Safety assessment of Monastery of Jerónimos, Lisbon

Transcription

1 Historical Constructions, P.B. Lourenço, P. Roca (Eds.), Guimarães, Safety assessment of Monastery of Jerónimos, Lisbon Paulo B. Lourenço and Sara Mourão University of Minho, Department of Civil Engineering, Guimarães, Portugal ABSTRACT: A study on the safety of Monastery of Jerónimos, Lisbon, Portugal under vertical loading and seismic loading is presented using non-linear finite element analyses. Given the large size of the monastery, dynamic loading is simulated by equivalent static forces applied horizontally. A discussion is held on the difficulties related to the need of adopting a very simplified geometry of the model. The non-linear analyses carried out seem to indicate that the global safety of the monastery is adequate. 1 INTRODUCTION Monastery of Jerónimos is, probably, the crown asset of Portuguese architectural heritage. The monumental set of constructions resisted well to the earthquake of November 1, Later, in December 1756, a new earthquake collapsed one column of the church that supported the vaults of the nave and resulted in partial ruin of the nave. In this occasion also the vault of the high choir partially collapsed. In addition to these collapses, during the 19 th century and later, several changes were made in the structure, namely changes in the structures of two towers and in the roofs. The effect of these changes in the seismic performance of the structure remained an open issue. The destructive potential of an earthquake depends of three main characteristics: the peak acceleration of the soil, the duration of the strong motion and its frequency content. This last characteristic is quite important in the definition of the type of structures that will be mostly affected by the shake. In order to increase the seismic safety, the following precautions can be identified: (a) built in hard soil (preferably rock), as well as, adequately compact the soil where the foundation will be placed; (b) use light pavements / roofs so that induced seismic loads remain admissible; (c) use robust walls and buttresses, and limit the height of the structure; (d) use good quality building materials and qualified workmanship, as irregular stones, weak mortars and large voids strongly reduce the strength of constructions subjected to dynamic loads. The case of Monastery of Jerónimos seem to be constructed in hard soil, using good quality masonry and, indeed, resorting to light roofs. The problem of assessment of safety in historical constructions is quite complex. In particular, little is known about the materials, the variability of properties, the existing damage, the inner core of the walls, columns and vaults, among other difficulties. But one key aspect of masonry is its reduced tensile strength which renders linear elastic analyses debatable. Therefore, the approach towards dynamic loading becomes rather unwieldy as modal superposition does not apply anymore and time integration is hardly applicable to large engineering problems such as the one presented here. The decision adopted in the present work was to introduce the seismic loading by static equivalent forces applied horizontally. This was combined with a non-linear analysis which can would be understood as an equilibrium / stability assessment. If such a stability requirement

2 698 Historical Constructions would not be met, it would seem questionable to accept the current condition of the structure. But if the stability requirement is met, not necessarily local collapses will be precluded from occurring. For the purpose of assessing the safety of Monastery of Jerónimos under seismic loading, five different load combinations were carried out, including vertical loading and seismic action along two orthogonal directions (both positive or negative). Due to the very large size of the construction, a rather simplified model is adopted. A discussion on the difficulties encountered in constructing the simplified model and the necessary corrections of intermediate models are also given. 2 HISTORICAL SYNOPSIS AND GEOMETRY Portugal is a small country, distant from the centre of Europe. As a result, the Gothic style was introduced late and with a specific national influence. The influence of e.g. the French and Spanish large and monumental Gothic structures was indeed minor but, when the style is introduced in the Centre and South of the country, it rapidly expanded and incorporated national developments, see Chicó (1981). The so-called late Gothic style was introduced by Kings D. Afonso V and D. João II ( ) but it is the brilliant period of D. Manuel I ( ) that exhibits a large variety of architectural influences and erudite motives become rapidly popular. The term Manuelino derives from D. Manuel I and was coined firstly by the German historian J.A. Varnhagen in 1841 (actually used not do define an architectural style but to define the decoration of windows and door frames). This term applies today to a specific architectural style, being the Church of Jesus, in Setúbal, the first construction associated with this style, see Fig. 1a. Nevertheless, the main Manuelino monuments are the Convent of Christ in Tomar, the Monastery of Jerónimos in Lisbon and the Belém Tower in Lisbon, see Fig 1b-d. (a) (b) (c) (d) Figure 1: Examples of Manuelino style in Portugal: (a) Church of Jesus, Setúbal; (b) window of Convent of Christ, Tomar; (c) Monastery of Jerónimos, Lisbon; (d) Belém Tower, Lisbon.

