An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary environments

Abstract

The angle of repose—i.e., the angle θr between the sloping side of a heap of particles and the horizontal—provides one of the most important observables characterizing the packing and flowability of a granular material. However, this angle is determined by still poorly understood particle-scale processes, as the interactions between particles in the heap cause resistance to roll and slide under the action of gravity. A theoretical expression that predicts θr as a function of particle size and gravity would have impact in the engineering, environmental, and planetary sciences. Here we present such an expression, which we have derived from particle-based numerical simulations that account for both sliding and rolling resistance, as well as for nonbonded attractive particle–particle interactions (van der Waals). Our expression is simple and reproduces the angle of repose of experimental conical heaps as a function of particle size, as well as θr obtained from our simulations with gravity from 0.06 to 100 times that of Earth. Furthermore, we find that heaps undergo a transition from conical to irregular shape when the cohesive to gravitational force ratio exceeds a critical value, thus providing a proxy for particle-scale interactions from heap morphology.