N4VP=

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

Teb STorCTroAi BbeAsflro ASSbSSMbNT lc dliabN MfibS sbSrsfAN sfiiAS Teolrde A SbfSMfC-sliCANfC nrfCh molCbarob BK caggianoNI AK cormisanoOI aK ae dregorioPI qK ae iucia4I cK jK jazzolaniR ABSToACT pince= prehistçric= timesI= human= life= has= been= influenced= by= natural= disastersK= eurricanesI= flççdsI=earthquakes=and=vçlcanic=eruptiçns=have=been=respçnsible=fçr=milliçns=çf=deaths=and=their=effects=have=çften=endangered=the=survival=çf=entire=civiliòatiçnsK=`ertainlyI=amçng=all=catastrçphic=eventsI=the=earthquake=has=prçduced=the=largest=number=çf=victimsW=since=NVMM=tç=dateI= it= is=estimated=that= abçut=six=milliçn=peçple=died=fçllçwing=an=earthquake=xNzK= fn=many =regiçnsI =especially =in =the =trçpicsI =the =òçnes =at =seismic =risk =are =sites =alsç =çf =active =vçlcançesI =there=the=eruptive=haòardI=characteriòed=by=different=vçlcanicJinduced=phençmenaI=such=as=lavaI=air=fall=depçsitsI=pyrçclastic=flçwsI=flying=debrisI=laharsI=tsunamisI=is=added=tç=the=seismic=çne=xOJTzK=Aim= çf= the= paper= is= the= applicatiçn= çf= a= quick= methçdçlçgy= useful= tç= a= glçbal= seismicJvçlcanic=vulnerability=assessment=çf= the=areas=at=riskI= thrçugh=a=relative=measure=çf= the=buildings=weaknesses=under=effect=çf=pçssible=cçmbinatiçns=çf=extreme=eventsI=cçnsidering=alsç=cçnstructiçns=belçnging=tç=cultural= heritageK= qhe= prçcedureI= inspired= by= multiJcriteria= decisiçnal= methçds= Ej`ajFI= prçvides=a=vulnerability=judgment=at=regiçnal=scaleI=çn=the=basis=çf=infçrmatiçn=çbtained=thrçugh=a=simple=visual=survey=çf=buildingsK=qhe=methçdçlçgy=is=applied=tç=the=sesuvian=regiçnI=at=great=vçlcanic=risk=EkaplesI=ftalyFK=qhe=analyòed=buildings=sample=is=an=impçrtant=pçrtiçn=çf=the=histçrical=and=artistic=heritage=çf=the=areaW=the=eighteenthJcentury=Barçque=and=oçcçcç=residencesI=knçwn=as=dçlden=jile=sillasK==heywordsW jultiJrisk analysisI peismicJvolcanic structural assessmentI eistorical buildingsI

nuick proceduresI jCaj methods NK fNTolarCTflN =fn =the =framewçrk =çf =the =burçpean =prçject =`lpq =Actiçn =`OS =“rrban eabitat Constructions under Catastrophic bvents“=EOMMSJOMNM=xUzFI=a=specific=methçdçlçgy=fçr=the=seismicJvçlcanic=vulnerability=assessment=çf=cçnstructiçnsI=inspired=by=the=multiJcriteria=decisiçnal=methçds=has=been=set=upK=ft=is=çf=quick=type=and=can=be=applied=tç=bçth=çrdinary=cçnstructiçns=and=mçnumental=buildingsK=qhe=methçdçlçgy=identifies= three=main=categçries=çf=vulnerability=elements=çf=cçnstructiçnsI=namely=seismic=EpFI=vçlcanic=EsF=and=mçnumental=EjF=parametersI=achievable=thrçugh=simple=visual=surveysK=cçr= each= element= categçryI= the= prçcedure= furnishes= a= vulnerability= index= in= the= range= xMI= NzI= which=quantifies=the=fragility=çf=cçnstructiçns=respectively=related=tç=seismic=actiçns EfspFI=vçlcanic=eruptiçns=EfssF= and= presence= çf= artistic= heritage EfsjF =if =it =is =the =caseK =A =glçbal =vulnerability =index =EfdF= is=

================================================N Assistant=mrçfessçrI=aepartment=çf=ptructural=bngineering=–=rniversity=çf=kaples="cedericç=ff"K=miaòòale=

qecchiç=UMI=UMNOR=kaplesI=faggianç]uninaKit=O=Assistant=mrçfessçrI=aepartment=çf=ptructural=bngineering=–=rniversity=çf=kaples="cedericç=ff"K=miaòòale=

qecchiç=UMI=UMNOR=kaplesI=antçfçrm]uninaKit=P mhKaKI=mifkfsp=ptudy=`entre=–=rniversity=çf=kaples="cedericç=ff"K=sia=qçledç=4MOI=UMNP4I=kaplesI=

danielaKdegregçriç]uninaKit==4 mhKaK=ptudentI=aepartment=çf=ptructural=bngineering=–=rniversity=çf=kaples="cedericç=ff"K=miaòòale=qecchiç=

