Numerical Re-Analysis of Natural Heat Convection Tests to Assess the Intrinsic Permeability of Rock-Fill

Abstract

Generally, heat transfer in soils is governed by conduction. In rock-fill materials, however, the pore sizes are large enough to promote heat convection from the motion of air under pressure gradient (forced convection) or temperature gradient (natural convection). It has been found that convection significantly influences the heat transfer in rock-fill embankments such as railways, roadways and embankment dam in cold regions. The material characteristics that influence the most the rate of convection heat transfer is the intrinsic permeability. In a previous study, Cote et al. (2011a) developed a heat transfer cell where natural convection conditions were applied to 1 m³ rock-fill samples in order to establish their intrinsic permeability. They analysed the experimental data using an analytical relationship between the Nusselt number (Nu) and the Rayleigh number (Ra). This theoretical relationship is valid for perfectly insulated and impervious 2-dimensional square enclosure. As shown by the deviation from intrinsic permeability models for porous materials, the use of the theoretical relationship as induces a bias in the experimental intrinsic permeability values. In this paper, the heat transfer within the actual experimental heat transfer cell is analysed using numerical modelling of natural convection allowing to account for heat transfer in and out the imperfectly insulated cubic cell. A new Nu-Ra relationship is developed for this experimental setup. The previous experimental data are re-analysed according this Nu-Ra relationship in order to establish more accurate intrinsic permeability for values for the studied rock-fill materials. The results are compared to existing permeability models.