparatelyevaluated,andrandomnessiscontainedinthephasesofthestochasticGreen’sfunctions.75)Itisalsopossibleiftheoriginofthetimeaxesofthemediumandsmallearthquakerecordsusedinequation(A-5.4)havebeenshifted,forexample,ifthetriggertimeisdifferentatdifferentgroundpoints.MethodsfordealingwiththeformerincludethemethodoftakingthesamestochasticGreen’sfunctionsattheseismicbedrockfortwopointsthatarenottoofardistant. Theaboveconsiderationscanalsobeappliedincaseswherethenon-uniformityofthegroundconditionsinthehorizontaldirectionisnotsignificant,butamoreconvenientapproachcanbeappliedasdescribedbelow.Ifthenon-uniformityinthehorizontaldirectionofthegroundconditionsisnotsignificant,themaincauseofspatialvariationinthegroundmotionisthewavepropagationeffectinthehorizontaldirection.Thestrainε(ω)inthegroundcausedby thewavepropagation effect is a functionof the amplitudeof thegroundmotionvelocityv(ω) and theapparentwavepropagationvelocityc(ω),whereωistheangularfrequency.

(A-5.11)

–266–


Ascanbeseenfromequation(A-5.11),ε(ω)isadecreasingfunctionofc(ω),sothesmallerthevalueofc(ω),themoredisadvantageous it is for thestructure. Theseismicwaves thatcauseawavepropagationeffect include thesurfacewavesandSwaves,butatanarbitraryω,thephasevelocityofsurfacewavesislowerthanthephasevelocityofSwaves.Also,amongthesurfacewaves,thephasevelocityislowestinthefundamentalmodeoftheLovewaveorthefundamentalmodeoftheRayleighwave.Therefore,takingintoconsiderationthefundamentalmodeoftheLovewaveorthefundamentalmodeoftheRayleighwaveisthemostdisadvantageousforthestructure. Thephasevelocityofthesurfacewavesdependsonthefrequency.Ifitisassumedthatc(ω)doesnotdependonω,eithertheeffectofthehighfrequencycomponentonthegroundstrainwillbeunderestimated,ortheeffectofthelowfrequencycomponentwillbeunderestimated.Therefore,itisimportanttoevaluatethefrequencydependenceofthephasevelocity.Itisdesirablethatthefrequencydependenceofthephasevelocitybeevaluatedbasedontheresultsof in-situarraymeasurements,on themicrotremoror theearthquakemotion,orbasedon theelasticwavevelocitystructureaboveandbelowthe topof thefirmground. Asanexample,Fig. A-5.2showstherelationshipbetweenthephasevelocityoftheLovewaveandfrequencyatacertainlocationinTokyoBay.ThesolidlineisthetheoreticalphasevelocitycalculatedfromtheSwavevelocitystructuremodelinTable A-5.2.TheSwavevelocitystructuremodelinTable A-5.2includesthedeepsedimentsdowntotheuppercrust.Ifamodelthatexcludesthedeepsedimentsisusedinthecalculation,thephasevelocityonthelongperiodsideisunderestimated.The■markinFig. A-5.2arethephasevelocitiesobtainedfromthearraymeasurementresults.Atthispoint,thephasevelocityofthefundamentalmodeofLovewaveisabout400m/sataperiodof1second,andabout750m/sataperiodof3seconds.Therefore,ifaconstantvalueof400m/sisusedasthephasevelocitywhichdoesnotvarywithfrequency,theeffectoftheLovewaveataperiodof3secondswillbeoverestimated.Conversely,ifaconstantvalueof750m/sisused,theeffectoftheLovewaveataperiodofabout1secondwillbeunderestimated.

