Discussion of “A new theoretical method to evaluate the internal stability of granular soils” 1Appears in the Canadian Geotechnical Journal, 49(1): 45–58 [doi: 10.1139/t11-083

Abstract

The authors mention that the constriction size distribution curve (CSD) was obtained according to Silveira (1965), and this method takes into account only the loose or dense soil relative density. Actually the method of Silveira (1965) takes into consideration only the densest soil state (maximum relative density). In that method, groups of only three particles are considered. The relations presented by the authors belong to the Silveira et al. (1975) method, in which Silveira et al. consider groups of four particles to represent the loosest soil state (minimum relative density). Equation [3] (in the paper under discussion) is basically applicable for the loosest soil state. To check its applicability for determining the CSD of the densest state, analyses were carried out through a computer program written by the discussers originally to determine the CSD for the densest and loosest soil states according to Silveira (1965) and Silveira et al. (1975), respectively. The program results were verified with some published data (e.g., Silveira 1965; Soria et al. 1993; Indraratna et al. 2007) and exact solutions were obtained. Small modifications were made to that program to determine the CSD for the densest state using the procedure described in the paper under discussion, i.e., determination of the angle a, which gives the minimum void area, instead of determination of the maximum void area as suggested by Silveira et al. (1975). The results of the analysis are shown in Fig. D1, in which the CSD curves for the densest state of the method (in the paper under discussion) and the method of Silveira (1965) are compared — it is obvious that there is a considerable difference between the two methods. The results of laboratory tests performed by Soria et al. (1993) show good agreement with the theoretical procedure of Silveira (1965), so the discussers believe that eq. [3] (in the paper under discussion) can not be applied to the determination of the CSD in the densest state. It is worth mentioning that, for the sake of comparison, the CSD curves shown in Fig. D1 are based on the finer percentage by weight, in accordance with the analyses carried out by Silveira (1965). Analyses (not included here) based on the finer percentage by number of particles using eq. [1] (in the paper under discussion) showed the same trend. The authors suggest that the percentages of finer are computed using eq. [1] (in the paper under discussion); actually, that equation represents the percentage of finer based on the number of particles, which over-represents the finer constrictions. Humes (1996) suggested that the percentage of finer based on surface area can represent the filtration analysis more accurately, with the percentage of finer based on surface area, PSA, computed using 1⁄2D1 PSAi 1⁄4 Pmi=Di XN i1⁄41ðPmi=DiÞ