PSI - Issue 11

P. Condoleo et al. / Procedia Structural Integrity 11 (2018) 290–297 P. Condoleo and A. Taliercio / Structural Integrity Procedia 00 (2018) 000–000

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where T c is the (corner) period at the end of the plateau in which the response spectrum is constant (0.8s for class D soils). Assuming a natural period of vibration T = 0.5s, the value in eq. (1) is obtained. 3.5. Finite element model The finite element model used in the numerical analyses consists of approximately 715000 4-node constant stress tetrahedra, with 500000 degrees of freedom. A sufficiently refined mesh is required to match the irregular geometry of the model (including cracks) with good accuracy. The base of the model and the external sides of the foundation walls are fixed, except for a part of the base where vertical displacements can be prescribed (Fig. 8(b)). 4. Numerical results The FE model of the farmhouse was analyzed under the following load conditions: (i) self-weight; (ii) self weight + ground settlements; (iii) self-weight + ground settlements + seismic actions. For each load condition, both the presumed original situation, in which the building is uncracked, and the current situation, in which cracks are open, were considered. The results will be presented in terms of contours of the maximum principal (tensile) stress, as compressions were never found to exceed the presumed compressive strength of the materials. 4.1. Original conditions (closed cracks) Fig. 9 shows the stress distribution in the building assumed to be uncracked. Unsurprisingly, Fig. 9(a) shows that the only service loads acting on the structure cannot explain the crack pattern in the building. On the contrary, the prescribed ground settlements induce significant tensile stresses in wide regions of the building: the grey areas in Fig. 9(b) correspond to stresses exceeding 0.2 MPa, which can be conventionally assumed to be a critical value for masonry in tension according to the literature (Lourenço 2002). Note that these areas roughly match the regions where most of the cracks are found in the walls overlooking the inner courtyard (see Fig. 4). Fig. 9(c) shows a detail of the region experiencing ground settlements: stress concentrations can be noticed on the front of the house facing the street, which match the deep vertical crack shown in Fig. 4. The situation worsens if the seismic action is taken into account (Fig. 9(d)). In the latter case, also the walls parallel to the assumed seismic load experience tensile stresses at approximately 45° degrees, which might induce the typical crack pattern of in-plane loaded shear walls. 4.2. Current conditions (open cracks) Fig. 10 shows the stress distribution in the building if cracks are assumed to be open, as in the current conditions. If no ground settlements existed, the stress in the building would not be of concern and would basically be the same computed in the uncracked building (compare Figures 9(a) and 10(a)). The stress in the building experiencing ground settlements is not significantly affected by the presence of cracks as far as the walls overlooking the inner courtyard are concerned (compare Figures 9(b) and 10(b)). On the contrary, in the wall facing the street the extension of the regions experiencing high tensile stresses is greater than in the uncracked building (compare Figures 9(c) and 10(c)), which means that the existing cracks are likely to grow further. The stress in the building experiencing seismic loads in addition to the previously considered actions does not significantly differ from that shown in Fig. 9(d) and is not reported here. 5. Concluding remarks The structural analysis of the farmhouse allowed the assumption regarding the origin of the main cracks in the building to be confirmed. A ground settlements, basically consisting in the rotation of part of the base of the building about the road axis, might explain most of the cracks (Sec. 4.1). If the existing cracks are incorporated in the numerical model, tensile stresses are found to increase further in some regions of the building, which indicates that cracks are likely to develop further (Sec. 4.2). Seismic loads might aggravate the crack pattern and additional cracks might develop.