A Homogenized-Based Model for Estimating the Thermal Conductivity of Unsaturated Granular Soils

Granular soils are usually unsaturated consisting of solid particles, pore water, and air, and the thermal conductivity of unsaturated granular soils is a basic parameter for evaluating the deformation properties of geothermal structures. However, the natural physical properties, structure evolution, and heat transfer mechanism were not fully considered in previous work. To this end, the unsaturated soil is considered a mixture of matrix (consisting of solid particles and pore water) and air inclusion. In this study, an effective model is developed based on the homogenization method to estimate the thermal conductivity of three-phase granular materials. It is done by introducing a structure variable related to the evolving soil structure, and a structure parameter is adopted to evaluate the sensitivity of the structure variable to the fraction of inclusion, which is affected by the shape, dimension, and size-polydispersity of the matrix. The structure parameter decreases significantly with the rising degree of saturation at first (Sr = 0%–25%) but varies slightly with a degree of saturation beyond 25%. Considering the similarity between the structure parameter–saturation curve and soil–water characteristic curve, the structure parameter is defined in relation to the degree of saturation that is analogous to the classical soil–water characteristic curve. A thermal conductivity model is proposed by integrating the structure parameter into the homogenization equation. It is verified based on the test data extracted from literature studies, demonstrating strong predictive capability for the thermal conductivity of granular soils across a broad range of saturation.