SUMMARYThis paper presents a finite element model based on mathematical non-linear programming in order to determine upper bounds of colapse loads of a mechanical structure.The proposed formulation is derived within a kinematical approach framework, employing two simultaneous and independent field approximations for the velocity and strain rate fields. The augmented Lagrangian is used to establish the compatibility between these two fields. In this model, only continuous velocity fields are used.Uzawa's minimization algorithm is applied to determine the optimal kinematical field that minimizes the difference between external and dissipated work rate. The use of this technique allows to bypass the complexity of the non-linear aspects of the problem, since non-linearity is addressed as a set of small local subproblems of optimization for each finite element.The obtained model is quite versatile and suitable for solving a wide range of collapse problems. This paper studies 3D strut-and-tie structures, 2D plane strain/stress and 3D solid problems.

a b s t r a c tThis paper addresses an implementation of the upper bound limit analysis theorem using a parallel mixed finite element formulation. The intrinsic characteristics of the adopted upper bound formulation proved to be suitable to adapt it to an efficient parallelization scheme. In order to illustrate the computational power provided by the new parallel processing method, accurate upper bound collapse load estimates, for 3D problems, are produced using a cluster of common PC machines.

Strip shallow foundations on random heterogeneous soil responding in undrained conditions are analyzed using three-dimensional upper limit analysis and Latin Hypercube sampling. The results obtained considering the three-dimensional variability of soil are compared with results using plane models, showing significant differences in terms of both mean and standard deviation of bearing capacity. An averaged two-dimensional model fitted to a small set of three-dimensional samples is shown to yield accurate predictions of the bearing capacity distribution.

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A three-dimensional (3D) numerical implementation of the limit analysis upper-bound theorem is used to determine passive horizontal earth-pressure coefficients. An extension technique allowing determination of the 3D passive earth pressures for any width-to-height ratios greater than 7 is presented. The horizontal passive earth-pressure coefficients are presented and compared with solutions published previously. Results of the ratio between the 3D and two-dimensional horizontal passive earth-pressure coefficients are shown and found to be almost independent of the soil-to-wall friction ratio. A simple equation is proposed for calculating this passive earth-pressure ratio.Key words: three-dimensional passive earth-pressure coefficients, upper-bound numerical analysis, finite elements.Résumé : Une application numérique en trois dimensions (3D) du théorème cinématique de l'analyse limite est utilisée pour déter-miner les coefficients horizontaux de butée. Une technique d'extension, qui permet de déterminer les pressions de butée en 3D pour des ratios de largeur sur hauteur de plus de 7, est présentée. Les coefficients horizontaux de butée sont présentés et comparés avec des solutions déjà publiées. Les résultats des ratios entre les coefficients horizontaux de butée en 3D et en deux dimensions sont montrés et sont presque indépendants du frottement sol-mur. Une équation simple est proposée pour calculer ce ratio de butée.Mots-clés : coefficients de butée en trois dimensions, analyse numérique à l'approche cinématique, éléments finis.[Traduit par la Rédaction]