Establishment of generalized soil-water characteristic curve theoretical model considering two stress state variables for unsaturated soils

Abstract: As one of the fundamental soil-water modeling equations, soil water characteristic curve (SWCC) equation is widely employed to study soil-water retention, permeability and strength characteristics in the fields of agricultural engineering, environmental engineering, geotechnical engineering, etc. In this study, we evaluated the current classic SWCC equations and proposed a generalized SWCC model. By summarizing the current models, we found that the current model considered only a single or two influential factors, the forms of the current equations were complex, they were sensitive to experimental data and the fitness accuracy was highly dependent on the numbers of the experimental points. And most of them couldn’t deal with the conditions of multimodal pore-size density probability function and hydro-mechanical coupling effects for the solid-liquid-gas materials in soil. Based on Fredlund et al’s two stress variables theory and van Genuchten’s soil-water characteristic equation, the concept of generalized SWCC was defined. Three characteristic suction zones included boundary-effect zone, transition zone and residual zone of unsaturation. We defined the generalized SWCC as spatial curves reflecting relationship between matric suction and soil water content under the condition affected by multiple factors such as pore structure, stress history and stress state. The relative volumetric water ratio was proposed. The stress history was expressed with initial void ratio and the stress state was described with void ratio. Thus, the relative volumetric water ratio was defined as a ratio of water content-related function and initial volume. Relative fluctuated volumetric water content was defined as the difference of volumetric water content and residual volumetric water content. Based on the relative fluctuated volumetric water content, the relative volumetric water ratio was expressed as the other form. Then, the figure of net normal stress-logarithm of matric suction-logarithm of relative volumetric water ratio corresponding to the characteristic suction zones was plotted. A good linear relationship (r>0.90, P<0.05) was found among the net normal stress, logarithm of matric suction and logarithm of relative volumetric water ratio. Thus, the generalized two stress state bimodal SWCC model was derived, which considered the multimodal pore-size density probability distribution function and soil deformation. Compared with the 2-parameter Brooks et al’s equation, 3-parameter van Genuchten equation as well as the 4-parameter Fredlund et al’s equation, the proposed generalized SWCC only had 3 parameters, 2 of which could be obtained by least-square linear fitting method in the plane of log-log coordinate system of relative volumetric water ratio versus matric suction and only one of which would be achieved by the nonlinear least-square fitting method. The model fitness needs at least 3 experimental points. The model provides with a new way to predict the soil-water retention, permeability, strength of soil quantitatively in an easier and timesaving process.