A micro mechanical model for isotropic cyclic loading of isotropically clastically compressed soil

This paper presents a simple micro mechanical model for the behaviour of overconsolidated soils. The simplest case of isotropic unloading and reloading is considered for a soil which has been subjected to isotropic plastic (clastic) or "normal" compression. Such a material has a wide disparity in particle sizes, such that small particles are kinematically unstable, and large particles are stable. A simple unit cell is defined with one of the largest grains at the centre, surrounded by a fractal matrix of finer particles. On unloading, the unit cell exhibits elastic behaviour followed by "kinematic yielding", which is the onset of sliding of grains. On reloading, kinematic yielding may not occur, but the inhomogeneous stresses in the cell may induce "clastic yielding" before re-joining the normal compression line. The unit cell is shown to reproduce micro mechanical features of a real aggregate having particle size disparity, and leads to realistic hysteresis loops which permit possible ratchetting on cyclic loading. A simple dilatancy rule is shown to offer micro mechanical insight into the form of the unloading curves evident in much of the soil mechanics literature.