Pressure-dependent elastic moduli of granular assemblies

Conventional homogenization theories developed for a matrix-inclusion system cannot be used for deriving the pressure-dependent elastic behaviour of a granular material. This is caused by the lack of a proper description of the high stress concentrations at the particle contacts. This paper discusses a more suitable homogenization theory, which follows from micro-structural considerations at the particle level. Accordingly, for an assembly of isotropically distributed, equal-sized spherical particles, expressions for the pressure-dependent shear modulus and the Poisson's ratio are derived. This is done for the case of hydrostatic compression. The derivation of these equations is based on the so-called best-fit hypothesis of the actual displacement field in the granular assembly. The usefulness of the equation derived for the shear modulus is illustrated via a comparison with experiment results. Copyright © 2000 John Wiley & Sons, Ltd.