Bifurcation in rolling of non-spherical grains and fluctuations in macroscopic friction

Abstract

The presence of granular matter between the sliding blocks (such as for example gouge in rock joints and faults) considerably affects friction. The effect of grain movement and rolling is often modelled by considering them as spherical. This paper investigates the influence of the grain/particle shape. We found that rolling of non-spherical particles leads to an apparent friction reduction related to the effect of the moment equilibrium about a point of contact. The collective behaviour of rolling non-spherical particles is affected by their interaction by the elasticity of the material of the sliding blocks. In the case of identical and symmetrical particles, there exists a uniform solution whereby all particles undergo identical displacements. This solution is, however, unstable; at certain magnitudes of the friction force and the corresponding values of the displacement the solution bifurcates such that different particles show different displacements. When many particles of different sizes are rolling without interaction, the friction force fluctuates, and as the displacement increases, the fluctuations reach a steady state. The amplitudes of the fluctuations depend upon the shape factor; they are the smallest when the particles have a square shape and considerably increase as the period of particle rolling approaches the diameter.