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

TL;DR

This study uses finite element simulations to investigate the maximum stable slope of non-cohesive granular piles, revealing that the friction angle is not always the limiting factor for slope stability, especially under Drucker-Prager conditions.

Contribution

The paper demonstrates that the maximum slope of a granular pile can exceed the friction angle when modeled with Drucker-Prager criteria, challenging traditional assumptions based on Mohr-Coulomb theory.

Findings

Stress distribution can satisfy equilibrium with slopes larger than the friction angle under Drucker-Prager.

The slope cannot surpass the friction angle when using Mohr-Coulomb criterion.

Cyclic rotations can modify the maximum angle of repose to match the friction angle.

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, 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 .