Analyse probabiliste des tassements d'un massif de sol granulaire
Starting from the elementary fact that a soil is a discontinuous particulate medium, it is attempted to describe the mechanical response of such a system to induced boundary energy, independently of the classical soil mechanics concepts which were derived from continuum mechanics. The dissertation deals specifically with dry (or fully drained) loose non-cohesive soils and proposes a new procedure for the prediction of expected settlements under static vertical surface loads. The thesis can be summarized by the following basic propositions : Soil is made of a very large number of discrete and randomly arranged grains, and of pores. The application of loads results in local changes of porosity and the propagation of these structural modifications produces apparent macroscopic settlements. These phenomena can be quantified using a probabilistic approach. As a first step in the theoretical development, a new definition is given for the internal tensions. It is shown that the classical effective stress concept represents only a first-moment approximation of the local demand in a granular assembly. The scatter of this random quantity increases with the porosity of the medium. This theoretical prediction is in agreement with experimental results published by Marsal. Two boundary-value problems are investigated : transient uniform compression of a granular layer with finite thickness, steady state plane strain deformation of a granular medium including stratifications under flexible or rigid foundation. In both cases, a simple random walk model is formulated, based on the concept of migration of voids in excess exchanging their position with solid particles. The generalization of this discrete model leads to Fokker-Planck type one-dimensional diffusion equations which are solved by a finite differences method. In case b), a complete solution is provided by the combination of the proposed model for the displacement computations with Harr's stress diffusion theory. From a comparison to X-rays measurements of the displacement fields in laboratory models, it is concluded that the theory is capable to predict the behaviour of loose particulate materials. The small number of parameters needed and their clear physical signification should allow further developments oriented to practical applications.