Three-Dimensional Seepage through Spatially Random Soil

Abstract

This paper brings together random field generation and finite-element techniques to model steady seepage through a three-dimensional (3D) soil domain in which the permeability is randomly distributed in space. The analyses focus on the classical problem of steady seepage beneath a single sheet pile wall embedded in a finite layer of soil. The analyses treat the soil permeability as a spatially random property with specified mean, variance, and spatial correlation length. The influence of the spatial correlation or “scale of fluctuation” is given special consideration, since this aspect is not always included in probabilistic geotechnical analysis. The value of permeability assigned to each element comes from a lognormally distributed random field derived from local averages of a normally distributed random field. The local averaging allows the element dimensions to be rationally accounted for on a statistical basis. The influence of three-dimensionality is given particular emphasis and contrasted with results that are obtained using an idealized two-dimensional model. For the computationally intensive 3D finite-element analyses, strategies are described for optimizing the efficiency of the code in relation to memory and central processing unit requirements. Monte Carlo simulations are performed to establish statistics relating to quantities of interest to designers such as the flow rate. The potential value of this approach is emphasized by presenting the results in the context of reliability-based design.