We study the steady plane shear flow of a dense assembly of frictional, inelastic disks using discrete simulation and prescribing the pressure and the shear rate. We show that, in the limit of rigid grains, the shear state is determined by a single dimensionless number, called inertial number I, which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasistatic regime of soil mechanics, while large values of I correspond to the collisional regime of the kinetic theory. Those shear states are homogeneous, and become intermittent in the quasi-static regime. When I increases in the intermediate regime, we measure an approximately linear decrease of the solid fraction from the maximum packing value, and an approximately linear increase of the effective friction coefficient from the static internal friction value. From those dilatancy and friction laws, we deduce the constitutive law for dense granular flows, with a plastic Coulomb term and a viscous Bagnold term. We also show that the relative velocity fluctuations follow a scaling law as a function of I. The mechanical characteristics of the grains (restitution, friction and elasticity) have a very small influence in this intermediate regime. Then, we explain how the friction law is related to the angular distribution of contact forces, and why the local frictional forces have a small contribution to the macroscopic friction. At the end, as an example of heterogeneous stress distribution, we describe the shear localization when gravity is added.

We show that the rheological properties of dry granular materials, as well as foams and emulsions, are similar to typical thixotropic fluids: under a sufficiently strong shear the viscosity decreases in time, leading to a hysteresis in an up-and-down stress ramp. This leads to a viscosity bifurcation around a critical stress: for smaller stresses, the viscosity increases in time and the material eventually stops flowing, whereas for slightly larger stresses the viscosity decreases continuously with time and the flow accelerates. These results show that all jammed systems exhibit strong mechanical similarities around the transition between a "fluid" and a "solid" state, and that the transition between these states is discontinuous. This similarity is further emphasized by the fact that both a simple model for the dynamics of a grain on a sandpile [Quartier et al., Phys. Rev. E 62, 8299 (2000)] and a simple model for the thixotropic behavior of (colloidal) pastes [Coussot et al., Phys. Rev. Lett. 88, 175501 (2002)] extrapolated to granular flows qualitatively predict this viscosity bifurcation.

We investigate experimentally the distribution of the free volume inside a bidimensional granular packing associated either to single grains or to clusters of grains. This is done for two different kinds of grains and two levels of compaction. The logarithm of the free volume distribution scales in a nonextensive way with the cluster size for cluster sizes up to a few hundred grains. Having factorized this size dependence, we characterize the distributions by two intensive parameters. We discuss the interpretation of these parameters and their possible relation to Edwards' compactivity.

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