Eur. Phys. J. B 8, 389-397 (1999)
https://doi.org/10.1007/s100510050704

Force distribution in an inhomogeneous sandpile

Loughborough University, Department of Mechanical Engineering, Loughborough LE11 3TU, UK

Received: 29 January 1998
Revised: 7 September 1998
Published online: 15 April 1999

Abstract

The force perturbation field in a two-dimensional pile of frictionless gravity-loaded discs or spheres arising from lattice distortions is derived to first order. The starting point is the model proposed by Liffman et al. (Powder Technology (1992) pp. 255-267) and Hong (Phys. Rev. E 47, 760-762 (1993)) in which discs of uniform size are arranged on a regular lattice: this predicts a uniform normal stress distribution at the base of the pile. The analysis is applied to two problems: (i) deformable (rather than rigid) grains that undergo Hertzian deformation at the points of contact; (ii) a pile containing a gradient in particle size from the centre to the free surfaces. The former results in the classical pressure dip at the centre; the latter also produces a dip if the larger particles are at the centre.