Dynamical stress in force chains of granular media traveling on a bumpy terrain and the fragmentation of rock avalanches

The dynamics of grain fragmentation is usually ignored in the study of rapid granular flows. This is realistic for experiments on small-scale chutes or in many industrial processes where the specific granular energy is too small for particles to break but is unrealistic for natural rock avalanches, where the extremely comminuted state is perhaps the most evident aspect of the deposit. Based on observations of natural landslide deposits, it has been suggested that the stress may increase along a sequence of force chains formed by the granular material. However, simple calculations show that rock avalanche deposits exhibit a much more advanced degree of fragmentation than explainable with the static chain model. It is thus deduced that fragmentation along force chains must be combined with the effect of a bumpy topography. A simple model of a force chain moving on a rugged incline is then introduced, which exhibits increased fragmentation rate in the presence of a bumpy topography. It is shown that both the wave number and amplitude of the topographic undulations are significant in the efficiency of fragmentation.