=

O4UM=

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

afpCobTb bibjbkT jlabiifkd lc jAplkov rpfkd iApbo pCAkkfkd aATA Mcfnerney gamesNI qrzcinski fanOI aegong Matthew gKP ABpToACT aiscrete=element=modelling=EabjF=provides=an=effective=way=to=model=the=stability=of=many=historic=masonry= structures= and= laser= scanning= has= proven= valuable= in= obtaining= the= required= geometryK=eoweverI= defining= modelling= geometry= directly= from= point= cloud= data= and= fully= utilising= abj=remains= a= challengeK= fn= the= first= part= of= this= paperI= methods= of= creating=Pa= geometric= models= from=laser= scanning= data= suitable= for= abj= are= investigatedK= qhe= first= method= involves= visualizing= point=clouds= in= a= CAa= environment= and= manually= drawing= masonry= units= directly= over= the= cloudK= qhe=second=method=involves=automatic=generation=of=masonry=unit= geometries=by= implementing=a= region=growing= algorithm= which= uses= distinguishing= information= EeKgK= colourI= intensityF= to= discern= jointsK=iaser =scanning=surveys=of =a =cloister =vault =from=the=kew=Court =at =ptK =gohn’s =College=and=a=fan=vault =from= hing’s= College=Chapel= were=conducted= and= provided= data= for= creating= abj= modelsK= oesults=highlight= the= need= for= increased= automation= in= the= geometry= defining= processI= but= clarify= its=dependence=on=data=qualityK=fn=the=second=part=of=this=paperI=abj=results=of=structural=analyses=of=the=vaults= are= presentedK= ppecificallyI= vault= thrustsI= required= fill= depthsI= and= the= response= to= support=displacements=were=determinedK=qhe=results=demonstrate=the=utility=of=abj=to=evaluate=existing=vault=displacements=and=possible=Pa=collapse=mechanismsK==

=heywords: iaser scanningI aiscrete blement ModellingI MasonryI saultI moint cloudI

pegmentationI aisplacement analysis NK fkTolarCTflk NKNK Background qhe=geometry=of=many=historic=masonry=structures=is=not=well=documentedI=and=these=structures=often=experience= a= complex= sequence= of= displacements= throughout= their= historyK= aisplacementsI= which=typically=concentrate=at=masonry=jointsI=can=be=large=before=collapse=is=a=concernI=making=modelling=of=stability= particularly= challengingK= fn= this= contextI= discrete= element= modelling= EabjF= is= a= suitable=alternative=to=model=historic=masonry=structures=because=of=its=ability=to=treat=masonry=units=as=separate=yet= interacting= bodiesK= abj= methods= differI= but= are= generally= established= to= model= contact= and=stabilityI=rather=than=stiffness=and=strengthK=lne=such=method=was=developed=by=Cundall=to=model= the=behaviour= of= geologic=rock= formations= xNz= and=granular= media= xOzK= qhe=separate=blocks= in=Cundall’s=approach=are=modelled=with=compliant=contacts=where=block=interJpenetration=is=controlled=by=normal=and=shear =joint =stiffnessK =Cundall =xPz =and=eart =et =alK =x4z =expanded=this =earlier =work=to=create =the=Pa=computer=program=PabC=xRzI=which=was=used=for=this=workK=thile=abj=methods=and=finite=element=modelling=EcbjF=methods=are=mergingI=abj=methods=are=distinguished=by=the=followingW=blocks=can=be=compressible=or= rigid= with=deformation=occurring= at= the= jointsI= interaction=between=blocks= is= via=point= Eor= lineF= contacts= at= the= jointsI= full= separation= between= blocks= and= large= displacements= are=inherently= accommodatedI= and= analyses= typically= utilize= explicit= timeJstepping= algorithms= xSzK= fn=contrastI=cbj=is= more=focused= on=elasticity=and=plasticity= in= the=context= of=a= continuumI= making= its=application=to=historic=masonry=less=than=idealK==

================================================N=aoctoral=oesearcherI=rniversity=of=CambridgeI=rhI=jbm4S]camKacKuk=O=jaster’s=oesearcherI=rniversity=of=CambridgeI=rhI=itOPU]camKacKuk=P=iecturerI=rniversity=of=CambridgeI=rhI=mjdVT]engKcamKacKuk=

