Author Response to Comment on: Laboratory Measurement and Analysis of the Deteriorated Layer Permeability Coefficient of Soil-Cement Deteriorated in a Saline Environment

Abstract

The authors thank Rui Neves for his discussions related to our work. Errors in the formula have been corrected as suggested by the discusser and data in the article have also been revised.

1. Introduction

The authors thank Rui Neves for his discussions related to our work on the deteriorated layer permeability coefficient of soil–cement deteriorated in a saline environment. Based on the discussions with Prof. Neves, some formulates in the paper have been corrected [1]. We have responded in the following aspects.

2. Reply

The first response is regarding the lapse in the development of the formula to compute the permeability coefficient in a specimen with different media. We found that Equations (7)–(10) in original paper were wrong due to some errors in the calculation procedure. In the original paper, Equation (7) in original paper is achieved after substituting Equation (6) in original paper in Equation (4) in original paper, which are shown below.

$$k_{\mathrm{d}}=\frac{2k_{\mathrm{c}}{k}_{\mathrm{m}}d}{k_{\mathrm{m}}H-k_{\mathrm{c}}{H}_{\mathrm{m}}}$$

(1)

$$k_{\mathrm{m}}=k_0\left(1-R_{\mathrm{a}}\right)+k_d{R}_{\mathrm{a}}$$

(2)

where k_d is the permeability coefficient of deteriorated layer; k_c is the equivalent permeability coefficient of the entire deteriorated specimen; k_m is the equivalent permeability coefficient of the middle section of the specimen; H is the total height of the specimen; H_m is the height of the middle section; k₀ is the permeability coefficient of the internal non-deteriorated region of the soil-cement; d is the deterioration depth of the cement–soil; and R_a is the cross-sectional area deterioration rate of the soil–cement specimen.

The relationship between H, H_m, and d is

H = H_m + 2 d

(3)

The mistakes occurred when we, in our paper, after substituting Equation (6) in Equation (4), divided the resulting expression by H, to introduce the R_h term. In our paper, we defined R_h = d/H. However, the ratio H_m/H was amiss and also taken as R_h in the calculation, causing errors in our original results. We are grateful to Prof. Neves for pointing out these problems. As the second response is also about this formula, the correct formula is shown below.

Second, the discusser points out that our paper adopted an approach where the mass flow in a homogeneous layer is homogeneous, regardless of the eventual heterogeneities in other layers previously crossed by mass. We have checked our paper and believe that the inaccurate equation might refer to Equation (5) in original paper, which is

$$Q_{\mathrm{m}}=k_{\mathrm{m}}{i}_{\mathrm{m}}A=k_0{i}_{\mathrm{m}}\left(A-A_{\mathrm{d}}\right)+k_{\mathrm{d}}{i}_{\mathrm{m}}{A}_{\mathrm{d}}$$

(4)

According to the suggestions made by Prof. Neves, the k₀ in Equation (4) is supposed to be replaced by k_m,SA, which is the equivalent permeability coefficient of the materials in SA. k_m,SA is calculated as

$$k_{m,SA}=\frac{d+H_m+d}{\frac{d}{k_d}+\frac{H_m}{k_0}+\frac{d}{k_d}}$$

(5)

Equation (5) in origin paper should be

$$Q_m=k_m{i}_{m}A=k_{m,SA}{i}_m\left(A-A_d\right)+k_d{i}_m{A}_d$$

(6)

Equation (4) in origin paper is calculated as

$$k_{\mathrm{d}}=\frac{2k_{\mathrm{c}}{k}_{\mathrm{m}}d}{k_{\mathrm{m}}H-k_{\mathrm{c}}{H}_{\mathrm{m}}}$$

(7)

By substituting Equations (5) and (6) into Equation (7), an equation equivalent to Equation (10) in the comment can be achieved. Equations (8)–(10) in original text is supposed to be replaced as

$$K_d=\frac{A+\surd B}{2R_a\left(1-2R_h\right)}$$

(8)

$$A=K_c+K_0{R}_a-K_0-2K_c{R}_h-2K_0{R}_a{R}_h$$

(9)

$$\begin{gathered} B=K_0^2{\left(1-R_a+2R_a{R}_h\right)}^2+2K_0{K}_C\left(R_a-1+2R_a{R}_h\right)\left(1-2R_h\right) \\ +K_c^2{\left(1-2R_h\right)}^2 \end{gathered}$$

(10)

In Figure 1, the values of k_d calculated by Equations (8)–(10) are shown.

Finally, as Equations (8)–(10) in origin paper have been revised, the function to model the evolution of the permeability coefficient of a deteriorated part of soil–cement also needs to be revised. According to Equations (8)–(10) the parameters presented in

Table 1. Fitting parameters.

Cement Content	ki (×10−8 cm/s)	ku (×10−8 cm/s)	tc (d)	p
7%	0.69	12.66	78.90	7.31
10%	0.04	13.81	75.92	7.42
15%	0.03	14.16	75.54	8.97

can be obtained.