Impulse propagation in granular media

Abstract

Grains can be described as elastic objects. When two grains are pushed against one another, they repel via Hertz’ nonlinear force law, F∝δn, n>2, δ≥0, being the overlap between the grains. We show that the propagation of an impulse of any magnitude in a 1D chain of grains at zero loading can be described as a solitary wave. The width of the solitary wave, L(n)→1 as n→∞, L∼5 grain diameters for typical granular contacts and L(n)→∞ when n→2. The condition δ≥0 leads to the formation of secondary solitary waves when two identical solitary waves propagating in opposite directions collide. Randomness in grain densities and sizes and restitutional losses lead to approximately exponential decays in distance of the energy of a propagating solitary wave. It turns out that impulses can be exploited to fingerprint a buried impurity mass in a 1D chain with and without gravity. In closing, we shall discussthe backscattering of an impulse from a buried object in 3D beds at shallow depths. Implications of this work with respect to humanitarian demining and related applications will be presented. [Work supported in part by U.S. Army Corps of Engineers and Sandia National Laboratories. Work done in collaboration with Marian Manciu (SUNY-Buffalo) and Alan J. Hurd (Sandia National Labs).]