Wide shear zones and the spot model: Implications from the split-bottom geometry

TL;DR

This paper critically examines the applicability of the spot model to wide shear zones in granular flows within a split-bottom Couette cell, highlighting limitations and suggesting possible extensions for better modeling such phenomena.

Contribution

The study provides a theoretical analysis showing the limitations of the simplest spot model in describing wide shear zones and discusses potential modifications to improve its accuracy.

Findings

The simplest spot model struggles to explain wide shear zones.

Diffusion and drift balance at small length scales conflicts with observed wide zones.

Extensions to the model may be needed to account for wide shear flows.

Abstract

The spot model has been developed by Bazant and co-workers to describe quasistatic granular flows. It assumes that granular flow is caused by the opposing flow of so-called spots of excess free volume, with spots moving along the slip lines of Mohr-Coulomb plasticity. The model is two-dimensional and has been successfully applied to a number of different geometries. In this paper we investigate whether the spot model in its simplest form can describe the wide shear zones observed in experiments and simulations of a Couette cell with split bottom. We give a general argument that is independent of the particular description of the stresses, but which shows that the present formulation of the spot model in which diffusion and drift terms are postulated to balance on length scales of order of the spot diameter, i.e. of order 3-5 grain diameters, is difficult to reconcile with the observed wide shear zones. We also discuss the implications for the spot model of co-axiality of the stress and strain rate tensors found in these wide shear flows, and point to possible extensions of the model that might allow one to account for the existence of wide shear zones.