Granta Gravel model of sandpile avalanches: towards critical fluctuations?

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Abstract
A theory which predicts the size of sandpile avalanches is given. It is based on the so-called Granta Gravel model which assumes rigid grains, plastic yielding and friction losses; it also takes into account dilatancy effects. According to our model, the avalanche size is controlled by the difference between the real pile density d and a critical density d c: macroscopic avalanches (i.e. first order process) are obtained when d > dc, since the slope of the pile becomes unstable for an angle larger than the friction angle but critical fluctuations of avalanche sizes (i.e. second order process) are expected when d = dc. This theory makes a link between the theory of Self-Organized Criticality of sand avalanches and experimental results