Structural safety assessment of geometrically complex masonry vaults by non-linear analysis. The Chapel of the Wurzburg Residence (Germany)

1Introduction TheWürzburgResidenceisalargeGermanBaroqueconstructionbuiltduringthefirsthalfofthe18thCentury,seeFig.1.ItwasdeclaredaWorldHeritageSitebyUNESCOin1981.Thechapelisintegrated into the main building and is located on its south-west corner. This chapel is a very singular construction, mainly due to the configuration of its vaults, with a complex spatial geometry, which includes warped intersectionsbetweenthem,andduetothehighleveloftechnologyrequiredfromaconstructionpointofview.Inthissense,itisoneofthefewexamplesthatcanbefoundinEuropewiththislevelofcomplexity[1]. Structuralsafetyassessmentofgeometricallycomplexmasonryvaultsbynon–-linearanalysis.TheChapeloftheWürzburgResidence(Germany) VíctorCompána [email protected] PabloPachóna,⁎ ppacho[email protected] MargaritaCámaraa mcama[email protected]s PauloB.Lourençob [email protected] AndrésSáezc [email protected] aDep.ofBuildingStructuresandSoilEngineering,UniversityofSeville,Spain bISISE,DepartmentofCivilEngineering,UniversityofMinho,Portugal cDep.ofContinuumMechanicsandStructuralAnalysis,UniversityofSeville,Spain ⁎Correspondingauthor. Abstract ThispaperaddressesthestructuralsafetyassessmentoftheChapeloftheWürzburgResidence(Germany),oneofthemostimportantchurchesoftheCentralEuropeanBaroque.Itwasdeclaredas WorldHeritageSitebyUNESCOin1981,oneofitsmostuniqueanddistinctivecharacteristicsisthegeometryofitscomplexvaults.Intersectionsbetweenvaultsarewarpedandvaultssurfaceswerebuilt usingonlyonelayerofbrickmasonry.Inthiswork,anonlinearfiniteelements(FE)modelhasbeendevelopedandusedtoassessthestructuralsafetyofthebuilding.Inordertoupdatethemodelby identifyingthedynamicresponseofthebuilding,experimentalambientvibrationtestshavebeenpreviouslysubsequentlycarriedout.OperationalmModalaAnalysis(OMA)hasbeenusedtoexperimentally identify both modal displacements and natural frequencies. The numerical FE model is them adjusted using genetic algorithms until its dynamic response resembles that experimentally observed, thus providingavalidmodeltofurtheranalysethestructuralbehaviourofthebuilding.AfterbrieflydescriptingtheChapel,themethodologyfollowedtoupdatethenumericalmodelandtheobtainedresultsfrom anon-linearanalysisonthisover-complexvaultedstructurearethemaingoalsofthepaper. Keywords:Masonryvaults;Ambientvibrationtest;Historicalbuilding;ChapeloftheWürzburgResidence;OperationalModalAnalysis;FEmodelupdating;Non-linearanalysis;Geneticalgorithms Oneofthemaindifficultiesthatneedtobeaddressedinstructuralanalysisofhistoricalbuildingsisthelevelofuncertaintyassociatedwithmanyfactorsaffectingthebehaviourofthestructure.Aspectslike themechanicalpropertiesofthestructuralmaterials,thebuildingconstructionprocess,theconnectionsbetweenstructuralpartsorthecrackingconditionofthebuildingmaycauseimportantchangesbetweenthe resultsobtainedfromanumericalanalysisandthoseexperimentallyobserved[2].Inthissense,non-destructivetechniquesappearasusefultoolstoprovideinformationaboutthestructuralbehaviourofthebuilding [3,4].Inparticular,dynamicpropertiesprovidedbyambientvibrationtechniqueshaveprovedtobequitewell-suitedtovalidateandupdatenumericalmodels[5]. OperationalModalAnalysis(OMA)hasconsolidatedasoneofthemostadequatemethodstoestimatethemodalparametersofastructure,duetothefactsthat:(i)itisanon-destructiveandnon-invasive techniqueand(ii)itcanbeperformedunderserviceconditions.Forthesereasons,OMAiscurrentlyrecognisedasaquiteconvenienttechniquetodynamicallycharacterisehistoricalbuildings,sincetheuseofthe strongerexternalexcitation(impacthammersorshakers)requiredtoperformthetraditionalExperimentalModalAnalysis(EMA)isnotneeded.TheinterestedreaderisreferredtoReferenceRef.