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In this paper we investigate the probability of failure of a cohesive slope using both simple and more advanced probabilistic analysis tools. The influence of local averaging on the probability of failure of a test problem is thoroughly investigated. In the simple approach, classical slope stability analysis techniques are used, and the shear strength is treated as a single random variable. The advanced method, called the random finite-element method ͑RFEM͒, uses elastoplasticity combined with random field theory. The RFEM method is shown to offer many advantages over traditional probabilistic slope stability techniques, because it enables slope failure to develop naturally by ''seeking out'' the most critical mechanism. Of particular importance in this work is the conclusion that simplified probabilistic analysis, in which spatial variability is ignored by assuming perfect correlation, can lead to unconservative estimates of the probability of failure. This contradicts the findings of other investigators who used classical slope stability analysis tools.

Soils with spatially varying shear strengths are modeled using random field theory and elasto-plastic finite element analysis to evaluate the extent to which spatial variability and cross-correlation in soil properties (c and ϕ) affect bearing capacity. The analysis is two dimensional, corresponding to a strip footing with infinite correlation length in the out-of-plane direction, and the soil is assumed to be weightless with footing placed on the soil surface. Theoretical predictions of the mean and standard deviation of bearing capacity, for the case where c and ϕ are independent, are derived using a geometric averaging model and then verified via Monte Carlo simulation. The standard deviation prediction is found to be quite accurate, while the mean prediction is found to require some additional semi-empirical adjustment to give accurate results for "worst case" correlation lengths. Combined, the theory can be used to estimate the probability of bearing-capacity failure, but also sheds light on the stochastic behaviour of foundation bearing failure.Key words: bearing capacity, probability, random fields, geometric averaging, c–ϕ soil, Monte Carlo simulation.

A fast and accurate method of generating realizations of a homogeneous Gaussian scalar random process in one, two, or three dimensions is presented. The resulting discrete process represents local averages of a homogeneous random function defined by its mean and covariance function, the averaging being performed over incremental domains formed by different levels of discretization of the field. The approach is motivated first by the need to represent engineering properties as local averages (since many properties are not well defined at a point and show significant scale effects), and second to be able to easily condition the realization to incorporate known data or change resolution within sub-regions. The ability to condition the realization or increase the resolution in certain regions is an important contribution to finite element modeling of random phenomena. The Ornstein-Uhlenbeck and fractional Gaussian noise processes are used as illustrations.

The paper investigates the probability of failure of slopes using both traditional and more advanced probabilistic analysis tools. The advanced method, called the random finite-element method, uses elastoplasticity in a finite-element model combined with random field theory in a Monte-Carlo framework. The traditional method, called the first-order reliability method, computes a reliability index which is the shortest distance ͑in units of directional equivalent standard deviations͒ from the equivalent mean-value point to the limit state surface and estimates the probability of failure from the reliability index. Numerical results show that simplified probabilistic analyses in which spatial variability of soil properties is not properly accounted for, can lead to unconservative estimates of the probability of failure if the coefficient of variation of the shear strength parameters exceeds a critical value. The influences of slope inclination, factor of safety ͑based on mean strength values͒, and cross correlation between strength parameters on this critical value have been investigated by parametric studies in this paper. The results indicate when probabilistic approaches, which do not model spatial variation, may lead to unconservative estimates of slope failure probability and when more advanced probabilistic methods are warranted.