The fractal crushing of granular materials

A study has been made of the micro mechanical origins of the irrecoverable compression of aggregates which comprise brittle grains. The terms ''yielding'' and ''plastic hardening'' are used in the discipline of soil mechanics to describe the post-elastic behaviour of granular media. These ''plastic'' phenomena are here related to the successive splitting of grains. Grains are taken to split probabilistically, the likelihood increasing with applied (macroscopic) stress, but reducing with any increase in the co-ordination number and with any reduction in particle size. When the effect of the co-ordination number dominates, a simple numerical model confirms published findings that a fractal distribution of particle sizes evolves from the compression of an aggregate of uniform grains. Taking the production of new surface area from the particle size distributions produced by the numerical model, a work equation is used to deduce the plastic compression of voids, for one-dimensional compression of the aggregate. This too is shown to be in agreement with experimental data, and in particular confirms the linearity of plots of voids ratio versus the logarithm of stress. The gradient of these plots is for the first time related to fundamental material parameters. Copyright (C) 1996 Elsevier Science Ltd.