Dilatancy in dry granular flows with a compressible μ(I) rheology

Dilatancy plays a key role in mixtures of grains and fluid but is poorly investigated in dry granular flows. These flows may however dilate by more than 10% in granular column collapses. We investigate here dilatancy effects in dry flows with a shallow depth-averaged model designed to be further applied to simulate natural landslides. We use a compressible μ(I), ϕeq(I) rheology with a dilatancy law, where ϕeq(I) is the volume fraction at the equilibrium (i.e. critical) state and I the so-called inertial number. This law is obtained by simply removing the fluid phase in the solid/fluid model of our previous work (Bouchut et al., 2016) [7] and derived from critical state theory. A numerical method is proposed to solve the equations, that have however singularities that are rather difficult to handle.