Clastic Soil Mechanics

Glenn R McDowell, Cambridge University, Geotechnical Engineering Group

**Abstract**

A study has been made of the micro mechanical origins of hardening in aggregates which comprise elastic-brittle grains. The compression of an aggregate of uniform grains is considered, and hardening at very small strains is explained in terms of elastic contacts between particles. In the discipline of soil mechanics the terms "yielding" and "plastic hardening" are used to describe the post-elastic behaviour of granular media. These "plastic" phenomena are here related to the splitting of grains. The term "clastic yielding" is used to describe the onset of grain fracture, which is followed by "clastic hardening", whereby particles split probabilistically depending on the applied macroscopic stress and the coordination number and size of each particle. When the effect of co-ordination number dominates, a simple numerical model confirms published findings that compression of the aggregate leads to the evolution of a fractal distribution of particle sizes.

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 "normal" 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.

The behaviour of "overconsolidated soil" is examined by considering the isotropic unloading and reloading of an isotropically normally compressed soil. The unload-reload behaviour of such a material is strongly affected by the disparity in sizes of neighbouring particles. A simple micro mechanical model provides a commentary for overconsolidated behaviour, such that on unloading, elastic behaviour is followed by "kinematic yielding", which is the onset of grain sliding. On reloading, kinematic yielding may not occur, but inhomogeneous stresses may induce "clastic yielding" early, leading to compaction on cyclic loading if the pores are drained.

**Keywords:** clastic, normal compression,
fractal, probability of fracture, compression index, particle size disparity, kinematic
yielding, micro mechanics