  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, without cohesion. It is found that when the yield
function is the Drucker-Prager one, stress distribution satisfying equilibrium
can be found even when one of the free-surface slopes is larger than the
friction angle. This means that piles with a slope larger than the friction
angle can be (at least) marginally stable and that slope rotation is not always
a destabilising perturbation direction. On the contrary, it is found that the
slope cannot overpass the friction angle 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 in both cases of the Mohr-Coulomb
criterion and of the Drucker-Prager one. It is then argued that the
Mohr-Coulomb criterion assumes a spontaneous symmetry breaking, as soon as the
two smallest principal stresses are different ; this is not physical most
likely; so this criterion shall be replaced by a Drucker-Prager criterion in
the vicinity of the equality, which leads to the previous anomalous behaviour ;
so these numerical computations enlighten the avalanche process: they show that
no dynamical angle larger than the static one is needed to understand
avalanching. It is in agreement with previous experimental results.
Furthermore, these results show that the maximum angle of repose can be
modified using cyclic rotations; we propose a procedure that allows to achieve
a maximum angle of repose to be equal to the friction angle .
