A homogenization-based model for estimating effective thermal conductivity of unsaturated compacted bentonites

Abstract

A homogenization-based effective thermal conductivity model was proposed for unsaturated compacted bentonites. The microstructure of soils was approximated with pores of spheroidal shape, diverse sizes and random orientation, and solid matrix of homogeneous properties (or soil particles of the same assumptions with pores for the self-consistent approach). With the consideration of preferential invasion of the wetting fluid (water) into pores of smaller sizes and by virtue of the analytical solution to Eshelby’s inclusion problem in heat conduction, the model was developed using homogenization techniques such as the dilute, Mori–Tanaka (MT), interaction direct derivative (IDD) and self-consistent (SC) schemes for different consideration of the interactions between pores and the solid phase. The proposed estimates are dependent on the thermal conductivities of the solid, liquid and gas phases, porosity, the degree of saturation, and the aspect ratios of pores and/or soil particles. The proposed model was validated against five sets of laboratory measurement data on the MX-80, FEBEX, Kunigel-V1 and GMZ01 bentonites. Compared to Chen’s series–parallel structural model recently developed for unsaturated compacted bentonites (Chen et al., 2014), the proposed model not only overall exhibits better performance, but as a great advantage, has much clearer physical mechanisms and significantly reduces the number of parameters by three or four, depending on the homogenization schemes adopted. It is demonstrated that the predictions by the MT, IDD and SC schemes strictly fall within the Weiner bounds and the Hashin–Shtrikman bounds over the full range of porosity and saturation, with the SC estimates overall having slightly better performance than the MT and IDD estimates.