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

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**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 s_{2} 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 s_{2}¹ s_{3};this is
not physical most likely; so this criterion shall be replaced by some
Drücker-Prager criterion in the vicinity of s_{2}=s_{3}; 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 j_{dyn}<j is needed to understand avalanching. It is in agreement with previous
experimental results. Furthermore, these results show that the maximum angle of
repose q_{M} can be
modified using cyclic rotations; we propose then a procedure which allows to
achieve q_{M} =j .

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

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