=

ORPS=

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

fNJpfTr TbpTp lN Teb fNTboNAi tbpTboN ClirMNp lc Teb mAoTebNlN ANa MlabifNd lc Teb glfNTp’ MbCeANfCAi molmboTfbp bleniJbva qoumbakariNI aimitrios bgglezosO ABpToACT qhe=paper=reports=aF=the=inJsitu=trial=load=testsI=which=were=carried=out=on=the=fourI=out=of=sixI=internal=columns=of=the=marthenon=western=sideI=the=lpisthodomosI=during=the=recent=restoration=project=EOMMNJ=JOMM4F=and=bF=the=analytical=assessment=of=their=structural=responseI=including=foundationI=based=on=the=obtained=experimental=dataKqhe=dismantling=of=the=entablature=members=during=the=anastylosis=projectI=gave=the=opportunity=for=the=performance=of=in=situ=trial=load=tests=in=order=to=study=the=response=of=the=columnsI=interacting=to=their=foundationK=qhe=testing=project=consisted=in=the=application=of=a=horizontal=force=of=NMJNNkk=at=the=capital=of=each=columnK=At=the=same=timeI=the=horizontal=displacement=of=the=capital=and=the=vertical=displacement=of=the=base=marble=blockI=were=measuredK=qhe=test=was=carried=out=twice=in=each=directionI=to=account=for=differences=in=the=foundation=conditionsK=cor=the=evaluation=and=the=interpretation=of=the=test=results=a=backJanalysis=was=performedK=cor=the=EPJd=nonlinear=elasticF=analysis=oockJjechanics=principles=were=appliedK=qhe=idea=is=that=dry=masonry=structureI=from=natural=rock=stone=blocks=connected=with=frictional=±joint”=forces=are=analogous=to=a=jointed=rockmass=systemK=qhe= comparison= of= measured= values= and= analytical= predictions= are= generally= in= good= agreementI=offering= increased= accuracyK= According= to= the= resultsI= discrete= modelling= with= properly= determined=parameters= for= monument’s= geomaterials= can= satisfactorily=be=applied= to= restoration=analyses= of= this=type=of= structure= and= could= form=the=base= for= more= complex= calculations= involving= dynamic= effects=eKgK=earthquakeK=

=heywords: eeritageI AcropolisI marthenonI ary masonryI gointsI fnJsitu testsI

aiscrete structure modeling NK fNTolarCTflN =qhe=project= described= in= this= paper= is= part= of= the=actions= undertaken= during= the= recent= EOMMNJOMM4F=restoration=project=for=the=anastylosis=of=the=lpisthodomos=EiKeK=the=internal=colonnade=of=the=western=sideF=of=the=marthenonK=

=NKNK The marthenon qhe=marthenonI=the=masterpiece=of=Classical=artI=was=built=on=the=Acropolis=of=Athens=in=a=short=period=of=timeI=between=the=years=44T=and=4P8=BKC=by=the=architects=fktinos=and=hallikrates=and=the=sculptor=mheidias=who=spent=R=years=moreI=to=place=the=sculptures=in=position=on=the=pediments=xNzK=qhe=templeI=dedicated= to= AthenaI= doddess= of= tisdomI= still= existsI= till= our= days= dominating= the= summit= of= the=Acropolis=eill=EcigK=NFK===

=

================================================N=ar=ptructural=bngineerI=eellenic=jinistry=of=CultureI=airectorate=for=the=oestoration=of=Ancient=jonuments=

etoumpakari]cultureKgr=O=Civil=bngineerI=mhaI=mapanikolaou=OMI=AthensI=dreeceI=degle]teeKgr=

=

ORPT=

==

cigK N=qhe=marthenonK=siew=from=the=korthJtest==

=

cigK O=mlan=view=of=the=marthenonK=fn=red=frame=the=lpisthodomos=collonadeK=arawing=by=jK=horres==

