Pomposa Abbey: FEM Simulation of Some Structural Damages and Restoration Proposals

Pomposa Abbey: FEM simulation of some structural damages and restoration proposals

E. Cosmi (2), G. Guerzoni (%), C. Di Francesco 0), C. Alessandri (%) W Soprintendenza Beni Ambientali Architettonici,

48100 Ravenna, Italy (2) Department of Architecture, University ofFerrara,

Via Quartieri 8, 44100 Ferrara, Italy EMail: [email protected]. it

Abstract

A static analysis of the Pomposa Abbey is proposed with the aim of verifying the effects of the tower self weight on the present deformed configuration of the church and the structural efficiency of the internal buttresses, added as reinforcements to the whole construction. In this paper the Authors present a kind of reinforcement to be considered as alternative to the existing ones; the proposal is supported by a numerical simulation carried out on a 3-D model of the Abbey, discretised and analised with FEM techniques. The structural solution is statically reliable and it allows to recover the unity of the internal space and to preserve the integrity of the existing structures.

1 Introduction

The Abbey of Pomposa (Fig. 2), located in the middle of the River Po Basin, between the ducal woods of Mesola and the Mezzano nature reserve, has its origin in the VI century, when a large part of Italy was under Longobard rule; it was a centre for culture, work and prayer for the Benedectine Monks who reclaimed vast areas of sorroundings marshlands and collected relics from the Classical world, which was then in the phase of full decline. Initially under the power of the church in Ravenna, later on Pomposa managed to gain its independence, and was especially favoured by Pontiffs and Emperors and, in this way, little by little, it was able to increase its power, and the Abbot, as well as having ecclesiastical power, began also to wield civil power over large areas of land. In the XI century the complex of Abbey buildings were extended and a library was founded. Pomposa reached the peak of

its power in the XIV century, when its jurisdiction spread to include lands in eighteen different Italian diocese. But, in the same period, as a result of the river Po breaking its banks in the XII century and changing its course, the land sorrounding the Abbey was gradually being invaded by marshlands, which was destroying the secular work of the Benedectines. The decline of Pomposa was imminent; only a few months remained at Pomposa which, in 1654, on the departure of the last monks, becomed a modest parish in the diocese of Comacchio. Only in the XIX century, when the

Italian Government took over possession of the Abbey, did the slow work of restoration and renaissance begin. All that remained of the old complex of Abbey buildings were the church, the bell tower, part of the monastery and the palace of justice. After being founded, the Abbey continued to grow until the XII century by the addition of apses, spans and an atrium. It shows clear architectural influences of the near city of Ravenna, expecially in the internal subdivision (quite usual in the late Byzantine basilicas) into a nave and two side aisles, with columnades and arcades (Fig. 1). The nave, more developed than the others in hight and width, ends up with a triumphal arch, a crypt and a semicircular apse. Wooden trusses and beams form the roof structures of nave and aisles, respectively. External and internal walls are formed of brick and mortar masonries which show no appreciable sign of physical decay but visible out-of-plane deformations and localised cracks due to a subsidence started during the construction of the near bell tower in the early XI century and continued afterwards. As a matter of fact, the enormous self-weight of the whole masonry tower, nearly 1 800 tons, distributed on a relatively small square base, produced uniform vertical settlements of the most compressible soil layers below and, as a consequence, the rotations and the above mentioned out-of-plumbs of the Abbey walls. In order to prevent a possible, further growth of these structural damages, a set of transverse masonry walls (Fig. 3) was built in the aisles and in the atrium between the XVI and the XIX century, long time after the occurrence of the first macroscopic subsidence. Although they had to behave as internal buttresses, serious doubts still remain about their static efficiency; moreover they have altered completely the perception of the internal spaces. For more than one year the Authors have been investigating alternative solutions to such a kind of reinforcement on the basis of results obtained in previous analyses and by using modern software packages for numerical modelling and 3-D visualisation. The results of this research are partially presented in this paper, expecially those concerning the structural analysis of the Abbey and the technical solution to be proposed in place of the buttresses. In particular, a static analysis was carried out to verify the effects of the tower self weight on the present deformed configuration of the Abbey, the actual structural efficiency of the internal buttresses and the validity of the new proposal; a well- known FEM code, MARC K62, was used to solve the various linear and nonlinear structural problems encountered. Although further investigations are needed, the solution proposed is statically reliable and allows to recover the unity of the internal space.

