On the formation of super-stable granular heaps

A super-stable granular heap is a pile of grains whose free surface is inclined above the angle of repose, and which forms when particles are poured onto a plane that is confined laterally by frictional sidewalls that are separated by a narrow gap. During continued mass supply, the heap free surface gradually steepens until all the inflowing grains can flow out of the domain. As soon as the supply of grains is stopped, the heap is progressively eroded, and if the base of the domain is inclined above the angle of repose, all the grains eventually flow out. This phenomenology is modelled using a system of two-dimensional width-averaged mass and momentum balances that incorporate the sidewall friction. The granular material is assumed to be incompressible and satisfy the partially-regularized µ (I) rheology. This is implemented in OpenFOAM® and compared against small-scale experiments that study the formation, steady-state behaviour and drainage of a super-stable heap. The simulations accurately capture the dense liquid-like flows as well as the evolving heap shape. The steady-uniform flow that develops along the heap surface has non-trivial inertial number dependence through its depth. Super-stable heaps are therefore a sensitive rheometer that can be used to determine the dependence of the friction µ on the inertial number I. However, these flows are challenging to simulate because the free-surface inertial number is high, and can exceed the threshold for ill posedness even for the partially-regularized theory.