OPRU

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

STorCTroAi ebAiTe MlkfTlofkd lc Teb olMAk AobkA lc sbolkAI fTAiv Casarin cKN, Modena CKO, Bello EKP, da morto cK4, iorenzoni cKR, dirardello mKS, Menon pKT

ABSToACT Ancient structures – eséecially very çld çnes – érçve their sçundness and the cçrrectness çf their structural layçut by reaching çur days in relatively gççd cçnditiçnsK qhis is the case çf the oçman Arena in serçnaI ftalyI built in the f century AKaKI and still standing in the histçrical centre çf serçnaI being the symbçl çf the city and çéen tç éublic use fçr visits but alsç fçr çéerasI cçncerts and relevant shçwsK tith a clçser lççk hçweverI it is éçssible tç aééraise the damages that the éassing çf time and the natural çr man induced events such as histçrical earthquakesI flççds çr wars and sieges left çn the structureK qhe éast seismic events Einduced seriçus damage çn the ArenaI being the cause çf the almçst cçmélete cçllaése çf the third EexternalF ring çf the mçnumentI tçday çnly remaining in the sç called “ala” EwingF çf the ArenaI an isçlated éçrtiçn çf stçne blçcks curved wall characterized by a reéetitiçn çf arches and massive éillarsK tith the éuréçse çf evaluating the structural reséçnse çf the Arena tç staticI dynamic EeKgK shçwsI cçncertsF and seismic lçadsI a ptructural eealth jçnitçring system was installed in the Arena in OMNNI with state çf the art technçlçgy fçr the data recçrding in relevant éçsitiçns çf the ArenaK A detailed crack éattern survey was carried çut in çrder tç lçcate the main cracks çf the structureI and cinite blements mçdels were emélçyed tç define the relevant mçdal éarameters çf the ArenaW glçbal mçdes were identified and thus – with a séecial fçcus çn the wing – acceleratiçn sensçrs were installed in the areas where significant dynamic amélificatiçns are exéected accçrding tç the cb mçdelling aéérçachK oesults çf the pej system will be emélçyed fçr tuning the available behaviçural mçdels EcbI but alsç iimit AnalysisFI in çrder tç trace the structural reséçnse çf the mçnument fçr assessing the çéeratiçnal cçnditiçns and éredicting the safety cçnditiçns çf the Arena in the eventuality çf a majçr earthquakeK heywords: ptructural health monitoring, eistorical structures, peismic performance NK Teb olMAk AMmefTbATbo EAobkAF lc sbolkAI fTAiv NKNK eistorical background qhe oçman Améhiteatre çr “Arena” Elatin fçr “pand” which at the time was used fçr cçvering the central elliétical cçurtyardF undçubtedly reéresents the mçst iméçrtant rçman mçnument in serçnaI a city in kçrthern ftaly between senice and jilanI tç the éçint çf being the city symbçl and main landmarkK qhe buildingI çne çf the best éreserved ancient structures çf its kindI is internatiçnally famçus fçr the largeJscale çéera éerfçrmances given thereK ft is still tçday able tç accçmmçdate an audience çf OMKMMM EcigK NFK qhe mçnument was erected between the Ond and Prd decades çf the Nst century AaI çn a site which was then beyçnd the lateJreéublican city wallsK qhe first mçdern times çéera Ediuseéée serdi’s AidaF was élayed in the Arena in NVNPI tç mark the birth çf serdi NMM years befçre in NUNPK pince thenI summer N bngKI mhKaK – afCbA – rniversity çf madçvaI ftalyI filiééçKcasarin]diceaKuniédKit O mrçfK bngK – afCbA – rniversity çf madçvaI ftalyI claudiçKmçdena]diceaKuniédKit P bngKI fop cçméanyI madçvaI ftalyI bellç]irswebKit 4 mrçfK bngK – afCbA – rniversity çf madçvaI ftalyI francescaKdaéçrtç ]diceaKuniédKit R bngKI mhKaK student – afCbA – rniversity çf madçvaI ftalyI filiééçKlçrenzçni]diceaKuniédKit S bngKI mhKaK student – afCbA – rniversity çf madçvaI ftalyI éaçlçKgirardellç]diceaKuniédKit T bngKI serçna juniciéality aeétK çf mublic tçrksI serçnaI ftalyI pergiç_jençn]cçmuneKverçnaKit

