Kinks, logarithmic tails, and super-stability in bi-disperse granular media

Determining the stability of granular matter piles is of basic concern in understanding many real-world phenomena (e.g. landslides, debris flow, and avalanches). While extensive literature exists dealing with the stability of mono-disperse systems, models for the dynamical behavior of poly-disperse media are still uncommon. Here, a simple experimental setup that probes the dependence of the repose angle (θθ) for different proportions of granular mixtures is described. We demonstrate that a cellular automata (CA) grid with rules based on gravitational effects can phenomenologically mimic the dynamics of experimental data in terms of: (1) the presence of disruptions or kinks in an otherwise perfectly straight slope; (2) a concave logarithmic tail, indicative of the nature of the granular medium; and (3) the existence of supra-maximal repose angles for binary mixtures such that θmix>θ1,θ2, which can lead to super-stability, or 90-degree slopes. This latter result has profound implications because of the ubiquity of vertical slopes in nature, while standard continuum approaches cannot account for such (because it entails an infinite value of the coefficient of friction).