Analytical Modeling of Unsaturated Soil Shear Strength during Water Infiltration for Different Initial Void Ratios

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

see attached file of 'sustainability-2731976 Comments01.pdf'.

Comments for author File: Comments.pdf

Author Response

This paper presented a model to predict the transient shear strength of soils for different void ratio conditions. The paper is of interest to the general readership of this journal. However, the technique is not described clearly, and the following issues are suggested to be revised.

Thank you for your valuable feedback. We have carefully considered all of your comments and revised the manuscript accordingly. The answers to each comment and the corresponding changes made in the manuscript are outlined below.

[1] Page 4 line 121: There are plenty of ‘Error! Reference source not found’, which has greatly influenced the understanding of the manuscript by this reviewer.

The figure references were correct when we submitted the document, but it was not in the journal's format guidelines. The error was made when the journal formatted the document before sending it to the reviewers. However, we have addressed and corrected this issue in the revised version of the manuscript.

[2] Page 4 line 130 Fig. 1: Why the unit of delta (d) is different between the one (KPa-1) in Fig. 1 and the one (M^-1LT²) below Eq. (4).

By inspection of Eq. (4), it can be deduced that the hydraulic fitting parameter has the inverse dimension of suction. Thus, while the dimension of suction is ML^-1T^-2, the dimension of d is M^-1LT². Regarding other variables, we used the SI units in the figures/results. For each variable’s definition in the literature review, we used general dimensions. No alteration was made in the manuscript regarding this comment.

[3] Page 5 line 158: “s_w = 0,07275 kN/m is the water surface”. A reference should be cited for such a number of s_w = 0,07275 kN/m.

This value represents the standard for typical water conditions in laboratory experiments. We have included a reference and a brief explanation to this effect in lines 146-150 of the revised manuscript.

[4] Page 6 line 201: ‘contribution of the capillarity effect within the. This effect ’. There is a grammar issue here. Please check.

We acknowledge that there was a typing error that went unnoticed. We have included the word “soil”, so the excerpt turns into “… within the soil.”, as indicated in line 199 of the revised manuscript.

[5] Page 8 line 245: ‘for the C parameter. However’ What does C parameter mean? Please check.

In lines 155-156, just after Eq. (13), the concept pertaining to the C parameter is elucidated. Further, lines 234-237 (previously cited as line 245 in the first version of the manuscript) clarify that it is not necessary to measure or estimate the 'C' parameter if the saturated hydraulic conductivity (ks) is measured for any given void ratio value. Consequently, no modifications have been made to the manuscript in response to this specific comment.

[6] Page 9 line 280: ‘does not contribute within the residual zone This’. A period is needed in this sentence.

We appreciate your attention in identifying another typographical error. This has been rectified in line 275 of the revised manuscript. Your feedback has prompted a comprehensive review of the manuscript to prevent similar issues. We thank you for your diligence in helping us improve the quality of our work.

[7] Page 15 line 446 Fig. 6: The vertical axial limits of Fig. 6a and 6c should be unified with 600 kPa.

Regarding the comment of another reviewer, we added a Figure 6, so the referred figure is now Figure 7.

Initially, we have unified the range of the vertical axis only for the shear strength (Figures 7b and 7d), because it is the focus of comparison between the figures (for different initial void ratios). At first, we preferred not to unify for Figures 7a and 7c because the range of the suction in Figure 7a is about 4,5 smaller than in Figure 7c. However, the vertical axis is now unified in the present revision of the manuscript for Figures 7a and 7c (lines 453-454).

[8] Page 17 Eq. (38) and Eq. (39): Please double check the difference of ln with log. Please unify if applicable for the main text. If possible, log10 is recommend.

The use of log (with base 10) arises from the semi-logarithmic scale of the SWRC plot, which is a convention in the geotechnical field. Since the tangent lines is defined in the semi-logarithmic scale, the log becomes necessary in the calculations. On the other hand, the ln (with base e = Euler number) arises from the SWRC equation. Thus, both are needed throughout the computation. We have double-checked the development of the equations and identified no mistakes in the application of both log and ln. No alteration was made in the manuscript regarding this comment.

Reviewer 2 Report

Comments and Suggestions for Authors

In the manuscript “Unsaturated Shear Strength Modelling During Water Infiltration for Different Initial Void Ratio” this research introduces a model that couples an analytical solution for one-dimensional water infiltration with an unsaturated shear strength model, yielding a transient shear strength model. This model further incorporates the impact of void ratio fluctuations on soil properties and state variables related to shear strength.
The comments are as follows:
1. The requirements for papers do not include a literature review section, so it is recommended to move it to the introduction.
2. From line 121, reference errors appear for all figures that need to be correct.
3. Some dimensions are not entirely clear, for example, in Figure 1, suction is measured in kPa, what does this mean, explanations are needed for other quantities too.
4. Unfortunately, the results of the work lack a comparison with other models and what specific results to better use of material resources in sustainable engineering the presented model can produce.

