New model to evaluate the effective thermal conductivity of three-phase soils

The aim of the present paper is to present a new model without empirical constants to evaluate the effective thermal conductivity of three-phase soils. In the model the soil is made of a quasi-spherical solid grain, and is surrounded by two phases, which can be air and water or air and ice. The effective thermal conductivity is obtained theoretically by the integration of the steady-state heat conduction equation under the thermal assumption of parallel heat fluxes. This new model allows to evaluate the effective thermal conductivity of soils with porosity (ratio between the volume of the voids and the total one) in the range between 0.0349 and 0.4734 at all degrees of saturation (ratio between the water volume and the void one) from dryness up to saturation. Comparisons with experimental data of unfrozen and frozen soils confirm that the model can predict the effective thermal conductivity with a fairly good agreement without using any empirical constant.