Dear Editors:

We are very grateful for your letter and for the comments concerning our manuscript entitled “Meso-structural evolution of sandstone under uniaxial loading: a study on microdefect compaction and transgranular crack formation mechanisms” (ID: PONE-D-24-51359). Those comments are very valuable and helpful for revising and improving our paper, as well as the important guiding significance to our research. We have studies the comments carefully and have made corrections which we hope meet with approval. Revised portions are marked in Revision Mode in the Revised Manuscript with Track Changes. The main corrections in the paper and the responses to the Editors’ comments are as follows:

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Revision notes (Reply in blue)

The first is the reference list that is too much Asia-centered. Please note that the used technique has been widely used worldwide so please consider worldwide literature. Here I just report three examples but the list is very long:

Trippetta F, Collettini C, Meredith PG, Vinciguerra S. Evolution of the elastic moduli of seismogenic Triassic Evaporites subjected to cyclic stressing. Tectonophysics. 2013;592:67-79.

Grindrod PM, Heap MJ, Fortes DA, et al. Experimental investigation of the mechanical properties of synthetic magnesium sulfate hydrates: Implications for the strength of hydrated deposits on Mars. Journal of Geophysical Research E: Planets. 2010;115(6):1-15. doi:10.1029/2009JE003552

Heap MJ, Faulkner DR, Meredith PG, Vinciguerra S. Elastic moduli evolution and accompanying stress changes with increasing crack damage: Implications for stress changes around fault zones and volcanoes during deformation. Geophysical Journal International. 2010;183(1):225-236. doi:10.1111/j.1365-246X.2010.04726.x

Faulkner DR, Mitchell TM, Healy D, Heap MJ. Slip on “weak” faults by the rotation of regional stress in the fracture damage zone. Nature. 2006;444(7121):922-925. doi:10.1038/nature05353

Reply: We sincerely appreciate the valuable comments and recommended literatures on our manuscript. Your suggestion are of great importance to our research, and we have carefully considered your comments, particularly regarding the concern that our Reference list was too Asia-centered. We have reflected deeply on this issue and have made significant revisions to ensure a more global perspective in our manuscript. Meanwhile, we acknowledge the global application of the techniques we have employed and recognize the necessity of expanding our literature to include studies from around the world.

Firstly, we have carefully reviewed the four literatures you recommended and believe they are highly relevant to our research. Therefore, we had added the above four literatures to the manuscript.

1. Faulkner DR, Mitchell TM, Healy D, Heap MJ. Slip on “weak” faults by the rotation of regional stress in the fracture damage zone. Nature. 2006;444: 922–925. doi:10.1038/nature05353 [added in the manuscript (please see Lines 35-38) and References (Lines 620-621)]

48. Heap MJ, Faulkner DR, Meredith PG, Vinciguerra S. Elastic moduli evolution and accompanying stress changes with increasing crack damage: Implications for stress changes around fault zones and volcanoes during deformation. Geophys J Int. 2010;183: 225–236. doi:10.1111/j.1365-246X.2010.04726.x [added in the manuscript (please see Lines 196-198) and References (Lines 774-776)]

49. Trippetta F, Collettini C, Meredith PG, Vinciguerra S. Evolution of the elastic moduli of seismogenic triassic evaporites subjected to cyclic stressing. Tectonophysics. 2013;592: 67–79. doi:10.1016/j.tecto.2013.02.011 [added in the manuscript (please see Lines 196-198) and References (Lines 777-779)]

54. Grindrod PM, Heap MJ, Fortes AD, Meredith PG, Wood IG, Trippetta F, et al. Experimental investigation of the mechanical properties of synthetic magnesium sulfate hydrates: Implications for the strength of hydrated deposits on mars. Journal of Geophysical Research: Planets. 2010;115. doi:10.1029/2009JE003552 [added in the manuscript (please see Lines 367-369) and References (Lines 801-804)]

Secondly, we have replaced the existing Asia literatures in our manuscript with References that provide a more comprehensive context and support for our research. Below are the additional references we have included.