3 P. B. Lourenço and S. Mourão 699 An interesting aspect appears in the beginning of the 16 th century, when the traditional three naves churches start to be replaced by a configuration with small difference in height for the naves, the German hallenkirchen. Here, the vault springs, in fact, from one external wall to the other, supported in thin columns that divide almost imperceptibly the naves. From the traditional art, only the proportions and roof remain, being the concepts of space and structure totally novel. The fusion of the naves in the Church of Saint Mary of Belém, Monastery of Jerónimos, see Fig.2, is more obvious than in other manifestations of spatial Gothic. For this purpose, arches are no longer visible, the slightly curved vault comprises a set of ribs and the fan columns reduce effectively the free span. Clearly some Renaissance influence can be perceived in plan and the combination of volumes. Figure 2: Church of Saint Mary of Bélem, Monastery of Jerónimos: (a) transversal cross-section; (b) vault on top of the choir; (c) aspect of the three naves. 2.1 The Monastery of Jerónimos The construction of the monastery started in 1499 or Due to the 5% tax of the gold and spices from Africa and India, the construction initially planned by Diogo Boitaca was of gigantic size (four times the size of the actual monastery), including four cloisters and four dormitories. In fact, only one dormitory and one cloister were completed. The monastery is built with limestone ( calcário de lioz ) quarried locally in Ajuda, Alcântara Valley, Laveiras, Rio Seco and Tercena. During the 16 th century, the construction of the monument was carried out in three successive phases. The works in the 17 th and 18 th centuries are merely decorative or minor. In the 19 th century, debatable works of re-composition or restoration were carried out and, in 1940, an attempt to correct previous mistakes and return the monastery to its original configuration was made. The monumental set has considerable dimensions in plan, more than m 2, and an average height of 20 m (50 m in the towers), see Fig. 3. The monastery evolves around two courts. The larger court is bordered by a long arcade of two levels that hosts the Ethnographic Museum of Archaeology and the Maritime Museum. The smaller court or the Cloister is bordered by the Church, the Sacristy, the Chapter Room, the Refectory. 3 DEVELOPMENT OF AN ADEQUATE SIMPLIFIED MODEL OF ANALYSIS The main objective of this research was to study the safety of the monumental set to horizontal loading (seismic action). For this purpose, a finite element analysis of the construction will be carried out. Given the size and complexity of the monastery, it is necessary to adopt a finite element model that simplifies the geometry to great extent. Next, the results of a preliminary investigation on the adequacy of adopting simplified finite element models are presented.

4 700 Historical Constructions (a) (b) Figure 3: Monumental set of Monastery of Jerónimos: (a) aerial view; (b) plan. 3.1 A refined model vs. a simplified model A first model of the Refectory using three-dimensional volume elements and a refined geometry, the so-called refined model, was compared with a second model using shell elements and a very simplified geometry, the so-called simplified model, see Fig. 4. The refined model included the openings with larger size and the actual thickness of the walls. Vaults were represented by curved shell elements located at the centre line of the elements. The simplified model did not include any openings and the vaults were replaced by flat slabs. The slabs were located at the upper vault level because the vaults have a low curvature and it was observed that better results could be obtained by placing the flat slabs at this level, instead of placing the elements at the mass centre of the vault. Additionally, in the simplified model, the vaults of the two compartments that form the entrance of the cloister were considered levelled and the staircase was substituted by a flat slab at medium height. (d) Figure 4: Models adopted for the Refectory: refined model (a) view and (b) longitudinal cross section; simplified model (c) view and (d) longitudinal cross section.

