The behaviour of an assembly of rotund, rigid, cohesionless particles. II

Abstract

A method is propounded for describing the state of anisotropy existing in an irregular array of uniform spherical particles, this being in terms of quantities referred to as the mean projected solid paths in the various co-ordinate directions. On the basis of these concepts, expressions are derived for the rates of strain in the principal directions in terms of the frequency and intensity of sliding between particles. It is shown that this analysis gives results for regular arrays corresponding to those obtained by Rowe using a different procedure. Strain rate and stress ratios are derived for certain axially symmetrical states of deformation realized in triaxial tests on assemblies of equal uniform spheres. An upper limit is derived for the maximum stress ratio in terms of the angle of solid friction between particles, the ultimate state of anisotropy being derived by considering the directions of the relative motions that exist between adjacent groups.