Frictional-dilatancy effect in the description of immersed granular motion

This study develops a dynamic model to better describe the frictional-dilatancy behavior of underwater granular motion. We employ the compressible Navier-Stokes equations as the continuum framework, and introduce mu(J) rheology in treating the constitutive law of the immersed granules. Within the compressible Navier-Stokes framework, the change in granular volume fraction that occurs when the granules undergo shear-induced volumetric dilation (contraction) is considered using the frictional-dilatancy law from soil mechanics. On introducing frictional dilatancy, the constant coefficient of friction at startup in mu(J) rheology, which governs the yielding limit of particles, is replaced by a particle-volume-fraction-dependent evolutionary variable. The proposed model enables an accurate description of the properties of quasi-static deforming granular mass. The validity of the model is verified by classical immersed granular collapse. A comparison with experimental and previous simulation results demonstrated that the introduction of frictional-dilatancy law delays the initiation of submarine granular flow.