1 5 O ct 1 99 8 Contact forces in regular 3 D granular pile

We present exact results for the contact forces in a three dimensional static piling of identical, stiff and frictionless spheres. The pile studied is a pyramid of equilateral triangular base (" stack of cannonballs ") with a FCC (face centered cubic) structure. We show in particular that, as for the two dimensional case, the pressure on the base of such a pile is uniform. The force propagation through a heap of granular materials is a controversial issue (see refs. [1, 2] and references herein) and still attracts much attention. Experiments in conical sand piles show the existence of a depression in the normal force on the base (a dip) under the pile's apex rather than the intuitively expected maximum [3, 4]. Much work has been done in this subject in order to explain this effect numerically and theoretically. Most of the results obtained in this domain are for models considering two dimensional (2D) piles of discs or It is unclear however, whether in general, these results can be directly generalized to three dimensions (3D). In the case of the continuum approach proposed in ref. [13] it was noticed that the choice of the second closure equation needed for the 3D case did not have an important impact on the results obtained, so that the 2D results survive the passage from 2 to 3 dimensions. This case is a priori unlikely when discrete models are considered. One difficulty might be that a simple 3D extension of a 2D pile, which is obtained by a revolution around the symmetry axis of a 2D pile is not any regular 3D piling of spheres but rather a 3D piling of tori. Another possible 1