Unconfined slumping of a granular mass on a slope

This study investigates the gravitationally driven dynamics of dense granular materials, released from rest and allowed to flow down a slope until they stop moving. Laboratory experiments were performed in which a measured volume of material was released from rest in a cylindrical tube and spread across an unconfined rigid plane inclined at angles less than the angle of repose. Upon release, the particles initially spread outward radially. However, up-slope motion is rapidly suppressed while down-slope motion is promoted, which leads to an approximately ellipsoidally shaped deposit once the flow has been fully arrested. The flows were modeled under the shallow layer approximation and integrated numerically to capture the motion from initiation to final arrest. In modeling, two types of Coulomb-type friction models were employed. One had a constant friction coefficient, and another had a friction coefficient that depends upon the dimensionless inertial number of the motion. When the initial aspect ratio of a granular mass is small and the slope angle is low (<5°), the model with a constant friction coefficient can capture the shape of the deposit. However, when the slope angle is increased, the friction model that is dependent on inertial number becomes more important. For granular columns of initially high aspect ratios, the shallow water model fails to reproduce some aspects of the experimental observations. Finally, the dependence of the shape and depth of the deposit upon dimensionless parameters that characterize the system is examined under the constant friction coefficient model, demonstrating that the deduced scaling arguments are borne out by the numerical simulations and laboratory data.