=

ONSO=

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

MbCeAkfCAi AkAivpfp lc Ak lia MAplkov Bofadb fk mAofp kathalie açmèdeNI qhçmas ptablçnOI Alain pellierP ABpToACT =qhis= communication= éresents= a= methodology= develoéed= to= assess= the= mechanical= behaviour= of=historical= constructions.= ft= is= aéélied= to= an= old= masonry= bridge= close= to= marisI= built= in= NVM4.= qhis=method=uses=a=calculation=tool=based=on=a=Pa=damage=model=imélemented=in=a=cbj=code.=qhe=model=uses= homogenized=éarameters= considering=masonry=heterogeneities.= qhe=coméuting=éart= is=éreceded=by=a= éhase= of= research= on= archival= documentsI= an= onJsite= investigation= éhaseI= and= an= exéerimental=éhase= carried= out= on= core= saméles= in= the= laboratory.= qhis= last= éhase= determines= the= éarameters=involved= in= the=homogenized=mechanical=behaviour= law=of= the=masonry.=qhe=model= is=based=on= the=theory=of=distributed=anisotroéic=cracking.=ft=considers=crackJreclosing=érocesses=and=the=éossibility=of=using= éreJdamage= of= the= material.= qhe= latter= ability= exélains= the= role= of= crack= oéening= and= crack=reclosing= in= the= actual= stiffness= of= the= structure.= qhe= crack= oéening= is= suéélied= by= the= model= and=facilitates=the=assessment=of=the=actual=state=of=the=structure=from=the=crack=oéening=measured=on=the=bridge.= lnce= the=actual= state=has= been= identifiedI= the= calculation= tool= is= able= to=determine= the=crack=éattern= induced= in= the= bridge= by= the= loads= and= other= actionsI= such= as= disélacements= of= additional=suééorts.=qhis=research=demonstrates=the=iméortance=of=considering=the=whole=history=of=a=structure=in=order=to=assess=its=current=state=and=suéélies=a=methodology=for=doing=so.= heywçrds: Masçnry bridgeI eçmçgenizatiçn methçdI aamage mçdelI `rackingI cbM NK fkTolarCTflk =qhis=article=éresents=the=methodology=develoéed=at=the=rniversity=of=qoulouse=EcranceF=for=assessing=old=masonry=arch=bridges.=qhis=research=was=suééorted=by=the=pociété=kationale=des=`hemins=de=cer=and =oéseau =cerré =de =cranceI =the =crench =railway =network. =qhe =aim=was =to =develoé =a =global =method =able=to=determine=the=serviceability=of=masonry=railway=bridges=and=to=oétimize=the=strengthening=that=could=be=needed.=qhe=global=bridge=éoéulation= in=buroée=includes=a=high=éroéortion=of=masonry=archesI=eséecially=on=the=railway=network=ESMB=according=to=lrban=in=OMMR=Elrban=xNzF.=qhese=bridges=are=old=Emore=than=a=hundred=years=oldFI= traffic= is= increasing=and=disordersI=cracksI=and=sometimes=collaéseI=occur.=qhat=is=why=research=érogrammes=have=been=develoéed=Ethe=history=of=the=calculation=of=masonry=bridges= is=described= in= mroske= and= san= derlder= xOzF.= qhey= use= various= aééroachesW= limit= analysisI= élastic= or=damage=analysis=with=a=macro=or=micro=aééroach.=A=review=of=the=methods=aéélicable=to=the=study=of=historical=masonry=constructions=is=given=in=m.=ooca=xPz.=At=the=rniversity=of=qoulouseI=works=on=the=behaviour= of= masonry= arch=bridges= focuses= on= the= emergence= of= crackingI= the= determination= of= the=disélacements= of= the= structure= and= of= its= damaged= zones.= qhe= final= aim= is= to= assess= the= current=behaviour=under=service=loads=and=to=forecast=the=ultimate=loads.=qhe=work=éresented=here=concerns=a=long= multiséan= stone=masonry=bridge.Because= the=éroblem= is= to= study= fullJscale= masonry= structures=with= large= dimensionsI= a= macro= analysis= using=a= homogenized= model= is= eméloyed.= ft= considers= the=elastic=and=inelastic=domains.=fn=the=research=éresented=hereI=the=mechanical=behaviour=of=the=masonry=

