SAHC2014 – 9th International Conference on Structural Analysis of Historical Constructions F. Peña & M. Chávez (eds.) Mexico City, Mexico, 14–17 October 2014 STRUCTURAL SAFETY OF THE MODENA CATHEDRAL T.Trombetti1, S. Silvestri1, G. Gasparini1, M. Palermo1 and S. Baraccani1 1 University of Bologna Viale Risorgimento 2, 40136 Bologna, Italy e-mail: [email protected] [email protected] [email protected] [email protected] [email protected] Keywords: Romanesque cathedral, structural behavior, static analysis, survey, multidiscipli- nary approach. Abstract. The Cathedral of Modena, built at the end of the XI century, is one of the most im- portant examples of the Romanesque art in Italy. In 1997, the monument was declared as “UNESCO World Heritage” site. The first phase for a meaningful interpretation of the struc- tural behaviour of such a complex monument is the static analysis, which first requires the study of the loads path to the ground. The objective of the present paper is to study the struc- tural behaviour of the Modena Cathedral through a multidisciplinary integrated approach, which makes use of the “survey” as a tool able to provide a comprehensive knowledge of the building. The “survey” is here intended as the integration between: (i) the historical recon- struction of the main interventions and modifications of the structural system over the years; (ii) the materials characterization, (iii) the topographic survey of the geometry of the super- structure and the evolution of the settlements; (iv) materials state of degradation. The infor- mation as obtained from the “survey” are fundamental to understand the global structural behaviour of the building and how the different portions of the buildings interact between each other. In this work, the reconstruction of the evolution of the structural configuration is analysed in order to identify the portions of the structure built in the same age as a unique structure, namely the “substructures” of the Cathedral. Each substructure is first analysed as an independent structure through simple limit schematizations in order to obtain the stress levels on the structural elements and correlate the results with the state of damages as ob- served in situ. Then, finite element models of increasing complexity (2D models, 3D models with fixed base conditions, and 3D models accounting for the soil-structure interaction) are developed. The results of the static analyses as obtained from FE models are finally com- pared with the results of the simple static analyses performed on the substructures. 1 T. Trombetti, S. Silvestri, G. Gasparini, M. Palermo and S. Baraccani 1 INTRODUCTION Historical monuments represent a considerable portion of the Italian cultural heritage, hence, their preservation and conservation is very important. Each historical building, by its own features and time evolution, represent a “unicum” difficult to analyse The Cathedral of Modena, a masterpiece of Romanesque architecture and sculpture of northern Italy, represents the main architectural reference site of the Catholic community of Modena. The Cathedral, consecrated in 1184, was declared as “UNESCO World Heritage in the 1997. Its construction began in 1099 under the coordination of the architect Lanfranco and sculptor Wiligelmo. The actual Cathedral has been constructed on the same location of a pre- existent churches whose foundations are still there. The crypt contains the corpse of the city's patron, Saint Geminianus. The construction of the lower portion, up to the fourth level, of the adjacent bell tower, called Torre Ghirlandina (86 m high), proceeded in parallel with the Ca- thedral. The upper part of the tower was built later, between 1261 and 1319 [1]. After the first works under Lanfranco's coordination, additional works on the façade and lateral entrances were realized at the beginning of 13th century under "Campionese-masters" coordination. Therefore, the actual configuration of the façade is the results of different styles. The majestic rose window was added in the 13th century, while the two lions supporting the entrance's col- umns are of Roman age and were discovered during the excavations for the realization of the foundations. The Cathedral of Modena, as can be admired today, is the result of numerous changes, renovations, additions and tampering that have taken place over time [2]. It clearly appears that, in order to study complex monuments such as the Cathedral, it is of fundamental importance to gain a comprehensive knowledge of the structure. For this pur- pose, a multidisciplinary/integrated approach, which makes use of the “survey” as a tool for obtain information has been used: (i) the historical reconstruction of the main interventions and modifications of the structural system; (ii) the materials characterization (typologies and mechanical properties); (iii) the topographic survey of the geometry of the superstructure and the evolution of the foundation settlements; (iv) an accurate description of the actual state of