Reply to the discussion by Dallo and Wang on “A new theoretical method to evaluate the internal stability of granular soils” 1Appears in the Canadian Geotechnical Journal, 49(7): 866–868 [doi: 10.1139/t2012-036

Abstract

In the original paper the authors proposed a new method to evaluate the internal stability of a granular soil. The method determines the critical diameter of suffusion, Dc, defined as the diameter of the largest particle passing across the constrictions of the soil solid skeleton. In particular, the method evaluates the constriction soil distribution (CSD) by the soil numerical percentage grain-size distribution. The discussers show instead their results in terms of the soil weight percentage grain-size distribution. They maintain that the CSDs in terms of the soil numerical percentage grain-size distribution have the same trend of the CSDs in terms of soil weight percentage grain-size distribution. Actually, the CSDs using the soil numerical percentage grain-size distribution are completely different from the CSDs using soil weight percentage grain-size distribution because the mass and number grain-size distributions are very different as demonstrated by several authors (Musso and Federico 1983; Moraci 1992). Equation [3] of the original paper has been applied to a values changing from amin to amax (eqs. [4] to [7] in the original paper) obtaining, for instance, the Sv(a) versus a curve shown in Fig. R1, for the case of four spheres shown in Fig. R2. For the case of the densest state, the minimum value Sv min is considered, while in the case of the loosest state, the maximum value Sv max is considered. For intermediate states of density, Sv values were determined by the a value using eq. [8] in the original paper. The CSD curves obtained by Simulfiltr for the dense and loose states show diameters of constrictions smaller than those obtained by the Silveira (1965) and Silveira et al. (1975) methods in terms of the soil numerical percentage grain-size distribution. This result is due to the different method used to evaluate the diameter of the equivalent circle of the constriction inside the groups of three or four particles. In the method proposed by the authors (Simulfiltr), the diameter of constrictions has been evaluated as the diameter of the equivalent circle in terms of the ratio of area to perimeter of void inside the group of contact spheres, following the ASTM (2002) D6767 standard, as follows: