Lattice model for the calculation of the angle of repose from microscopic grain properties

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Abstract
We study a simple lattice model for granular heap, which aims at calculating the macroscopic angle of repose from the microscopic grain properties. The model includes the effects of dissipation of the energy in the particle-particle collisions, and sticking of the particles to the pile. We obtain that, due to the discretization of the space, the angle of repose of the pile behaves as a complete devil’s staircase as a function of the model parameters. We present numerical and analytical considerations which characterize the properties of this staircase.