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Peer-Review Record

Evolution Characteristics of Roof Stress in Horizontal Segmental Mining of Steeply Inclined Coal Seams

Processes 2025, 13(5), 1317; https://doi.org/10.3390/pr13051317
by Guojun Zhang 1,2,3,*, Yong Zhang 3, Shigen Fu 1,2 and Mingbo Chi 1,2,3,*
Reviewer 1: Anonymous
Reviewer 2: Anonymous
Reviewer 3: Anonymous
Processes 2025, 13(5), 1317; https://doi.org/10.3390/pr13051317
Submission received: 4 March 2025 / Revised: 16 April 2025 / Accepted: 22 April 2025 / Published: 25 April 2025
(This article belongs to the Topic Advances in Coal Mine Disaster Prevention Technology)

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper's topic (Evolution Characteristics of Roof Stress in Horizontal Seg-mental Mining of Steeply Inclined Coal Seams) is interesting and needs some revisions before publishing. Please address the following comments:

  1. The maximum horizontal primary stress angle, lateral pressure coefficient, inclination angle, and burial depth are all examined in this study. The authors should explain their choice of these four criteria over others that could affect the distribution of stress (e.g., mining process, rock mass characteristics).
  2. More information about the study's use of FLAC3D finite element numerical simulation software includes:

Boundary conditions (their application and impact).

Mesh resolution (was an investigation of mesh sensitivity done?).

Material properties: are they predicated on values that have been assumed or on field data?

  1. Which validation techniques were applied to guarantee that the FLAC3D simulation results correspond to actual circumstances?
  2. Was the time-dependent behaviour of rock stress redistribution following excavation taken into account in the study?
  3. Reproducibility would be enhanced by these specifics.
  4. To what extent are the outcomes affected by variations in lateral pressure coefficients?
  5. The authors do not offer a quantitative comparison with field measurements, but they do relate their findings to broad patterns.
  6. To compare simulated and actual stress distributions, they ought to think about using statistical error analysis (such as RMSE and correlation coefficients).
  7. Although geological conditions differ in actual mines, the analysis makes the assumption that rock qualities are uniform.
  8. What effects might differences in lithology, fractures, or faults have on the distribution of stress?
  9. Would results from a heterogeneous model be more accurate?
  10. Although stress distribution patterns are presented in the research, it is unclear how these findings might be used to increase mining safety.
  11. Recommendations for roof control techniques, support system design, or early warning signs for mine stability would be beneficial.
  12. English needs some improvement.
Comments on the Quality of English Language

English needs some improvement.

Author Response

Comments 1: The maximum horizontal primary stress angle, lateral pressure coefficient, inclination angle, and burial depth are all examined in this study. The authors should explain their choice of these four criteria over others that could affect the distribution of stress (e.g., mining process, rock mass characteristics).

Response 1: Thanks for your good question. Compared with other factors that may affect the stress distribution, these four factors have the characteristics of universality, directness and controllability in the study of stress distribution, which can more comprehensively describe and explain the main features and changing rules of stress distribution.

(1)Maximum horizontal principal stress angle: This angle determines the direction of the maximum horizontal principal stress, which is often directional in the mechanical properties of materials such as rocks. Different angles of maximum horizontal principal stresses lead to different forms of stress distribution within the object under the same external force.

(2)Lateral pressure coefficient: It reflects the relative magnitude of the horizontal stresses in relation to the vertical stresses. In many geomechanically problems and engineering scenarios, the lateral pressure coefficient directly affects the ratio of horizontal and vertical loads on a structure.

(3)Inclination: In this context, inclination usually refers to the inclination of the level of the body or the inclination of the structural surface, for example. The change of inclination will change the path and distribution of stresses inside the geoid. Because of the different inclination, the stress component caused by gravity and other external forces inside the geoid will be different, and the inclination will also affect the mechanical behavior of the structural surface, such as shear strength.

(4)Depth of burial: As the depth of burial increases, the weight of the overlying rock layer increases, leading to an increase in vertical stress, while the horizontal stress will also change accordingly. Moreover, at different depths of burial, the temperature, humidity and other environmental conditions in which the geologic body is located will be different, and these factors will affect the mechanical properties of the geologic material, which in turn will indirectly affect the distribution of stress.

Comments 2: More information about the study's use of FLAC3D finite element numerical simulation software includes: Boundary conditions (their application and impact). Mesh resolution (was an investigation of mesh sensitivity done?).Material properties: are they predicated on values that have been assumed or on field data?

Response 2: Thanks for your good question. The different maximum horizontal principal stress angles and lateral pressure coefficients in the paper are realized by adjusting the boundary conditions of the model, and the stress boundary conditions in the boundary conditions are set according to equation (2). Mesh sensitivity analysis requires running multiple simulations to calculate the results under different mesh densities, which will significantly increase the computational time and resource consumption, and due to the limited computational resources, the mesh sensitivity analysis could not be carried out. To complete the study within the limited computational resources, a validated meshing method is used in this paper. The material properties for numerical simulations were based on field drilling data, and cores were obtained by drilling, and the drilled cores were brought back to the laboratory for uniaxial compression, triaxial compression, Brazilian disc test, and elastic wave test to obtain the basic mechanical parameters used for numerical simulations. We have also revised the article.

Comments 3: Which validation techniques were applied to guarantee that the FLAC3D simulation results correspond to actual circumstances?

Response 3: Thanks for your good question. The model is run several times under different conditions, and the results show small changes, indicating that the simulation results have high stability. The boundary conditions and initial conditions are set according to the field measured data and engineering experience, which ensure the rationality of the simulation results.

Comments 4: Was the time-dependent behaviors of rock stress redistribution following excavation taken into account in the study?

Response 4: Thanks for your good question. The study ensured that the maximum unbalanced force coefficient of the model was less than 10-5 after each opening by setting the maximum unbalanced force coefficient to 10-5, which fully considered the redistribution of rock stress after excavation.

Comments 5: Reproducibility would be enhanced by these specifics.

Response 5: Thanks for your valuable suggestion. We elaborate on the details of the numerical simulations related to the text.

Comments 6: To what extent are the outcomes affected by variations in lateral pressure coefficients?

Response 6: Thanks for your good question. The transverse pressure coefficient determines the relative magnitude of the horizontal stress in relation to the vertical stress. When the transverse pressure coefficient increases, it means that the horizontal stress increases relative to the vertical stress. This can lead to changes in the distribution of stresses around structures such as underground caverns and tunnels, and the concentration of stresses in the horizontal direction may increase, making the walls of the cavern more susceptible to shear or tensile damage and affecting the stability of the structure. The change of transverse pressure coefficient has a significant effect on the results, and it is one of the parameters to be focused on in many rock mechanics and geoengineering problems, and the exact degree of its influence needs to be quantitatively analyzed through numerical simulation, physical experiments, and on-site monitoring in conjunction with specific engineering or geological problems by a variety of means.

Comments 7: The authors do not offer a quantitative comparison with field measurements, but they do relate their findings to broad patterns.

Response 7: Thanks for your good question. We recognize that we really do not provide quantitative comparisons with field measurements. Instead, we focus on linking our findings to broader patterns observed in previous studies or to general trends in the field. This approach aligns our findings with established knowledge and highlights the consistency of our findings with existing research. By emphasizing broad patterns, we aim to contribute to a holistic understanding of the phenomenon rather than providing specific, quantifiable validation based on field data.

Comments 8: To compare simulated and actual stress distributions, they ought to think about using statistical error analysis (such as RMSE and correlation coefficients).

Response 8: Thanks for your valuable suggestion. To effectively compare simulated and actual stress distributions, incorporating statistical error analysis methods—such as Root Mean Square Error (RMSE) and correlation coefficients—would indeed be highly valuable. These statistical tools provide a quantitative measure of the differences between the simulated results and field measurements, offering a clear and objective way to assess the accuracy of the model. Root Mean Square Error (RMSE) would quantify the average magnitude of the differences between simulated and actual stress values, providing insight into the overall error in the model’s predictions. Correlation coefficients would assess the degree of linear relationship between the simulated and actual data, indicating how well the model captures the trends and patterns in the field measurements. By employing these statistical methods, the authors could not only validate the reliability of their simulations but also identify areas where the model may need refinement. This approach would strengthen the credibility of their findings and provide a more rigorous basis for comparing their results with real-world observations.

Comments 9: Although geological conditions differ in actual mines, the analysis assumes that rock qualities are uniform.