================================================N=Associate=érofessorI==rniversité=de=qoulouseX=rmpI=fkpAX=ija`=Eiaboratoire=jatériaux=et=aurabilité=

des=`onstructionsF=cranceI=nathalie.domede]insaJtoulouse.fr=O=aoctorI=thomas.stablon]etud.insaJtoulouse.fr=P=mrofessorI=alain.sellier]insaJtoulouse.fr=

=

ONSP=

is=described=using=a=continuum=damage=model.=tith=this=modelI=initially=develoéed=by=pellier=x4z=for=concreteI= and= adaéted= for= masonryI= the= cracks= can= aééear= anywhere= in= the= bridge= and= go= in= any=directionI =in =both=tensile =and=coméressive=zonesI =then=éossibly=recloseI =according=to=the=strain=state. =qhe=efficiency=of=this=model=to=describe=masonry=mechanical=behaviour=was=éresented=at=pAe`=OMNM=Eaomede=xRzF.=pince=thenI=imérovements=have=been=madeI=éarticularly=concerning=the=crack=reclosing=managementI=as=will=be=described=later.=qhe=current=behaviour=of=the=masonry=is=éartially=assessed=by=means=of=laboratory=tests=done=on=saméles=and=is=coméleted=by=a=homogenization=method=and=blockJmortar=interface=éreJdamage.=ButI=because=of=the=major=influence=of=existing=cracks=in=the=structureI=the= global= mechanical= behaviour= of= an= old= bridge= is= strongly= deéendent= on= its= history= Einitial=building=érocess=and=subseèuent=movement=of=the=baseI=which=governs=its=current=stiffness=Eptablon=xSzF.=qo=assess=this=aséectI=we=carried=out=investigations=on=the=bridge=in=èuestionW=measurements=of=crack=oéenings=and=vault=disélacements=under=train=loads.=qhe=coméarison=between=relevant=values=and=results=of=calculations=was=used=to=fit=the=base=movements=exélaining=the=crack=éattern=and=the=current=masonry=stiffness.=A=realistic=calculation=of=the=bridge=was=then=éossibleI=under=service=and=ultimate=loads.==OK Teb MbCeAkfCAi BbeAsflro Mlabi =qhe= aééroach= is= a= “macro”= one= regarding= the= healthy= masonry= as= a= homogeneous= material.= qhis=section= éresents= the= continuum= orthotroéic= damage= model= usedI= introduced= in= an= cbj= code= to=describe=the=cracking=of=this=homogeneous=masonry. OKNK mresentation of the model qhe=model= is= a= variant= of= the= initial= concrete=model= described= in=detail=by=pellier= and=Bary=x4z=and=coméleted=in=OMNM=to=consider=the=éossibility=of=crack=reJclosure.=ft=uses=a=oankine=multiJcriterion=in=tension=and=a=arucker=mrager=criterion=in=coméression.=tith=this=Pa=damage=modelI=the=beginning=of=cracking=and= the= width=of= crack= oéening= is= determined= according= to= local= strainI= without= any= initial=assumétion= on= crack= location= or= orientation.= qhe= cracks= and= damage= zones= are= the= natural=conseèuences=of=the=localization=érocess=induced=by=the=softening=éhase=of=the=behaviour=law.==At=the=beginning=of=the=loadingI=the=effective=stress=EσeffFI=is=calculated=according=to=ENFW=== ( ) ( )eeff ε`σ M= = ENF=

=whereW=EεeF=Z=elastic=strainI=`M=Z=healthy=material=stiffness=matrix=EunJcrackedF.=qhenI=this=effective=stress=EσeffF=is=seéarated=into=a=negative=éart=EσcF=in=coméression=and=a=éositive=éart=EσtF=in=tension.=qhe=internal=variables=that=characterize=the=damage=state=of=the=masonry=are=ac= in=the=coméressive= domain= and= at= in= tension.= fn= coméressionI= the= negative= éart= EσcF= is= used= to= assess=a=arucker=mrager=eèuivalent=stress=EOFI=on=which=the=damage=variable=ac=deéends.==

=PSNO fδgσ d

am += = EOF=

=whereW=gOd=Z=second=invariant=of=the=deviator=of=EσcFI=fN=Z=trace=of=EσcFI=δ==Z=the=arucker=mrager=constantI=which=deéends=on=the=internal=friction=angle=φ=as=follows=in=EPF.=δ=is=determined=by=exéerimental=tests=on=saméles.==

=jj

sinPsinPOδ

-= = EPF=

=fn =tensionI =a =oankine =`riterion =Ejaximal =qensile =ptress =criterionI =also =called =jqp=by =brdogan =and =pih=xTz=is=used=to=assess=the=tensile=damage=tensor=at.=ft=affects=the=effective=stress=in=tension=EσtFI=so=as=to=include=the=crack=reJclosure=éhenomenon=in=the=mechanical=behaviour=of=the=masonry.=qhe=aééarent=stress= to= be=used= at= integration=éoints= of= the= finite= element= code= is= obtained= by= E4FI= where= f= is= the=identity=tensor.=

=

ONS4=

= ( ) ( ) ( )( ) ( )úúú

û

ù

êêê

ë

é-+--=43421

ft

éefftefftc σσaσafafσs

= E4F=

=fn= eèuation= E4FI= EσéF= is= a= élastic= stress= following= a= crack= reJclosure= yield= function= described= in=ptablon’s=work=xSz.=ft=is=eèual=to=EσeffF=during=the=damage=érocessI=such=that=the=stress=in=the=localized=cracks=EσftF= stays= eèual= to=zero=until=a= crack=reJclosure= is= activated.= qhe=behaviour= law=of= the=sound=material= in= uniaxial= loading= is= reéresented= on= cigure= N.= ln= this= figureI= the= strengths= are=noted= fc= in=coméression=and=ft=in=tensionI=and=the=éeak=strain=in=coméression=is=εcIéeak.=Before=damageI=the=law=is=characterized= by= the= same= elastic= modulus= in= uniaxial= coméression= and= tensionI= noted= b.= qhese= 4=éarameters=EfcI =ftI=bI=εcIéeakF=have=to=be=determined=exéerimentally.=qhe=éeak=strain= in=tension= εtIéeak= is=given=by=ERF=W==

=bft

éeakt =Ie = ERF=

=As=illustrated=on=cigure=NI=the=damage=leads=to=a=éostJéeak=softening=éhase=in=relation=with=the=fracture=energy=in=tension=dft=and=in=coméression=dfc.=qo=avoid=a=deéendence=of=the=finite=element=solution=on=the=mesh=sizeI= the=damage= evolution= law=has= to=deéend=on=the=finite=element=size.=cor= this=éuréoseI=a=volumic=cracking=energy=“gft”=Eor=“gfc”F=is=used=Ebèuations=ESF=and=ETFFI=deéending=on=the=orientation=of= the= crackI= and= chosen= in= such= a= way= that= the= energy= under= the= tensile= curve= eèuals= dft= Eor =dfcF=whatever=the=size=of=the=element=in=the=direction=éeréendicular=to=the=crack.==== mftft lgd ´= = ESF=

=

= ( )ò -+=to

éeakt

dabb

fg tt

ft

e

e

eeI

NO

O

= ETF=

=whereW=lm=is=the=finite=element=length=in=the=direction=éeréendicular=to=the=crack.=A= method= has= been= develoéed= to= determine= the= length= of= the= finite= element= éeréendicularly= to= the=crackI=i.e.=in=the=main=stress=directionI=and=the=tensile=energy=dissiéated=in=that=direction=Eptablon=xSzF.=cinallyI= the=softening=éhase=of=the=behaviour=law=deéends=on=the=finite=element=size=in=an=anisotroéic=wayI= thus= ensuring= that= the= global= reséonse= of= the= cbj= will= be= indeéendent= of= the= mesh.= qhis=technièue=allows=the=structure=to=be=meshed=indeéendently=of=the=forecasted=cracking=éattern.=qhe =model =also =allows =a =variable =to =be =élotted =that =is =very =interesting =for =éractitionersW =the =`rack =jouth=léening=aisélacement= E`jlaF.= ft= can=be=calculated= directly= at= the=dauss= éoint= during= the=finite= element= solving= érocedureI= or= éostJtreated= at= the= end= of= the= whole= calculation= for= each= steé.=`jla=deéends=not=only=on=the=damage=state=but=also=on=the=strain=state.=fn=the=éresent=modellingI=it=correséonds=to=the=average=crack=oéening=disélacement=coméuted=assuming=a=single=localized=crack=in=each= element= damaged= in= tension.= ft= is= aééroached= using= EUF= in= a= main= direction= of= the= oankine=effective=stress.==

= ( ) ( ) ÷÷ø

öççè

æ

--

-úúû

ù

êêë

é

--

=tIéeak

tIéeaktmtom

tIéeak

tIéeaktmemm af

aaKefσKe

afaa

KεKl`Mla = EUF=

=whereW=lm=Z=finite=element=length=in=the=main=direction=of=cracking=“m”X=atm=Z=qensile=damage=value=in=the=correséonding=main=direction=‘m’X=atIéeak=Z=aamage=value=at=éeak=in=tension=Eéoint=N=in=cigure=NFX=σom=Z=`urrent=value=of=the=oankine=criterion=in=the=direction=‘m’X=eEuF=Z=eeaviside=function=defined=by=eEuF=Z=f=for=u=[=MI=M=otherwise.=An=illustration=of=the=advantage=of=using=this=variable=instead=of=the=classic=damage=variable=is=the=fact=thatI= even= if= many= limited= cracks= occur= in= a= massive= structureI= only= the=main= cracks= will= stay= oéen=until= failureI=and=all=the=surrounding=ones=will=be=reclosed.=`jla=is= then=able=to=caéture=this=main=crack=among=the=multiéle=damaged=elements.=

=

ONSR=

OKOK mreJdamage qo=aééroach=the=current=masonry=stiffnessI=and=eséecially=the= initial=brittle=state=of= the=mortarJblock=interfaceI= initial= damage=of= the=masonry=can=be=used.= ActuallyI= laboratory= tests=have=shown=thatI= for=masonryI= the= stiffness= in= tension= and= the= stiffness= in= coméression= are= different.= curthermoreI= at= the=very=beginning=of=the=loadingI=the=exéerimental=curves=in=coméression=show=a=érogressive=increase=of=the=stiffness=until= the=voung=modulus=b= is= reached.= qhis=éhenomenon=comes= from=the= fact= that= the=material=contains=micro= initial=cracks= that= reclose=in=coméression.= fn=additionI= in=masonry=structuresI=the=shrinkage=of=the=mortar=joints=between=the=stonesI=at=construction=timeI=creates=éores=and=cavities=that=influence=the=stiffness=of=masonryI=as=demonstrated=by=ptablon=xUz.=qhese=exéerimental=results=are=considered=in=the=model=by=means=of=a=“éreJdamage”=éarameter=atMI=transforming=the=behaviour=law=of=the=sound=material=into=a=éreJdamaged=material=behaviour=lawI=as=illustrated=in=cigure=N.=cinallyI= the=damage=model=éroéosed=for= the=masonry=reèuires=V=éarameters= that=have=to=be=determined=initially= by= exéerimental= tests= in= the= laboratory= and= a= homogenization= methodW= elastic= modulus= bI=moisson’s=ratio=νI=coméressive=strength=fc=and=strain=at=éeak=in=coméression=εcIéeakI=tensile=strength=ftI=the=fracture=energy=in=tension=and=coméression=dfc=and=dftI= the=arucker=mrager=éarameter=δI=and=the=initial=damage=in=tension=atM=that=allows=a=éreJexisting=crack=or=any=localized=disorder=to=be=taken=into=account.==

s

e

pound materialmreJdamagedmaterial

tension

coméression

rnloadingin=tensionthen loadingincoméressionwith crackreJclosure and stiffnessrecovery

ft

fc

ecIéeak

b

ENJatMFb

=

cigK N=`oméarison=between=the=sound=material=and=the=éreJdamaged=material==qhe= model= calculates= P= internal= variable= tyées= EacI =atI =`jlaFI =useful =to =estimate =the =state =of =the =structure.=qhe=calculation=érocess=determines=the=locations=and=the=directions=of=the=main=cracks=that=develoéI=indeéendently=of=the=mesh.==OKPK eomogenization process in compression fn= a= macro= aééroachI= a= homogenization= law= is= used= to= reéresent= the= mechanical= behaviour= of= the=healthy= masonry= Ewithout= any= crack= or= éreJdamageF.= As= it= isI= of= courseI= not= éossible= to= remove=a=reéresentative= volume= of= the= various= coméonents= from= the= bridge= masonryI= a= numerical=homogenization= érocess= is= éerformed= to= determine= the= mechanical= éarameters= of= the= masonry=behaviour= law.= qhe= mechanical= éarameters= of= each= coméonent= of= the= masonry= EstonesI= mortarI= and=interface= between= joints= and= blocksF= are= determined= seéaratelyI= then= introduced= into= a= numerical=calculation= of= a= masonry= elementary=volumeI= as= suggested= in= a= érevious= study=éresented= at= pAe`=OMNM=Eaomede=xRzF.=qhe=steés=of=the=homogenization=method=can=be=summarized=as=followsW=