5 P. B. Lourenço and S. Mourão 701 The models will be compared via a modal analysis because the main concern of the work is the performance under seismic action. The material properties are the same for both models: Young s modulus E = 2.7 GPa, Dyngeland and Pinto (1997), Poisson ratio ν = 0.2 and a weight per unit volume of 23 kn/m 3. In order to obtain similar results between the two models, the thickness of the walls in the simplified model had to be increased so that the bending stiffness of the walls includes the additional restraint effect of the nodes (associated with transversewalls), see Fig. 5. It can be seen that, for shorter walls, the increase in thickness is around 12%, which results in an increase of stiffness of around 40%. Without this correction the difference in the results also substantial, see Mourão and Lourenço (1999). Of course, it seems debatable to adopt such a correction in the thickness for non-linear finite element analysis due to the inherent larger strength of the corrected stiffness walls. Figure 5: Plan view with thicknesses of the walls (inside parentheses is the actual value and outside is the adopted value). A modal analysis of the structure has been carried out and reasonable agreement is found between the refined and the simplified refined model, see Table 1 and Fig. 6. Table 1 shows the natural frequencies associated with the first six global vibration modes and the average difference is only 6% (the difference in mass has been compared and it is just 4%). Nevertheless it is stressed that the simplified model exhibits a significantly large number of local modes due to the vertical modes associated with the flat slabs. For this reason, in Table 1, the frequencies Table 1: Natural frequencies associated with the first six global modal shapes (Hz). Refined model f 1 = 1.79 f 2 = 2.26 f 4 = 3.34 f 5 = 3.78 f 7 = 4.70 f 8 = 5.41 Simplified model f 1 = 1.61 f 2 = 2.41 f 4 = 3.25 f 7 = 3.98 f 9 = 4.39 f 12 = 5.31 (d) (e) (f) Figure 6: Shape of the first three vibration modes: (a-c) refined model; (d-f) simplified model.

6 702 Historical Constructions have been compared only to equivalent global modes. In Fig. 6, the modal shapes associated with the three first frequencies are shown. It can be seen that the two first global modes agree well in shape, whereas the local 3 rd mode is different in both models. Of course that the local modes affect mostly the element selected and hardly the entire structure. It seems that it is possible to conclude that the corrected simplified model allows an adequate representation of the dynamic behaviour of the construction. It seems also possible to conclude that the free vibration of the flat slabs should not be allowed in the analysis. 3.2 Complete model of the Monastery In the complete model only the very large openings were considered. The geometry of the model was referred to the average surfaces of the elements. All the walls, columns, buttresses, vaults and towers were included in the model, with the exception of a few minor elements, see Fig. 7. The vaults were, initially, represented as a flat slab with constant thickness due to their geometric complexity. The finite element mesh is predominantly rectangular and structured, but, for the towers and local refinements, triangular finite elements are also adopted. All elements possess quadratic displacement fields. The mesh includes around 8000 elements, nodes and degrees of freedom. The time necessary for total mesh generation, including definition of supports, loads and thicknesses, can be estimated in three months. Figure 7: Model of the complete Monastery. A first analysis of the structure subjected to its self weight has been carried out. The results clearly indicated that the initial mesh needed several corrections as the maximum displacements (up to 0.25 cm) and maximum tensile stresses (up to 0.45 MPa) were unacceptable. Fig. 8 illustrates these results. Figure 8: Unacceptable results in the preliminary model: (a) large displacements at the vaults with constant stiffness; (b) large tensile stresses at the transept; (c) large tensile stresses at the arcade.

7 P. B. Lourenço and S. Mourão 703 The mesh was corrected by introducing tyings at the flat shells, replacing the constant thickness of the vaults by variable thickness and introducing new elements to better represent the large openings, see Fig. 9. After these corrections, it was found that the maximum tensile stresses in the structure for vertical loading are still relatively large (up to 0.35 MPa) and occur in the buttresses. These stresses are related to the double curvature of the buttresses associated with the flexural behaviour of the flat slabs, see Fig. 10a, and are debatable. Namely, an outwards displacement due to the thrust action of the vault cannot be found in the present model. It can be also seen that the tensile stresses in the corrected areas have been significantly reduced, see Fig. 10b. Finally, it is stressed that the average compressive stresses seem adequate (around 0.7 MPa), with higher values in the columns and in a wall not belonging to the monument, where little structural information exists. (d) Figure 9: Examples of the corrections in the geometry of the preliminary model: transept (a) before and (b) after correction; arcade (c)before and (d) after correction. Figure 10: Linear elastic results for vertical loads: (a) peak tensile stresses at the buttresses; (b) smaller tensile stresses at the transept; (c) peak compressive stresses in adjacent bodies of the monument. 4 SAFETY ASSESSMENT FOR EARTHQUAKE ACTIONS The analyses carried out assuming linear elastic behaviour of the material allowed to conclude that the tensile stresses present in the structure are reasonably high and above the tensile strength of masonry. For the safety assessment, five independent non-linear analyses were carried out, namely for vertical loads and for seismic loading along two directions (with positive and negative sign). Therefore, for practical reasons, the seismic action was considered by horizontal static loads proportional to the vertical loads. According to the Portuguese Code, it was assumed that the horizontal loads are 22% of the vertical loads, magnified by a loading safety factor of 1.5. For the non-linear analyses, a tensile strength of 0.1 N/mm 2 was adopted, see Meli (1998). Detailed information on the analyses can be found in Mourão (2001). For the design values of the loads, the deformed meshes of the analyses are given in Fig. 11 for seismic loading along two orthogonal directions: the longitudinal X direction and the transversal Z direction. It can be seen that the towers of the Museum are the critical structural ele-

