=

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SWrucWural Analysis of HisWorical ConsWrucWions – Jerzy Jasieńko (ed) © 2012 DPNH ProcławH PolandH ISSN 0860-2395H ISBN 978-83-7125-216-7

NlNifNbAo ANAivpfp lc A TAii efpTlofCAi MAplNov Tltbo =a’Ambrisi=AngeloNI=jariani=salentinaOI=jezzi=jarcoP=

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ABpToACT qhis=paper=deals=with=the=nçnlinear= mçdeling=and= the=pushçver=analysis=çf= the=dhirlandina= tçwer= çf=jçdenaI= aimed= at= the= vulnerability= assessment= çf= the= structure= that= represents= çne= çf= the= mçst=impçrtant=tçwers=in=ftalyK=A=Pa=finite=element=mçdel=çf=the=structure=has=been=set=upI=calibrated=çn=the=available= results= çf= an= experimental= campaignK= qhe= nçnlinear= behaviçur= çf= the= masçnry= has= been=simulated=accçrding=tç= the= tçtal= strain=rçtating=crack=mçdel= with=elasticJperfectJplastic=behaviçur= in=cçmpressiçn= and= linear= sçftening= in= tensiçnK= qhe= sçilJstructure= interactiçn= has= been= alsç= mçdelled=thrçugh= springs= and= dashpçts= whçse= stiffness= and= damping= have= been= evaluated= accçrding= tç= the=theçry=çf= impedances=by=dazetas= xNzK=qhe=seismic=vulnerability=assessment= çf=the=structure=has=been=carried=çn=by=means=çf=pushçver=analysisI=accçrding=tç=the=current=ftalian=standards=and=tç=predefined=cçllapse=criteriaK=qhe=perfçrmed=analysis= investigated= the=effect=çf= the=sçil=mçdelling= in= the=seismic=behaviçur= çf= the= tçwer= and= pçinted= çut= hçw= the= current= ftalian= cçdes= çverestimate= the= dissipative=capacity= çf= this= kind= çf= structures= in= terms= çf= excessively= high= values= çf= the= behaviçur= factçr= qK=jçreçver=the=implementatiçn=çf=the=material=nçnlinearity=allçwed=tç=evaluate=the=damage=levels=and=the=cçllapse=mechanisms=çf=the=structure=under=seismic=actiçnsK===heywords:= eistorical=masonry=towerI=konlinear=analysisI=peismic=assessment===N. fNTolarCTflN =fn =the =last =decadesI =the =interest =çf =scientific =cçmmunity =fçr =the =preservatiçn =çf =histçrical =and =architectural= heritage= has= grçwn= significantlyK= jçst= çf= histçrical= cçnstructiçns= cçnsist= çf= masçnry=structures= and= are= çften= lçcated= in= earthquake= prçne= sitesK= qherefçre= the= seismic= assessment= and=retrçfit=çf=such=buildings=has=became=çne=çf=the=main=tçpics=çf=interest=in=the=wçrld=çf=cçnstructiçnsK=qhis= issue= implies= several= difficultiesK= qhis= is= firstly= due= tç= the= wide= variety= çf= structural= fçrms=characterizing=the=mçnumental=buildings=and=the=different=materials=that=can=be=fçund=alçng=centuries=çf= histçry= çf= human=civilizatiçnK= jçreçver= these=cçnstructiçns= were=usually=cçnceived= accçrding= tç=the=rules=çf=thumbI=mçstly=based=çn=the=effect=çf=gravity=lçads=and=did=nçt=prçvide=fçr=adequate=lateral=resistance=and=ductilityK==Amçng=the=different=structural=typçlçgies=characterizing=the=architectural=heritageI=masçnry=highJrise=structures=are=very=widespread=all=çver=the=wçrld=and=especially=in=burçpeK=fn=the=last=decade=many=çf=them=have=been= the=çbject=çf= investigatiçns=and=analysis= xOJ4zK= fn=this= framewçrkI= the=present=paper=deals= with= the= nçnlinear= analysis= çf= the= dhirlandina= tçwer= çf= jçdenaI= çne= çf= the= mçst= famçus=histçrical= masçnry= tçwers= in= ftalyK= A= nçnlinear= finite= element= mçdel= çf= the= tçwer= has= been= set= upI=including= the= effect= çf= the= adjacent= cathedral= and= the= sçilJstructure= interactiçnK= A= nçnlinear= static=analysis=has=been=carried=çut=aimed=at=the=seismic=vulnerability=assessment=çf=the=structureI=accçrding=tç=the=prescriptiçns=çf=the=current=ftalian=Building=Cçde=EkqCF=xRz=and=tç=the=ftalian=guidelines=fçr=the=seismic=assessment=çf=histçrical=cçnstructiçns=xSzK===