2 Historical Analysis

Still readable traces on the monument, as well as the testimony of some historians [1-3], allow to subdivide the whole construction process of the church into twelve phases. In each of them the building was subjected to morphologic transformations which gave rise to considerable changes in the mechanical behaviour of structures and subsoil. The oldest part of it, dating back to the half of the VIII century, was originally two span shorter than the present building, without minor apses and crypt

but with the same three naves as nowadays. A two-level atrium, adorned with double

lancet windows, was built before the end of the X century in correspondence of the first two present spans. The XI century sees the beginning of a great deal of works: frescoes, mosaic floorings and marble "tarsie". Probably, by that time, the church had been already enlarged by incorporating with other two spans the previous atrium, the facade of which, modified by the addition of a tympanum, the closure of the double lancet windows and the reduction of the entrance portal, became the new front of the church. The construction of the semicircular apses of the side aisles (the Southern apse was demolished in the XIV century to allow a direct access to

the Monastery) and of the crypt under the main altar goes back to the same period. After a short time the present atrium and the whole monastery were added. Meanwhile, in 1063 the imposing bell tower began to be built; its construction spanned over some decades corresponding to the economic and cultural bloom of the Abbey. The alignment of bell tower and atrium facade allows to suppose that the latter was built previously or, at most, at the same time. About 1150 the Northern apse was re-built, together with a part of the otside wall, after a collapse occurred for still unknown reasons; meanwhile the decline of Pomposa begins: the break of the river Po in the nearby (1152) leads to a slow but inexorable worsening of the

geo-climatic conditions of the area and, in particular, to its progressive swamping. By the end of the XIII century the roofs of the side aisles were lifted up to the present level and the central part of the atrium facade was re-made, probably in consequence of a collapse occurred some years earlier, as confirmed by an oral, although not documented, tradition. Probably in baroque time, when most of the churches were modified in accordance with the new liturgical rules issued by the Council of Trento, the original crypt was demolished and the whole apsidal zone was brought to the same level as the nave. The construction of the eleven transverse masonry walls, supposed to behave as buttresses, represents the final stage of the

architectural and structural transformation process of the church. Such a cumbersome consolidation work, the motivations of which will be explained in the next Sections, was carried out in two stages: all the buttresses, with the exception of the first of the right aisle and of the ones in the atrium, were built between the XVI and XIX century; the remaining ones were added in 1858, as reported in some historical documents. The successive works carried out on the church were mainly maintenance works and preserved the structural aspects characterising the building in the second half of the XIX century; the only exception is the crypt which was re-built in 1927 in the same place as the previous one and with an imaginary typology.

3 The Present State

Some investigations carried out between 1985 and 1992 allowed to evaluate the physical state of the whole building [4]. The masonries, for instance, are not

deteriorated and visible cracks interest only small wall portions. Nevertheless, the costruction of the church by successive additions of different parts caused inhomogeneities and irregularities in the masonry and in the brick textures and, in particular, a remarkable weakening of the connections between not coeval masonry structures. Tha transverse buttresses, for instance, are not clamped to any other structure: they are completely disjoined from the outside walls of the side aisles andfi tagains t columns and walls of the nave and of the facade by means of mortar joints. The foundations are superficial and formed of squared sedimentary stones over a layer of bricks-on-edge in direct contact with the soil. Most of the masonry walls show remarkable and visible deformations consisting of out-of-plumbs in the

