Multiscale Analysis of the Stress State in a Granular Slope in Transition to Failure

TL;DR

This study uses contact dynamics simulations to analyze how stress distribution in a granular slope evolves as it approaches failure, revealing a transition characterized by a percolation of overloaded grains and metastability.

Contribution

It introduces a multiscale analysis linking stress ratios, a coarse-graining length, and a percolation transition to understand slope failure mechanisms.

Findings

The coarse-graining length increases with slope angle.

A transition occurs at an angle below the repose, marked by a jump in the length scale.

Overloaded grains percolate, indicating a metastable state.

Abstract

By means of contact dynamics simulations, we analyze the stress state in a granular bed slowly tilted towards its angle of repose. An increasingly large number of grains are overloaded in the sense that they are found to carry a stress ratio above the Coulomb yield threshold of the whole packing. Using this property, we introduce a coarse-graining length scale at which all stress ratios are below the packing yield threshold. We show that this length increases with the slope angle and jumps to a length comparable to the depth of the granular bed at an angle below the angle of repose. This transition coincides with the onset of dilatation in the packing. We map this transition into a percolation transition of the overloaded grains, and we argue that in the presence of long-range correlations above the transition angle, the granular slope is metastable.