A continuous hyperplasticity model for sands under cyclic loading

Soils exhibit truly elastic behaviour at only very small strains, so that cycling at small to moderate strains involves hysteretic behaviour. As the amplitude of cycling increases the secant modulus decreases and the damping ratio increases. These facts are well established experimentally, but theories that successfully describe this behaviour are less well developed. We present here a simple model for the behaviour of sand under cyclic loading, that is able to capture the main features of small-strain cycling. An essential part of the model is that volume changes (or effective stress changes in the case of undrained loading) are modelled realistically. The model is described using the "continuous hyperplasticity" framework. Essentially this involves an infinite number of yield surfaces, thus allowing smooth transitions between elasticity and plasticity. The framework allows soil models to be developed in a relatively succinct mathematical form, since the entire constitutive behaviour can be determined through the specification of two scalar functionals. Dilation and compression is incorporated through the use of kinematic constraints, and dilation is accompanied by the development of anisotropy in the sand.