UMI=UMNOR=kaplesI=tçnyKdelucia]uninaKit==R mrçfessçr=bmeritusI=aepartment=çf=ptructural=bngineering=–=rniversity=çf=kaples="cedericç=ff"K=miaòòale=

qecchiç=UMI=UMNOR=kaplesI=fmm]uninaKit=

N4V4=

calculated=thrçugh=the=cçmbinatiçn=çf= these=indexesK= ft=expresses=relative=fragility= judgments=amçng=buildings=at=territçrial=scaleI=sç=identifying=specific=critical=situatiçnsK=Accçrding= tç= multiJcriteria= apprçachesI= the= methçdçlçgy= is= articulated= in= fçur= main= phasesW=NF=Assignment=çf= weights= tç=each=criteriçnX=OF=petJup= çf= the=aecisiçn=jatrix=and=its=nçrmaliòatiçnX=PF=oanking=çf=alternativesX=4F=pensitivity=analysisK= fn=the=fçllçwing=sectiçnsI=each=phase=is=illustrated=with =reference =tç =the =special =sample =çf =buildingsI =represented =by =the =sç =called =sesuvian sillas= çr=dolden jiles sillasI=dated=usfff=centuryI=lçcated=in=the=neighbçurhççds=çf=kaples=EftalyFK==OK sbSrsfAN sfiiAS ANa Tebfo sriNboABfifTv cACTloS =sesuvian=sillas=mçnumental=cçmplex=is=lçcated=in=the=keapçlitan=area=brçaden=at=the=fççt=çf=pçmmaJsesuvius=vçlcançI=which=is=cçnsidered=as=the=burçpean=regiçn=at=greatest=vçlcanic=riskK==fn=NTPUI=`harles=de=BçurbçnI=king=çf=kaplesI=and=his=wifeI=jaria=Amalia=çf=paxçnyI=cçmmissiçned=the= erectiçn= çf= the= oçyal= malace= in= mçrticiK= AfterwardsI= the= keapçlitan= nçbility= fçllçwed= cçurt’s=exampleI =sç =that =they =built =their =summer =residences =in =the =sesuvian =areaK =Alçng =the =rçad =axis =extending=fçr=çne=mile=alçng=the=sesuvian=cçastI= the=sçJcalled=dçlden=jile=EcigK=NFI =mçre=than=NMM=barçque=and=rçcçcç=style=villas= were=designed=by= impçrtant= architectsI= such=as=diçffredçI= panfeliceI=saccarçI=cuga=and=sanvitelliK===

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cigK N=qhe=dçlden=jile=at=the=sesuvian=slçpe=EkaplesI=ftalyF=

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cigK O=qhe=nine=sesuvian=sillas=examined==

Amçng=themI= nine=sillas=were=selected=fçr= the=applicatiçn=çf= the=setJup=quick=methçdçlçgy=fçr= the=seismicJvçlcanic=vulnerability=EcigK=OFW=in=brcçlançI=NKsilla=`ampçlietç=Es`FI=OKsilla=ouggierç=EsoFI=

N4VR=

PKmarcç =sul =mare =di =silla =cavçrita =EmscFI =4Ksilla =Aprile =EsAFX =in =qçrre =del =drecçI =RKsilla =delle =dinestre= EsdFI= SKsilla= jacrina= EsjcFX= in= pan= diçrgiç= a= `remançI= TKsilla= Brunç= EsBFI= UKsilla=sannucchi=EssFX=in=mçrticiI=VKsilla=jascçlç=EsjsFK=

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aF=

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cF==

dF= eF= fF=

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cigK P=silla=sanucchiW=prçspect=street=frçnt=EaF=rear=prçspect=EbFX=silla=`ampçlietçW=plan=layçut=EcF=stairs=viewI==EdF=frescçs=EeFX=marcç=sul=mare=di=silla=cavçritaW=mçsaics=EfFX=silla=jacrinaW=panelled=ceiling=EgF=

=Table N sulnerability=elements=EcriteriaF=and=relative=weights=xMJNz=fçr=seismicI=vçlcanic==

and=mçnumental=categçries==

SbfSMfC blements ECriteriaF teight

pN içwJquality=masçnry=andLçr=reduced=masçnry=area=alçng=çne=çr=bçth=directiçns=EBF= MIPMV=pO mresence=çf=steel=tieJbeams=andLçr=rKcK=stringcçurses=E`F= MIOMT=pP clççrs=badly=cçnnected=tç=the=walls=E`F= MINSS=pQ aistance=between=bracing=walls=EBF= MIMU4=pR mushing=structure=andLçr=absence=çf=wallJrççf=cçnnectiçn=EBF= MIMST=pS sariatiçn=çf=the=structural=system=at=upper=levels=EBF= MIMRP=pT mresence=çf=staggered=levels=EBF= MIMPU=pU mresence=çf=added=structures=with=different=stiffness=andLçr=lçcaliòed=cçnnectiçns=EBF= MIMPM=pV mresence=çf=lintel=E`F= MIMO4=pNM içcal=reductiçn=çf=the=masçnry=sectiçn=EfluesI=nichesI=etcKFK=EBF= MIMOO=qotal weights NIMMM