Response 9: Thanks for your good question. While the analysis assumes uniform rock qualities for simplification, it is important to acknowledge that geological conditions in actual mines can vary significantly. This assumption allows for a more straightforward modeling approach and provides a foundational understanding of the system’s behavior. However, it may limit the direct applicability of the results to real-world scenarios where heterogeneity in rock properties (e.g., strength, elasticity, and fracture patterns) plays a critical role. To address this limitation, future studies could incorporate more realistic geological variability by integrating field data on rock heterogeneity or using stochastic modeling techniques. This would enhance the model’s accuracy and make the findings more representative of actual mining conditions. By acknowledging this assumption and its potential impact, the authors lay the groundwork for further refinements and more nuanced analyses in subsequent research.

Comments 10: What effects might difference in lithology, fractures, or faults have on the distribution of stress?

Response 10: Thanks for your good question. Differences in lithology, fractures, or faults can significantly influence the distribution of stress in geological formations. Here’s how each factor might affect stress distribution:

(1)Lithology: Different rock types have varying mechanical properties, such as strength, elasticity, and density. For example, harder rocks like granite may resist deformation and concentrate stress, while softer rocks like shale may deform more easily, redistributing stress unevenly. Variations in lithology can create stress gradients at boundaries between rock types, leading to localized stress concentrations or stress shielding effects.

(2)Fractures: Fractures act as discontinuities that can alter stress pathways. They may either absorb stress, reducing its transmission, or act as stress concentrators, particularly at fracture tips. The orientation and density of fractures can influence the anisotropy of stress distribution, causing stress to vary significantly depending on direction.

(3)Faults: Faults are major structural features that can dramatically redistribute stress. Active faults can create zones of high stress accumulation due to tectonic forces. The type of fault (e.g., normal, reverse, or strike-slip) and its orientation relative to the regional stress field can determine how stress is redistributed in the surrounding rock mass.

These factors can lead to complex, non-uniform stress distributions that deviate from idealized models. Ignoring such heterogeneity may result in inaccurate predictions of stress behavior, which could have implications for engineering design, mining safety, and hazard assessment. Incorporating detailed geological data and advanced modeling techniques can help better capture these effects and improve the reliability of stress distribution analyses.

Comments 11: Would results from a heterogeneous model be more accurate?

Response 11: Thanks for your good question. We think it will be accurate, but it will require a lot of in-situ engineering tests to be carried out:

(1)Accuracy from model characteristics: Heterogeneous models consider the non-uniformity and variability within a material or system, and can describe the actual situation in more detail. For example, in rock mechanics, the actual rock often exists non-uniform characteristics such as pores, cracks, etc. The heterogeneous model can reflect these differences by setting different material properties, structural parameters, etc. Compared with the homogeneous model, which treats the rock as a homogeneous medium, it can more accurately reflect the stress distribution and deformation of the rock when subjected to stresses, and the results of the heterogeneous model will be more accurate in this case.

(2)Accuracy from data requirements: Heterogeneous modeling requires a large amount of detailed data to accurately portray the heterogeneity of a material or system. If the amount of data is insufficient or the quality of data is not high enough to accurately reflect the actual heterogeneous properties, then the constructed heterogeneous model may have bias, resulting in inaccurate results. For example, when studying the stress distribution of soil, if the data on the distribution and content of different components in the soil are not comprehensive, the heterogeneous model may not be able to simulate accurately due to data deficiencies, and may even be less accurate than the homogeneous model based on simplified assumptions.

(3)Accuracy from model complexity: Heterogeneous models usually have higher complexity and contain more parameters and variables, which makes the model solution and calculation process more complicated and easier to introduce errors. And complex models may suffer from overfitting problems, i.e., the model over-adapts to the noise and details in the training data and ignores the general pattern of the data, resulting in poor performance when predicting or simulating new data. For example, when simulating the stress distribution of groundwater flow, an overly complex heterogeneous model may fail to accurately predict the overall flow stress trend due to overfitting to local details.

Heterogeneous models can theoretically describe systems with non-uniform characteristics more accurately, but the accuracy of their results in practical applications is constrained by various factors such as data quality and model complexity, and it is necessary to consider various factors comprehensively and construct and apply heterogeneous models reasonably to improve the accuracy of the results.

Comments 12: Although stress distribution patterns are presented in the research, it is unclear how these findings might be used to increase mining safety.