================================================N=mrçfessçrI=rniversity=çf=clçrenceI=aepartment=çf=Cçnstructiçns=and=oestçratiçnI=angelçKdambrisi]unifiKit=O=mhaI=rniversity=çf=clçrenceI=aepartment=çf=Cçnstructiçns=and=oestçratiçnI=valentinaKmariani]unifiKit==P=mrçfessçrI=rniversity=çf=merugiaI=aepartment=çf=Civil=and=bnvirçnmental=bngineeringI=mKmezzi]unipgKit=

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qhe=dhirlandina= tçwer= is= a= relevant= histçrical= masçnry=cçnstructiçnI= symbçl= çf= the=city=çf= jçdenaK=qhe=tçwer=is=part=çf=a=grçup=çf=buildingsI=tçgether=with=the=Cathedral=and=the=qçwn=eallI=that=are=çf=great =histçrical =and =artistic =significanceI =inscribed =since =NVVT =in =the =rnescç’s =tçrld =eeritage =iistK =qhe=building=çf= the=dhirlandina= started= in=NMVVI= tçgether= with= the=cathedralI= and= invçlved=different=cçnstructiçn=phasesK=After=an=accurate=analysis=çf=all=the=histçrical=dçcumentsI=Cadignani=xTz=identified=five=main=cçnstructiçn=phasesI=that=develçped=until=NPNVI=finally=leading=tç=the=present=appearance=çf=the=tçwer=Ecigure=NaFK==qhe=tçwer=is =featured=by=a =square=part =RM=m=highI =with=a =sectiçn=çf =NMKT=m=sideK =qhe=external =walls =have=a=thickness=varying=frçm=abçut=O=m=at= the=base=tç=NKO=m=at= the=tçpK=peveral=levels=çf=mulliçned=windçws=characterize=the=façadesK=Abçve=the=square=part=there=is=an=çctagçnal=part=with=a=thickness=çf=MKU=mI=tçpped=by=a=high=cuspK=qhe=tçtal=height=çf=the=tçwer=is=US=mK=cçur=pillars=rise=up=in=the=inner=cçrners=çf=the=tçwerI=suppçrting=bçth=the=grçin=vaults=and=the=stairs=that=lead=up=tç=the=tçpK=qwç= masçnry= arches= çn= the= sçuthern= side= çf= the= tçwer= cçnnect= the= tçwer= tç= the= cathedralK=keverthelessI=the=interactiçn=between=the=twç=cçnstructiçns=is=mainly=due=tç=the=settlements=that=cause=the=tçwer=tç=tilt= tçwards=the=cathedralK=fndeed=the=tçwer=has=been=affected=by=fçundatiçn=settlements=since=his= early=cçnstructiçnI= that=cause=the=suspensiçn=çf= the=wçrk=after= the=first= cçnstructiçn=phaseK=cçr= this= reasçnI= during= a= campaign= çf= restçring= interventiçnsI= geçlçgical= studies= and= tests= çn= the=fçundatiçn= sçil= have= been= carried= çut= xTzK= jçreçverI= sçme= samples= çf= brick= and= mçrtar= have= been=extracted= and= tested= in= labçratçry= tç= evaluate= the= mechanical= prçperties= çf= the= materialsK= All= these=results=have=been=used=in=the=present=paper=fçr=the=evaluatiçn=çf=the=sçilJstructure=interactiçnI=and=fçr=the=mçdeling=çf=the=nçnlinear=behaviçur=çf=the=masçnryK=

P. cfNfTb bibMbNT Mlabi ANa mobifMfNAov ANAivpbp =P.N. Modeling aspects A=Pa=finite=element=mçdel=çf=the=tçwer=Ecigure=NbF=has=been=built=up=using=the=sçftware=aiana=VKO=xUzK=qhe=geçmetry=çf=the=structure=has=been=accurately=reprçduced=using=Pa=brick=elements=fçr=the=square=bçdy=çf=the=tçwer=and=flat=shell=elements=fçr=the=upper=çctagçnal=part=and=fçr=the=cuspK=qhe=fçur=inner===

===================

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masçnry=vault=

masçnry=vault=

inner=cçrner=pillar=

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== = = =======EaF== = = = ============EbF=

cig. N=EaF=pçuthJbast=view=çf=the=dhirlandina=tçwerK=EbF=bxplçded=sectiçn=çf=the=Pa=finite=element=mçdel=shçwing=the=main=cçnstituent=elements=

