ABSTRACT
Let us consider a granular material made of particles of diameter d and density ρp under a confinement pressure P. The material is sheared at a given shear rate γ˙ . Results from numerical simulation using molecular dynamics method (Da Cruz et al. 2004; Iordanoff & Khonsari 2004) suggest that the shear stress τ is proportional to the confining pressure and can be expressed as follows:
The friction coefficient µ depends on a single dimensionless parameter I defined by:
As discussed in a recent collective paper (GDR MiDi 2004), an interpretation of the parameter I can be given in terms of the relevant time scales controlling grains motion. Let us consider the motion of one grain during a simple shear. The grain first follows the mean deformation γ˙ but eventually reaches an unstable position when passing over the crest of the particle just below. It is then rapidly pushed back in the next hole due to the confining pressure P. The time of this microscopic rearrangement can be estimated by a simple free fall of the particle of diameter d and density ρp under a force Pd2 over a distance d: tmicro = d/
√ P/ρp.
The parameter I is interpreted as the ratio between this rapid time of rearrangement tmicro and the mean time tmean = γ˙−1 taken by the particle to move from one hole to the next one. Notice that the dimensionless number I could be seen as the square root of the
