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

Abstract

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 , rheology with a dilatancy law, where 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.

Simulations of granular collapses on horizontal and sloping beds show that the maximum height of the deposits changes as a function of the initial volume fraction with higher (lower) deposits for initially denser (looser) granular masses, as observed with Discrete Element simulations. The front position and the deposit shape behind it are on the contrary poorly affected by the initial volume fraction, as if the flow had almost forgotten its initial state. However subtle effects can be observed with the occurrence of low velocity regimes on steep slopes that strongly depend on the initial volume fraction. Simulations show complex compression/dilation effects during the flow, in particular with front dilation (compression) during the acceleration (deceleration) phases. These effects may dramatically change the effective friction that is observed to decrease at the front in some situations, while the rheology without dilatancy would have predicted an increasing friction. The model predicts an increasing dilation of the mass for increasing slopes by up to 10% in the studied configurations, in agreement with laboratory experiments. Our results suggest that this compressible model contains key features to describe granular dilatancy.