– bxéerimental=characterization=of=– qhe=mortar=and=the=stones=by=means=of=coméressive=testsI=– qhe=stoneJmortar=interface=by=means=of=PJéoint=bending=testsI=

– citting=of=the=individual=mortar=and=stone=behaviour=laws=with=the=damage=modelI==– kumerical=calculation=of=an=elementary=volume=of= masonry=and=fitting=of= the=éarameters=of= the=

homogenized=masonry=damage=law=used=for=the=bridge=calculation.=qhe= reéresentative= elementary= volume= chosen= is= a= numerical= wallI= the= dimensions= of= which= are=defined= in= the=buroéean= standard=séecifications= Ebk=NMROJNI=NVVVF.=qhe=wall= is= loaded=by=aéélying=a=vertical=disélacement=inducing=coméression=and=transverse=tensions=in=the=coméosite=wall.=

=

ONSS=

PK Teb Bofadb pTrafba

PKNK aescription of the current state of the bridge qhe=bridge=studied=Ecigure=OF=was=a=long=stone=masonry=viaduct=built=in=NVM4=EV=séansI=total=length=NPS=mF=in=the=close=neighbourhood=of=maris.=qraffic=on=the=two=lines=is=very=intense=and=the=bridge=suééorts=the=reéeated=éassage=of=suburban=éassenger=trains=and=freight=trainsI=with=UM=to=NRM=crossings=daily.==

=

péandrell wall

saultmiers

Abutmentsoing

péandrell wall

saultmiers

Abutmentsoing

=

cigK O=qhe=masonry=bridge=studied=EV=séans=about=NO.RM=m=longI=U=m=wideF.=Archive=élan=NVM4==ln= this= bridgeI= disorders= have= aééeared= in= the= éastW= disélacements= of= foundationsI= and= transversalI=longitudinal=and=skew=cracks=Ecigure=PF.=oeinforcements=have=been=made=by=adding=steel=arches=under=some=arches= of= the=viaduct.=`oncrete=and=steel=microJéiles=were= installed=beside=the=original= timber=éiles=in=OMMU.=`racks=can=be=seen=on=the=séandrel=wall=and=in=the=intrados=of=the=vaults.=qhey=aééear=in=the= mortar= joints= between= the= stone= blocks= Eeséecially= longitudinal= and= skew= cracks= under= the=intradosFI=and=also=through=the=stones=themselves.==

=========

=

cigK P=qransversal=crack=in=a=séandrel=wall=EleftF=and=longitudinal=crack=in=the=intrados=ErightF==PKOK Measurement of displacements and crack opening under service loads All=the=measurements=were=made=while=a=freight=train=was=crossing=the=bridge.=qhey=includedW=

– jeasurement=of=relative=and=absolute=deflection=under=the=intrados=at=mid=séanI=– jeasurement=of=horizontal=and=vertical=disélacement=at=4=éointsI=– jeasurement=of=width=of=cracks=Eérecision=NM.NMJS=mF.=

At=the=same=timeI=train=weightI=teméerature=and=relative=humidity=were=noted.==PKPK bxtraction of cores from the masonry elements fn=guly=OMMU=and=ganuary=OMMVI=R=cores=were=extracted=from=the=bridgeI=in=the=third=séanI=from=under=the= intrados= of= the= vault.= qhe= cores= are= M.T= to= N.OM= m= longI= with= a= diameter= of= V.R= cm= Ecigure=4F.=bxamination=of= the=cores=shows= that=O= tyées=of=stone=exist= in=this= masonry=bridgeW=a=beigeI= exterior=facing=stone=Eat=left=on=the=éhotoF=and=anotherI=grey=stone=for=interior=masonry=Eat=right=on=the=éhotoF.=qhe=mortar=that=links=the=stone=blocks=consists=of=small=and=large=aggregates.=crom=these=coresI=small=saméles=were=extracted=in=each=of=the=P=coméonents=to=determine=their=individual=éroéertiesI=and=in=the=mortar= above=the=mortarJblock= joints= to=determine= its= behaviour=when=embedded=between=two=stone=blocks.=qhe=behaviour=of=the=mortarJstone=interface=was=also=investigatedI=as=described=later.==4K bumbofMbkTAi TbpTp fk iABloATlov

