Dynamique de l’interaction sol structure par la méthode des éléments spectraux.

Abstract

This work consists of the simulation of the behavior of the soil-structure interaction, using the spectral element method (SEM). First, we analyzed the static interaction between a beam and a stratified soil using a two-parameter elastic foundation with the finite element method. The behavior of the ground medium and of the beam is supposed to be linear, homogeneous and isotropic. Using the strain energy expressions, the shear strains of the beam element and the subgrade are taken into account. In this approach, the stiffness matrix of each component is developed and integrated into the finite element analysis. Several examples are treated to show the effectiveness of the proposed approach and the capacity of the digital program developed. Then, a parametric study is carried out to highlight the influence of the mechanical properties of the soil on the soil-beam contact interface and on the responses of the beam, the effect of the depth of the soil, of the ballast layer on the response of the interface and of the beam itself. Second, we made an analysis of the soil-structure interaction by the spectral element method. We used the Finite Element Method (FEM) too, but only to prove the robustness of the SEM. The numerical results show that the convergence of the SEM is very fast compared to that of the FEM. The resolution of the problem with the eigenvalues is made, the natural frequencies are tabulated for the first three modes of vibration. A modal analysis with and without elastic medium is realised. We established a parametric study to investigate the behavior of the concrete beam on an elastic foundation, the effect of the length of the beam, the effect of soil properties and the influence of non-classical boundary conditions. Finally, we have shown that the dynamic response of the beam on an elastic foundation is highly affected by the contribution of rotational springs. Various results are obtained and commented.