STRUCTURAL ANALYSIS DF HISTORICAL CONSTRUcrlONS P. Roca, J.L. González, A. R. M~rí and E. On~te (Eds.)

© CIMNE, Ba rcelona 1996

ANAL YSIS, DIAGNOSIS AND PRESERVA TION OF ANCIENT MONUMENTS: THE ST. MARK'S BASILICA IN VENICE

F. Mola [JoliteCllico di Mifrmo

P.zza L. Da Villci 32

20133 Milano

Ita/y

SUMMARY

R. Vitaliani 15 ti/ l/fa di Sciwza e TeCllica de/lc Costruziolli

Facoltii di hlgeglleria-Ulliversifii di Padava

Via Marzolo 9

35131 Padova

It a/y

An operadonal procedure for the analysis. lhe prognosis and lhe monitoring of lhe structural behaviour of ancient monuments is presenled. After a delailed discussion of lhe basic aspects of the lechniques necessary to collect significanl data about lhe state of stress and strain of lhe monumental complex. lhe results derived from a wide survey_of experimental tests performed on lhe S1. Mark's Basilica in Venice are presented. Panicular emphasis is devoted to lhe flat-jack tests and to the ones connectcd with lhe evaluation of the main propenies of the stIUctural materiaIs. The criteria followed in order to fonnulate a fmite element modelo the results obtained from some panicularly significant case studies and the basic aspects of lhe monitoring equipment are lhen exposed. Finally the general assumptions which have govemed lhe assessment of lhe statical reliability of the monument are discussed, wilh the basic aspects of lhe restoration works which have been prescribed for some structural parts exhibiting an unreliable statical behaviour. Some concluding remarks and the charactenstics of lhe future works necessary to assure an adequate staticaI behaviour of the monumenl elose lhe paper.

I. INTRODUCnON

The problem connected with the preservation of lhe statical efficiency of andent monuments has assumed great importance in lhe last two decades as a consequenee of the development of operational techniques whieh have allowed to scientifically proceed for lhe analysis and lhe diagnosis of these particular structures. The procedure can be subdivided into three main slages, namely: diagnosis, conceming lhe assessment of the structural reliability prognosis, defining possible restoration works and prediction of the time evolution of lhe strllctural behaviour based on the results derived by means of a proper monitoring cquipmcnt. Owing to the complexity of the statical behaviour of ancient monumcnts, lhe three preceding stagcs require to be exhaustively investigated to take into account many aspects whieh are nOl strict1y connected with lhe typical ones pertaining to structuraI mechanics, so that other complementaI)' concepts have 10 be in troduced. 'l'he first is lhe historical investigation about lhe major events which took place during the strUctural life-time, in order to deteet degrading phenomena and lhe works done for gening rid of them. The following step , concerning lhe geometrical description of lhe monument, represents a quite difficult task since lhe architectural shapes are always complex and extremely variable. The third step is re lated to the investigations necessary to achieve an adequate knowledge about the mechanical properties of the various suuctural materiaIs. This can be perfonned by means of a conveniem sei of experimental tests carried out on specimens eXtr"J.cted from particularly sil,,'T1ificant struc tural pans.

It is Ihen necessary to achieve reliable informations about lhe 51ate of stress and strain of the structure in order to obtain a reaIistic picture of the strUctural behaviour for the calibration of the theoretical methods of strllctural analysis. The collection of geometrical

F. MOLA and R. VITALl AN I I SI. Mark's Basil ica in Vcnicc 167

and mechanical data allows to formulate a lheoretical model, based 00 lhe fmite elements technique, in order to correctly describe the complexity of the various structural arrangements.

The approach now discussed in its basic steps has been codified by means of specific documents published by the Associations dealing with lhe statical preservation of ancient monuments. In particular, lhe Proceedings of the Symposia and of the Conferences recently held on this arguments, [e.g. I, 2, 3] represent a valuable contribution in enhancing lhe knowledge for lhe theoretical and practical solution of such many complex and critical problems.

2. BASIC ASPECTS RELA TED TO lHE ANAL YSIS OF ANClENT MONUMENTS

2.1 Historjcal sUlyey

The maio goal of historical surveys is lhe achievement of data able to give a reliable and detailed picture of lhe struclural behaviour. The complete lack of documents regarding the hislory of a monument is a quite extraordinary event, since during its life· time lhe monument has generally been observed and deeply s[Udied, 50 lhal a number of documents and reports is available. From these documents and from local inspections we ean derive usefuJ informations about events occurred in lhe pasl, which have produced a marked structural degrading, i.e. frres , partial collapses, seisms.

Moreover we have to observe that many monuments have been continuously eontrolled during their life·time so that it is generally possible, especially for lhe monuments built in lhe second millennium, 10 have ai our disposal historical documents describing lhe events whieh have driven lhe structures to lheir present configuration. This represents the initial condition for the structural analysis and for a correel formulation of lhe basic hYPolhcses governing lhe suuetural response under the applied actions.

2 2 Gcometrieal Descriotion

The geometrical identificarion of lhe various structural elements is a fundamental step for a correet modelling of the structural behaviour. This operarion requires high precision and it is quite complex, as the structuraI members present a marked variety of shapes.

