Seismic Wave Propagation in Soil-Structures Systems

Abstract

A discrete formulation of the seismic wave propagation in times domain is presented in order to calculate the seismic response of an idealized city. The buildings are modelled as being the prolongation of the continuous medium, and are subjected to the vertical shear wave propagation. The layers of the ground and the rock substratum under the base of the foundations are introduced in the formulation to take account of the effects of soil-structure interaction. The seismic response is expressed according to the travel time of the waves between the layers of the ground, the coefficients of reflexion and transmission and of the interfaces. In the developed equations one takes account of the effects of filtering dependent on the frequency which appear in the foundation and storey levels. The calculation of the response is thus reduced to a simple system of equations with finite elements for each layer, which can be solved starting from the rock substratum. Compared with the formulation generally used in the dynamics of structures which consists in using the concept of vibration, the formulation based on wave propagation provides several advantages, among which, simplified calculations, better representation of damping, the possibility of taking account of the effects of the stratification of the ground under the foundation, and better tools for identification and the detection of the damage in the case of seismic recordings. The examples presented in this article show the versatility of the method.

Keywords: Soil-structure interaction, Site-city effects, Shear wave propagation, Finite element approach.