3-DIMENSIONAL SEEPAGE THROUGH SPATIALLY RANDOM SOIL

This paper brings together random field generation and finite-element techniques to model steady seepage through a three-dimensional (3D) so il 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 analy ses treat the soil permeability as a spatially random property with sp ecified mean, variance, and spatial correlation length. The influence of the spatial correlation or ''scale of fluctuation'' is given specia l consideration, since this aspect is not always included in probabili stic geotechnical analysis. The value of permeability assigned to each element comes from a lognormally distributed random field derived fro m local averages of a normally distributed random field. The local ave raging allows the dement dimensions to be rationally accounted for on a statistical basis. The influence of three-dimensionality is given pa rticular 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 th e 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 pres enting the results in the context of reliability-based design.