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pillars=have=been=mçdelled=taking=alsç=intç=accçunt=the=hçles=where=the=stairs=run=tç=reach=the=tçp=çf=the=tçwerK=Alsç=the=masçnry=vaults=have=been=reprçduced=with=sçlid=çr=flat=shell=elementsK==qhe= tçwerJcathedral= interactiçn= has= been= mçdelled= thrçugh= interface= elements= characterized= by=a=nçnlinear= elastic=behaviçurI= stiff= in=cçmpressiçn=and=weak=in=tensiçnK=qhe=axial=stiffness=has=been=estimated=thrçugh=a=lçcal=mçdel=representing=çne=çf=the=twç=masçnry=walls=cçnnecting=the=tçwer=tç=the=cathedral=and=a=pçrtiçn=çf=the=çrthçgçnal=wall=çf=the=cathedralK=qhe=effect=çf=the=walls=in=the=tangential=directiçn=has=been=neglectedI=assuming=a=tangential=stiffness=equal=tç=zerçK==PKNKNK jaterial=nonlinear=modeling qhe= nçnlinear= behaviçur= çf= the= masçnry= material= has= been= defined= accçrding= tç= the= qçtal= ptrain=oçtating=Crack=jçdel=xVzI=with=elastic=perfect=plastic=behaviçur=in=cçmpressiçn=and=linear=sçftening=in=tensiçnK=A=cçmpressive=strength=equal=tç=PKO=jma=has=been=assumedK=qhis=value=is=equal=tç=the=average=çf=the=range=suggested=by=the=kqC=xSzI=and=is=alsç=cçnsistent=with=the=average=value=çbtained=frçm=the=experimental=tests=çn=the=extracted=samples=xTzK=qhe=tensile=strength=has=been=assumed=equal=tç=NMB=çf=the=cçmpressive=çneK=A=maximum=cçmpressive=strain=çf=PKR‰=and=an=ultimate=cracking=strain= crk

ulte =çf=N‰=have=been=assumedK===PKNK2K poilJstructure=interaction qhe=study=çf= the=sçilJstructure=interactiçn=has=been=a= keyJaspect= in=the=mçdeling=çf= the=dhirlandina=tçwerI=because=çf=the=settlements=prçblem=affecting=the=tçwer=since=its=cçnstructiçnK=qhe=evaluatiçn=çf=the=sçilJstructure= interactiçn=has=been=carried=çut= accçrding= tç= the= theçry=çf= impedances=by=dazetas=xNzK=qhe=impedance=is=defined=by=the=expressiçnW=== = Cihp w+= = ENF==where= h =is=the=dynamic=stiffnessI=that=describes=the=stiffness=and=inertia=çf=the=suppçrting=sçilI=and=== b

wh2CC r += == EOF=

=is= the= damping= cçefficientI= that= describes= the= damping= generated= in= the= systemI= due= tç= hysteretic=energy=dissipatiçn=in=the=sçil=Eexpressed=by=the=damping=cçefficient=βF=and=energy=prçpagatiçn=thrçugh=waves= spreading=away=frçm=the=fçundatiçn= ECrFK=qhis= apprçach=suggests= tç=mçdel=the=sçilJstructure=interactiçn= by= suppçrting= the= fçundatiçn= with= a= spring= and= a= dashpçt= characterized= by= the=afçrementiçned=parameters= h =and=CK=tith=the=aim=çf= submitting=the=structure=tç=a=nçnlinear= static=analysis=çnly=the=stiffness=values=have=been=assumedK=fn=the=present=caseI=three=values=çf=stiffness=have=been=cçnsideredI=related=tç=translatiçn=in=the=vertical=directiçnI=rçtatiçn=arçund=x=and=y=directiçnK==qhe=evaluatiçn=çf= the=stiffness= vectçr= is= carried=çut= by=means=çf= tables=and=graphs= xNz= invçlving= the=geçmetry= çf= the= sçilJfçundatiçn= interfaceI= the= features= çf= the= sçil= prçfile= and= the= geçtechnical=characteristics= Eshear= mçdulus= dI= shear= wave=velçcity=ss= and=mçissçn=cçefficient= υF=and=the=angular=frequency=ω=2π·f=I=where=f=is=the=frequency=çf=the=exciting=actiçnI=eKgK=çne=çf=the=main=frequencies=çf=the= design= seismic= actiçnK= cinallyI= the= values= çf= axial= stiffness= zh = and= rçtatiçnal= stiffness=

jh respectively=equal=tç=OKTR·NMV=k·mJN=and=NKR·NMNN=k·m=have=been=assumedK==P.O. mreliminary modal and dead load analyses qhe=first=step=in=the=structural=analysis=çf=the=masçnry=tçwer=has=been=the=running=çf=a=mçdal=analysisK=cigure =O =shçws =the =first =six =eigenmçdes =çf =the =structureK =qhe =first =twç =frequencies =are =quite =clçse =because= çf= the= substantial= symmetry= çf= the= structureK= qhe= first= mçde= is= in= u= directiçn= because= the=behaviçur=in=v=directiçn=is=affected=by=the=presence=çf=the=interactiçn=with=the=cathedralI=which=makes=the=structure=slightly=stiffer=in=that=directiçnK==Befçre= perfçrming= the= seismic= analysisI= a= preliminary= dead= lçad= analysis= has= been= carried= çutI= tç=check=the=stress=levels=çf=the=tçwer=subjected=çnly=tç=self=weightK=qhe=vertical=stresses=at=the=base=çf=the= tçwer= reach= values= ranging= frçm= MKU= tç= NKN= jmaI= that= is= arçund= ORJPRB= çf= the= cçmpressive=strengthK=pçme=few=cracks=already=çccurredI=in=the=keystçne=çf=the=windçwsI=in=the=cçnnectiçn=çf=the=vaults=with=the=masçnry=walls=and=at=the=baseI=in=cçrrespçndence=çf=the=main=entranceK=

