A Series-Parallel Model for Estimating the Thermal Conductivity of Unsaturated Soils

Abstract

The effective thermal conductivity of unsaturated soils was estimated by an enhanced series-parallel model of conduction heat flow through a unit cell of soil. The cell is composed of three heat flow paths: solid contacts, solids + miniscule pores (filled with air and water, both parallel to heat flow direction), and a fluid path (water and air). The two basic characteristics of the soil cell, namely, the solid contact path volume fraction and the miniscule pore volume fraction, were estimated by simultaneously solving the model expressions at dryness and saturation with known measured thermal-conductivity data at these two states. In addition, the model utilized data on the thermal conductivity of soil solids and the degree of saturation of miniscule pores. The degree of saturation of miniscule pores was modeled as a function of the degree of saturation of the soil with a miniscule pore water retention factor. Water and air, in the fluid path, were modeled as being arranged in series or in parallel to the direction of heat flow. The model was calibrated using experimental thermal-conductivity data of five soils of different texture (coarse, medium, and fine). Then, empirical relations for all the model parameters were developed. The obtained thermal conductivity estimates of tested soils closely follow experimental data.