[6] for a more involveddiscussiononthepracticalandtechnicaldifferencesbetweenOMA and EMAwhen appliedfor testingofmasonryvaults. Subsequently, modalpropertiesprovidedbytheapplicationofOMA allowsthe adjustmentofnumericalmodelsinordertoobtainanaccurateestimationoftheactualbehaviourofthestructure.Inthissense,updatedFEmodelscanbeusedtocarryoutastructuralanalysisunderexisting conditionsorfurtherpredicttheeffectsofdifferentstructuralsituationsthatthestructurecouldundergo.Inthelastdecades,manycasesofapplicationofambientvibrationteststoupdatenumericalmodelscanbe foundinhistoricalbuildings[7–12].However,theapplicationsofOMAtoassessstructuralbehaviourofspecificcomplexpartsofabuilding,suchasdomesorvaults,aremuchmorelimited[6,13,14]. Themainpurposeofthisstudyistoevaluatethecurrentstructuralstateofthevaultsofthechapelinordertogainfurtherknowledgeoversuchcomplexstructureandestimateitscurrentsafetylevel.Abrief descriptionofthechapel,themethodologyfollowedtodynamicallycharacterisethebuilding,theupdatingprocessandtheresultsobtainedfromanonlinearanalysiswillbepresentedinthispaper.Thepaperis organised as follows: Section 2 summarizes the main characteristics of the chapel together with a historical overview and a brief description of its architectural configuration. Section 3 presents the dynamic characterisationofthevaultsofthechapelbyusingtheOperationalModalAnalysismethod.Itfurtherdescribestheinitialfiniteelementmodeldevelopedtoestimatethemodalparametersofthesystem.Section4is devotedtodiscusstheupdatingofthefiniteelementmodelbasedontheexperimentallyobtainedmodalparameters.InSection5,the updatedfiniteelementmodelisthenusedtofurtheranalysethenonlinear behaviourofthevaultswhensubjectedtoverticalloadsuntilreachingcollapse.Finally,Section6drawsthemainconclusionsofthisstudy. 2ChapeloftheWürzburgResidence 2.1HistoricalAspects TheconstructionoftheWürzburgResidence[15]datesfromtheearlyeighteenthcenturywhentheSchönbornfamilydecidedtobuildapalacetorelocatetheEpiscopate.BalthasarNeumann[16,17]wasthemainworkmaster foroverthirtyyears.TheChapelexhibitsanimpressiveBaroquedecoration,seeFig.2. Fig.1FrontoftheWürzburgResidence(Germany). Duringthebuildingdesignprocess,thechapelwasplacedatdifferentlocationswithinthewholecomplex,untilBalthasarNeumann,finally,locateditatthesouth-westcorneroftheResidence(Fig.3).JohannDientzenhofer wasinvolvedinthedesignofthechapel[18].HewasaGermanarchitectwithawideexperienceonthedesignandconstructionofgeometricallycomplexbrickmasonryvaults. 2.2Architecturalconfigurationandconstruction Thearchitecturalconfigurationofthechapelpresentsaspatialviewwithaclearlongitudinalcharacter,composedbythreemainspatialcellsconnectedbytwoothercells,asillustratesFig.4.Thewallsareparticularlyslender (15.2mhighwithavariablethickness,between1.20and2.00m)andwithahighpercentageofvoids,greaterthan50%ofthefaçadesurface. Therearetwomainreasonswhythechapelvaultsareuniqueintheircomplexity.Afirstfeature,fromageometricalpointofview,isthattheceilingismadebyfivein-planovalvaultswithwarpedintersectionsamongthem (Fig.4).Eachoneoftheseintersectionswasgeometricallydeterminedbytheintersectionbetweentwocylinderswithorthogonalaxisanddifferentdiameters.Thesecylindricalshapewasessentialintheconstructionprocess,because intersectionsweredefinedfirstasedgesofthevaultsboundaries,andthenthesurfaceofthevaultswasbuiltaccordingtotheintersections.Asecondfeatureisthattheconstructiontechniqueusedwasquiterefined.Vaultssurfaces aremadeofonlyonelayerofbrickmasonry(30cmthick),withneitherribsnoranysortoflocalreinforcementatwarpedintersections[15].Forconstructivereasons,vaultsonlyincrease15cmtheirthicknessattheirbaseandat smallradialribslocatedonselectedlocationsofthethreemainvaults(Fig.4andFig.5). Fig.2ChapeloftheWürzburgResidence.Altarviews. Fig.3WürzburgResidence.LocationofthechapelattheSWcorner. Fig.4StudyofthetraceoftheChapeloftheWürzburgResidence. 3AmbientvibrationtestsandOperationalModalAnalysismethod ThedynamiccharacterizationoftheChapeloftheWürzburgResidencehasbeenperformedbymeansofambientvibrationtests.Thesetestswerecarriedoutbetween14and17ofJuly2014,withtheaimof identifyingthenaturalfrequencies,modeshapesanddampingratiosofthevaults. 3.1Initialfiniteelementmodel The application of the Operational Modal Analysis usually requires the creation of an initial model (Fig. 6) in order to estimate the natural frequencies and mode shapes and thus determine adequate positions of the accelerometers. ThisinitialFEmodelwasbuiltusingAbaqus/CAE6.13Software[19].Themodelconsistsmainlyoftwocomponents,namelywallsandvaults,modelledusingsolidelements.Thefinalmodelcomprises1,606,908 elements,329,472nodesand988,416degreesoffreedom.Materialpropertieswereinitiallyestimatedfrombibliography[17,20].Forbrickmasonryofthevaults,theadoptedpropertieswere:density,1980kg/m3;Young’sModulus, 1100MPa;Poisson’sratio,0.2.Similarly,thefollowingvalueswereconsideredforthestonemasonry:density,2100kg/m3;Young’sModulus,2200MPa;Poisson’sratio,0.2.Furthermore,theweightoftheroofoverthevaultswastaken intoaccountintheFEmodel,aswellastheconnectionsbetweenthechapelandtherestoftheResidenceBuilding,bymeansofspringelements[7,8]. Fig.5ChapeloftheWürzburgResidence.Vaultsextrados. Fig.6InitialFEmodel. Basedonthelargestmodaldisplacementsobtainedfromthisinitialmodel,theappropriatepositionforthereferenceaccelerometersisset.Fig.7illustratesthefirstthreevibrationmodestogetherwiththeircorresponding naturalfrequencies. 3.2Ambientvibrationtests FollowingtheresultsobtainedfromtheinitialFEmodel,Fig.8showsaschematicrepresentationofthesensorsarrangement.Theset-upconsistsofatotalof51measuringpoints,whichisaratherdensemesh.Itisalsonoted that,duetotheboundaryconditionsimposedbyitsintegrationintoalargecomplex,thestructureisnotsymmetrical.Allofthemeasuringpointsweresetinthethreeprincipaldirections,inordertocapturetheglobalvibrationmodes inthelongitudinal,lateralandverticaldirectionofthevaults.Sinceonlyeightaccelerometerswereavailableforthetestingprocessandtwoofthem(placedatpoints17–19,Fig.8)werekeptfixedforreference,aseriesoftwenty-five set-upswerenecessarytocoverallmeasuringpoints.Ineachoneoftheseset-ups,accelerationswererecordedwithasamplingrateof100Hzandasamplingtimeof12min.Theseassumptionsensurethatnaturalfrequenciesinthe rangefrom1to50Hzcouldbeproperlyrecorded.However,inordertoperformamoreaccurateanalysisandtotakeintoconsiderationthattheexpectednaturalfrequenciesarebelow10Hz,adecimationfactorof5waspreviously