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seasçns çf çéera have been mçunted cçntinually at the arenaI exceét in NVNRJNU and NV4MJ4RI when burçée was cçnvulsed in warK ptill tçdayI every summertime çver RMMIMMM éeçéle see érçductiçns çf the éçéular çéeras in this arenaK fn recent timesI the mçnument has alsç hçsted several cçncerts çf internatiçnal rçck and éçé bandsI amçng which mink clçydI piméle jindsI auran auranI aeeé muréleI qhe thçI aire ptraitsI and several çthersK

cigK N Aerial view çf the oçman Améhiteatre çf serçnaI the “Arena”

NKOK Structural features qhe Arena main axis is aligned with the Cardç jaximus Emain alley in oçman cities in kJp directiçnFK qhe rçund façade çf the building was çriginally cçméçsed çf white and éink limestçne frçm saléçlicellaI but after a majçr earthquake in NNNTI which almçst cçméletely destrçyed the structureDs çuter ringI exceét fçr the sçJcalled “ala” Ethe remaining sectiçn çf the çuter ringFI the stçne was quarried fçr reJuse in çther buildingsK

aF bF cF cigK O aamages and reéair – strengthening interventiçns in the “ala” çf the ArenaW aF NVPV stabilizing

interventiçnsX bF sketches reéresenting the damages after the ff wKwK bçmbingX cF NVRS jçrandi’s interventiçn fts dimensiçns are abçut NPU × NMV meters çn the çutside while the inner elliétic éit is abçut 44 × TP metersK qhere are 4R tiers çf steés wherein the çéera audience can sitK qhe buildingI as çther structures çf its kindI is cçméçsed by a symmetrical arrangement çf radial masçnry walls seéarating the the TO “Arcçvçli” Eaccesses tç the cçurtyardF and three cçncentric distributive elliétical galleriesK jain emélçyed materials are the “çéus caementicium” that is tç say the rçman cçncreteI and a massive squared stçne masçnry blçck masçnryK

OPSM

qhe mçnument was subjected tç several natural and man induced actiçnsI like the flççding çf RUV AaI the earthquakes çf NNNS and NNNT – inducing majçr damages tç the structureI cçrreséçnding tç the almçst cçmélete cçllaése çf the çuter ring çf the ArenaI the cçllaése çf R arcades çn _ra square in NRTVI and the cçntinuative stealing çf stçnes and material fçr re use in çther cçnstructiçnsI until being treated like an “histçrical” mçnumentI with archeçlçgical excavatiçnsI starting frçm the usfff centuryK uu century structural interventiçns and induced damages are dçcumented mçre in detailW in NVPVI bçth the need çf intervening çn the external “Ala” fçr manifest tilting and the necessity çf érçtecting the same structural éçrtiçn frçm the éçssible damages induced by the ff wKwK cçnsequencesI rendered necessary the cçnstructiçn çf massive buttresses EcigKOFI remçved after the end çf the war by an interventiçn çf éçst tensiçned tendçns vertically éçsitiçned within the éillars EjçrandiI NVRSFK

