Analysis of Elastoplastic Mechanical Properties of Non-Uniform Frozen Wall Considering Frost Heave
Round 1
Reviewer 1 Report
This article is well written, and I am willing to accept it in present form.
Author Response
Thank you very much for your opinion.
Reviewer 2 Report
This study proposed analytical method for discussing elastoplastic mechanical properties of nonuniform frozen wall considering frost heave. The method would be useful to estimate the behavior of the frozen wall and surrounding unfrozen area with limited computational resources. However, I found some unclear points in the manuscript. Please find the comments for the unclear points as follows.
1. The assumptions to get the solutions
Many things are assumed in this study, e.g. L115-L125. However, I am not sure whether these assumptions are adequate for the analyses or not. Are there any references in which these assumptions are validated, or any explanations how these assumptions are good for the analyses? Please add such information.
2. Symbol of temperature gradient
The symbol of the temperature gradient is displayed just alpha. The subscript of the symbol looks blank.
3. Display of the formula
The formula that has large height is displayed as inline one in L.200. The similar formulae are sometimes found in the other part of manuscript as well. It would be better if this kind of formula is displayed separately.
4. “The volume of the frozen wall is incompressible” in L.238
I wonder how the frozen wall keeps its volume in plastic state. It means that the frozen wall behaves like incompressible fluid? Are there no dilative behaviors? Please add references or explanation.
5. k in L.277
In L.277, k is introduced as 2. Is this a general value? How this parameter is determined.
6. Figure 4
In the legend, there are texts from “-100m” to “-600m”. It seems these are the depth of the model. Please add explanation in the legend. The similar cases are found in following Figures as well. Please modify the figures. By the way, are there the frozen walls that depth is 600m????
7. L.289-L.295
Three state, elastic limit state, elastic-plastic state (elastoplastic state can be found in L 293 as well.) and plastic limit state are introduced in this paragraph. However, the definitions of these states are not introduced. Please add explanations and how the state is represented in the analyses.
8. Figure 5
There are no explanations about the legends as well. What the filled symbols and unfilled symbols mean? Further, the different numeric is displayed in the lines of square, triangle and circle. What these numerics mean? It seems the states changes with p. Please add the explanation.
9. L.298 to L.314
The authors calculated the bearing capacity with different criteria. I understood the bearing capacity changes if different criterion is adopted. I think it is natural and which criterion is adequate for estimating the behavior of frozen wall as consequence? It looks the remaining parts just discussed the mathematical characteristic of the proposed method, and I wonder that there is no information how these results can be used practically.
Author Response
Response to the Referees’ Comments
Dear Editors and Reviewers:
Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “Analysis of Elastoplastic Mechanical Properties of Non-Uniform Frozen Wall Considering Frost Heave” (applsci-2125213). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researchers. We have studied comments carefully and have made correction which we hope meet approval. Revised portion are marked in red in the paper. The responds to the reviewer’s comment are as following:
Responds to the reviewer’s comment:
Comment 1: The assumptions to get the solutions. Many things are assumed in this study, e.g. L115-L125. However, I am not sure whether these assumptions are adequate for the analyses or not. Are there any references in which these assumptions are validated, or any explanations how these assumptions are good for the analyses? Please add such information.
The author's response：
Thank you very much for your opinion. The basic assumptions we put forward in this paper are all based on the existing research results, and specific reference sources are indicated after each hypothesis in this revision.
Comment 2: Symbol of temperature gradient. The symbol of the temperature gradient is displayed just alpha. The subscript of the symbol looks blank.
The author's response：
Thank you very much for your opinion. As for the symbol of temperature gradient, we refer to the existing relevant achievements. Most papers are marked in this form. In order to unify the form and avoid misunderstanding, we have not changed this symbol for the time being.
Comment 3: Display of the formula. The formula that has large height is displayed as inline one in L.200. The similar formulae are sometimes found in the other part of manuscript as well. It would be better if this kind of formula is displayed separately.