NKOK The lpisthodomos qhe=lpisthodomosI=the=western=part=of=the=temple=EcigK=OFI=was=directly=exposed=to=the=disastrous=fire=in=OST= AKaK= and= experienced= the= explosion= of= NS8T= –= which= resulted= in= the= collapse= of= the= eastern= and=middle=part= of= the=building=–= as=well=as= the=various= earthquakes=that= have=occured=in=the=Athens= areaK=qhereforeI= it= bears= the= signs= of= a= complicated= mechanical= historyK= qhe= structural= restoration= of= the=lpisthodomos=was=the=main=target=of=the=anastylosis=between=OMMNand=OMM4=xOzK=fn=the=years=OMMNJOMMO=the= totality= of= the= architrave= blocks= were= removed= in= order= to= be= repairedI= leaving= the= four= northern=lpisthodomos=columns=standing=free=Ethe=southern=two=columns=are=in=contact=to=the=medieval=staircase=masonryFK= lne=of= the=actions= undertaken=in=OMMOJOMMP=was=the=planning=and=execution=of= inJsitu= trial=load=tests=on=those=four=columnsI=in=order=to=assess=their=structural=and=foundation=conditionsK====NKPK The coundation marthenon=is=based=partly=on=the=natural=limestone=of=the=hill=andJ=due=to=the=slopy=ground=of=the=hillJ=on=an=artificial= stereoJprism=consisting= of= discrete= large= stone=blocks= from=soft= rock= material= Eporos=stoneF=from=the=miraeus=coast=EcigK=PFK=qhe=height=of=the=foundation=prism=is=NN=m=on=the=pb=edgeI=S=m=on=the=pt=and=O=m=on=the=ktK==

=

ORP8=

=aF======= bF= cigK P=deometry=of=marthenon’s=foundation;=aF=bast=view=Ep=to=kF=and=bF=mlan=viewK=araw=by=AK=lrlandos=ENVT8F==

=OK TbpTfNd molgbCT =fn=order=to=carry=out=the=trial=load=testsI=first=a=reinforced=scaffolding=was=built=and=testedI=to=serve=as=the=reaction=frameK=A=force=up=to=NM=kk=was=gradually=applied=at=the=middle=of=each=side=of=the=capitals=by= means= of= a= simple= scaffolding= screw= abutted= on= the= reaction= frameK= qhe= applied= force= was=measured= with= a= load= cell= and= the= horizontal= displacement= of= the= capital= as= well= as= the= vertical=displacement= of= the= isolated= marble= blockI= on= which= each= column= standsI= were= measured= with=mechanical=extensometer=and=isaqs=respectively=xPzK==As=a=totalI=PM=trial=load=tests=were=carried=out=and=the=corresponding=loadJdisplacement=curves=of=the=lpisthodomos= columns= lhNI= lhOI= lhP= and= lh4= and= their= foundation= were= obtained= in= the= 4=directions=Eto=the=northI=southI=eastI=westFK==

=PK ANAivTfCAi bsAirATflN ANa fNTbomobTATflN lc TbpT obpriTp =cor=the=evaluation=and=the=interpretation=of=the=test=results=in=respect=to=the=foundationI=an=analytical=approach= was= performedK= qhis= analysis= was= based= mainly= on=oockJjechanics= principlesK= qhe=basic=idea =was =that =the =nature =of =structural =materialsI =that =isI =natural =rock =stone =blocks =Emarble =or =suchF =connected= with= frictional= ±joint”= forces= in= a= dry= masonry= structureI= are= fully= analogous= to= a= jointed=rockmass= systemK= AccordinglyI= the= loaded= columns= are= simulated= as= a= discrete= element= structure=consisting= of= the= column= drums= and= the= column= capitalI= with= frictional= compressionJonly= springs=between=aF=successive=drums=and=bF=the=column=base=and=the=underlying=monument=base=Ecrepis=and=foundation=blocksF=lying=upon=limestone=bedrockK===

