A microscopic study on stress-dilatancy relationship of granular materials by DEM

Matsuoka (1974) proposed a stress-dilatancy relationship of granular materials on the mobilized plane, which was expressed as tau / sigma (N) = lambda (-d epsilon (N) /d gamma) + mu. In this paper, the stress ratio tau / sigma (N) and the strain increment ratio -d epsilon (N)/d gamma are approximated to be tan (x) over bar and tan <(<theta>)over bar>, respectively, on the basis of the numerical simulation results of a simple shear test by DEM. Here, (x) over bar and <(<theta>)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. There is a difference delta between (x) over bar and <(<theta>)over bar>. It is found that the value of delta depends weakly on the interparticle friction angle phi (mu) except in the lower range of phi (mu). The difference delta is interpreted to be a function of the average interparticle contact force f(0), the rising gradient k of the straight line representing the frequency distribution of the average interparticle contact force and the average interparticle contact angles <(<theta>)over bar> on the mobilized plane.