Is the friction angle the maximum slope of a free surface of a non cohesive material?


A. Modaressi  &  P. Evesque: Lab MSSM, UMR 8579 CNRS, Ecole Centrale Paris, 92295 Châtenay-Malabry, France,


Abstract: Starting from a symmetric triangular pile with a horizontal basis and rotating the basis in the vertical plane, we have determined the evolution of the stress distribution as a function of the basis inclination using Finite Elements method with an elastic-perfectly plastic constitutive model, defined by its friction angle j , without cohesion. It is found that when the yield function is the Drücker-Prager one, stress distribution satisfying equilibrium can be found even when one of the free-surface slopes q is larger than j. This means that piles with q>j can be (at least) marginally stable and that slope rotation is not always a destabilising perturbation direction. On the contrary, it is found that q cannot overpass j when a Mohr-Coulomb yield function is used. Theoretical explanation of these facts is given which enlightens the role plaid by the intermediate principal stress s2 in both cases of the Mohr-Coulomb criterion and of the Drücker-Prager one.

It is then argued that the Mohr-Coulomb criterion assumes a spontaneous symmetry breaking,as soon as s2¹ s3;this is not physical most likely; so this criterion shall be replaced by some Drücker-Prager criterion in the vicinity of s2=s3; as this Drücker-Prager criterion leads to some anomalous friction behaviour, since the present work demonstrates that the slope q of a pile obeying this modelling can be larger than the friction angle j ,  these numerical computations enlighten the avalanche process: they show that no dynamical angle jdyn<j is needed to understand avalanching. It is in agreement with previous experimental results. Furthermore, these results show that the maximum angle of repose qM can be modified using cyclic rotations; we propose then a procedure which allows to achieve qM =j .


poudres & grains 12 (5), 83-102 (juin 2001)