Simulation of Lateral Impulse Induced Inertial Dilation at the Surface of a Vacuum-Exposed Granular Assembly

Abstract

We demonstrate for the first time that a lateral impulse experienced by a granular channel can induce an inertial bulk dilation over long distances across a granular medium with a mechanically free surface. The surface dilation requires zero overburden pressure (exposure to vacuum) and is precipitated by the passing of waves traveling barely above the sound speed (> Mach 1.05). We simulate this phenomenon using open source Soft Sphere Discrete Element Method (SSDEM) software. We prepare channels of monodisperse, cohesive spherical particles exposed to vacuum and modeled as Hertzian springs. We validate our model by recreating acoustic wave, strong shock, and shear dilation behavior. We then create shocks within the channel to determine the sensitivity of surface dilation to wave speed, wave type, initial packing fraction, and boundary effects. The shocks we create undergo a rapid decay in strength and appear to propagate as solitary waves that can be sustained across the channel. We find that an inertial surface dilation is induced by compressive solitary waves, is insensitive to channel length, increases with bed height, and increases substantially with initial packing fraction. A hard subsurface floor is required to maintain this wave over the entire channel. Free surface dilation induced by laterally propagating impulse loading could be implicated in the formation of Lunar Cold Spots, distal regions of low thermal inertia surrounding young craters on the Moon.