6. Göğüş ÖD, Avşar E. Stress levels of precursory strain localization subsequent to the crack damage threshold in brittle rock. PLOS ONE. 2022;17: e0276214. doi:10.1371/journal.pone.0276214 [added in the manuscript (please see Lines 38-40 and Lines 287-288) and References (Lines 632-633)]

14. Cheng H, Yang X, Zhang Z, Li W, Ning Z. Damage evaluation and precursor of sandstone under the uniaxial compression: Insights from the strain-field heterogeneity. PLOS ONE. 2021;16: e0262054. doi:10.1371/journal.pone.0262054 [added in the manuscript (please see Lines 49-51) and References (Lines 655-657)]

19. Brantut N, Petit L. Micromechanics of rock damage and its recovery in cyclic loading conditions. Geophys J Int. 2023;233: 145–161. doi:10.1093/gji/ggac447 [added in the manuscript (please see Lines 53-55) and References (Lines 673-674)]

38. Wang Z, Wang R, Li T, Qiu H, Wang F. Pore-scale modeling of pore structure effects on P-wave scattering attenuation in dry rocks. PLOS ONE. 2015;10: e0126941. doi:10.1371/journal.pone.0126941 [added in the manuscript (please see Lines 101-102, Lines 111-112, Lines 206-207 and Lines 349-350) and References (Lines 729-730)]

39. Stan-Kłeczek I, Idziak AF. The changes of P-wave velocity of rock samples over time. Procedia Engineer. 2017;191: 483–487. doi:10.1016/j.proeng.2017.05.207 [added in the manuscript (please see Lines 101-102 and Lines 111-112) and References (Lines 734-735)]

40. Olatinsu OB, Olorode DO, Clennell B, Esteban L, Josh M. Lithotype characterizations by nuclear magnetic resonance (NMR): A case study on limestone and associated rocks from the eastern dahomey basin, nigeria. J Afr Earth Sci. 2017;129: 701–712. doi:10.1016/j.jafrearsci.2017.02.005 [added in the manuscript (please see Lines 115-116 and Lines 236-238) and References (Lines 740-742)]

41. Kleinberg RL, Kenyon WE, Mitra PP. Mechanism of NMR relaxation of fluids in rock. J Magn Reson A. 1994;108: 206–214. doi:10.1006/jmra.1994.1112 [added in the manuscript (please see Lines 120-121) and References (Lines 745-746)]

42. Dijk P, Berkowitz B, Bendel P. Investigation of flow in water-saturated rock fractures using nuclear magnetic resonance imaging (NMRI). Water Resources Res. 1999;35: 347–360. doi:10.1029/1998WR900044 [added in the manuscript (please see Lines 123-124 and Lines 240-242) and References (Lines 750-752)]

43. Keller WD, Reynolds RC, Inoue A. Morphology of clay minerals in the smectite-to-illite conversion series by scanning electron microscopy. Clays Clay Miner. 1986;34: 187–197. doi:10.1346/CCMN.1986.0340209 [added in the manuscript (please see Line 131 and Lines 241-242) and References (Lines 753-755)]

45. Vos K, Vandenberghe N, Elsen J. Surface textural analysis of quartz grains by scanning electron microscopy (SEM): from sample preparation to environmental interpretation. Earth Sci Rev. 2014;128: 93–104. doi:10.1016/j.earscirev.2013.10.013 [added in the manuscript (please see Line 131 and Lines 241-242) and References (Lines 762-764)]

51. Daigle H, Johnson A, Thomas B. Determining fractal dimension from nuclear magnetic resonance data in rocks with internal magnetic field gradients. GEOPHYSICS. 2014;79: D425–D431. doi:10.1190/geo2014-0325.1 [added in the manuscript (please see Lines 234-236) and References (Lines 786-788)]

We believe that with these additional references, our research will be more comprehensive and have a greater international impact.

Moreover the structure of the paper, after a quick reading, seems to be not so clear. Please clearly separate what comes from data, what are the discussions and what are the main scientific conclusions.

Reply: We appreciate your observation regarding the clarity of the manuscript’s structure and agree that a well-organized presentation is crucial for effective communication of our research findings. Upon your suggestion, we have revisited the structure of our manuscript to ensure that the data, discussions, and main scientific conclusions are clearly separated and distinctly presented.