Fig. A-5.2 Relationship between the Phase Velocity of the Love Wave and Frequency at a Certain Location in Tokyo Bay 84)

Table A-5.2 S Wave Velocity Structure Model 84)

Thickness(m) S-wavevelocity(m/s) Density(t/m3)

50 250 1.8

120 410 1.9

1580 800 1.9

1250 1200 2.1

3100 2600 2.6

– 3400 2.6

Normally the ground motions evaluated by the methods of 1.2 Level 1 Earthquake Ground Motions used in Performance Verification of Facilities, and1.3 Level 2 earthquake ground motions used in Performance Verification of Facilities include several frequency components, and each frequency component can cause awavepropagationeffect.Inthiscase,thespatialvariationofagroundmotioncanbesimplyevaluatedtakinginto


–267–

considerationthefrequencydependenceofthephasevelocitybythefollowingmethod.Assumethegroundmotiontimehistoryevaluatedatareferencepoint(x=0，y=0)attherelevantdepthofthehorizontallylayeredgroundbasedonthemethodsof1.2 Level 1 Earthquake Ground Motions used in Performance Verification of Facilities,and1.3 Level 2 earthquake ground motions used in Performance Verification of Facilities,isa0(t).Also,assumethefrequencydependentphasevelocitycorrespondingtothepointisc(ω).Inthesecircumstancesthegroundmotiontimehistorya(t)atanarbitrarypoint(x,y)atthesamedepthcanbedefinedasfollows:

(1)TaketheFouriertransformofa0(t).

(2)CalculatetheFouriertransformofa(t)fromthefollowingequation.

(A-5.12)

(A-5.13)

(A-5.14)

where A0(ω):fouriertransformofa0(t) A(ω) :fouriertransformofa(t) θ :anglebetweenthepositivedirectionofthex-axisandthedirectionofpropagationoftheseismic

wave

(c) TaketheinverseFouriertransformofA(ω)toobtaina(t).Ideally,c(ω)shouldbedefinedtakingintoaccountthetypeofseismicwavesincludedinthegroundmotionsa0(t)evaluatedatacertainpointbythemethodsof 1.2 Level 1 Earthquake Ground Motions used in Performance Verification of Facilities,and1.3 Level 2 Earthquake Ground Motions used in Performance Verification of Facilities.However,inrealitytheevaluatedseismicwavefrequentlyincludesvarioustypesofwave,suchassurfacewavesandSwaves,etc.,soitisnoteasytoextractthesurfacewavesonly.Therefore,consideringthemostdisadvantageousconditionsforthefacilities,thesmallerofthephasevelocityofthefundamentalmodeofLovewaveandthefundamentalmodeofRayleighwavemaybeusedasthec(ω)inequation(A-5.13)andequation (A-5.14).Theangleθmaybetakentobethedirectionthatismostdisadvantageousforthefacility.

References

1) Sawada,S.,etal.:Propagationpathandsitecharacteristicsofphasespectrumofstrongearthquake,The10thSymposiumofEarthquakeEngineering,pp.915-920,1998

2) Aki,K.:Scalinglawofseismicspectrum,J.Geophys.Res.,Vol.72,pp.1217-1231,19673) Aki,K.:GenerationandpropagationofGwavesfromtheNiigataearthquakeofJune16,1964.2,Estimationofearthquake

moment, released energy, and stress-strain drop fromGwaves pectrum,Bulletin of theEarthquakeResearch Institute,Vol.44,pp.23-88,1966

4) Irikura,K:StrongmotioncausedHanshinEarthquakeDisaster,AnnualRept.ofDisasterPreventionCenter,KyotoUniv.,No.39A,pp.229-245,1996

5) Kouketsu,K:CaliforniaDisasterEarthquakeandSouthernHyogoEarthquake,Science,Vol.66No.2,pp.93-97,19966) Takemura,M.,T.MoroiandK.Yashiro:CharacteristicsofStrongmotionfromtheviewpointofdamagesduetoshallow

earthquakesinceMeijiera,Earthquake2,Vol50,pp.485-505,19987) Somerville,P.G.,N.F.Smith,R.W.GravesandN.A.Abrahamson:Modificationofempiricalstronggroundmotionattenuation

relationstoincludetheamplitudeanddurationeffectsofrupturedirectivity,SeismologicalResearchLetters68,pp.199-222,1997

8) NOZU,A.,SusumuIAIandWilfredD.IWAN:AStudyonPredominantDirectionofNear-sourceGroundMotionandIt’sApplication,TechnicalNoteofPHRIVol.40No.1,pp.107-167,2001