===

cigK 4=deotechnical=conditions=below=the=column=base=Ej=Z=marbleI=m=Z=marlI=a=Z=dolomiteF==qhe=subJbase=crepis=and= the=underlying=discrete= foundation=Econsisting=mainly=of=marly=blocks=with=potential=existence=of=soil=intercalationsI=and=locally=of=dolomite=blocksFI=is=simulated=as=a=two=layered=half= space= on= rigid= limestone= bedrockK= fn= this= case= the= geomaterials= are= modeled= as= an= elastic= –=perfectly=plastic=materialK=qhe=typical=formation=of=the=opisthodomos=column=subJbase=is=presented=in=the=section=of==cigK=4=x4zK=ft=is=obvious=that=the=column=is=based=on=a=two=layered=half=spaceI=consisting=of= the=superficial= marble=crepis= and= the=Emuch= thickerF= foundation= from=marly= Eor= locally=dolomiteF=blocksK=qhe=geometry=of=this= layering=is=differentiated=in=respect=to=the=direction=Ewest=vs=eastF=of=the=underlying=geomaterialsI=due=to=the=thickness=of=the=marble=crepis=EMKSOm==thick=to=westside=–=MKPM=m=thick=to=the=eastsideFK=

katural=oock=

=

ORPV=

PKNK deomaterials qhe=geomaterials=involved=for=analytical=interpretation=of=the=results=are=the=followingW

– jarble=drums=and=Crepis=– moros=cooting=Blocks=Emarly=limestoneF=– aolomite=cooting=Blocks=– iimestone=Bedrock=

qhe=footing=blocks=came=from=the=rocky=geological=formation=of=the=miraeus=coastI=known=as=AktiteI=which=appears=typically=either=as=a=soft=rock=Emarl=to=marly=limestoneF=or=as=a=dolomiteK=

Table N=jechanical=properties=of=deomaterials=

=

= fntact=oock= oockmass== b==EjmaF= v= qu=EjmaF= γ=EkkLmPF= dpf= boj=EjmaF=

jarble= TMMMM= MKOM= 8M= OTKM= TM= RMMMM=jarl=== OMMM= MKOR= NN= ORKM= SM= NMMM=aolomite= N8MMM= MKOM= SM= OSKM= SM= NPMMM=iimestone= RMMMM= MKOM= NMM= OSKM= TM= PRMMM=

= =qhe=assignment=of=mechanical=and=geostructural=properties=to=the=above=materials=Evoung=jodulus=bI=moisson=ratio=vF=is=a=prerequisite=for=the=conduction=of=the=analytical=calculationsK=pince=these=materials=are=classified=as=rockI=the=application=of=dpf=method=xRJTz=applies=for=the=estimation=of=the=rockmass=with=application=of=ooclab=software=code=x8zK=fndeedI=as=it=has=been=shown=in=previous=research=ExVzI=xNMzFI= large= scale= dry= masonry= structures= from= discrete= blocks= Eas= the= case= in= hand= of= the= large=foundation=of=marthenonF=consisting=of= rocky=blocksI= may=successfully=be=simulated=as=a= continuumI=applying=rockJmechanics=principles=to=fractured=rockmassK=fn=additionI=this=approach=may=also=apply=in=small=scaleI=for=evaluation=of=isolated=structural=block=properties=Eaccounting=for=ageing=effects=and=presence=of=microfracture==netFK=qhe=initial=mechanical=parameters=for=application=of=the=dpf=method=Euniaxial= compressive= strength=qu=and=b=of= intact=rockFI=are=obtained=from=relevant= literature=xVJNOzI=while= the= value=of=dpf= is= based=on=expertise=macroscopic= estimationK= qhe= initial=parameters= and= the=results=for=rock=mass=properties=are=summarized=in=qable=NK==PKOK Analytical procedure qhe=comparison=of= experimental=measurements= to=analytical= predictions= allows= for= aF= calibration=of=geomaterial= parameters= andI= bF= interpretation= of= experimental= results= on= the= basis= of= geotechnical=conditions=prevailing=below=the=base=of= the=columnsK=pince= the=horizontal= loading=of=lpisthodomos=columns= was=kept= in= relatively=low= levelsI= the=unloading=of= the=column=was= fully= reversibleK= =qhusI=a=nonlinear=elastic=approach=is=justified=for=predictionI=according=to=the=following=stepsW==

– Application= of= elastic= solutionsI= for= calculation= of= EelasticF= settlementsLsubsidence= at= the=measurement=points=

– Assignment= of= geostructural= properties= to= proper= complex= springsI= for= modeling= the= contact=surfaces= of= the= column= drums= discrete= structure= Einterface= springsF= and= the= behavior= of= the=foundation=underneath=Ebase=springsFK=