We have made the following revisions to enhance the clarity and organization of our manuscript:

Relocation of “Mesoscopic phenomena and discussion”: we have moved the content that was originally under the section “Mesoscopic phenomena and discussion” to the “Experimental results and analysis” section (please see Lines 232-332). Additionally, we have renamed this section to “Mesoscopic phenomena of specimens” to better reflect the focus of the content and to align it more closely with the experimental results. Meanwhile, the section now includes two distinct subsubsections: “Microdefect propagation under low loading stresses” (please see Lines 246-301) and “Meso-structure transformation under high loading stresses” (please see Lines 302-332). This relocation ensures that the mesoscopic phenomena of specimens is directly associated with the macro-mechanical characteristics of specimens, providing a more coherent narrative and clearer understanding of our findings.

Reorganization of “Damage parameters based on mechanical data”: The section previously titled “Damage parameters based on mechanical data” has been shifted to the “Discussion” section (please see Lines 334-371). This section allows for a more focused analysis of the damage parameters, facilitating a deeper exploration of their implications and significance in the context of our research.

Following the structure revisions to our manuscript, we have also updated the figure numbering to reflect the new order of content. The changes are as follows: (1) Figure originally labeled as “Fig 7” is now renumbered to “Fig 6” (please see Lines 266-268). (2) Figure originally labeled as “Fig 8” is now renumbered to “Fig 7” (please see Lines 270-272). (3) Figure originally labeled as “Fig 9” is now renumbered to “Fig 8” (please see Lines 300-301). (4) Figure originally labeled as “Fig 10” is now renumbered to “Fig 9” (please see Lines 321-322). (5) Figure originally labeled as “Fig 6” is now renumbered to “Fig 10” (please see Lines 346-348).

We believe that these modifications will improve the logical progression of the paper and make it easier for readers to follow the narrative from experimental results to their implications and broader scientific conclusions.

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at

https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf

and

https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf

Reply: Thank you for your guidance on ensuring that our manuscript adheres to the style requirements of PLOS ONE. We have reviewed the formatting templates provide on the PLOS ONE website and have made the necessary adjustments to our manuscript to comply with these standards.

Specifically, we have update the formatting of our sections to better align with the journal’s guidelines.

(1) Section Title Change: We have changed the section title from “1. Introduction” to simply “Introduction” (please see Line 34) removing the numeral to maintain consistency with the non-numbered style typically used for introductory sections in academic papers.

(2) Section Title Change: We have renamed the section previously titled “2. Experimental Materials and Scheme” to “Experimental materials, equipment, and process” (please see Line 83). This new title provide a more comprehensive overview of the content covered in this section, which includes the materials used, the equipment involved, and the process followed in our experiments.

Subsection Title Changes: The subsection previously titled “2.1 Preparation of Experimental Materials” is now “Preparation of experimental materials” (please see Line 85). The subsection previously titled “2.2 Experimental methods” is now “Experimental equipment” (please see Line 106). The subsection previously titled “2.3 Experimental scheme and procedure” is now “Experimental process” (please see Line 136). These changes ensure that our section headings are not only consistent with the non-numbered style typically used for introductory sections but also more accurately reflect the content of each subsection, enhancing the readability and navigability of our manuscript.

(3) Section Title Change: We have renamed the section previously titled “3. Experimental Results and Analysis” to “Experimental results and analysis” (please see Line 182). This change aligns with the journal’s preference for non-numbered headings and provides a clearer and more direct title for the section.

Subsection Title Changes: The subsection titled “3.1 Macro-mechanical Characteristics of Specimens” is now “Macro-mechanical characteristics of specimens” (please see Line 183). This change removes the numeral to maintain consistency with the non-numbered style and better reflects the content of the subsection.

(4) In response to your feedback and to enhance the structure of our manuscript, we have introduced a standalone “Discussion” section (please see Lines 333-563). This section has been carefully curated to provide a comprehensive analysis of our findings and their implications. We have organized this section into two main parts, with further to ensure clarity and depth in our discussions.