9) Nozu,A.andK.Ikeda:Layoutplanofearthquakeproofwharfconsideringthedirectionoftremorofearthquakegroundmotioninepicentralarea,PortandHarbour,Vol.78,No.9,pp.48-51,2001

10) IndependentAdministrativeCorporationPARI,MinistryofTransport:Handbookofdirectionalityofearthquakemotionforportplanning,CD-ROM,2003

11) Kikuchi,M.andK.Yamanaka:Failureprocessofhistoricallargeearthquakes;Identificationofasperity,Seismo,5(7),pp.6-7,Jul.,2001

12) Street,R.,R.HerrmannandO.Nuttli:SpectralcharacteristicsoftheLgwavegeneratedbycentralUnitedStatesearthquakes,Geophys,J.R.Astr,Soc.,Vol.41,pp51-63,1975

13) Kudo,K:Progressofearthquakeengineering research in strongmotionearthquakes,Earthquake2,Vol.46,pp.151-159,1993,

14) Tsuchida,H.andS.Iai:EarthquakeEngineeringforconstructionengineers:Sankai-doPublishing,1991

–268–


15) Kinoshita,S.:KyoshinNet(K-net),Seim.Res.Lett.,Vol.69,pp.309-332,199816) Aoi,S.,Obara,K.,Hori,S.,Kasahara,K.andOkada,S.:Newstrong-motionobservationnetwork:KiK-net,EOS.Trans.Am.

Geophys.Union,Vol.329,200017) Osaki,S.:newEditionIntroductiontospectralanalysisofearthquakemotion,KajimaPublishing,199418) Iwata, T., K. Irikura: An attempt to segregate characteristics of epicenter, propagation passage and the soils near the

observationpoint,Earthquake2,VoL39,pp579-593,198619) Yamada,M.,A.NozuandT.Nagao:AstudyontheselectionofbaseRocksiteinthespectruminversion,ProceedingofJoint

ConferenceofJapanGeosciencesUnion,(CD-ROM),200420) Aki,K.andP.B.Richards:QuantitativeSeismology,SecondEdition,UniversityScienceBooks,200221) NOZU,A.,Y.SATOandTakahiroSUGANO:CharacteristicsofGroundMotionsObserved atHanedaAirport (Second

Report)SiteAmplificationFactors,Rept.ofPHRIVol.42No.2,pp.251-283,200322) NOZU,A.andT.NAGAO:Siteamplificationfactorsforstrong-motionsitesinJapanbasedonspecialinversiontechnique,

TechnicalNoteofPHRINo.1112,200523) M.Tai,K. Irikura andA.Kowada: Examination on evaluationmethods for empirical site amplification characteristics,

Earthquake2,Vol.50,pp.215-227,199724) Nagao,T.,N.MorishitaandA.Nozu:StudyoneffectofsitecharacteristicsintheevaluationofKevel1earthquakemotion,

ProceedingofOffshoreDevelopment,Vol.22,200625) Nagao, T. et al.: Study on reproduction of seismic coefficient of damage earthquake at Takamatsu Port, Proceeding of

OffshoreDevelopment,Vol.22,200626) Mori, S. and T. Tawara: Estimation of 3-dimensional structure of Matsuyama Plain by observation of micro tremor,

ProceedingsofStructuralEng.Vol.47A,pp.529-538,200127) Adachi,M.etal.:ExaminationofS-wavevelocitystructureofNagoyaPortbyobservationofmicrotremor,Proceedingsof

the27thConferenceofEarthquakeEng.Study,CD-ROM,200328) Yamanaka,H.,andN.Yamada:constructionof3-dimensionalSwavevelocitymodelofKantoPlainbyArrayobservation

ofmicrotremor,GeophysicalExploration,Vol.55,No.1,pp.53-65,200229) Sato,T.,H.KawaseandN.Matushima:Differencebetween thegroundcharacteristicsdeterminedbymicro tremorand

