Microscopic Interpretation on a Stress-Dilatancy Relationship of Granular Materials

Abstract

Matsuoka (1974) proposed a two-dimensional stress-dilatancy equation of granular materials on the mobilized plane through the direct box shear tests on assemblies of aluminum and photoelastic rods, which was expressed as τ/σN=λ(−dεN/dγ)+μ. In this paper, the stress ratio τ/σN and the strain increment ratio −dεN/dγ are approximated to be tan x¯ and tan θ¯, respectively, on the basis of the numerically simulated results for a simple shear test by DEM. Here, x¯ and θ¯ denote the average angle of the interparticle forces to the normal of the mobilized plane and the average interparticle contact angle on the mobilized plane, respectively. It was found that the difference between x¯ and θ¯, denoted as δ, varies slightly during shear. The angle δ is related to the average interparticle contact force f0, the slope k of the straight line that characterizes the distribution of the average interparticle contact forces against the contact angle, and the average interparticle contact angles θ¯ on the mobilized plane. The intercept μ in the stress-dilatancy equation is interpreted as tan δ. The influences of interparticle surface friction, grain shape and confining pressure on the stress-dilatancy relation are examined. It was found that the angle δ is not very sensitive to the interparticle surface friction angle ϕμ, except in the lower value of ϕμ, and independent of the confining pressure. However, it is affected to some extent by grain shapes. Various results of the newly developed in-situ direct shear tests on various granular soils are presented to support the arguments in this paper.