Bearing capacity of a foundation resting on a soil improved by a group of columns

A new design method for a foundation on a soil reinforced by columns is described. A lower bound of the bearing capacity is determined within the framework of the yield design theory. It takes into account the three-dimensional nature of the problem and is applicable to a wide range of geometries. A parametric study on the improvement of the bearing capacity as a function of the proportion of reinforcement, and on the strength characteristics, is presented. A complete analytical solution is given for the strength of a composite cell subjected to a triaxial loading, which provides an insight into the reinforcement mechanism

Stability analysis of homogenized stone column reinforced foundations using a numerical yield design approach

International audienceThis paper deals with the ultimate bearing capacity of soft clayey soils, rein-forced by stone columns, analyzed in the framework of the yield design theory. Since such geotechnical structures are almost impossible to analyze directly due to the strong heterogeneity of the reinforced soil, an alternative homogenization approach is advocated here. First, numerical lower and upper bound estimates for the macroscopic strength criterion of the stone column reinforced soil are approximated in a rigorous way with convex ellipsoidal sets, which makes the approximated criteria much easier to handle than the initial ones. Then, both static and kinematic approaches are carried out numerically on the homoge-nized problem using the above approximated macroscopic strength domains in an adapted finite element method. The whole numerical procedure is applied on one classical geotechnical problem: the ultimate bearing capacity of stone column reinforced foundations. The strength capacity of the structure is rigor-ously framed and the efficiency of the proposed numerical method is highlighted in terms of accuracy and calculation time

Bearing capacity of a foundation resting on a soil improved by a group of columns

A new design method for a foundation on a soil reinforced by columns is described. A lower bound of the bearing capacity is determined within the framework of the yield design theory. It takes into account the three-dimensional nature of the problem and is applicable to a wide range of geometries. A parametric study on the improvement of the bearing capacity as a function of the proportion of reinforcement, and on the strength characteristics, is presented. A complete analytical solution is given for the strength of a composite cell subjected to a triaxial loading, which provides an insight into the reinforcement mechanism

A general method for calculating the traffic load-induced residual settlement of a platform, based on a structural analysis approach

International audienceA general computational procedure is developed in this paper for calculating the long term response, and more specifically the evolution with time of the accumulated residual settlement of a traffic platform under the action of repeated vehicle loading. It is based on a structural analysis approach, which incorporates as an essential feature, the use of a cyclic constitutive law for the constituent materials, formulated on the basis of cyclic triaxial tests. A numerical tool has been set up with the help of a finite element code, in order to simulate experimental tests performed on reduced scale models of a railway track platform. A first comparison is being made between the numerical simulations and the experimental results, as regards the long term evolution of the residual settlement

A computational procedure for predicting the long term residual settlement of a platform induced by repeated traffic loading

International audienceA general structural analysis approach is developed in the present paper, allowing the evaluation of the residual settlement of a platform induced by repeated traffic loading. It notably relies upon the formulation of a cyclic constitutive law, which describes the progressive accumulation of irreversible (permanent) deformations locally exhibited by the different underlying granular materials when subjected to long term stress cycling generated by the traffic loading. This constitutive law is incorporated into a step-by-step numerical scheme where two kinds of elastic calculations are implemented: the first one concerns the determination of the so called reference stress cycles. while the second one is aimed at calculating the residual displacement and stress fields of the platform derived from the integration of the permanent non elastic deformations. The whole procedure is illustrated on the simplified model of a moving strip-load acting upon a homogeneous half-space, adopting a cyclic constitutive law formulated for a particular unbound granular material used in road pavements

Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1d case

International audienceIn this paper we address some ill-posed problems involving the heat or the wave equation in one dimension, in particular the backward heat equation and the heat/wave equation with lateral Cauchy data. The main objective is to introduce some variational mixed formulations of quasi-reversibility which enable us to solve these ill-posed problems by using some classical La-grange finite elements. The inverse obstacle problems with initial condition and lateral Cauchy data for heat/wave equation are also considered, by using an elementary level set method combined with the quasi-reversibility method. Some numerical experiments are presented to illustrate the feasibility for our strategy in all those situations. 1. Introduction. The method of quasi-reversibility has now a quite long history since the pioneering book of Latt es and Lions in 1967 [1]. The original idea of these authors was, starting from an ill-posed problem which satisfies the uniqueness property, to introduce a perturbation of such problem involving a small positive parameter ε. This perturbation has essentially two effects. Firstly the perturbation transforms the initial ill-posed problem into a well-posed one for any ε, secondly the solution to such problem converges to the solution (if it exists) to the initial ill-posed problem when ε tends to 0. Generally, the ill-posedness in the initial problem is due to unsuitable boundary conditions. As typical examples of linear ill-posed problems one may think of the backward heat equation, that is the initial condition is replaced by a final condition, or the heat or wave equations with lateral Cauchy data, that is the usual Dirichlet or Neumann boundary condition on the boundary of the domain is replaced by a pair of Dirichlet and Neumann boundary conditions on the same subpart of the boundary, no data being prescribed on the complementary part of the boundary