Rolling friction in the dynamic simulation of sandpile formation

Abstract

The contact between spheres results in a rolling resistance due to elastic hysteresis losses or viscous dissipation. This resistance is shown to be important in the three-dimensional dynamic simulation of the formation of a heap of spheres. The implementation of a rolling friction model can avoid arbitrary treatments or unnecessary assumptions, and its validity is confirmed by the good agreement between the simulated and experimental results under comparable conditions. Numerical results suggest that the angle of repose increases significantly with the rolling friction coefficient and decreases with particle size.

Introduction

The formation of a heap of particles is important in all industries dealing with particulate materials ranging from agricultural products such as flour and grains to minerals such as coal and metal ores. It is related to almost all typical phenomena associated with granular materials, and many aspects of heaping, including particle segregation [1], packing [2], and stress distribution [3], [4], have been studied in the past. In recent years, many efforts have been made to understand the governing mechanisms involved, which are linked to important phenomena such as self-organisation [5], [6] and stratification [7], [8] that have stimulated the interest in particulate science and technology significantly [9], [10], [11].

The bulk behaviour of a particle system depends on the collective interactions of individual particles. Therefore, it is very useful to study the heaping process on the particle scale. In the past, various computer simulation techniques have been developed for this purpose, including Monte Carlo [12], [13], [14], [15], cellular automation [16], and granular dynamic simulations [17], [18]. The latter is probably most realistic, because it explicitly takes into account not only the geometrical factors but also the forces involved. In recent years, it has been used by various investigators to study the formation of two-dimensional sandpiles [19], [20], [21], [22]. However, to form a stable heap of particles with a finite angle of repose, special treatments or assumptions have to be employed in a simulation. For example, Lee and Herrmann [19] and Luding [20] ignored the rotation of particles or tangential forces, Elperin and Golshtein [21] set the velocities of all particles to zero after every 5000–15 000 iterations and Baxter et al. [22] started their simulation with a static substrate consisting of a row of equally spaced particles. Theoretically, such treatments are arbitrary and may distort reality, leading to inaccurate information.

The purpose of this paper is to propose a simulation method that can simulate the formation of a stable heap of spheres under three-dimensional conditions. The method is essentially that originally proposed by Cundall and Strack [17], but modified by introducing a rolling friction torque based on the experimental and theoretical analysis of Beer and Johnson [23] or Brilliantov and Poschel [24]. The effect of the rolling friction coefficient on the formation of a sandpile is studied in detail. The validity of the proposed modification is confirmed by the good agreement between the simulated and measured results under comparable conditions.