=

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4. pbfpMfC ANAivpfp =4.N. aefinition of collapse criteria=peveral=failure=criteria=have=been=defined=tç=identify=the=cçllapse=limit=state=fçr=the=structureI=each=çne=cçnsidering= a= different= cçntrçl= parameterK= qhe= failure= criteria= can= be= grçuped= in= twç= different=apprçachesI=described=in=the=fçllçwing=sectiçnsK==

========jlab=N==============jlab=O= =jlab=P============jlab=4= jlab=R=============jlab=S=============fN===MK4MS=sJN=========fO===MK4O4=sJN=========fP===NKP4=sJN========f4===NKPT=sJN===========fR===OKPS=sJN=========fS===OKSM=sJN=

cig. O=cirst=six=mçdal=shapes=and=frequencies=çf=the=tçwer==

4KNKNK fdentification=of=a=progressive=collapse=mechanism=A=cçllapse=mechanism=is=activated=when=the=çnset=çf=sçme=crackedLcrushed=parts=çf=masçnry=entails=the=divisiçn=çf=the=structure=Eçr=part=çf=itF=in=several=macrçJblçcks=that=rçtate=rigidlyK=oeferring=tç=the=specific=analyzed=caseI=the=fçllçwing=mechanisms=can=be=addressed=tç=the=present=apprçachW=- Criteriçn=NAK=ft=cçnsiders=a=mechanism=due=tç=excessive=drift=çf=the=pillars=separating=the=mulliçned=

windçwsK= then= the= structure= undergçes= lateral= fçrcesI= the= pillars= separating= the= mulliçned=windçws=are=subjected= tç= lateral= drift= that= results= in=a=bending=mçment= at= the= ends= çf= the=pillarK=jçreçver= these=bending=mçments=are= increased=by= the=mJdelta= effect=assçciated= tç= the=driftK= qhis=phençmençn=invçlves=the=fçrmatiçn=çf=hinges=at=the=ends=çf=the=pillars=and=leads=tç=cçllapse=fçr=the=drift=duIbend=Ecigure=PaFK=An=excessive=value=çf=drift=can=alsç=lead=the=pillars=tç=cçllapse=fçr=lçss=çf=stabilityK=qhis=cçnditiçn=çccurs=when=the=axial=lçad=çn=tçp=çf=the=pillars=is=nç=lçnger=centered=but=mçves=sideways=until=reaching=the=çverturning=çf=the=pillarsK=qhe=cçllapse=fçr=lçss=çf=stability=arises=when=the=axial=lçad=falls=çutside=the=base=sectiçnI=that=is=fçr=a=drift=duIlost===NMM=mmI=equal=tç=half=the=sectiçn=çf=the=pillarsI=as=shçwn=in=cigure=PbK=

- Criteriçn= NBW= ft= cçnsiders= a= mechanism= due= tç= excessive= drift= çf= the= interstçrey= between= the=mulliçned= windçwsK= qhis= criteriçn= is= based= çn= the= prescriptiçns= cçncerning= the= maximum=interstçrey=driftK=qhe=kqC=xRz=suggests=a=limit=value=Δdmax===MKSB=assçciated=tç=the=life=safety=limit=state= and= this= value= is= net= çf= the= displacement= due= tç= rigid= rçtatiçn= çf= the= masçnry= elementK=jçreçver= the= kqC= allçws= fçr= an= increase= çf= NMMB= in= presence= çf= sçme= particular= layçutI= eKgK=cantilever=cçnfiguratiçnK=fn=the=present=case=the=drift= is=nçt=related=tç=the=defçrmability=çf=a=wallI=but=tç=that=çf=a=sçrt=çf=frame=system=made=çf=masçnry=pillars=and=beamsK=jçreçver=the=defçrmatiçn=is=alsç=affected=by=rigid=cçntributiçnsK=Cçnsidering=all=these=aspectsI=a=final=limit=value Δdmax===OB=assçciated=tç=the=ultimate=limit=state=EripF=has=been=assumedK=cigure=Pc=shçws=the=values=çf=limit=interstçrey=drift=Δdmax=in=cçrrespçndence=çf=the=different=levels=çf=mulliçned=windçwsI=identified=by=the=abbreviatiçns=e4LePI=ePLe2I=e2LeN=and=eNLeMK=

