On flow rule in granular media: phenomenological and multi-scale views

In the companion paper (Int. J. Numer. Anal. Methods Geomech. 2005, this issue), we investigated an outstanding feature of the mechanical behaviour of granular assemblies, namely their incrementally non-linear character. For this purpose, two types of constitutive models were considered: a phenomenological model and a micro-mechanical model. The purpose of the present paper is to compare these two models with respect to another basic issue regularly raised about granular assemblies: the possible existence of a regular flow rule. This comparison brings out the essential micro-mechanical origins of singular flow rules. As a consequence of the frictional model used to describe the sliding between adjoining granules, a flow rule only exists in two-dimensional conditions, but disappears in three dimensions. Copyright © 2005 John Wiley & Sons, Ltd.