An Analytical Elastic Solution for Right-Angle Trapezoidal Opening in Steeply Inclined Coal Seam

Round 1

Reviewer 1 Report

In mining engineering, the quantitative assessment of the deformations of the rock mass in mine workings is a constantly relevant area, since the safety of mining operations and the cost of repairing a mine work are based on this.
A detailed study of the presented study made it possible to identify comments and recommendations formulated on their basis to improve the presentation of the research quality:
1. The abstract of the article is very concise, presented in a generalized manner and does not reflect the scientific results obtained. It is recommended to improve it. There are different fonts in the annotation.
2. In the introduction, we would like the authors to give a more detailed analysis of the right-angle trapezoidal shape of mine workings. Why is this form applied? Under what conditions? Several links should be provided. An explanation should also be given in section 2 why mining is carried out in the specified form.
3. In section 2, I would like to see more extended mining and geological information of the object of study. At what depth is the mining carried out, what kind of rocks surround the coal seam? What are the properties of rocks and coal?
4. All presented graphic materials are of poor quality and absolutely not presentable:
Rice. 1 - low image quality and scale; the drawing is preferably presented in color.
Rice. 2 - poor image quality, no inscriptions are visible. Also, why show the application of loads to the boundaries, if this is a scheme for the location of a mine working in a rock mass, and not a calculation scheme for modeling.
Rice. 4 - poor image quality.
Rice. 5, 6, 7, 8 are not representative. It is recommended to remove the green background on the graphs, to make the axis labels as the text font. It is recommended to build the graphs themselves thinner and more distinctly.
5. Formulas are not typed in Microsoft Equation editor and look unpresentable.
6. The elastic modulus and Poisson's ratio obtained by the analytical method should also be indicated at the end of Section 4.
7. It is recommended to compare the results of analytical studies of displacements in a mine working with the results of other authors, for example, with numerical simulations (in line 249). This will show the level of reliability of the method proposed by the authors.
8. The conclusions look generalized and unrepresentative, do not fully disclose the essence of the research and the new results obtained. It is recommended to present the results obtained in quantitative indicators.

Author Response

In mining engineering, the quantitative assessment of the deformations of the rock mass in mine workings is a constantly relevant area, since the safety of mining operations and the cost of repairing a mine work are based on this.
A detailed study of the presented study made it possible to identify comments and recommendations formulated on their basis to improve the presentation of the research quality:
1. The abstract of the article is very concise, presented in a generalized manner and does not reflect the scientific results obtained. It is recommended to improve it. There are different fonts in the annotation.

Answer: Authors have revised the content in manuscript with red font according to the reviewer’s comment.

2.In the introduction, we would like the authors to give a more detailed analysis of the right-angle trapezoidal shape of mine workings. Why is this form applied? Under what conditions? Several links should be provided. An explanation should also be given in section 2 why mining is carried out in the specified form.

Answer: Authors have revised the content in manuscript with red font according to the reviewer’s comment.

3. In section 2, I would like to see more extended mining and geological information of the object of study. At what depth is the mining carried out, what kind of rocks surround the coal seam? What are the properties of rocks and coal?

Answer: Authors have revised the content in manuscript with red font according to the reviewer’s comment.

4. All presented graphic materials are of poor quality and absolutely not presentable:
Rice. 1 - low image quality and scale; the drawing is preferably presented in color.
Rice. 2 - poor image quality, no inscriptions are visible. Also, why show the application of loads to the boundaries, if this is a scheme for the location of a mine working in a rock mass, and not a calculation scheme for modeling.
Rice. 4 - poor image quality.
Rice. 5, 6, 7, 8 are not representative. It is recommended to remove the green background on the graphs, to make the axis labels as the text font. It is recommended to build the graphs themselves thinner and more distinctly.

Answer: Authors have revised the content in manuscript with red font according to the reviewer’s comment.

5. Formulas are not typed in Microsoft Equation editor and look unpresentable.

Answer: Authors have revised the content in manuscript with red font according to the reviewer’s comment.

6. The elastic modulus and Poisson's ratio obtained by the analytical method should also be indicated at the end of Section 4.

Answer: The elastic modulus and Poisson's ratio are obtained by laboratory testing with the rock specimen from Chen-man-zhuang mining project.

7. It is recommended to compare the results of analytical studies of displacements in a mine working with the results of other authors, for example, with numerical simulations (in line 249). This will show the level of reliability of the method proposed by the authors.

Answer: The results of analytical studies of displacements are compared with those of numerical calculation in FLAC software. Authors have revised the content in Fig.5 to Fig.8.

8. The conclusions look generalized and unrepresentative, do not fully disclose the essence of the research and the new results obtained. It is recommended to present the results obtained in quantitative indicators.

Answer: Authors have revised the content in manuscript with red font according to the reviewer’s comment.

Author Response File: Author Response.docx

Reviewer 2 Report

Review report for manuscript processes-1471655

An analytical elastic method was used to calculate the displacements in x and y directions around a trapezoidal cross-section opening. The transformation function of conformal mapping along with complex potential was used to obtain the stress and displacement around the opening. The literature review of the current study is insufficient and the final accuracy of the presented results is ambiguous. It is advised to consider the following comments in the manuscript:

General comments:

1. The elastic deformation around opening using the analytical solution is an old topic and too many researchers have already performed a considerable amount of researches about it even using conformal mapping. The novelty or new findings of this study should be mentioned in the “Introduction” part. In addition, this study lacks information about the previous literature. The authors should add efforts and findings of previous researchers in chronological order and explain the gap of science that they have filled.     
2. In the introduction part of the project in section 2 “Chen-man-zhuang mining project”, authors are encouraged to add supplementary explanations about why they are interested and why it is important to know the stress and displacement around this specific kind of mine coal?
3. P2L59 and P2L61: It is recommended to use the same amount of coal layer thickness.
4. P2L60-62: The expression “seam is excavated for 3402 mining face.” is somehow unclear for readers. Rephrase or add more explanation to clarify this part. Also, is the “3-top” name of the seam? If it is so, please mention it.
5. P5L142-143: Please explain how the authors have derived Eq. (4) using the complex potential function in more detail?
6. P6L149: Eq. (6) defines B’+iC’. It looks that the expression B’-iC’ should be defined instead, as Eq. (5) mentions the B’-iC’.
7. Please create a flowchart and show the flow of work between all parts involved in the analytical solution.
8. The effect of support or lining around the opening is not considered in this study. Please mention it and add a further explanation about it if necessary.
9. P7,8 L 195,196: how the values of principal stresses in the x and y direction were decided? The same is for values of elastic modulus and Poisson ratio in L236. Explain or add required information to the manuscript.
10. Section 5: The authors have shown the displacements in the x and y axes around an opening using analytical results, however, there is no comparison of these results with any other methods such as numerical or direct field measurement to verify the magnitude and accuracy of distribution of the calculated values. Authors are strongly recommended to verify the calculation results by any of the aforementioned methods and add its data to Figs. 5 to 8.

Editorial comments:

1. P1L14: The font of the Abstract should be adjusted with other parts of the manuscript.
2. P6L158: Eq.(1) and (2) should be Eqs. (1) and (2). Also, it seems that “left integral item of Eq.(1)” should be changed into “left integral item of Eq.(4)”, please check it.
3. In P9L224 “radial, tangential and shear stresses denoted as σθ, σr, τρθ, respectively”, probably should be “radial, tangential and shear stresses denoted asσr,σθ,τρθ, respectively”. Please check it.

Comments for author File: Comments.pdf

Author Response

1) The elastic deformation around opening using the analytical solution is an old topic and too many researchers have already performed a considerable amount of researches about it even using conformal mapping. The novelty or new findings of this study should be mentioned in the “Introduction” part. In addition, this study lacks information about the previous literature. The authors should add efforts and findings of previous researchers in chronological order and explain the gap of science that they have filled.

Answer: Authors have revised the content in manuscript with red font according to the reviewer’s comment.

2) In the introduction part of the project in section 2 “Chen-man-zhuang mining project”, authors are encouraged to add supplementary explanations about why they are interested and why it is important to know the stress and displacement around this specific kind of mine coal?

Answer: Authors have revised the content in manuscript with red font according to the reviewer’s comment.

3) P2L59 and P2L61: It is recommended to use the same amount of coal layer thickness.

