The physics of sand piles. Phenomenological description of stress propagation in granular materials.

Summary This thesis deals with the description of the way forces propagate in granular media such as sand. This category of materials is in fact very vast, and being able to predict satisfactorily the distribution of stresses within a granular system is a real and concrete industrial issue. But this is difficult. One of the reasons is that this distribution is very inhomogeneous: the forces applied to a stack are mostly supported and carried by only a fraction of the grains, which then form real force chains - or vaults. It follows, for example, that the pressure profile under a pile of sand depends on the way it has been built. To describe these effects quantitatively, we have proposed a phenomenological relation of friction between the vaults. The resulting differential equations are of hyperbolic type. This means in particular that there are privileged lines of propagation called characteristics, which we have made coincide with these vaults. These models reproduce well the experimental data, and allow among other things to explain the presence of a depression in the center of the heap when it is built with a funnel. They also improve the predictions of the janssen model for the silo. We have also investigated the fluctuations of these stresses, and we have highlighted the brittle character - i. E. Rearrangement - of a granular stack. This has been studied in particular within a very simple scalar model which allows to visualize the variations of the internal structure of a granular system and the resulting changes in the distribution of forces.