=4KNK2K fdentification=of=stressLstrain=limit=values=qhis=type=çf=criteria=is=related=tç=the=definitiçn=çf=limit=values=fçr=stresses=and=strainsK=qhe=stress=limit=value=is=set=up=by=the=cçnstitutive=lawI=bçth=in=tensiçn=and=in=cçmpressiçnK=An=additiçnal=limit=has=tç=be=impçsed=tç=the=strain=valuesK=ClearlyI=this=type=çf=criteria=can=nçt=be=strictly=related=tç=the=attainment=çf=the=limit=strain=in=a=single=integratiçn=pçint=in=the=finite=element=mçdelK=qhe=cçllapse=limit=state=has=tç= be= defined= criticallyI= taking= intç= accçunt= the= extensiçn= çf= damageK= oeferring= tç= tensiçn= and=cçmpressiçn=respectivelyI=the=fçllçwing=twç=criteria=have=been=assumedW=

=

N4SN=

- Criteriçn=OAK=ft=limits=the=value=çf=cracking=strainK=Accçrding=tç=the=prescribed=stressJstrain=relatiçn=fçr=the=masçnry=materialI=the=pçst=peak=behaviçur=implies=a=linear=sçftening=branch=in=tensiçnK=qhe=assumptiçn=çf=the=ultimate=strain=çf=the=tensile=sçftening=curve=as=limit=value=fçr=the=cçllapse=limit=state=is=nçt=reasçnable=becauseI=especially=in=the=analysis=çf=largeJscale=structuresI=crack=strains=can=reach=pçsitiçns=far=beyçnd=that=valueI=as=pçinted=çut=by=oçts=and=fnvernizzi=xNMzK=qhe=definitiçn=çf=a=limit=value=fçr=the=cracking=strain= crke =can=be=deduced=frçm=the=prescriptiçn=çf=a=maximum=value=fçr= the= crack= width= wK =qhe =twç =parameters =are =cçnnected =by =the =crack=bandwidth=h= thrçugh= the=fçllçwing=relatiçnW=

=

= hw crk ×= e = E4F==

qhe =value =çf =the =crack =width =tç =identify =the =cçllapse =limit =state =fçr =the =structure =has =been =cçnventiçnally=assumed=equal=tç=wmax===RM=mmK=pince=h=is=equal=çn=average=tç=RMM=mm=the=relatiçn=abçve=led=tç=a=maximum=cracking=strain=çf=NMBK==

=cig. P=iimit=value=çf=drift=assçciated=tç=cçllapse=fçrW=EaF=fçrmatiçn=çf=hinges=at=the=ends=çf=the=pillarsX=EbF=lçss=çf=

stabilityX=EcF=bvaluatiçn=çf=the=interstçrey=drifts=fçr=the=different=levels=çf=the=mulliçned=windçws==Criteriçn=OBK=ft= limits= the=value=çf=crushing=strainK=kç= limitatiçn=tç=the=cçmpressive=strain=has=been=impçsed=within=the=mçdel= in=the=perfçrmed=analysesK=qherefçre=the=cçmpatibility=çf=the=strain=levels=has=been=verified=a=posterioriI= assuming=an=ultimate=cçmpressive=strain=equal= tç=PKR‰K=Cçnsidering=that=the=strain=cçrrespçnding=tç=the=attainment=çf=the=cçmpressive=strength=is=equal=tç=εy

crs===OKN‰I=the=criteriçn=implies=a=limit=crushing=strain=çfW= == ‰4KNJ‰RKP crs

ymax == ee crs == ESF==

4.O. Nonlinear static analysis=qhe= nçnlinear= static= EkipF= analysis= has= been= perfçrmed= applying= incremental= lateral= fçrcesI=prçpçrtiçnal= tç= the= masses= and= the= nçrmalized= mçdal= shapeI= each= time= in= çne= çf= the= fçur= principal=directiçns=uHI=vHI=uJI=vJK=qhe=perfçrmed=analyses=pçinted=çut=that=the=cçllapse=çf=the=structure=çccurs=because =çf =the =creatiçn =çf =a =mechanism =in =the =upper =part =çf =the =tçwerI =as =shçwn =in =cigure =4I =that =repçrts=the=develçpment=çf=the=cracking=pattern=fçr=the=analysis=in=uJ=directiçnK=Cracks=arise=frçm=the=cçrners=çf=the=windçwsI=which=are=the=weakest=pçintsI=and=then=they=grçw=within=the=masçnry=panels=between= twç= rçws= çf= mulliçned= windçwsK= qhe= mechanism= invçlves= alsç= the= crushing= çf= the= small=

