Force distribution in an inhomogeneous sandpile
Loughborough University, Department of Mechanical Engineering,
Loughborough LE11 3TU, UK
Revised: 7 September 1998
Published online: 15 April 1999
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.
PACS: 81.05.Rm – Porous materials; granular materials / 46.10.+z – Mechanics of discrete systems / 83.70.Fn – Granular solids
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999