The most reliable technique for lhe geometrical description of structural members is the photograrnmetrical analysis. This technique, even if some negative criticisms have been addressed to it in lhe past, has shown good precision and general applicability, so that at present time it represents lhe main operational procedure for lhe geometrieal description, [4] . The results of the photogrammetrical analysis, togelher wilh the ones conneeled with lhe direet survey of cracks and dislocations, for which it is possible 10

proceed by means of a careful visual check, allow to reliably define lhe struc tural configurarion and to proceed for the modelling Df the structural behaviour.

2 3 Experimental Tests

The structural members of ancient monuments are generally constructed by masonry or stones, whieh should be experimentally investigated to define their physieal, chemical and mechanieal properties by using appropriale tests. In order to perform the experimental tests it is necessary to extract some specimens, pnxiucing local damages in the structural members. This is not always possible and in any case lhe local damages have to be redueed at the maximum extent. Therefore it is nOI generally possible to fully perform ali the necessary experimental tests. In fac! it is well known thal a realistic evaluation of lhe bearing capaeity of a masonry structural member ean be derived only extraeting a quite large specimen, bUI this represents an intolerable damage for a monumental complex, so lhat a different approach has to be followed.

168 STRUCTURA L ANALYS 1S OF 1-II STOR1 CAL CONSTR UCTIONS

For this reason the tests perfonned 00 cylindrical specimens of small diameter (Le. $ ~ 100 mm), extracted by a drilling machine, assume great imponance. These tests introouce only small damages, and therefore they can be perfonned with convenient care also in monuments of particular value. The drilling operarion, which can be driven 10 a significant depth, allows to obtain a conrinuous boring able to give reliable data about the mechanical propenies of the materials up to the inner parts of the members. In the bores produced by the drilling machines, it is possible to execute tests for evaluaring the soundness of the internaI material by using micro video-camera investigations, or ultrasonic tomography. In particular the last operation does not produce local damages, so Ihat it can be also used in the zones where decoralions do not allow to perfonn destructive tests. Finally, the data regarding the state of stress and strain parameters can be achieved by using lhe flat -jack technique. This methoo, introducing a small local damage, is of greal imponance and it allows to correctly define the structural properties to be introouced in the mathemarical model.

The basic stages of lhe experimental analysis here recalled, are exhausrively discussed in [5], and the theorerical and practical requirements of the flat-jack tests have been stated by Rossi in [6, 7]. The aforementioned operations have been applied for the ana1ysis aod the diagnosis of ooe of lhe most important historical monuments in Italy: lhe SI. Mark's Basilica in Venice. During lhe years 1990-1994 lhe ISMES Co., Bergamo - ltaly, under the supervision of the authors, has perfonned a detailed survey of e:ICperimental tesls on the Basilica, together wilh the implementation of a mathemarical mooel for the structural analysis which has allowed 10 reliably assess lhe structur-ll safely and to derive some interesling infonnations about the time evolution of Lhe structural behaviour of the monwnent.

3. ANAL YSIS DF THE STATICAL BEHA VIDUR DF THE ST. MARK'S BASILICA

SI. Mark's Basilica in Venice (ltaly), Figure I, is one of lhe mosl important ltalian monuments and its historical heritage is well known world-wide. In the year 1994, nine hundred years elapsed since lhe Basilica dedicarion and to celebrate this exceplional event the ltalian Ministry of Public Works (MPW) charged ISMES Co. to perfonn a wide program of experimental tests in order to check lhe statical reliability of lhe structural complex and to develop a malhematical model for the theoretical analysis. The authors were charged to supervise the procedure, to define the various operational stages and to state reliable criteria for the formulation of lhe assessment of structural safety.

The suggested procedure has been developed in five stages, namely: historical analysis; geometrical description; experimental tests; fonnulation of a mathematical model; placing of a monitoring equipment. The procedure, which is in agreement with lhe general discussion expressed in the preceding points, has suggested to prescribe restoration works for a structural member exhibiting ao unreliable statical behaviour. The most significant results derived f TOm the various steps of lhe diagnostic procedure are discussed in the following, pointing oul the aspecls connected with lhe correct formularion of the theoretical model for the structural analysis.

3.1 Experimental Tests

The main features of the Se Mark's Basilica are shown in Figure 2. The construction phases have been developed during three periods, e:ICtending from the early IX cenlury until the dedication year 1094. In Figure 2 we can observe the primary kernel of lhe Basilica, with five domes and a planimetric arrangement having the fonn of Greek cross. The bearing structures can be subdivided in elementary sub-systems fonned by four arrangements, each one composed by four pillars, disposed at the corners of a rectangle. These sub-systems represent lhe bearing structures of the women's gallery and of four arches bearing the domes, connected with them by a cylindrical tambour and by four spherical triangles.