=

O4UN=

rsing=abjI=iemos= xTz= investigated=the=seismic=behaviour=of= intersecting=masonry=arches=–=a= main=component= of= cross= vaultsK= jechanisms= were= effectively= determined=and= demonstrate= the=utility= of=abjI=but=Pa=stability=is=only=briefly=consideredK=qheodossopoulos=et=alK=xUz=and=wessin=et=alK=xVz=have=investigated= the= behaviour= of= cross= vaults= and= domesI= respectivelyI= using= experimental= discrete=methodsK= fn= the= case= of= Oa= structuresI= traditional= limit= analysis= can= accurately= define= mechanisms=without= masonry=crushing=or=slidingK=eoweverI= in=structures=with=doubly=curved=geometryI=collapse=mechanisms=often=involve=significant=sliding=or=crushingI=making=abj=particularly=usefulK=fn=generalI=abj=of=masonry=vaultsI=with=particular=focus=on=Pa=behaviourI=is=limitedK=jeanwhileI= laser= scanning= has= emerged= as= an= attractive= option= for= capturing= the= Pa= geometry= of=historic= masonry= structuresI= as= it= is=nonJinvasive=and= becoming=faster= and=more=affordableK= aevices=using=laser=technology=for=obtaining=geometric=data=from=objects=were=developed=soon=after=the=advent=of= lasers= xNMzX= howeverI= laser= scanning= devices= for= terrestrial= applications= only= became= widely=available=beginning=in=the=NVVMsK=Although=the=potential=exists=for=using=this=data=in=maintenance=and=structural=modellingI=a=common=end=product=of=the=laser=scanning=process=is=a=Pa=record=for=heritage=preservation= EeKgK= xNNzFK= juch= of= the= work= in=utilizing=point= cloud= data= for= structural=modelling= has=focused= on= defining= surface= geometry= for= cbj= EeKgK= xNOzFK= oesearch= specifically= dealing= with=constructing=discrete=models=from=point=cloud=data=exists=EeKgK=xNPzFI=although=it=is=relatively=limitedK=qhe= problem= of= recognizing= masonry= units= in= point= cloud= data= is= one= of= segmentationK= aiscerning=information= in=the=point=cloud=can=be=used=to=distinguish=featuresK=dordon=et=alK=xN4z=commented=on=point= cloud=data= where=bricks= and=mortar= were= distinguished= based= on=reflectanceK= sosselman=et=alK=xNRz= provide= a= survey= of= various= techniques= and= algorithms= used= in= recognizing= structures= in= point=cloudsK=jany=of=these=segmentation=methods=involve=region=growingI=beginning=with=seed=points=and=incrementally=expanding=the=region=to=incorporate=all=points=in=the=cloud=comprising=that=featureK=qhe=potential=for=this=work=to=aid=in=the=automatic=generation=of=abj=geometry=from=point=cloud=data=has=not=been=fully=realizedK= NKOK lbjectives mrevious=studies= indicate=that=abj=has=the=potential=to=reveal=the=Pa=behaviour=of=historic=masonry=structuresX=howeverI=modelling=geometry=must=first=be=definedK=iaser=scanning=is=an=efficient=method=of= obtaining= geometry= of= masonry= structures= but= this= data= remains= underutilized= in= the= context= of=defining=abj=geometryK=fn=this=contextI=the=aim=of=this=research=is=to=investigate=the=use=of=manual=and=automatic=methods=of=defining=geometry=for=abj=using=point=cloud=data=and=to=demonstrate=how=resulting=abj=models=can=be=used=to=evaluate=structural=behaviour=and=capacityK=

