Derivation and Validation of a New Soil Pore-Structure-Dependent Flux–Saturation Relationship

Recently, a method based on the soil water flux (F)–saturation (Θ) relationship, F(Θ), assumed to be independent of time and soil properties, has become an important technique to simplify solving Richards’ equation so as to develop a simple, rapid, and low-cost approach to estimate soil hydraulic properties. However, the actual F(Θ) is soil pore-structure dependent. So far, there exists no theory that can provide a specific functional form of soil pore-structure-dependent F(Θ). In this research, we derived a general soil moisture profile function and then a general expression of F(Θ): F = Θ[1 + a₂(1 − )]. The only parameter in F(Θ), a₂, is a function of the initial soil water saturation and the soil pore structure index that reflects the shape of the soil water retention curve. Infiltration experiments with three test soils and four actual soils were conducted to test the proposed relationships. The results verified the independence of F(Θ) on time at small time scales. The results also indicated that the derived formula predicted F(Θ) in good agreement with what was measured for all test soils under different initial soil moisture conditions. In addition, the upper and lower limit curves of F(Θ) calculated by the proposed formula were consistent with the theoretical curves. Compared with other empirical relationships, the new formula was the best for describing the theoretical upper limit curve of F(Θ). Furthermore, the new theoretical relationship was also found to be appropriate for horizontal absorption. Generally, the developed relationship is more accurate and helpful to solve Richards’ equation.