Pore shapes, volume distribution and orientations in monodisperse granular assemblies

Abstract

The complex mechanical behaviour of granular materials is commonly studied by considering the evolving particle contact network. An often overlooked feature is the influence of micro-scale geometric configuration of pores on the macroscopic response. This paper presents a series of tools to quantify the shape, volume distribution and orientation characteristics of the pore space. The proposed approach is compared against data extracted from physical and numerical experiments with monodisperse assemblies of spheres. Individual pores are represented by polyhedral pore unit cells obtained by combining the Delaunay tessellation with an algorithm for merging Delaunay cells based on the concept of maximal inscribed sphere, after Al-Raoush et al. (Soil Sci Soc Am J 67(6):1687–1700, 2003). A pore shape parameter is proposed that considers pore volume and surface, and is analytically related to the void ratio and the number of edges forming the polyhedral pore unit cell. The pore volume distribution is shown to be uniquely described by the analytical k-gamma distribution proposed by Aste and Di Matteo (Phys Rev E 77(2):021309, 2008). A pore orientation tensor is introduced to define the principal orientation of individual pore units. This is subsequently used to define a global orientation tensor that reveals an isotropic pore network for the reference monodisperse assemblies. The global orientation tensor is analytically expressed in terms of the parameters defining the pore volume distribution.