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www.e-ache.com HormigónyAcero2018;69(285):147–161 www.elsevierciencia.com/hya
Original
Seismic
isolation
of
structures.
Part
I:
Concept,
review
and
a
recent
development
Aislamiento
sísmico
de
estructuras.
Parte
I:
concepto,
revisión
y
evolución
reciente
Mohammed
Ismail
a,b,caSENERIngenieríaySistemas,08290,Barcelona,Spain
bStructuralEngineeringDepartment,ZagazigUniversity,44519Zagazig,Egypt cUniversitatPolitécnicadeCatalunya–BarcelonaTECH(UPC),08034Barcelona,Spain
Received26March2017;accepted22October2017 Availableonline13February2018
Abstract
Thispaperisthefirstoftwocompanionpapersonseismicisolationofstructures.Thosetwopaperspresentthetopicsinceitsfundamentalconcepts;
passingthroughitsdevelopmenthistoryandcomparisonsofdevelopedisolationsystemsovertime;uptoaddressingoneofthemostrecentisolation
devices,besidesadetailedcasestudyofitsimplementationunderseverenear-faultearthquakesconsideringclosely-spacedasymmetricmultistory
structures.Thepresentpaper,PartI,introducesbrieflytheconceptofseismicisolationanditsdevelopmenthistory.Thenpresentsforanapplication
usingarecentlyproposedseismicisolationsystemsnamedRoll-in-Cage(RNC)isolator.Theobjectiveofthesecondcompanionpaper,PartII,isto
minimizetwistofisolatedasymmetricstructures,togetherwiththeirtorsionalpoundingwithadjacentstructures,consideringinsufficientseismic
gapsandstrongnear-faultgroundmotions,bymeansoftheRNCisolator.
©2017Asociaci´onCient´ıfico-T´ecnicadelHormig´onEstructural(ACHE).PublishedbyElsevierEspa˜na,S.L.U.Allrightsreserved.
Keywords:Seismicisolation;Concept;History;Asymmetricstructures;Pounding;Roll-in-Cageisolator
Resumen
Esteartículoeselprimerodedosartículoscomplementariossobreaislamientosísmicodeestructuras,quepresentaneltemadesdesusconceptos
básicos,pasandoporlahistoriadesudesarrolloylascomparacionesdesistemasdeaislamientodesarrolladosalolargodeltiempo,hastaabordar
unodelosdispositivosdeaislamientomásrecientes,ademásdeuncasoprácticodetalladodesuimplementaciónencondicionesdeterremotos
intensoscercadelafallaconlavaloracióndeestructurasasimétricasdevariospisosconpocoespacioentresí.Elpresenteartículo,laparteI,
presentabrevementeelconceptodeaislamientosísmicoylahistoriadesudesarrollo.Luegosepresentaunaaplicaciónqueutilizaunsistemade
aislamientosísmicopropuestorecientemente,denominadoaisladorroll-in-cage(RNC).Elobjetivodelsegundoartículocomplementario,laparte
II,esreducirlatorsióndeestructurasasimétricasaisladas,asícomoelgolpeteotorsionalconestructurasadyacentes,considerandoloscasosde
espacioinsuficienteentrelasestructurasydefuertesmovimiemtossísmicosporproximidadaunafalla,pormediodelaisladorRNC.
©2017Asociaci´onCient´ıfico-T´ecnicadelHormig´onEstructural(ACHE).PublicadoporElsevierEspa˜na,S.L.U.Todoslosderechosreservados.
Palabrasclave: Aislamientosísmico;Concepto;Historia;Estructurasasimétricas;Golpeteo;Aisladorroll-in-cage
E-mailaddresses:[email protected],[email protected],[email protected]
https://doi.org/10.1016/j.hya.2017.10.002
1. Introduction
Seismicbaseisolationhasbeenusedwithincreasing popular-itytoprotectstructures,togetherwiththeiroccupants,secondary systemsandinternalequipment,fromthedamagingeffectsof earthquakes.Thispaperaddressessuchpopularprotection strat-egy, against devastating seismic events, through three steps: highlighting its fundamental concepts; reviewing briefly its developmenthistory;andgivingachallengingapplication exam-pleofseismicisolationintocloselyspacedasymmetricbuildings usingtherecentRNCisolator.
2. Philosophybehindseismicisolation
Seismicisolationisadesignstrategybasedonthepremise thatitisbothpossibleandfeasibletouncoupleastructurefrom the ground andthereby protect it from the damaging effects oftheearthquakemotions.Toachievethisresult,whileatthe same timesatisfying all of the in-service functional require-ments,additionalflexibilityisintroducedusuallyatthebaseof thestructure.Additionaldampingisalsoprovidedtocontrolthe deflections,whichoccuracrosstheisolationinterface.
Decouplingastructure fromthe horizontalcomponentsof aground motiongives thestructure afundamentalfrequency that ismuchlowerthanits fixed-basefrequencyandthe pre-dominantfrequenciesofthegroundmotion.Thefirstdynamic modeoftheisolatedstructureinvolvesdeformationonlyinthe isolationsystem;thestructureaboveisbeingtoallintentsand purposesrigid.Thehighermodesthatproducedeformationin thestructureareorthogonaltothefirstmode,andconsequently, tothe groundmotion. Thesehighermodes donotparticipate in motion, so that the high energy in the ground motion at thesehigherfrequenciescannotbetransmittedtothestructure. The isolation system does not absorb the earthquake energy, butratherdeflectsitthrough thedynamicsofthesystem;this effectdoesnotdependondamping,butacertainlevelof damp-ingisbeneficialtosuppresspossibleresonanceattheisolation frequency.
Based on fundamental vibration period perspective, an insightintothebenefitsofusingbaseisolatorsinstructurescan begainedbyconsideringthespecialcaseofasingle-storylinear undampedstructure,whichisseparatedfromthegroundby flex-iblebearingsoflaterallinearstiffnesskbasshowninFig.1(a). Thebearingsareconnectedtogetherthroughabasemass,which
(a) m
mb
xg xg
y2 m y2
y1 mb y1
k
kb/2 kb/2 kb/2 kb/2
2
k k
Isolation system 2
(b)
Figure1.Singlestorybase-isolatedstructure.
isarigidhorizontaldiaphragmofmassmbjustabovethe bear-ings.The wholesystemisidealizedas a2DOFs spring-mass systemasshowninFig.1(b).Thegoverningequationsofmotion are
mby¨+k(y1−y2)+kb(y1−x2)=0 (1a)
my¨2+k(y2−y1)=0 (1b) wheremisthemainmass,kisthestiffnessofthestructureabove theisolatorandy1andy2arethetotaldisplacementsofthebase andthemainmasses,respectively.Iftherelativedisplacements betweenthemassesandthesupportsaredefinedtobe
x1=y1−xg (2a)
x2=y2−xg (2b)
ItthenfollowsfromsubstitutingEq.(2)intoEq.(1)that
mbx¨1−kx2+(k+kb)x1=−mbx¨g (3a)
mx¨2+kx2+kx1=−mx¨g (3b)
Considerthespecialcasewherembisverysmallandsois assumedzero.Therefore,Eq.(3a)becomes
−kx2+(k+kb)x1=0 (4) Solvingforx1intermsofx2inEq.(4)gives
x1=
k
k+kb
x2=
1 1+(kb/ k)
x2 (5)
The displacement x1 is the displacement of the base iso-lator relative to the ground. Eq. (5) gives the value of x1 in terms of x2 and the ratio of the isolator stiffness to that of the structure. Note that if kb goes toward infinity (i.e. very stiff bearing), thenx1 goes toward zero. In addition, if kb is equal to k, then x1 is equal to one-half of x2. The ideal, or perfect, isolation case is attained if kb goes toward zero. In thiscase,x1=x2whichtranslatesintozerostorydrift, perfect rigid-body vibrationof thestructureandfullstructure-ground separationinthehorizontaldirection.SubstitutingEq.(5)into Eq. (3b) gives the equation of motion for this spring-mass systemas
mx¨2+
1−
1 1+(kb/ k)
Oneimportanteffectofthepresenceofbaseisolators,seenin Eq.(6),isthemodificationofthenaturalfrequencyofvibration ofthesystem.Inthisspring-masssystem,thenaturalfrequency ofvibrationis
ωnb=
k m
1−
1 1+(kb/ k)
=C1ωn (7)
whereωn=√k/m,andC1isthebaseisolatednaturalfrequency ofvibrationcoefficient,definedas
C1=
1−
1 1+(kb/ k)
(8)
Thenaturalperiodofvibrationis
Tnb=
2π ωnb =
2π
k m
1− 1+(kb/ k1 )
=
C2Tn (9)
whereTn=2π/ωn,and
C2=
1
1− 1+(kb1/ k)
=
1
C1
(10)
Insightintothemeaningof arigid,orfixed, basestructure canbegainedfromEq.(7).Ifkbismuchgreaterthank1,thenthe terminthedenominator,thatis,1+(kb/k),ofEq.(7)becomes large,andthereforeωnbapproachesthenaturalfrequencyofa
rigidbasesystem√k/mandTnbapproachesthenaturalperiod
ofvibrationofarigidbasesystem2π/√k/m.