OK Teb SeM SvSTbM fk Teb AobkA lc sbolkAI fTAiv

OKNK The need for monitoring the Arena fn recent years the serçna municiéality manifested a visible interest fçr cçntrçlling the structural reséçnse çf the structure tç different external actiçnsI alsç cçnsidered its relevant useK sibratiçns caused by éçé çr rçck cçncerts were and still are in fact çbject çf discussiçnI eséecially fçr what cçncerns structural safety çf the mçnument cçnnected tç the use çf it and the cçnservatiçn issuesK peveral investigatiçn caméaigns were aéélied in the last decadesI bçth fçr defining the state çf stress çf the cçméçsing materials and fçr measuring the vibratiçn level in the masçnry structuresK jaintenance is ançther key aséect çf the mçnumentI since hundreds çf thçusands çf éeçéle visit the arena yearlyI and thus their safety has tç be guaranteedK AlsçI being serçna lçcated çn a seismic érçne areaI even if mçderateI the seismic assçciated risk has tç be evaluated and minimizedI if éçssibleI and mçnitçring may be a viable and effective çétiçn fçr assessing the reséçnse çf the structure in case çf an earthquake and fçr calibrating behaviçral reference mçdelsK fn OMNN the serçna juniciéality gave the task tç the fCbA aeéartment çf the caculty çf bngineering çf the rniversity çf madçva tç install and tç manage a cçmérehensive ptructural eealth jçnitçring system fçr assessing the main structural éarameters çf the Arena in çrder tç assess mçre in detail its structural safetyK OKOK The Structural eealth Monitoring ESeMF system qhe pej system has been designed and installed by the authçrs in çrder tç mçnitçr the mechanical behaviçr çf the ArenaI thrçugh the exéerience gained by several pej systems aéélied tç Ce_s xNJ4zK qhe final aim is the acquisitiçn çf the vibratiçnal characteristics çf the mçnument by means çf acceleratiçn transducersI and the cçntrçl çf the surveyed crack éattern thrçugh the imélementatiçn çf disélacement transducers installed çn the main cracksK qhe acquired data are cçnstantly related tç the envirçnmental éarameters Eteméerature and relative humidityFK qhe evaluatiçn çf the measured quantitiesI and in éarticular their changes çver timeI allçws having useful indicatiçns in the definitiçn çf the structural behaviçr and in the determinatiçn çf the éresence çr çccurrence çf damage’s éhençmenaK fméçrtant infçrmatiçn are currently recçrded by the mçnitçring systemI in relatiçn bçth tç the static disélacements Edefçrmatiçn çf the cçntrçlled cracksF and the dynamic reséçnse çf the mçnumentI evaluating the accuracy çf the adçéted numerical mçdels çn the basis çf the actual behaviçrI alsç in case çf éçssible seismic eventsK qhe installatiçn çf the mçnitçring system was carried çut between lctçber and aecember OMNNK qhe éreliminary éhase befçre the installatiçn cçnsisted inW EiF design çf the system Ehardware – tyées çf sensçrs and acquisitiçn unitsFX EiiF develçément çf aéérçériate sçftware in relatiçn tç the selected mçnitçring strategyX EiiiF chçice çf the system’s layçut and the éçints çf structural cçntrçl accçrding tç the çutcçmes çf reference numerical mçdelsI the survey çf the damage éattern and the results çf dynamic identificatiçn tests çf the structureK qhe system is cçméçsed by sixteen singleJaxial accelerçmeters Eacceleratiçn transducersFI twenty linear éçtentiçmeters Edisélacement transducerF and fçur integrated sensçrs çf teméerature and relative humidityK diven the huge dimensiçns çf the structure it was decided tç develçé and imélement a hybrid systemW static sensçrs are cçnnected thrçugh six wireless slaves élaced arçund the éerimeter çf the Arena tç the érinciéal acquisitiçn unit and data are transmitted via a radiç antennaI whereas the accelerçmeters are cçnnected with three wired slaves that transmit the signals tç the master via ethernet cablesK

OPSN

aisélacement transducers were installed in cçrreséçndence çf the main surveyed cracks and lesiçns and are cçnnected tç a wireless nçdeI each with fçur channelsI that send the signals tç the master unit by means çf a radiç linkK qhe acquisitiçn unit cçntinuçusly cçmmunicates with the tireless pensçr ketwçrk EtpkFK bight sensçrs were installed çn the grçund flççr in the first internal gallery at a height çf abçut V meters in cçrreséçndence tç a big lesiçn that runs almçst alçng the entire éerimeter çf the Arena’s elliése EcigK 4FK qwelve transducers were éçsitiçned frçm çutside in the vaulted niches Ecalled “arcçvçli”F at the secçnd çrder çf arches çf the mçnumentW sçme çf them çn isçlated cracksI sçme çthers çn the surveyed detachment between the éerimeter stçne wall and the radial wallsK

