Mechanisms of Overburden and Surface Damage Conduction in Shallow Multi-Seam Mining

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

• The paper provides a sound technical investigation into how mining-induced damage propagates from underground coal seams through the overburden to the surface. Using the Shigetai Mine in western China as a case study, the authors employ physical similarity simulation, field monitoring, and mechanical modelling to analyse the evolution of stress, deformation, and fracturing associated with multi-seam mining.
• The study contributes to the understanding of strata behaviour in shallow coal mining and offers a valuable foundation for optimising ground control strategies in similar geological settings.
• The integration of real-time stress and deformation monitoring with physical simulation, supported by digital speckle and PIV analysis strengthens the study. The progressive excavation of two adjacent seams (2-2 and 3-1) enables the authors to trace the temporal and spatial evolution of overburden collapse and main fracture development. The use of a large-scale, stratigraphically accurate model, with well-defined material similarity ratios and boundary conditions, demonstrates strong experimental design. The clear correlation between experimental results and field data, including working face resistance and observed surface deformation, also adds confidence to the conclusions drawn.
• The authors suitably identify that arch-shaped fracture propagation and layered overburden failure are dominant mechanisms of damage transmission to the surface. The identification of pressure-relief effects in the upper seam goaf during lower seam excavation is relevant for safety design in multi-seam mining. The mechanical modelling of the overburden as a sequence of beam structures (fixed-fixed, cantilever, and semi-supported) reflects a sound understanding of strata mechanics. This model, combined with failure criteria based on tensile and shear stress thresholds, provides a coherent framework for predicting fracture evolution and subsidence onset.
• The mathematical derivation of the deflection and stress equations, although technically correct, could be more readable if supported by clear diagrams or step-by-step explanations. Many readers, especially those with a mining rather than structural mechanics background, can struggle with the dense mathematical presentation. Where possible, assumptions (e.g., uniform load distribution, neglect of abutment pressure) should be justified in relation to mining realities.
• While the results of the strain and stress sensor analysis are valuable, their interpretation would benefit from statistical summarisation or visualisation enhancements. Heatmaps showing zones of high stress concentration across the model could help consolidate the multiple sensor profiles. Discussing the implications of observed stress-relief phenomena in the context of rockburst potential or support optimisation would also broaden the impact of the findings.
• Although the authors note that the collapse patterns follow a ‘step-like’ and ‘progressive’ nature, the effect of varying inter-seam distances, rock lithology, and key stratum thickness on this progression is underexplored. Including a sensitivity discussion, or even referencing prior parametric studies, would help situate the conclusions in a broader design framework.
• The engineering validation section demonstrates the consistency between simulation and field observations, but more detail is needed. What are the magnitudes of discrepancies between predicted and observed surface fracture locations or subsidence rates? A quantitative error analysis would enhance the reliability assessment of the model.
• In terms of broader relevance, the authors could strengthen the conclusion by highlighting how their proposed damage conduction model can influence seam sequencing strategies, safety pillar sizing, or hydraulic support design. The paper currently ends with a strong summary of findings but offers limited forward-looking guidance.
• No major language issues were noted in the paper.
• Figures are mostly clear. High resolution text should be used in Figures 6 and 7.
• References used in the paper are relevant.

