Stochastic finite element method applied to non-linear analysis of embankments

Abstract

The deterministic Finite Element Method (FEM) is a valuable tool for understanding and predicting the mechanical behaviour of earth structures. The main difficulty in the application of this technique generally arises from the large uncertainties affecting the mechanical properties of materials to be introduced in the analysis. In many instances, these parameters should actually be considered as random variables or random fields. The Stochastic Finite Element Method (SFEM) should then be used to assess the results of the analyses in probabilistic terms. In this paper, the usefulness of the SFEM approach for engineering purposes is discussed and illustrated by analyses of embankments constructed by placing successive lifts of compacted soil. Construction materials are assumed to follow a simple non-linear constitutive law (Duncan JM, Chang CY. Non-linear analysis of stress and strain in soils, Journal of the Soils Mechanics and Foundation Division, ASCE 1970;96(5):1629–1653). Stochastic finite element analyses are performed using both the First Order-Second Moment method (FOSM) and Monte Carlo simulations (MC). A simple example shows that SFEM analyses can be useful to evaluate the relative influence of each of the parameters of the constitutive model on the results. Uncertainties affecting displacements, strains and stresses predictions for a large earth dam are also presented.