=OK abcfkfkd abj dbljbTov OKNK iaser scan survey iaser= scans=of= two=masonry= vaulted=structures= in=CambridgeI= rh= were=conducted=using= the=cAol=cocus= Pa= EphaseJbasedF= laser= scanner= and= initially= processed= and= registered= using= cAol= pcene=software= EcAolI= ptuttgartI= dermanyFK= qimeJofJflight= scanners= determine= the= distance= to= objects= by=measuring=the=return=time=of=the=laser=signalK=qhese=work=well=for=long=rangeI=howeverI=data=capture=rate=is=limitedK=ConverselyI=phaseJbased=scanners=have=limited=range=but=very=high=rate=of=data=capture=as=they=determine=distances=by=measuring=the=phase=difference=between=outgoing=and=returning=signalsK=pcanners=can=also=obtain=nonJgeometric=data=such=as=intensityI=which=is=a=measure=of=the=returning=to=outgoing= signal= energyI= and= colourI= captured= using= an= integrated= cameraK= fntensityI= which= tends= to=depend=on=material=and=angle=of=incidenceI=and=colourI=which=is=affected=more=by=lighting=conditionsI=can=both=be=used=to=discern=masonry=jointsK=qhe=first=structure=studied=was=a=cloister=vault= in=the=kew=Court=at=ptK=gohn’s=CollegeK=qhis=structure=was= designed= by=architects= qhomas= oickman=and=eenry=eutchinson= in= the=dothic= revival= style=and=completed=between=NUOS=and=NUPN=xNSzK=cigure=N=shows=a=colour=laser=scan=and=geometric=model=of=this=structure=created=using=mointools=EBentley=pystemsI=aublinI= frelandF and=ohino=EjckeelI=peattleI=tAI= rpAFI= respectivelyK=qhe= joints=defining=masonry=unit=boundariesI= required=to=define=individual=blocks=for=abjI=are=clearly=evident=in=the=laser=scan=dataK=Access=to=the=top=side=of=this=vault=was=not=possible=and=so=the=fill=depth=was=surmised=from=cracking=evident=on=the=intrados=and=vault=thickness=was=measured=from=below=through=various=small=holesK==qhe=second=structure=studied=was=a=fan=vault=of=hing’s=College=ChapelK=qhe=vault=was=constructed=by=master=mason=gohn=tastell=in=the=late=dothic=style=between=NRNO=and=NRNR=xNTzI=and=has=the=largest=

=

O4UO=

span=of=any=fan=vault=in=the=worldK=cigure=O=shows=an=intensity=laser=scan=of=this=structure=along=with=a=section=through=the=point=cloud=of=a=fan=vaultK=cortunatelyI=full=access= to=the=extrados=of= the=hing’s=College=vault=was=possible=and=so=both=fill=depth=and=vault=thickness=could=be=directly=measured=from=the=aligned= intrados=and=extrados=point=cloudsK=qhe=section=shown=was= taken=at= the=quarter=point=and=clearly=indicates=the=minimum=thickness=present=in=the=vaultK==

= =

cigK N=Colour=point=cloud=with=masonry=joints=evident=EleftF=and=geometric=model=ErightF=of=ptK=gohn’s=College=cloister=vault=

==

=

= =

cigK O=fntensity=point=cloud=Ebottom=leftFI=geometric=model=Ebottom=rightFI=and=section=EtopF=of=the=hing’s=College=Chapel=fan=vault=

=OKOK janual process jasonry= units= were= drawn= in= the= CAa= environment= using= the= location= of= points= in= the= cloud= as=a=guideK=jasonry= joints=evident= in=the=point=cloud=were=used=to=discern=block=boundariesK= fn=generalI=planar=block=faces=were=first=drawn=along=the=profile=of= the=vault= edges=and=were=then=extruded=and=trimmed=to=define=the=Pa=solid=blocks=of=a=single=vault=quadrantK=cigure=P= illustrates=this=processK=fn=the=case=of=the=ptK=gohn’s=College=vaultI=linear=extrusion=was=usedI=while=in=the=case=of=hing’s=College=Chapel=vaultI=the=planar=block=faces=drawn=at=the=edge=of=the=vault=were=rotated=to=construct=the=blocks=EcigK=PbFK=lnce=the=blocks=for=one=vault=quadrant=were=constructedI=they=were=copied=to=complete=the=remaining= three= quadrants= to= simplify= the= model= construction= processK= eoweverI= to= fully= take=advantage= of= the= complete= existing= geometry= of= the= vaultI= unique= blocks= could= be= drawn= for= all=sections=of=the=vaultI=but=some=automation=would=be=required=to=make=this=feasibleK=

pection=

ievel=of=fill=

bxtrados=of=vault=

fntrados=of=vault=

jinimum=vault=thickness=

=

O4UP=

==

=

=

=

=

=

= =

==

=

EaF=moint=cloud= EbF=arawing= EcF=CAa=model= EdF=abj==

=cigK 3=janual=generation=of=abj=geometries=from=point=clouds=for=vault=at=ptK=gohn’s=College=EtopF=and=hing’s=College=EbottomF=showing=dimensions=