EaF=

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=

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pillars= that= separate=the=mulliçned=windçwsK=einges= develçp=at= the= ends= çf= the=pillars= that= turn= intç=rçdsK= qhe= cçllapse= dçes= nçt= entail= significant= crushed= areas= and= the= cçmpressive= strain= exceeds= the=limit= crushing= value= defined= in= the= criteriçn= 2B= çnly =in =limited =areas =arçund =the =pillarsK =fn =all =the =analyzed=casesI=the=abçve=mentiçned=criteria=fçr=the=definitiçn=çf=the=cçllapse=limit=state=NAI=NB=and=2A=çccur=almçst=simultaneçusly=and=are=all=cçnnected=tç=the=fçrmatiçn=çf=a=mechanism=in=the=upper=part=çf= the= tçwerI= as=previçusly= discussedK= At= the=cçllapse= lçad=stepI= the=drifts=and= the=crack=width=have=çvercçme=the=limits=defined=in=the=adçpted=criteriaK=ln=the=çther=handI=cçncerning=the=2B=criteriçnI=an=extensive=crushing=pattern=has=nçt=been=çbserved=at=the=cçllapseI=since=crushing=phençmena=have=been=lçcalized=çnly=in=the=pillars=and=in=sçme=cçrners=çf=the=mulliçned=windçwsK==qhe=pushçver= curves= çbtained=in= the= fçur=directiçns= uHI=uJI=vHI=vJ=are=repçrted= in=cigure=RaK=qhe=keystçne=çf=the=vault=at=the=tçp=çf=the=square=part=çf=the=tçwer=as=been=assumed=as=cçntrçl=pçintK=qhe=mçst=cçnservative=curve=has=been=then=adçpted=tç=perfçrm=the=vulnerability=assessmentK===

= =step 0 step OR step 3R step 4R step RR step SR

cig. 4=aevelçpment=çf=cracking=pattern=fçr=nçnlinear=static=analysis=in=uJ=directiçn==4.P. Assessment of the seismic vulnerability=qhe=mçst=critical=pushçver=curveI=characterized=by=the=lçwer=tçp=displacement=and=base=shear=valuesI=has=been=the=çne=çbtained=in=the=vJdirectiçn=and=has=been=assumed=fçr=the=vulnerability=assessmentI=accçrding=tç=the=ftalian=guidelines=fçr=the=seismic=assessment=çf=histçrical=cçnstructiçns=xSzK=qhis=is=the=directiçn= in= which= the= tçwer= shçws= the= maximum= slçpe= that= results= in= a= reductiçn= çf= the= tçp=displacement=capacityK==Cçncerning= the= cçnfidence= factçr= cC= prçvided= by= the= abçve= mentiçned= cçdeI= it= has= been= assumed=cCN===cC2====M=because=çf=the=exhaustive=survey=çf=the=geçmetrical=and=structural=characteristics=and=the=deep=study=çf=the=cçnstructiçn=phasesK=qhe=values=çf=the=mechanical=prçperties=are=cçnsistent=with=the=average=values=suggested=by=the=kqC=xRz=and=with=the=data=cçming=frçm=the=experimental=campaign=perfçrmed=çn=the=tçwerK=qherefçreI= cCP=has=been=assumed=equal=tç=zerçK=cinallyI=despite=the=prçblem=çf=subsidence=that=clearly=affected=the=tçwer=fçr=centuriesI=it=has=been=assumed=cC4===MI=because=çf=the=exhaustive= campaign= çf= geçlçgical= and= geçtechnical= studies= and= investigatiçns= perfçrmed= çn= the=fçundatiçn= sçilK= jçreçver= the=sçilJstructure= interactiçn= has= been= accurately= cçnsidered= in= the= finite=element=mçdelI=with=nç=need=çf=assuming=larger=safety=index=çn=the=mechanical=prçpertiesK=Based=çn=these=assumptiçns=a=glçbal=cçnfidence=factçr=cc===N=has=been=çbtainedK=qhe=pushçver= curve=cçnsidered= in=the=vulnerability= assessment= represents= the=capacity=çf= the=multiJdegree=çf=freedçm=system=EjalcFK=qhe=curve=has=been=prçcessed=tç=çbtain=the=relative=curve=çf=the=equivalent=singleJdegree=çf=freedçm=system=EpalcFI=dividing=displacements=and=shear=values=by=the=mçdal=participatiçn= factçr=Γ= == NKRSK= qhe= çbtained= curve= has= been= finally= transfçrmed= in= a= bilinear=Eenergetically= equivalentF= curveK= qhe= bilinear= curve= has= then= been= repçrted= in= the= acceleratiçnJdisplacement=respçnse=spectrum=EAaopF=plane=fçr= the=rip= verificatiçn=Ecigure=RbFK=qhe=sçlid= light=

=

N4SP=

line=in=cigure=Rb=represents=the=elastic=rip=demand=spectrum=characterized=by=the=design=peak=grçund=acceleratiçn= p×ag= == MKOVP= gI= being= ag= == MKNSP= g= the= peak= grçund= acceleratiçn= çn= the= bedrçck= and=p===NKU=the=sçil=amplificatiçn=factçrK=qhe=dashed=line=is=the=reduced=elastic=demand=spectrum=cçnsistent=with=the=structural=capacity=that=prçvides=a=value=çf=the=rip=peak=grçund=acceleratiçn=arip===MKO4S=gK=qhe=guidelines=quantifies=the=seismic=vulnerability=çf=a=structure=thrçugh=the=seismic=safety=index=fppW===

= = = = === =====g

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= =======================================================ETF=

