Robust calibration and evaluation of a percolation-based effective‐medium approximation model for thermal conductivity of unsaturated soils

Abstract

Thermal conductivity (λ) is a property characterizing heat transfer in porous media, such as soils and rocks, with broad applications to geothermal systems and aquifer characterizations. Numerous empirical and physically-based models have been developed for thermal conductivity in unsaturated soils. Recently, Ghanbarian and Daigle (G&D) proposed a theoretical model using the percolation-based effective-medium approximation. An explicit form of the G&D model relating λ to water content (θ) and equations to estimate the model parameters were also derived. In this study, we calibrated the G&D model and two widely applied empirical λ(θ) models using a robust calibration dataset of 41 soils. All three λ(θ) model performances were evaluated using a validation dataset of 58 soils. After calibration, the root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R2) of the G&D model were 0.092 W−1 m−1 K−1, 0.067 W−1 m−1 K−1 and 0.97, respectively. For the two empirical models, RMSEs ranged from 0.086 to 0.096 W−1 m−1 K−1, MAEs from 0.063 to 0.071 W−1 m−1 K−1, and R2 values were about 0.97. All three metrics indicated that calibration improved the performance of the G&D model, and it had an accuracy similar to that of the two empirical λ(θ) models. Such a robust performance confirmed that the theoretically-based G&D model can be applied to study soil heat transfer and potentially other related fields.

Keywords

• Percolation-based effective-medium approximation
• Saturation
• Thermal conductivity
• Water content