elastomeric seismic isolation bearings including t

EARTHQUAKEENGINEERINGANDSTRUCTURALDYNAMICSEarthquakeEngngStruct.Dyn.2009;38:157–180Publishedonline26August2008inWileyInterScience().DOI:10.1002/eqe.847AmechanicalmodelforelastomericseismicisolationbearingsincludingtheinfluenceofaxialloadSachieYamamoto1,∗,†,MasaruKikuchi1,MasaikiUeda1andIanD.Aiken21DepartmentofArchitecturalandStructuralDesign,GraduateSchoolofEngineering,HokkaidoUniversity,Kita-13,Nishi-8,Kita-ku,Sapporo060-8628,Japan2SeismicIsolationEngineering,Inc.,114465thStreet,UnitD,Emeryville,CA94608,U.S.A.SUMMARYForthepurposeofpredictingthelarge-displacementresponseofseismicallyisolatedbuildings,ananalyt-icalmodelforelastomericisolationbearingsisproposed.Themodelcomprisesshearandaxialspringsandaseriesofaxialspringsatthetopandbottomboundaries.Thepropertiesofelastomericbearingsvarywiththeimposedverticalload.Atlargesheardeformations,elastomericbearingsexhibitstiffeningbehaviorunderlowaxialstressandbucklingunderhighaxialstress.Thesepropertiesdependontheinteractionbetweentheshearandaxialforces.Theproposedmodelincludesinteractionbetweenshearandaxialforces,nonlinearhysteresis,anddependenceonaxialstress.Toconfirmthevalidityofthemodel,analysesareperformedforactualstaticloadingtestsoflead–rubberisolationbearings.Theresultsofanalysesusingthenewmodelshowverygoodagreementwiththeexperimentalresults.Seismicresponseanalyseswiththenewmodelarealsoconductedtodemonstratethebehaviorofisolatedbuildingsundersevereearthquakeexcitations.Theresultsobtainedfromtheanalyseswiththenewmodeldifferinsomecasesfromthosegivenbyexistingmodels.Copyrightq2008JohnWiley&Sons,Ltd.Received20February2008;Revised8July2008;Accepted15July2008KEYWORDS:seismicisolation;elastomericisolationbearing;largedeformation;axialforce;nonlinearhysteresismodel;seismicresponseanalysisINTRODUCTIONSeismicisolationisthemosteffectivetechnologyforprotectingstructuresfromthedamagingeffectsofearthquakes.Ithasbeenextensivelyusedworldwideoverthelastthreedecades.Thewidespreaduseofseismicisolationhasnecessitatedbetterunderstandingofsomeofthemore∗Correspondenceto:SachieYamamoto,DepartmentofArchitecturalandStructuralDesign,GraduateSchoolofEngineering,HokkaidoUniversity,Kita-13,Nishi-8,Kita-ku,Sapporo060-8628,Japan.†E-mail:[e-mail]/grantsponsor:PublishingArtsResearchCouncil;contract/grantnumber:98-1846389Copyrightq2008JohnWiley&Sons,Ltd.158S.YAMAMOTOETAL.complexaspectsofisolationdevicebehavior,suchasunderlargesheardeformationsorhighcompressivestresses.Lead–rubberbearingsandhigh-dampingrubberbearingsaretwocommonlyusedtypesofseismicisolationdevice.Elastomericisolationbearingsexhibitstiffeningorbucklingbehavior,influencedbytheimposedcompressivestressatlargesheardeformations.Thechangeinshearstiffnessduetohighcompressivestressisanimportantbehaviortoconsiderforelastomericbearingswhenisolatedbuildingsexperienceextremeearthquakeshaking.Theactualbehaviorexhibitedbyanelastomericisolatordependsontheinteractionbetweenshearandaxialforces.Takingtheshear–axialinteractionintoaccount,KohandKellyproposedasimplemechanicalmodel(two-springmodel)forelastomericbearings[1].Thetwo-springmodelisacombinationofashearspringandarotationalspringandarigidcolumnconnectedabovethesprings.Theresultsofseismicresponseanalyseswiththetwo-springmodelshowthatneglectingP–effectscanleadtoconsiderableerrorsforbearingswithlowbucklingsafetyfactors[2].Animprovementofthetwo-springmodelwasrefinedtogivetheso-calledKoh–Kellymodel,whichhasrotationalspringsatthetopandbottomandtherotationalspringsareconnectedbyrigidcolumnswithashearspringatmid-height[3].SincetheKoh–Kellymodelconsistsoflinearsprings,itisnotsuitablefortheanalysisofelastomericbearingsthatexhibitnonlinearbehavioratlargesheardisplacements.Inordertobetterpredictthelarge-displacementbehaviorofelastomericbearings,Iizukaintroducedfinitedeformationandnonlinearhysteresisintothetwo-springmodeltoproducetheso-called‘macroscopicmodel’[4].Themacroscopicmodelsuccessfullypredictsskeletoncurvesenvelopingtheshearforce–displacementrelationshipsobtainedfromcyclicloadingtests.Ryanetal.examinedtheeffectsofshearstrainlevelandappliedverticalloadonthepropertiesofelastomericisolationbearingsusingresponsedatafromcharacteristictestsofthreedifferenttypesofbearingsandproposedananalyticalmodelforlead–rubberbearingsbythemodifyingtheKoh–Kellymodelwithabilinearhystereticrelationshipandanempiricalequationforbearingyieldstrength[5–7].Theauthorshavealsoproposedananalyticalmodelforelastomericisolationbearingsunderlargesheardeformations,throughtheintroductionofnonlinearhystereticrelationshipstotheKoh–Kellymodel[8].Theactualhystereticbehaviorofisolationbearingsunderastructuresubjectedtosevereearth-quakeshakingisnotthesameasthatobtainedfromcyclicsheartestswithconstantaxialstressbecauseofthevariationofverticalloadduetooverturningforces[9].Fortheresponseofisolatedstructures,especiallyforthosestructuresinwhichlargeoverturningforcesoccur,theinfluenceofthevariationofverticalloadonbearingbehaviormaybesignificant.BuckleandLiuexaminedtherelationshipbetweenlossoflateral