Hysteretic model for fitting soil-water characteristic curves considering contact angle and grain-size distribution

The soil-water characteristic curve (SWCC) describes the relationship between water content (or saturation) and matric suction (or soil-water potential) in unsaturated soils. It is worth noting that the amount of water stored in soils during the drying process caused by evaporation or gravity drainage is more than that during the wetting process caused by infiltration and capillary rise under the same matric suction level. This phenomenon is described by the hysteretic behavior of the SWCCs. Based on existing knowledge, the contact angle and the ink-bottle effect caused by the grain-size distribution (or pore-size distribution) are the two main factors that affect the hysteretic behaviors of the SWCCs. First, the behaviors of a liquid drop sitting on an inclined surface are investigated by the numerical method, and a relationship between the contact angle and the water content during the wetting and drying processes is proposed based on the principle of the minimum potential energy. Second, the expression for the volume of the liquid bridge is modified to make the Young-Laplace equation keep valid in calculating the matric suction in the boundary affected zone, transition zone and the part of the residual zone on the w-lns plane. Finally, an analytical model for analyzing the hysteretic behaviors of SWCCs is proposed after introducing the Roshin-Rammler grain-size distribution function. The model has a clear physical meaning, and the parameters can be obtained easily. Moreover, the model can describe the hysteretic behaviors of the SWCCs. Taking the SWCC of recompacted loess in a foundation pit in Qujiang, Xi'an as an example, the model is verified. The results show that the proposed model can well reflect the nonlinear relationship between the matric suction and the water content. The model can also be used for studying the shear strength and the constitutive model for unsaturated soils.