Derivation of an Explicit Form of the Percolation-Based Effective-Medium Approximation for Thermal Conductivity of Partially Saturated Soils

Thermal conductivity is an essential component in multi-physics models and coupled simulation of heat transfer, fluid flow and solute transport in porous media. In the literature, various empirical, semi-empirical, and physical models were developed for thermal conductivity and its estimation in partially saturated soils. Recently, Ghanbarian and Daigle (GD) proposed a theoretical model, using the percolation-based effective-medium approximation, whose parameters are physically meaningful. The original GD model implicitly formulates thermal conductivity λ as a function of volumetric water content θ. For the sake of computational efficiency in numerical calculations, in this study we derive an explicit λ(θ) form of the GD model. We also demonstrate that some well-known empirical models, e.g., Chung-Horton, widely applied in the HYDRUS model, as well as mixing models are special cases of the GD model under specific circumstances. Comparison with experiments indicates that the GD model can accurately estimate soil thermal conductivity