Temporally disordered granular flow: A model of landslides

TL;DR

This paper introduces a stochastic cellular automaton model for granular flows that captures landslide dynamics, revealing critical states with multifractal properties and scaling behaviors consistent with real-world landslides.

Contribution

It presents a novel numerical model incorporating temporal disorder to simulate landslide phenomena and analyzes critical scaling and multifractal properties of granular avalanches.

Findings

Large landslides occur at low diffusion probability parameter values.

Critical steady states exhibit multifractal scaling with variable exponents.

Model results align with observed Himalayan landslide distributions.

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 $1-\mu (t)$ around threshold value $1-\mu_0$ 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 $\mu_0$ is lower than the critical value $\mu_{0}^\star \approx 0.4$, the dynamics is dominated by occasional huge sandslides. For the range of values $\mu_{0}^\star \le \mu_0 < 1$ the critical steady states occur, which are characterized by multifractal scaling properties of the slide distributions and continuously varying critical exponents $\tau_X(\mu_0)$. The mass distribution exponent for $\mu_0\approx 0.45$ is in agreement with the reported value that characterizes Himalayan sandslides. At $\mu_{0}= \mu_{0}^\star$ 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.