An effective thermal conductivity model for unsaturated compacted bentonites with consideration of bimodal shape of pore size distribution

Abstract

An effective thermal conductivity model was proposed for unsaturated compacted bentonites with consideration of the bimodal shape of pore size distribution curves. The pores of soils were grouped into two dominant pore size modes corresponding to the intra- and inter-particle pores, and were simulated with randomly distributed spheroidal inclusions of different aspect ratios. With the assumption of preferential invasion of the wetting fluid (water) into pores of smaller sizes and by virtue of the analytical solution to the inhomogeneous inclusion problem in heat conduction, the model was developed using the Mori-Tanaka (MT), Ponte Castaneda-Willis (PCW) and self-consistent (SC) homogenization approaches for different considerations of the interactions between pores and the solid phase. The proposed model is functions of the thermal conductivities of the solid, liquid and gas phases, porosity, the degree of saturation, the aspect ratios of pores and/or soil particles, and the fraction of the smaller group of pores. The proposed model was validated against five sets of laboratory measurement data on the MX-80, FEBEX, Kunigel-V1 and GMZ01 bentonites, showing a good agreement between the model predictions and the laboratory measurements. The responses of the model with respect to the geometries of pores and solid particles were examined. Compared to series-parallel structural models, the proposed model may overall exhibit better performance if proper homogenization schemes are adopted, but as an advantage, the model has clearer physical mechanisms and a smaller number of parameters.