Thesituationofinterestforabaseisolatedstructureisthecase wherekbislessthank.Inthelimitifkbisverysmall,thenωnb
goestozero,seeEq.(7),andthenaturalperiodofvibrationof thestructureTnbgoestoinfinity,seeEq.(9)whichcorresponds
tothefullyisolatedcondition.Eq.(5)canberewrittentoexpress theratiox1/x2asafunctionoftheratiokb/k.Inthiscase,ifkb/k becomeslarge,thenx1/x2tendstozero. Thisisthefixedbase condition.
3. Historicaldevelopmentofisolationsystems
Seismicisolationisnotaverynewidea.Morethana cen-tury ago, in1885,John Milne, a professorof engineering in Japan,builtasmallwoodenhouseonballsincast-ironplates withsaucer-likeedgesontheheadsofpiles,todemonstratethat astructurecouldbeisolatedfromearthquakeshaking[1]. How-ever,thebuildingbehaviorunderwindloadswasnotsatisfactory. Therefore,hereducedtheballsdiameterfrom10inchto1/4inch. By thismean,the buildingbecamestable againstwind loads andwasevidentlysuccessfulunderactualearthquakeaction.In 1891,afterNarobiearthquake,aJapaneseperson,Kawai, pro-posedabaseisolatedstructurewithtimberlogsplacedinseveral layersinthelongitudinalandtransversedirection[2].
In1906,JacobBechtoldofGermanyappliedforaU.S.patent inwhichaseismic-resistantbuildingistobeplacedonrigidplate supportedonsphericalbodiesofhardmaterial[3].In1909,a medical doctorfrom England,Calentarients,hadsubmitted a
patentapplicationtothe Britishpatentofficefor amethodof buildingconstruction.Inhismethod,abuildingisconstructed onalayeroffinesand,mica,ortalcthatwouldallowthebuilding toslideinanearthquake,therebyreducingtheforcetransmitted tothebuildingitself[4].In 1929,RobertdeMontalkofNew Zealandfiledapatentapplicationforaninventioncomprisinga meanswherebyabedisplacedandretainedbetweenthebaseof abuildinganditssolidfoundation.Thebedwasbeingcomposed ofmaterialwhichwillabsorborminimizeseismicshocks[5].
Therearealmostahundredknownproposalsforaseismic isolationsystemsmadepriorto1960,butasfarascanbe deter-mined,nonewereeverbuilt.Themostprobablereasonisalack ofpracticalityandthefactthattheengineeringprofessionofthe dayhadlittleornoconfidenceintheirsuccess[3].Onenotable historic structure,however,is FrankLloydWright’s Imperial HotelinTokyo,completedin1921.Thisbuildingwasfounded onashallowlayeroffirmsoil,whichinturnwassupported,by anunderlyinglayerofmud.Cushionedfromdevastatingground motion,thehotelsurvivedthe1923Tokyoearthquakeandlater Wrightwroteinhisautography[6]ofthe“mercifulprovision” of60–70feetofsoftmudbelowtheupper8footthicksurface soillayerwhichsupportedthebuilding.TheimperialHotelwas anevidencethatbaseisolationworksandseismicprotectioncan beachievedbyrelativelysimplemeans.
Sincethe1920stherehavebeenother“accidents”inwhich some structures have survived earthquakes while neighbor-ing buildings have collapsed. Several unreinforced masonry buildingswereonlylightlydamagedinthe1933LongBeach earthquake because they were able to slide on their grade beams.Atleastonemasonryhousesurvivedthe1976Tangshan earthquakebecauseitalsoslidonitsfoundationinadvertently. Reconnaissancereportsalsodescribeinstancesofslender struc-turessurvivingearthquakesbecause oftheirabilitytorockor sidesway.Watertanksandstatues,chandeliersandsuspension bridgesaresomeexamples.
Attemptsweremadeinthe1930stoprotecttheupperfloors of multistory buildings by designing very flexible first-story columns.Itwasproposedthatthefirst-storycolumnsshouldbe designedtoyieldduringanearthquaketoproduceisolationand energy-absorbingactions.However,toproduceenough damp-ing,severalinchesofdisplacementsisrequired,andayielded columnhasgreatlybucklingloads,provingtheconcept impracti-cal.Topreventthestructurefrommovingtoofar,thefirststoryis constructedundergroundandenergydissipatorsareinstalledat thetopofthisstory[7].Toovercometheinherentdangersofsoft supportsatthebase,manytypesofrollerbearingsystemshave beenproposed.Therollersandsphericalbearingsareverylow indampingandhavenoinherentresistancetolateralloads,and thereforesomeothermechanismsthatprovidewindrestraintand energyabsorbingcapacityareneeded.Alongdurationbetween two successiveearthquakesmayresultinthecoldweldingof bearingsandplates,thus causingthe systemtobecome rigid afteratime.Therefore,theapplicationoftherollingsupports wasrestrictedtotheisolationofspecialcomponentsoflowor moderateweight[8].
solution for increasing the flexibilityof the system.The first use of a rubber isolation system to protect a structure from earthquakeswasin1969forathree-storyelementaryschoolin Skopje,RepublicofMacedonia.Thebuildingwasconstructed of reinforced concreteshearwalls andsupportedby 54large blocks of hard rubber. Theserubber blocks were completely unreinforced,sotheweightofthebuildingcausesthemtobulge sideways.Toimprovethebuildingstabilityunderminor vibra-tions,glassblocksactingasseismicfuzesareintendedtobreak when theseismicloadingexceeds acertainthreshold. Owing tohavingthesamestiffnessoftheisolationsysteminall direc-tions,thebuildingbouncesandrocksbackwardsandforwards
[9].Thesetypesof bearingsareunsuitable fortheearthquake protectionofstructures.
Thesubsequent developmentof laminatedrubberbearings in1970shasmadeseismicisolationapracticalreality[10–12]. Thesebearingsareverystiffintheverticaldirectiontocarrythe structuralweightbutareveryflexiblehorizontallytoenablethe isolatedstructuretomovelaterallyunderstronggroundmotion. In theearly1980s, developments inrubbertechnologyled to newrubbercompounds,whichweretermedhighdamping rub-ber(HDR)[13].Later,alargenumberofisolationdeviceswere developedincludingrollers,springs,frictionslipplates,capable suspension,sleevedpiles,androckingfoundations.Now seis-micisolationhasreachedthestageofgainingacceptanceand replacingtheconventionalconstruction,atleastforimportant structures.
Itisnotjusttheinventionoftheelastomericbearing,which hasmadeseismicisolationapracticalreality.Threeother par-allel, butindependent,developments havealso contributedto its success. The first of these was the development of reli-ablesoftwareforthecomputeranalysisofstructurestopredict theirperformanceanddeterminedesignparameters.Thesecond developmentwastheuseofshakingtables,whichareableto sim-ulatetheeffectsofrealrecordedearthquakegroundmotionson differenttypesofstructures.Athirdimportantdevelopmentis intheskilloftheengineeringseismologistinestimatingground motionsataparticularsite.
Table 1 summarizes the advantages and disadvantages of themostcommonlyused devicesfor seismicisolation.These advantagesanddisadvantagesarebrief,generalandmaynotbe comprehensive.Further,thelisteddisadvantagesmayapplytoa generictype;somemanufacturesmayhavespecificprocedures toalleviateoneormoreofthedisadvantages.
RoughinspectionofTable1confirmsthefactthateachofthe seismicisolationsystemsmentionedabovehasspecificdynamic propertiesandfunctionsbutnodeviceisperfect.Thismotivates the efforts either toenhance the existing devices or to inno-vateotherswiththeaim ofattainingthemaximumprotection levelofstructuresthroughseismicisolation.Unfortunately,most ofthe isolationsystemsreportedintheliteraturearepatented products(thesameisalsotruewithmostnewlyinvented prod-ucts),notallofthemarereadilyavailableforprocurementand directenhancement.Therefore,the intention maybedirected towardcreatingmoreefficientisolationdevices.Thenext sec-tion presentsfor acasestudy using anovelseismicisolation systemnamedRoll-in-Cage(RNC)isolator,whichisanattempt
Table1
Advantagesanddisadvantagesofcommonlyusedisolationsystems.