F. MOLA and R. VITALlA NI I SI. Mark's Basilica in Vcnict: 169

Fig. I The SL Mar"'". B,I .... d ll.:a 111 lI ... pn.~ .... el1l t:o nfigll lilllOIl

5

FI !! J General vicw of lhe plan 0 1" Ih~ H,N Ilt:a

1 Dome 01 San Glovannl 2 Dome of Penlecosle

or 01 lhe SPlrlIO Sanlo :3 Cenl ral Dome 01 lhe A:;CUlI'~ IUIIU 4 Dome 01 lhe Chorus or 01 Enullanucle 5 Dome of San Leonardo

170 STRUCTURAL ANALYSIS OF HISTORICAL CONSTRUCn ONS

The elementary sub-systems, shown in Figure 3a, are connecled in the volumetric di sposition of Figure 3b, where the central sub-system represents lhe basic structural arrangement. It is notewonhy to observe lhat the horizontal reacrions for lhe equilibrium of the domes are almost fully supplied by the sub-systems as the externai walls are ralher thin and consequent1y unable to counteract significant lateral forces. The masonry domes have a spherical configurarion and are overhung by external w<X>den domes covered by lead scales. The woodeo domes do not represent structural bearing parts, they have only an architectural charaCler.

The slatical configuratioo existing at present time is lhe result of valious restoration operations, done in lhe pasl centuries and described by Saccardo [8J, Forlati [9] and the Restoration Division llO]. The first experimental tests planned were lhe vertical and horizontal drilling operations to be perfonned on the foundation structures, in lhe bearing soi! and in the masonry structural members. The drill-holes were aIso used for lhe ultrasonie tomography tests and the video-camera inspeetion, while funher holes were drilled to proceed to complementary sonic tests eonsisting in measuring the propagation velocity of a some wave between two parallel holes. The results related lO lhe foundation structures and to the foundarion soil are ilIustrated in Figures 4 and 5.

The correlation between the results of lhe bore-hole lests and the sonic ones has allowed to define, even if in an approximale way due to the small number of data, Lhe prerequisites of statieal efficieney of the fouodation arrangement. Regarding the sonic teslS the following eathegories eonnected with Lhe measured propagarion velocity of the sonic waves in me various parts were stated:

v < 2500 m/s is associated to a discontinuous or highly degraded material;

2500 rn/s < v < (4000 + 5000) m/s is eonneeled with a moderately discontinuous material, exhibiting a suffieienl preservation state; v > 5<XXl rn/s belongs to a well preserved material with negligible discontinuities.

The cathegories here introdueed have allowed to subdivide lhe foundation sttucture in four zones, namely:

poor zones where coarse macro-cavities are present together with v < 2500 m/s. In these zones the structures present high degrading; uncertain zones, where moderate cavities are associated to a velocity v < 2500 m/s. The material even if sufficient1y dose, presents sigmficant degrading; rather reliable zones, where macro-cavities are associated to good values of the propagation velocity. The material, even if discontinuous, exhibits a good preservarion state; reliable wnes, where small discontinuities are present together with high velocities.

The di slocation of the results has JX>inted out thal lhe poor zones are prevailing. They are extending over 50% of the tested zones while the uncertain zones and lhe reliable zones respectively represent 30% and 20% of the tested zones.

Even if the negative results are more frequent, we have to observe that the small number of lests is oot sufficient to exhaustively assess lhe statical efficiency of lhe foundation structures and to detect the need of prescribing restoration works in short time. Refening to lhe zones exhibiting high uncertainties it appears necessary to place a monitoring equiprnent in order to collect data about lhe stnJctural behaviour. The teslS performed on the foundation have also been prescribed for the vertical bearing structures, in the zone of the women's gallery, which was lhe only one where moderately destructive tests could be performed since in the inferior parts lhe structures are covered by marble plates and in the upper parts golden mosaics are presenL

Ultrasonic lomography has pointed out a marked scauering of the results as the measured velocities belorig to lhe interval 600 m/s < v < 2000 m/s, with a prevalence of the lower values connected with materials exhibiting poor mechanical properties.

F. MOLA and R. VJTALlAN I I SI. Mark's Basilica in Venice 171

a )

Fig. 3 a) Basic struclural sub-assembly: b) general view or lhe spatial structural arrangement

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172 STRUCTURAL ANALYSIS OF HISTOR1CAL CONSTRUCT10NS

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Fig. 4 Experimental tests on foundations: soil stratigraphy and investigation on masonry walls

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Fig. 5 Resu lls of the ullrasonic lesls performed on (he foundation

F. MOLA :md R. VITALlANI I SI. iIo b rk's Basilica in Vcnicc 173

These results have been confinned by the ones derived from lhe bore-holes tests, poinring out the poor quality of the masonry structures from which, in many cases, it was rather impossible to exlract solid specimens as only desegregated material was found. The video-camera investigations have also pointed out frequent and significant cavities associated to a material with reliable strength disposed only on the external surface of lhe pillars, exhibiting a ralher small thickness. At the in terior of this external shell, a ralher homogeneous material exhibiting poor mechanical prerequisites is present, so that from lhe statical point of view, lhe pillars can be assumed as hollow-core members.

