Force structure of frictionless granular piles

A striking attribute of nominally homogeneous, noncohesive granular piles is the wide range of normal forces exerted on the substrate. Presumably the particular distribution of force fluctuations is a consequence of the disorder of the pile. This connection is made for 2D frictionless piles, where the degree of disorder is set by the template of grains placed on the substrate. The intergranular forces are calculated by solving the vertical and horizontal force balance equations at each grain; in the event a tensile force is thereby obtained, that contact force is set equal to zero and the resulting vertical force balance equation is solved. Maximally disordered piles produce a normalized normal-force (weight) distribution P(w) w exp(−2w), in agreement with a simple theory, while more-ordered piles produce a distribution that decays linearly. In both cases the piles contain high-stress and low-stress “chains” of contacting grains at which compressive stress is concentrated or absent, respectively.