4KNK fndividual mechanical characteristics of stones and mortar qhe= mechanical= éarameters= of= each= coméonent= of= the= masonries= EstonesI= mortarI= and= mortarJstone=interfaceF= were= determined= seéarately= by= means= of= a= PJsteé= exéerimental= érocedure.= collowing= this=exéerimental=éhaseI=the=comélete=behaviour=laws=for=mortar=and=stones=were=fitted=with=the=damage=model.=

=

ONST=

pteé N: individual exéerimental characterizatiçn çf the mçrtar and the O stçnes qhe=two=stones=are=calcareousI=homogenous=and=isotroéic.=qhe=characteristics=given=in=qable=N=result=from=classical=mechanical=tests=carried=out= in=the=laboratory=EvolumeI=mass=and=éorosity=according=to=bkNVPSI= uniaxial= coméression= tests= as= defined= in= bkNVOS= and= bkN4RUMI= sélit= tensile= test= with=kcmV4J4OOJRF.==

Table N=marameters=used=for=individual=materials==

Material moisson coefficient

b xdmaz

fc xMmaz

dfc xMgLmOz

ecIpeak xmmLmz

ft xMmaz

dft xMgLmOz

fnterior=stone= M.OS= TS=±SB= NTO=±UB= M.OV= P.T= U=±NUB= T.NMJ4=

cacing=stone= M.OR= PV=±UB= NOM=±PB= M.NR= P.O= NM=±NPB= O.NMJ4=

jortar= M.NV= R=±NB= NV=±RB= M.MO= O.U= N.O=±NTB= M.OR.NMJ4==pteé O: exéerimental characterizatiçn çf the cçnfinement effect çf mçrtar qhis= was= achieved=by= means= of= coméression= tests= on= stoneJmortarJstone= multilayers.= kine=uniaxial=coméression=tests=were=carried=out=on=cylindrical=cores=Ediameter=O.SR=cmI=height=S.S=cm=to=V.OR=cmF=including=mortar=embedded=between=two=éieces=of=stone=Ecigure=4F.=qhe=failure=of=the=saméle=resulted=from= failure= of= the= mortar= when= the= mortar= width= was= large= relative= to= that= of= the= stoneI= but= from=failure=of=the=stone=Eaxial=crackF=when=the=mortar=width=was=smallI=because=of=the=confinement=effect=aéélied=to=the=mortar=joint=by=the=bonded=stone=blocks.==pteé P: exéerimental characterizatiçn çf the stçneJmçrtar interface in tensiçn pix= PJéointJbending= tests= were= carried= out= on= séecial= saméles= made= of= a= mortar= joint= embedded=between=O=éieces=of=stone=as=can=be=seen=on=cigure=4=Edisélacement=increasing=by=M.MN=mmLminF.=qhe=éarameters=chosen=for=the=mortar=are=given=in=qable=N.==

====== = =

cigK 4=`ore=coméression=tests=EleftF=and=P=éointsJbending=test=on=multilayers=ErightF==

A= numerical= analysis= of= this= test= determined= the= confinement= éarameter= δ Z= M.RO= Erelative= to= an=internal=friction=angle=φ Z=OP°F.==4KOK eomogenization qhe=general=érinciéle=adoéted=for=the=homogenization=érocess=was=the=followingW=

– fn=tensionW=the=homogenized=behaviour=was=that=of=the=mortarJstone=interface=but=with=additional=éreJdamage=to=simulate=the=weakness=of=the=mortarJblock=bondI=as=exélained=éreviously.=qhe=law=adoéted=is=shown=in=cigure=R.=qhe=éreJdamage=in=tension=atM=was=M.V.=