Comments on the Quality of English Language

Moderate editing of English language required.

Author Response

In the manuscript “Unsaturated Shear Strength Modelling During Water Infiltration for Different Initial Void Ratio” this research introduces a model that couples an analytical solution for one-dimensional water infiltration with an unsaturated shear strength model, yielding a transient shear strength model. This model further incorporates the impact of void ratio fluctuations on soil properties and state variables related to shear strength.

The comments are as follows:

1. The requirements for papers do not include a literature review section, so it is recommended to move it to the introduction.

Although not mandatory, we believe that the literature review section (which is extensive in this case) arranges better the ideas throughout the article, as in other papers in Sustainability (for example, the paper in https://www.mdpi.com/2071-1050/16/1/313). In light of this, no changes were made in the manuscript regarding this comment.

2. From line 121, reference errors appear for all figures that need to be correct.

The figure references were correct when we submitted the document, but it was not in the journal's format guidelines. The error was made when the journal formatted the document before sending it to the reviewers. However, we have addressed and corrected this issue in the revised version of the manuscript.

3. Some dimensions are not entirely clear, for example, in Figure 1, suction is measured in kPa, what does this mean, explanations are needed for other quantities too.

As far as we know, the measurement of suction in kPa is very common in the literature for unsaturated soil mechanics. Also, all the units are required to be in the SI (International System of Units). No changes were made in the manuscript regarding this comment.

4. Unfortunately, the results of the work lack a comparison with other models and what specific results to better use of material resources in sustainable engineering the presented model can produce.

We have included a new figure in the Results/Discussion section (Figure 6, lines 438) to elucidate the connection between our modeling approach and its implications for more sustainable engineering practices and optimized design. Additionally, to draw comparisons with other models, we have incorporated relevant text in the Introduction (lines 53-56) and in the Concluding Remarks (lines 493-496).

Reviewer 3 Report

Comments and Suggestions for Authors

The paper, lacking of novelty, is only limited to a specific engineering case, and don’t provide great guiding value to the engineering field or scientific research scholars.

 

Comments on the Quality of English Language

Please check the citation format of all references.

Author Response

The paper, lacking of novelty, is only limited to a specific engineering case, and don’t provide great guiding value to the engineering field or scientific research scholars.

Thank you for your insightful comment. We have restructured the Introduction and Concluding Remarks sections to better elucidate the significance of our work in the field of unsaturated soil mechanics and its relevance to sustainability. We welcome and look forward to more specific feedback on distinct parts of our paper, as this will provide further opportunities for constructive dialogue and enhancement of our work. The revised version now submitted incorporates numerous amendments based on the comments from the other five reviewers.

Reviewer 4 Report

Comments and Suggestions for Authors

In this manuscript, authors report their study on soil shear strength variation during water infiltration under different initial void ratio conditions. This research is of interest to the geotechnical engineering field. It is recommended that the manuscript be reconsidered after major revision.

1.       This research is performed within the scope of soil mechanics, it would be better to reflect this in the title.

2.      Please consider reorganizing the introduction section. Now it’s not concise enough and the significance of understanding the phenomena within the unsaturated soil needs to be made more obvious.

3.      Please double check the Figure, it shows “Figure Error!” in the manuscript.

4.      What is the main limitation of this simulation?

5.      Can the authors please report or give a summary, compared to other published methods, what specific improvements were made regarding this methodology?

Comments on the Quality of English Language

Please improve the writing.

Author Response

In this manuscript, authors report their study on soil shear strength variation during water infiltration under different initial void ratio conditions. This research is of interest to the geotechnical engineering field. It is recommended that the manuscript be reconsidered after major revision.

Thank you for your valuable feedback. We have carefully considered all the comments and accordingly revised the text. Detailed responses to each comment, along with the corresponding revisions made to the manuscript, are summarized below.

1. This research is performed within the scope of soil mechanics, it would be better to reflect this in the title.

We agree with the suggestion. Accordingly, the title was changed from “Unsaturated Shear Strength Modelling During Water Infiltration for Different Initial Void Ratio” to “Analytical Modelling of Unsaturated Soil Shear Strength During Water Infiltration for Different Initial Void Ratio”.

2. Please consider reorganizing the introduction section. Now it’s not concise enough and the significance of understanding the phenomena within the unsaturated soil needs to be made more obvious.

We have shortened the Introduction and incorporated more references. This reorganization of the Introduction aims to more effectively highlight the importance of the unsaturated soil approach. We trust that these modifications have clarified the significance of this perspective.