142 Structural Studies, Repairs and Maintenance of Historical Buildings

North-South direction for the longitudinal walls (they are leaning towards the bell tower except for the right outside wall which is leaning to the right) and of out-of- plumbs in the East-West direction for the front walls (they are leaning to the outside) (Fig. 4 - 5). It is worth noting that the values of such out-of-plumbs increase considerably near the North-West corner of the church, i.e. in proximity of the bell tower; however, some measurements surveyed between 1940 and 1989 show that the phenomenon is not progressing. As far as the bell tower is concerned, no out- of-plumb was ever surveyed: it is still perfectly vertical. The crack patterns are mostly concentrated on the front parts of the church (atrium and facade) and in proximity of the apse: some cracks go through the whole thickness of the masonry, whereas others are visible only on one surface; however, some of them are now hidden by the mortar sealings made during the restoration works carried out on some frescoes. A number of tie rods were located as reinforcements either inside the buttresses or in the longitudinal direction with the aim of contrasting the movements of the walls induced by the settlements of the soil under the bell tower. The stratigraphic and penetrometric investigations carried out around the whole complex by the end of the eighties revealed a number of soil layers characterised by a nearly absolute homogeneity in horizontal directions and by a strong inhomogeneity in the vertical direction. The following approximate stratigraphy can be considered: wide sand layers, characterised by high bearing capacities, are alternated with four clay layers at the depth of 8,15,20 and 27 metres, respectively, which are responsible for the considerable decrease of the average bearing capacity of the whole set of layers, as proved by the edomerric tests carried out on the samples extracted from the four more compressible layers. Some piezometric tests carried out "in situ" to measure the groundwater level and the interstitial pressures would let suppose that the soil consolidation due to the weights of the church and the bell tower has come to an end.

4 F.E.M. Simulations

The analysis of the surveyed data allowed to verify a hypothesis, formulated recently [4], according to which the instability of the structures, resulting in the out-of- plumbs of walls and columns, started since the erection of the bell tower: its weight, too high if compared with the low bearing capacity of the soil, would have caused uniform vertical displacements of the tower and a consequent leaning to the North of most of the masonry walls. That would have justified the erection in the past centuries of the transverse masonry walls as buttresses contrasting their movements toward the tower. This hypothesis was validated on the basis of the classical theories of Geomechanics and, in particular, according to the Boussinesq theory, by defining the pressure bulbs corresponding to the loads tranferred to the soil by the foundations. It is immediate to note the large dispropotion between the bulb under the bell tower and the one under the wall of the nave (Fig. 6 - 7): the first one goes through several compressible layers and gives rise to considerable uniform settlements under the tower, whereas the latter, limited to the more superficial sand layers, causes quite small settlements of the nave foundations. Therefore, the deformed profile of the soil shows a deep subsidence under the tower and decreasing slopes on both sides of it. The perpendiculars to such a profile from the intersection points of the profile itself with the middle-planes of the longitudinal walls allow to obtain an approximate estimate of the rotations these walls underwent and of the consequent out-of-plumbs (Fig. 8), The comparison between the surveyed data and the estimated values is

Structural Studies, Repairs and Maintenance of Historical Buildings 143

satisfactory. Another set of results was obtained by means of a numerical simulation of the mechanical behaviour of the church since its construction: the FEM code used was MARC K62 [5] installed on a Silicon Graphics Solid Impact 10 000 and the numerical analyses were carried out with reference to a 3-D model discretised with 9 595 finite elements. In particular 6 830 3-D eight-node, isoparametric, arbitrary hexahedral elements were used to model buttresses and soil, 2 621 2-D, four-node, thick-shell elements for the remaining walls of the church, 144 one- dimensional straight, Euler-Bernoulli beam elements for columns and tie-rods; the nodes were 12 617, corresponding to 75 702 degrees of freedom. Four types of materials were considered: masonry, marble, steel and soil; nonlinear analyses were carried out for masonries, considered as elastic-fragile materials with low tensile strength, and to determine unilateral contact surfaces and pressures at the intersection of buttresses and longitudinal walls. Moreover, 111 rigid connections were imposed to the nodes in correspondence of capitals and tie-rods tips. The geometrical 3-D model was firstly built up by using ALIAS/WAVEFRONT Studio, version 8.5, and successively imported into MARC with .iges extension. The model was then discretised by means of an authomatic conversion of ALIAS surfaces into MARC finite elements. The masonry constitutive law assumes in compression a higher strength than in tension. Moreover, in compression the stress-strain diagram denotes an elastic-plastic behaviour with a highly nonlinear work-hardening phase after the linear one (Fig. 9); the values assumed for the Young's Modulus (E), Poisson ratio