=OK3K pteps toward automation aistinguishing= characteristics= such= as= colourI= intensityI= geometryI= etcK= can= be= used= to= aid= in= the=segmentation= of= features= EeKgK= masonry= blocksF= in= point= cloudsK= fn= order= to= contain= sufficient= detail=EeKgK= for= discerning= masonry= jointsF= high= resolution= scans= must= often= be= obtained= for= use= in= this=automatic= segmentation= processK= Accommodating= these= large= data= sets= is= a= significant= challenge=particularly=as=many=segmentation=algorithms=involve=multiple=visits=to=each=point=in=the=unordered=list=of=points=comprising=the=cloudK=fn=this=studyI=the=faces=of=individual=masonry=blocks=comprising=a=wall=were=automatically= segmented= from= the=point= cloud= using=a= region= growing= algorithm= where=block=boundaries=EeKgK= jointsF=and=block=faces=were=recognized=by=their=unique=intensityK=Although=not=done=in= this= studyI= other= discerning= information= such= as= colour= or= local= geometry= could= be= utilisedK= qo=reduce=data=size=while=still=preserving=sufficient=detailI=point=clouds=were=first=automatically=reduced=to=array=data=structuresK=cigure=4=shows=intensity=point=clouds=and=equivalent=arrays=for=masonry=walls=of=brick=with=mortar=and=rough=cut=stone=with=mortarK=Also=shown=are=the=dimensions=of=each=wall=and=size=of=each=point=cloudK==moint=cloud=data=was=first=stored=in=pixel=EarrayF=formatK=qhe=plane=of=the=wall=was=divided=into=a=grid=significantly= smaller= in= size= than= the= point= cloud= but= still= large= enough= to= be= representative= of= the=geometry= of= the= wallK= An= array= of= cells= corresponding= to= this= grid= was= then= definedI= and= intensity=thresholds=were=then=used=to=denote=array=cells=as=corresponding=to=a=joint=or=a=blockK=cor=exampleI=by=using=an=intensity=threshold=of=MKSPI=the=mortar=joints=between=bricks=in=cigK=4a=become=well=definedK=Again=note=that=cigure=4=contains=intensity=data=onlyI=not=colour=dataI=so=the=lack=of=reflectance=of=the=clay=brick=relative=to=the=mortar=allows=blocks=to=be=identifiedK=fn=this=way=the=large=cloud=of=unordered=points=with=a=spectrum=of= intensity=values=was=reduced=to=an=efficient= array=with=discrete=cell=values=Eblock=or=jointF=representative=of=the=masonry=wall=itselfK=A=script= was= then=developed=to=recognise=block= faces= and=automatically=generate= the= corresponding=coordinates= of= blocks= comprising= the= wallK= qhe= algorithm= proceeded= by= finding= the= next= unvisited=array= cell= Einitially= ENINFFK= ff= this= cell= was= denoted= a= block= cellI= then= the= current= block= region= was=defined= as= having= coordinates= corresponding= to= this= single= array= cellK= qhe= algorithm=proceeded= by=visiting=all= adjacent= cellsI= expanding= EiKeK= ‘growing’F= the=block= region=accordingly=until= all= adjacent=cells =denoted =as =block =cells =were =visitedK =qhe =extent =of =the =block =region =was =thus =definedI =and =the =corresponding=coordinates=defining=the=block=were=storedK=qhe=algorithm=continued=until=all= cells= in=the=array=EiKeK=all=locations=on=the=wallF=were=visitedK=cinallyI=a=PabC=data=file=was=created=that=defined=

