A shear rate dependent critical state theory to describe the initiation of dense granular flows
Seminar Room 1, Newton Institute
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 . 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  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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