Stress Distribution in Granular Media and Nonlinear Wave Equation

Abstract

We propose phenomenological equations to describe how forces propagate within a granular nledium. Trie linear part of these equations is a wave equation, where the vertical coordinate plays trie rote of time, and trie horizontal coordinates trie raie of space. This means that (in two dimensions) trie stress propagates along light-cones; trie angle of these canes is related (but not equal to) trie angle of repose. Dispersive corrections to trie picture, and various types of nonlinearity are discussed. Inclusion of nonlinear terms may be able to describe trie arching phenomenon, which has been proposed to explain trie nonintuitive hor- izontal distribution of vertical pressure (with a local minimum or dip under the apex of trie pile) observed experimentally. However, for physically motivated parameter choices, a hump, rather than a dip, is predicted. This is aise true of a perturbative solution of the continuum stress equations for nearly-flot piles. The nature of trie force fluctuations is aise briefly discussed.