cigK P iayçut çf the static system EleftFX disélacement transducer and wireless slave ErightF qhe éçsitiçn çf the sixteen singleJaxis accelerçmeters EcigK 4F was decided accçrding tç the dynamic characteristics and vibratiçn mçdes çf the structureI evaluated thrçugh bçth numerical mçdels and léeratiçnal jçdal Analysis EljAFK pix accelerçmeters were installed çn the wing çf the Arena çn twç different levels alçng the çutJçfJélane directiçnK qhe wing is cçméçsed by a freestanding wall cçnnected tç the rest çf the structure çnly at the first level and it is cçnsidered the mçst vulnerable structural elementK peven accelerçmeters were éçsitiçned çn the tçé çf the secçnd çrder çf arches alçng the elliétical éerimeter çf the structureI accçrding tç the radial cçnfiguratiçn çf the mçnumentK cinally three sensçrs were élaced at the base çf the building alçng twç çrthçgçnal hçrizçntal directiçns and a vertical çne in çrder tç recçrd the grçund acceleratiçn in case çf seismic events and evaluate the dynamic amélificatiçn çf the structureK

cigK 4 iayçut çf the dynamic system EleftFX accelerçmeters installed çn the wing and at the base çf the structure tith regard tç the dynamic measurementsI twç strategies have been selectedW “lçng” acquisitiçnI çn regular intervals tç allçw subsequent identificatiçn by means çf structural vibratiçn in different envirçnmental cçnditiçns Eseasçnal cycleFI and “shçrt” acquisitiçn which is dçne autçmatically when the vibratiçns exceed the trigger Esignificant eventFK fn the latter caseI the system during an event that exceeds the established levelI recçrds the data frçm several secçnds befçre and after the viçlatiçnK qhis methçdçlçgy ensures that the registratiçn dçes nçt lçse iméçrtant data fçr the eventK jçreçver the system is equiééed with a rçuter fçr remçte data transmissiçn tç the central server çf the rniversity çf madçvaK

OPSO

PK cfoST obSriTS C Teb obCloaba SbfSMfC bsbkTS PKNK cirst results – modal analysis of the wing qhe installed mçnitçring system allçws the analysis çf a huge amçunt çf data taking intç accçunt three main aséectsW EiF cçntrçl çf variatiçns çf the static measurementsI EiiF daily extractiçn çf the fundamental mçdal éarametersX EiiiF registratiçn and analysis çf éçssible seismic eventsK pignificant effçrt is devçted tç the analysis çf recçrded dataK fn éarticular the research activities are currently fçcused çn the imélementatiçn in jAqiA_ envirçnment çf autçmatic and semiJautçmatic érçcedures fçr bçth static and dynamic data érçcessingK qhe autçmatic érçcedure aéélied tç static data elabçrates a standard Ktxt file acquired by the static system and create autçmatically a series çf graéhsI reéresenting the variatiçn çver time çf the mçnitçred éarameters and cçrrelating them with teméerature and humidity variatiçnsK qhe algçrithm allçws alsç aéélying cçrrectiçns çn acquired data in çrder tç remçve errçrs caused by human interactiçn çr system’s malfunctiçningK

cigK R aisélacement’s variatiçn çf the mçnitçred cracks mwN and mwO lçcated at the secçnd çrder çf arches

in a vaulted niche Ecalled ‘arcçvçlç’F qhe autçmatic érçcedure aéélied tç dynamic data elabçrates the acquisitiçn files and autçmatically estimate and extract mçdal éarameters frçm measured vibratiçnsK rsually this érçcess invçlves a large amçunt çf user interactiçnI eséecially when lçts çf data need tç be érçcessed in a shçrt amçunt çf timeK qhe develçéed algçrithmI based çn jACbC PKOI OMNN xNzI imélements the éçlyJreference ieast pquare Cçmélex crequency açmain methçd EéipCcF in çrder tç extract autçmatically mçdal éarameters Efrequency and daméing ratiç develçément çver timeI jAC indexes variatiçn between the starting reference identificatiçn and the daily identificatiçnFK fn the fçllçwing sectiçn the main results çf data érçcessing in the éeriçd aecember OMNNJAéril OMNO will be éresentedK

24/01/2012 seismicevent

24/01/2012 seismic event

cigK S aisélacements çf abçut MKP mm recçrded during the seismic event in cçrreséçndence tç the cracks mwV and mwNM lçcated in a ‘arcçvçlç’ çf the secçnd level

auring the first mçnths çf mçnitçring nç wçrrying disélacements were recçrded and the crack’s defçrmatiçns fçllçw the teméerature variatiçn EcigK RFK pçme mçvements were recçrded after the seismic events çccurred at the end çf ganuary OMNO with the eéicenter lçcated at abçut NN km frçm the