The results derived from a bore-hole test are shown in Figure 6, while two tomography tests, related to a not-restored and a restored pillar are shown in Figures 7a and 7b respectively. It is noteworthy to observe that lhe tests based on lhe measure of lhe propagarion velocity of lhe ultrasonic waves is an efficient 1001 to define lhe soundness of lhe material at the interior of the structural members. As it appears from Figure 7a, lhe most frequent situation, confumed by lhe bore-hole tests, is lhe one correlaled to the presence of poor material, exhibiting a low propagation velocity. In lhe pillm reslored by means of mortar injeclions, lhe velocity, as shown in Figure 7b, exhibits high values in some zones of significant extension, but not everywhere. The results derived from the uhrasonic tornography pointed out that the restoration technique based on mortar injection has nOl given reliable results as the physical and mechanical properties of the material present at lhe interior of the pillars are not sufficienl for reaching a reliable degree of soundness and homogeneity.

The single flat-jack teSlS perfonned to derive infonnation aboul the slatt:: of stress in the various parts. are also affected by a marked scauering, as we easily can deduce from Figure 8. This scattering takes place not only as a consequence of lhe different planimetrical position and geometry of the pillars, bUI it is also connected with lhe restaration works performed on these s(fUctural rnembers which have modified the structural stiffness producing stress redistribution.

The stresses higher lhan 1.2 MPa represem significantly high state of stresses in pillars exhibiting poor material. Analogous considerations can be rnade regarding the elastic moduli which, evaluated by double flat-jack tests, took place at the interior of lhe inlerval 700 MPa < E < 5000 MPa, or in a more detailed way we can write 700 MPa < E < 2000 MPa for nOl restored masonry, 1()(X) MPa < E < 4000 MPa for restored masonry with monar injection, 4000 MPa < E < 5000 MPa for pillars wholly rebuilt aboul 30 years ago. The correlalion between the results have allowed to define four situations associated to four intervals for the elastic moduli, fo r lhe propagation velocilY of uloasonic waves and for the state of stress as spedfied in lhe following:

E > 5000 MP" 3200 m/s < v < 4200 m/s, O MP. < (J < 0.4 MP.;

3000 MP. < E < 5000 MP., 2200 m/s < v < 3200 m/s, 0.4 MP. < (J < 0.6 MP.;

1500 MP. < E < 3000 MP., 1200 m/s < v < 2200 m/s, 0.6 MP. < (J < 0.8 MPa;

700 MPa < E < 1500 MPa, 400 m/s < v < 1200 m/s, 0.8 MP. < (J < 1.2 MP • .

The preceding situalions are reported in Figures 9, 10, 11, wherc the lcttcrs A, B, C, D painl out the direction of increasing risk, associaled to low velocity and small elastic moduli . Figure 12 points out lhe highly degraded or lhe mechanically poor elements, for which only 70% of lhe material extracted by the bore-holes lesls was sufficienlly compact. The contemporary presence of the letter O for lhe whole set of lhe perfonned tests is connected with situations of high statical ri sk.

Another interesting informa.tion deriving from single ar double flat-jack tests, is the indication af lhe state of stress present in lhe masonry on the stress-strain diagrams. As illustraled in the Figure 13, the stress-strain relationships can be assumed as three-linear diagrams, where the achieving of stresses belonging to lhe second or lO the third branch of lhe diagram points oul a stalical behaviour exhibiting significantly non linear aspects. This fact has been found in one pillar, where the contemporary presence of nega tive results in ali the other tests has induced to proceed to restorarion works.

174 STRUCTURA L ANALYSIS or HISTORICAL CONSTRUCTIONS

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Fig. 6 Bore-hole test performed on masonry structures

F. MOLA nnd R. VITALIANI I SI. Mnrk's Basilica in Vcnicc

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175

176 STRUCTURAL ANALYSIS OF HISTORICAL CONSTRUCTIONS

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Fig. 8 Results of single flat-jack lesls

A [ > 5000 t.lPo

B E '" .!IOOO - 5000 I.IPo

C ('" 1500 - JOOO )'!Po

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Fig. 10 Mean exper. values of the elastic moduli

y '" J200 - .(200 m/~

2200 - J200 m/s 1200 - 2200 m/s

y :; .(00 - 1200 m/.

Fig. 9 Results of lomography tests

0= 0.0 - 0 . .( l.I f'o

Fig. 11 Mean exper. values of lhe stresses

F. MOLA and R_ VITALl AN I / SI. M:1Tk's Basilica in Vcnice

percentage 01 voids

Fig. 12 Masonry in a poor preservation state

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Fig. 13 Stress-strain diagram for masoory stmctures. with the iodicatioo 00 the actual measured statc of stress

178 STRUCTU RAL ANALYS IS OF HISTORICAL CONSTRUCrI ONS

Thc elaboration Df lhe resu lts has allowed to fonnulatc a j udgemenl abQul lhe cfficiency and lhe preservation af lhe slruclural alTangcmen t, based on lhe fo llowing situations:

conlemporary presence of negalive results in ali lhe perfonned te ... I .... The structure is statically inadcqualc and even ir further invesligalions can be prcscribed in order to bettcr define lhe repairi ng lechniques, restoratian wo rks have to bc pcrfonned within shon time;

presence Df dcgrading phenomena togelher w ith signilicant discontinuities in homogeneous material subjecled to low stresses. In Ihese cases il is recommendable to imposc lhe s ingle nat-j ack teslS in arder to check lha! lhe slresses are sufficien tly low. This condition is essent ial to consider statically efficicnt a structural member even if affcc tcd by significa0! mechanical inadequacies:

presencc of slalically effeclive configural ion which does nOI rcquire restoration works.

