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

Abstract

The effect of the interparticle friction coefficientμ on macroscopic, continuum characteristics, such as shear strength and dilatancyrate, of granular materials in quasi-static deformation is investigated usingtwo-dimensional discrete element simulations of biaxial tests with various values forμ. 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’ valuesfor μ, showing that interparticle friction does not form the exclusive microscopic origin of themacroscopic frictional behaviour of granular materials. Based on the results of the discreteelement simulations, a stress–dilatancy relation is formulated. Furthermore, the effect ofinterparticle friction on the evolution of the energy distribution is investigated. It is shownthat the ratio between the energy in the tangential springs and the energy in the normalsprings does not change appreciably with imposed strain. The investigation of theinfluence of interparticle friction on the dissipative characteristics shows thatmacroscopic dissipation is present even in the limit cases and and , i.e. when microscopic friction is effectively absent. A dissipation function is formulatedthat describes the observed dissipative characteristics, for the various values ofμ considered, reasonably well.