Author Response

• Comments 1: The paper provides a sound technical investigation into how mining-induced damage propagates from underground coal seams through the overburden to the surface. Using the Shigetai Mine in western China as a case study, the authors employ physical similarity simulation, field monitoring, and mechanical modelling to analyse the evolution of stress, deformation, and fracturing associated with multi-seam mining.
• Response 1:We sincerely appreciate the reviewer's positive assessment and are grateful for the recognition of our technical investigation into mining-induced damage propagation. Below we provide a point-by-point response to further elaborate on the key contributions of this study: (1) Multi-methodological Approach. Our integrated methodology combining digital speckle correlation, PIV analysis, and comprehensive stress-strain monitoring successfully captured the dynamic propagation of mining-induced damage from underground extraction zones to the surface. This multi-pronged approach enabled us to: Quantify the real-time evolution of fractures and stress redistribution. Validate physical simulation results with field measurements. (2) Key Mechanistic Insights. The study revealed critical phenomena that govern damage propagation: The distinctive "layered fracture → arch expansion → loose layer settlement" failure sequence, stress threshold behaviors in coal pillars and goaf areas, pressure-relief effects during multi-seam mining interactions. (3) Practical Applications.Our findings directly contribute to: Improved support system design (as validated in the 31305 working face), enhanced prediction of surface subsidence patterns, mere effective aquifer protection strategies in shallow coal seam mining. (4) Future Research Directions. Building on these findings, we are currently investigating: Long-term stability of arch structures, water-rock interactions in fractured zones, machine learning applications for damage prediction.
• Comments 2: The study contributes to the understanding of strata behaviour in shallow coal mining and offers a valuable foundation for optimizingground control strategies in similar geological settings.
• Response 2: We sincerely appreciate the reviewer's recognition of our work's contribution to understanding strata behavior in shallow coal mining conditions.
• Comments 3: The integration of real-time stress and deformation monitoring with physical simulation, supported by digital speckle and PIV analysis strengthens the study. The progressive excavation of two adjacent seams (2-2 and 3-1) enables the authors to trace the temporal and spatial evolution of overburden collapse and main fracture development. The use of a large-scale, lithographicallyaccurate model, with well-defined material similarity ratios and boundary conditions, demonstrates strong experimental design. The clear correlation between experimental results and field data, including working face resistance and observed surface deformation, also adds confidence to the conclusions drawn.
• Response 3:We sincerely appreciate the reviewer’s insightful comments and their recognition of the methodological rigor and empirical validation in our study.
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• Comments 4: The authors suitably identify that arch-shaped fracture propagation and layered overburden failure are dominant mechanisms of damage transmission to the surface. The identification of pressure-relief effects in the upper seam goaf during lower seam excavation is relevant for safety design in multi-seam mining. The mechanical modelling of the overburden as a sequence of beam structures (fixed-fixed, cantilever, and semi-supported) reflects a sound understanding of strata mechanics. This model, combined with failure criteria based on tensile and shear stress thresholds, provides a coherent framework for predicting fracture evolution and subsidence onset.
• Response 4: We sincerely appreciate the reviewer’s insightful analysis of our work and their recognition of the key mechanical insights and modeling approaches presented in this study.
• Comments 5: The mathematical derivation of the deflection and stress equations, although technically correct, could be more readable if supported by clear diagrams or step-by-step explanations. Many readers, especially those with a mining rather than structural mechanics background, can struggle with the dense mathematical presentation. Where possible, assumptions (e.g., uniform load distribution, neglect of abutment pressure) should be justified in relation to mining realities.
• Response 5: Thank you very much for the valuable comments provided by the reviewers. These suggestions have important guiding significance for improving the readability and rigor of this article. We fully agree with the expert's viewpoint and will carefully revise according to the suggestions. The specific revision ideas are as follows: for the mathematical derivation of the deflection and stress equations, we will supplement clear schematic diagrams (such as mechanical model diagrams, force analysis diagrams, etc.) to visually display the physical models and mechanical relationships involved in the derivation process. At the same time, we will refine and break down the derivation process, using a step-by-step approach to clarify the physical meaning and mathematical logic of each derivation step, reducing the understanding barriers caused by dense mathematical expressions. Considering that some readers have a background in mining engineering, we will add more textual explanations in the mathematical derivation process, combining abstract mechanical concepts with practical scenarios in mining engineering (such as tunnel support, surrounding rock stress in mining sites, etc.) to help readers better understand the engineering significance of the derivation. For key mathematical formulas, we will provide additional explanations on their applicable conditions and specific application scenarios in mining engineering. For the assumptions mentioned in the article, such as uniformly distributed load distribution