Importance of Periodic Boundaries or Frictionless Walls in Simulating Elementary Response of Angular Particles

Abstract

In the discrete element method (DEM), the granular response is affected by the selection of boundary conditions, thereby emphasizing the importance of their careful consideration [1]. Replicating the boundary conditions employed in experiments is crucial to have a quantitative agreement between the response observed in the simulation and laboratory test [2]. In this study, a calibrated and validated DEM model was utilized to perform a series of simulations featuring regular polygons with varying numbers of corners subjected to different boundary conditions. The aim was to examine the combined effect of particle shape and boundary conditions on the mechanical response of granular assemblies. Simulations were performed under three boundary conditions: rigid frictional walls (in which the friction between the particle-wall interface is equal to that between the particle-particle interface), rigid frictionless walls, and periodic boundary conditions (PBC). Interestingly, it was observed that qualitatively, the effect of particle shape on granular response was invariant, irrespective of boundary conditions employed. However, quantitatively, the shear strength of all shapes was significantly affected by boundary settings, with the maximum and minimum strengths exhibited under rigid frictional walls and periodic boundaries, respectively. The magnitude of the decrease in shear strength due to boundary conditions was contingent upon the particle shape, with angular assemblies demonstrating a significant change in strength relative to round assemblies. Angular particles in contact with rigid wall frictional boundaries exhibited lesser rotations, thereby inducing relatively significant shear forces on the walls, particularly those parallel to the shearing direction. On the other hand, round particles in contact with walls rotated to a greater extent, resulting in little or negligible shear forces with the walls. Furthermore, boundary conditions also affected deformation patterns, including the development of shear bands.