A Simple Thermal Conductivity Model for Unsaturated Geomaterials Accounting for Degree of Saturation and Dry Density

Abstract

This paper proposes a simple thermal conductivity model for geomaterials accounting for the combined effect of both degrees of saturation and dry density. The model only requires the determination of the thermal conductivity under dry conditions (i.e., at a degree of saturation equal to zero) and as little as two additional measurements of thermal conductivity performed at different levels of degree of saturation and dry density. The model is a function of only two fitting parameters, namely the moisture factor {m}_{f} and the density factor {m}_{d}. Despite its simplicity, the model can correctly predict the thermal conductivity of geomaterials and this has been validated against five sets of experimental data obtained on a very broad range of materials ranging from fine (e.g., bentonite) to coarser soils (e.g., a mix of gravel, coarse sand and silt) tested at different levels of degree of saturation and dry density. The paper also shows that the model can be applied to different engineering contexts such as (a) the thermal behaviour of earth materials used for building construction, (b) the thermal performance of bentonites employed for the storage of nuclear waste and (c) the estimation of the heat exchange in shallow geothermal reservoirs. Finally, the proposed model can be easily implemented in a finite element code to perform numerical simulations to study the heat transfer in unsaturated geomaterials.