S-wave,P-waveandcodaanditstheoreticalinterpretation,Earthquake2,VoL51,pp.291-318,199830) Nagao,T.,M.YamadaandA.Nozu:StudyonZoningmethodsofcoastalareasconsideringdeepgroundstructure,Proceedings

ofOffshoreDevelopment,Vol.21,pp.951-956,200531) Nagao,T.,M.YamadaandA.Nozu:ProbabilisticseismichazardanalysiswithfocusonFourieramplitudeandgroupdelay

time,Jour.JSCENo.801/1-73,pp.141一158,200532) Utsu,T.:EarthquakesanddamageearthquakescatalogueinthevicinityofJapanhavingmagnitudesof6.0andhigher:1885-

1980,Bull.Earth.Res.Inst.Univ.Tokyo,Vol.57,pp.401-463,198233) ActiveFaultResearchGroupEdition:(NewVersion)Activefaults inJapan-distributionMapanddata.TokyoUniversity

Press,199134) Tanaka,K.T.ImaizumiEdition:Digitalmapofactivefault,TokyoUniversityPress,200235) Sato,R.(Edition):HandbookofparametersofEarthquakefaultsinJapan,KajimaPublishing,198936) Yoshida,N.andS.Iai:Nonlinearsiteresponseanditsevaluationandprediction,TheEffectsofSurfaceGeologyonSeismic

Motion,Irikura,Kudo,Okada&Sasatani(eds),Balkema,199837) InternationalOrganization forStandardization: ISO23469,Bases fordesignof structures-Seismic actions fordesigning

geotechnicalworks,200538) Shnabel,P.B., J.Lysmer andH.B. Seed: SHAKE,A computer program for earthquake response analysis of horizontally

layeredsites,ReportNo.EERC72-12,UniversityofCaliforniaatBerkeley,197239) Lysmer,J.,T.Udaka,C.F.TsaiandH.B.Seed:FLUSH,Acomputerprogramofapproximate3-Danalysisofsoil-structure

interactionproblems,ReportNo.EERC75-30,UniversityofCaliforniaatBerkeley,197540) Yoshida,N.:ApplicabilityofPracticalprogramSHAKE,ProceedingsofSymposiumonamplificationofearthquakemotion

insoftground,ResearchCommitteeonamplificationofearthquake insoft souland thedamage, JapaneseGeotechnicalSociety,

41) Sugito,M.,H.GodaandT.Masuda:Frequencydependentequi-linearizedtechniqueforseismicresponseanalysisofmulti-layeredground,Jour.JSCEVol.493/II-27,pp.49-58,1994,

42) Yoshida,N. and I. Suetomi: “DYNEQ” a program for the earthquake response analysis based on the equivalent linearmethods,ReportofTechnicalInstitute,SatoEngineering,pp.61-70,1996.

43) lai,S,,Y.MatsunagaandT.Kameoka:Strainspaceplasticitymodelforcyclicmobility,SoilsandFoundations,Vol.32,pp.1-15,1992

44) Nozu,AandH.Sugano:SimulationofStrongGroundMotionsfromShallowCrustalandSubduction-Zoneearthquakebasedonsite-specificamplificationandphasecharacteristics,TechnicalNoteofPARINo.1120,2006

45) lai,S.,T.Morita,T.Kameoka,Y.MatsunagaandK.Abiko:Responseofadensesanddepositduring l993KushiroOkiearthquake,SoilsandFoundations,Vol.35,pp.115-132,1995

46) CoastalDevelopmentInstituteofTechnology(CDIT):Handbookofliquefactionofreclaimedland(RevisedEdition),19747) Imai,T.andK,Tonouchi:CorrelationofNvaluewithSwavevelocityandShearModulus,Proc.2ndESOPT,198248) KoukiZEN,HiroyukiYAMAZAKI,YasufumiUMEHARA:ExperimentalStudyonShearModulusandDampingRatioof


–269–

NaturalDepositsforSeismicResponseAnalysis,,Rept.ofPHRIVol.26No.1,pp.41-113,198749) TatsuoUwabe,HajimeTsuchida,EiichiKurata:SeismicResponseAnalysisofCompledWater-StructureSystembased