and neglecting bridge abutment pressure, we will provide a detailed argumentation process. Based on the actual situation of mining engineering (such as ore body occurrence conditions, mining methods, surrounding rock properties, support structure characteristics, etc.), analyze the rationality and applicability of these assumptions, clarify their engineering significance and limitations in the context of mining engineering, and make the hypotheses more convincing. For example, regarding the assumption of uniformly distributed load distribution, we will compare and analyze the load distribution characteristics of the mining site to demonstrate the approximate rationality of this assumption under specific mining conditions; For the assumption of neglecting bridge abutment pressure, the applicable scenarios will be explained based on the actual stress characteristics of relevant structures in mining engineering.
• Comments 6: While the results of the strain and stress sensor analysis are valuable, their interpretation would benefit from statistical summarisation or visualisation enhancements. Heatmaps showing zones of high stress concentration across the model could help consolidate the multiple sensor profiles. Discussing the implications of observed stress-relief phenomena in the context of rockburst potential or support optimisation would also broaden the impact of the findings.
• Response 6:Thank you for the constructive comments from the reviewers. These suggestions are of great significance for deepening the interpretation of research results and enhancing their practical value. We will revise and improve according to the following ideas: based on the analysis results of strain and stress sensors, we will supplement the statistical summary of the system, combine with the actual needs of rock burst prevention and support optimization in mining engineering, and deeply analyze the observed stress release phenomena. Through the above modifications, we hope to present the inherent patterns of sensor data more clearly and further expand the engineering application scenarios discovered in the research, enhancing the academic influence and practical guidance significance of the results.
• Comments 7: Although the authors note that the collapse patterns follow a ‘step-like’ and ‘progressive’ nature, the effect of varying inter-seam distances, rock lithology, and key stratum thickness on this progression is under explored. Including a sensitivity discussion, or even referencing prior parametric studies, would help situate the conclusions in a broader design framework.
• Response 7:Thank you for the insightful comments from the reviewer. The insufficient exploration of the influence of interlayer spacing, rock lithology, and key layer thickness on the evolution of collapse modes that you pointed out is highly enlightening for us to improve our research framework. We fully agree with the importance of these factors in controlling the collapse process. In future research, we will systematically explore the effects of interlayer spacing, rock lithology, and key layer thickness on the "stepped" evolution characteristics of collapse. By comparing the differences in the starting position, advancing speed, range, and shape of collapse under different parameter combinations, quantifying the sensitivity coefficients of each factor, and clarifying their regulatory mechanisms on the collapse process. At the same time, we will also review the parameterization research results in relevant fields at home and abroad, focusing on citing classic literature on interlayer interactions, lithological differences, and key layer control effects. By comparing the similarities and differences between the conclusions of this study and existing results, we will clarify the supplements and extensions of this study in the analysis of parameter influence mechanisms, thereby placing the conclusions in a broader engineering design framework and enhancing their reference value for optimizing mining schemes under similar geological conditions.
• Comments 8: The engineering validation section demonstrates the consistency between simulation and field observations, but more detail is needed. What are the magnitudes of discrepancies between predicted and observed surface fracture locations or subsidence rates? A quantitative error analysis would enhance the reliability assessment of the model.
• Response 8: Thank you for the insightful comments from the reviewer. Your suggestion to supplement quantitative analysis in the engineering validation section is crucial for improving the rigor of model reliability evaluation. We will make targeted modifications in the following aspects: we will calculate the plane distance deviation between the simulated predicted cracks and the actual observed cracks on site, clarify the robustness boundary of the model prediction, and more comprehensively verify the reliability of the model.
• Comments 9: In terms of broader relevance, the authors could strengthen the conclusion by highlighting how their proposed damage conduction model can influence seam sequencing strategies, safety pillar sizing, or hydraulic support design. The paper currently ends with a strong summary of findings but offers limited forward-looking guidance.
• Response 9:Thank you for the insightful suggestions from the reviewer. Your suggestions on strengthening the correlation between research conclusions and engineering practice, and supplementing forward-looking guidance are of great significance for enhancing the application value of the research. We will increase our prospects for future research, including: coupling damage conduction models with real-time monitoring data (such as microseismic and stress sensor data) to construct a dynamic damage warning system; Expand the applicability of the model under multiple physical fields (such as seepage damage coupling) to cope with deep high water pressure mining environments, and provide extensible directions for subsequent research.
• Comments 10: Figures are mostly clear. High resolution text should be used in Figures 6 and 7.