sliCANfC MlNrMbNTAi

blements ECriteriaF teight blements ECriteriaF teight sN aistance=frçm=the=crater=E`F= MIN4M= jN crescçes=quality=EBF= MINTM=sO lrientatiçn=EBF= MINNV= jO maintings=quality=EBF= MINRN=sP B=çf=çpenings=in=the=expçsed=facade=EBF= MIMV4= jP pculptures=quality=EBF= MINOR=sQ lpening=cçnditiçn=E`F= MIMVN= jQ jçsaics=quality=EBF= MIMUM=sR oççf=structure=E`F= MIMUT= jR Bççks=quality=EBF= MIMTU=sS mrçtectiçn=çf=large=çpenings=E`F= MIMTV= jS curnishK=accessK=quality=EBF= MIMRU=sT mrçtectiçn=çf=medium=çpenings=E`F= MIMRV= jT curniture=quality=EBF= MIMR4=sU mrçtectiçn=çf=small=çpenings=E`F= MIMRN= jU ptuccçes=quality=EBF= MIM4T=sV oççf=geçmetry=E`F= MIM4V= jV jçuldings=quality=EBF= MIM4S=sNM jaterial=çf=large=çpenings=E`F= MIM44= jNM crescçes=quantity=EBF= MIMPS=sNN jaterial=çf=medium=çpenings=E`F= MIMPR= jNN maintings=quantity=EBF= MIMPS=sNO jaterial=çf=small=çpenings=E`F= MIMPO= jNO pculptures=quantity=EBF= MIMPN=sNP kumber=çf=large=çpenings=EBF= MIMOV= jNP jçsaics=quantity=EBF= MIMOM=sNQ kumber=çf=medium=çpenings=EBF= MIMOP= jNQ Bççks=quantity=EBF= MIMNS=sNR kumber=çf=small=çpenings=EBF= MIMOM= jNR curnishK=accessK=quantity=EBF= MIMNR=sNS tall=thickness=E`F= MIMNR= jNS curniture=quantity=EBF= MIMNR=sNT `ladding=type=E`F= MIMN4= jNT ptuccçes=quantity=EBF= MIMNN=sNU jax=height==EBF= MIMNM= jNU jçuldings=quantity=EBF= MIMNM=sNV cirst=level=height=EBF= MIMMU= = = =qotal weights NIMMM qotal weights NIMMM

EBFZ=Benefit=criteriçnX=E`FZ=`çst=criteriçn

=crçm= the= architectural= pçint= çf= view= the= sillas= examined= have= the= typical= characteristics= çf= the=Barçque=and=oçcçcò=stylesW=spectacular= tasteI=masterly=use=çf=perspective=effects=with=sesuvius=and=the=sea= as= backgrçund=çf=architecturesI= unbiased= mixture=çf=architectural=çrdersK= lne=çf= the=cçnstant=aspects= is= the= duplicity= çf= the= cçnfiguratiçn= at= the= frçnt= and= at= the= backI= such= as= the= adçptiçn= çf=

N4VS=

a=cçmpact=prçspect=at=the=street=sideI=aligned=with=the=façade=çf=neighbçuring=buildingsI=fçr=achieving=the=unifçrmity=with=the=urban=cçnstructiçns=EcigK=PaFI=while=at=the=back=side=the=prçspect=is=richly=mçre=articulated=EcigK=PbFK==qhe =plan =layçutI =quite =always =symmetricalI =has =an =axial =walk =as =cçnstant =characteristicK =ft =can =be =cçvered=çr=çpenedI=based=çn=the=sequence=pçrtal=–=atrium=–=cçurt=–=exedra=–=gardenI=with=an=çptical=main=axisI=which= transversal=and=diagçnal=patterns= intersectK=A=typical= example= is= silla=`ampçlietç=EcigK=PcFK=ptairs=have=particular=impçrtanceI=they=being=structural=bçdies=peculiar=çf=the=cçntempçrary=keapçlitan=architectureK=qhey=are=cçmmçnly= inserted=in= the=atriaI= generally= in=a= symmetric=pçsitiçn=EcigK= PdFI= çpen= stairs= with= flying= buttress= çn= the= cçurt= are= realiòed= thrçugh= a= singular= variety= çf=particular=sçlutiçns=frçm=bçth=the=mçrphçlçgical=and=dimensiçnal=pçints=çf=viewsK=qç= the= elements= abçve= evidenced= as= peculiarI= such= as= axialityI= pluriaxialityI= patterns= alternatively=cçveredLçpenedI=alsç=decçratiçns=like=stuccçsI=frescçsI=mçsaicsI=shçuld=be=added=EcigK=PeJPgFK=qhe= cçnstructiçn= dataI= indispensable= fçr= the= methçdçlçgy= applicatiçnI= were= cçllected= during= the=survey=activity=cçnducted=in=ganuary=OMMV=under= the=prçmçtiçn=çf=the=`lpq=Actiçn=`OS=prçject=xVzK=fn= this= çccasiçnI= a= special= survey= fçrm= was= cçmpiledI= it= including= three= categçries= çf= vulnerability=parametersI=such=as=seismic=piI=vçlcanic=si=and=mçnumental=ji Eqable=NFK=qhe=fçrm=is=çbtained=by=the=integratiçn=çf=three=existent=survey=fçrms=that=are=jbabA=xNMz=fçr=seismic=issuesI=mifkfsp=xNNz=fçr=vçlcanic=issues=and=mAiAwwf=xNOz=fçr=artistic=issuesK=

=PK SbfSMfC – sliCANfC sriNboABfifTv lc Teb sbSrsfAN sfiiAS

=PKNK teight matrices qhe= first= step= is= the= cçmpilatiçn= çf= the= weight matrices= with= reference= tç= seismicI= vçlcanic= and=mçnumental =criteriçn =categçriesK =qhe =aim =is =tç =define =a =çrder =çf =relative =priçrity =amçng =the =vulnerability=criteria=within=each=categçryK=qhe=assignment=çf=priçrity=is=carried=çut= thrçugh=the=Aem=methçd= xNPzI= çn= the=basis= çf= binary=cçmparisçns= amçng=criteria= accçrding= tç= the=paaty’s= preference=scaleI=presented=in=qable=O=xNPzK===

Table O=qhe=paaty’s=preference=scale=xNPz==

sAirb=EaijF= abcfkfqflk=N= bqual=impçrtance=çf=bçth=elements=P= jçderate=impçrtance=çf=çne=element=çver=ançther=R= ptrçng=impçrtance=çf=çne=element=çver=ançther=T= sery=strçng=impçrtance=çf=çne=element=çver=ançther=V= bxtreme=impçrtance=çf=çne=element=çver=ançther=