MKNN4m=

4KS4m=

RKURm=

NOKUPm=

SKU4m=

4KUSm=

4K4Om=PKUNm=

MKMTm= NKVNm=

NKOUm=

NKVNm=

=

O4U4=

a=discrete=block=model=of=the=wall=using=the=block=coordinates=and=a=wall=thicknessK=mreliminary=results=summarizing=this=process=are=shown=in=cigure=R=for=a=masonry=wall=of=dry=cut=stoneK==

= =

= =EaF=NKOP=×=MKT=SmI=N4PRVN=pts=

fntensity=≥=MKSP=EbF=MKUM=×=MKUM=mI=NUVMR=pts=

fntensity=≤=MKRS=

cigK 4=fntensity=point=clouds=of=masonry=walls=EtopF=and=corresponding=arrays=EbottomF=EkoteW=arrays=are=NMM=×=NMM=cellsF=

A= threshold= is= also= defined= in= the= algorithm= ensuring= that= only= block= regions= of= sufficient= size=prescribe= blocksK= CurrentlyI= the= algorithm= requires= block= regions= to= be= closed= EiKeK= they= must= be=completely=bounded=by=joint=cellsFK=jany=of=the=block=regions=evident=in=cigure=4=are=not=completely=closedI=but=tolerances=could=be=integrated=into=the=algorithm=to=establish=the=extent=of=block=faces=for=less= than= ideal=dataK=thile=this= work= is= in=a=preliminary= stageI=ongoing=research=will=aim=to=further=evaluate=the=extent=to=which=automatic=block=generation=is=feasibleK==

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

cigK R=Automatic=generation=of=abj=of=masonry=wall=from=point=cloud==

=3K afpCobTb bibjbkT jlabiifkd 3KNK jodels aiscrete=element=models=of=the=cloister=vault=in=the=kew=Court=at=ptK=gohn’s=College=and=the=ceiling=vault=at=hing’s=College=Chapel=were=created=and=dimensions=of= these=are=shown= in=cigure=PdK=cor=the=ptK=gohn’s=College=vault=the=ribs=are=independent=from=the=vault=stones=and=were=not=included=in=the= modelK= qhereforeI= continuous= joints= were= assumed= at= the= groinsI= resulting= in= three= ‘separate’=vault= surfaces= in= each=quadrant= EcigK=SFK=cor= the=hing’s=College=Chapel=vault= the=ribs= are=integral=with=the=vault=stones=and=were=also=not= included=in=the=modelK=eoweverI= for=simplicity=continuous=

abj=moint=cloud=

Array=à=point=cloud=stored=in=array=à=if=intensity=

satisfies=threshold=denote=as=‘block=

cell’==NKNO=×=NKPP=mI=SNROU=pts=

==à=‘block=region’=expanded=

à=final=region=defines=block=coordinates=

=

fntensity=≥=MKVVV===

=

O4UR=

joints= were= assumed=along= each= of= the= five= radial= ribs= resulting= in= six= ‘separate’= vault= surfaces= in=each=quadrant=EcigK=SFK===

=

cigK S=fntensity=point=clouds=of=the=vault=intrados=at=ptK=gohn’s=College=EleftF=and=hing’s=College=ErightF==kote= that= near= the=springing= of= each=vaultI= well= below= the= fill= levelI= the= ribs= and=vault= blocks=are=integral=and=were=thus=modelled=as=solid=blocksK=ptatic=equilibrium=analyses=were=performed=on=both=vaults= simulating= fill= by= fixing= the= blocks= below= the= assumed= fill= levelK= fn= this= wayI= minimum=required=fill=depth=was=determined=along=with=thrusts=present=in=the=vaultK=qhe=response=of=the=vaults=to=vertical=displacements=was=also=evaluated=to=determine=collapse=mechanismsK=fn=all=analysesI=the=following= material= properties= were= assumedW= density= Z= OTMM= kgLmPI= friction= Z= PR°I= normal= joint=stiffness=Z=NMM=dmaLmI=and=shear=joint=stiffness=Z=TM=dmaLmK=qhe=blocks=were=modelled=as=rigid=and=the=joints=were=assumed=to=have=no=tensile=capacity=or=cohesionK==3KOK oesults qable= N= contains= the= actual= fill= depths= and= the= minimum= depths= required= for= stabilityI= along= with=thrusts=present=at=each=corner=of=the=vaultsK=kote=that=the=vault=weight=values=correspond=to=one=quarter=of=the=weight=of=the=structure=above=the=fill=level=EiKeK=equivalent=to=vertical=reaction=at=each=cornerF=and=the=thrust=values=correspond=to=those=present=at=the=fill=levelK=qhe=thrust=values=were=very=similar=for=each= fill= depth= and= those= corresponding= to= the= larger= span= directions= were= greatest= as= expectedK=iongitudinal= and= transverse= thrusts= for= the=vault= at= ptK= gohn’s= College= were=almost= equal=due= to= the=approximately=square=plan=of= the=vault=and=were=as=high=as=NMRB=and=VPB=of= the=vertical=reactionI=respectivelyK=ConverselyI= longitudinal= and= transverse= thrusts= for= the=vault= at=hing’s=College=Chapel=were=significantly=different= due=to=the=highly=rectangular=plan=of= the=vault=and=were=as=high=as=URB=and=NOTB=of=the=vertical=reactionI=respectivelyK===