Response 10: hank you to the reviewer for their detailed feedback. We fully agree with the suggestion regarding the clarity of the text in Figures 6 and 7, which is crucial for improving the readability of the charts. We have optimized Figures 6 and 7 by replacing the text with high-resolution versions to ensure that the text is clear and distinguishable at different scaling ratios, avoiding blurring issues caused by insufficient resolution. After modification, the overall presentation effect of all charts will be rechecked to ensure the match between text and chart content and visual coordination.

Reviewer 2 Report

Comments and Suggestions for Authors

The article presents an interesting investigation and contributes to the ongoing discourse in the field. The clarity of the research question and the overall robustness of the methodology are evident. However, several areas require attention based on the following comments before publication.

1. The methodology is well-detailed, incorporating digital speckle techniques, PIV algorithms, and stress monitoring devices. However, the paper could benefit from more quantitative detail on sensor calibration, spatial layout of measurement devices, and validation procedures for data accuracy. Furthermore, boundary conditions for the structural models should be clarified for reproducibility.
2. The dynamic analysis of rock movement and stress patterns is insightful. The observations—such as stress behavior in coal pillars and goafs—are well-explained and linked to physical mechanisms. The identification of pressure-relief effects between seams is particularly noteworthy. However, graphical representation of stress trends and fracture development over time would strengthen interpretability.
3. The development of three beam-equilibrium structural models provides a strong theoretical underpinning for observed phenomena. The use of yield criteria to assess stability is appropriate. Yet, the derivation or assumptions of these models are not fully elaborated—especially regarding tensile and shear stress distributions. A schematic comparison between model predictions and field data would enhance credibility.
4. The validation using working resistance measurements from the 31305 working face is a strong point. This correlation supports the physical and theoretical interpretations. However, the extent to which these findings are generalizable to other mining settings or seam configurations should be discussed.
5. While the abstract is dense and content-rich, the readability could be improved with clearer segmentation of methods, results, and conclusions. Terms like "arch expansion" and "cut-end coal pillar" should be defined for broader readership. Paragraph transitions should also be smoother to help readers follow the progression of ideas.
6. Expand on how geological heterogeneity was considered in model development.
7. Include temporal data visualizations to show stress evolution clearly.
8. Discuss the implications of your findings for surface ecological restoration and aquifer safety in more depth.
9. Clarify how the findings align or differ from existing literature on overburden damage evolution.

Recommendation

Given the potential impact of the study, I recommend acceptance with major revisions. Addressing the mentioned concerns will significantly strengthen the manuscript.

