Abstract
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 μ(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 μ(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.
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