Section 4-4
The characteristics of the Section 4-4 FEM are shown in Figure 11. The soil is characterized by 4-node plane strain elements and the maximum size of computation mesh elements is determined by the following relation, in order to perform correctly the next dynamic analysis:
\(h\le h_{\max}\ =\ \frac{V_s}{\left(5\ -\ 8\right)f_{\max}}=6.83\ m\)
\(\)where fmax is the maximum frequency of the seismic signals adopted in this study, equal to 15 Hz. The dimensions of the model have been fixed in order to avoid the boundary effects and in this case have been taken equal to three times the size of the structure (in horizontal and vertical direction). 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 E, was adopted. The contact between soil and walls was modeled by using elastic-perfectly plastic interface elements, with a friction angle equal to 20° [10]. The values of the stiffness of the interface elements are evaluated according to [6]:
\(K_n=\frac{E_{0ed,i}}{t_v}\)
\(K_t=\frac{G_i}{t_v}\)
where:
\(G_i=R\cdot G_{soil}\)
\(E_{0ed,i}=2G_i\frac{\left(1-\nu_i\right)}{\left(1-2\nu_i\right)}\)
and
- tv = the virtual thickness which depends on the difference in stiffness between soil and structure and the value varies from 0.01 to 0.1. In this study the value considered is equal to 0.05 for each model;
- R = strength reduction factor taken as 1.
Known the geometry and the values of the static loads, the results are obtained in terms of bending moments acting on the retaining walls (Figure 12). The maximum values of the bending moment acting on the retaining walls obtained in static conditions is equal to 600 kNm.