3. Please double-check the Figure, it shows “Figure Error!” in the manuscript.

The figure references were correct when we submitted the document, but it was not in the journal's format guidelines. The error was made when the journal formatted the document before sending it to the reviewers. However, we have addressed and corrected this issue in the revised version of the manuscript.

4. What is the main limitation of this simulation?

The main limitation is that the soil layer simulated must be homogeneous and above any phreatic zone. We added lines 476-482 to clarify this in the Concluding remarks.

5. Can the authors please report or give a summary, compared to other published methods, what specific improvements were made regarding this methodology?

Based on this comment, we have added more references in the Introduction (lines 53-56) and reformulated the Concluding remarks (as in lines 493-496).

Reviewer 5 Report

Comments and Suggestions for Authors

The figure numbers in the text are not cited properly (See the highlighted parts in the attached file) and the paper is not readable. I cannot make sense of the Figures based on the explanation in the manuscript. The authors should fix the error and resubmit the paper for review. 

Comments for author File: Comments.pdf

Comments on the Quality of English Language

No comment.

Author Response

The figure numbers in the text are not cited properly (See the highlighted parts in the attached file) and the paper is not readable. I cannot make sense of the Figures based on the explanation in the manuscript. The authors should fix the error and resubmit the paper for review.

Thank you for your comment. We apologize for the mistake in citing the figures. The figure references were correct when we submitted the document, but it was not in the journal's format guidelines. The error was made when the journal formatted the document before sending it to the reviewers. However, we have addressed and corrected this issue in the revised version of the manuscript.

Reviewer 6 Report

Comments and Suggestions for Authors

The article concerns unsaturated shear strength modeling during water infiltration for different initial void ratio. It is a continuation of the authors' previous articles.

I have included detailed comments and questions about the article below.

1. Please correct references to figures in the text (e.g. line 121).

2. Please check whether the subscripts have been added correctly in the descriptions of the quantities appearing in the equations (e.g. line 158).

3. In the Abstract, it would be worth adding information for what types of soils you propose to use the developed model.

4. Why did you choose such e values? Has the simulation been performed for other values of e?

Author Response

The article concerns unsaturated shear strength modeling during water infiltration for different initial void ratio. It is a continuation of the authors' previous articles.

I have included detailed comments and questions about the article below.

Thank you for your valuable feedback. We have carefully considered all the comments and accordingly revised the text. Detailed responses to each comment, along with the corresponding revisions made to the manuscript, are summarized below.

1. Please correct references to figures in the text (e.g. line 121).

The figure references were correct when we submitted the document, but it was not in the journal's format guidelines. The error was made when the journal formatted the document before sending it to the reviewers. However, we have addressed and corrected this issue in the revised version of the manuscript.

2. Please check whether the subscripts have been added correctly in the descriptions of the quantities appearing in the equations (e.g. line 158).

We have thoroughly reviewed the equations for any inconsistencies in the presentation and description of variables and found none. Consequently, no alterations have been made to the manuscript in response to this comment.

3. In the Abstract, it would be worth adding information for what types of soils you propose to use the developed model.

We added more information (lines 20-24) in the Abstract to elucidate the applicability of the present modelling while adhering to the recommended 200-word limit for the Abstract.

4. Why did you choose such e values? Has the simulation been performed for other values of e?

The simulation was conducted using typical geotechnical parameters for a theoretical soil. Despite testing various soil parameters, no significant deviation from the presented results was observed, with the overall behavior remaining within the same order of magnitude. We have addressed this point in the lines 475-481.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript has been seriously revised and improved. However there are minor notes:
1. According to the instructions of the journal (https://www.mdpi.com/journal/sustainability/instructions), the literature review section is added only in review articles, therefore it is recommended that authors respect the requirements of the journal and align the structure of the work.
2. As for comparing the results of this work with other models, this issue has not been discussed enough. It is not clear how Figure 6 answers this question, as well as lines 53-56 and 493-496. A more thorough comparison is needed.

Comments on the Quality of English Language

Minor editing of English language required.

Author Response

The manuscript has been seriously revised and improved. However there are minor notes:

Thank you for your valuable feedback. We have carefully considered the comments again and revised the manuscript accordingly. The answers to each comment and the corresponding changes made in the manuscript are outlined below. In the manuscript, the red fonts concern the first revision while the blue fonts concern the present revision.

1 - According to the instructions of the journal (https://www.mdpi.com/journal/sustainability/instructions), the literature review section is added only in review articles, therefore it is recommended that authors respect the requirements of the journal and align the structure of the work.