The “Discussion” section now include:

Damage parameters based on mechanical data: This part of the discussion focuses on the interpretation of damage parameters derived from our mechanical data. It provides insights into the quantitative aspects of material behavior under the conditions of our experiments. (please see Lines 334-371)

Meso-structure evolution of sandstone under uniaxial loading: This section delves into the meso-scale structural changes observed in sandstone when subjected to uniaxial loading (please see Lines 470-563). It is further divided into two sub-sections for a more detailed examination:

Theoretical analysis based on granular mechanics: Here, we discuss the theoretical framework that underpins our observations of granular mechanics and how it relates to the meso-structure evolution of sandstone. (please see Lines 483-551)

Significance of mineral evolution behavior in the rock stress-strain process: In this sub-section, we explore the role of mineral evolution and its impact on the stress-strain behavior of the rock, highlighting the significance of these behaviors in the context of our study. (please see Lines 552-563)

These additions and subdivisions are intended to provide a more structured and in-depth discussion of our results, facilitating a better understanding of the implications of our research.

(5) We have revised the section title from “6. Conclusion” to “Conclusion” (please see Line 564), removing the numerical adhere to the journal’s preference for unnumbered headings in the presentation of key sections such as the conclusion.

We believe these revisions enhance the readability and organization of our manuscript, aligning it more closely with the stylistic standards of PLOS ONE and improving the overall presentation of our research.

2. We note that this submission includes NMR spectroscopy data. We would recommend that you include the following information in your methods section or as Supporting Information files: 1) The make/source of the NMR instrument used in your study, as well as the magnetic field strength. For each individual experiment, please also list: the nucleus being measured; the sample concentration; the solvent in which the sample is dissolved and if solvent signal suppression was used; the reference standard and the temperature. 2) A list of the chemical shifts for all compounds characterised by NMR spectroscopy, specifying, where relevant: the chemical shift (δ), the multiplicity and the coupling constants (in Hz), for the appropriate nuclei used

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Submitted filename: Response to Reviewers.doc

Response Letter

Dear Editors and Reviewers:

We are very grateful for your letter and for the comments from Reviewers and Editors concerning our manuscript entitled “Meso-structural evolution of sandstone under uniaxial loading: a study on microdefect compaction and transgranular crack formation mechanisms” (ID: PONE-D-24-51359R1). These comments have been very valuable and helpful in revising and improving our paper, and they provide important guidance for our research. We have carefully studies the comments and made corrections that we hope will meet with your approval. All changes to the manuscript are marked in Revision Mode in the Revised Manuscript with Track Changes. The main corrections in the paper, as well as our responses to the Reviewers’ and Editors’ comments, are as follows:

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Reviewer Comments:

Response to reviewer #1:

The meso-structural evolution of sandstone under uniaxial loading was examined by NMR and SEM in this study. The effect of different stress level on rock damage was discussed. However, the current experimental results were insufficient to demonstrate the proposed mechanism. Further analysis and discusses are required to derive some quantitive conclusions.

Reply: We sincerely appreciate your valuable suggestions regarding our manuscript and have given them thorough consideration. Regarding your concern that the current experimental results are insufficient to demonstrate the proposed mechanism, we will enhance the data analysis and further expand the discussion to derive more quantitative conclusions. We plan to include additional experimental data and provide a deeper analysis of the existing results to better clarify the impact of different stress levels on rock damage and its underlying mechanisms. Furthermore, we will incorporate more quantitative analyses to strengthen the conclusions and ensure their robustness.

Once again, thank you for your constructive suggestion. We will address these issues in the revised manuscript and aim to improve its quality.

Some of my concerns are listed below.

Comment #1.1:

What does the symbol εl and εl ^d in the title description of Fig.3 represent?

Reply: We apologize for any confusion caused to the Reviewer. In the title description of Fig.3, the symbol represents the lateral strain, while the symbol represents the lateral strain corresponding to the crack damage stress . Additionally, to avoid ambiguity, we have added a description of these symbols in the revised manuscript. (Lines 149-153) Furthermore, we have also included the symbol explanations in Figure 3 to provide further clarity.