applied. Fig.7InitialFEmodel.Modaldisplacementsofthefirstthreevibrationmodes(f1=2.59,f2=3.04andf3=4.15Hz). Excitationsduringambientvibrationtestswereassociatedwithenvironmentalloads.Theequipmentusedforthesetestswascomposedbyeightuniaxialforcebalanceaccelerometerswithabandwidthrangingfrom0.01to 200Hz,adynamicrangeof140dB,asensitivityof10V/gand0.35kgofweight(modelES-U2).Theseaccelerometerswereconnectedviaeight40mlongcablestoatwelve-channeldataacquisitionsystemwitha24-bitADC,provided with anti -aliasfilters(modelGRANITE).TheequipmentismanufacturedbythecompanyKINEMETRICS(Fig.9). 3.3OperationalModalAnalysis Insituobtaineddatawereprocessedusingtwodifferentidentificationmethods:oneoftheminfrequencydomain,theEnhancedFrequencyDomainDecomposition(EFDD)technique[21];andtheotherinthetimedomain,the StochasticSubspaceIdentification(SSI)method[22].BothmethodsareimplementedinthesoftwareArtemis[23](Fig.10). Fig.8Accelerometerlocationsanddirections(planviewofthechapel).Ref.accelerometersinred. Fig.9Measurementequipment. Fig.10showsthatalmostallidentifiedmodalfrequencies–usingtheSSItechnique–exhibitslightchangesbetweenthedifferenttestset-ups.Thisfactmaybeexplainedprovidedthatthemeasurementswereperformed duringthreeconsecutivesummerdays,withsimilarbutnotequalenvironmentalconditions.Severalresearchstudieshaverecentlyprovedthatdifferenttemperatureorhumidityconditionscanslightlymodifythedynamicproperties ofamasonrystructure[23–26].Bearinginmindthisconsideration,themodalfrequencies,dampingratiosandmodeshapesweredeterminedbyapplyingbothmethods–EFDDandSSI–andwerelatercorrelatedusingtheModal AssuranceCriterion(MAC)[27]betweenbothsetsofresults,inordertoassesstheaccuracyoftheobtainedmodeshapes: where and arethetwomodestobecomparedand T denotesthetranspose. Dataprocessingresults,includingthestandarddeviationofmodalfrequenciesanddampingratios,arepresentedinTable1. Table1ResultsOMA:naturalfrequencies(f),dampingratios(ξ)andstandarddeviation(Std). SSI EFDD MAC f(Hz) Std.f ξ(%) Std.ξf(Hz) Std.f ξ(%) Std.ξ Mode1 2.77 0.01 1.12 0.40 2.77(0,0%) 0.01 0.89(26%) 0.28 0.99 Mode2 3.28 0.05 1.50 0.68 3.30(0,6%) 0.37 0.92(63%) 1.24 0.87 Mode3 4.52 0.05 2.36 0.66 4.46(1,4%) 0.20 1.79(32%) 0.91 0.88 Mode4 5.26 0.03 1.24 0.48 5.25(0,2%) 0.02 0.88(61%) 0.28 0.90 Mode5 6.48 0.04 2.04 0.95 6.48(0,0%) 0.03 1.11(84%) 0.46 0.82 ThepercentagewithinparenthesisindicatestherelativedifferencebetweenSSIandEFDDresults(SSIresultsasreference). AsTable1shows,theambientvibrationtestsallowedtoaccuratelyidentifythefirstfivevibrationmodesinafrequencyrangeupto10Hz.Thefrequencieswereidentifiedwithrelativedifferenceslowerthan1.5%,takingthe Fig.10Ambienttestssetup(EFDDandSSI). (1)     resultsoftheSSImethodasreference.Theresultsforthedampingratioshowashighervariability(upto84%),withaveragemodaldampingratiosofthebuildingbeing1.65%and1.18%forSSIandEFDDtechniques,respectively. Thisresultisnotsurprisingandhigherexcitationseemstoberequiredinordertoobtainreliablemeasuresofdamping,whichisnotneededforstaticstructuralanalyses,asdonelaterinthispaper.Withrespecttomodeshapes,MAC valueswerealwayshigherthan0.80,whichindicateagoodcorrelationbetweenbothmethods.Thesecondmodeshowsalongitudinaltranslationmode,whiletheothermodescorrespondtobendingmodesofthevaults(Fig.11). 