Reply to the discussion by Wang and Dallo on “Hydraulic conductivity of saturated granular soils determined using a constriction-based technique” 1Appears in the Canadian Geotechnical Journal, 49(10): 1221–1222 [doi:10.1139/t2012-078

Abstract

1. Equation [6] has been typed incorrectly and the correct equation is indeed the one given by the Discussers. The correct equation and its derivation have been given in the Ph.D. thesis of co-Author Nguyen (2012), and the computer program uses the correct equation. A corrigendum has already been submitted to the Canadian Geotechnical Journal giving the correct equation, which has subsequently been published (Indraratna et al. 2012). 2. The papers by Silveira (1965), Silveira et al. (1975), and Locke et al. (2001) discuss various aspects of the constriction-size distribution (CSD) corresponding to a given particle-size distribution (PSD). Locke’s (2001) Ph.D. thesis at the University of Wollongong extended the classical work of Silveira (1965) and Silveira et al. (1975) considerably. However, papers published later by Indraratna and Raut (2006), Indraratna et al. (2007), and Raut and Indraratna (2008) further extended the work of Locke et al. (2001) by introducing the novel concept of critical constriction size, Dc35. The Discussers have clearly overlooked the most important aspect that these recent papers have proposed in terms of critical constriction size for the accurate assessment of filtration effectiveness. 3. The Authors agree with the Discussers that the Kozeny– Carmen (KC) equation cannot be applied unless the void ratio is known or assumed. As the void ratios were not provided in past studies, the Authors employed the approach proposed by Aberg (1992) for the determination of the void ratios based on the PSD and associated relative densities. Given that this technique takes into account the compacted density in addition to PSD, indirectly, it can be considered equivalent to the CSD approach. 4. In this study, the Authors used the KC equation (eq. [2] in the paper) that is mathematically arranged to obtain another form (Carrier 2003) in which the shape factor, SF, captures the angularity ranging from 6.0 to 8.4. As the materials used for testing were mainly sand of high angularity, and having calibrated the experimental data for a range of SF values, the Authors determined SF 8.4 to be the most appropriate value for the KC equation for these angular sand particles. Any value of SF less than 8.4 within the range presented above will induce significant discrepancies (overprediction) when using the KC equation. Therefore, the data presented in Table 3 are related to SF 8.4. SF 1.36 cited by the Discussers is not appropriate for any realistic sandy material that contains predominantly angular grains. 5. The Authors agree that if the specific surface area is determined accurately, the predictions using the KC equation are proper. However, in this manner, using the KC equation requires more dependence and calibration using laboratory data, and this in itself shows the disadvantage of the KC equation. Empirically, SF needs to be estimated, presenting the inaccuracies of this approach. Therefore, the Discussers are correct in pointing out that poor predictions can be encountered if the surface areas of silty sands and similar particle gradations are not properly evaluated. Besides, for highly anisotropic materials, the KC equation hardly gives an accurate estimation of the hydraulic conductivity, and for materials such as uniform fine sand that are closer to being isotropic in pore distribution, Chapuis and Aubertin’s (2003) statement “. . . the KC equation provides good predictions for vertical hydraulic conductivity . . .” makes little sense. For very small particles, the Melvern particle-size analyser and other electronic and laser techniques are now being used for better estimation of the surface areas of particles.