Response of a randomly inhomogeneous layered media to harmonic excitations

We present a unified formulation of an analytical method for evaluating the response of a random soil medium to surface or earthquake excitations. Specifically, we are interested in this study to the case of a horizontally stratified layered soil profile. Soil properties, mass density and shear modulus of each layer are modeled as spatial random fields. The soil profile is laying on a homogeneous half-space. Integro-differential equations are formulated and solved using the Laplace transform method. Numerical results are, firstly, obtained in terms of effects of soil properties on distributions of mean dimensionless displacement and stress with depth. Then, the amplification function of the surface layer of a soil profile is formulated and a parametric study is conducted to examine the effects of stochastic variations of mass density and shear modulus on the amplification function. We, lastly, computed the seismic response of a site located in the basin of Metidja in Algeria to base rock accelerations which were recorded at Keddara's station during the May 21, 2003 Boumerdes earthquake, in terms of free surface Fourier spectrum amplitudes and accelerations. Comparison between computed accelerations and recorded ones at Dar Elbeida site has proved the effectiveness of the approach.