4Modelupdating StandardFEmodelsofhistoricalbuildingsusuallyincludeuncertaintiesbecauseofparameterssuchasunknownmaterialproperties,poorlyknownboundaryconditions,existingdamage,complexinternal compositionofstructuralelementsandmodellingapproximations.Therefore,calibratingthemodelwiththeaidofexperimentalinformationbecomesnecessaryinordertoappropriatelymodeltheactualstructural behaviour.Forourpurposes,resultsobtainedfromambientvibrationtestswillbeusedtoupdateandimprovetheinitialFEmodel. Inthiscase,theFEmodelupdatingbasedontheobtainedexperimentaldynamicpropertiesofTheChapelwasperformedbymeansofiterativemethods[28];thatis,modelupdatingarisesfromchanges appliedonsomewell-definedstructuralphysicalparametersselectedbytheusers.Forthispurpose,asensitivestudywascarriedoutinordertoidentifythephysicalparametersofthestructurethathaveastronger influenceonitsdynamicbehaviour.TheseparametersweretheYoung’smodulusofthemasonrybrick(Eb)andthestone(Es),thespringsstiffnessthatsimulatetheconnectionwiththepalace(Sp)andtheinertial massassociatedtotherestofthebuilding(Ip)(Fig.12).Theselectionoftheselasttwoparameterswasessentialtoperformthecalibrationprocess.ItisimportanttorememberthattheChapelmodelledisincluded Fig.11Modeshapesassociatedwiththeexperimentalresults(SSI). withinalargercomplex,whoseinfluenceonthemodalbehaviourofthechapelhastobeconsidered.Theselectionofmoreparameterswouldunnecessarilycomplicatethephysicalinterpretationoftheupdating process. Giventhehighqualityoftheexperimentallydetectedfirstfourvibrationmodes,theyhavebeenchosentocarryouttheupdatingprocess.Onlynaturalfrequenciesvalueswereselected,duetothelower reliabilityoftheidentifiedmodeshapesincomparisonwiththemeasurednaturalfrequencies.Therefore,consideringfouridentifiednaturalfrequencies,fourresidualcomponentswereadjustedandminimisedduring modelupdating.Theupdatingprocesshasbeenperformedviaanoptimizationalgorithm,namelygeneticalgorithms[29],asimplementedinMatlabsoftware[30],accordingtothefollowingfitnessvalue l (θ): where are the frequencies obtained from the numerical model, which are related to the physical parameters of the model, (elastic moduli of masonry brick and stone, springs stiffness and inertial mass),whicharetheobjectoftheadjustment.Thevariables representthesamefrequenciesobtainedfromexperimentaldata,specifically,thevaluesobtainedfromtheEFDDmethod.Thedifferencesbetween theexperimentalandnumericalparametersaredenotedasresidues, .Aweightvariable couldbeestablishedforeachresiduetotakeintoaccountthedifferentreliabilityoftheidentifiedmodalparameters. Inourcase, =1( j =1−4)isadopted. SeveraliterativemethodshavebeenproposedintheliteraturetoupdateFEmodelsinstructuraldynamics.Foramoreinvolveddiscussionondifferentalternatives,theinterestedreaderisreferredtothe bookbyMarwala[31].Forourpurposes,geneticalgorithmsareselectedtoconducttheoptimization,astheyexhibitahigherprobabilitytoconvergetoaglobaloptimalsolutionthangradient-basedmethods.Genetic algorithms[29]aimatfindingsuchoptimalsolutionamongapopulationofpossiblesolutionsbyapplyingtheprinciplesofevolutionarybiology(crossover,mutation,selectionandreproduction)tocomputerscience. Geneticalgorithmshaveprovensuccessfulwhenappliedtocomplexoptimizationproblemsand,inparticular,whenappliedtoFEupdating(see,e.g.,Marwala[31]andreferencestherein). Fig.13illustratesthesummaryoftheupdatingprocessandshowsitsimportanceforobtainingreliablemodelsthatreplicatetheactualresponseofthestructures.Basedonthepropertiesoftheinitialfinite