A bounding surface hysteretic water retention model for deformable soils

The paper presents a soil water retention model that takes into account the effects of void ratio and hydraulic hysteresis on the variation of degree of saturation. Based on a modified form of the van Genuchten equation, the model defines two bounding surfaces, namely a main drying surface and a main wetting surface, which delimit the region of admissible soil states in the space of degree of saturation, suction and void ratio. Suction and void ratio are then combined into a single auxiliary variable, termed scaled suction, and the main surfaces are recast as main curves in the plane of degree of saturation and scaled suction. The effects of both suction and void ratio on the drying/wetting behaviour of the soil are simply incorporated by relating degree of saturation to scaled suction. The soil is dried when the scaled suction is increased and is wetted when the scaled suction is decreased. The model assumes that, inside the region of admissible soil states, the derivative of degree of saturation with respect to the scaled suction depends on the distance of the soil state from the main curves. This assumption ensures a smooth transition of the drying and wetting paths towards their respective main curves. Interestingly, the derivative of degree of saturation with respect to scaled suction can be integrated in a closed form and all wetting and drying paths can therefore be described by two explicit equations (one for drying paths and one for wetting paths), where different wetting or drying paths are characterised by different values of the integration constant. The integration of the model in a closed form facilitates its implementation into numerical codes. The model requires seven parameters, whose values can be obtained from a single drying-wetting test. Predictions are validated against two different data sets published in the literature, which shows the capability of the model to capture the behaviour observed during laboratory tests on fine-grained soils.