Numerical Analysis

The analysis of the seismic behaviour of the metro stations is carried out  considering static and dynamic loads. Two finite element models representing  both structure and soil are implemented. The two bi-dimensional models  implemented by [6] software represents  the section 4-4 of the Zone 2 (Figure 6) and the section 2-2 representing both  Zone 1 and Zone 3 (Figure 7). The  FEMs are characterized by plane strain elements and an example of geometry and the  relative computation grid are shown in Figure 8. The maximum size of  computation mesh elements has been fixed in order to allow the correct  propagation of harmonic with 15 Hz maximum frequency, which is the maximum  frequency of the seismic signals adopted in this study, according to [4]. The  formulation to optimize the size of the mesh is given in [7]. For each model, the boundary conditions are the  following: vertical supports in the base nodes to restrain the vertical  displacements and horizontal supports in the lateral nodes of the mesh to permit vertical soil settlements. In dynamic conditions, in order to minimize reflection effects on vertical lateral boundaries of the grid, free field boundary conditions available in MIDAS GTS library have been used. The structure is represented, in the first approach, by linear elastic beams while for the soil an elastic perfectly plastic model with Mohr-Coulomb strength rule, characterized by the mechanical properties shown in Table 3, was adopted. The soil hysteretic behaviour was modeled using the shear modulus decay curves given by [9] and [11]. The hysteretic damping is, however, computed by applying the generalized Masing criteria implemented in the computer code mentioned before. The contact between soil and walls was modeled by using elastic-perfectly plastic interface elements, with a friction angle equal to 20°.