(v) and crushing strain (e<,rush) were respectively E = 60 000 kg/cm^ for buttresses, E = 40 000 kg/cm2 for all the other masonry walls, E = 400 000 kg/cm^ for marble, v = 0.2 and £crush ~ 0.5 everywhere. In tension the behaviour is linear elastic until a critical cracking stress a^ = 1 kg/cm^ is achieved; after this limit value the behaviour becomes softening and it is characterised by a descending branch in the tensile stress-strain diagram with a tension-softening Modulus Es = E/10. As no experimental test could be carried out on material samples, the mechanical properties of masonries were obtained by the technical literature and the Italian Codes for masonry constructions. The nonlinear analysis was carried out by means of an incremental iterative procedure based on the application of the Newton-Raphson method. Other nonlinear problems were provided by the unilateral contact occurring at the interface between buttresses and longitudinal walls; the contact was assumed as frictionless and only non-penetration constraints were imposed. At each load increment the solution of the problem, i.e. nodes in contact and corresponding contact pressures, was obtained within an iterative procedure which ended when the non- penetration condition and the non-positiveness of the contact tractions (only contact pressures are statically admissible) were verified for all the nodes in contact. For mere computational reasons, only a small portion of soil was considered under the church: it is a parallelepiped including both church and bell tower, simply supported at all the nodes of the base and of the lateral surface, divided into four main layers the physical properties of which are obtained as mean values of the properties referred to the actual layers contained in each of them. For the sake of simplicity, the soil behaviour is assumed linear elastic. The weight of the bell tower is applied to the free surface portion corresponding to its print on the soil. In the first place, a discretised model of soil and church without buttresses was considered with the aim of defining a motivation for the erection of the buttresses (Fig. 10). The weight of the bell tower should have been applied in fifty steps but already at the sixth load increment two cracked regions, characterised by tensile stresses exeeding the critical one, appeared on the front wall of the atrium, just over the arcade, and beyond the half of the left outside wall, the latter for the entire height of the wall and with the

144 Structural Studies, Repairs and Maintenance of Historical Buildings

maximum width on the top (Fig. 11). Acourious and interesting correspondence between this result and some written and oral testimonies can be stated: as a matter of fact, the central part of the atrium front wall, as well as the Northern apse and part of the longitudinal wall close to it, were probably re-built between the XII and

XIV century after collapsing. The heterogeneity of the masonry texture in such zones are still evident. The incremental process was re-started after introducing into the FEM model a physical discontinuity between the elements belonging to the cracked zones. Further cracks in vertical direction occurred on the walls of the nave, mostly concentrated in the central parts of them and in proximity of the triumphal arch (Fig. 12). Other cracked regions appeared near the keystones of the trimphal arch and the minor arch of the left aisle (Fig. 13). They all correspond to the still visible cracks on the inside. The deformed shape of the church, so obtained, as well as the computed wall rotations and top horizontal displacements are very similar to the corresponding data surveyed. The analysis was repeated with the only addition of the buttresses in unilateral contact with the orthogonal walls. The results showed that such buttresses followed the movement of all the rest of the church without interacting with the longitudinal walls. Only the right buttresses showed compressive stress concentrations near the ends of the internal tie rods which, stretched by the progressive spacing of the longitudinal walls, induced compression in the masonry.

