Validating the Generality of a Closed-Form Equation for Soil Water Isotherm

Total soil water potential ${\psi }_{\mathrm{t}}$ is conventionally defined as the sum of matric potential ${\psi }_{\mathrm{m}}$ and osmotic potential ${\psi }_{\mathrm{o}}$, i.e., ${\psi }_{\mathrm{t}}={\psi }_{\mathrm{m}}+{\psi }_{\mathrm{o}}$, when gravitational potential is ignored. Soil water isotherm (SWI) is the constitutive relationship between ${\psi }_{\mathrm{t}}$ and soil water content $w$, i.e., ${\psi }_{\mathrm{t}}(w)={\psi }_{\mathrm{m}}(w)+{\psi }_{\mathrm{o}}$, where ${\psi }_{\mathrm{m}}(w)$ is called soil water retention curve (SWRC) or soil water characteristic curve. SWI and SWRC are arguably the two most important soil constitutive relationships because they govern virtually all phenomena in soil such as flow, stress and deformation, and biological activities. A closed-form SWI, recast from a generalized SWRC equation for adsorption and capillarity, is experimentally validated for its generality in representing SWI. Adsorption isotherms of 49 soils, covering all spectrum of soil types with plasticity index up to 185% and specific surface area up to ${600\mathrm{m}}^2/\mathrm{g}$, are used to validate the SWI equation. It is shown that the SWI equation can nearly perfectly represent the isotherms of these soils with almost all of the coefficients of determination $R^2\ge 0.99$, validating the generality of the SWI equation. Comparative analysis is also conducted by using two existing SWI equations, namely, the Brunauer–Emmett–Teller (BET) equation and the augmented BET (A-BET) equation. It is demonstrated that the SWI equation is superior to the BET and A-BET equations in representing soil–water interactions by adsorption and capillarity, and in the full relative humidity range.