– PJa= nonlinear= elastic= analysis= with= use= of= moros= cooting= Blocks= Eeither= marly= limestone= or=dolomiteF=

qhe=presentation=of=the=above=analyses=is=made=in=the=following=paragraphsK==

PKPK blastic solutions for calculations of settlements Lsubsidence cor= calculation= of= settlementsLsubsidence= of= a= layered= halfspaceI= uniformly= loaded= on= circular= or=rectangular=superficial=areaI=the=following=well=established=analytical=solutions=were=appliedW==

NK=According=to=tinterkorn=and=cang=xNOINPz==

=b

vqBcs d FNE O-= = =ENF=

=

OK=According=to=pteinbrenner=xNPI=N4z==

= ( )cffffbvqBs IIN

ON

O-= = EOF=

=

OR4M=

fn=the=above=formulaeI=cd=accounts= for= the=geometry=of= foundationI= BZdiameter= of= circular= areas=orI=width=of=rectangular=ones=and=fi=Z=factors=depending=on=geometryK==As=far=as=the=geometry=of=loaded=surface=is=concernedI=two=cases=are=examinedW=

– uniform= press= on= circular= superficial= footing= of= diameter= equal= to= that= of= the= lpisthodomos=column=base=Ea=≈=NKTN=mF=

– uniform=press=on=a=square=surface=with=area=equal= to=half=the=circular=area=of=the=lpisthodomos=column=baseI=in=order=to=account=for=the=eccentric=vertical=loading=mv=of=the=column=baseI=arising=from=the=horizontal=thrust=of=the=column=capital=Ecouple=of=forces=–mvI=mv=≈=NMM=kkFK=

= cinallyI=for=each=column=ElhN=–=lh4F=four=layered=profiles=were=considered=EtotK=NS=profilesF=– qwo=plate=thick=marble=EMKSO=mF=on=marly=halfspace=EfoundationF=–=referring=to=the=west=side=of=

the=column=base=– lne=plate=thick=marble=EMKPM=mF=on=marly=halfspace=EfoundationF=–=referring=to=the=east=side=of=the=

column=base=– qwo=plate=thick=marble=EMKSO=mF=on=dolomite=halfspace=EfoundationF=–=referring=to=the=west=side=

of=the=column=base=– lne=plate=thick=marble=EMKPM=mF=on=dolomite=halfspace=EfoundationF=–=referring=to=the=west=side=of=

the=column=base=qhe=limestone=bedrock=of=the=rockhill=is=considered=rigidI=since=it=appears=in=a=practically=non=affected=from=the=loaded=surface=depthK==

Table O Base=pprings=EjkLmPF==

= morous===Blocks= aolomite=Blocks=bast= test= bast= test=

lhJN= NMMM= N8OR= 4NOR= RORM=lhJO= 88M= NRTR= PVMM= 48RM=lhJP= T8P= NPTP= PTRM= 4R48=lhJ4= TM8= NOOP= PSNR= 4PNR=

=qotallyI= S4= parametric= analyses= were= performed= EO= methods= ×= O= loaded= areas= ×= NS= geotechnical=profilesFK= fndicative= results= of= the= analyses= Evalues= of= base= springs= for= sqK= surfaceI= according= to=tinterkorn=C=cangF=are=summarized=in=qable=OK====PK4K deostructural parameters Espring constantsF qhe=mechanical=properties=of=geomaterials=and=the=analytical=results=from=subsidence=calculations=are=used= for= the= estimation=of=proper= spring=constantsI= accounting= for= the= simulation=of= contact= surface=between=the=drums=and=subbase=foundationI=respectivelyK==PK4KNK fnterface EcontactF pprings qhe=interface=springs=ENO=peripheral=and=one=centralF=per=unit=areaI=are=calculated=according=to==

= NMLI nso

in kk

hb

k »= = EPF=

=where=kn=represents=compressionJonly=properties=and=ks=frictional=behaviorK==fn=the=above=formulaeI=the=voung=jodulus=bi=refers=to=a=notional=loose=geomaterialI=filling=the=joints=between=drumsI =while =ho=Z=N=mmI= is=the=nominal= joint=openingK=qhese=springs=are=considered=to=have=constant=unit=area=value=for=all=the=peripheral=and=the=central=spring=respectivelyK=qwo=sets=of=contact=springs=are=examined=for=bi=Z=NRMMM=kkLmO=and=bi=Z=TRMM=kkLmO=respectivelyK===PK4KOK EsubFBase pprings qhe=subJbase=springs=are=evaluated=according=to=the=definition=formulaW==

= NMLI vsv

v kksqk == = =E4F=

=thereI=q=Z=contact=press=on=the=loaded=area=of=the=column=base=and=sv=Z=the=relevant=subsidenceI=on=the=assumption=of=rigid=baseK=

=

OR4N=

=

cigK R=PJa=modeling=of=opisthodomos=columns==

PK4KPK PJa Analyses qhe=results=of= the=previous=paragraph=Espring=valuesF= are=utilized=for=nonlinear= elastic=PJa=analysesK=qhe=modeling=comprises=the=exact=Eidealized=geometryF=of=the=columnsI=with=contact=springs=between=the=drums=and=base=springs=for=modeling=of=the=subJbase=foundation==EcigK=RFK=qhe=PJa=analyses=results=are= more= or= less= consistent= to= the= measured= valuesK= qotallyI= VS= analyses= were= performedI=corresponding=to=aF=different=base=springsI=arising=from=the=elastic=calculations=of= the=PKN=paragraphI=bF=difference= in= geotechnical= subbase= conditions= Emarly= or= dolomite= blocksF= and= cF= difference= in=contact= spring= constantsK= qhe= results= of= caclulated= horizontal= drift= and= subsidence= from= the= PJa=analyses=are=summarized=in=qable=PK===

Table P jeasurements=vs=mredictions= =

MbAprobMbNTp = δhEmmF sv(μmF = E-W2 W-E2 N-S2 S-N2 E-W2 W-E2 N-S2 S-N2

lhJN NKR8= = NKVM=P= NK8TP= NK8M= J= J= J= J=NKRO= =====NK4M= NK8PP= ======NK8MP= = = = =

lhJO ==OKNM=P= NKVV= NKV8P= OKNR= R4= PO= 4MP= R8=OKMM= NKVV= NKV8P= = JO4= NP= 84= =

lhJP ==OKRMP= OK4V= OKPMP= =OKP4P= 48= JOP4= PT= OO== OKMM= OK4RP= ======OKRMP= = 44= N=4= NS=

lhJ4 ===OKOMP= OK4S= OKOMP= OKN8= 4NP= PM= PT=P= 4O=======OKOMP= =====OKRM= ===========EKSNIKSTINKNTFR= ======OKNS= 4VP= PO= ENPINTIOOFR= 48=

mobafCTflNp Eelastic solutionsFN = δhEmmF sv(μmF = moros=coundation== E-W2 W-E2 N-S2 S-N2 E-W2 W-E2 N-S2 S-N2

lhJN

=

NO= OO=lhJO N4= OR=lhJP NS= O8=lhJ4 N8= PN=

= aolomite=foundation== E-W2 W-E2 N-S2 S-N2 E-W2 W-E2 N-S2 S-N2

lhJN

=

4= R=lhJO 4= S=lhJP R= S=lhJ4 R= S=

mobafCTflNp EPJa analysesF = δhEmmF sv(μmF = E-W2 W-E2 N-S2 S-N2 E-W2 W-E2 N-S2 S-N2

lhJN =JOKNS= = = OKNS= JOKNV= OKNV= N8= OS= OP= OP=lhJO =JOKOM= = = OKOM= JOKON= OKON= OM= OV= OS= OS=lhJP =JOKOR= = = OKO4= JOKOS= OKOS= O4= PP= PM= PM=lhJ4 =JOKOT= = = OKOV= JOKPM= OKPM= OS= PT= PP= PP=

=

ENF=tinterkornCcang=EequivK=square=to=half=circular=baseFI=EOF=loading=directionI=EPF=extrapolation=for=mhZNMkkI=E4F=dolomite=foundationI=ERF=for=mhZPI4IS=kk=respectivelyK=

