Granular column collapse under gravity is a benchmark problem for several applications from geophysics to industry. It has been shown experimentally, for granular columns of initial aspect ratio a=h_i/r_i (height/width or radius), that for large enough values of a, the final width or radius r_∞, reached after spreading, obeys the scaling law (r_∞- r_i) / r_i ≈ a^2/3 in 2D and a^1/2 in 3D flows. It was also shown that the normalized distance-time data (t, x) plot exhibits a universal shape, independently of the grain type.

Recently, Jop et al. proposed a pressure dependent viscoplastic continuum model called mu(I), where the extra-stress is defined using an effective friction coefficient that varies from low (quasi-static regime) to high values (inertial regime) when the inertial number I=|γ|d(ρ/p)^1/2 (where γ=strain rate tensor, d=grain diameter, ρ=grain density and p=pressure) reaches the (material dependent) parameter I0.

In this paper, we study the pertinence mu(I) to predict 2D and 3D granular column collapse flows. A time-dependent regularization algorithm is proposed to solve this model, combined with anisotropic mesh adaptation to capture accurately the quasi-static vs. inertial flow zones, and using a variational multiscale method. A Level-Set method aims to capture and follow efficiently the interface between the fluid/air domain.

We show that (i) the mu(I) model exhibit non unique solutions at early times (acceleration phase): mesh dependent short lengthscale instabilities (shear bands) appear, (ii) these instabilities do not subsist during the steady front velocity and deceleration phases, (iii) the universal distance-time plot shape is retrieved.

Moreover, 2D and 3D results show that most of the flow is in a quasi-static regime, the inertial regime being only reached in a small volume at the front flow. 2D and 3D initial aspect ratio scaling laws for spreading distance are then accurately predicted. An accurate sensitivity analysis to rheological parameters is finally performed.