Response 12: Thanks for your good question. The research on stress distribution patterns provides valuable insights that can be directly applied to enhance mining safety in several ways:

(1)Identifying High-Risk Zones: By understanding stress distribution, mining engineers can identify areas of high stress concentration, which are more prone to rock bursts, collapses, or other failures. This allows for targeted monitoring and reinforcement in these zones to prevent accidents.

(2)Optimizing Mine Design: The findings can inform the design of mine layouts, including the placement of tunnels, pillars, and extraction sequences. By avoiding high-stress areas or redistributing stress more evenly, the risk of structural failures can be minimized.

(3)Support System Design: Knowledge of stress patterns helps in designing more effective support systems, such as rock bolts, shotcrete, or steel arches, tailored to the specific stress conditions of different areas within the mine.

(4)Predicting and Mitigating Hazards: Stress distribution data can be used to predict potential hazards like rock bursts or ground subsidence. Early warning systems and preventive measures, such as controlled blasting or stress relief techniques, can be implemented to mitigate these risks.

(5)Improving Worker Safety Protocols: By mapping stress patterns, mining operations can develop safer work practices, such as restricting access to high-stress areas during critical periods or scheduling maintenance activities when stress levels are lower.

(6)Enhancing Monitoring Systems: The research can guide the deployment of advanced monitoring technologies, such as micro seismic sensors or stress meters, to continuously track stress changes and provide real-time data for decision-making.

While the research presents stress distribution patterns, its practical application requires collaboration between researchers, engineers, and safety professionals to translate these findings into actionable strategies. By integrating this knowledge into mining operations, safety can be significantly improved, reducing the likelihood of accidents and ensuring a safer working environment for miners.

Comments 13: Recommendations for roof control techniques, support system design, or early warning signs for mine stability would be beneficial.

Response 13: Thanks for your valuable suggestion. We have modified the discussion section and the conclusion section。

Comments 14: English needs some improvement.

Response 14: Thanks for your valuable suggestion. We'll get a specialized language editing agency to do the language editing.

Reviewer 2 Report

Comments and Suggestions for Authors

Dear authors

Thank you very much for the submission entitled "Evolution Characteristics of Roof Stress in Horizontal Segmental Mining of Steeply Inclined Coal Seams". Although it is a well-established paper, several parts major revisions. General comments are listed below:

1- The quality of English is not satisfactory for publication. There are some inappropriate sentence structures, typing errors and unclear parts, especially in Section 4. Therefore, proofreading is required.

2- The abstract is too long to comprehend. Please prepare a concise abstract, highlighting the most important findings obtained from your analysis results.

3- The introduction section is weak. Please enlarge this section by considering additional previous studies that encompass numerical analyses on the same issue. In this regard, it recommend you to prepare a table where your additional studies and their fundamental characteristics are mentioned.

4- Figure 1 cannot be clearly seen or understood. Please provide a higher-resolution version of this figure. 

5- In line 120: Moore-Coulomb yield criterion is not a correct term. It should be "Mohr-Coulomb failure criterion".

6- The titles of Table 2 and Table 3 can be revised, as they are written awkwardly

7- The title of Section 4 should be regarded as Result and Discussion section.

8- The axis titles in Figure 6 are missing. 

9- The units of x-axis in Figure 15 (Normal stress in kPa or MPa ?) are missing.

10- Discussion section does not seem to represent all of your findings. Please revise it by highlighting some quantitative data which are ciritical in your work.

11- Conclusion section should also be revised based on the comments raised by the reviewers.

I hope they would be beneficial when revising your manuscript.

Kind regards

Comments on the Quality of English Language

The quality of English is not satisfactory for publication. There are some inappropriate sentence structures, typing errors and unclear parts, especially in Section 4. Therefore, proofreading is required.

Author Response

Comments 1: The quality of English is not satisfactory for publication. There are some inappropriate sentence structures, typing errors and unclear parts, especially in Section 4. Therefore, proofreading is required. 

Response 1: Thanks for your valuable suggestion. We will get language editing from a specialized language touch-up agency, as well as a careful proofreading of Section 4 of the article.

Comments 2: The abstract is too long to comprehend. Please prepare a concise abstract, highlighting the most important findings obtained from your analysis results.

Response 2: Thanks for your valuable suggestion. We have streamlined the abstracts of the articles while highlighting important findings from the analysis.

Comments 3: The introduction section is weak. Please enlarge this section by considering additional previous studies that encompass numerical analyses on the same issue. In this regard, it recommends you to prepare a table where your additional studies and their fundamental characteristics are mentioned.

