Review Reports - A Universal Graphical Solution to Calculating Seepage in Excavation of Anisotropic Soils and Non-Limited Scenarios

Round 1

Reviewer 1 Report

The article is devoted to the problem of fluid filtration in anisotropic soil during its excavation. A model of fluid seepage in geotechnical structures has been developed, and the solution is reduced to a dimensionless form using the Pi theorem. The numerical results of calculations are obtained using the Modflow package. Regularities in geometric and mechanical parameters for the flow process are revealed.

Remarks.

1) Line 48 mentions the x and y axes, but they are not shown in Figure 1.

2) In lines 74–76, formulas are given with typos.

3) It is not clear where the parameters h1, h2, in formulas (6)–(7) are taken from.

4) The calculations were modeled according to the scenario of 200 years; it is not clear where such a long digging of the pit takes place.

5) In line 159, parameters h1, h2, are used as height, although in formula (1) line 72 they are used for hydraulic head. You must enter another notation.

6) There is no comparison of analytical results with numerical calculations in the work. Although line 303 says that they were confirmed numerically.

Author Response

We appreciate the reviewers' comments. They have improved the article considerably.

Reviewer 1. General Comment

Remarks.

1) Line 48 mentions the x and y axes, but they are not shown in Figure 1.

It has been accordingly addressed.

2) In lines 74–76, formulas are given with typos.

It has been edited.

3) It is not clear where the parameters h1, h2, in formulas (6)–(7) are taken from.

h1 and h2 are specific values of h. They are measured in the “y” direction and are shown in Figure 2. It´s been clarified in line 88.

4) The calculations were modeled according to the scenario of 200 years; it is not clear where such a long digging of the pit takes place.

We agree with this comment. To clarify it, Lines 140-142 of original manuscript have been modified in the reviewed manuscript (lines 161-163). After cehquing that the transient time varies from less than 1 day to 2 days, the models have been run in steady states conditions. That was equivalent to previous 200 years running period.

5) In line 159, parameters h1, h2, are used as height, although in formula (1) line 72 they are used for hydraulic head. You must enter another notation.

The value of the hydraulic head at a point is calculated by measuring the height that the water reaches within a piezometer located at the same point. It is measured relative a reference system. So, h1 and h2 are specific values of hydraulic head h and are measured as height (m). Formulas 6 and 7 represents the hydraulic boundary conditions h=h1 and h=h2. h1 and h2 change from one simulation to other.

Lines 181-185 has been included to clarify this aspect.

6) There is no comparison of analytical results with numerical calculations in the work. Although line 303 says that they were confirmed numerically.

In this work we have presented semi-analytical solutions (pi theorem approach) and numerical solutions. The first were verified by numerical simulations.

The MODFLOW software has been validated with numerous benchmark problems (Elder, Yusa, Henry...). We believe that the software provides accurate results that are only dependent on the meshing.

Reviewer 2 Report

Comments and Suggestions for Authors.

Notes on the figures.

1. Figure 1 shows the coordinate directions. For a better understanding, in my opinion, it is necessary to designate the origin and the directions of the x and y coordinates. The same is shown in Figure 2.

2. In Figure 2, the difference between the mark of the top of the soil mass and the bottom of the excavation is indicated as Δh, which is associated with a pressure drop. This value in some tasks may not coincide with the difference in marks. In my opinion, this value in accordance with Figure 1 can be denoted as b – a.

3. In Figure 3, the designations of geometric quantities do not coincide with the designations in Figure 1.

Comments on the text.

1. In formula (7), the Y-coordinate boundary is incorrectly indicated: it is necessary to b-a ≤ y ≤T; similarly, in formula (9) it is necessary: 0 ≤ y ≤ b-a.

2. In lines 74 and 75, correct the notation of the derivatives ∂Vx/∂x, ∂Vy/∂y .....

3. There is no parenthesis after the derivative in line 76.

4. Line 127: the name of the table "Verification of dependencies 2, 3 and 4". Apparently, these are dependencies (10), (11), (12). Then it's probably f1 ;f2; f3?

5. Line 207: The signs are mixed up in comparison of the values T* and L* (correct on line 247).

6. line 269: in parentheses should be "isotropic"

7. Lines 160-161 say: «the path lines are perpendicular to the potential iso-lines». In fact, it is known from the filtration theory that in the case of anisotropic filtration, they may not be perpendicular, as can be seen in Figure 4.

