Microscopic foundation of the $\mu$(I) rheology for dense granular flows on inclined planes
Abstract
Macroscopic and microscopic properties of dense granular layers flowing down inclined planes are obtained from Discrete-Element-Method simulations for both frictionless and frictional grains. Linear dilatancy laws with the inertial number $I$ are observed. They do not depend on the frictional nature of the grains besides the value of the jamming packing fraction. In sharp contrast, for the friction law relating the effective, macroscopic friction coefficient $\mu$ to the inertial number, two distinct behaviors are observed: a linear relationship with $I$ for frictional grains and a square root evolution for frictionless ones. Regarding the microscopic properties of the flowing grains, a temperature is defined from the velocity fluctuations, and related to the diffusion coefficient along the direction perpendicular to the flow. A correlation length emerges from the dimensionless fluctuations. The microscopic description of the granular system allows us to propose a theoretical foundation for the macroscopic laws and to recover the Bagnold velocity profile and the $\mu(I)$ rheology observed for frictionless systems.