Microscopic foundation of the $\mu$(I) rheology for dense granular flows on inclined planes

TL;DR

This paper develops a theoretical model for dense granular flows on inclined planes, linking microscopic grain dynamics to macroscopic flow laws without empirical parameters.

Contribution

It introduces a microscopic-based scaling model that explains fundamental laws of granular flows, bridging microscopic cluster formation and macroscopic rheology.

Findings

The model accurately predicts the critical stress and velocity profiles.

Transient clusters are key to understanding flow behavior.

The approach unifies granular flow laws with a microscopic perspective.

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. Three fundamental observations for dense granular flows are recovered, namely the occurrence of a critical stress, the Bagnold velocity profile, as well as well-defined friction and dilatancy laws. The microscopic aspects of the grain motion highlight the formation of transient clusters. From this microscopic picture, we derive a theoretical scaling model without any empirical input that explains quantitatively the fundamental laws of dense granular flows in incline plane and shear geometries. The adequacy between the model and the observed results suggests that granular flows can be viewed as flows from thermal fluids of hard spheres.