Response 3: Thanks for your valuable suggestion. We have revised the introduction to the article.

Comments 4: Figure 1 cannot be clearly seen or understood. Please provide a higher-resolution version of this figure.

Response 4: Thanks for your valuable suggestion. We have reworked Figure 1, along with a high-resolution image.

Comments 5: In line 120: Moore-Coulomb yield criterion is not a correct term. It should be "Mohr-Coulomb failure criterion".

Response 5: Thanks for your valuable suggestion. We have revised it and proofread the full text.

Comments 6: The titles of Table 2 and Table 3 can be revised, as they are written awkwardly

Response 6: Thanks for your valuable suggestion. We have revised the titles of Table 2 and Table 3.

Comments 7: The title of Section 4 should be regarded as Result and Discussion section.

Response 7: Thanks for your valuable suggestion. We have revised the title of Section 4.

Comments 8: The axis titles in Figure 6 are missing.

Response 8: Thanks for your valuable suggestion. We have revised the axis titles in Figure 6.

Comments 9: The units of x-axis in Figure 15 (Normal stress in kPa or MPa ?) are missing.

Response 9: Thanks for your valuable suggestion. We have added the units of the x-axis.

Comments 10: Discussion section does not seem to represent all your findings. Please revise it by highlighting some quantitative data which are critical in your work.

Response 10: Thanks for your valuable suggestion. We have modified the discussion section and the conclusion section

Comments 11: Conclusion section should also be revised based on the comments raised by the reviewers.

Response 11: Thanks for your valuable suggestion. We have modified the discussion section and the conclusion section.

Thank you and best regards.

Yours sincerely

 

Reviewer 3 Report

Comments and Suggestions for Authors

Review

processes-3537089

Evolution Characteristics of Roof Stress in Horizontal Seg-mental Mining of Steeply Inclined Coal Seams

 

There are some questions and remarks to be answered:

 

  1. A lack of obtained results in Abstract
  2. A part of text in Introduction is without appropriate citation. Citations should be given in different forms, namely, like: [1], [2], and so on.
  3. Authors should mark what is the scientific novelty of this paper. In Introduction should be presented usually used models with their bottlenecks and problems to solve.
  4. How have the Authors chosen the parameters for simulations?Text should be corrected, some mistakes, lack of spaces, application of capital letters and another time small letters, especially in tables.
  5. There is a lack of error analysis of presented data and methods used for verification and validation of proposed models.
  6. The quality of Figure 15 and 16 should be improved. Also, all the axes should be described in Fig.15 and 16.
  7. The description of data in Table 6 and 7 should be more developed.
  8. A lack of obtained data in Conclusions.
  9. Authors should compare the obtained results with usually used methods to prove that this model is much better or at least comparable.
  10. The References should be supplied with additional literature positions.

 

 

 

Author Response

Comments 1: A lack of obtained results in Abstract

Response 1: Thanks for your valuable suggestion. We have streamlined the abstracts of the articles while highlighting important findings from the analysis.

Comments 2: A part of text in Introduction is without appropriate citation. Citations should be given in different forms, namely, like: [1], [2], and so on.

Response 2: Thanks for your valuable suggestion. We have modified the citation format for references.

Comments 3: Authors should mark what is the scientific novelty of this paper. In Introduction should be presented usually used models with their bottlenecks and problems to solve.

Response 3: Thanks for your valuable suggestion. We have modified the introductory part of the article tweed, clarified the scientific novelty of the paper, and added the commonly used models and their bottlenecks and problems that need to be solved.

Comments 4: How have the Authors chosen the parameters for simulations? Text should be corrected, some mistakes, lack of spaces, application of capital letters and another time small letters, especially in tables.

Response 4: Thanks for your valuable suggestion. The material properties for numerical simulations were based on field drilling data, and cores were obtained by drilling, and the drilled cores were brought back to the laboratory for uniaxial compression, triaxial compression, Brazilian disc test, and elastic wave test to obtain the basic mechanical parameters used for numerical simulations. Errors in the text, such as missing spaces, incorrect use of uppercase and lowercase letters, and mistakes in the tables, should be carefully identified and corrected to ensure accuracy and professionalism in the document.

Comments 5: There is a lack of error analysis of presented data and methods used for verification and validation of proposed models.