8 704 Historical Constructions ments featuring displacements of around 0.10 m in each case and cracks of around 0.01 m. Other cracks are visible in the church, see Fig. 12. (a) (b) Figure 11: Deformed meshes and contour of maximum displacements (maximum displacement for design loads is around 0.1 m): Seismic load along the (a) longitudinal X and (b) transversal Z axis of the model. Figure 12: Cracking for seismic action along Z axis: (a) tower; (b) wall in the transept; (c) opening in the church. The maximum crack width is around 0.01 m.

9 P. B. Lourenço and S. Mourão 705 Fig. 13 indicates the areas of maximum compressive stresses, which reach excessive values around 4.0 N/mm 2. These values are very localised in the buttresses, in one of the bodies adjacent to the monument and in the arcade. Given the fact that this is an accidental loading condition and that the stresses are very localised, it is assumed that the structure is not at risk. The average maximum values are around N/mm 2, which seem acceptable, Meli (1998). Finally, Fig. 14 shows the force-displacement diagram of the tower top, for the critical seismic loading, along the Z axis. The analysis was continued further until collapse of the tower, which occurred for a load 25% higher than the applied design load, at a displacement larger than 0.25 m. Figure 13: Maximum compressive stresses for seismic action along Z axis: (a) buttresses; (b) adjacent bodies to the monument; (c) arcade. The maximum stress compressive is around 4.0 N/mm 2. Load factor g Displacement (cm) Figure 14: Force-displacement diagram for seismic action acting along the Z axis. 5 CONCLUSIONS A simplified model of Monastery of Jerónimos was presented. The validity of the model was assessed by a comparison of modal analysis between a simplified model and a refined model. The difficulties inherent to the adoption of simplified models were addressed. Namely, special care seems necessary when (a) using shell elements, as the out-of-plane bending stiffness of walls seem to become rather incorrect, and (b) using flat shells to represent complex vaults, as erroneous bending deformation of the walls seem to occur. Non-linear analyses of the simplified model seem to demonstrate that Monastery of Jerónimos is a safe construction in what concerns the wall behaviour. As the vaults have not been properly considered in the model, a conclusion regarding the safety of the vaults is not possible at this stage.

10 706 Historical Constructions ACKNOWLEDGMENTS The authors acknowledge the support of Eng. V. Cóias e Silva in this study. The work was partially supported by project PRAXIS-C-ECM funded by the Portuguese Science and Technology Foundation (FCT). REFERENCES Chicó, M.T Gothic architecture in Portugal (in Portuguese). Lisbon: Livros Horizonte. Dyngeland, T., Vaz, C. T., Pinto, A Linear Dynamic Analyses of the São Vicente de Fora Monastery in Lisbon, Portugal. Special Publication No. I Lisbon: LNEC Meli, R Structural engineering of historical buildings (in Spanish). Ciudad de Mexico: Fundación ICA. Mourão, S., Lourenço, P.B Comparison between two models of the Refectory of Monastery of Jerónimos (in Portuguese). Report 99-DEC/E-6. Guimarães: Universidade do Minho. Mourão, S Study on the seismic behaviour of the Monastery of Jerónimos (in Portuguese). M.Sc. Dissertation. Guimarães: Universidade do Minho.