elementmodel,andestablishingarangeofvaluesforeachupdatingparameter(Table2)andtheupdatingobjective,thecalibrationprocessstarted.Ineachiteration,apopulationof1000vectorswascreatedthat, usingthegeneticalgorithmrules(asimplementedinMatlabsoftware),minimizedtheobjectivefunction(2).Suchcalibrationprocessterminatedwhenthedifferencebetweenthemeanvalue(bluepoints,Fig.13)and thebestvalue(blackpoints,Fig.13)ofthepopulationwaslessthan1×10−4.Table2showstheconsideredlowerandupperboundsfortheupdatingparametersandtheircorrespondinginitialandupdatedvalues.As itcanbeseen,updatedvaluesdifferupto30%withrespecttovaluesdefinedintheinitialmodel. Fig.12Finiteelementmodelandgroupofmaterial/elementtypesconsidered. (2)             SpecialthankstotheInstituteofBuildingDesignandConstructionoftheUniversityofStuttgartandparticularlytoProfessorMatthiasRottner.Thisworkwouldnothavebeenpossiblewithouttheirsupport. ThisworkhasbeenfinanciallysupportedbyResearchProjectP12-TEP-2068,“TratamientoyRecuperacióndelPatrimonioEdificado.LaInyeccióncomoMétododeConsolidacióndeEstructurasdeFábrica”, fundedbytheRegionalGovernmentofAndalusia,Spain. References [1]V.Compán,M.CámaraandF.González,ThegeometricprinciplesofwarpedribvaultsincentralEuropeanbaroquearchitecturefromguarinitotheDientzenhoferfamilyandBalthasarNeumann, NexusNetwork J 17,2015,183–206. [2]S.AtamturkturandJ.Laman,Finiteelementmodelcorrelationandcalibrationofhistoricmasonrymonuments, StructDesTallSpecBuild 21(2),2012,96–113. [3]M.Diaferio,D.FotiandN.Giannoccaro,IdentificationofthemodalpropertiesofabuildingoftheGreekheritage, KeyEngMater 628,2015,150–159,http://dx.doi.org/10.4028/www.scientific.net/KEM.628.150. [4]G.Lacanna,M.Ripepe,E.Marchetti,M.ColiandC.Garzonio,DynamicresponseoftheBaptisteryofSanGiovanniinFlorence,Italy,basedonambientvibrationtest, JCultHeritage 2016. [5]M.FriswellandJ.Mottershead,Finiteelementmodelupdatinginstructuraldynamics,1995,KluwerAcademicPublishers. [6]S.Atamturktur,P.FanningandT.Boothby,Traditionalandoperationalmodaltestingofmasonryvaults, ICEEngComputMech 163,2010,213–223,ISSN:1755-0777,E-ISSN:1755-0785. [7]C.GentileandA.Saisi,Ambientvibrationtestingofhistoricmasonrytowersforstructuralidentificationanddamageassessment, ConstrBuildMater 21,2007,1311–1321. [8]C.Gentile,A.SaisiandA.Cabboi,Structuralidentificationofamasonrytowerbasedonoperationalmodalanalysis, IntJArchitHeritage 9,2015,98–110. [9]F.Aras,L.Krstevska,G.AltayandL.Tashkov,Experimentalandnumericalmodalanalysesofahistoricalmasonrypalace, ConstrBuildMater 25,2011,81–91. [10]L.F.Ramos,R.Aguilar,P.B.LourençoandS.Moreira,DynamicstructuralhealthmonitoringofSaintTorcatoChurch, MechSystSignalProcess 35,2013,1–15. [11]D.Foti,Non-destructivetechniquesandmonitoringfortheevolutivedamagedetectionofanancientmasonrystructure, KeyEngMater 628,2015,168–177, http://dx.doi.org/10.4028/www.scientific.net/KEM.628.168. [12]M.Diaferio,D.Foti,N.GiannoccaroandS.Ivorra,Optimalmodelthroughidentifiedfrequenciesofamasonrybuildingstructurewithwoodenfloors, IntJMech ISSN:1998-4448,8,2014,282–288. [13]I.Calık,A.Bayraktar,T.TurkerandH.Karadeniz,Structuraldynamicidentificationofadamagedandrestoredmasonryvaultusingambientvibrations, Measurement 55,2015,462–472. [14]S.Atamturktur,B.Luke,H.FrançoisandA.Sezer,Vibrationcharacteristicsofvaultedmasonrymonumentsundergoingdifferentialsupportsettlement, EngStruct 