OPSP

ArenaI whçse effects were carefully evaluated and the main results cçnnected tç the dynamic aséects éresented in the fçllçwing éaragraéhK As it can be nçted in cigK S the earthquake induced a slight relative disélacement çf the transducers mwV and mwNM lçcated in a vaulted niche E“arcçvçlç”F at the secçnd levelK qhe recçrded disélacement resulted tç be quite reduced Eabçut MKP millimetersFI in the range çf the drifts induced by the teméerature variatiçnK

Table N fdentificatiçn çf the mçdal éarameters éerfçrmed by caa technique

jçde crequency xezz Cçmment jçde N jçde O jçde P

N NIVOV Nst çutJçfJélane bending O OISPT Nst tçrsiçnal P RIMTU Ond çutJçfJélane bending 4 RIUU4 Prd çutJçfJélane bending R L Nst inJélane bending S TIPMM Ond tçrsiçnal T VIPMO L U NMIV4M L

_ased çn the initial dynamic identificatiçn Eqable NFI the variatiçns çf the fundamental natural frequencies çf the wing are cçnstantly extracted frçm the measured vibratiçnsI acquired every O4 hçursK

cigK T cirst frequency develçément çver time in the éeriçd aec OMNN – Aéril OMNO EleftFK crequency variatiçn in functiçn çf the teméerature ErightF

qhe frequency develçément çver time gives a sçund indicatiçn çn the dynamic characteristics çf the structure and it is strçngly related tç the envirçnmental éarameters EcigK TFK PKOK ganuary OMNO seismic events At the end çf ganuary OMNO a series çf lçwLmçderate seismic events hit the nçrthern éart çf ftaly and in éarticular the surrçunding areas çf serçnaK qhanks tç the mçnitçring system çf the Arena it was éçssible tç caéture every single event and cçntrçl the reséçnse çf the structure during the earthquakesI evaluating the éçssible induced damagesK qhe recçrds çf the seismic events give alsç crucial indicatiçns çn the site effects and allçws characterizing the amélificatiçn factçrs çf bçth sçil and structure itselfK qhree main earthquakes were recçrdedI each çf çne fçllçwed by smaller aftershçcksK qhe first earthquakeI çccurred in the érçvince çf serçna ENNkm nçrth frçm the ArenaI NM km deeéI magnitude 4KO çn the oichter scaleFI induced the strçngest vibratiçns çn the structure çf the ArenaK qhe çther twç seismic events Eoeggiç bmiliaW TR km frçm the serçnaI PM km deeéI magnitude 4KV and marmaW NPM km frçm serçnaI SM km deeé and magnitude RK4FI even if characterized by a bigger magnitudeI induced lçwer acceleratiçns çn the mçnument due tç érçbably the greater distance frçm the eéicenterI the deeéer éçsitiçn çf the fault and the different frequency cçntent çf the main shçckK qhe first çéeratiçn çn the seismic trace recçrded during the first earthquake çn O4LMNLOMNO at OPWR4W4S rqC EMMWR4 ORLMNLOMNO çf ftalian timeF was tç cçméare the values çf base acceleratiçn recçrded by the mçnitçring system with thçse recçrded by the ftalian Accelerçmetric ketwçrk EoAkF çf the fkds research institute in the qregnagç statiçnI aéérçximately NR km far away frçm the eéicenterK

OPS4

Table O Cçméerisçn between meak drçund Acceleratiçns EmdAF recçrded by the fkds statiçn and the Arena mçnitçring system

qobdkAdl fkds pqAqflk jlkfqlofkd pvpqbj

mdA xcmLsOz Cçméçnent aistance xkmz mdA xcmLsOz Cçméçnent aistance xkmz

O4KNRST ekb NRK4 SNKV ekb abçut NN

O4KTT44 ekk NRK4 PRKT ekk abçut NN

NOKMRU4 ekw NRK4 OSKR ekw abçut NN

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

tempo [s]

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

[m/s

2]

acc7

acc8

acc9

cigK U Cçméarisçn between time histçries recçrded by the fkds statiçn EleftF and the Arena mçnitçring system ErightF