As we can observe in Figure 14, the zones cxhibiting a not negligible risk are quile smal!. They have 10 bc subjected to restoration works as the degrading and their intrinsic inadequacy have produced situations which are not consistent with lhe prescribed safely leveis.

A P1IIOrt c lo.slll. " o. typ. I

P~loro c!o n iU. d o. "rl>. 2

5 0'" P'-Iro Trlt>uno 50 ... Clom onl. Tribuno

Fig. 14 Zones wilh significant slatical !'i sk

4. THE MATHEMATICAL MODEL AND T I-IE NUMERICAL ANA LYS IS

The results of the experimental lesls !lave allowed to get ready a Iheoretical model for the structllral analysis based on lhe sub-assemblies FEM techniqlle. The model has been employed fo r lhe cvalllation of lhe slale of stress in lhe various slmclural members and lhe rclatcd displacements produced by lhe following actions:

F. 1\ 10 LA ,:md R. VITALlA NI I SL Mark's Basi lica in Vcnicc 179

local load. evaIuated for the structural pans as volume force proportional to the density of lhe material. Regarding the pans which have nOl slruclural tasks, the permanent load, connected with their presence has been introduced as e:ltternal nodaI force applied to the bearing rnembers; two lemperalure fields applied at the e:ltternal surface of the scructuraI members. The first related to a temperature variation of 1 CO. with respect lhe isothermal slate unifonnly applied at the externaI surface of all elements; the second connected with a temperature variation of 1 C" with respect the isothermaI state unifonnly applied at lhe top surlace of the roof; imposed displacements to foundation structures according to the resuhs obtained by means of lhe monitoring equipment. The values are normalised assuming as a referenee unit displaeement the maximum measured one having value 1.39 mm.

The presence of cracks and dislocations, particularly frequent in lhe roof has been taken into aceount in two different ways. The firsl way provides for lhe adoption of a reduced elastic modulus in the zones where there is a diffuse microcracking. We can so take imo account, by an approximate but substantialJy correct approaeh, lhe local reduction of StruClural stiffness produced by cracking. The second way can be used when lhe cracks are wider and more localized and it consisls in intrc:xlucing an opportune splitting of two adjacent elements crossed by the crack. It is so possible to introduce in the structural mode! lhe degrees of freedom corresponding lO lhe disconnection operated by lhe cracks. making il more realistic and dose to the aCluaI struclural behaviour.

The geometricaI discretization of the struclural comp!ex has been performed following the results derived from the photogrammeoical analysis. while the mechanical properties of lhe malerial have been assumed, as flTst approximation, consistent Wilh a linearly elastie homogeneous and isotropic behaviour. The numerical values have been assumed according to the experimental teslS perfonned on the masonry members, in particular the double nat-jack ones. The numerical analysis has been carried out by means of the MSC/NASTRAN Code [11], working in the linearly elastic domain while the geomeoical discretization has been operated by AUTOCAD [12]. FinaUy lhe graphical elaborarion of the obtained results has been processed by the I-DEAS Code 1"13). The complexity of the model and lhe dramatical1y high number of the degrees of freedom (about 2.5 x lOS) has suggesled to operate by means of the sub-assembly techniques. In this way besides making the numerical calculations less cumbersome we can take into account without particular difficulty the differenl mechanical behaviour which can take place in parts subjected to high stresses or exhibiting marked degrading phenomena. In fact we can vary the mechanical behaviour only with reference to the sub-assembly affected by degrading. assuming lhe remaining surrounding parts as an elastic srructure interacting with lhe sub-assembly in the linking nodes. assuming as unknowns lhe related displacements which can be processed by means of the condensed stiffness matrices.

The srructural complex has been subdivided into the nine sub-assemblies represenled in Figure 15. namely lhe foundalion mal together with a convenient stratum of the bearing sai!, the six pillars, lhe externai walls and lhe roof. The model, in its complete configuratian is shawn in Figure 16a, while Figures 16b and 16c show respectively the soil-foundation discretization and the venicaI section of the complete finite element mode!. The sub-assemblies have been chosen in order to correctly evaluale the stale of stress in the strUclural pans panicularly sensitive to stress variations. This assumption is quite useful for the analysis of lhe pillars, for which the experimental tests have induced 10 improve lhe analysis assuming a non linear behaviour. Finally the sub-assemblies have been identified assuming c1early defined interfaces requiring for their kinematic description a moderate number of linking nodes.

The elemems used to describe the various sub-assemblies are quite different. In particular six-nodes exaedrical elements have been assumed for lhe soil stratum, represenled by a prism having squared plane with base of 180 m and 30 rn high. The pillars have been described by solid tetraedric elements and the wall s have been associated to plate triangular elemenls.

