Friction in inertial granular flows: competition between dilation and grain-scale dissipation rates

Friction plays an important role in the behavior of flowing granular media. The effective friction coefficient is a description of shear strength in both slow and rapid flows of these materials. In this paper, we study the steady state effective friction coefficient mu in a granular material in two steps. First, we develop a new relationship between the steady state effective friction coefficient, the shear rate, the solid fraction, and grain-scale dissipation processes in a simple shear flow. This relationship elucidates the rate-and porosity-dependent nature of effective friction in granular flows. Second, we use numerical simulations to study how the various quantities in the relationship change with shear rate and material properties. We explore how the relationship illuminates the grain-scale dissipation processes responsible for macroscopic friction. We examine how the competing processes of shearing dilation and grain-scale dissipation rates give rise to rate-dependence. We also compare our findings with previous investigations of effective friction in simple shear.