Strong EarthquakeMotion Record of Large-scale Composite Breakwaters , Report of the Port And Harbour ResearchInstituteV61.22No.2,pp.289～326,1983

50) Kazui,Y.,S.IaiandT.Morita:Analysisofcausesofdamagesofbreakwatersbytressanalysis,ProceedingsofAcademicpresentationconferenceonHanshin-AwajiLargeEarthquakeDisaster,JSCE,pp.397-404,1996

51) Kunio, G., A. Sakurai andY. Esaki: Development soil testingmethod covering small to large strains utilizing triaxialcompressionapparatusanditsapplicationtophysicaltestofsand,Proceedingsof14thconferenceofgeotechnicalengineeringstudypresentation,pp513-516,1979

52) Usui,T.M.KazamaandT.Inatomi:Oneffectofconfiningpressuredependencyofshearstiffnessontheresultofequivalentlinear earthquake response analysis, Proceedings of Symposium on behavior of ground and earth structures duringearthquake,pp.219-224,1989

53) TokyoAstronomicalObservatoryEdition:ChronologicalScienceTables,2007,200654) Usami,M.:CatalogofDamagingearthquakeinJapan(LatestEdition)[416]-2001,TokyoUniv.Press,,200355) JSCE:Proposalsandcommentaryonseismicdesignmethodsofcivilengineeringstructures,200056) Takemura,M.:ScalinglawofearthquakesinearthcrustinJapanIslands-Relationshipbetweeneffectofgroundfaultsand

earthquakedamages,Earthquake2,Vol.51,pp.211-228,199857) Kanamori,H.Edition:PhysicsofEarthquake,IwanamiPublishing,199158) Kataoka,S.,T.Kusagabe,J.MurakoshiandK.Tamura:StudyondeterminationmethodofLevel2earthquakebasedon

assumedearthquake,ResearchReportofNationalInstituteforLandandInfrastructureManagementNo.15,200359) Esherby,J.D.:Thedeterminationofaelasticfieldofanellipsoidalinclusionandrelatedproblems,Proc.RoySoc.Lond.,Ser.

A241,pp.376-396,195860) Wald,D.J.,andP.G.Somerville:Variable-sliprupturemodeloftheGreatl923Kanto,Japan,Earthquake:geodeticandbody-

waveformanalysis,BulletinoftheSeismologicalSocietyofAmerlca,Vol.85,pp.159-177,199561) CentralDisasterPreventionConference:SubcommitteeonsurveyofEastNankai.NankaiEarthquake(7thMeeting)Figures

andDiagrams,200262) Irikura,K.:Recipeofstrongearthquakeprediction-predictionmethodofstrongmotionduetolargeearthquake-Manual

ReportofDisasterPreventionCenter,KyotoUniv.No.47A,200463) Somerville, P.G.,K. Irikura,R.Graves, S. Sawada,D.Wald,N.Abrahamson,Y. Iwasaki, T.Kagawa,N. Smith andA.

Kowada:Characterizingcrustalearthquakeslipmodelsforthepredictionofstronggroundmotion,SeismologicalResearchLetters,Vol.70,pp59-80,1999

64) Irikura, K. and H. Miyake: Prediction of strong motion under scenario earthquake, Journal of Earth ScienceVo1.110,No.6,pp.849-875,2001

65) Irikura,K.andH.Miyake:Modelingofepicenterforprediction,JournalofEarth,ExtraEdition,No.37,pp.213-223,200266) Takemura,M.:RelationshipbetweenMagnitudeofshallowearthquake inJapanIslandsandvicinityand theearthquake

moment,Earthquake2,occurringVoL43,pp.257-265,199067) Irikura,K.:PredictionofstrongaccelerationmotionsusingempiricalGreen’sfunctions,Proc.7thJapanEarthq.Eng.Symp.,

pp.151-156,198668) Takemura,M.andT.1keura:Asemi-empiricalmethodusingahybridstochasticanddeterministicfaultmodels:Simulation

ofstronggroundmotionsduringlargeearthquakes,J.Phys,Earth,36,pp.89-106,198869) Dan,K.,T.WatanabeandT.Tanaka:Asemi-empiricalmethodtosynthesizeearthquakegroundmotionsbasedonapproximate

far-fieldshear-wavedisplacement,J.StructuralandConstructionEngineering(TransactiopsofAIJ),396,pp.27-36,198970) Kamae,K.,K.IrikuraandY.Fukuchi:StrongMotionpredictionduringlargeearthquakebasedonscalinglawofearthquake,