The author's response：
Thank you very much for your opinion. We have carefully studied your suggestions and carefully checked the content of the manuscript. As there are up to 44 formulas in the manuscript, if some formulas are divided and displayed separately, the number of formulas is too large, and the research focus of the paper is not easy to be highlighted, so we have not adjusted this part of content for the time being.
Comment 4. “The volume of the frozen wall is incompressible” in L.238.I wonder how the frozen wall keeps its volume in plastic state. It means that the frozen wall behaves like incompressible fluid? Are there no dilative behaviors? Please add references or explanation.
The author's response：
Thank you very much for your opinion. In the case of isotropy, since it is assumed that the frozen wall is an ideal elastic-plastic material, the density change is small after entering the plastic state, which can usually be ignored, and the volume strain is 0, that is, the volume is incompressible. Most scholars adopt the above assumption to simplify the calculation reasonably when studying the homogeneous or heterogeneous frozen wall plastic state. This conclusion is supported by a large number of research results. In this revision, we have marked specific references at the end of this sentence.
Comment 5: k in L.277.In L.277, k is introduced as 2. Is this a general value? How this parameter is determined.
The author's response：
Thank you very much for your opinion. The uneven frost heave coefficient K reflects the frost heave difference in different directions, and the experiment shows that the value of coefficient K is usually between 1 and 3. Therefore, 2.0 is taken for this calculation. And where k is valued, specific references are marked.
Comment 6. Figure 4. In the legend, there are texts from “-100m” to “-600m”. It seems these are the depth of the model. Please add explanation in the legend. The similar cases are found in following Figures as well. Please modify the figures. By the way, are there the frozen walls that depth is 600m?
The author's response：
Thank you very much for your opinion. The main external load of the frozen wall comes from formation pressure. Therefore, with the increase of the depth, the external load keeps increasing, and the stress state of the frozen wall changes accordingly. In the construction of shaft freezing method, the depth of the frozen wall depends on the buried depth of mineral resources. For example, the freezing depth of Polby potash salt mine in the UK reached 930m, and the freezing depth of the auxiliary shaft of Hutaoyu coal mine in China's Gansu Province reached 950m. According to the opinion of the reviewer, we have added relevant explanatory sentences in lines 32-35 and 274-276 of the manuscript.
Comment 7: L.289-L.295.Three state, elastic limit state, elastic-plastic state (elastoplastic state can be found in L 293 as well.) and plastic limit state are introduced in this paragraph. However, the definitions of these states are not introduced. Please add explanations and how the state is represented in the analyses.
The author's response：
Thank you very much for your opinion. In the process of the increase of the external load, the stress state of the frozen wall will go through 3 stages, namely, the elastic stage, the elastic-plastic stage and the plastic stage. When the external load is small, the whole frozen wall is in elastic state. When the external load increases to a certain critical value, the frozen wall enters the elastic-plastic state. The critical load from the elastic state into the plastic state is called the elastic limit load. When the frozen wall is in the elastic-plastic state, the frozen wall is divided into plastic zone and elastic zone from the inner edge to the outer edge. When the external load of the frozen wall increases further, the plastic zone expands gradually. When the whole frozen wall enters the plastic state, the corresponding external load is the plastic ultimate load. The stress state plays an important role in determining the stability of the frozen wall. The stress distribution of the frozen wall varies greatly under different stress states. This addition is found on lines 287-297 of the manuscript.
Comment 8: Figure 5.There are no explanations about the legends as well. What the filled symbols and unfilled symbols mean? Further, the different numeric is displayed in the lines of square, triangle and circle. What these numerics mean? It seems the states changes with p. Please add the explanation.
The author's response:
Thank you very much for your opinion. In this revision, we have added an explanation of the symbols in the Figure 5.
Comment 9: L.298 to L.314.The authors calculated the bearing capacity with different criteria. I understood the bearing capacity changes if different criterion is adopted. I think it is natural and which criterion is adequate for estimating the behavior of frozen wall as consequence? It looks the remaining parts just discussed the mathematical characteristic of the proposed method, and I wonder that there is no information how these results can be used practically.
The author's response:
Thank you very much for your opinion. There are various yield criteria applicable to frozen soil. Currently, the commonly used ones are Mohr–Coulomb strength criteria, Druker–Prager strength criteria, Tresca strength criteria and Twin shear unified failure criterion. Scholars usually choose one of these criteria as the basis for the calculation of mechanical properties of frozen wall. In order to compare the difference of calculation results based on different criteria, the mechanical characteristics of frozen wall were calculated and analyzed with different yield criteria based on the same engineering condition in this study. We have added an explanation of this problem to the manuscript, and the content is added in lines 308 to 314.
Author Response File: 
Author Response.docx
Reviewer 3 Report
Thanks for the authors to preparing interesting research.
Thanks for the authors to preparing interesting research. There are some modification for the article as following:
1- Majority of references are from chines, please cited references that available in English.
2-Based on similarity check the the article has 36% . Please kindly reduce to 18%.
3-There is no verification or validation the result.
4- There is no research flowchart.
5- What is the effect of ice properties on elastoplastic model.
6-Please using and cited the following references which related to your work in your paper.
https://link.springer.com/article/10.1007/s42452-020-2742-z
http://www.ajbasweb.com/old/ajbas/2010/5894-5907.pdf
https://www.emerald.com/insight/content/doi/10.1108/17260531111121495/full/html
https://www.emerald.com/insight/content/doi/10.1108/17260531211241167/full/html?fullSc=1
http://psasir.upm.edu.my/id/eprint/32808/
http://psasir.upm.edu.my/id/eprint/48470/1/FK%202012%20116R.pdf
Comments for author File: 
Comments.pdf
Author Response
Response to the Referees’ Comments
Dear Editors and Reviewers:
Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “Analysis of Elastoplastic Mechanical Properties of Non-Uniform Frozen Wall Considering Frost Heave” (applsci-2125213). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researchers. We have studied comments carefully and have made correction which we hope meet approval. Revised portion are marked in red in the paper. The responds to the reviewer’s comment are as following:
Comment 1: Majority of references are from chines, please cited references that available in English.
The author's response:
Thank you very much for your opinion. It should be noted that important studies on formulas for calculating mechanical properties of frozen wall and frozen surrounding rock are mainly done by Chinese scholars, and the engineering background is mainly the Qinghai-Tibet Railway project in China and the coal mine shaft construction project in eastern China. Therefore, most of the achievements of this part are in Chinese. According to the author's suggestion, we add several references in foreign languages, including papers recommended by reviewers.
Comment 2: Based on similarity check the the article has 36% . Please kindly reduce to 18%.
The author's response:
Thank you very much for your opinion. After communicating with the editor of the journal, we found that the repetition rate of this journal is less than 30%. We have modified the statement of the paper, and now the repetition rate of the manuscript has met the requirements of the journal.
Comment 3: There is no verification or validation the result.
The author's response:
Thank you very much for your opinion. The purpose of this study is to provide a method for the calculation of frost heave and stress of frozen wall. We will verify this method through engineering examples in the subsequent work, and constantly upgrade and optimize the calculation method.
Comment 4: There is no research flowchart.
The author's response:
Thank you very much for your opinion. In this revision, we add research flowchart to line 147-148 of the manuscript.
Comment 5: What is the effect of ice properties on elastoplastic model.
The author's response:
Thank you very much for your opinion. When the temperature of soil decreases below the freezing temperature, the water in soil is transformed into ice. At this time, soil particles and ice together form frozen soil. The elastic modulus of frozen soil increases with the decrease of soil temperature. We explain this problem in line 135-139 of the manuscript.
Comment 6: Please using and cited the following references which related to your work in your paper.
The author's response:
Thank you very much for your opinion. From several papers recommended by reviewers, we selected several papers related to our research as references, and the newly added documents are in lines 460-467 of the manuscript.
Round 2
Reviewer 3 Report