=qhe= seismic= safety= index= fçr= the= dhirlandina= tçwer= resulted= fpp===MKU4I= that= clearly= highlights= the=inability=çf=the=structure=tç=resist=tç=the=design=seismic=actiçnK=crçm=the=palc=bilinear=capacity=curve=is=alsç=pçssible=tç=evaluate=the=behaviçur=factçr=qI=as=the=ratiç=between= the= maximum= displacement= duls===NUP= mm= and= the= yielding= displacement= dy===NNM= mmK=Cçnsidering=the=previçus= displacement= valuesI= a= behaviçur= factçr= q===NKSS=has=been=çbtainedI= that= is=significantly=lçwer=than=thçse=suggested=by=kqC=xRz=and=by=the=guidelines=xSzI=respectively=equal=tç=P=and=PKSK=qhis=result=was=already=pçinted=çut=by=a’Ambrisi=et=alK=x4z=in=the=study=çf=the=civic=tçwer=çf=pçncinç= which=presented= a= behaviçur= factçr= q= ranging= frçm=NKPU=and=NKT4K= fn= the=present= caseI= the=kqC=and=the=guidelines=seem=tç=çverestimate=the=dissipative=capacity=çf=the=tçwer=çf=a=factçr=equal=tç=NKU=and=OKO=respectivelyK===4.4. The influence of the soil in the seismic performance of the structure=fn=seismic=analysis= the=effect= çf=the=sçil= is=partially= taken= intç=accçunt= thrçugh=the=sçil=factçr= pI= that=can=lead=tç=an=increase=çf=the=seismic=actiçn=up=tç=UMB=fçr=very=sçft=sçilsK=keverthelessI=its=effect=çn=the= seismic= behaviçur= çf= the= structure= can= be= even= beneficial= in= sçme= casesK= Cçnsidering= the=impedance= çf= the= sçilLfçundatiçn= system= alsç= implies= the= intrçductiçn= çf= a= stiffness= and= damping=cçntributiçnK=ff=the=sçil=is=quite=defçrmableI=it=will=prçvide=fçr=a=lçw=stiffness=cçntributiçnI=leading=tç=an=increase=çf= the=fundamental=periçd=çf=the=structureK=qhis= increase=may=result= in=a= reductiçn=çf=the=seismic=demandK==fn= the= present= caseI= the= first= fundamental= periçd= çf= the= dhirlandina= tçwer= is= equal= tç= qppf===OK4S= sI=çbtained=cçnsidering=the=sçilJstructure=interactiçn=Emçdel=ppfFI=whilst= in=the=hypçthesis=çf= the=tçwer=fully =restrained =at =the =base =Emçdel =oFI =the =first =fundamental =periçd =reduces =tç =qo== =O =sI =with =an =increase=çf=the=seismic=spectral=demand=çf=ORBI=frçm=peIppf===MKNUg=tç=peIo===MKO4gK===

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aesign demand spectrum

oeduced demand spectrum

dy= duls= ddem=

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cig. R=EaF=mushçver=curves=çbtained=in=the=fçur=directiçns=çf=analysisI=assuming=the=tçp=çf=the=vault=as=cçntrçl=pçintK=EbF=serificatiçn=çf=the=rip=in=the=Aaop=plane=

=cigure= S= shçws= the= increase= çf= the= seismic= vulnerability= çf= the= fully= restrained= tçwer= Emçdel= oFI=cçmpared=tç=the=tçwer=cçnsidering=the=sçilJstructure=interactiçn=Emçdel=ppfFK=fn=case=çf=mçdel=oI=it=has=been= çbtained= arip===MKONT= g= leading= tç= a= seismic= safety= index= fppIo===MKT4= that= is= NOB= lçwer= than=fpp===MKU4I=previçusly=çbtained=with=the=mçdel=ppfK=ln=the=çther=handI=a=value=çf=the=behaviçur=factçr=q===NKTV= has= been=çbtained=with= mçdel=oI= that= is= higher= than= the=çne=çbtained=with= the=mçdel=ppfI=equal=tç=NKSSI=but=still=cçnsiderably=lçwer=than=the=values=suggested=by=the=cçdes=xRJSzK==ln=the=çther=handI=the=ultimate=limit=state=due=tç=the=sçil=cçllapse=has=nçt=been=cçnsidered=due=tç=lack=çf=necessary=infçrmatiçnK=curther=investigatiçns=aimed=at=a=cçmplete=definitiçn=çf=the=prçperties=çf=the=sçil=wçuld=be=necessary=fçr=a=mçre=accurate=mçdeling=çf=the=sçilJstructure=interactiçnI=that=hçwever=is=beyçnd=the=scçpe=çf=the=present=paperK==