OI=4I=SI=U= fntermediate=values=NLVI=NLUI=KKKI=NLO= fnverse=value=çf=çne=element=as=respect=tç=ançther=

=qhe=sçJdetermined=values=are=çrganised=intç=seismicI=vçlcanic=and=mçnumental=Anxn weight matricesI=designated= respectively= as AS Eqable= PFI= AV= Eqable= 4F= and= AM= Eqable= RFI= where= the= rçws= and= the=cçlumns =are =the =criteria =and =the =generic =term =aij= has= the= fçllçwing= prçpertiesW= aiiZN= and= ajiZNLaijK=qherefçreI= the=weight= wj=çf =each=criteriçn=is =calculated=by=dividing=the=geçmetric =mean=EjgFI=amçng=the=terms=çf=each=rçw=çf=the=weight=matrixI=by=the=sum=çf=the=geçmetric=means=çf=all=criteriaW==

wj=Z=jgi/Σi=jgi================whereW=jgi=Z=EaNj=G…G=anjFNLn ENF==qhe=weights=calculated=fçr=each=criteriçn=and=fçr=each=categçry=are=indicated=in=qable=NK==

Table P=peismic=weight=matrix=EASF==

= pN= pO= pP= p4= pR= pS= pT= pU= pV= pNM=pN= N= 4= 4= R= R= S= S= T= S= T=pO= NL4= N= P= S= R= 4= R= 4= S= T=pP= NL4= NLP= N= S= R= 4= R= 4= S= T=p4= NLR= NLS= NLS= N= P= 4= 4= S= P= O=pR= NLR= NLR= NLR= NLP= N= R= P= S= O= O=pS= NLS= NL4= NL4= NL4= NLR= N= P= 4= R= P=pT= NLS= NLR= NLR= NL4= NLP= NLP= N= O= P= P=pU= NLT= NL4= NL4= NLS= NLS= NL4= NLO= N= P= P=pV= NLS= NLS= NLS= NLP= NLO= NLR= NLP= NLP= N= O=pNM= NLT= NLT= NLT= NLO= NLO= NLP= NLP= NLP= NLO= N=

N4VT=

Table Q=sçlcanic=weight=matrix=EAsF==

= sN= sO= sP= s4= sR= sS= sT= sU= sV= sNM= sNN= sNO= sNP= sN4= sNR= sNS= sNT= sNU= sNV=sN= N= NLP= 4= 4= R= 4= 4= 4= R= 4= 4= 4= 4= 4= 4= R= R= S= T=sO= P= N= 4= O= R= P= P= P= R= O= O= O= O= O= O= S= S= S= T=sP= NL4= NL4= N= R= NLO= S= R= P= N= R= 4= O= R= 4= O= R= 4= S= T=s4= NL4= NLO= NLR= N= NLP= S= T= T= NLO= 4= R= S= 4= R= S= R= 4= R= S=sR= NLR= NLR= O= P= N= 4= P= O= 4= 4= P= O= 4= P= O= P= S= 4= R=sS= NL4= NLP= NLS= NLS= NL4= N= NLR= NLS= 4= P= 4= R= 4= R= S= 4= P= R= S=sT= NL4= NLP= NLR= NLT= NLP= R= N= NLT= NLO= 4= R= S= 4= R= S= R= 4= R= S=sU= NL4= NLP= NLP= NLT= NLO= S= T= N= N= 4= R= S= 4= R= S= R= 4= R= S=sV= NLR= NLR= N= O= NL4= NL4= O= N= N= P= O= N= P= O= N= O= R= 4= R=sNM= NL4= NLO= NLR= NL4= NL4= NLP= NL4= NL4= NLP= N= NLO= NLP= P= 4= R= 4= P= 4= R=sNN= NL4= NLO= NL4= NLR= NLP= NL4= NLR= NLR= NLO= O= N= NL4= P= 4= R= R= 4= 4= R=sNO= NL4= NLO= NLO= NLS= NLO= NLR= NLS= NLS= N= P= 4= N= P= 4= R= R= 4= 4= R=sNP= NL4= NLO= NLR= NL4= NL4= NL4= NL4= NL4= NLP= NLP= NLP= NLP= N= NL4= NLR= 4= P= 4= R=sN4= NL4= NLO= NL4= NLR= NLP= NLR= NLR= NLR= NLO= NL4= NL4= NL4= 4= N= NLS= R= 4= R= S=sNR= NL4= NLO= NLO= NLS= NLO= NLS= NLS= NLS= N= NLR= NLR= NLR= R= S= N= R= 4= S= T=sNS= NLR= NLS= NLR= NLR= NLP= NL4= NLR= NLR= NLO= NL4= NLR= NLR= NL4= NLR= NLR= N= R= 4= R=sNT= NLR= NLS= NL4= NL4= NLS= NLP= NL4= NL4= NLR= NLP= NL4= NL4= NLP= NL4= NL4= NLR= N= R= S=sNU= NLS= NLS= NLS= NLR= NL4= NLR= NLR= NLR= NL4= NL4= NL4= NL4= NL4= NLR= NLS= NL4= NLR= N= 4=sNV= NLT= NLT= NLT= NLS= NLR= NLS= NLS= NLS= NLR= NLR= NLR= NLR= NLR= NLS= NLT= NLR= NLS= NL4= N=

