Discussion of "Analytical and numerical solutions for a single vertical drain including the effects of vacuum preloading"

The authors are to be congratulated on presenting four solutions for the average excess pore pressures of axisymmetric and plane strain unit cells; in these solutions, two solutions are under conventional surcharge preloading condition (eqs. [2a] and [4a]) and the other two are under vacuum-surcharge preloading condition (eqs. [20] and [23]). For matching the equivalent plane strain and axisymmetric unit cells under vacuum-surcharge preloading, the authors equated eq. [20] with eq. [23] under the condition that the vacuum pressure applied to the plane strain cell is equal to that of the axisymmetric cell (eq. [28]). By doing so, they obtained eq. [25] that shows the relationship between the equivalent plane strain and axisymmetric permeability coefficients. However, regarding this equation, there are some points that need further discussion. Tran and Mitachi 1403 The authors wrote that “The equivale t vacuum pressure can be determined by eq. [28]”; therefore, we understand that choosing the equivalent vacuum pressure for the plane strain unit cell equal to that of the axisymmetric unit cell is one of many ways. However, we think that eq. [28] may be the only way. That is because if the vacuum pressure applied to the plane strain cell was not equal to that of the axisymmetric cell, then when we equate eq. [20] with eq. [23] we would be unable to obtain an explicit equation between the plane strain and the axisymmetric permeability coefficients as eq. [25]. Therefore, eq. [25] is the only explicit equation to determine the equivalent permeability in plane strain condition for the vacuum-surcharge preloading problem. On the other hand, under the conventional surcharge preloading condition, the authors modified two solutions for the average excess pore pressure, one of Hansbo (1981) for the axisymmetric unit cell, and the other one of Indraratna and Redana (2000) for the plane strain unit cell; these two modified solutions are eqs. [2a] and [4a]. It can be shown that, by equating these two solutions, an equivalent permeability equation for the plane strain unit cell is obtained, and this equation is the same as eq. [25] in the paper. Therefore, eq. [25] appears to be the same solution under both conventional surcharge and vacuum-surcharge preloading conditions.

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