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

Wednesday 7th January 2009 - 11:45 to 12:10
INI Seminar Room 1
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. [1] A. Daerr and S. Douady Sensitivity of granular surface flows on preparation Europhys. Lett. 47 (3), pp. 324-330 (1999) [2] A. Schofield and P. Wroth Critical Soil Mechanics (McGraw-Hill, London , 1968) [3] S. Roux and F. Radjai "Statistical approach to the mechanical behavior of granular media." in Mechanics for a New Millennium, H. Aref and J. W. Philips (eds), Kluwer, Netherlands, pp. 181-196 (2001). [4] P. Jop, Y. Forterre, and O. Pouliquen, a constitutive law for dense granular flows, Nature 441, 727 (2006).
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons