Numerical Limit Analysis of the Stability of Reinforced Retaining Walls with the Strength Reduction Method
Round 1
Reviewer 1 Report
This manuscript studies the damage law of MSE wall caused by material parameters and seismic parameters in detail, summarizes the reinforcement effect of reinforcement measures for structures under different conditions, and gives optimization suggestions. The study is novel and meaningful and fits the scope of the journal. However, there are some unclear problems in the manuscript, which need a major revision.
Comments to the Author:
This paper has done a lot of work, and the suggestions given are also very pertinent. There are still some confusing problems and subtle errors in the manuscript. Please explain them in detail and make appropriate modifications:
1. In line 24, MSE first appeared in the manuscript. What does it mean? The abbreviations that appear for the first time should be explained.
2. Eq. 3 defines a function, which includes the inequality relationship with stress as the independent variable, but does not explain the meaning of function f. Please explain it.
3. In line 24, The author gives a comprehensive description of Figures 5 to 11, but in fact, these figures show the geometric shape, influence and failure model, which is the process of numerical simulation. Therefore, the reviewer believes that there is no need to use this expression to summarize these figures, which will make readers ambiguous.
4. In section 4.4, it is mentioned that the horizontal seismic load is applied to the model. What is the way of applying the load, and whether the wave effect and the absorption and reflection conditions of seismic waves are considered?
Author Response
Response to Reviewer #1
Reviewer #1: This paper has done a lot of work, and the suggestions given are also very pertinent. There are still some confusing problems and subtle errors in the manuscript. Please explain them in detail and make appropriate modifications:
Response: The authors would appreciate the positive comments of the reviewer on our manuscript.
- Comment: In line 24, MSE first appeared in the manuscript. What does it mean? The abbreviations that appear for the first time should be explained.
Response: We are sorry for this mistake. Explanations have been added to the revised version.
- Comment: Eq. 3 defines a function, which includes the inequality relationship with stress as the independent variable, but does not explain the meaning of function f. Please explain it.
Response: MC criterion stipulates that when the ratio of shear stress to normal stress on the shear plane reaches the maximum, the material will yield to failure. Therefore, when the function is greater than 0, the material yields. We have added further explanations in the revised version.
- Comment: In line 198, The author gives a comprehensive description of Figures 5 to 11, but in fact, these figures show the geometric shape, influence and failure model, which is the process of numerical simulation. Therefore, the reviewer believes that there is no need to use this expression to summarize these figures, which will make readers ambiguous.
Response: The authors would appreciate the reviewer for the suggestion. The expression has been revised in the revised version.
- Comment: In section 4.4, it is mentioned that the horizontal seismic load is applied to the model. What is the way of applying the load, and whether the wave effect and the absorption and reflection conditions of seismic waves are considered?
Response: The loading mode of seismic load in this study adopts the input mode of artificial boundary and equivalent load, which absorbs the reflected seismic wave through special boundary elements and avoids the influence of excess external forces. It is an advanced loading mode.
Thank you again for your time and effort, and for helping us improve the manuscript.
Reviewer 2 Report
The authors studied the failure mechanism of MSE walls via numerical analysis with the finite element strength reduction method, which was verified as an effective technique by simulating the experimental results reported in previous papers. To avoid the unavoidable errors experienced in common numerical analysis, caused by the assumptions of the failure mode and complex input parameters, a finite element program was applied to explore the effects of reinforcement, geometry and seismic parameters on failure mechanism control at the design stage of MSE walls. The research parameters included the wall height, length and spacing of the geogrid-reinforced retaining wall and seismic load.
In general, the results indicated that the wall height and reinforcement length play a major role in failure mode change. When the reinforcement length is less than 2 m, overturning failure could occur, which was unrelated to the other parameters in all cases studied in this paper. In this paper, the parametric study results were presented by evaluating the critical reinforcement length, generating the failure surface pattern and summarizing design recommendation charts. The paper is well written, and I have no hesitation to recommend it for pblication. Only minor revision in English language is required (e.g., some typos), thus, a check in language is suggested by reviewer.
Author Response
Response to Reviewer #2
Reviewer #2: The authors studied the failure mechanism of MSE walls via numerical analysis with the finite element strength reduction method, which was verified as an effective technique by simulating the experimental results reported in previous papers. To avoid the unavoidable errors experienced in common numerical analysis, caused by the assumptions of the failure mode and complex input parameters, a finite element program was applied to explore the effects of reinforcement, geometry and seismic parameters on failure mechanism control at the design stage of MSE walls. The research parameters included the wall height, length and spacing of the geogrid-reinforced retaining wall and seismic load.
In general, the results indicated that the wall height and reinforcement length play a major role in failure mode change. When the reinforcement length is less than 2 m, overturning failure could occur, which was unrelated to the other parameters in all cases studied in this paper. In this paper, the parametric study results were presented by evaluating the critical reinforcement length, generating the failure surface pattern and summarizing design recommendation charts. The paper is well written, and I have no hesitation to recommend it for publication. Only minor revision in English language is required (e.g., some typos), thus, a check in language is suggested by reviewer.
Response: The authors would appreciate the positive comments of the reviewer on our manuscript. The authors have checked and revised the language of the manuscript to ensure that there are no errors and omissions.
