Friction law in dense granular flows

The understanding of the dense granular flow regime (intermediate between quasi-static and collisional regimes) has recently progressed significantly. We shall review the results concerning the friction law, which we have obtained with the help of discrete numerical simulations of flow of assemblies of disks in various geometries (homogeneous plane shear, annular shear and inclined plane). In the case of cohesionless quasi-mono-dispersed and rigid grains, the analysis of the dependencies of the effective friction coefficient, ratio of shear to normal stress, on the shear state (defined by the shear rate and pressure) and on the mechanical characteristics of the material has made possible the formulation of a local constitutive law. This has shown the crucial role of a dimensionless parameter, called inertial number, which rules the friction law in the dense regime. This law remains true in the case of bi-dispersed flows, as early as the average diameter of the grains in taken into account. It is also true in the case of cohesive grains, once a second dimensionless number, characterizing the intensity of cohesion, is introduced.