Experimental Study on Permeability Evolution of Sandstone during Triaxial Compression Damage

Round 1

Reviewer 1 Report

Reviewer Comments:

- The English language of the manuscript needs to be revised.
- For readers to quickly catch the paper´s contribution, it would be better to highlight major difficulties and challenges, and the author´s original achievements to overcome them, in a clearer way in the abstract and introduction.
- Please add a sentence or two to clearly recap how your study differs from what has already been done in the literature to ascertain the contributions more strongly.
- Some assumptions are stated in various sections. Justifications should be provided for these assumptions. Evaluation of how they will affect the results should be made.
- More explanation is needed for where there is a research gap and what the goals of the research are. The research gap and the goals of the research are not explained in detail which leads to the reader missing the significance of the research.
- Some key parameters are not mentioned. The rationale for the choice of the particular set of parameters should be explained in more detail. Have the authors experimented with other sets of values? What are the sensitivities of these parameters on the results?

English need minor revision

Author Response

1. 1. The English language of the manuscript needs to be revised.

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

We had revised thoroughly the manuscript to improve the quality of English language usage, ensuring that it is clear, concise, and adheres to proper grammar and syntax.

2. For readers to quickly catch the paper´s contribution, it would be better to highlight major difficulties and challenges, and the author´s original achievements to overcome them, in a clearer way in the abstract and introduction.

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

We had revised the abstract and introduction sections to more prominently highlight the major difficulties and challenges addressed in our study and clarify the original achievements made in overcoming them. This will help readers quickly grasp the paper's contribution:

Contribution: This paper presents a comprehensive study on the deformation behavior, permeability characteristics, and damage progression of sandstone under both dry and saturated conditions. Our primary contribution lies in shedding light on the intricate relationship between rock permeability, stress, and damage, offering valuable insights into rock engineering and hydrogeological applications.

Major Difficulties and Challenges:

• Understanding the behavior of sandstone under varying stress conditions, especially during hydromechanical testing, presented a significant challenge due to its complex deformation patterns.
• Tracking the evolution of permeability throughout different stages of deformation and damage was challenging, as it required precise measurement and analysis.
• Quantifying and characterizing the evolving internal fractures and damage within the rock under changing stress conditions demanded advanced analytical techniques.

3. Please add a sentence or two to clearly recap how your study differs from what has already been done in the literature to ascertain the contributions more strongly.

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

We had added a sentence or two in the introduction section to explicitly recap how our study differs from existing literature. This will strengthen the understanding of the unique contributions of our research.

Our primary contribution lies in shedding light on the intricate relationship between rock permeability, stress, and damage, offering valuable insights into rock engineering and hydrogeological applications. Unlike previous studies that primarily focused on individual aspects of rock behavior, our research holistically examines the interplay between deformation, permeability, and damage, providing a comprehensive framework for understanding sandstone behavior.

4. Some assumptions are stated in various sections. Justifications should be provided for these assumptions. Evaluation of how they will affect the results should be made.

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

We provided justifications for the assumptions made in various sections of the paper. Additionally, we evaluated and discussed how these assumptions may impact the results, ensuring transparency and robustness in our analysis.

5. More explanation is needed for where there is a research gap and what the goals of the research are. The research gap and the goals of the research are not explained in detail which leads to the reader missing the significance of the research.

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

We understood the importance of clarifying the research gap and research goals in more detail. We expanded upon these aspects to help readers better appreciate the significance of our research and understand its context within the existing literature.

6. Some key parameters are not mentioned. The rationale for the choice of the particular set of parameters should be explained in more detail. Have the authors experimented with other sets of values? What are the sensitivities of these parameters on the results?

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

In our study, we conducted hydromechanical tests on sandstone specimens to investigate its deformation behavior, permeability characteristics, and damage progression under various conditions. We recognize the importance of the choice of parameters in our research, and we would like to provide a more detailed explanation of our rationale.

The selection of specific parameters, such as confining pressure gradients, seepage pressure gradients, and stress loading rates, was made based on a combination of theoretical considerations and practical constraints. Our aim was to capture a range of conditions that are representative of geological scenarios commonly encountered in rock engineering and hydrogeological contexts.

While we did perform preliminary sensitivity analyses for some parameters during the experimental design phase, it is essential to acknowledge that variations in these parameters could potentially influence the results. However, due to limitations in time, resources, and the complexity of the testing setup, we chose a set of values that we believed would yield meaningful insights into sandstone behavior without making the study overly complex. Future research endeavors may explore the sensitivities of these parameters more comprehensively.

In the following sections, we will discuss the specific parameters chosen for our experiments, their implications, and how they relate to our research objectives. We acknowledge that further investigations with different parameter sets could provide additional insights and are an avenue for future research in this field.

By providing a more detailed rationale for parameter selection and acknowledging the potential sensitivities, the authors address concerns about the experimental design and parameter choices more comprehensively. This approach helps readers understand the decision-making process and encourages further exploration of parameter sensitivities in future research.

Author Response File: Author Response.pdf

Reviewer 2 Report

Please refer to the attached file for comments and suggestions.

Comments for author File: Comments.pdf

Needs minor editing on the quality of English language.

Author Response

Reviewer 2:

1. The manuscript can still be improved as it has minor errors in sentence structure and grammar.

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

The authors have revised and embellished the manuscript again, the detail can be seen in the highlighted sentence. These changes may have improved the clarity, accuracy and flow of the original text.

