A three-dimensional hysteretic soil-water retention curve

One of the most important features in unsaturated soil mechanics is the soil-water retention curve and its coupling to the mechanical component of soil behaviour. It has long been recognised that the retention curve exhibits significant hysteresis, and that it is affected by the specific volume. Several attempts have been made in the past to model this behaviour. A novel approach is proposed herein, which accounts for both the hydraulic hysteresis and the specific volume dependence of the retention relationship in a three-dimensional formulation. The primary and the scanning paths are simple geometric curves, which have a common tangent at the point of intersection, ensuring a smooth transition from scanning to primary paths. A small number of parameters are required to define the primary paths, and no fitting parameters are necessary for generation of the scanning paths. As knowledge of the specific volume and its variation is required, the retention model needs to be employed in conjunction with a constitutive model capable of reproducing the complex behaviour of unsaturated soils. To guarantee consistency with the retention model, the degree of saturation needs to be incorporated in the specific volume–suction relationship adopted within the constitutive model. To accommodate such a feature when absent, a new expression for the soil compressibility with suction as a function of the degree of saturation is proposed. Simulations of laboratory experiments on unsaturated soils, involving cyclic changes of applied suction, demonstrate the effectiveness of the proposed modelling approach.