Strength of Granular Materials in Transient and Steady State Rapid Shear

This paper discusses relationships between the frictional strength of a flowing granular material and quantities including porosity and grain-scale energy dissipation. The goal of the paper is to foster an understanding of frictional strength that will facilitate the development of constitutive laws incorporating important physical processes. This is accomplished in several steps. First, a friction relationship is derived for a steady state simple shear flow using an energy balance approach. The relationship shows that friction is explicitly related to porosity, grain connectivity, and grain-scale dissipation rates. Next, the friction relationship is extended to describe transient changes in frictional behavior. The relationship shows that, in addition to the processes important for steady flows, the rate of dilatation and changes in internal energy play a role in the frictional strength of a granular material away from steady state. Finally, numerical simulations are performed to illustrate the accuracy of the friction relationships and illuminate important scaling behavior. The discussion of numerical simulations focuses on the rate-dependence of frictional strength and the partition of macroscopic energy dissipation into its grain-scale components. New interpretations of existing constitutive laws and ideas for new constitutive laws are discussed.