– fn=coméressionW=the=mortar=and=the=stone=behaviours=were=unified=by=calculating=a=reéresentative=elementary=volume=as=exélained=in=section=O.P.=te=obtained=the=éarameters=given=in=qable=O=Eqhe=stone=blocks’=dimensions=were=4M=cm=×=OM=cm=×=PM=cm.=qhe=mortar=joint=thickness=was=O=cmF.=

=

=

cigK R=eomogenized=behaviour=law=in=tension=

=

ONSU=

Table O=marameters=of=homogenized=behaviour=law=of=masonries=in=coméression==

Masonry moisson coefficient

b xdmaz

fc xMmaz

dfc xMgLmOz

ecIpeak xmmLmz

fnterior=stone= M.OR= 4N= NNS= M.PT= P.T=

cacing=stone= M.OR= OT= U4= M.OP= P.S=

=ko =saméles =of =the =backfill =were =taken =Ecoring =too =shortF. =te =assumed =that =the =backfill =acted =as =cohesive= sandW= it= was= modelled= using= a= arucker= mrager= criterion= with= a= negligible= cohesion= and=negligible=tensile=strength.==RK krMbofCAi AkAivpfp lc Teb Bofadb pTrafba

RKNK Mesh and boundary conditions cor=numerical=caéacity=reasonsI=only=P=séans=were=modelled=with=the=model=imélemented=in=the=cbj=code=Ansys.=qhey=were=séans=numbers=OI=P=and=4.=qhe=mesh=was=built= in=such=a=way= that= the=final=calculation=tool=could=be=used= for=any=masonry=arch.=qhe=bridge=was=divided= into=R=zones=Ecigure=OI=the=éiers=are=not=modelledFW=the=vaultI=embedded=between=the=two=séandrel=walls=and=the=two=ringsI=the=abutments=and=the=backfill.=qhe=rails=and=the=ballast=were=added=on=to=the=bridge=E4=lines=as=can=be=seen=on= cigure= UFI= by= means= of= Oa= elements= with= an= elastic= linear= law= linked= to= the= structure= by= joint=elements= Erelative= density= Z= N.TX= b= Z= PM=dmaX= ν Z= M.OX= vertical= rigidity=Z=NMM= jmaLmX= longitudinal=rigidity=Z=NMMM=jmaLmF.=qhe=vertical=élanes= located=at= each=end=of= the=three= calculated=séans=were=blocked=horizontally=in=order=to=simulate=the=continuum=of=the=bridge=on=each=sideI=symmetrically.=qhe=soil=and=foundations=under=the=bridge=were=modelled=by=means=of=elastic=joint=elementsI=the=rigidity=of=which=was=calculated=with=reséect=to=the=results=of=onJsite=investigations=Edisélacements=of=éile=bases=under= freight= train= loads= as= described= in= P.OF.= A= first= calculation= of= the= bridge= determined= the=foundation=rigidity= in=such=a=way=that= the=vertical=disélacement=of= the=foundations=under= the=freight=train=reached=the=mean=value=measured=EM.OO=mmF.==RKOK Methodology and results of calculation qhe=bridge=was=calculated=under=P=successive=loadingsW=selfJweightI=foundation=disélacementsI=train.==pelfJweight rnder=selfJweightI=the=vault=deflection=was=O.O=cm.=A=few=cracks=aééeared=symmetrically=Ecigure=SF.==

=

cigK S=`jla=and=cracking=scheme=under=selfJweight==aisélacements çf fçundatiçns fn=order=to=create=a=skew=crack=under=the=intrados=of=the=third=séanI=as=actually=observedI=the=following=disélacements=were=aééliedW=NO=cm=for=one=sideI=R=cm=for=the=other=Ecigure=TF.=kote=that=these=iméosed=disélacements=were=not=measured=on=siteI=but=fitted=to=exélain=the=current=crack=éattern=observed.==qrain lçad cinallyI= a= train= load= was= aéélied= to= the= cracked=bridge=and= was= increased=until= collaése= Eqhe= worst=éosition=of=the=train=had=been=determined=in=advance=by=means=of=a=simélified=elastic=calculationF.=qhe=cracking=scheme=to=collaése= is=given=on=cigure=U=and= the= loadJdisélacement=curve=on=cigure=V.=qhe=calculation=was=stoééed=at=the=éeak=load=of=OR=jkI=i.e.=a=train=load=of=NR=jk.=te=observed=that=the=deflection =calculated =under =service =load =was =about =N =mmI =i.e. =three =times =those =measured =Eabout =M.P=mmF.=te=think=that=the=éarameters=introduced=in=the=crack=reJclosure=function=could=be=iméroved.=qhis=is=feature=that=needs=further=study=considering=the=real=deflection=of=the=bridge=under=service=load.=

