A soil–water retention model with differentiated adsorptive and capillary regimes

Abstract

Knowledge of the soil–water retention curve (SWRC) is crucial for understanding the hydro-mechanical behaviour of unsaturated soils. Traditional SWRC models were developed based on bundles of cylindrical capillaries (BCCs) using a residual water content, but they failed to accurately describe water adsorption in the dry end of the curve. In this paper, a new soil–water retention model over full suction range explicitly accounting for adsorptive and capillary processes was developed. A new equation for adsorptive water retention curve (AWRC) was derived from the Dubinin’s theory for the water volume filling in micropores. A new equation for capillary water retention curve (CWRC) was developed by applying Young–Laplace equation to macro-pores with assumed Weibull pore size distribution (PSD). Meanwhile, with introduction of an anti-sigmoid condensation (or cavitation) probability function, the transition between the adsorption and capillary regimes was smoothly described. Then, by superposition of the AWRC and CWRC terms, a new SWRC model was proposed with seven physical parameters representing key characteristic states or rates of adsorption and capillarity. Finally, the robustness of the proposed model was verified against 269 SWRCs of 207 soils collected from the UNSODA 2.0 database and literature, involving various textures from clay to sand. For six representative soils, the proposed model performs better than three well-known existing models (VG, FX and Lu models). The differentiated adsorptive and capillary regimes of these soils accord well with the Lu model and experimental evidence. Of the seven model parameters, the estimated adsorption capacity ($S_{\text{ra}}^{\max }$) depends linearly on the volumetric proportion of micro-pores (e_m/e) and the capillary characteristic suction (ψ_c) relates to void ratio following a power law, while the remaining parameters are insensitive to variation of void ratio. Accordingly, the proposed model was successfully extended to predict SWRCs of soils with different void ratios.