Temporally disordered granular flow: A model of landslides

Abstract

We propose and study numerically a stochastic cellular automaton model for the dynamics of granular materials with temporal disorder representing random variation of the diffusion probability $1-μ(t)$ around threshold value $1-μ_0$ during the course of an avalanche. Combined with the slope threshold dynamics, the temporal disorder yields a series of secondary instabilities, resembling those in realistic granular slides. When the parameter $μ_0$ is lower than the critical value $μ_{0}^\star \approx 0.4$, the dynamics is dominated by occasional huge sandslides. For the range of values $μ_{0}^\star \le μ_0 < 1$ the critical steady states occur, which are characterized by multifractal scaling properties of the slide distributions and continuously varying critical exponents $τ_X(μ_0)$. The mass distribution exponent for $μ_0\approx 0.45$ is in agreement with the reported value that characterizes Himalayan sandslides. At $μ_{0}= μ_{0}^\star$ the exponents governing distributions of large relaxation events reach numerical values which are close to those of parity-conserving universality class, whereas for small avalanches they are close to the mean-field exponents.