=

ONSV=

=======

=cigK T=aisélacements=of=foundations=to=create=the=initial=cracked=stateI=and=`jla==

=

=

cigK U=`jla=and=cracking=scheme=under=train=load==

qota

l=loa

dEj

kF

aisélacement EmFM====================M.MR=================M.NM=================M.NR==================M.OM================M.OR

OU

O4

OM

NS

NO

U

4

M

pelfJweight

aisélacement of=foundations

qrain=load

=

cigK V=mosition=of=the=axle=load=EleftF=and=deflection=of=the=vault=under=train=load=until=collaése=ErightF=

=SK ClkCirpflkp =

A= global= methodology= has= been= éroéosed= to= assess= masonry= bridge= behaviour.= ft= is= based= on=a=numerical= model= able= to= describe= the= crack= éattern= and= to= consider= the= initial= damage= in= the=homogenized=material.=qhe=imélementation=of=the=model=in=a=Pa=cb=code=allows=the=whole=history=of=the=structure= to=be=simulated= from= its= construction= onwards.= An= iméortant= steé= in= the= method= is= to=observe=the=current=cracked=state=of=the=bridgeI=considered=as=the=initial=state=of=the=calculation=under=traffic= load.= cor= thatI= just= after= aéélying= the= selfJweightI= a= foundations= disélacement= field= is=determined= in= order= to= obtain= coméatibility= between= the= onJsite= crack= éattern= and= the= numeric=reséonse.=qhe=calculation=of=the=bridge=under=loads=is=carried=out=until=collaése.=cinallyI=the=calculation=results= érovide= a= realistic= descriétion= of= the= masonry= behaviour= in= terms= of= crackingI= and= give=interesting= information= for= éractitionersW= crack= oéening= under= éassage= of= a= freight= trainI= éile=movements=andI=of=courseI=maximal=loading=to=assess=the=safety=level.=

=

ONTM=

AChkltibadbMbkTp =qhe =financial =suééort =by =the =pk`c =and =occ =granted =to =the =ija` =laboratory =for =this =research =is =gratefully=acknowledged.= obcbobkCbp xNz= lrban=w.I=rf`.= EOMMRF= fméroving=assessment= oétimization=of= maintenance=and=develoément=of=

database=for=masonry=arch=bridgesI=mrogress=reéort.=xOz= mroskeI=a.=san=derlderI=m.=EOMMVF=pafety çf histçrical stçne arch bridgesI=péringer.=xPz= oocaI= m.I= `ervera= j.I= dariué= d.I= mela= i.= EOMNMF= ptructural= analysis= of= masonry= historical=

constructions.= `lassical= and= advanced= aééroachesI= Archives çf `çméutatiçnal Methçds in bngineering NTWOVVJPOR.=

x4z= pellier=A.I=Bary=B.=EOMMOF=`ouéled=damage=tensors=and=weakest= link=theory=for=describing=crack=induced=orthotroéy=in=concreteI=bngineering cracture Mechanics=NSOV.=

xRz= aomède= k.I= pellier= A.= EOMNOF= bxéerimental= and= numerical= analysis= of= behaviour= of= old= brick=masonriesI=fnW=mrçcK fntK `çnfK pAe` OMNMI=phangaiI=`hina.=

xSz= ptablon=q.= EOMNNF= Méthçdçlçgie éçur la reèualificatiçn des éçnts en maççnnerieI =mha =thesisI =rniversité=de=qoulouse.=

xTz= brdogan=c.I=pih=d.`.=ENVSPF=ln=the=crack=extension=in=élates=under=élane=loading=and=transverse=shearI=gçurnal çf Basic engineeringI=URWRNVJROT.=

xUz= ptablon=q.I=pellier=A.I=aomede=k.I=mlu=B.I=aieleman=i.=EOMNNF=fnfluence=of=building=érocess=on=stiffnessW= numerical= analysis= of= a= masonry= vault= including= mortar= joint= shrinkage=and= crack= reJclosure=effectI=Materials and ptructure.=