180 STRUCTURAL ANALYS IS OF HISTOR ICAL CONSTRUCTIONS

a) b)

c) d)

Fig. 15 Sub-assemblies assumed for the mathematical modcl: a) foundations: b) bcaring wall s: c) pillars; d) roof

F. MOLA and R. VITALlANII 51. Mark's Basilica in V\!nicl! 181

,,)

Fig. 16 Thc finitc clemcnt rnodel: a) the global di!<.crctization: b) lhe soi l roundation dl .... <:rctization

182 STRUCTURAL ANALYSIS OF HISTOR 1CAL CONSTRUCTIONS

Fig. 16c The vertical section of the complete tinite element model

Finally quadrangular and ttiangular pIate elements have been used for the domes, the arches and lhe spherical ttiangles, whi1e eight-nodes brick: elements have been assumed for lhe tambours. This discretization required some interconnection operations between lhe generalized displacements of rwo different elements. This is the case of lhe interfaces zones between lhe domes and lhe related tambours where the pIate elements of lhe domes, having six degrees of freedom are connected with the solid exaedrical elements of lhe tambours having onIy three degrees of freedom. In order to make compatible these different elements lhe rotations of lhe pIate eIements have beeo related to lhe nodal displacements of lhe exaedrical elements by means of convenient connecrion functions. This technique has beeo applied according to the procedure outlined in [14].

The mechanical description of the various strucrural pans has beeo perfonned as follows: for the e)(ternal walls and lhe pillars lhe high number of experimental tests has allowed to formulate a Slatistical treatment of lhe results, by defining the cumulative distribution function of lhe elastic modulus, showing three calhegories corresponding to poor, sufficient and good masonry. These cathegories are connected wilh values lesser lhan lhe 33% fractile of lhe result distribution, or lying wilhin lhe interval 33% - 67% fractile ar greater than lhe 67% fractile, respecrively. The corresponding numerical values are: El = 850 MPa, E2 = 2000 MPa, E3 = 6000 MPa. For lhe roof, where lhe domes, lhe arches and lhe spherical triangles have beeo subjected to restorarion worlG in lhe past, lhe value E = 5000 MPa has. heco assumed, while for lhe tambours, where a diffuse state of cracking is present, lhe reduced value E = 3000 MPa was chosen. For all lhe structural members lhe subsequent values for the density "t. lhe Poisson's ratio v and lhe linear thermal expansion coefficient a. have been selected: y=18kN/m3• v=O.15. a. =4.SxIo-6 °C·l . Regarding lhe stratum of foundation soil, the results of the standard penetrarion tests have suggested. to subdivide it into three partial strata, having lhiclrness 3.5 m; 10 m; 16.5 m and elastic moduli Et \ = 1500 MPa, Ea = 500 MPa. Et3 = 250 MPa, respectively. The Poisson's ratio has been assumed. v = 0.3.

In the Figures 17a, 17b and 17c some results of lhe numerical investigations are shown in a graphical fonn. In particular Figures 17a and 17b show the displacements and the state of stress in the roof due to pennanent loads, while Figure 17c shows lhe displacements due to pennanent loads in the vertical section of the Basilica.

F. MOLA .1nd R. VITALlANII SI. Mark's Basilica In Vcnicc 183

Fig. 17a Displacements due to permanem loads in the transverse section of lhe roof

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Fig. 17b State of stress in the roof, due to permanem loads

184 STR UCTUR AL ANALYSIS OF HI STORtCAL CONSTRUCTtONS

Fig. 17c Displacements due to permanent 10ads in the vertical section of the Basilica

These results al low to formulate some considerations about the reliability of the mathematical modelo Regarding the pillars the calculated. stresses are generally in a sarisfactory agreement with the experimental ones. The results of the theoretical model are underestimated of about 20% and in quite restricted. zones the theoretical values of the stresses are one half or one third of the corresponding experimental values. On the contrary, in tbe roof we observe a stress distribution which, even if globally in agreement witb the experimental stresses, assumes in some restricred zones values which are too high when eompared with the strength of the material. In the connective zones be[Ween the tambours and the arches the theoretieal tensile stresses, even if in good agreement with the presenee of cracks. have too high values. which, if effectively present, would represent a serious situarion of starieal risk for the roof. However we have to take into aecount that the inferior surface of the domes is covered by precious golden mosaics. so that the execution of experimental tests for the evaluation of the stresses was not possible. For this reason we are lacking of the direet eomparison between theoretical and experimental results, and the only cheek is related to the contemporary presenee of theoretieal tensile stresses and of a diffuse eracking state. As the fust are evaluated by means of a theoretical model considering lhe structural members in the uncracked stale, high values of the tensile stresses numerically computed ean justify the presence of cracks. The obtained results point out a substantial correlarion between computed stresses and observed cracks, so that the theoretical medel seems able to correctly predict the structural behaviour even if some local results cannot be considered sufficiently reliable.

GeneralJy speaking we can state thar the theoretical result.'\ show a sufficient1y reliable distriburion of stiffoess with regard the pillars while tOO high stiffness is present in the connecrion zones between domes, tambours and arches. We have also to consider mar the peak-stresses experimentally evaluated in some pillars and not emerging in the theoretical analysis suggest to operate a convenient refinement of the mechanical descriprion of the material in the sub-assemblies representing the pilIars, while for the edge zones of the domes this refinement should be accomparued. by a more detailed geometrical descriprion.