Device Advantages Disadvantages
Elastomeric Lowstructuralaccelerations Largedisplacements
Relativelylowcost Lowdamping
Limitedrecenteringcapacity Shearstrainreducescapacity Minimumflexibilitylimit Noresistancetoserviceloads Nobuffer
P-influence
HDR Moderatestructural
acceleration
Straindependentstiffness
Resistancetoserviceloads Straindependentdamping Moderatetohighdamping Complicatedanalysis
Scragging-changeproperties Narrowrangeofstiffness Narrowrangeofdamping Nobuffer
P-influence
Limitedrecenteringcapacity
LRB Moderatestructural
acceleration
Cyclicchangeinproperties
Resistancetoserviceloads Bearingareareduction Widerangeofstiffness P-influence
Widerangeofdamping Notforlow-massstructures
Highdampinglevels Nobuffer
Limitedrecenteringcapacity
Flatsliders Simpleinconcept Highstructuralacceleration Resistancetoserviceloads Changingfrictioncoefficient Nostrainhardening Highinitialstiffness
Lowprofile Norecenteringmechanism
Highdampinglevels Nobuffer
Earthquakeindependent Structureindependent
Curved sliders
Lowprofile Highstructuralacceleration
Resistancetoserviceloads Changingfrictioncoefficient Relativelywidedamping
range
Highinitialstiffness
Reducedstructuraltorsion Highcost
Highdampinglevels Curvature-dependent
vibrationperiod Upliftedstructurewith motion
Likelypermanenteccentricity
Rollers Verylowstructural acceleration
Nodamping
Simplemeansandconcept Nobuffer
Greathorizontalflexibility Norecenteringmechanism Notforheavymasses Flatteningofcontactsurfaces
Springs Provide3Disolation Nodamping
Commonlyusedfor machinery
Producesvertical accelerations Nobuffer
Norecenteringmechanism Notforheavymasses
Hysteretic dampers
Controldisplacements Addforcetosystem Lowcost
Upper bearing plate
Anchors Anchors
Dampers Dampers
Dampers
Dampers Dampers
Elastomeric cylinder
Elastomeric cylinder
Lower bearing plate Lower bearing plate
Elastomeric cylinder Elastomeric cylinder
Upper rubber plate
Upper rubber plate
Upper bearing plate
Lower rubber plate
Rolling core
Rolling core
Upper bearing plate
Elastomeric cylinder
Elastomeric cylinder
Lower rubber plate
Lower rubber plate
Lower bearing plate
Lower bearing plate
Upper rubber plate Upper rubber plate
Upper bearing plate
Figure2.TheRNCisolator:(a)fullisometricview;(b)verticalhalf-sectionalviews;(c)three-dimensionalpartialsectionalview.
thataimstocombinethebestfeaturesofthepresentday isola-tionsystems,whileavoidingtheirmaindrawbacks,inasingle unit.Detailednumericalresultsarepresentedanddiscussedinto thecompanionpaper,PartII.
The Roll-in-Cage (RNC) isolator has been recently pro-posed,[14,15], as an attempt of enhancement, see Fig. 2. It is a rolling-based isolation system to achieve the maximum possiblestructure-ground decoupling, andtherefore, to mini-mizethe seismic forcetransferto the isolated structure. Itis
features: (1) a self-stopping (buffer) mechanism to limit the isolator displacement under severe seismic excitations, such as near-faultearthquakes, to apreset value by the structural designer; (2) a linear gravity-based self-recentering mecha-nismthatpreventsresidualdisplacementafterearthquakes(such recenteringmechanismisaresultofadoptingaquasi-ellipsoidal shapeoftherollingcore);and(3)significantresistanceto ver-ticalaxialtensionprovidedbymetallicyielddampersalongits perimeter.
Besidestherolling-basedmotionmechanism,whichrequires less lateral forces to initiate and maintain high degree of structure-grounddecouplingcomparedtoothermotion mech-anisms of the elastomeric-based and friction-based isolation systems,theRNCisolatorisprovidedwithaconsistentdesign ofthelateralstiffnessmechanismtogetthemostbenefitofthat rolling-basedmotionmechanism.Suchdesignadvantageliesin theindependencyofbothverticalbearingmechanismandthe mechanismthatprovideslateralpre-yieldstiffnessagainstminor vibrationloads.Thisindependencyallowsfor accuratetuning of the initialpre-yield stiffness topermitthe commencement of the seismic isolation process, or structure-ground decou-pling,justafterthe seismicforcesexceedthe maximumlimit ofminorvibrationloads,contrarytotheavailableisolation sys-tems. To supportheavy and extraheavy structures, the RNC isolatorisprovidedwithalinearhollowelastomericcylinder, withadesignedthickness,aroundtherollingcoretorepresent themainverticalloadcarryingcapacity,whiletherollingcore itselfworksasasecondarysupportinthiscase.TheRNCisolator canbeavailableindifferentotherformstosuitthestructureor objecttobeprotected.Moredetaileddescriptionandthorough treatmentoftheRNCisolatorisfoundinreference[14].
4. Seismicisolationofadjacentasymmetricbuildings usingtheRNCisolator
4.1. Introduction
Torsionadverselyaffectstheresponseofconventional struc-tures,aswellas seismicisolated structures.Itwasfoundthat 42%of thecollapsesthat occurredinMexico Cityduringthe 1985earthquakewererelatedtothetorsionalresponseof asym-metricbuildings[16].Manyofthebuildingsbeingconstructed todaydisplaytorsioneffectswhendynamicallyexcited.These effectsareclearlytobeexpectedifthecenterofmass(CM)ofthe buildingissignificantlyoffsetfromitscenterofrigidity(CR).In suchacasethebuilding’scolumnsaresubjectedtoloadsarising frombothtranslationandrotationoftheoverallbuilding.The magnitudeofthetorsionalresponseswithrespecttothe transla-tionalonesisgovernedbytheparticipationfactorsoftherelevant modes.Althoughthetotalinter-storyshearforcesinan eccen-tricstructure canbe reducedby theparticipationof torsional modesofvibration,theshearforcesanddisplacementsofany givencolumntendtoincreaseasitsdistancefromthestructural centerofrigidityincreases.Over-stressingofstructural compo-nentsisthereforemorelikelyinabuildingwhichhasitsCM offsetfromitsCRthaninonethatdoesnot.Practicalproblems suchasmaterialinhomogeneitiesprecludestheconstructionof
buildings withperfectcoincidentcentersofmassandrigidity. Forthisreasonalone,torsionaleffectswouldbepresenttosome extentinallbuildings.
Asaconsequence,fordesignpurposes,itwouldbedesirable torestrictsuchnegativeeffectsthroughminimizingoreven elim-inatingoftorsionalresponsesofasymmetricstructures[16–18]. Passive seismic isolation systems are devised tomitigate the destructiveeffectsofearthquakesinbuildingsandtheircontents bycontrollingtheseismicinput.Practically,theeffectivenessof seismic-isolatedstructures’performanceisstronglyinfluenced byitstorsionalbehavior.Almostallstructuresexperience three-dimensional response during ground motions due to lack of symmetrybetween thestructure’s centerof rigidity(CR)and centerofmass(CM).Oneormoredominantlateralnatural fre-quenciesofthestructuremaytunewithitstorsionalfrequency
[19].Severalresearchershaveinvestigatedthecoupled lateral-torsionalresponseoffixed-baseandseismic-isolatedbuildings
[20–24].Mostinvestigationshavefoundthatcouplingbetween translationalwiththerotationalmodessignificantlyaffectsthe behaviorofseismic-isolatedstructureandthiseffectneedstobe rigorouslyconsideredinanalysisanddesign.
Regarding the seismicbehaviorof asymmetric multi-story isolated structures, the available literature shows that the response of isolatedasymmetricstructures isstill anongoing researchtopicwithrelativelyfewworksavailable.Someofthe first reported research studies on simple rigid superstructure models could be foundin[20,21]andon multi-story models in [25].They haveconcluded that aseismic isolation system withzeroorasmallamountofeccentricitysignificantlyreduces torsioninthosesystems causedbysuperstructureasymmetry. Using multi-story models, [23] concluded that the isolation system eccentricityas wellas asymmetry and dynamic char-acteristicsof thesuperstructureare bothimportantgenerators of torsioninseismicisolatedstructures,nevertheless,that the torsionalamplificationsarereducedduetotheisolationsystem. Similarly,[24]concludedthatthebaseisolationsystembecomes lesseffectiveforgreatereccentricities,sincethedisplacements of the seismic isolation systemare increased dueto alarger contributionoftorsion.
forthetorsionallyflexibleseismicisolationsystemsandsmaller baseeccentricities,themaximumamplificationoftheresponse occursatthestiffedge.Otherwise,fortorsionallystiffisolation systems,themaximumamplificationsoccurattheflexibleedge. Seismicallyisolatedstructurescanexperiencelarge displace-mentsattheisolationlevelduringstrongearthquakeexcitations, especiallyforlong-periodimpulsenear-faultgroundmotions. Tosimplyaccommodatesuchlargedisplacements,asufficiently wideclearanceisprovidedaroundthestructuretoaccommodate theselargebearingdeformations.However,thewidthofa cho-senseismicgapislimitedbecauseofpracticalandarchitectural constraintsandthe associated costespecially inmetropolitan areas. Therefore, seismic pounding between adjacent struc-turesbecameacommonlyobservedphenomenonduringmajor earthquakes.Poundingmaycausebotharchitecturalaswellas structuraldamagesand,insomecases,itmayleadtocollapse ofthewholestructure.Forexample,theearthquakethatstruck MexicoCityin1985showedthatpoundingwaspresentinover 40%of330collapsedorseverelydamagedbuildingssurveyed, andin15%ofallcasesitledtocollapse,asreportedby[27,28]. Duringthe1989LomaPrietaearthquake,therewereover200 poundingoccurrencesinvolvingmorethan500buildings[29].
