A micromechanical study of dilatancy of granular materials

In micromechanics of granular materials, relationships are investigated between micro-scale characteristics of particles and contacts and macro-scale, continuum characteristics. Dilatancy is an important property of granular materials, defined as volume changes (dilative or compressive) induced by shear deformation. To obtain detailed information at the micro-scale, two-dimensional Discrete Element Method simulations of isobaric tests with disk-shaped particles have been performed. The required information includes the fabric tensor which characterizes statistical properties of the contact network.The dependence of the dilatancy rate on the shear strength and the fabric tensor has been investigated, based on the results of the simulations employing a dense and a loose initial system. The dilatancy rate depends in a complex, non-unique way on the shear strength, while the dependence on the fabric tensor is more amenable to analytical description. Two micromechanical mechanisms of dilatancy have been identified: (i) dilatancy due to deformation of loops that are determined by the interparticle contact network and (ii) dilatancy due to topological changes in the interparticle contact network that correspond to the creation or disruption of contacts. For the first mechanism the anisotropy in the contact network is the primary parameter, while for the second mechanism the average number of contacts per particle is the primary parameter.A fabric-based micromechanical relation for the dilatancy rate has been formulated that describes these identified mechanisms. Parameters present in this relation are determined by fitting this relation to the results of the Discrete Element Method simulations, using combined data for the dense and the loose initial system. Employing these fitted coefficients, good agreement is obtained between the results of the simulations and the predictions of the micromechanical dilatancy relation.