Shear strength, dilatancy, energy and dissipation in quasi-static deformation of granular materials

The effect of the interparticle friction coefficient μ on macroscopic, continuum characteristics, such as shear strength and dilatancy rate, of granular materials in quasi-static deformation is investigated using two-dimensional discrete element simulations of biaxial tests with various values for μ. Qualitatively, the macroscopic behaviour observed in the limit cases and (when the microscopic behaviour at the contacts is elastic) is the same as in the cases with 'normal' values for μ, showing that interparticle friction does not form the exclusive microscopic origin of the macroscopic frictional behaviour of granular materials. Based on the results of the discrete element simulations, a stress–dilatancy relation is formulated. Furthermore, the effect of interparticle friction on the evolution of the energy distribution is investigated. It is shown that the ratio between the energy in the tangential springs and the energy in the normal springs does not change appreciably with imposed strain. The investigation of the influence of interparticle friction on the dissipative characteristics shows that macroscopic dissipation is present even in the limit cases and and , i.e. when microscopic friction is effectively absent. A dissipation function is formulated that describes the observed dissipative characteristics, for the various values of μ considered, reasonably well.