The majority of slope stability analyses performed in practice still use traditional limit equilibrium approaches involving methods of slices that have remained essentially unchanged for decades. This was not the outcome envisaged when Whitman & Bailey (1967) set criteria for the then emerging methods to become readily accessible to all engineers. The finite element method represents a powerful alternative approach for slope stability analysis which is accurate, versatile and requires fewer a priori assumptions, especially, regarding the failure mechanism. Slope failure in the finite element model occurs 'naturally' through the zones in which the shear strength of the soil is insufficient to resist the shear stresses. The paper describes several examples of finite element slope stability analysis with comparison against other solution methods, including the influence of a free surface on slope and dam stability. Graphical output is included to illustrate deformations and mechanisms of failure. It is argued that the finite element method of slope stability analysis is a more powerful alternative to traditional limit equilibrium methods and its widespread use should now be standard in geotechnical practice. En grande majorité, les analyses de stabilité de pente menées dans la pratique continuent à utiliser les méthodes traditionnelles d'équilibre limite et des systèmes de tranches qui n'ont pratiquement pas changé depuis des dizaines d'années. Ce n'était pas le résultat envisagé quand Whitman et Bailey (1967) ont établi des critères pour que ces méthodes alors émergeantes puissent devenir facilement accessibles à tous les ingénieurs. La méthode d'éléments finis qui représente une alternative puissante pour les analyses de stabilité de pente, est exacte, polyvalente et demande moins d'hypothèses ‘a priori’, surtout en ce qui concerne les mécanismes de rupture. La rupture de pente dans le modèle à éléments finis se produit ‘naturellement’ à travers des zones dans lesquelles la résistance au cisaillement du sol est insuffisante pour résister aux contraintes tangentielles. Cet exposé décrit plusieurs exemples d'analyses de stabilité de pente utilisant les éléments finis et établit des comparaisons avec d'autres méthodes, comme l'influence d'une surface libre sur la stabilité d'une pente et d'une digue. Nous joignons une représentation graphique pour illustrer les déformations et mécanismes de rupture. Nous avançons que la méthode d'éléments finis pour analyser la stabilité des pentes constitue une alternative plus puissante aux méthodes traditionnelles d'équilibre limite et que son utilisation devrait maintenant devenir une pratique standard en géotechnique.

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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.

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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.

Slope stability analysis is one of the oldest applications in geotechnical engineering, yet it remains one of the most active areas of study in both research and practice. The vast majority of slope stability analyses are performed in two dimensions under the assumption of plane strain conditions. Even when two-dimensional (2D) conditions are not appropriate, three-dimensional (3D) analysis is rarely performed. There are a number of reasons for this. The majority of work on this subject strongly suggests that the 2D factor of safety is conservative (i.e. lower than the 'true' 3D factor of safety). Even when 3D may be justified on geometric grounds, the available methods, being often based on extrapolations of 2D 'methods of slices' to 3D 'methods of columns', are complex, involve numerous assumptions, and are not readily modified to account for realistic boundary conditions in the third dimension such as sloping abutments. The power and versatility of the elasto-plastic finite element approach to slope stability analysis in 2D are well known, and these advantages are even more attractive in 3D. The paper demonstrates some 3D slope stability analyses by finite elements, placing the results in context with 2D solutions and validating the results where possible against alternative methods. L'analyse de la stabilité des versants représente l'une des plus anciennes applications en ingénierie géotechnique. Elle reste pourtant l'une des disciplines d'étude les plus actives, en recherche et en pratique. La grande majorité des analyses de stabilité des versants est réalisée en deux dimensions, en considérant des conditions de déformation plane. Même lorsque des conditions à deux dimensions ne sont pas adaptées, il est rare que des analyses à trois dimensions soient effectuées, et ce pour un certain nombre de raisons. La majorité des travaux à ce sujet suggère fortement que le coefficient de sécurité 2D est conservateur (c'est-à-dire inférieur au « vrai » coefficient de sécurité 3D). Même lorsque des raisons géométriques justifieraient la 3D, les méthodes disponibles, souvent basées sur des extrapolations de « Méthode de coupes » 2D en « Méthode de colonnes » 3D, sont complexes, s'appuient sur de nombreuses hypothèses et ne peuvent être aisément modifiées pour tenir compte de conditions de frontière réalistes en 3D, telles que des culées inclinées. La puissance et la versatilité de l'approche des éléments finis en comportement élasto-plastique pour l'analyse de la stabilité des versants en 2D sont bien connues, et ces avantages sont encore plus prometteurs en 3D. Cet article présente certaines analyses de stabilité de versants en 3D en adoptant la méthode des éléments finis, mettant les résultats en contexte avec les solutions 2D et les validant contre des méthodes alternatives lorsqu'il est possible.

A framework is described for modelling an elastic continuum using a grillage of beam-like structural elements derived from discrete element concepts. The beam element properties are derived in detail and implemented in a structural analysis code for validation against classical two-dimensional plane elasticity solutions. The framework o ers the possibility of modelling the onset and propagation of fracture in materials that are initially continuous, without the need for specialized elements or remeshing in the context of traditional ÿnite elements.