Rate effects in dense granular materials: Linear stability analysis and the fall of granular columns

In this paper, the suitability of rate-dependent constitutive relationships to model the rheology of granular materials is investigated. In particular, the formation of shear bands as predicted by this approach is studied. First, a rate-dependent model is investigated in terms of a linear stability analysis. It turns out that at low to moderate strain rates, the orientation of shear bands tends to vary from the so-called Roscoe and Coulomb solutions towards a unique admissible orientation with an increase of the so-called inertial number I. This effect is confirmed by numerical simulations of a compression test performed with a particle in cell finite element program. To further assess the validity of continuum approaches for the simulation of dense granular flows, a quasi-static fall of a granular column is studied numerically and the results are confronted to available experimental data. It is shown that a satisfying agreement is obtained at different aspect ratios and for the two materials investigated in this paper, i.e. sand and glass beads. The results reported in the present paper demonstrate the relevance of continuum approaches in the modelling of dense granular flows.