Table R=jçnumental=weight=matrix=EAMF=

=

= jN= jO= jP= j4= jR= jS= jT= jU= jV= jNM= jNN= jNO= jNP= jN4= jNR= jNS= jNT= jNU=jN= N= O= P= 4= R= S= S= T= T= S= P= 4= R= S= T= T= U= U=jO= NLO= N= 4= P= R= R= R= S= S= P= S= R= S= S= S= S= T= T=jP= NLP= NL4= N= O= 4= S= S= S= S= R= R= T= S= O= S= T= T= T=j4= NL4= NLP= NLO= N= P= R= 4= S= S= 4= NLR= NLP= S= R= S= R= T= S=jR= NLR= NLR= NL4= NLP= N= R= P= S= S= S= S= NLR= S= S= S= 4= T= T=jS= NLS= NLR= NLS= NLR= NLR= N= NLP= P= P= S= S= S= S= P= S= T= 4= 4=jT= NLS= NLR= NLS= NL4= NLP= P= N= P= P= S= T= S= S= O= 4= NLS= 4= 4=jU= NLT= NLS= NLS= NLS= NLS= NLP= NLP= N= O= S= S= S= S= O= R= T= S= P=jV= NLT= NLS= NLS= NLS= NLS= NLP= NLP= NLO= N= S= S= S= S= P= 4= T= S= S=jNM= NLS= NLP= NLR= NL4= NLS= NLS= NLS= NLS= NLS= N= O= R= S= S= S= S= T= T=jNN= NLP= NLS= NLR= R= NLS= NLS= NLT= NLS= NLS= NLO= N= 4= 4= P= T= S= S= S=jNO= NL4= NLR= NLT= P= R= NLS= NLS= NLS= NLS= NLR= NL4= N= P= O= 4= 4= R= R=jNP= NLR= NLS= NLS= NLS= NLS= NLS= NLS= NLS= NLS= NLS= NL4= NLP= N= P= R= 4= S= S=jN4= NLS= NLS= NLO= NLR= NLS= NLP= NLO= NLO= NLP= NLS= NLP= NLO= NLP= N= NLO= P= NLO= NLO=jNR= NLT= NLS= NLS= NLS= NLS= NLS= NL4= NLR= NL4= NLS= NLT= NL4= NLR= O= N= N= 4= R=jNS= NLT= NLS= NLT= NLR= NL4= NLT= S==== NLT= NLT= NLS= NLS= NL4= NL4= NLP= N= N= O= O=jNT= NLU= NLT= NLT= NLT= NLT= NL4= NL4= NLS= NLS= NLT= NLS= NLR= NLS= O= NL4= NLO= N= 4=jNU= NLU= NLT= NLT= NLS= NLT= NL4= NL4= NLP= NLS= NLT= NLS= NLR= NLS= O= NLR= NLO= NL4= N=

PKOK aefinition of the aecision Matrix and its normalization qhe=secçnd=step=is=the=cçmpilatiçn=çf=the=three=mxn=“decisiçn=matrices”=DSI=Ds and DMI=with=reference=tç= seismicI= vçlcanic= and= mçnumental= parametersI= respectivelyK= qhe= m= rçws= are= the= nine= sillas=examined=Es`I=soI=mscI=sAI=sdI=sjcI=sBI=sjsFI=whereas=the=n cçlumns=are=the=criteria=piI=siI=jiK=qhe= matrix= terms= dij= are= indicatçrs= quantifying= çr= qualifying= the= criteria= fçr= each= villaI= such= as= the=measure=çf=the=villa=perfçrmance=as=respect=tç=the=criteriçnK=aefinitelyI= fçr= each= categçryI= the= measures= dij= çf= the= criteriçn j= with= respect= tç= the= alternative= i= are=cçllected= in= the= decisiçn= matrix= Dmxn= En =Z =number =çf =criteria =fçr =each =categçryX =m =Z =number =çf =villasFI=whçse=generic=terms=EdijF=are=chçsen=çn=different=basisW=·= fçr=seismic criteria= EDSI=VxNMI=qable=SFI=dij= is=N=çr=M=when=the=vulnerability=element=pi= fçr =the=iJth=

villa=is=present=çr=absentI=respectivelyX=·= fçr=volcanic criteria=EDsI=VxNVI=qable=TFI=dij=isW=

-= a=direct=measure=çf=the=criteriçn=jW=distance=frçm=the=vent=xkmzX=expçsed=façade=çrientatiçn=x°zX=percentage=çf=çpenings=xBzX=rççf=slçpe=x°zX=number=çf=smallI=medium=and=large=çpenings=xn°zX=wall=thickness=xcmzX=maximum=height=xmzX=first=level=height=xmzK=

-= a=mechanical=characteristic= xkmmJOzW=fçr= the=criteriçn=relating=tç=the=rççf=structureI=dij= is= the=cçllapse=lçad=under=vertical=lçads=prçduced=by=ash=fall=depçsits=xN4zX=fçr=the=criteria=related=tç=the=typçlçgy=and=material=çf=claddingsI=çpening=and=prçtectiçn=systemsI dij=is=the=cçllapse=lçad=under=hçriòçntal=lçads=prçduced=by=pyrçclastic=flçws=xNRzK===

-= a=numerical=scçre=cçrrespçnding=tç=a=verbal= judgmentW=çpening=cçnditiçns=Epççr=OI=mediçcre=RI=gççd=UI=excellent=NMFK=

·= fçr=monumental criteria=EDMI=VxNUI=qable=UFI=dij=is=a=numerical=scçre=Eabsent=MI=pççr=MKMNI=medium=MKNN=and=high=MKUUF=determined=thrçugh=a=further=applicatiçn=çf=the=Aem=methçdK=

