Model of soil thermal conductivity in the form of a truncated sphere

The model is designed for a three-phase soil system: mineral part, water, and air. The model's input parameters are porosity and water saturation coefficient, which characterize the volumetric ratio of the main components in the soil. The soil thermal conductivity model is represented as a sphere of the mineral part in the sphere of water. A cube - a unit volume, truncates both spheres. The main design parameters are the radii of the spheres of water and air. A single volume was divided into several heat flow paths with the same set of soil components, for each of which the thermal conductivity was calculated as for a multilayer wall. The total thermal conductivity was calculated by averaging, taking into account the cross-sectional areas of each of the paths. Depending on the values of the design parameters and their relationship, the model has identified three design cases. An analytical solution is obtained for each design case. Comparison of the calculation results using the developed model showed good agreement with experimental data and existing thermal conductivity models.