Microscopic interpretation on a stress-dilatancy relationship of granular materials

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 tau/sigma(N) = lambda(- depsilon(N)/dgamma) + mu. In this paper, the stress ratio tau/sigma(N) and the strain increment ratio -depsilon(N)/dgamma are approximated to be tan (x) over bar and tan (θ) over bar, respectively, on the basis of the numerically simulated results for a simple shear test by DEM. Here, (x) over bar and (θ) over bar 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) over bar and (θ) over bar, denoted as delta, varies slightly during shear. The angle delta is related to the average interparticle contact force f(0), 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) over bar on the mobilized plane. The Intercept mu in the stress-dilatancy equation is interpreted as tan delta. The influences of interparticle surface friction, grain shape and confining pressure on the stress-dilatancy relation are examined. It was found that the angle delta is not very sensitive to the interparticle surface friction angle phi(mu), except in the lower value of phi(mu), 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.