2. Provide a discussion about “damage variables” that were mentioned in the Abstract.

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

The authors have added a discussion and introduction of “damage variables”, the detail can be seen in the highlighted sentence:

The study utilizes the Weibull distribution formula to examine the progression of fracture damage in different working conditions and ascertain the correlations between permeability evolution and damage variables, to describe the progression of damage within sandstone as it approaches failure.

3. Define the term "crack strain" and distinguish it from the other strains (e.g., volumetric strain, axial strain).

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

The authors have added a discussion and introduction of “crack stain”, the detail can be seen in the highlighted sentence.

This approach entails the examination of the correlation between volume strain () and axial strain (), along with the relationship between axial strain () and crack strain () , which is calculated by removing calculated elastic strains. The precise values of volume strain () and crack strain () can be computed using the following equations.

4. Expound the significance and application of the results of this study.

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

The significance of this study lies in its contribution to the understanding of sandstone behavior under hydromechanical conditions. The results offer valuable insights for rock engineering, hydrogeology, and geotechnical applications. By comprehensively analyzing deformation, permeability, and damage characteristics, our findings aid in designing safe and efficient structures in rocky environments, optimizing groundwater resource management, and enhancing the assessment of geological formations stability. These results have practical implications for infrastructure development, environmental protection, and resource exploration, making them relevant to a wide range of scientific and engineering disciplines.

5. Use a small letter ”k” for the permeability coefficient.

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

The authors have used a small letter “k” for the permeability coefficient, the detail can be seen in the highlighted sentence:

Within the permeability evolution curve of sandstone, six critical permeability values are identified: (1) Initial permeability under static hydrostatic pressure (k₀); (2) Minimum permeability (k_min); (3) Permeability at the maximum volumetric compression point (k_c); (4) Permeability at the zero volumetric strain point (k_z); (5) Permeability at the peak stress point (ks); (6) Maximum permeability (k_max).

6. In Table 4, indicate the units of k values.

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

The units of k values had been added in Table 4, the detail can be seen in the highlighted sentence:

Table 4. Six key permeability values of sandstone during whole stress-strain process under different conditions

2. It is suggested to change the table title of Table 6 as the contents refer to the predictive models of k.

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

The title of Table 6 had changed, the detail can be seen in the highlighted sentence:

Table 6.  The fitting parameters for the relationship between permeability and volumetric strain of sandstone under different seepage pressure.

3. As part of the conclusion, discuss the implications of the findings for future research and potential applications.

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

Our study's findings have significant implications for future research and applications. Understanding the complex interplay between deformation, permeability, and damage in sandstone under hydromechanical conditions can inform more accurate modeling of geological processes. This knowledge can guide engineering practices in areas such as reservoir management, geotechnical engineering, and hydrogeology. Future research can delve deeper into specific geological scenarios, while practical applications may include optimizing rock engineering designs and enhancing the safety and sustainability of subsurface projects. These findings pave the way for more informed decision-making and innovative solutions in the field of rock mechanics.

4. Some suggested corrections and comments made by the reviewer are highlighted in the manuscript with sticky notes. Please refer to the manuscript with annotated comments.

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

All suggested corrections had been accepted and revision completed accordingly, the detail can be seen in the highlighted sentence in the manuscript.

Author Response File: Author Response.pdf

Reviewer 3 Report

Good day,

thank you for the interesting work, I have a few questions.

Is at least a minimal comparison with the experiments of other scientists possible?

If possible, in Fig. 5-6, also indicate the angle.

Could you write more in text, why permeability kcc can be approximated as the minimum permeability k_min. 

Check the presentation of the presentation of equations and their numbering.

Check citation of reference no. 19.

Author Response

Reviewer 3:

1. Is at least a minimal comparison with the experiments of other scientists possible?

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

Thank you very much for the reviewer's comments again, later the authors will compare and discuss the findings of this paper with those of previous research to further enhance the value of the paper!

2. If possible, in Fig. 5-6, also indicate the angle.

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

All suggested corrections had been accepted and revision completed accordingly, the detail can be seen in Figure 5 ~8.

3. Could you write more in text, why permeability kcc can be approximated as the minimum permeability k_min. 

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

Permeability k_cc can be approximated as the minimum permeability k_min under certain conditions because they coincide during specific stages of rock deformation. This approximation is related to the behavior of the sandstone and the changes in its permeability during different phases of deformation, especially in the context of hydromechanical testing.

The minimum permeability k_min typically represents the lowest permeability value observed during these initial stages of deformation when fractures and voids are closing. This is often considered the "tightest" state of the rock in terms of permeability.

The permeability k_cc, which represents the permeability at the closure stress of rock fractures, tends to align closely with k_min during these initial deformation stages because it captures the point at which fractures and voids are undergoing closure, resulting in a minimal permeability state.

4. Check the presentation of the presentation of equations and their numbering.

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

All suggested corrections had been accepted and revision completed accordingly.

5. Check citation of reference no. 19.

Response: Thank you very much to the reviewers for their careful review of the manuscript and very valuable suggestions.

All suggested corrections had been accepted and revision completed accordingly.

19. Martin C D, Chandler N A. The progressive fracture of Lac du Bonnet granite[J]. International Journal of Rock Mechanics & Mining Science, 1994, 31(6):643-659.

Author Response File: Author Response.pdf