Response 5: Thanks for your valuable suggestion. We acknowledge that data error analysis was not adequately performed in the study and that there was a lack of verification and validation methods for the proposed model. This is a limitation of this study and we will improve on it in our subsequent work. Due to the time and resource constraints of the study, we were not able to delve into the sources of data errors and their impact on the results. Also, the verification and validation methods of the model could not be fully implemented at this stage. In future studies, we will take the following measures to remedy these shortcomings: conduct detailed error analysis of the data, including the assessment of systematic and random errors; introduce multiple validation methods, such as cross-validation, comparison with experimental data, or comparison with the results of other models. Despite these shortcomings, the models and methods proposed in this study provide new perspectives and preliminary explorations in related fields, and lay the foundation for subsequent research. We thank you for your valuable questions and will take these suggestions seriously to enhance the rigor and scientific validity of the study. We look forward to further refining the model and data analysis methods in our future work.

Comments 6: The quality of Figure 15 and 16 should be improved. Also, all the axes should be described in Fig.15 and 16.

Response 6: Thanks for your valuable suggestion. We have revised Figure 15 and 16, and Also added a description of the axes.

Comments 7: The description of data in Table 6 and 7 should be more developed.

Response 7: Thanks for your valuable suggestion. We have added a description of Table 6 and 7.

Comments 8: A lack of obtained data in Conclusions.

Response 8: Thanks for your valuable suggestion. We add to our conclusions the data that have been obtained.

Comments 9: Authors should compare the obtained results with usually used methods to prove that this model is much better or at least comparable.

Response 9: Thanks for your valuable suggestion. We fully agree that it is essential to compare the model of this paper with the existing commonly used methods, which can reflect the strengths and weaknesses of the present model more comprehensively, and this will be the focus of our later research.

Comments 10: The References should be supplied with additional literature positions.

Response 10: Thanks for your valuable suggestion. We have carefully revised the formatting of the references as well as the location of the labels.

Thank you and best regards.

Yours sincerely

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Accept in present form.

Author Response

Dear Reviewer,

Thank you very much for your positive feedback and for accepting our manuscript in its present form. We are delighted to hear that our work meets the standards of your esteemed journal. We appreciate the time and effort you have dedicated to reviewing our manuscript and are grateful for your support.

Best regards

Reviewer 2 Report

Comments and Suggestions for Authors

Dear authors

Thank you very much for your revisions. Most of my comments have been considered in detail. However, the abstract section is still too long to comprehend. Please make it simpler by highlighting the most important findings.

Author Response

Dear Reviewer,

Thank you for your valuable feedback and for taking the time to review our revised manuscript. We appreciate your constructive comments and are pleased to hear that most of your concerns have been addressed.

Regarding the abstract, we acknowledge your point about its length and complexity. We have carefully revised it to make it more concise and focused, highlighting the most important findings of our study. We hope the revised version now meets your expectations and improves the clarity of our work.

Please find the updated abstract below for your review:

Steeply inclined coal seams, characterized by their significant inclination angles and complex storage conditions, are globally recognized as challenging seams to mine. An orthogonal test was conducted to study the influence of four key factors, including burial depth, inclination angle, lateral pressure coefficient and maximum horizontal principal stress direction angle, on the force on the top slab of the sharply inclined extra-thick coal seam. The research findings indicate that: The normal stress in the hollow area above the working face increases with greater burial depth, and the normal stress in the mining hollow area above the working face increases with an increase in the lateral pressure coefficient. within the range of 4 meters from the top edge of the seam, the normal stress distribution is approximately linear, and the influence of each factor on the average value of normal stress is in the following order: inclination angle > depth of burial > angle between the maximum horizontal principal stress and the strike angle of the seam > lateral pressure coefficient; outside the range of 4 meters from the top edge of the seam, the distribution of normal stress is approximately linear, and the influence of each factor on the average value of normal stress is in the following order: angle between the maximum horizontal principal stress and the strike of the formation > inclination angle > depth of burial > lateral pressure coefficient.

Best regards

Reviewer 3 Report

Comments and Suggestions for Authors

The authors responded appropriately to most of the comments.

Author Response

Dear Reviewer 

Thank you for your positive feedback and for acknowledging our responses to your comments. We are pleased to hear that our revisions have addressed most of your concerns. Your constructive suggestions have significantly improved the quality of our manuscript, and we are grateful for your time and expertise in reviewing our work.

Best regards,

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