The text, equations and figures within Section 2 are fundamental for the Section 3, which works as the methodology. The models presented in Section 2 can also be seen as “Materials” for the modelling. However, we insist that the Section 2 remains as the “Literature Review” since there are other recent papers in Sustainability with this section (for example: https://www.mdpi.com/2071-1050/16/1/313 or https://www.mdpi.com/2071-1050/16/3/1178).

Additionaly, the section “Free format submission” in the journal instructions affirms that “We do not have strict formatting requirements, but all manuscripts must contain the required sections: Author Information, Abstract, Keywords, Introduction, Materials & Methods, Results, Conclusions, Figures and Tables with Captions, Funding Information, Author Contributions, Conflict of Interest and other Ethics Statements”.

For now, we prefer to maintain the Section 2 as “Literature Review”. If the editorial office determines that it has to be changed, we will try to adapt accordingly.

2 - As for comparing the results of this work with other models, this issue has not been discussed enough. It is not clear how Figure 6 answers this question, as well as lines 53-56 and 493-496. A more thorough comparison is needed.

As an alternative, we included a typical unsaturated shear strength model adopted in other studies such as Vanapalli et al. (1996) and Lu et al. (2010). We added the Figure 4 and the Figures 6b and 6d was modified to address this point. The lines 373-393 and 441-449 were added to discuss these figures.

 

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript introduces a model that couples an analytical solution for one-dimensional water infiltration with an unsaturated shear strength model. This manuscript is significantly improved after revision, while some issues should be addressed before publication.

 

1.         As unsaturated soils are multi-phase media, the internal structure’s content can significantly affect their overall properties. To provide a broader and more comprehensive review of the topic. Some typical studies should be added, such as: International Journal of Heat and Mass Transfer 2020, 151, 119383; Acta Materialia (2023), 242, 118472.

2.         Besides, the authors mentioned that “Once experimental research on unsaturated soils is generally costly, time-consuming, and difficult to conduct [5], the reliance on empirical, semi-empirical, and analytical mathematical strength models becomes crucial for predicting the mechanical behaviour of unsaturated soils.” Some relevant references should also be provided.

3.         In the last section, the author mainly summarized some valuable conclusions. What’s the critical significance and limitation of this work?

 

4.         In addition, the language used in this manuscript also needs to be thoroughly revised (such as the capital and small letter, unit, …).

Comments on the Quality of English Language

   In addition, the language used in this manuscript also needs to be thoroughly revised (such as the capital and small letter, unit, …).

Author Response

This manuscript introduces a model that couples an analytical solution for one-dimensional water infiltration with an unsaturated shear strength model. This manuscript is significantly improved after revision, while some issues should be addressed before publication.

Thank you for your valuable feedback. We have carefully considered the comments again and revised the manuscript accordingly. The answers to each comment and the corresponding changes made in the manuscript are outlined below. In the manuscript, the red fonts concern the first revision while the blue fonts concern the present revision.

1 - As unsaturated soils are multi-phase media, the internal structure’s content can significantly affect their overall properties. To provide a broader and more comprehensive review of the topic. Some typical studies should be added, such as: International Journal of Heat and Mass Transfer 2020, 151, 119383; Acta Materialia (2023), 242, 118472.

We added the suggested references in lines 386-388.

2 - Besides, the authors mentioned that “Once experimental research on unsaturated soils is generally costly, time-consuming, and difficult to conduct [5], the reliance on empirical, semi-empirical, and analytical mathematical strength models becomes crucial for predicting the mechanical behaviour of unsaturated soils.” Some relevant references should also be provided.

Besides reference [5] (Vanapalli et al., 1996), we added the more recent reference Tran and Fredlund (2021) in line 44.

In the last section, the author mainly summarized some valuable conclusions. What’s the critical significance and limitation of this work?

The main limitations of the present modelling are: i) the applicability to homogeneous soil only; ii) the accuracy of the shear strength evaluation relies on a reasonably good fitting of the SWRC using only the fitting parameters a and b (for at least two known void ratios). We hope that lines 554-555 clarify this point (together with lines 514-515 and 533-539 in the Concluding Remarks). The main significance of this work is the ability to easily implement closed-form equations to predict variations in the unsaturated shear strength during water infiltration for different initial void ratios. Lines 561-564 address this point (along with lines 529-532 in the Concluding Remarks).

4 - In addition, the language used in this manuscript also needs to be thoroughly revised (such as the capital and small letter, unit, …).

We noticed an incongruence of capital letters in the section titles, the keywords, and reference 34, which were corrected. About units, we revised lines 103, 128, 145 and 162. We revised the writing throughout the manuscript and identified no other mistakes. However, we hope to correct any minor writing errors specified in further revisions or by the editorial office before publication.

 

Reviewer 4 Report

Comments and Suggestions for Authors

N/A

Author Response

Thank you for your approval of the revised manuscript.