Reply to the discussion by Chapuis, Weber, and Duhaime on “Intrinsic permeability of materials ranging from sand to rock-fill using natural air convection tests” 1Appears in the Canadian Geotechnical Journal, 49(11): 1319–1322 [doi:10.1139/t2012-073

Abstract

The authors thank the discussers for their interest in this paper and for expanding and updating a previous discussion on representative elementary volume (Chapuis et al. 2006). We also appreciate the opportunity to clarify some issues of our experimental method and to introduce a recent updated analysis of our experimental data. The experimental determination of permeability of rock-fill materials represents a challenging task. It was shown in the paper that hydraulic permeability tests were mostly inappropriate because turbulent flow dominates (even under very low hydraulic gradients) and Darcy’s law is thus not valid. Natural air convection testing within a heat transfer cell was therefore selected to overcome this issue. The intrinsic permeability was obtained using the well-established analytical solution to natural convection in a square enclosure of Schubert and Straus (1979). The study clearly showed that the inferred intrinsic permeability values were well within the narrow bounds formed by the extrapolation of two predictive equations previously established to estimate the permeability of sands. The discussers acknowledged that these were amongst the best equations to predict permeabilities of nonplastic materials. These results are excellent given the somewhat untypical and innovative experimental testing method and given that the predicting equations had to be extrapolated 3 to 5 orders of magnitude higher than the typical permeability range of sands for which these equations were validated. For example, predictions from Chapuis’ (2004) equation were on average only 2.5 times lower than the inferred permeability values. The discussers focused on specimen representativeness and support their thoughts with studies on arrangements of spheres — arrangements known to have marked sidewall effects. This is definitely not representative of our study. The specimens in the paper were made of randomly shaped natural cobbles that were hand-placed one by one into the heat transfer cell (see Fig. 5 in companion paper by Fillion et al. 2011). This allowed obtaining homogeneous specimens. For example, a particle placed on one edge of the cell had its flattest side facing out, greatly reducing sidewall effects. Horizontal sand blankets were also put on the top and bottom of the heat transfer cell, further eliminating sidewall effect and ensuring optimized thermal contact with the heat transfer systems. Bias due to specimen preparation can thus be considered as insignificant. In a recent study (Dhyser et al. 2012), it was demonstrated that the analytical solution to natural convection induced a slight overestimation of permeability values. The analytical solution used at the time of the study was developed for a perfectly insulated and impervious square enclosure. The heat transfer cell was air-tight, but did not meet the perfectly insulated boundary condition of the Schubert and Straus (1979) solution. In the new study, a numerical solution to natural convection (heat and mass transfer) within a domain representing the experimental cell was developed. This numerical solution was used to re-evaluate the permeability values from the original test results. It turns out that the newly inferred permeability values are now very close to the estimated ones using Chapuis’ (2004) equation, as shown in Fig. R1. The new values are now within the 0.5–2 times precision range found by Chapuis (2004). It can therefore be concluded that the original bias between the experimentally inferred permeability values and the predicted ones was due mostly to a preliminary assessment using an analytical solution to convection heat transfer. A more accurate numerical solution adapted to the experimental heat