A non-linear hysteresis model for soil-water retention behaviour

Hysteresis is common in soil-water phenomena, and the soil-water retention relationship is not a one-to-one relationship between the effective degree of saturation and the matric suction. Existing theoretical soil-water retention models are usually derived by applying a capillary law that does not depend on the contact angle to the cumulative distribution function of soil pores. These theoretical models usually contain equations only for the main drying and wetting branches, so additional empirical scanning laws are needed to model hysteresis behaviour between these branches. This paper proposes a contact angle-dependent model in incremental form to reproduce soil-water hysteresis behaviour. The change in suction during scanning wetting and drying processes leads to a change in both the effective degree of saturation and the liquid-solid contact angle. An allocation proportion function is proposed to divide suction increments into two parts, one of which is allocated to the change in the effective degree of saturation and the other consumed by changing the contact angle. The proposed hysteresis model contains only four parameters that can be conveniently calibrated by the main drying branch and a scanning wetting curve. Test results are included to validate the proposed hysteresis model.