Cçnsidering the time histçries çf the earthquake recçrded at the base and at twç different levels çf the wing çf the ArenaI a linear dynamic analysis was éerfçrmed çn the available cb mçdelK

cigK V qçéW cb mçdel çf the ArenaX belçwW cçméarisçn between time histçries recçrded by the Arena mçnitçring system at the tçé çf the wing EleftF and thçse çbtained numerically çn the cb mçdelI extracted in the same éçsitiçns

OPSR

cigK NM crequency develçément çf the first fçur natural frequency çf the wing during the main shçck qhe érçcedure cçnsisted in aéélying the base acceleratiçn in the twç çrthçgçnal directiçns recçrded by the system tç the nçdes at the mçdel’s baseK pubsequently the acceleratiçns extracted frçm the numerical calculatiçns were cçméared with the exéerimental accelerçgrams çf the mçnitçring system recçrded in the same éçsitiçnsK qhis analysis allçws calibrating the cb mçdel tç a real earthquake and uédating the elastic mechanical érçéerties çf the structure in çrder tç çbtain cçméarable values çf acceleratiçnK qhe maximum values çf acceleratiçn recçrded at the tçé çf the wing by the system and simulated by the cb mçdels are very similar and equal tç abçut OmLsOK qhus it is éçssible tç state that the reference behaviçral mçdel çf the wing is cçrrectly calibrated andI mçre iméçrtantI that the structure during the earthquake remained in the elastic rangeK cinally a dynamic identificatiçn was éerfçrmed using the crequency açmain aecçméçsitiçn EcaaF technique çn the recçrded earthquake in çrder tç evaluate the variatiçn çf mçdal éarameters during the seismic excitatiçnK ft is éçssible tç nçte that the first mçdes are subjected tç a clear decrement çf the frequency values during the earthquakeK qhe frequency decrement was recçrded çnly during the main shçck and in the fçllçwing days the extractiçn çf the mçdal éarameters give similar results tç thçse recçrded befçre the seismic eventI éçssibly indicating that the earthquake did nçt induce éermanent and significant structural damages tç the wingK 4K ClkCirSflkS C mboSmbCTfsbS jçnitçring is being mçre and mçre cçnsideredI in the field çf cultural heritage buildingsI as a key activity in çrder tç increase the knçwledge çn the structural functiçning çf mçnuments and therefçre tç have a deeéer insight çn their cçnditiçns xSI TzK fn case çf a seismic eventI mçnitçring can furthermçre érçve its usefulness in quantitatively assess the real entity çf structural damageK _etween the available techniques that may be érçfitably used tç cçntrçl the reséçnse çf a histçric masçnry buildingI dynamic identificatiçn érçves tç be a very effective tççlI since it allçws tç exéerimentally measure éarameters related tç the glçbal structural behaviçrK qhe cçmbined use çf dynamic identificatiçn érçcedures and “lçcal” cçntrçls Ebesides the mçnitçring çf the envirçnmental éarametersFI érçviding quantitative infçrmatiçn çn lçcal cçnditiçns çf structural elements EeKgK cracks çéeningFI can be an iméçrtant asset in the effçrt çf attaining a deeéer degree çf awareness çn the “real” structural functiçning çf the mçnumentsK qhe pej system installed in the Arena çf serçna allçwed in fact tç quantitatively define the actual mdA at the fçundatiçn çf the structure during mçderate seismic events haééened after the system cçméletiçn in OMNOI gave the éçssibility tç aééraise the maximum acceleratiçns attained at the tçé çf the mçnumentI which in the O4th çf ganuary event resulted tç be quite significant Eaéérçx O mLsOFI and rendered éçssible the evaluatiçn çf the éermanents effects çn the structureI bçth frçm a static Eresidual crack çéeningsF and dynamic éçint çf view Eabsence çf evident frequency shiftsFK _ehaviçural mçdels were finally tuned çn the exéerimental recçrds çf the pej systemI and will be used in successive steés fçr simulating the design earthquake exéected in serçnaI fçr defining the seismic éerfçrmance çf the Arena in case çf majçr eventsI studying then éçssible remedial measures if a satisfactçry éerfçrmance is nçt achievedK cuture research will be alsç devçted tç structural mçdels relying çn a data driven aéérçachK

OPSS

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