Multi-scale analysis of the stress state in a granular slope in transition to failure

By means of contact dynamics simulations, we analyze the stress state in a granular bed slowly tilted toward 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 dilation in the packing. We map this transition into a percolation transition of the overloaded grains, and discuss it in terms of long-range correlations and granular slope metastability.