Comments for author File: Comments.pdf

Author Response

• Comments 1: The methodology is well-detailed, incorporating digital speckle techniques, PIV algorithms, and stress monitoring devices. However, the paper could benefit from more quantitative detail on sensor calibration, spatial layout of measurement devices, and validation procedures for data accuracy. Furthermore, boundary conditions for the structural models should be clarified for reprehensibility.
• Response 1:Thank you for the detailed comments from the reviewers. We will supplement quantitative details on sensor calibration, spatial layout of measurement equipment, data accuracy verification procedures, and boundary conditions of structural models based on the review comments to enhance the rigor and reproducibility of the methodology.
• Comments 2: The dynamic analysis of rock movement and stress patterns is insightful. The observations—such as stress behavior in coal pillars and goafs—are well-explained and linked to physical mechanisms. The identification of pressure-relief effects between seams is particularly noteworthy. However, graphical representation of stress trends and fracture development over time would strengthen interchangeability.
• Response 2: Thank you for the reviewer's suggestions. I have followed the reviewer's comments and started by adding dynamic graphs of stress trends and crack development to enhance the intuitiveness and interchangeability of the results.
• Comments 3: The development of three beam-equilibrium structural models provides a strong theoretical underpinning for observed phenomena. The use of yield criteria to assess stability is appropriate. Yet, the derivation or assumptions of these models are not fully elaborated—especially regarding tensile and shear stress distributions. A schematic comparison between model predictions and field data would enhance credibility.
• Response 3:We have made detailed supplements in the derivation, assumptions, and comparison with on-site data of the three beam balanced structure model according to the review comments. By refining the deduction logic and clarifying the core assumptions, the theoretical foundation of the model can be made more solid; At the same time, supplement stress distribution characteristics and comparative diagrams to further enhance the credibility and interchangeability of the model.
• Comments 4: The validation using working resistance measurements from the 31305 working face is a strong point. This correlation supports the physical and theoretical interpretations. However, the extent to which these findings are generalizationto other mining settings or seam configurations should be discussed.
• Response 4: Thank you for the affirmation and suggestions from the reviewer. Your discussion on the universality of the verification results of the 31305 working face in other mining environments and coal seam configurations is crucial for clarifying the application boundaries of the research. We have discussed the results of measuring and verifying the working resistance of the 31305 working face, explored its generalization in other mining environments and coal seam configurations, analyzed the applicable conditions and limitations, and improved the relevant discussions.
• Comments 5: While the abstract is dense and content-rich, the readability could be improved with clearer segmentation of methods, results, and conclusions. Terms like "arch expansion" and "cut-end coal pillar" should be defined for broader readership. Paragraph transitions should also be smoother to help readers follow the progression of ideas.
• Response 5: Thank you for the detailed suggestions from the reviewer. The abstract you pointed out needs to strengthen the methods, division of results and conclusions, clarify professional terminology, and optimize paragraph transitions, which are crucial for improving the readability of the abstract. We will improve the readability of the abstract by clearly dividing the methods, results, and conclusion sections, defining professional terminology, and optimizing paragraph transitions according to the review comments.
• Comments 6: Expand on how geological heterogeneity was considered in model development.Include temporal data visualizations to show stress evolution clearly.
• Response 6: Thank you for the in-depth suggestions from the reviewer. Your suggestion to supplement the consideration of geological heterogeneity in model development and the visualization of stress evolution time series is of great significance for improving the authenticity of the model and the intuitiveness of the results. We will provide a detailed explanation of the consideration of geological heterogeneity in model development, and supplement the visualization of time-series data that can clearly display stress evolution to improve the relevant parts.
• Comments 7: Discuss the implications of your findings for surface ecological restoration and aquifer safety in more depth.
• Response 7: Thank you to the reviewing experts for their in-depth suggestions. The rock mass movement laws, crack development characteristics, and stress evolution mechanisms revealed in the research have important guiding significance for surface ecological restoration and aquifer safety. We will further explore the specific impact of research results on surface ecological restoration and aquifer safety, analyze their mechanisms from aspects such as rock mass movement and crack development, and propose targeted protection strategies.
• Comments 8: Clarify how the findings align or differ from existing literature on overburden damage evolution.
• Response 8: Thank you to the reviewing experts for their in-depth questions, which clarify the correlation and differences between our research results and existing literature in the field of overburden damage evolution. This will help to highlight the innovative positioning of our research more clearly. We will compare existing literature on the key characteristics, influencing factors, and protection strategies of overlying rock damage evolution to clarify the similarities and differences between our research results and them, in order to clarify the positioning and value of the study.

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Authors, the manuscript Mechanism of damage conduction from overburden to surface in shallow multi-seam mining, Manuscript ID: eng-3818067, has some weaknesses that must be revised appropriately before any further actions are made by the Eng journal, if allowed by the handling Editor.