Answer: Authors have revised the content in manuscript with red font according to the reviewer’s comment.

4) P2L60-62: The expression “seam is excavated for 3402 mining face.” is somehow unclear for readers. Rephrase or add more explanation to clarify this part. Also, is the “3-top” name of the seam? If it is so, please mention it.

Answer: Authors have revised the content in manuscript with red font according to the reviewer’s comment.

5) P5L142-143: Please explain how the authors have derived Eq. (4) using the complex potential function in more detail?

Answer: Eq. (4) is a classical solution in the theory of complex potential functions for the hole problems in elastic mechanics. Therefore, authors think that deriving Eq.(4) is repeating previous research work and it is not necessary to derive Eq.(4) again.

6) P6L149: Eq. (6) defines B’+iC’. It looks that the expression B’-iC’ should be defined instead, as Eq. (5) mentions the B’-iC’.

Answer: B’-iC’ is complex conjugates of B’+iC’, therefore, authors think that there is no necessary to define the B’-iC’.

7) Please create a flowchart and show the flow of work between all parts involved in the analytical solution.

Answer: Authors believe that the derivation process of analytical solution is very clear and the flowchart is not helpful to the study content of this manuscript. Therefore, authors don’t create a flowchart in this manuscript.

8) The effect of support or lining around the opening is not considered in this study. Please mention it and add a further explanation about it if necessary.

Answer: The Elastic mechanics is feasible to solve the problem under the action of uniform load, but the bolt support belongs to the problem under concentrated force and elastic mechanics is not feasible to solve this problem, especially, it is impossible to theoretically solve the problem under concentrated force with the theory of complex function. Therefore, authors don’t consider the theoretical study with bolt support.

9) P7,8 L 195,196: how the values of principal stresses in the x and y direction were decided? The same is for values of elastic modulus and Poisson ratio in L236. Explain or add required information to the manuscript.

Answer: Authors have revised the content in manuscript with red font according to the reviewer’s comment.

10) Section 5: The authors have shown the displacements in the x and y axes around an opening using analytical results, however, there is no comparison of these results with any other methods such as numerical or direct field measurement to verify the magnitude and accuracy of distribution of the calculated values. Authors are strongly recommended to verify the calculation results by any of the aforementioned methods and add its data to Figs. 5 to 8.

Answer: Authors have revised the content in manuscript with red font according to the reviewer’s comment.

Editorial comments:

1) P1L14: The font of the Abstract should be adjusted with other parts of the manuscript.

Answer: Authors have revised the content in manuscript with red font according to the editorial comment.

2) P6L158: Eq.(1) and (2) should be Eqs. (1) and (2). Also, it seems that “left integral item of Eq.(1)” should be changed into “left integral item of Eq.(4)”, please check it.

Answer: Authors have revised the content in manuscript with red font according to the editorial comment.

3) In P9L224 “radial, tangential and shear stresses denoted as σθ, σr, τρθ, respectively”, probably should be “radial, tangential and shear stresses denoted asσr,σθ,τρθ, respectively”. Please check it.

Answer: Authors have revised the content in manuscript with red font according to the editorial comment.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors have done a good job of making corrections. The quality of the research presented has been significantly improved.

Author Response

Authors have revised the content in manuscript according to the reviewer’s and editorial comments, and the revisions made to the manuscript are marked up using the “Track Changes” function in MS Word.

Reviewer 2 Report

Main comments:

• Section 5: The authors added the numerical results using FLAC. The least amount of information about numerical analyses such as overall mesh, boundary conditions, material properties, and applied loads are better to be added.      

Editorial comments:

• P1L39: “is applied …” should be “are applied”.
• P2L54: “from 15 to 16” should be “15 and 16”.
• P4L16: “Where” should be written as “where”. Indentation is not needed. The same is for P5L143. Please apply it to other similar occasions.
• P7L173: “A expansion” should be “An expansion”.
• P7L177: “is obtained” should be “are obtained.”
• There are too many other grammatical mistakes, the manuscript should be proofread thoroughly once more.

Author Response

Authors have revised the content in manuscript according to the reviewer’s and editorial comments, and the revisions made to the manuscript are marked up using the “Track Changes” function in MS Word.