Finite element model for the probabilistic seismic response of heterogeneous soil profile

This paper deals with the numerical simulation of heterogeneous soil profile and its behavior under uniform seismic environment. Soil properties of interest are shear modulus, fraction of critical damping and Poisson ratio, modeled as spatially random fields. Shear modulus is modeled using the lognormal distribution, which enables analyzing its large variability. Because fraction of critical damping and soil Poisson ratio are bounded in practice between two extreme values, their random fields are obtained from the Beta distribution, where the Beta field is determined, by performing a mapping technique on the lognormal probability distribution function diagram. In this frame, the seismic response is carried out via Monte Carlo simulations combined with deterministic finite element method. Also, the performance of two approximate techniques, using stationary stochastic process tools, and accounting for the nonstationnarity in an implicit way, are investigated for the purpose to determine statistics of extreme ground surface acceleration. It is found that both techniques are not appropriate for determining the statistics of a highly heterogeneous medium. The analysis integrates the influence of, coefficient of variation of the three soil properties, the inter-property correlation coefficients, as well as horizontal and vertical correlation lengths. Results of this analysis indicate that heterogeneity highly influences the behavior of the soil profile which induces differential movement at ground surface and makes evident the filtering effect of frequencies, making hence the simulated soil softer. Obtained results indicate that a positive correlation between shear modulus and fraction of critical damping favors seismic wave amplification, and that shear modulus and fraction of critical damping are of prime importance. So, Poisson ratio variability can be neglected in a dynamic analysis of a soil profile.