STRESS-DISTRIBUTION IN GRANULAR MEDIA AND NONLINEAR-WAVE EQUATION

We propose phenomenological equations to describe how forces ''propaga te'' within a granular medium. The linear part of these equations is a wave equation, where the vertical coordinate plays the role of time, and the horizontal coordinates the role of space. This means that (in two dimensions) the stress propagates along ''light-cones''; the angle of these cones is related (but not equal to) the angle of repose. Dis persive corrections to the picture, and various types of nonlinearity are discussed. inclusion of nonlinear terms may be able to describe th e ''arching'' phenomenon, which has been proposed to explain the nonin tuitive horizontal distribution of vertical pressure (with a local min imum or ''dip'' under the apex of the pile) observed experimentally Ho wever, for physically motivated parameter choices, a ''hump'', rather than a dip, is predicted. This is also true of a perturbative solution of the continuum stress equations for nearly-hat piles. The nature of the force fluctuations is also briefly discussed.