N4VU=

Table S=peismic=decisiçn=matrix=EDSF==

= pN= pO= pP= p4= pR= pS= pT= pU= pV= pNM=s`= M= N= N= N= M= N= M= N= M= M=so= M= N= N= N= N= M= N= M= N= M=msc= M= N= M= M= M= N= M= N= N= N=sA= N= N= M= N= M= M= M= M= M= N=sd= M= N= M= N= N= N= N= N= N= M=sjc= M= M= M= N= N= N= N= N= M= N=sB= N= N= M= N= N= N= M= M= N= M=ss= M= N= M= N= N= N= N= M= M= M=sjs= N= N= N= N= N= N= N= N= M= M=

=Table T=sçlcanic=decisiçn=matrix=EDsF=

=

= sN= sO= sP= s4= sR= sS= sT= sU= sV= sNM= sNN= sNO= sNP= sN4= sNR= sNS= sNT= sNU= sNV=s`= NO= VM= OR= S= O= M= M= M= M= O= O= O= NO= NM= P= NMM= TIT= O4= NM=so= NO= VM= RM= P= P= M= M= M= M= O= O= O= NN= NU= O= UM= TIT= NV= R=msc= NO= VM= NM= S= P= M= M= M= OM= O= O= O= 4= V= N= SM= TIT= NO= R=sA= NO= SM= RM= S= P= M= M= M= OM= O= O= O= 4= OU= NS= SR= TIT= NR= R=sd= NT= VM= NM= S= P= M= M= M= M= O= O= O= O= P= N= UM= TIT= V= 4=sjc= NS= VM= NM= S= O= M= M= M= M= O= O= O= V= P= 4= SM= TIT= NR= 4=sB= NO= VM= OR= S= O= M= M= M= M= O= O= O= P= O= NR= NMM= TIT= N4= S=ss= NP= VM= OR= S= P= M= M= M= OM= O= O= O= NR= OT= PM= TM= TIT= NS= R=sjs= NR= 4R= OR= V= O= 4= 4= 4= M= O= O= O= 4= M= NR= NMM= TIT= NR= P=

Table U=jçnumental=decisiçn=matrix=EDMF=

=

= jN= jO= jP= j4= jR= jS= jT= jU= jV= jNM= jNN= jNO= jNP= jN4= jNR= jNS= jNT= jNU=s`= MIUU= MIMN= MIMM= MIMM= MIMN= MIMN= MIMN= MIMN= MIMN= MIUU= MIMN= MIMM= MIMM= MIMN= MINN= MINN= MIUU= MIUU=so= MINN= MIMM= MIMN= MIMM= MIMN= MIMM= MIMM= MINN= MINN= MIMN= MIMM= MIMN= MIMM= MIMN= MIMM= MIMM= MINN= MINN=msc= MIUU= MIMM= MIMM= MIUU= MIMM= MIMM= MIMM= MIMN= MIMN= MIUU= MIMM= MIMM= MIUU= MIMM= MIMM= MIMM= MIMN= MIMN=sA= MIMM= MIMN= MINN= MIMN= MIMN= MIMM= MIMM= MIMN= MIMN= MIMM= MINN= MIMN= MINN= MIMN= MIMM= MIMM= MIMN= MIMN=sd= MIMN= MIMN= MIMM= MIMM= MIMN= MIMM= MIMN= MIMM= MIMN= MIMN= MINN= MIMM= MIMM= MIMN= MIMM= MINN= MIMM= MIMN=sjc= MIMN= MINN= MIMN= MIMM= MIUU= MIMM= MIMM= MIMN= MIMN= MINN= MIMM= MIMN= MIMM= MIUU= MIMM= MIMM= MIMN= MIMN=sB= MINN= MIMN= MIMN= MIMM= MIMN= MIMM= MINN= MINN= MIMN= MIMN= MIMN= MIMN= MIMM= MIMN= MIMM= MIMN= MIMN= MINN=ss= MINN= MIMM= MIMN= MIMM= MIMM= MIMM= MIMM= MINN= MIUU= MIMN= MIMM= MIMN= MIMM= MIMM= MIMM= MIMM= MINN= MIUU=sjs= MIMN= MIMM= MIMM= MIMM= MIMM= MIMM= MIMM= MINN= MINN= MIMN= MIMM= MIMM= MIMM= MIMM= MIMM= MIMM= MINN= MIMN=

=lnce= the= decisiçn= matrices= are= definedI= the= matrix= terms= shçuld= be= nçrmalised= fçr= çbtaining=adimensiçnal= termsI= aiming=at= the=data= hçmçgeniòatiçnK=qhe=nçrmalisatiçn=can=be=achieved=thrçugh=simple=mathematical=functiçns=that=çperate=çn=the=matrix=rçw=termsK=fn=the=study=caseI=the=terms=çf=the=nçrmalised=decisiçn=matrix=are=determined=as=fçllçwsW== diIjLE=Σi=diIj=

OFNLO= EOF==aefinitelyI= the= nçrmaliòed= matrices= çf= decisiçn= Dmxn= are =cçmbined =with =the =weights =çf =criteria =çbtaining=new=matrices=Vmxn EspI=ssI=sjFI=whçse=generic=terms=are=achieved=as=it=fçllçwsW== vijZ=wj·diIjLE=Σi=diIj=

