Granular elasticity: general considerations and the stress dip in sand piles

Granular materials are predominantly plastic, incrementally nonlinear, preparation-dependent, and anisotropic under shear. Nevertheless, their static stress distribution is well accounted for, in the whole range up to the point of failure, by a judiciously tailored isotropic nonanalytic elasticity theory termed granular elasticity. The first purpose of this paper is to carefully expound this view. Then granular elasticity is employed to consider the stress distribution in two-dimensional sand piles (or sand wedges). Starting from a uniform density, the pressure at the bottom of the pile is found to show a single central peak. It turns into a pressure dip, if some density inhomogeneity, with the center being less compact, is assumed. These two pressure distributions are remarkably similar to recent measurements, made in piles obtained, respectively, by rainlike pouring and funneling. In an accompanying paper, the stress distributions in silos and under point loads, calculated using the same method, are also found to agree with experiments.