Table N=oesults=of=abj==

sault cill depth [m] ¼ sault weight above fill [kk]

iongitudinal thrust at fill level [kk]

Transverse thrust at fill level [kk]

ptK=gohn’s= MKSMEminF= VKO= TKM= SKR=NKOUEactualF= TKS= UKM= TKN=

hing’s= PKPN=EminF= TOKS= 4SKP= TNKT=4KS4=EactualF= RPKR= 4RKR= SUKO=

=cigure=T=shows=the=displaced=shapes=of=both=vaults=subjected=to=vertical=displacement=at=one=supportK=kote=that=not=all=sections=of=the=vaults=fully=collapsedK=qhe=collapse=was=initiated=by=the=instability=of=successive=sections=of=vaultK===3K3K aiscussion qhe= vaults= were= modelled=using= only= the= minimum= thickness= measured= on=siteK= qhusI= the= effect= of=thicker= portions=of= the=structure=Eincluding= ribsF=on=the=forces=present= in= the=vault= and=displacement=behaviour=was=not=includedK=cixing=blocks=in=the=model=that=were=located=lower=than=the=vault=fill=also=strongly= influenced= behaviourK= qhe= point= cloud= data= could= be= further= exploited= for= more= accurate=modelling=geometry=and=a=more=sophisticated=treatment=of=vault=fill=should=be=made=for=future=studiesK==

N= O=

P=

N= O=P=

4=R=S=

=

O4US=

=

= =

cigK T=Collapse=mechanisms=caused=by=vertical=support=movement=of=the=vault=at=ptK=gohn’s=College=EtopF=and=hing’s=College=EbottomF=EkoteW=the=foremost=support=was=displaced=in=each=caseF=

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x4z eartI=oKI=CundallI=mK=AKI=C=iemosI=gK=sK=ENVUUFK=cormulation=of=threeJdimensional=distinct=element=modelJpart=ffK=jechanical=calculations=for=motion=and=interaction=of=a=system=composed=of=many=polyhedral= blocksK fnternational gournal of oock Mechanics and Mining pciences and deomechanics Abstracts=OREPFW=NNTJNORK==

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xVz wessinI=gKI=iauI=tKI=C=lchsendorfI=gK=EOMNMFK=bquilibrium=of=cracked=masonry=domesK=bngineering and Computational Mechanics 1SP=peptember=fssue=bjPW=NPRJN4RK=

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xNNz creidinI= AK= vK= EOMMTFK= qhreeJdimensional= laser= scanning= and= its= application= for= imaging=architectural=structures=and=the=restoration=of=monumentsK=gournal of lptical qechnology=August=T4EUFW=R4RJR4VK=

xNOz iubowieckaI= fKI= ArmestoI= gKI= AriasI= mKI=C=iorenzoI=eK= EOMMVFK=eistoric=bridge=modelling=using=laser= scanningI= ground=penetrating=radar= and=finite=element= methods= in= the=context= of= structural=dynamicsK bngineering ptructures PNENNFW=OSSTJOSTSK=

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