OFNLO= EPF= PKPK Calculation of the orders among the alternativesW the vulnerability indexes Accçrding= tç= the= qlmpfp= Eqechnique= fçr= lrder= mreference= by= pimilarity= tç= fdeal= pçlutiçnF= multi=criteria=methçd=xNSzI=aiming=at=çbtaining=the=final=ranking=thrçugh=the=vulnerability=indexesI=the=çrder=çf=each=alternatives=EAF=is=requiredK=qhe=real=alternatives=are=characterised=by=the=rçws=çf=the=decisiçn=matrix=nçrmalised=and=weighted=EsFI=each=çne=is=represented=by=the=rçwJvectçrW== Ai=Z={viINI=viIOI=…I=viIn}= E4F==qherefçre =it =is =pçssible =tç =determine =twç =virtual =sçlutiçnsW =the =pçsitive =ideal =EAHF=and=negative= ideal==EAJF =alternativesK =qhey =are =çbtained =by =cçnsidering =fçr =each =criteriçn =respectively =the =best =and =the =wçrst= perfçrmance= çffered= by= the= examined= alternativesK= qhe= best= perfçrmance= cçrrespçnds= tç= the=maximum =scçre =in =case =çf =Benefit =EBF =criteria =and =the =minimum =scçre =in =case =çf =`çst =E`F =criteriaX =viceversa= in=case=çf= the= worst= perfçrmanceK =fn =qable =NI =criteria =are =assçciated =tç =letters =B =çr =`I =in =relatiçn=tç=their=prçperty=tç= increase=çr=decrease=the=vulnerability= judgmentI= respectivelyK=aefinitelyI=the=ideal=alternatives=EAH

I=AJF=are=represented=by=the=fçllçwing=vectçrsW=

N4VV=

AHZ{Emax=vij, jÎgbFI=Emin=vij, jÎgcFI=j=Z=NI=OI…I=n}=Z={vNHI=vO

HI…I=vnH}= ERF=

= AJZ{Emin=vij, jÎgbFI=Emax=vij, jÎgcFI=j=Z=NI=OI…I=n}=Z={vN

JI=vOJI…I=vn

J}= ESF==

where=gb=and=gc=are=the=Benefit=and=the=̀ çst=criteriçn=setsI=respectivelyK=qhe=alternatives=A=can=be=cçnsidered=as=pçints=in=a=nJdimensiçns=space=En=being=the=criteriaFI=where=the=jJaxis=is=the=measure=çf=the=perfçrmance=nçrmalised=and=weighted=EvijF=çf=the=alternatives=as=respect=tç=the=jJcriteriçnK=fn=this=viewI=the=buclidean=distances=between=the=real=alternative=Ai=and=the=ideal=çnes=can=be=calculated=as=it=fçllçwsW== pi

H=Z=I=Ai=–=AH=I===xΣjZNI…In EviIjJvjHFOzNLO= ETF=

= pi

J=Z=I=Ai=–=AJ=I===xΣjZNI…In EviIjJvjJFOzNLO= EUF=

=fn=cçnclusiçnI =the=relative=distance=çf =each=alternative=frçm=ideal =çnes=is =the=reference=parameter =fçr =their= classificatiçnI= such= as= the= sulnerability= fndexK= fn= particularI= çn= the= basis= çf= the= buclidean=distances= calculated= fçr= the= three= categçriesI= the= vulnerability= seismic= EfspFI =vçlcanic =EfssF= and=mçnumental=EfsjF=indexes=are=expressed=thrçugh=the=fçllçwing=relatiçnshipsW== fsp=Z={pi

JLEpiH=H=pi

JF}sesmicX=== fss=Z={piJLEpi

H=H=piJF}vçlcanicX===fsj=Z={pi

JLEpiH=H=pi

JF}mçnumental= EVF==qhe =vulnerability =indexes =range =between =xMI =NzK =fn =fact =if =the =alternative =Ai= is= cçincident= with= the=negative= ideal= sçlutiçn= AJI= pi

J= is= equal= tç= M= and= therefçre= the= vulnerability= indexes= are= equal= tç= MX=cçntrary= if= the= alternative= Ai= is= cçincident= with= the=pçsitive= ideal= sçlutiçn= AHI= pi

H= is= equal= tç=M= and=therefçre=the=vulnerability=indexes=are=equal=tç=NK==cinallyI= these= single= judgments= can= be= cçmbined= in= çrder= tç= define= a= glçbal= vulnerability= indexI=thrçugh=the=fçllçwing=geçmetrical=meanW== fdZ=Ef’sp=G f’ss=G=f’sj=FNLP= ENMF=

=cçr=the=nine=sesuvian=sillas=examinedI=the=vulnerability=indexes=determined=thrçugh=the=methçdçlçgy=setJup=are=indicated=in=qable=V=and=plçtted=in=cigK=4K===

Table V=peismic=EfspFI=vçlcanic=EfssFI=mçnumental=EfsjF=and=glçbal=EfdF=vulnerability=indexes==çf=the=sesuvius=sillas=examined=