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Top displacement (mmF

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aesign demand spectrumpalc capacity curve model ppIoeduced demand spectrum model ppIpalc capacity curve model ooeduced demand spectrum model o

dyIo= dulsIo= ddemIo=

=cig. S=fncrease=çf=the=seismic=vulnerability=çf=the=restrained=tçwer=Emçdel=oFI=with=respect=tç=the=tçwer=

cçnsidering=the=sçilJstructure=interactiçn=Emçdel=ppfF=

=R. ClNCirpflNp =A=study= çn= the= nçnlinear= seismic= behaviçur= çf= a= histçrical= masçnry= tçwer= has= been=carried=çnK= qhe=study=has=been=based=çn=an=advanced=nçnlinear=finite=element=mçdellingI=that=tççk=intç=accçunt=fçr=the=sçilJstructure=interactiçnK==qhe=vulnerability=assessment=çf=the=tçwerI=perfçrmed=thrçugh=pushçver=analysis=and=accçrding=tç=the=kqC=and=the=guidelines=fçr=histçrical=cçnstructiçnsI=pçinted=çut=the=insufficient=seismic=capacity=çf=the=structureI=that=resulted=unable=tç=resist=the=rip=design=seismic=actiçn=çf=the=siteK==qhe= study=alsç= investigated= the= influence= çf= the= sçilJstructure= interactiçn= mçdelling= çn= the= seismic=perfçrmance=çf=the=tçwerK=qhe=sçft=fçundatiçn=sçil=resulted=tç=be=beneficial=in=the=seismic=respçnse=çf=the=structureI= leading= tç=an= increase=çf=ORB= çf= the=fundamental=periçd=çf= the=sçilJtçwer= system=and=thus=tç=a=reductiçn=çf=the=seismic=actiçnK=qhe=effect=çf=the=sçil=in=upgrading=the=seismic=capacity=çf=the=structure=has=been=alsç=highlighted=by=an=increase=çf=the=seismic=vulnerability=index=frçm=MKT4=tç=MKU4K=crçm=the=palc=bilinear=curve=çbtained=frçm=the=pushçver=curveI=the=value=çf=the=behaviçur=factçr=q=has=been=estimatedK= ft= resulted=significantly= lçwer= than= the= values= suggested=by= the=kqC= and=by= the=guidelines= fçr= the= histçrical= cçnstructiçnsI= çf= a= factçr= respectively= equal= tç=NKU= and=OKOK= qhis= result=evidenced=hçw=the=use=çf=respçnse=spectrum=analysis=wçuld=led=tç=an=çverestimatiçn=çf=the=dissipative=capacity=çf=the=structureK= obcbobNCbp =xNz dazetas=dK=ENVVNF=cçrmulas=and=charts=fçr= impededances=çf=surface=and=embedded=fçundatiçnsK=

gournal=of=deotechnical=bngineeringI=ApCb=NNTEVFW=NPSPJNPUNK=xOz Carpinteri= AKI= fnvernizzi= pKI= iacidçgna= dK= EOMMRF= fn= situ= damage= assessment= and= nçnlinear=

mçdelling=çf=a=histçrical=masçnry=tçwerK=bngineering=ptructures=OTW=PUTJPVRK=xPz Cerçni=cKI=mecce=jKI=janfredi=dK=EOMNMF=peismic=assessment=çf=the=bell=tçwer=çf=panta=jaria=ael=

CarmineW=prçblems=and=sçlutiçnsK=gournal=of=barthquake=bngineering=N4ENFW=PMJRSK=x4z a’Ambrisi=AKI= jariani= sKI= jezzi=jK= EOMNOF=peismic= assessment= çf= a= histçrical= masçnry= tçwer=

with= nçnlinear= static= and= dynamic= analyses= tuned= çn= ambient= vibratiçn= testsK= bngineering=ptructures=PSW=ONMJONVK=

xRz kqC= EOMMUFK= kçrme= tecniche= per= le= cçstruziçniK= aKjK= jinisterç= fnfrastrutture= e= qraspçrti= N4=gennaiç=OMMUI=dKrKoKfK=cebruary=4I=OMMUI=oçmaI=ftalyK=

xSz amCj= EOMNNFK= salutaziçne= e= riduziçne= del= rischiç= sismicç= del= patrimçniç= culturale= cçn=riferimentç= alle= kqC= N4= gennaiç= OMMUK= amCj= V= febbraiç= OMNNI= dKrKoKfK= cebruary= OSI= OMNNI=oçmaI=ftalyK=

xTz Cadignani=oK=EOMNMF=qhe=dhirlandina=qower=–=Conservation=mrojectK=iuca=pçssella=bdKI=oçmeK==xUz afAkA=finite =elements =analysisK =rser’s =manual =–=oelease=VKP=–=jaterial =iibrary=EOMMUFK =qkl=

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fçr=cçncrete=based=çn=a=cçJrçtatiçnal= cçnceptK= =Cçmputatiçnal=mçdelling=çf=cçncrete=structuresK=mrçcK=brolJC=NVVUI=bdsK=oK=de=Bçrst=et=alKI=ppK=NPJOOI=BalkemaI=oçtterdamK=

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