Role of gravity or confining pressure and contact stiffness in granular rheology

TL;DR

This study investigates how gravity and contact stiffness influence granular flow rheology, revealing a new dimensionless number and linking contact network anisotropy to macroscopic friction in different flow regimes.

Contribution

It introduces the importance of a second dimensionless number involving softness and stress timescales in granular rheology, extending the traditional inertial number framework.

Findings

A second dimensionless number is necessary to describe flow behavior.

Density increases and macroscopic friction decreases with particle softness and gravity.

Linear correlation between macroscopic friction and deviatoric fabric in steady state.

Abstract

The steady shear rheology of granular materials is investigated in slow quasi-static states and inertial flows. The effect of the gravity field and contact stiffness, which are conventionally trivialized is the focus of this study. Series of Discrete Element Method simulations are performed on a weakly frictional granular assembly in a split-bottom geometry considering various gravity fields and contact stiffnesses. While traditionally the inertial number, i.e., the ratio of stress to strain-rate timescales describes the flow rheology, we find that a second dimensionless number, the ratio of softness and stress timescales, must also be included to characterize the bulk flow behavior. For slow, quasi-static flows, the density increases while the macroscopic friction decreases with respective increase in particle softness and gravity. This trend is added to the $\mu(I)$ rheology and can be traced back to the anisotropy in the contact network, displaying a linear correlation between macroscopic friction and deviatoric fabric in the steady state. Interestingly, the linear relation holds when the external rotation rate is increased for a given gravity field and contact stiffness.