5 Restoration Proposals

The results obtained from these analyses allowed to consider the possibility of removing the buttresses and finding technical solutions which guaranteed an almost rigid behaviour of the whole masonry structure, such as to avoid the occurrence of stress concentrations and deformations in the masonry and the consequent loss of stability in the case of further settlements of the soil. In other words, new structural elements, in replacement of the buttresses, had to be provided in order to give a majors stiffness to the whole structure and to make it similar to a box structure. But, numerous and irremovable constraints were imposed by the monumentality of the building: the interior of the church is frescoed nearly everywhere and the outside walls have a crown formed of bricks laid on edge and on bed; moreover, the facade of the atrium, with its rich decorations, required the absolute concealment of every reinforcement. For these reasons the restoration project had to be, as much as possible, non-invasive and non-destructive toward the existing structures. The present roof structure seemed to be suited to such a purpose. Each pitch, in fact, could be transformed into a doubly ribbed wooden slab (with ribs provided by rafters and purlins) by using highly resistant structural plywoods. That was possible by joining tightly, through the entire thickness and with stiff connectors, all the wooden structural elements (plywood, boards, purlins and rafters)(Fig. 14). A particular attention had to be paid to the connection between the roof structure and the outside walls in order to minimise the horizontal displacements on top of these walls and the stress concentrations in the masonry. Simple equilibrium considerations showed that such a goal could be achieved by taking into account the frictionforc e acting on the surface supporting the roof structure, provided that the concentrated loads transferred by rafters and trusses were distributed quite uniformly on the masonry. Therefore continuous wooden wall plates were proposed on top of the outside walls and over the rafters. They were thought slightly spaced from the rafters in such a way as to allow the transferring of the concentrated loads from the

rafters to the masonry when they had to be tightened to the rafters by means of bolts drowned in epoxy resin (Fig. 15). Where this technical solution is not possible, for instance at the junction between pitches and nave walls or front wall, the use of angle irons anchored to wood and masonry with bolts and epoxy resins was proposed. Epoxy resins were preferred to cement mortars because they are thought to be less dangerous for the internal frescoes. The new stress and strain state of the church was defined with MARC by assuming the existing roof structures replaced with the proposed stiffened pitches and all the buttresses removed. As in the previous analyses the weight of the bell tower was applied in fifty steps. A linear elastic behaviour was supposed for the wooden structural elements; in particular four- node, thick-shell elements were used for the plywood slabs and beam elements for trusses, rafters and purlins. The results showed a satisfying box structure like behaviour of the whole complex: the relative displacements were considerably reduced and the deformed shape of the structure turned out to be more regular than the ones previously obtained. Nevertheless, at the twelfth load increment, some cracks occurred on the left outside wall, in proximity of the atrium facade and along a semicircular directrix, as if in that area the masonry could not be "sustained" entirely by the roof reinforcement (Fig. 16). Other vertical cracks were still visible on the wall of the triumphal arch, although confined to a small region. Therefore, despite the satisfactory results obtained so far, some more work should be done in order to guarantee the absolute safety of the proposed project.

References

[1] Salmi, M., L'abbazia di Pomposa, Ed. A. Pizzi, Milano, 1966. [2] Pavan, G., Ricerche e lavori a Pomposa, in "L'arte sacra net Ducati Estensf', Ed. Sate, Ferrara, 1984.

[3] Russo, E., Profile storico-artistico dellachiesa abbaziale di Pomposa, in "L'arte sacra nei Ducati Estensf\ Ed. Sate, Ferrara, 1984. [4] Di Francesco, C., Mezzadri, G., Indagini e rilievi per interventi strutturali nella chiesa abbaziale di Santa Maria di Pomposa, in "// Cantiere della Conoscenza,

il Cantiere delRestauro\ Proceedings Nat. Conf, Bressanone, 1989, Ed. Li- breria Progetto. [5] MARC Analysis Research Corp., Palo Alto, CA 94306, USA- 16129 Genova, Italy.

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Figure 1: Present church - Horizontal view

146 Structural Studies, Repairs and Maintenance of Historical Buildings

^#^:<;.W^__ Figure 2: Front of the Abbey Figure 3: Internal buttresses

Figure 4: Out-of-plumbs - Horizontal view

Figure 5: Out-of-plumbs - Vertical view

Structural Studies, Repairs and Maintenance of Historical Buildings 147

Figure 6: Pressure bulbs

Figure 8: Computed soil settlements Figure 9: Masonry constitutive law

Figure 10: FKM discretisation Figure 11: Irst set of cracks

148 Structural Studies, Repairs and Maintenance of Historical Buildings

u u

Figure 12: 2nd set of cracks Figure 13: 2nd set of cracks

Figure 14: Details of the new roof structures

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Figure 15: Rafter - wall plate joint Figure 16: Cracks in reinforced model