ProceedingsofStructuralengineering,ArchitecturalInstituteofJapan,Vol.430,pp.1-9,199171) Kamae,K.,Irikura,K.andPitarka,A.:AtechniqueforsimulatingstronggroundmotionusinghybridGreen’sfunction,

BulletinoftheSeismologicalSocietyofAmerica,Vol.88,pp.357-367,199872) Matsushima,S. andH.Kawase:Proposal of plural number of asperitymodels and simulation of strong seismicmotion

utilizingthemodels,ArchitecturalInstituteofJapan,StructuralEngineeringJournalVol.534,pp.33-40,200073) Science andTechnologyAgency: Proceedings of the First PresentationMeeting onSubsoil Structure ofAlluvial Plain,

200074) Kowada,A.,M., Tai, Y., Iwassaki and J. Irikura: Evaluation of horizontal and vertical strong seismicmotion utilizing

empiricalamplificationandphasecharacteristicsofthesite,ArchitecturalInstituteofJapan,JournalofStructuralEngineeringVoL514,pp.97-104,1998

75) Boore,D.M.:Stochasticsimulationofhigh-frequencygroundmotionsbasedonseismologicalmodelsoftheradiatedspectra,BulletinoftheSeismologicalSocietyofAmerica,Vol.73,pp.1865-1894,1983

76) Brune, J.N.:Tectonic stress and the spectraof seismic shearwaves fromearthquake, J.Geophys.Res.,Vol.75,pp.4997-5009,1970

77) Brune,J.N.:Correction,J.Geophys.Res.,Vol.76,p.5002,197178) Sato,T.,K.Tatsumi:Epicenter,PropagationandSitecharacteristicsofInlandearthquakeandmarinetrenchearthquakebase

onstrongearthquakeinJapan,ProceedingsofStructuralEng,ArchitecturalInstituteofJapanNo.556,pp.15-24,200279) Tsuruki,M.S.Sawada,M.MiyajimaandM.Kitaura:Re-evaluationofsiteamplificationcharacteristicsinKansaiRegion,

–270–


ProceedingsofStructuralEng.Vol.48A,pp.577-586,200280) Kato,K.:ExaminationsofEpicenters,propagationpathandamplificationcharacteristicsofgroundofgroupearthquakesin

NorthwestareaofKagoshimaPrefecturein1997,ProceedingsofStructuralEngineering,ArchitecturalInstituteofJapan,Vol.543,pp.61-68,2001

81) Irikura,K., T.Kagawa and T. Sekiguchi: Improvement of strongmotion predictionmethod utilizing empiricalGreen’sfunction,ProceedingsofConferenceofSeismologicSocietyofJapanNo.2,B25,1997

82) Miyake, H., Iwata, T. and Irikura,K.: Source characterization for broadband round-motion simulation: kinematicheterogenious source model and strong motion generation area, Bulletin of the Seismological Society of America,Vol.93,pp.2531-2545,2003

83) Study Group of Theoretical EarthquakeMotion Edition: Earthquake motion- synthesis and profile processing. KajimaPublications,1994

84) Nozu,A.,M.Yasunaka,Y. Satou andT.Kanno:Characteristics ofGroundMotionsObserved atHanedaAirport(FirstReport)CharacteristicsofSurfaceWaves,TechnicalNoteofPARI,No.1022,2002

Documents

Chapter 4 Earthquakes - OCDI 一般財団法人 国際 …ocdi.or.jp/tec_st/tec_pdf/tech_235_270.pdfPART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 4 EARTHQUAKES – 237

Chapter 4 Earthquakes - OCDI 一般財団法人国際 …ocdi.or.jp/tec_st/tec_pdf/tech_235_270.pdfPART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 4 EARTHQUAKES – 237