=

= s`= so= msc= sA= sd= sjc= sB= ss= sjs=

fsp= MIRVM= MIRU4= MITO4= MIP4U= MISV4= MIUMT= MIPPP= MISVV= MIMTP=

fss= MITSP= MIU4P= MISRV= MITRU= MISTS= MISVO= MITSU= MITP4= MIOPM=

fsj= MITOV= MITNT= MISP4= MIPTT= MISRR= MISU4= MIUPM= MISUN= MIRVP=

fd MISVM MITMT MISTN MIQSP MISTR MITOS MIRVT MITMQ MIONR

=eistçgrams= in= cigK=4= shçw= that= the= vulnerability= çf= sillas= is= dependent= frçm= the= categçry= çf=vulnerability=cçnsideredK=cçr=exampleI=in=seismic=caseI=the=mçst=vulnerable=residence=is=silla jacrina EsjcFI=due=tç=the=presence=çf=numerçus=fragility=factçrsI=such=as=absence=çf=tieJbeamsI=large=distance=between=bracing=wallsI=masçnry=vaultsI=variatiçn=çf=the=structural=system=at=upper=levelsI=rççfs=badly=cçnnected= with= the= walls= and= presence= çf= added= structures= with= different= stiffness= andLçr= lçcaliòed=cçnnectiçnsK=BesidesI=in=vçlcanic=caseI=the=mçst=vulnerable=residence=is=silla ouggiero EsoFI=because=çf= its= prçximity= tç= the= crater= ENO= kmF= and= the=presence=çf= a= façadeI= çrthçgçnal= tç=pyrçclastic= flçws=EVM°FI= with= a= large= percentage= çf= large= ENNF= and= medium= ENUF= çpenings= withçut= prçtectiçns= ERMBFK=cinallyI= in= mçnumental= caseI= the= mçst= vulnerable= residence= is= silla Bruno EsBFI= because= çf= the=presence= çf= a= large= number= çf= impçrtant= artistic= elements= EfrescçesI= paintingsI= sculpturesI= bççksI=furnituresI=stuccçes=and=mçuldingsFK=qhe=cçmbinatiçn=çf= the=three=vulnerability=indexes= EfdF =shçws=a=new=rankingI =which=summarises =the=three=single=vulnerability=classificatiçnsK=silla=jacrina=results=as= the=residence=having=the=maximum=glçbal=vulnerability=indexK=

NRMM=

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Villa Campolieto

Villa Ruggiero

Parco Vul Mare Villa Favorita

Villa Aprile Villa delle GineVtre

Villa Macrina

Villa Bruno Villa Vannucchi

Villa MaVcolo

IVS

12 34

5 6

7 8

9

aF==

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Villa Campolieto

Villa Ruggiero

Parco Vul Mare Villa Favorita

Villa Aprile Villa delle GineVtre

Villa Macrina

Villa Bruno Villa Vannucchi

Villa MaVcolo

IVV

685

73

14 2

9

bF==

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Villa Campolieto

Villa Ruggiero

Parco Vul Mare Villa Favorita

Villa Aprile Villa delle GineVtre

Villa Macrina

Villa Bruno Villa Vannucchi

Villa MaVcolo

IVM

47 56

2 3

9

1

8

=cF=

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Villa Campolieto

Villa Ruggiero

Parco Vul Mare Villa Favorita

Villa Aprile Villa delle GineVtre

Villa Macrina

Villa Bruno Villa Vannucchi

Villa MaVcolo

IG

16 354 2

8

7

9

dF=

cigK Q draphical=representatiçn=çf=seismic=EaFI=vçlcanic=EbFI=mçnumental=EcF=and=glçbal=EdF=vulnerability==indexes=fçr=the=sesuvian=sillas=examined=

=PKQK Sensitivity analysis At=the=end=çf=the=decisiçnal=prçcedureI=a=sensitivity=analysis=is=perfçrmedK=qhe=aim=is=tç=evaluate=the=influence=çf=the=persçnal=chçices=çf=the=decisiçnJmaker=çn=the=analysis=resultsK==qhe=sensitivity=analysis=is=carried=çut=with=reference=tç=twç=stepsK==qhe=fçrmer=step=assesses=the=weights=cçnsistencyI=examining=the=pçssible=subjectivity=induced=by=the=persçnal=judgments=çf=the=decisiçnJmaker=in=the=weights=definitiçnK=ft=is=based=çn=the=paaty’s=methçdI=thrçugh=xNPz= the=calculatiçn=çf= the=cçnsistency=ratiç= oC=between=the=`çnsistency=fndex=EfCF =and=the=oandçm=`çnsistency=fndex=EfCoFK=fn=particularI=the=`çnsistency=fndex=Ef`F=isW=

=

=( )( )Nmax

--

=n

nfC

l= ENNF=

=where=λmax=and=n=areI=respectivelyI=the=eigenvalue=and=the=rçws=number=çf=the=weight=matrix=AI=while=the=oandçm=`çnsistency=fndex=Ef`oF=is=given=by=paaty=as=a=functiçn=çf=the=parameter=n=Eqable=NMFK==

Table NM=oandçm=`çnsistency=fndex=f`o=as=a=functiçn=çf=the=rçws=number=n=çf=the=teight=matrix=A=xNPz==

n N= O= P= 4= R= S= T= U= V= NM= NN= NO= …=

fCo MKMM= MKMM= MKRU= MKVM= NKNO= NKO4= NKPO= NK4N= NK4R= NK4V= NKRN= NK4U= …=

=qhe= binary= cçmparisçns= are= cçnsidered= as= cçherent= when= oC= is =smaller =than =NMBK =fn =the =present =applicatiçnI=this=cçnditiçn=is=satisfiedK=qhe =secçnd =step =assesses =the =ranking =stability =Eqable =VF =as =a =functiçn =çf =the =assigned =weight =values =Eqable= NFK= fn= fact= the= sçlutiçn= shçuld= nçt= change= with= small= changes= çf= weightsK= Accçrding= tç=qriantaphyllçu’s=prçcedure=xNTzI= the=reference=parameter=is=the=sensitivity=s=çf=the=three=çrders=fspI fss=and=fsj=Eqable=VF=with=respect=tç=each=criteriçn=jI=where=s=is=the=ratiç=between=the=weight=wj=Eqable=NF=and=the=absçlute=variatiçn=çf=weightI=the=sçJcalled=Absolute qop=EAqFI=able=tç=generate=a=change=çf=the=first=pçsitiçn=in=the=rankingW===

Aqw

s j= ENOF=

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