### A shear rate dependent critical state theory to describe the initiation of dense granular flows

Pouliquen, O; Pailha, M *(CNRS-Aix Marseille)*

Wednesday 07 January 2009, 11:45-12:10

Seminar Room 1, Newton Institute

#### Abstract

It is well know that the initiation of flow of a dry granular material strongly depends on its preparation. For example, the collapse of a column of grains initially compacted under vibrations is dramatically different from the collapse of a loose column [1]. To capture the role of the initial volume fraction in hydrodynamics model of granular flows, there is a need to take into account dilatant or contractant behaviors. Critical state theories developed in soil mechanics are simple ways to describe the initial deformation of a granular sample under quasi-static deformations and to model the coupling between stresses and volume fraction [2,3]. However, such theories are shear rate independent and are thus unable to describe the development of free surface flows like avalanches. In this work we show how a recent viscoplastic model suitable to describe the viscous behavior of granular flows in various configurations [4] can be adapted to take into account dilatancy effects. The idea consists in considering the rheology given by the visco-plastic approach as a shear rate dependent critical state and in introducing a dilatancy angle to couple volume fraction and stress tensor variations. The predictions of the model are illustrated for the problem of the initiation of flow of a granular layer on an inclined plane. Depending on the initial volume fraction, the route to reach the steady state aooears to be different.
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media." in Mechanics for a New Millennium, H. Aref and J. W. Philips (eds), Kluwer,
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441, 727 (2006).