8. The scenarios presented in Table 2 consider cases for which the value a/b = .0.25; T/b =24.25. Figures 5-7 show curves for the cases a/b= .0.25; 0.50; 0.75 and T/b = 30,00; 25,00; 20,00. Maybe it should be noted in the text that other scenarios were considered?

Author Response

We appreciate the reviewers' comments. They have improved the article considerably

Reviewer 2.

Notes on the figures.

Figure 1 shows the coordinate directions. For a better understanding, in my opinion, it is necessary to designate the origin and the directions of the x and y coordinates. The same is shown in Figure 2.

It has been addressed.

In Figure 2, the difference between the mark of the top of the soil mass and the bottom of the excavation is indicated as Δh, which is associated with a pressure drop. This value in some tasks may not coincide with the difference in marks. In my opinion, this value in accordance with Figure 1 can be denoted as b – a.

We agree. Figure 2 has been edited accordingly. We clarified this aspect in lines 100-101.

In Figure 3, the designations of geometric quantities do not coincide with the designations in Figure 1.

Figure 3 has been edited accordingly.

Comments on the text.

In formula (7), the Y-coordinate boundary is incorrectly indicated: it is necessary to b-a ≤ y ≤T; similarly, in formula (9) it is necessary: 0 ≤ y ≤ b-a.

The origin of the coordinates axe has been located on top of the retaining structure in Figures 1 and 2, as previously mentioned. Equations 7, 8 and 9 have been modified. Lines 94-96 have been included to clarify this aspect.

In lines 74 and 75, correct the notation of the derivatives ∂Vx/∂x, ∂Vy/∂y .....

It has been addressed.

There is no parenthesis after the derivative in line 76.

It has been addressed.

Line 127: the name of the table "Verification of dependencies 2, 3 and 4". Apparently, these are dependencies (10), (11), (12). Then it's probably f1 ;f2; f3?

It has been addressed.

Line 207: The signs are mixed up in comparison of the values T* and L* (correct on line 247).

It has been addressed.

line 269: in parentheses should be "isotropic"

It´s been edited accordingly.

Lines 160-161 say: «the path lines are perpendicular to the potential iso-lines». In fact, it is known from the filtration theory that in the case of anisotropic filtration, they may not be perpendicular, as can be seen in Figure 4.

Graphical resolution procedures in anisotropic media perform geometric transformations that deform equipotentials and flow lines. This means that Laplace's equation is not fulfilled and, therefore, neither is the orthogonality between these lines. However, the numerical simulation does satisfy the Laplace equation and the velocity vectors (we have represented them with pathlines using the particle tracking package) are always orthogonal to the equipotentials. We have tried to explain in the original manuscript that the pathlines do not define flow tubes, as is the case in the representation of flow networks (lines 172-180 in the reviewed manuscript.

The scenarios presented in Table 2 consider cases for which the value a/b = .0.25; T/b =24.25. Figures 5-7 show curves for the cases a/b= .0.25; 0.50; 0.75 and T/b = 30,00; 25,00; 20,00. Maybe it should be noted in the text that other scenarios were considered?

The values chosen for table 2 are arbitrary. They were chosen exclusively to verify that the relationships established from pi's theorem were correct (see section 3).

The values chosen for the drawing of the type curves correspond to specific cases. Different values of these relationships would result in different curves, which can also be obtained by interpolation of those already obtained.

Reviewer 3 Report

General Comment

The submitted manuscript presents a methodology using numerical simulations to build abacuses to assist geotechnical designers to calculate the seepage in excavations under embedded retaining wall structures. The novelty is the consideration of anisotropic media and non-limited scenarios regarding the vertical depth to the impervious subtract and horizontal extend at the back of the wall. For this, the concept of a characteristic depth and length is defined and used.

After a literature review on the topic, the mathematical and methodological framework to build the dimensionless curves is presented. For this, several scenarios are described and simulated numerically to compute the solution points to build the curves. To validate and exemplify the proposed abacuses, they are used in tree examples (a real case, a benchmark problem and a theoretical case). The obtained results are presented and discussed.

The topic of the manuscript is very interesting and important because simplified methods to assist designers of geotechnical structures to get approximate results, before using more refined and time consuming methods, are need. For this reason, the proposed abacuses could be very useful for practice.

I consider that the manuscript requires some revision before it can be accepted for publication. I made few comments in order to improve the manuscript. The authors should take the comments into account and revise their manuscript.