=

OR4O=

cromI=the=results=it=is=obvious=that=the=best=simulation=corresponds=aF=to=subbase=springs=arising=from=a=uniform=loaded=square=with=area=equal=to=that=of=the=half=circular=column=baseI=for=the=elastic=solution=according= to= tinterkorn= and= cang= xNNz= and= bF= to= contact= springs= for= notional= infill= material= of=bi=Z=TRMM=kkLmPK=fndicative=comparison=between=measurements=and=analytical=predictions=for=column=lhJ4=are=shown=in=cigK=SK==

==

cigK S=Comparison=between=measurements=and=analytical=predictions=for=column=lhJ4==Eloading=directionW=p=to=kF=

=4K ClNCirpflNp =qhe=main=general=conclusions=arising=from=this=research=can=be=summarized=as=followsW=

– qhe= large= scale= nonJdestructive= testing= is= invaluable= for= the= interpretation= of= the= structural=behavior=of=monuments=

– qhe=performance=of=loaded=dry=masonry=structures=is=simulated=satisfactorily=with=the=application=of=rockJmechanics=principles=

– qhe= proper= analytical= procedures= supported= by= experimental= results= offer= a= stiff= frame= for=successful=estimation=of=the=essential=mechanical=parameters=of=monuments’=geomaterialsK=

fn= additionI= the= main= findings= from= the= interpretation= of= the= experimental= results= comprise= the=followingW=

– qhe=columns=horizontal=drift=is=governed=mainly=by=the=mechanical=properties=of=contact=surfacesK==– qhe=subsidence=depends=mainly=on=the=subJbase=foundation=material=propertiesK=qhe=assumption=

that= the=foundation=is=made=from=soft= rock=marly=limestone=blocks= interprets= the=relatively=high=subsidence=measurementsK=ln=the=other=hand=the=rather=limited=number=of= low=value=subsidence=measurements=may=be=attributed=to=the=local=presence=of=dolomite=foundation=blocksK==

qhe=practical=±equal”=drift=and=the=settlements=that=have=been=measured=on=columns=lhJP=and=lhJ4=verify=that=the=effect=of=foundation=thickness=is=limited=to=caK=RJS=m=below=the=lpisthodomos=column=baseK=cinallyI= according= to= the= resultsI= the= modeling= of= discrete= structures= with= properly= determined=parameters= for= monument’s= geomaterialsI= could= satisfactorily=be=applied= to= restoration=analyses=and=could= form=the=base= for= more=complex= calculations= involving= dynamic= effects= eKgK= earthquakeK= qhe=comparison=of=measured=values=and=analytical=predictions=are=generally= in=good=agreementI= offering=increased= accuracyK= qhe= proposed= modeling= approachI= supported= by= the= carefully= planned= and=executed=trial=load=procedureI=offers=a=well=–=founded=basis=for=the=analysis=of=the=highly=complex=and=demanding=issues=of=classical=monuments’=restorationK==AChNltibadMbNTp =qhe=authors=express=their=gratitude=to=the=Committee=for=the=mreservation=of=the=Acropolis=jonuments=for=having=supported=the=actionI=to=mrofK=bK=sintzileou=and=the=late=mrofK=fK=sardoulakis=for=having=lent=the=isaqs=and=to=ar=hK=wambasI=former=airector=of=the=Acropolis=oestoration=perviceI=for=his=advices=and=overall=supportK=

=

OR4P=

obcbobNCbp =xNz kK= qoganidisI= marthenon= oestoration= mrojectI= mrocK uuf fnternational CfmA pymposiumI= MNJMS

lctober=OMMTI=AthensI=dreeceK=xOz bKJbK=qoumbakariI=ptudy of the bearing structure and description of the actions carried out for

the lpisthodomos structural restoration=EvolK=4FI=jinKof=CultureI=OMMTK=xPz bKJbK= qoumbakariI= oeport to the Committee for the mreservation of the Acropolis Monuments

Eas=well= as= Archives= of= the= Acropolis= oestoration= perviceFI= jinKof= CultureI= ganuary= OMMOI=cebruary=OMMO=C=jay=OMMOK=

x4z lrlandos=AKI=qhe architecture of the marthenonI=NV4SK=xRz bK= eoekI= CK= CarranzaJqorresI= and= BK= CorkumI= eoekJBrown= criterion= –= OMMO= editionI= mrocK

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