Granta Gravel model of sandpile avalanches: towards critical fluctuations?

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>d c , since the slope of the pile becomes unstable for an angle larger than the friction angle but critical fluctuations of avalanches sizes (i.e. second order process) are expected when d=dic. This theory makes a link between the theory of Self-Organized Criticality of sand avalanches and experimental results En nous inspirant du modele de «Granta Gravel», nous proposons une approche theorique des avalanches de billes ou de sable qui postule des grains rigides, des pertes par frottement solide, des deformations plastiques et des effets de dilatance. On montre en particulier, que la taille des avalanches est controlee par la difference entre la densite d de l'empilement et une densite critique d c . Lorsque d=d c , les pertes peuvent etre dissipees localement et le processus d'avalanche peut presenter des fluctuations critiques. Lorsque d>d c , la theorie predit des avalanches macroscopiques et un phenomene du premier ordre. Notre description jette un pont entre la theorie d'etat critique auto-organise de P. Bak et al. et les resultats experimentaux