1.1 Description of the structure
The church analyzed in this paper is the Basilica of Santa Maria all'Impruneta (Fig. 1), located in Impruneta near Firenze (Italy). The plan view (see Fig. 2) shows the typical basilica layout with a single nave and a polygonal apse.
The original Romanesque structure was built around the XI century followed by various additions and alterations that extensively modified the original structure (that was quite different from the Renaissance profile that is seen today). It is interesting to highlight the presence of a pronaos (dating back to XVII century), the major architectural feature of the church.
The last major restoration of the Church was made in the fifties of the last century. During the Second World War the Church was seriously damaged: on July 26-27, 1944 all the apse area was destroyed by an air attack. After Second World War, the apse and the timber roof were completely reconstructed using the original on site materials.
Figure 2. Plan layout of the Basilica of Santa Maria. 1.2 Geometry and materials
The main dimensions of the nave were a maximum length of about 4.0 m, a maximum width of 15.0 m and a wall height of about 15.0 m. The masonry wall thickness ranges between 0.70 m (nave walls) and 0.80 m (apse walls). The church roof (nave) is a timber structure.
The walls are single-leaf and several types of masonry weaving characterize the church wall, differing both in materials (stone, brick, etc.) and shape ("opus incertum", "opus mixtum", etc.). This variegated picture reflects the modifications endured during centuries by the building. However, despite these differences, the construction is mostly made of irregular sandstone masonry (local stone) with thick lime mortar joints. Local stone is used also for the windows and doors jambs.
Due to budgetary reasons, a complete characterization of these materials was not performed in this
study. Conservative values for historic masonry have been assumed considering the Authors experience on similar material (Chiostrini et al. 1997, Chiostrini et al. 1998).
Two combined approaches are applied to evaluate the seismic vulnerability of the church. The first is a global analysis by the FEM technique, for which a finite element model of the building by the code ANSYS have been built.
The masonry walls have been modeled by means of Solid65elements; Shell143elements have been used to model the main vault on the first floor in the annexes. Beam44 elements have been used for the queen truss of the timber roof.
The model accurately reproduces the geometry of the structure, focusing on the variations in the wall thickness, the irregularities and the wall connections. The major openings in the building are reproduced. The final 3D model consists of 27779 joints, 76895 3D Solid45 elements, 1751 2D Shell63 elements and 547 1D Beam44 elements, that correspond to 81021 degrees of freedom.
The material properties of masonry walls (Young modulus E, Poisson coefficient u, own weight W) are differentiated by taking into account each area present in the building (Fig. 3). The non-linear behavior of the masonry elements have been reproduced assuming a Mohr-Coulomb type failure criterion with tension cut-off type behavior.
In particular the yield Drucker-Prager criterion with associated flow rule have been assumed (it is assumed then that the yield surface does not change with progressive yielding, i.e. there is no hardening rule). The yield criterion is joined with the Willam
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