Approximate pore-scale model for the stagnant effective thermal conductivity of porous/granular geomaterials

This paper provides a novel geometric hypothesis, i.e. ortho-triangular prism unit cell, to estimate the stagnant effective thermal conductivity (ETC) of porous and granular geomaterials. At the pore-scale, the liquid phase in geomaterials is assumed as capillary water while the geometry of the solid particles and air phase is described respectively as quasi-spheres and residual space-filling bodies embedded in a trigonal prismatic unit cell. Following the homogenization theory of micro-mechanics, the model is physically and mathematically established using the lumped parameter thermo-electric analogy method, leading to an explicit formula for the ETC of geomaterials. The proposed new model overcomes the inherent spatial correction defects of the spherical and cylindrical unit cells used in previous upscaling models, and extends the applicability to a porosity of 0–0.6 and to unsaturated to fully-saturated media, which covers most natural soil-rock media (with void ratios up to 1.5). To validate the proposed model, the calculated values are compared with predictions from three kinds of previously developed models (hybrid model, cell model and empirical model), and with experimental values under different conditions. The results indicate that the error of the current model is significantly lower than those of previous unit cell models, in which the root mean squared error and normalized root mean squared error are respectively 0.358 W/(m•K) and 14.7 %, very close to those of empirical models. • An ortho-triangular prism unit cell was proposed to evaluate the ETC of geomaterials. • The model was deduced using the lumped parameter thermo-electric analogy method. • The model avoids spatial correction defect of spherical and cylindrical unit cells. • The model extends its applicability to a porosity of 0–0.6 for natural geomaterials. • Component and structure may have evolutionary effects on geomaterial's ETC.