Many investigations have been carried out on pounding damage caused by past earthquakes [30–33], on mitigation of pounding hazards [34–38], and on modeling of pounding betweenstructures[39–45].Poundingbetweenadjacent struc-turesisaverycomplexphenomenon,whichmayinvolveplastic deformation,localcrushingaswellasfracturingatthecontact. Thesenonlinear deformationsarenoteasytobeincorporated into the modeling of pounding. Therefore, idealizations and assumptions haveinevitably been used in theoretical models
[39–41,44].Forexample,structureshavebeenidealizedasrigid barriers,single-degree-of-freedomoscillators or multi-degree-of-freedomoscillators;poundingbetweenstructureshavebeen modeledbylinear dashpot-springsystemor nonlinear impact model. Despite of these simplifications, theoretical analyses have been valuable in providing insight into the pounding mechanisms [42,43,45]. Several recent research works have investigated different issues of structural pounding including modeling,mitigationandfiniteelementinvestigation[46–50].
An experimental investigation into an effective relaxation methodforreducingseverestructuraldamageduetopounding was presented by [51]. They found that the force, accelera-tion and velocity produced by earthquake-induced structural poundingare remarkablymitigatedby insertingasoft shock-absorbingmaterialintotheseparationseismicgap.Theeffects of seismic pounding on the response of base-isolated rein-forced concretebuildings under bidirectional excitationwere investigatedby[52].Itwasfoundthatconsidering unidirecti-onalexcitationinsteadofbidirectionalexcitationfornear-fault motionsprovideshighlyunconservativeestimatesof superstruc-turedemands.AslopedV-shapedmulti-rollerisolationsystem wasproposed by [53]andexperimentally verified toprovide poundingpreventionmechanism.
However,none of the above studieshas reduced torsional responsesofisolatedasymmetricstructurestoadegreecloseto itsentireelimination.Thisisbecausetheyalldependonseismic
isolationsystemshavinginherentlydependentbearingand elas-ticstiffnessmechanisms,whichimposesseriouslimitationson tuningtheisolator’selasticstiffnesswithoutaffectingitsbearing anddampingmechanismsinadditiontothedimensionsofthe isolationunitandconsequentlyitsoverallbehavior.Moreover, noneoftheabovementionedstudiesconsideredthepotentialof torsionalpoundingastheresearchinthisareaisstillongoing. Alternatively,thispaperattemptstopresentanothersolutionfor significantlyimprovingtheseismicperformanceofasymmetric seismically-isolatedbuildingsundersevernear-fault(NF) earth-quakesusingtheRoll-in-Cage(RNC)isolator[14,15,50,54–57]. Someofthemostdevastatingearth-quakesarenear-faulttype. Ingeneral,thenear-faultearthquakearenearlythemostsevere anddestructivegroundmotions.Thestudyconsiders minimiz-ing, or even entirely eliminating, the torsional responses of RNC-isolatedasymmetricbuildings,besidespreventionoftheir torsional pounding withadjacentstructuresunder insufficient separation gapswiththesurrounding adjacentstructures.The mainobjectiveofthispaperistheminimization/eliminationof torsionalresponsesofisolatedbuildingsanditseffectontheir torsionalpounding mitigation/eliminationwithcloselyspaced adjacentstructuresundernear-faultearthquakes.
To minimize or preventstructural torsionof RNC-isolated structures,theRNCisolatorhasinherentlyindependentbearing andpre-yield elastic stiffness mechanisms toallowfor accu-rateandpropertuningofitselasticstiffnessasrequiredwithno influenceonitsbearingmechanismnorontheresultingoverall dimensionsandbehavioroftheRNCisolatorunit.To prevent seismicpoundingofRNC-isolatedasymmetricsuperstructure, theRNCisolatorhasaninherentself-stoppingorbuffer mecha-nism,whichisabletodrawdownallthepossiblepoundingofthe superstructuredownwardtobeinsidethesolidbodyoftheRNC isolator.Thisbuffermechanismisactivatedifthepeakbearing displacementexceedsacertaindesigndisplacementpreviously selectedbythestructuraldesigner.Formoreinformationonthe RNCisolatorpleaserefertotheabovereferencesbytheauthors. Allstudiesarecarriedoutusingnonlineartimehistoryanalysis providedbythespecializedcomputercodeSAP2000([58]),as explainedindetailsby[59].Itistobeemphasizedthatpossible frictionalpoundingofasymmetricbuildingswiththeirclosely spacedadjacentstructuresisnotconsideredinthisstudy.The reasonisthattheproposedmethodologyforminimizingoreven eliminatingtorsionaimsatforcingtheasymmetricbuildingto nearlybehaveasasymmetricbuildingexhibitingnotwistaround averticalaxis,whichistheonlysourceoffrictionalpounding. Accordingly,thelikelyfrictionalpoundingisassumed negligi-bleuntilachievingtheobjectivesofthispaperwithoutnegatively influencingitsscope.
4.2. Asymmetricbuildingstructureconsidered
Fixed-base rigid adjacent structure
Gap element Gap element
Gap element Gap element
Gap element
Fixed-base rigid adjacent structure
Rigid adjacent structure
Y X
Rigid adjacent structure
Rigid foundation
Rigid founda tion
RNC-isola ted asy
mmetr ic structure under consider
ation
Figure3.RNC-isolated10-storyasymmetricbuildingpartiallysurroundedwithfixed-baserigidL-shapedadjacentstructure.
Inaddition,suchselectionofthatadjacentstructurerepresents avirtualverticalsurroundinglimitsthatmustnotbeexceeded bytheRNC-isolatedasymmetricstructureunderconsideration inordertoapproacharealistic caseof study inmetropolitan near-faultzones.TheL-shapeoftheadjacentrigidstructure,of the sameheight, ischosen toconsiderpossible simultaneous poundinginXandYdirections.Thestructureisanasymmetric 3Dbuildingof5bays,eachof8.0mspan,withouterend can-tileversof2.5mlengthinbothhorizontaldirections.Ithas10 floorsbesidestheisolatedbasefloorwithatypicalstoryheightof 3.0m.Thehorizontalstructure’seccentricitiesbetweenthe cen-tersofmass(CM)andrigidity(CR)are2.5098mand0.9020m inXandYdirectionsandarereferredtoasexandey, respec-tively.Thoseeccentricitiesareequivalentto12.55%and4.50% ofhalfthein-planstructuraldimensionsinXandYdirections, respectively.Thebaseisolatedbuildingismodeledasashear typestructuresupportedon36heavy-loadRNCisolators,[50], oneundereachcolumn.Eachfloorhastwolateraldisplacement degreesoffreedom(DOF)besideonerotationalDOFaroundthe verticalaxis.Thestructureisexcitedbyuni-andbidirectional horizontalearthquakecomponentsXXandYYdirections.
The superstructure is assumed to remain elastic during the earthquake excitation andimpact phenomenon. The con-struction material of the isolated structure is normal-weight reinforcedconcretewithatotalmaterialvolumeof3738.40m3 andthestructurehasatotalweightof93,460.0kN.The struc-turalfoundationisassumedrigidandsupportedonrockysoil. Thefixed-basestructurehasafundamentalperiodof0.47696s, while the first twentynatural modes of vibration are consid-eredintheanalysis.Thestructuraldampingratioforallmodes isfixedto2.50%of thecriticaldamping,[60,61].The reason of using alow fundamentalperiod inthisstudy isto getthe isolated superstructuremoreaffectedbythe ground accelera-tionsbesidesthe containeddisplacementsandvelocitypulses inthe near-faultground motions. The intention is to investi-gate the proposedRNC isolatorin thesechallenging loading conditions.
