Sandpile physics - A phenomenological description of stress propagation in granular materials

This work deals with the stress distribution in dry granular media such as sand. As a matter of fact, the granular family is amazingly wide: raw materials used in building, chemical or food industries are made of little grains. Predicting how forces propagate and fluctuate into granular media is then a real and concrete challenge. This goal is not easy to reach. One reason is that the stress distribution is strongly inhomogeneous: the forces applied on a granular system will be supported almost entirely by a fraction of the grains which form chains, or arches. As a consequence, the stress profile beneath a sandpile depends on the way that the pile was built. In order to describe quantitatively these effects, we proposed a phenomenological friction relation between arches. The differential equations which come out from this modelling are of hyperbolic type, which means that there exists particular lines for propagation called characteristics. We managed to match these characteristics with arches. These models fit well with experimental data, and can explain for example the dip of pressure observed beneath the apex of a pile made with a hopper. They also significantly improve Janssen's predictions for the silo. We also looked at stress fluctuations, and showed that granular material are intrinsically fragile when subjected to changing external forces or perturbations. This property has been particulary studied within a scalar arching model with which we were able to visualize changes of stress paths and subsequent changes of the stress distribution.