Reviewer 3 Report
The research results are interesting and meaningful. However, there are issues that should be addressed before the paper could be recommended for publication:
1. In line 24, It is mentioned in the manuscript that Drucker and Prager put forward some theories and carried out some applications, but there is no reference to explain them. Please list the references to support this reason.
2. The physical quantities defined in equations 4 and 5 contain many superscripts and subscripts, which is puzzling. Please elaborate on the physical meaning of these superscripts and subscripts.
3. What does J@2% in Table 4 mean? Is there any mistake in it? Please confirm the variables in the manuscript to avoid errors.
4. The part of this article that explains the results of numerical experiments and draws conclusions is deficient in English language. Please optimize the corresponding part.
Author Response
Response to Reviewer #3
Reviewer #3: The research results are interesting and meaningful. However, there are issues that should be addressed before the paper could be recommended for publication:
Response: The authors would appreciate the positive comments of the reviewer on our manuscript.
- Comment: In line 106, It is mentioned in the manuscript that Drucker and Prager put forward some theories and carried out some applications, but there is no reference to explain them. Please list the references to support this reason.
Response: The authors would appreciate the reviewer for the suggestion. We have added the reference in this section.
- Comment: The physical quantities defined in equations 4 and 5 contain many superscripts and subscripts, which is puzzling. Please elaborate on the physical meaning of these superscripts and subscripts.
Response: The authors apologized firstly for our negligence, and now we have defined and explained them in the revised manuscript.
- Comment: What does J@2% in Table 4 mean? Is there any mistake in it? Please confirm the variables in the manuscript to avoid errors.
Response: The authors apologized firstly for our negligence, and now we have corrected this mistake in the revised manuscript.
- Comment: The part of this article that explains the results of numerical experiments and draws conclusions is deficient in English language. Please optimize the corresponding part.
Response: The authors would appreciate the reviewer for the suggestion. The authors have checked and revised the language of the manuscript to ensure that there are no errors and omissions.
Reviewer 4 Report
This paper investigates the effect of various parameters in the behavior of MSE walls using numerical limit analysis. It provides a very good insight about the behavior of MSE walls and all make sense qualitatively. The paper gives credibility to numerical limit analysis method as a tool to study the behavior of MSE. IN general, the reviewer believes the paper needs to better highlight or clarify what is new in this study that has not been done before. Without such justification, it is not clear what this paper adds to the body of knowledge.
The following are comments for the authors to consider in revising their manuscript;
- The English is good. An overall English technical editing is required. Some typos, grammatical and terminology issues exist. For example. Page 1, Line 33, MES should read MSE. In Page 2, Line 59, what is RSW. Terms need to be defined first time they are used.
- The abbreviate MSE needs to be defined where it first appears. I suggest to include a photo of an actual MSE in the introduction and describe its elements, terminology and construction method. For people who are not familiar with this retaining wall system, it is quite difficult to follow the paper.
- Starting from Equation 1 forward, all parameters and terms need for be defined immediately after they first appear.
- Figure 2. How do you explain the difference in the failure mode from FLAC (limited to the bottom of the wall itself and within the wall) and Optum (extended into the soil below and behind the wall?
- Line 175 seems to have ended incomplete and part of the text missing.
- Section 3.2, Case 3-2. The results show a good agreement between the failure modes. What about the strength/safety factors?
- Section 3- Verification of the numerical model. Term verification in finite element is normally sued to check the new model against an available theoretical results, in another word, it focuses on the mathematical aspects and as how accurate the solution is. Validation on the other hand deals with how well the model captures the physical behavior and normally is achieved by comparing the numerical results with experimental results. The authors seem to have in their “verification” discussion an incomplete mix of verification and validation. This needs to be clarified since the validity of the remaining analysis depends on this.
- Line 197-198- “occurred parallel” to what?
- Line 208, “Figures 5 to 11 show critical ….” This does not make sense, Figures 5 to 11 do not show the critical values?
- Lines 214 to 218- The geometry and sizes described in the text does not match those in Figure 5. There must be a mistake here.
- Table 4- The units for stiffness and strength are given in KN/m. Please explain why it is not in KN/m2 or kPascal.
- Table 5. How was the interface between the Reinforcement soil and wall was modeled?
- The paper needs to better highlight or clarify what is new in this study that has not been done before.
- Section 4.4- How would be the effect of vertical acceleration of earthquake, and why this study did not consider that?
- Section 5- The intent of this section is not clear. The section starts with pointing out the shortcoming of the existing design methods without clearly describing what is proposed instead. A new design procedure will need more than a limited parametric study. The authors used a specific configuration for MSE with specific material properties etc. This cannot in any way replace an inclusive design procedure. The authors need to first point out the limitations of their study and describe how it can be used. This section does not seem to offer any design chart, so the term “Design Chart” in the title is misleading. The section should be limited to a set of recommendation on how to analyze the MSE and what parameters need to be considered. Etc. that are supported by the study performed in this study.
Author Response
Please see the attachment.
Author Response File: 
Author Response.docx
Round 2
Reviewer 1 Report
The revised manuscrip has been modified according to the reviewer's comments. It can be accepted in the current version.
Reviewer 3 Report
Before publication, the representation of the manuscript needs to be further improved.
Reviewer 4 Report
Thank authors for responding to comments and revisions.