Please refer to the list below of the most crucial issues:

1. The Abstract section does not properly introduce to the area of study. The problem resolved must be derived to the proper area of research. Please try o reference the general meaning of the analysis provided.
2. Still, the Abstract section is long but messy respectively, the main line of the study is not suitably hughlighted. This section must be shortened but more detailed.
3. According to the Introduction section, each of the cited items should be presented separately and a review of the strong and weak issues addressed in each of them must be listed.
4. Still, if the advantages and disadvantages are not listed, the explanation of the references is not accomplished, respectively, the meaning of the cited items to the content is not included.
5. The flow chart of the procedure is suggested that the main line of the study is not clear.
6. Authors must support the below sentence ‘Additionally, based on historical data from previous similarity simulation model tests, the material composition ratios for each rock layer in the similarity simulation experiment were designed, as detailed in Table 2.’ with some detailed information from previous results.
7. How can be ‘Upon reaching an excavation length of 50 meters, the initial collapse of the basic roof occurred, with a collapse height of 18 meters and crack propagation heights of about 14.5 meters at both ends.’ this occurrence explained and justificated.
8. ‘The main fractures extend outward in an arch shape from the intact rock mass above, with the basic roof and key strata fracturing at specific intervals.’ How can it be originated?
9. From all of the formulas in the paper, they should be referenced to the primary sources since they are not newly proposed by the Authors. It looks like the Authors put their novelty with the equations, but it is not a part of the main proposal.
10. The Outlook section should be added that there are no future proposals mentioned.

From the above, the reviewed manuscript must be improved suitably before any further actions are made by the Eng journal.