Allstudiesarecarriedoutinthispaperusingnonlineartime historyanalysis.Particularly,byusingthemethodoffast nonlin-earanalysisofSAP2000,whichisamodaltimehistoryanalysis basedonload-dependentRitzvectors.Thenumberofstructural vibration modes included inthe analysis are 20 modes.This numberofmodeswasselectedtoachievestaticmodalload par-ticipationratiosof100%inbothXandYdirections,inaddition todynamic modal loadparticipationratios of100%inXand Y directionstoo. Moreover,thisnumberofmodes wasfound necessary to entirelyand properlycapture the localizedhigh frequencyresponsesinthenonlinearlinkelementsdueto seis-micpounding.Table2liststhemaincharacteristicsofthose20 consideredvibrationmodesofthefixed-baseasymmetric struc-ture.Thetableshowsthatthemajorityofthenaturalvibration modes (13 modes out of 20) of the consideredstructure are torsionalmodes.Tomakesurethatthedrawnconclusionsare notbiasedbyanalysisassumptions,somespotresultsarelater checkedusingthetime-consumingdirectintegrationnonlinear timehistoryanalysis.
4.3. PropertiesoftheusedRNCisolators
Several RNC isolators are designed for this study. For example, onedesign is able toaccommodate a traveldesign displacement,xdes,of650mmwithoutlosingitsrestoring capa-bility. Justafterexceedingthatselectedxdes,theself-stopping (buffer)mechanismisdirectlyactivatedtostopmotionovera stoppingdistancexbrake.Thestoppingdistancedependsmainly onpoundingforceintensity,FbB,andtheselectedbuffer stiff-nesskb.That designedRNCisolatorexample is1.35mhigh. Theouterdiameteroftheupperandlowerbearingsteelplates is2.43m.Itisprovidedwith16hystereticmildsteeldampers,
Table2
Maincharacteristicsoftheconsidered20naturalvibrationmodesofthefixed-baseasymmetricstructure.
Mode Period Frequency Circ.freq. Modalparticipationmassratio Remarks
No. (s) (Cyc/s) (rad/s) SumXdir.(unitless) SumYdir.(unitless)
1 0.47696 2.0966 13.173 0.027434 0.378701 Torsionalmode
2 0.419375 2.3845 14.982 0.79579 0.430967
3 0.370151 2.7016 16.975 0.820907 0.830063 Torsionalmode
4 0.17319 5.774 36.279 0.840567 0.863519 Torsionalmode
5 0.166683 5.9994 37.696 0.924516 0.878284
6 0.155804 6.4183 40.328 0.927107 0.929638 Torsionalmode
7 0.106399 9.3986 59.053 0.931865 0.937044 Torsionalmode
8 0.104327 9.5852 60.226 0.959147 0.942289
9 0.10268 9.739 61.192 0.961456 0.960815 Torsionalmode
10 0.080553 12.414 78 0.963858 0.966774 Torsionalmode
11 0.077928 12.832 80.628 0.973382 0.976665
12 0.07683 13.016 81.78 0.981536 0.981107 Torsionalmode
13 0.06406 15.61 98.083 0.982614 0.984939 Torsionalmode
14 0.06302 15.868 99.702 0.98884 0.987604
15 0.062464 16.009 100.59 0.990439 0.990432 Torsionalmode
16 0.052794 18.942 119.01 0.991504 0.992628 Torsionalmode
17 0.052285 19.126 120.17 0.996003 0.994693
18 0.051629 19.369 121.7 0.997019 0.997081 Torsionalmode
19 0.046724 21.402 134.47 0.997047 0.997689 Torsionalmode
20 0.045928 21.773 136.8 0.998772 0.997808
itselfworks as asecondaryverticalsupport inthiscase. The innerandouter diameters of the hollow elastomeric cylinder are1.73mand2.33m,respectively.Thislinearelastomericpart wasinitiallydesignedtofollowsomeavailable recommenda-tionsoftheUniformBuildingCode,[62],andAASHTO,[63], toprovide aminimum verticalloadcapacityof 4000.0kN at theextremedeformedpositionofbufferandtoprovideseveral timesthatcapacityatneutralorlessdeformedpositions.
4.4. Gapelementmodel
The direct seismic pounding of RNC-isolated asymmetric structureandtheinnerpoundingoftheRNCisolatoraremodeled usingaLink/SupportpropertyofSAP2000namedtheGap ele-mentor“compression-only”property.TheGapelementcanbe assignedtoanydeformationaldegreeoffreedomindependently.
Fig.4 demonstratesthemaincomponentsandconnectivityof theGapelementincaseofbeingusedtomodelseismic pound-ingofthesuperstructure,asshowninFig.4(a),andtomodelthe innerpoundingoftheRNCisolator,asshowninFig.4(b).The nonlinearforce-deformationrelationshipoftheGapelementis givenby:
Fpounding=
k
(d+open) if(d+open)<0
0 otherwise (11)
wherek is the spring constant, and“open” is the initial gap opening,whichmustbezeroorpositive.
TheinnerRNC isolator’spounding as wellas theseismic pounding of the RNC-isolated asymmetric structure are sim-ulatedusingthe gapelements.Thegapelementsrepresenting RNCisolatorpoundingarelocatedhorizontallyattheisolation level,whilethosegapelementsrepresentingstructuralpounding areplacedhorizontallyatthetopmostsharededgesandcorners
(a) Stiffness
of adjacent structure
Buffer stiffness
Design displacement
seismic gap Open
Stiffness Open
Adjacent structure Asymmetriic
building
End j of the buffer End i of
the buffer (b)
Figure4.(a)AGapelementtomodelseismicpoundingofsuperstructure;(b) AGapelementtomodeltheRNCisolator’sinnerpounding.
Structural weight Neutral position Structure F
(a) (b) (c)
F F F Structural weight Structural weight Design disp. Design disp. Reaction Design displacement
- Dmax
ke Dy kp ke keff Dy Ke Ke Keff Fy K e Q Kp
Dmaxxb
kB Fb Dy Kp Fy Q Fy Q ke kg keff Pounding peak at the left side
Pounding peak at the right side
Design displacement
Design displacement Design displacement Design displacement
Design displacement
Post-yield stiffness Post-yield stiffness
Post-yield stiffness
Post-yield stiffness
Post-yield stiffness Post-yield stiffness
Pre-yi eld s
tiffn ess Pre-yi eld s tiffn ess Pre-yie ld s
tiffn ess
Pre-yield s tiffn
ess
Pre-yiel d s
tiffne ss
Pre-yield s tiffn ess Effectiv e stiffnes s Effectiv e stiffness Effectiv e stiffnes s Effectiv e stiffness Effectiv e stiffness Effectiv e stiffnes s Reaction Reaction
Neutral position To-the-right maximum deformed position To-the-left maximum deformed position
Corresponding force-displacement relationship to-the-left maximum deformed position
Corresponding force-displacement relationship to-the-right maximum deformed position Corresponding force-displacement relationship
neutral position
Ground
Xdes Xdes
Figure5.TheintegratedbuffermechanismoftheRNCisolatoratdifferentpositionsandthecorrespondingforce–displacementrelationships:(a)to-the-leftmaximum deformedposition;(b)neutralposition;and(c)to-the-rightmaximumdeformedposition.
orcollinearwiththegapelements.Theotherlimitationofthegap elementsliesintheirinabilitytomodeldamping.Therefore, col-lisiondampingwasconservativelyneglectedfromthenumerical simulationmodels,includingstructuralandinnerRNCisolator impactforces.Therefore,theproposedapproachisconservative andisvalidaslongasthecollisiondampingisrelativelysmall andcouldbeignored,aswasassumedinthispaper.Toapproach arigidbehavioroftheRNCisolator’sbuffer,itsbiaxiallateral stiffnessischosen as2.50×106kN/m.Similarly,the bidirec-tionallateralstiffnessoftheadjacentrigidstructureistakenas 2.50×106kN/mforthesamereason.
4.5. RNCisolator’sbuffermechanism
Fig.5 showsaRNCisolatordesign,for light tomoderate weightstructures,atneutralandmaximumdeformedpositions together withthe corresponding force–displacement relation-shipineachcase.Theforce–displacementrelationshipsshown inFig.5areidealizationsofthoseobtainedusingbothnumerical andexperimentalstudies[64].DifferentcomponentsoftheRNC isolatorareconfiguredtoprovideabuilt-inbuffermechanism. The upper andlowerbearing plates haveverticalright angle edge-walls,alongtheirouterperimeters,toconformtotwo cor-respondingright-anglegroovesthatarecutintherollingcore’ solidbody.Bothright-angleedge-wallsandgroovesconstitute astifflockmechanismafteracertaindesigndisplacement,xdes, thatarespecifiedbythestructuraldesigner,asshowninFigs.5(a andc).