Even if the theoretical model points out too high local stresses, the numerical results, together with the experimental ones, have allowed tO reliably assesss the structural safety of the Basilica and to state an oprimal srrategy for its sttuctural preservarioo which wiIl be briefly illustrated in the following.

F. iVIO L;\ anel R V ITALl AN I I SI. Mark's Basilica in Venict! 185

5. OPERATIONAL STRATEGY FOR TIIE PRESERVATION OFTIIE STATICAL EFFICIENCY

The results of lhe theorerical and experimental anaIyses have pointed out quite high stresses in two pans of the structural complex, namely in lhe south-wesl pillar of lhe San Giovanni Dome, Figure 14 and in the connective zones between the domes and the arches. The high compressive stresses in lhe pillar and the marked tensile stresses in lhe edge zones of lhe domes have been obtained experimentally in the pillar and theoretical1y in the domes. These different sources for the knowledge of lhe state of stress. have suggested to consider statically inadequate the pillar prescribing for it immediate restorarion works, while the lack of experimental data has induced to prescribe lhe placement of a monitoring equipment for lhe domes in order to control lhe time evolution of their structural behaviour.

Sefore proceeding to lhe restoration of lhe pillar, an additional set of experimentaI tests has been perfonned at lhe pillar base, after removing the marble plates. The resuIts, substantially similar to lhe previous ones, have confumed the statical unreliability of lhe pillar justifying lhe immediate starting of lhe restoration works. The repairing operation consisled flrst1y in lhe whole substitution of the mortar existing in lhe externaI surface of the pillar, extended along the totaI lhickness of the bearing parts. The second operarion consisted in injecting, under low pressure, the internaI pan of lhe pillar with cementitious, moderatel)' expansive mortar. The chernical-physical and mechanical properties of the mortar have beeo established by assuming lhe compatibility with lhe pre­existing materiaIs in terms of linear thennal expansion coefficienl and permeability, avoiding mortars able to produce chemicaI composites containing sulphates or to generate ao increase of lhe internai humidity of the pillar. Another aspect concems the value of the elastic modulus and of the strength of the repaired pillars which has been calibrated on the basis of the corresponding value of a well preserved masonry. In this way no concentrations of stiffness have been introduced.

In Figure 18, a detail of lhe restoration works is shown. The possible slatical inadequacies connected with lhe high stresses theoretically obtained in the edge zones of the domes have beeo controlled by means of a monitoring equipment opponunely placed. The quantities to be measured are: the relative aod absolute generalized di splacemenls of significant points of the structure. the opening of cracks and their width. lhe thennal variation, lhe interstilial pressure of the soil, the relative displacement between lhe foundation mat and lhe olher peinlS of the bearing soil.

The monitoring equipmenl consisls of wire extensomelers, pendulum with telecoordinometer, inclinometers. extensometers, thermo-couples. electrical piezometers, assestometers. These equipments, extensively illusttated in the technical lilerature, e.g. [151. have been placed according to the scheme of Figure 19 and the related data are continuously recorded by means of electronic stations which are able to represent in a numerical or graphical form lhe collecled results. Particularl)' signiflcant for lhe evaluation of lhe possible negative statical effects connecled with the high state of stress in the domes, are the wire eXlensometers placed along lhe chords of the bearing arches, the inclinometers placed on the pillars , the extensometers and the lhermo-couples. These instruments allow to point oul the time evolution of lhe defonnations induced by temperature and by the associate state of Stress.

In Figure 20 lhe diagrams performed in lhe year 1992 are reported. We can see thal lhe displacement measured by the wire extensometers are in good agreement with the lemperature variarion

Funhennore aI lhe end of lhe flrst year of recording the residual displacements are practically negligible so Ihat we can state that the presem statical situarion of lhe complex fonned by lhe domes and by the arches is substanlially stationary. This fact has suggested 10 nOl prescribe immediate restoralion works of lhese parts, poslponing this decision when the data derived from lhe monilOring equipment shall indicale tha! lhe structure is oriented to ao unreliable staticaI behaviour.

186 STR UCTU RAL ANALYSIS DF l-llSTDRICAL CDNSTR UCTI DNS

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Fig. 18 The rCSloralion works of lhe pillar in lhe San Giovanni Dome

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F. MOLA a lld R. VITA Ll Ai'\I l I SI. Mark's B:tSilica in Vcnicc 187

6. CONCLUSI0NS AND FUTURE WORKS

The experimental tests perfonned on the St. Mark's Basilica and lhe subsequent fonnulation of a theoretical model for the numerical analysis, have allowed to achieve a fLfst consistent set of data for the assessment of structural safety and for formulating correct decisions about the need of restoration works. The process which has govemed the diagnostic approach is based on a sequence of operations which, with reference to experimental phases, can be considered well defined and accepled world-wide.

