A mixture model for the compaction of saturated sand

Free draining water saturated sands and dry sands compact progressively under cyclic shear loading, and the rate of compaction increases as the shear strain amplitude increases, independent of the confining stress magnitude. As the sand grains are relatively incompressible, this compaction is essentially an irreversible porosity decrease induced by rearrangement of the granular structure. We present a constitutive model of differential type for porosity variation which has the minimal ingredients necessary to reflect the observed cyclic loading phenomena, and determine the associated material functions of a particular form by correlation with cyclic loading data. A hypoelastic shear response is also correlated to cyclic loading data to complete an isotropic constitutive model. Pore pressure generation under cyclic loading in undrained conditions is evaluated to illustrate the predictions of the model.