The rigid rollingcorecanworkas arigidlink memberin compression between the upper and lower bearing plates to stop the isolator motion at thispoint within a small braking distance.Suchbrakingdistancedependsmainlyontheshock severityandthelateralstiffnessoftheedge-wallsofthe bear-ingplates.Theweightoftheisolatedshearstructureprevents therollingcorefromsteppingovertheverticaledge-walls.The buffermechanismaimsatpreventinguncontrolledisolator dis-placementandtomaintaintheisolatedstructurestabilityunder earthquakes strongerthanadesign earthquake.In addition,it couldbeparticularlyusefulinavoidingdirectpoundingof RNC-isolatedstructureswithsurroundingadjacentstructuresincase oflimitedseismicgapsespeciallyunderseveregroundmotions, whichisthemainobjectiveofthispaper,sincepounding(ifany) willtakeplaceonlywithinthesolidmetallicbodyoftheRNC isolator.
Remaining gap for peak structural drift (RNC des. displacement is consumed) Initial seismic gap
= RNC des. disp. + Peak structural drift
Isolated structure
(b) (a)
After
Excitation
Foundation
Deformed position Neutral position
Adjacent structure Foundation Adjacent structure
Ground motion Isolated structure
Figure6.Mitigationstrategyofdirectstructure-to-structurepoundingusingtheRNCIsolator.
Thefollowedstrategyinthispapertominimizeoreliminate torsional responsesof RNC-isolated asymmetric structuresis explainedindetailsinthecompanionpaper,PartII,whilethe strategyofseismicpoundingeliminationof theRNC-isolated superstructureisschematicallyexplainedinFig.6.According toFig.6,theseismicgapbetweenaRNC-isolatedstructureanda surroundingadjacentstructureischosentobealittlebiggerthan thesumoftheRNCisolator’sdesigndisplacementandthepeak fixed-basestructuraldrift,asshowninFig.6(a).Duringsevere groundshaking,asshowninFig.6(b),thepeakbearing displace-mentislimitedtothepreviouslychosendesigndisplacement, whilethe remainingof the seismicgapcould accountfor the peakstructuraldrift.Sincethereisoftenalimitforseismicgaps, thestructuraldesignercoulddesigntheRNCisolatortoalways preventdirectseismicpoundingoftheRNC-isolated superstruc-turewithcloselyspacedsurroundingadjacentstructuresintwo differentways.Thefirstwayistopermitinnerpoundingofthe RNCisolator(iftheamplifiedstructural responsesduetothat innerpoundingarewithinacceptablelimits),whilethesecond wayistoentirelyavoidtheinnerRNCisolator’spoundingby meansofchoosingmoreappropriatecharacteristicsoftheRNC isolator.
4.6. Equationsofmotion
Thefollowingassumptionsappliestothe structuralsystem underconsideration:(1)thesuperstructureremainswithinthe elasticlimitduringtheearthquakeexcitationandthenon- lin-earity is concentrated only at the isolation elements; (2) the floors are assumed rigid in its own plane; (3) the structural columnsareinextensible verticallyprovidingthe lateral stiff-nessofthestructure;(4)theeffectsofsoil-structureinteraction
areneglected.Theequationsofmotionforfixed-basestructure underearthquakegroundaccelerationareexpressedas
Msx¨s+Csx˙s+Ksxs=−Msrxg,¨ (12) where Ms, Cs and Ks are the mass, damping, and stiffness matricesofthesuperstructure,respectively;xs={x1,x2,..,xN}T, ˙
xs and x¨s the unknown relative floor displacement,
veloc-ity andacceleration vectors,respectively; vector of influence coefficients;x¨gistheearthquakegroundacceleration;andris
thevectorofinfluencecoefficients.
Inthecaseofisolatedstructure,Eq.(12)becomes
Msx¨s+Csx˙s+Ksxs=−Msr(¨xb+xg¨ ), (13)
wherex¨bistherelativeaccelerationofthebasemass.The
corre-spondingequationofmotionforthebasemassunderearthquake groundaccelerationisexpressedby
mbx¨b−c1x˙1−k1x1+ηFb=−mbxg,¨ (14)
wherembandFbarethebasemassandtherestoringforce devel-opedintheisolationsystem,respectively;c1andk1arethefirst storydampingandstiffness,respectively;andηisthenumber ofisolators.Theoverallrestoringforce,Fb,oftheRNCisolator isexpressedasfollows:
Fb=
FbH+FbR if|xb|<xdes
FbH+FbR+FbB if|xb|>xdes
(15)
standard form of the Bouc–Wen model of smooth hysteresis
[65–67]as:
FbH =αkx+(1−α)Dykz, (16)
˙
z=D−y1(Ax˙−β|x˙||z|n−1z−γx˙|z|n), (17)
wherexisthedisplacement,zisanauxiliaryvariable, FbH is theisolatorrestoringforceduetohystereticyielddampers,αkx is theelastic forcecomponent, z˙ denotesthe timederivative, n>1isaparameterthatgovernsthesmoothnessofthetransition fromelastictoplasticresponse(yieldingexponent),Dy>0isthe yieldconstantdisplacementand0<α<1representsthepostto pre-yieldingstiffness ratio (kp/ke),while A,β andγ are non-dimensionalparametersthat governtheshapeandsize ofthe hysteresisloop.
Thetotalrecenteringrestoringforce,FbR,oftheRNCisolator isexpressedmathematicallyas:
FbR=
1 2pJrθ¨r+
1
2mr(¨xr+x¨g)
+ 1
2pWs xb
2 +c
+ 1
2pWrc (18)
wherexr isthe relative-to-ground horizontal displacementof theellipsoidalrollingcore’scenterofgravity;θristherotation angleoftherollingcore;xbisthehorizontaldisplacementofthe isolatororthebasemassrelativetotheground;mr andJr are themassandthemomentofinertiaoftherollingcore;x¨gisthe
groundacceleration;Wsisthestructuralweight;mrandWrare themassandweightoftherollingcore;expressionp=asinθ
sinθr+bcosθcosθr ishalftheverticaldistancebetweenthe loweranduppercontact pointsof therollingcorewithupper andlowerbearingplates,respectively;c=asinθcosθr–bcos
θsin θr ishalfthehorizontaldistancebetweentheupperand lowercontactpoints;aandbarethemajorhorizontalandminor verticalradiiof the ellipsoidalrollingcore;θ isthe eccentric angle.MoreonfullmathematicalmodelingoftheRNCisolator isfoundinRef.[57].
Toexpressmathematicallythethirdcomponentofthe restor-ingforcecausedbybuffer,FbB,twocaseshavetobeconsidered: (1) the isolator, or the isolated base, displacement xb due to groundmotionexcitationislessthanthedesigndisplacement xdes.Inthiscase,therestoringbufferforcecomponentFbBisset tozero;(2)theisolatordisplacementexceedsthepreviouslyset designdisplacementxdes,thebufferrestoringforceFbBbecomes nonzeroandis proportionaltothe bufferstiffness kB andthe amountofxbbeyondxdes.Aforce-basedimpactmodelisused tomodelthe bufferdamping,assuming animpactspring and animpactdamperexerting,inparallel,impactforcestothe col-lidingRNCisolator’selementswheneverthedesigndistances areexceeded.Inparticular,whenacontactisdetected,theRNC isolator’simpactrestoringforcecomponentFbBisestimatedat eachtimestepusingthefollowingformulas:
FbB =
0 if|xb|<xdes
kB(t+t)δ(t)+cBδ˙(t) if|xb|>xdes
(19)
whereδ(t)istheinterpenetrationdepth(xb(t)–xdes), ˙δ(t)isthe relativevelocitybetweenthecollidingbodies,kB isthebuffer spring’sstiffnessandcBisthebufferimpactdampingcoefficient. Thelatteriscomputedaccordingtothefollowingformulas, pro-videdby[31],andbasedontheconservationofenergybefore andafterimpact:
CB=2ξB
kB
m1m2
m1+m2
(20)
ξB=−
In(COR)
π2+(In(COR))2 (21)
wherem1,m2arethemassesofthetwobodies,whicharethe superstructureabovetheRNCisolatorandthefoundation sub-structure belowthe RNCisolator;andCORisthecoefficient ofrestitution,whichisdefinedastheratioofrelativevelocities afterandbeforeimpact(0<COR≤1),[33,68].
4.7. Near-faultearthquakes
Near-fault (NF) earthquakes’ ground motion are charac-terized by one or more intense long-period velocity and displacementpulses thatcanleadtoalargeisolator displace-ment, [69,70]. Therefore, three pairs of NF ground motions havingdifferentintensities,velocityanddisplacementpulsesare consideredtoevaluatethe performanceof theRNCisolator’s self-stopping (buffer)mechanism. These pairs of NF ground motionsareorientedindirectionsnormalandparalleltothefault, wheretheywereobtainedfromthenear-moststationstothetheir fault rupture,withintensitiesthatrange from0.27g to1.23g torepresentrelativelylowtosevereintensityNFearthquakes. Thepeakgroundaccelerations(PGA),velocities(PGV)and dis-placements(PGD)againsttheircorrespondingtimeinstantsof eachgroundmotionarelistedinTable3.Onmeasuringthe inten-sityofNFgroundmotions,[71]revealedthat,thepeakground accelerationisabetterrepresentativeintensitymeasurethanthe peakgroundvelocity.Accordingly,theusedNFgroundmotions aresortedbytheirPGAinanascendingorder.