The obtained resuIts are good and they allow to define the most imponant factors goveming lhe slructural behaviour. In particular the slale of stress and the strain parameters evaluated by means of single or double flat-jack tests stand as basic reference points to which compare any olher result deriving from complementary approaches, both experimental and theoretical. The evaluation of the mechanical properties by means of bore-holes, video-camera and sonic tomography tests has allowed to compare the actual stresses existing in lhe structure with the srrength of the material and 10 derive a reliable judgement about the statical adequacy of the monument. The theoretical model has provided results in good agreement with lhe experimental ones. However, the presence of local anomalies has suggested to refine the model and this task will represent one of lhe mOSI importanl items of the future works. On this subject the improvement of the geometrical description and the refinement of the mechanical properues have to be ta.k:en imo account. About the fLfSt point, a more detailed kinematic description of the interface zones is necessary, while lhe second pcint requires a more realistic approach taking into account the non linearities which are unavoidably related to cracking phenomena or to marked compressive stresses. The models able to descnbe lhe non linearity of lhe materiais, associated lO the development of the degrading process, like the model described in [161, seem to be profitable for a generalized improvement of the theoretical structural model.

In the authors' opinion it is however possible to state that lhe operations perfonned for the experimental and theoretical analysis of lhe statical state of the S1. Mark's Basilica, illustrated and descnbed in [17], represent a basic reference point. When the procedure will be funher refined by means of the improvemenls previously discussed and of lhe additional data denved from the monitoring equipment, it wiU give reliable results for a correct and realistic fonnulation of a judgement about the statical efficiency of this monumenl which is lhe living expression of a unique historical heritage.

REFERENCES

1. Balasubramaniam A.S .• Ed., Proc. of lhe Symp . on Geolechnical AspecIs of Restoration Works on Infraslruclures and Monumenrs , Bangkok, 1988, A.A. Balk.ema, Rouerdam/Brookfield, 1990.

2. lABSE (IntemationaJ Association for Bridge and Structural Engineering), Proc. of lhe Intern . Symp . on Structural Preservation of lhe Architecrural Herieage, lABSE Repon. printed with the financial suppon of Italian National Research Council, Rome, 1993.

3 . Brebbia C.A ., Leftheris B., Ed. Proc. of ehe Symp. on SlrucluraJ Srudies of Historical Buildings . Chania - Greece, 1995, Comp. Mech, Publ. , Southampton, UK, 1995.

4. Vio E., Galeazzo G., Vitaliani R., Rilievi, controlli dimensionali e analisi strutturale nella Basilica di S. Marco in Venezia (in Italian), Bo/lettino SIFET, Società Italiana di Topografia e FOlogrammeJria, N. 3/4,1988.

5. Riccioni R., Rossi P.P., Restauro Ediliúo e Monumenrale (in Italian), i1 Cigno Galileo Galilei. Edizioni di Ane e Scienza, Roma, 1990.

188 STRUCTURAL ANALYSIS OF HISTORICAL CONSTRUCTIONS

6. Rossi P.P., Peano A., Carabelli E., Determinazione sperimentale delle caratteristiche meccaniche delle murature (in ltalian), Comportamento Slatico e sismico delle strutture murarie, Sacchi G., Riccioni R. Ed. eLUP, Milano, 1982.

7. Rossi P.P., Recent development of the fla t-jack test on masonry structures, USA-Italy Workshop on Evaiuation and Retrofit of Masonry Structures, 1987.

8. Saccardo P., 1 restauri deUa Basilica di S. Marco dai 1878 in poi (in Italian), Venezia, 1905.

9. Forlati F., La Basilica di S. Marco attraverso i suoi restauri (in Italian), Trieste, 1975.

10. Direzione dei restauri della Basilica di S. Marco, Rapporti sulio stato dei lavori di restauro dell'Angolo di S. Alipio daI 1909 ai 1914 (in Italian), Procuratoria di S. Marco, Sezione Documenti, Venezia.

11. MSC/NASTRAN version 67, The MacNeal-Schwendler Corporation, Los Angeles, 1992.

12. AUTOCAD version 12, Autodesk inc., 1992.

13. I-DEAS, Structural Dynamics Research Corporation, 1990.

14. Bathe KJ., Finite Element Procedures in Engineering Analysis, Prentice Hall, Inc., Englewood Cliff, New Jersey, 1982.

15. Malerba P. G. ed., Monitoraggio delle strutture dell'ingegneria civile (in Italian), CISM International Centre for Mechanical Sciences, Collana di Ingegneria Strutturale, Vol.N.9, Udine, 1995.

16. Creazza G., Saetta A., Scotta R., Vitaliani R., Oõate E., Mathematical Simulation of Structural Damage in Historical Buildings, Proc. oflhe Symp . on Structurai Studies of Historical Buildings, Chania - Greece, 1995, Comp. Mech. Publ., Southampton, UK, 1995.

17. Mola F., Rossi P.P., Vilaliani R., Melhodological Approach for Sttuctural Analysis and Inspection in the S1. Mark's Basilica, Venice, Proceedings of the Symposium on StructuraJ Studies of Historicai Buildings, Chania, Greece 1995, Computational Mechanics Publications. Southampton, UK, 1995.