Specific Comment 1

The manuscript needs a revision to correct formatting issues (for instance, the equations inserted in the text in page 3) and the numbering of the sections.

Specific Comment 2

In the introduction section, the literature review on the topic is somewhat poor and limited, and should be improved. In addition, the related references should also be updated.

Specific Comment 3

In Figures 1 and 2, please add symbols “x” and “y” next to the respective axes.

Specific Comment 4

Equations presented in page 3 should be supported by references.

Typos and formatting issues must be corrected.

Author Response

We appreciate the reviewers' comments. They have improved the article considerably

Reviewer 3. General Comment

Specific Comment 1

The manuscript needs a revision to correct formatting issues (for instance, the equations inserted in the text in page 3) and the numbering of the sections.

It has been addressed. See lines 85-86 and numbering of the sections

Specific Comment 2

In the introduction section, the literature review on the topic is somewhat poor and limited, and should be improved. In addition, the related references should also be updated.

It has been addressed. 9 new references related to the topic and methodology have been included.

Specific Comment 3

In Figures 1 and 2, please add symbols “x” and “y” next to the respective axes.

It has been accordingly addressed.

Specific Comment 4

Equations presented in page 3 should be supported by references.

Two new basic references have been included

Reviewer 4 Report

· In accordance with the journal guidelines, it is important to incorporate the significant findings within the abstract of the article.

· What are the main issues with traditional techniques that prompted the authors to conduct this study? Additionally, the authors believe that their approach is comparatively superior in addressing seepage-related concerns.

· It is imperative for the authors to include a real-time field problem as part of this study.

· Model validation is necessary.

· How did the authors go about selecting the input parameters for their model?

· Please rephrase the conclusion section, ensuring that it is based on the results obtained from this study. Avoid methodology and discussion at this stage.

· Provide a definition of the applications and limitations of the curves in the field problem.

· Implement the curves in a real field problem and analyze the outcomes in detail.

· Literature must be enriched enough to define the research problem.

Author Response

Reviewer 4. Comments and Suggestions for Authors

In accordance with the journal guidelines, it is important to incorporate the significant findings within the abstract of the article.

It has been addressed.

What are the main issues with traditional techniques that prompted the authors to conduct this study? Additionally, the authors believe that their approach is comparatively superior in addressing seepage-related concerns.

The question has been addressed (lines 48-51)

We believe that in no case we have made a comment on whether or not the proposed technique is superior to others. We have mentioned that the use of these abacuses is simple and direct (Line 18). What we have tried to emphasize is the reliability of the techniques we have applied.

It is imperative for the authors to include a real-time field problem as part of this study.

This work is a fundamentally theoretical study, so the authors consider that it is not appropriate to incorporate real-time field problem. Some examples were included in the paper (section5) in order to illustrate the use of abacuses.

Model validation is necessary.

We don't think we understand this comment.

In this work we have presented semi-analytical solutions (pi theorem approach) and numerical solutions. The first were validated by numerical simulations.

The MODFLOW software has been already validated with numerous benchmark problems (Elder, Yusa, Henry...). We believe that the software provides accurate results that are only dependent on the meshing.

How did the authors go about selecting the input parameters for their model?

We have included new lines to address this comment (lines 109-115). We want to let the reviewer know that we work with dimensionless groups of parameters rather than with specific parameter values, so that it is the monomial value that really determine the dependencies or solutions.

Please rephrase the conclusion section, ensuring that it is based on the results obtained from this study. Avoid methodology and discussion at this stage.

Lines 304-305 in the original manuscript have been deleted. The conclusions contain the results.

Provide a definition of the applications and limitations of the curves in the field problem.

We think that the application of these type curves has been addressed in section 5. New lines have been included in the reviewed manuscript to define the limitations (235-241).

Implement the curves in a real field problem and analyze the outcomes in detail.

As mentioned before, this is a manuscript mainly based on theoretical aspects. Nevertheless, an example based on a real case was included in section 5. This section is aimed to enlighten the use of the abacuses.

Literature must be enriched enough to define the research problem.

It has been addressed. 9 new references related to the topic and methodology have been included.

Round 2

Reviewer 3 Report

I received and read the revised version of the manuscript “Universal graphical solution to calculate seepage in excavation for anisotropic soils and non-limited scenarios”, as well as the authors’ replies to my previous comments. The authors have modified and improved the manuscript according to all my comments. I consider that the manuscript can now be accepted for publication.

Reviewer 4 Report