degradation (main cracks, tilts of the external walls). The information obtained from the “survey” has been used to study the structural behavior, i.e. recognize the structural elements and the actual load paths and to identify the materials properties. Based on the construction phases, from a structural point of view, the entire mon- ument can be subdivided into portion of structures built at the same time, namely “substruc- tures”. Each substructure has been analysed through simple limit schematizations in order to obtain a robust evaluation (order of magnitudes) of the internal forces acting on the elements. In addition to the simple limit schematizations, finite element models of increasing complexi- ty (2D models, 3D models with fixed base, 3D models accounting for the soil-structure inter- action) have been developed. The results of the static analyses as obtained from FE models are finally compared with the results of the simple static analyses performed on the substruc- tures. The results of the static analyses have been used to interpret the cracking patterns as obtained from in situ surveys and the deformations related to changes in the geometrical con- figuration as obtained from the topographic surveys 2 THE CATHEDRAL OF MODENA The Cathedral of Modena has a Latin cross plant with three naves, a false transept and the chancel (the area of the liturgical altar) in an elevated position, which confirms the presence of the crypt. The geometry of the cathedral is 24.95 m wide (in the transversal direction) and 65.7 m long (in longitudinal direction), for an area of approximately 1650 m2 (Figure 1(a)). 2 Structural safety of the Modena Cathedral The structural configuration is composed of heavy walls and sturdy pillars supporting the weight of the impressive dome. Both the central nave and the site aisles have four spans. The spans of the nave (larger than those of the aisles) have a dome twice as long as those of the spans of the aisles. The maximum height of the dome of the central nave is around 20 m, while that of the side aisles is approximately 13m. The maximum roof height is approximate- ly 24 m. All the heights are referred with respect the ground floor (figure1(b)). (a) (b) Figure 1: (a) A 3D view of the Modena Cathedral (Google Earth); (b) Cross-section of the Cathedral of Modena 2.1 The assumed material properties Structural interventions and diagnostics on historical buildings must preserve and respect the historical identity of the construction, ensuring non-invasive and compatible solutions. On the other hand, the knowledge of the main material properties is fundamental to provide a re- liable structural assessment of the building. For this purpose non-destructive tests are typical- ly used for the case of historical buildings and the usually a minimum number of tests is allowed to be performed. The mechanical parameters of the masonry and stones used to build the Cathedral as obtained from the limited non destructive tests provide therefore only partial or punctual information not able to comprehensively characterize the intrinsic resistance of the masonry. This means that the obtained experimental values should be critically analyzed provided that they are affected by large uncertainties. A simple methodology to critically ana- lyzed the materials mechanical characterization based on limited experimental tests have been recently proposed by the authors and applied for the case on an ancient masonry Tower locat- ed in bologna (known as “Asinelli” Tower). In that study [3], experimental values have been compared/validated with typically values suggested by codes or literature and or values based on material models. A similar approach has been used for the Cathedral of Modena in order to estimate materials elastic properties and strength. For masonry and stones the following val- ues of Young's modulus (E) are assumed: Em =180000 MPa for masonry walls, Es=250000 MPa for marble columns. For the wood, considering mechanical properties degradation over time, the lower bounds suggested by codes [4] have been used. In detail, the values of the Young's modulus E, compression strength fm and mean density ρm are collected in table 1. Table 1: Values of the materials mechanical properties of wood beams. Young's modulus Compression Mean density Material 3 E (MPa) strength fm (MPa) ρm (Kg/m ) Pine 600 14 350 3 T. Trombetti, S. Silvestri, G. Gasparini, M. Palermo and S. Baraccani 2.2 The applied loads and constrains Generally speaking, the actions on the building can be classified into: (i) dead loads (i.e. permanent loads such as the structure self-weight and non structural self-weight); (ii) live loads (i.e. loads produced by the use and occupancy of the building or other structure and do not include construction or environmental loads, flood load or dead load); (iii) environmental loads (such as wind load, snow load, rain load, earthquake load, hurricanes…). The structural dead loads are basically composed of the self-weight of the roofs and ma- sonry walls.