Author Response

• Comments 1: TheAbstract section does not properly introduce to the area of study. The problem resolved must be derived to the proper area of research. Please try o reference the general meaning of the analysis provided. Still, the Abstract section is long but messy respectively, the main line of the study is not suitably hughlighted. This section must be shortened but more detailed. 
• Response 1:Thank you to the reviewer for your precise pointing out. Your suggestions for the abstract section hit the core, which is crucial for improving the logic and efficiency of conveying core information in the abstract. We will comprehensively revise the abstract according to the following ideas: clarify the positioning of the research field and anchor the scope of the problem. Sort out the main line and strengthen the logical chain. Simplify redundancy and achieve 'short and refined'.
• Comments 2: According to theIntroduction section, each of the cited items should be presented separately and a review of the strong and weak issues addressed in each of them must be listed. Still, if the advantages and disadvantages are not listed, the explanation of the references is not accomplished, respectively, the meaning of the cited items to the content is not included.
• Response 2:Thank you for the meticulous guidance of the reviewer. Your suggestion that the cited references in the introduction should be analyzed separately for their advantages and disadvantages, as well as their relevance to this article, is of great value in enhancing the academic rigor and logical coherence of the introduction. We will comprehensively revise the introduction section according to the following approach: presenting the literature separately and providing a systematic review to strengthen the connection between the literature and the content of this article. Sort out the current research progress in the field, naturally lead to the entry point of this study, and strengthen the persuasiveness of innovative points.
• Comments 3: The flow chart of the procedure is suggested that the main line of the study is not clear.
• Response 3:Thank you for your valuable feedback. The unclear main line of the research flowchart you pointed out is crucial for improving the visualization of the research logic.
• Comments 4: Authors must support the below sentence ‘Additionally, based on historical data from previous similarity simulation model tests, the material composition ratios for each rock layer in the similarity simulation experiment were designed, as detailed in Table 2.’ with some detailed information from previous results.
• Response 4:When designing the material composition ratio of each rock layer in the similar simulation experiment, we fully referred to the historical data of similar simulation model experiments in the past. Many previous research achievements have provided us with valuable references, and we will supplement relevant content and cite relevant references in this section.
• Comments 5: How can be ‘Upon reaching an excavation length of 50 meters, the initial collapse of the basic roof occurred, with a collapse height of 18 meters and crack propagation heights of about 14.5 meters at both ends.’ this occurrence explained and justificated.
• Response 5: Thank you for the rigorous questions from the reviewer. Your concern about the mechanism and rationality of the initial collapse of the basic roof when the excavation length reaches 50 meters (collapse height of 18 meters, crack propagation height at both ends of about 14.5 meters) is a result of similar simulation experiments. Experimental observations show that when the excavation length reaches 50m, the basic top simulation layer first fractures in the middle of the beam due to the bending moment of the cantilever beam structure exceeding the material's bending limit. Subsequently, the upper direct top simulation layer collapses due to the loss of support, and the accumulated height after the basic top fragmentation and expansion is combined to form a total collapse height of 18m. The height of the crack propagation at both ends is 14.5m, and the constraint effect of the rock mass on both sides mainly distributes the tensile stress concentration zone in the range of 1.4-1.5cm above the coal pillar, which is consistent with the crack propagation height in the experiment and conforms to the mechanical logic of "boundary constraint controls the range of crack development".
• Comments 6: ‘The main fractures extend outward in an arch shape from the intact rock mass above, with the basic roof and key strata fracturing at specific intervals.’ How can it be originated?
• Response 6: Thank you for the in-depth questions from the reviewer. The cause of your concern about "the main cracks extending outward in an arch shape from the intact rock mass above, and the basic top and key layers breaking at specific intervals" can be comprehensively explained from three aspects: the distribution of mining stress field, the structural characteristics of the rock mass, and the energy release law. The specific details are as follows:
• (1) The mechanical root of the extension of arched cracks: the guiding effect of mining induced stress arches. After excavation in the mining area, the stress of the overlying rock mass will be redistributed, forming a "pressure arch" (also known as a "natural equilibrium arch") centered on the goaf—this is a typical characteristic of self regulating stress in the rock mass. According to the theory of elasticity, in the intact rock mass above the goaf, the trajectory of the principal stress will exhibit an arched distribution: compressive stress is transmitted along the axis of the arch, while tensile stress is concentrated at the edge of the arch (i.e. the starting position of the crack). Due to the fact that the tensile strength of the rock mass is much lower than its compressive strength, the tensile stress concentration zone will preferentially rupture, and the direction of crack propagation will extend outward along the tensile stress trajectory line (i.e. arch shape), ultimately forming an arch shaped crack shape that diverges from the intact rock mass towards the goaf.
• (2) Causes of key inter-layer fractures: coupling of rock heterogeneity and critical energy release. The "specific interval fracture" between the basic top and key layers is the result of the combined effect of structural differences and energy accumulation release laws of the rock mass itself: there are natural bedding, joints, or weak interlayers inside the key layers of the rock, and the tensile/shear strength of these weak zones is significantly lower than that of the intact rock mass. When the mining stress is transmitted to the key layer, the stress will preferentially concentrate at the weak zone, causing cracks to first  bedding planes or joints - which directly determines the "interval" of the fractureinitiate along these (the interval distance is consistent with the height of the bedding/joint spacing).
• In summary, arch shaped cracks are the result of concentrated tensile stress under the guidance of mining induced stress arches, while the interval fractures of key layers originate from the coupling effect of weak zones and critical energy release in the rock mass, both of which comply with the basic laws of rock mechanics.
• Comments 7: From all of the formulas in the paper, they should be referenced to the primary sources since they are not newly proposed by the Authors. It looks like the Authors put their novelty with the equations, but it is not a part of the main proposal.
• Response 7:Thank you for the rigorous correction from the reviewer. Your opinion on the need to clearly cite the original source and distinguish innovative points in the formula is crucial for improving the academic standardization of the paper. We fully agree with this viewpoint. We have traced and supplemented the citations of all non original formulas in the paper one by one, while also explaining their specific roles in this study, so that the citation of formulas is closely integrated with the research main line, rather than isolated theoretical stacking.
• Comments 8: The Outlooksection should be added that there are no future proposals mentioned.
• Response 8:Thank you for the important suggestions from the reviewer. The issue you pointed out about the lack of future research directions in the outlook section will be improved, and relevant content will be supplemented based on the limitations of this study and the development trends in the field.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have satisfactorily addressed the review comments, and the manuscript can be published in the Eng Journal.

Reviewer 2 Report

Comments and Suggestions for Authors

I would like to thank the authors to incorporate the important comments required to improve the quality of this article. Based on the comments incorporated, I have decided to accept this article in its current form.

Reviewer 3 Report

Comments and Suggestions for Authors

Paper is suitable for publication.