  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.