Another measure of the ground motion characteristics is throughcomparingtheirresponsespectra.Fig.7comparesthe acceleration,velocityanddisplacementresponsespectraofthe used threeNF ground motionsas wellas the meanspectrum ineachcase.Figs.7(aandb)justifytheselectionofan exam-ple structurewithafundamentalperiodless than0.50s.Such selectionproduceshighstructuralresponsesunderthethreeNF earthquakesbecauseofhighspectralaccelerationsand veloci-tieswithin thatzone.Thisprovidesachallengingsituationto examinetheproposedsolutionofresponseimprovementusing theRNCisolator.
In the companion paper, Part II, the dynamic behavior improvement of RNC-isolated asymmetric structures is pre-sented.Detailednumericalresultsareexplainedanddiscussed.
5. Summaryandconclusions
Table3
MaincharacteristicsoftheNFgroundmotionsusedinthisstudy.
No. Earthquakename Tobeappliedindirection Year Stationname Magnitude PeakPGA Accel.(g)time
1 Kobe,Japan0◦ X 1995 Takarazuka 6.90 0.69 6.02
Kobe,Japan90◦ Y 1995 Takarazuka 6.90 0.67 6.16
2 Northridge18◦ X 1994 Sylmar–Conv.SE 6.69 0.83 3.51
Northridge288◦ Y 1994 Sylmar–Conv.SE 6.69 0.49 6.59
3 SanFernando164◦ X 1971 Pacoimadam 6.61 1.23 7.76
SanFernando254◦ Y 1971 Pacoimadam 6.61 1.16 8.53
Elastic response spectra, Acceleration, 2.50% damping
Kobe Northridge
San−Fernando Mean spectrum
Kobe Northridge
San−Fernando Mean spectrum
Kobe Northridge
San−Fernando Mean spectrum
(a)
40
35
30
25
Sa (m/sec
2
)
Sv (m/sec)
Sd (m)
20
15
10
5
0
2.5
2
1.5
1
0.5
0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.5 1 1.5
Period (sec)
Period (sec)
Period (sec)
2 2.5 3 3.5 4
0 0.5 1 1.5 2 2.5 3 3.5 4
0 0.5 1 1.5 2 2.5 3 3.5 4
(b)
(c)
Elastic response spectra,
Velocity, 2.50% damping
Elastic response spectra,
Displacement, 2.50% damping
Figure7.ElasticresponsespectraoftheusedNFgroundmotionsappliedintheXXdirection,whichrepresentthestrongerseismiccomponentsofeachusedNF earthquake.
comparesavailable (most widelyused) seismicisolation sys-tems, highlighting their advantages anddisadvantages. Next, it motivates theneed for continuous improvementof seismic isolation systems to attain (economic) high protection lev-els(againstseismichazards)simultaneouslywithminimizing
ofeliminating,oratleastminimizing,thetorsionalresponsesof isolatedasymmetricstructuresusingtheRNCisolator consid-eringnear-fault(NF)groundmotions.Introductionofsuchcase studyispresentedinthepresentpaper,PartI.
References
[1]G.W.Housner,L.A.Bergman,T.K.Caughey,A.G.Chassiakos,R.O.Claus, S.F.Masri,R.E.Skelton,T.T.Soong,B.F.Spencer,J.T.P.Yao,Structural control:past,present,andfuture,J.Eng.Mech.ASCE123(1997)(Special Issue).
[2]M. Izumi, State-of-the-art report: base isolation and passive seismic responsecontrol,in:IXConferenceonEarthquakeEngineering,vol.8, Tokyo,Japan,1988,pp.385–396.
[3]I.G.Buckle,R.L.Mayes,Seismicisolationhistory:applicationand perfor-mance–aworldreview,Earthq.Spectra6(1990)161–201.
[4]J.M.Kelly, Seismicbaseisolation:reviewandbibliography,SoilDyn. Earthq.Eng.5(1986)202–216.
[5]R.W.DeMontalk.Shockabsorbingorminimizingmeansforbuildings. U.S.PatentNo.1,847,820(NewZealandPatentGranted1929),1932. [6]F.L.Wright,AnAutobiography:FrankLloydWright,HorizonPress,New
York,1977.
[7]C.Arnold,Architecturalconsiderations,in:TheSeismicDesignHandbook, 2nded.,F.Naeim,2001,pp.275–326.
[8]M.S.Caspe,Baseisolationfromearthquakehazards:andideawhosetime hascome,in:VIIIWorldConferenceonEarthquakeEngineering, San Fransisco,CA,1984.
[9]D.Jurukovski,Z.Rakicevic,Vibrationbaseisolationdevelopmentand application,in:TenthEuropeanConferenceonEarthquakeEngineering, Dumaed.,Balkema,Rotterdam,1995,pp.667–676.
[10]W.H.Robinson,A.G.Tucker,Alead-rubbersheardamper,Bull.N.Z.Natl. Soc.Earthq.Engl.Natl.Soc.Earthq.Eng.10(3)(1977)151–153. [11]W.H.Robinson,A.G.Tucker,Testresultsforlead-rubberbearingsforthe
WilliamM.Claytonbuilding,toetoebridge,andwaiotukupunabridge, Bull.N.Z.Natl.Soc.Eng.14(1)(1983)21–33.
[12]R.G.Tyler,W.H.Robinson,High-straintestsonlead-rubberbearingsfor earthquakeloadings,Bull.N.Z.Natl.Soc.Earthq.Eng.17(1984)90–105. [13]C.J.Derham,J.M.Kelly,A.G.Tomas,Nonlinearnaturalrubberbearings
forseismicisolation,Nucl.Eng.Des.84(3)(1985)417–428.
[14]M. Ismail, An Innovative Isolation Device for Aseismic Design. PhD thesis. Doctoralprogram, Earthquake Engineering andStructural Dynamics, Technical UniversityofCatalonia,Barcelona, Spain, 2009, http://www.tdx.cat/handle/10803/6265(accessed10.10.09).
[15]M.Ismail, J.Rodellar,F.Ikhouane, Method for theseismicisolation ofasupportedobject.Patentsno.WO2010000897A1,ES20080002043, P200802043,PCT/ES2009/000351,SpanishOfficeofPatentsandMarks, 2008.
[16]A.Tena-Colunga,J.L.Escamilla-Cruz,Torsionalamplificationsin asym-metricbase-isolatedstructures,Eng.Struct.29(2)(2007)237–247. [17]A. Tena-Colunga,.L.A. Gómez-Soberón, Torsional response of
base-isolatedstructuresduetoasymmetriesinthesuperstructure,Eng.Struct. 24(12)(2002)1587–1599.
[18]A.Tena-Colunga,C.Zambrana-Rojas,Dynamictorsionalamplifications ofbaseisolatedstructureswitheccentricisolationsystem,Eng.Struct.28 (1)(2006)72–83.
[19]J.M.Kelly,EarthquakeResistantDesignwithRubber,Springer,London, 1993.
[20]D.M.Lee,Baseisolationfortorsionalreductioninasymmetricstructures underearthquakeloading,Earthq.Eng.Struct.Dyn.8(1980)349–359. [21]T.C.Pan,J.M.Kelly,Seismicresponseoftorsionallycoupledbaseisolated
structures,Earthq.Eng.Struct.Dyn.11(1983)749–770.
[22]R.K. Goel, A.K. Chopra, Inelastic seismic response of one-story asymmetric-plan systems: effect of stiffnessand strength distribution, Earthq.Eng.Struct.Dyn.19(1990)949–970.
[23]S.Nagarajaiah,A.M.Reinhorn,M.C.Constantinou,Torsionalcouplingin slidingbaseisolatedstructures,J.Struct.Eng.119(1993)130–149.
[24]R.S.Jangid,T.K.Datta,Nonlinearresponseoftorsionallycoupledbase isolatedstructure,J.Struct.Eng.120(1994)1–22.
[25]M.Eisenberger,A.Rutenberg,Seismicbaseisolationofasymmetricshear buildings,Eng.Struct.8(1)(1986)2–8.
[26]C.E.Según,H.C.DelaLlera,J.L.Almánza,Base–structureinteractionof linearlyisolatedstructureswithlateral-torsionalcoupling,Eng.Struct.30 (1)(2008)110–125.