33(9),2011,2472–2484, http://dx.doi.org/10.1016/j.engstruct.2011.04.020,ElsevierLtd. [15]C.Norberg-Schulz,KilianIgnazDientzenhoferyelbarrocobohemio,1993,OikosTaus,ISBN:84-0809-9. [16]W.Hansmann,BalthasarNeumann,2003,Dumont.ISBN:3-8321-7167-3. [17]V.Compán,Comportamientoestructuraldelasgeometríasarquitectónicasdelbarrococentroeuropeo,[Ph.D.thesis]2010,UniversityofSeville. [18]M.VilímkováandBruckerJ.Dientzenhofer,EinebayerischeBaumeisterfamilieinderBarockzeit,1989,RosenheimerVerlagshaus.ISBN:3-475-52610-7. [19]UsersManuals,Dassaultsystemes,SIMULIA,ABAQUSv.6.13-3,2015. [20]AugentiN,ParisiF,AcconciaE.MADA:onlineexperimentaldatabaseformechanicalmodellingofexistingmasonryassemblages.In:Proc.15thWorldConferenceonEarthquakeEngineering, Lisbon(Portugal);24–28September2012. [21]R.Brincker,C.VenturaandP.Anderser,Dampingestimationbyfrequencydomaindecomposition,In: 19thInternationalSeminaronModalAnalysis, 2001,IMAC;Kissimmee,USA. QueriesandAnswers Query:Yourarticleisregisteredasaregularitemandisbeingprocessedforinclusioninaregularissueofthejournal.IfthisisNOTcorrectandyourarticlebelongstoaSpecialIssue/Collectionplease contact[email protected]immediatelypriortoreturningyourcorrections. Answer:Thisiscorrect.Thearticleisaregularitem. Query:Theauthornameshavebeentaggedasgivennamesandsurnames(surnamesarehighlightedintealcolor).Pleaseconfirmiftheyhavebeenidentifiedcorrectly. Answer:Theauthornameshavebeenidentifiedcorrectly. Query:Highlightsshouldonlyconsistof85charactersperbulletpoint,includingspaces.Thehighlightsprovidedaretoolong;pleaseeditthemtomeettherequirement. Answer:Thehighligtshavebeenmodifiedtomeettherequirement. [22]P.OverscheeandB.DeMoor,Subspaceidentificationforlinearsystems:theory,implementation,applications,1996,KluwerAcademicPublishers;London. [23]SVS.ARTeMISExtractor2010release5.0.<http://www.svibs.com>;2010. [24]C.GentileandA.Saisi,Post-earthquakediagnosticinvestigationofahistoricmasonrytower, JCultHeritage 16,2015,602–609. [25]M.Masciotta,J.Roque,L.RamosandP.B.Lourenço,Amultidisciplinaryapproachtoassessthehealthstateofheritagestructures:thecasestudyoftheChurchofMonasteryofJerónimosinLisbon, ConstrBuild Mater 116,2016,169–187. [26]A.Saisi,C.GentileandA.Ruccolo,Pre-diagnosticpromptinvestigationandstaticmonitoringofahistoricbell-tower, ConstrBuildMater 122,2016,833–844. [27]AllemangRJ,BrownDL.Acorrelationcoefficientformodalvectoranalysis.In:Proceedings,internationalmodalanalysisconference;1983.p.110–116. [28]A.Teughels,Inversemodellingofcivilengineeringstructuresbasedonoperationalmodaldata,[Ph.D.thesis]2003,KatholiekeUniversiteitLeuven. [29]J.H.Holland,Geneticalgorithms, SciAm 267,1992,66–72. [30]User'sManual,MathWorks,MATLABR2008a,2008. [31]T.Marwala,Finite-element-modelupdatingusingcomputationalintelligencetechniques:applicationstostructuraldynamics,2010,Springer. [32]S.Atamturktur,F.M.HemezandJ.A.Laman,Uncertaintyquantificationinmodelverificationandvalidationasappliedtolargescalehistoricmasonrymonuments, EngStruct 43,2012,221–234. [33]A.Hillerborg,M.ModeerandP.E.Petersson,Analysisofcrackformationandcrackgrowthinconcretebymeansoffracturemechanicsandfiniteelements, CemConcrRes 6,1976,773–782. [34]J.Lubliner,J.Oliver,S.OllerandE.Oñate,Aplasticdamagemodelforconcrete, IntJSolidsStruct 25,1989,299–329. Highlights •Geometricallycomplexbrickmasonryvaultshavebeenanalysedtoassesstheirstructuralsafety. • operationalOperationalmodalModalanalysisAnalysistechniqueis usedtodynamicallycharacterise masonryvaults. •Geneticalgorithmsareusedfornumericalmodelsupdating. •UpdatedFEmodelisusedtoperformanonlinearanalysis. Ambientvibrationtestsand are historical