[27]E.Rosenblueth,R.Meli,The1985Earthquake:CausesandEffectsin MexicoCity,Vol.8(5),ConcreteInternational,AmericanConcrete Insti-tute,1986,pp.23–24.
[28]S.A.Anagnostopoulos,C.E.Karamaneas,Collisionshearwallsto mit-igate seismic pounding of adjacent buildings, in: The 14th World ConferenceonEarthquakeEngineering,October12–17,Beijing,China, 2008.
[29]K.Kasai,B.F.Maison,Buildingpoundingdamageduringthe1989loma prietaearthquake,Eng.Struct.19(3)(1997)195–207.
[30]S.A.Anagnostopoulos,K.V.Spiliopoulos,Aninvestigationofearthquake inducedpoundingbetweenadjacentbuildings,Earthq.Eng.Struct.Dyn. 21(1992)289–302.
[31]S.A.Anagnostopoulos,Poundingofbuildingsinseriesduringearthquakes, Earthq.Eng.Struct.Dyn.16(1988)443–456.
[32]K.Kasai,A.R.Jagiasi,V.Jeng,Inelasticvibrationphasetheoryforseismic poundingmitigation,J.Struct.Eng.ASCE122(1996)1136–1146. [33]V.K.Agarwal,J.M.Niedzwecki,J.W.VandeLindt,Earthquakeinduced
poundinginfrictionvaryingbaseisolatedbuildings,Eng.Struct.29(2007) 2825–2832.
[34]B.D.Westermo,Thedynamicsofinter-structuralconnectiontoprevent pounding,Earthq.Eng.Struct.Dyn.18(1989)687–699.
[35]R.Jankowski,K.Wilde,Y.Fujino,Poundingofsuperstructuresegments inisolatedelevatedbridgeduringearthquakes,Earthq.Eng.Struct.Dyn. 27(1998)487–502.
[36]J.Penzien,Evaluationofbuildingseparationdistancerequiredtoprevent poundingduringstrongearthquakes,Earthq.Eng.Struct.Dyn.26(1997) 849–858.
[37]A.Filiatrault,M.Cervantes,Separationbetweenbuildingstoavoid pound-ingduringearth-quakes,Can.J.CivilEng.22(1995)164–179. [38]S.Mahmoud,A.Abd-Elhamed,R.Jankowski,Earthquake-induced
pound-ingbetweenequalheightmulti-storeybuildingsconsideringsoil–structure interaction,Bull.Earthq.Eng.11(2013)1021–1048.
[39]R.O.Davis,Poundingofbuildingsmodeledbyanimpactoscillator,Earthq. Eng.Struct.Dyn.21(1992)253–274.
[40]H.S.Jing,M.H.Young,Randomresponseofasingle-degree-of-freedom vibro-impactsystemwithclearance,Earthq.Eng.Struct.Dyn.19(1990) 789–798.
[41]G.D.Hahn,M.C.Valenti,Correlationofseismicresponsesofstructures, J.Struct.Eng.ASCE123(1997)405–413.
[42]J.P.Wolf,P.E.Skrikerud,Mutualpoundingofadjacentstructuresduring earthquakes,Nucl.Eng.Des.57(1980)253–275.
[43]M.Papadrakakis,C.Apostolopoulou,A.Zacharopoulos,S.Bitzarakis, Three-dimensionalsimulationofstructuralpoundingduringearthquakes, J.Eng.Mech.ASCE122(1996)423–431.
[44]R.Jankowski,Non-linearviscoelasticmodellingofearthquake-induced structuralpounding,Earthq.Eng.Struct.Dyn.34(2005)595–611. [45]S.Muthukumar,R.DesRoches,Ahertzcontactmodelwithnon-linear
dampingforpoundingsimulation,Earthq.Eng.Struct.Dyn.35(2006) 811–828.
[46]P.Komodromos,Simulationoftheearthquake-inducedpoundingof seis-micallyisolatedbuildings,Comput.Struct.86(2008)618–626. [47]R.Jankowski,NonlinearFEManalysisofpounding-involvedresponseof
buildingsundernon-uniformearthquakeexcitation,Eng.Struct.37(2012) 99–105.
[48]D.R.Pant,A.C.Wijeyewickrema,Structuralperformanceofabase-isolated reinforcedconcretebuildingsubjectedtoseismicpounding,Earthq.Eng. Struct.Dyn.41(2012)1709–1716.
[50]M.Ismail,J.R.Casas,Evaluationandrefinementofclosely-spaced build-ings’performanceundernear-fault groundmotions,Struct.Infrastruct. Eng.(2015,January),http://dx.doi.org/10.1080/15732479.2014.993660. [51]H.Takabatake,M.Yasui,Y.Nakagawa,A.Kishida,Relaxationmethod
forpoundingactionbetweenadjacentbuildingsatexpansionjoint,Earthq. Eng.Struct.Dyn.43(2014)1381–1400.
[52]D.R.Pant,A.C.Wijeyewickrema,Performanceofbase-isolatedreinforced concrete buildings under bidirectional seismic excitation considering pounding with retainingwalls including friction effects,Earthq. Eng. Struct.Dyn.43(2014)1521–1541.
[53]S.J.Wang,J.S.Hwang,K.C.Chang,C.Y.Shiau,W.C.Lin,M.S.Tsai, J.X.Hong,Y.H.Yang,Slopedmulti-rollerisolationdevicesforseismic protectionofequipmentandfacilities,Earthq.Eng.Struct.Dyn.43(2014) 1443–1461.
[54]M. Ismail, J. Rodellar, F. Ikhouane, An innovative isolation bear-ing for motion-sensitive equipment, J. Sound Vib. 326 (3–5) (2009) 503–521.
[55]M.Ismail,J.Rodellar,F.Ikhouane, Aninnovativeisolationdevicefor aseismicdesign,J.Eng.Struct.32(2010)1168–1183.
[56]M.Ismail,J.Rodellar,F.Ikhouane,Performanceofstructure-equipment systemswithanovelroll-n-cage isolationbearing,Comput.Struct.87 (2009)1631–1646.
[57]M.Ismail,J.R.Casas,J.Rodellar,Near-faultisolation ofcable-stayed bridgesusingRNCisolator,Eng.Struct.56(2013)327–342.
[58]SAP,SAP2000release16documentation,ComputersandStructuresInc., Berkeley,CA,2013.
[59]M.Ismail,F.López-Almansa,A.Benavent-Climent,L.G.Pujades-Beneit, Finiteelementcode-basedmodellingofamulti-featureisolationsystem andpassivealleviationofpossibleinnerpounding,Int.J.Adv.Struct.Eng. 6(3)(2014)1–23.
[60]D.R.Pant,A.C.Wijeyewickrema,M.A.ElGawady,Appropriateviscous dampingfornonlineartime-history analysisofbase-isolatedreinforced concretebuildings,Earthq.Eng.Struct.Dyn.42(2013)2321–2339. [61]J.Scheller,M.C.Constantinou,Responsehistoryanalysisofstructureswith
seismicisolationandenergydissipationsystems:verificationexamples forprogramsap2000.TechnicalReport,Buffalo,NewYork, MCEER-99-0002,1999,pp.14260–14300.
[62]UBC,Uniformbuildingcode,in:InternationalConferenceofBuilding Officials,California,USA,1997.
[63]AASHTOLRFD,BridgeDesignSpecifications,SIUnits,thirded., Amer-icanAssociationofStateHighwayandTransportationOfficials,2005. [64]M.Ismail,Anisolationsystemforlimitedseismicgapsinnear-faultzones,
Earthq.Eng.Struct.Dyn.44(7)(2015)1115-1137.
[65]Y.K.Wen,Methodforrandomvibrationofhystereticsystems,J.Eng. Mech.Div.102(EM2)(1976)246–263.
[66]F.Ikhouane,V.Ma˜nosa,J.Rodellar,Dynamicpropertiesofthehysteretic Bouc-Wenmodel,Syst.ControlLett.56(2007)197–205.
[67]M.Ismail,F.Ikhouane,J.Rodellar,ThehysteresisBouc-Wenmodel,a survey,J.Arch.Comput.MethodsEng.16(2009)161–188.
[68]P.Komodromos,P.C.Polycarpou,L.Papaloizou,M.C.Phocas,Responseof seismicallyisolatedbuildingsconsideringpoundings,Earthq.Eng.Struct. Dyn.36(2007)1605–1622.
[69]R.S.Jangid,J.M.Kelly,Baseisolationfornear-faultmotions,Earthq.Eng. Struct.Dyn.30(2001)691–707.
[70]D. Murat, B. Srikanth, Equivalent linear analysisof seismic-isolated bridgessubjectedtonear-faultgroundmotionswithforwardrupture direc-tivityeffect,Eng.Struct.29(2007)21–32.