Fig 3. Determination of the stress threshold: (a) curve between axial stress ( ) and volumetric strain ( ), i.e., , where is the axial strain and is the lateral strain ; (b) curve between axial stress ( ) and relative compression strain ( ), i.e., , where is the lateral strain corresponding to the crack damage stress ; (c) curve between axial stress ( ) and axial strain ( ), and (d) uniaxial stress–strain curve of the specimens. (Lines 149-153)

Comment #1.2:

Please provide the actual unloading stress-strain curves besides Fig.4 to illustrate the residual plastic strain.

Reply: Thank you for your valuable suggestion and for highlighting the need to provide unloading stress-strain curves to illustrate the residual plastic strain. Due to the limitations of our testing equipment, once the loading stress reaches the preset value, the system immediately unloads, which prevents us from accurately capturing the true unloading axial strain data. As a result, we were unable to obtain precise residual plastic strain during the unloading process. However, in response to your comment, we have included the loading stress-strain curves for the 12 specimens under 5 MPa, 15 MPa, 30MPa, and 40 MPa loading conditions. These loading curves are provided in the revised manuscript (Figure 4b), and the corresponding data have been made available in the S1 Data section. While we are unable to provide the actual unloading stress-strain curves, we believe the inclusion of the loading curves and the detailed loading paths will still offer valuable insights into the mechanical behavior of the specimens.

We would also like to thank you for the excellent suggestion regarding unloading axial strain measurements. We will focus on incorporating these measurements in our future research to obtain precise residual plastic strain data.

Fig 4. Loading damage process of the specimens: (a) axial stress-loading time curve of sandstone under uniaxial loading; and (b) axial stress-axial strain curve for sandstone under different loading stress. (Lines 174-175)

Comment #1.3:

The 15 specimens were divided into five groups, and so there should be 3 points under every test condition. But there seem to be only one or two points in Fig.10. Please explain it.

Reply: Thank you for your valuable comment. We apologize for any confusion caused regarding the data points in Figure 10. As you correctly noted, the 15 specimens were divided into five groups, and ideally, each test condition should have three data points. In fact, Figures 10a and 10b do include three data points for each group. However, for the total porosity presented in Figure 10c, the data was obtained through Nuclear Magnetic Resonance (NMR) testing, which requires the specimens to be saturated. To minimize the impact of saturation on the specimens, we selected only one specimen per group for the NMR testing. This is why Figure 10c shows only one data point per group for total porosity. Furthermore, the degree of deterioration in Figure 10d was calculated as the average of the data presented in Figures 10a, 10b, and 10c, which is why it also contains only one data point per group.

We sincerely apologize for any confusion caused by this explanation. To clarify the experimental process, we will revise the manuscript as follows: (4) NMR tests were applied. After the P-wave velocity tests, one specimen from each group were saturated in a vacuum saturator for more than 24 h and then tested using NMR to determine the total porosity, pore size distribution, and MRI characteristics. (Lines 181-184)

Comment #1.4:

Please provide the stress-strain curves for every test listed in the Table.3. Only one of every group of samples was illustrated in Fig.5, please draw the curves for other two samples.

Reply: Thank you for your suggestion. We appreciate your careful review of the manuscript. Regarding your request to provide the stress-strain curves for every test listed in Table 3, we apologize for the oversight in Figure 5. As you pointed out, only one specimen from each group was illustrated. We will revise the manuscript to include the stress-strain curves for the other two specimens in each group to ensure all data points are represented clearly. Additionally, we will also include all stress-strain curve data in the S1 Data section to provide full access to the underlying data.

Fig 5. Uniaxial stress–strain curves of specimens subjected to different loading stresses.

Comment #1.5:

As shown in Table.3 and Table.4, the elastic modulus is increased to 24.52 from 12.80, but the P-wave velocity is increased to only 2576 from 2545. The variation of elastic modulus is far distinct to that of P-wave velocity. The elastic modulus is increased almost two times, but the P-wave velocity is almost unchanged. Please explain it.

Reply: Thank you for your insightful comment and for pointing out the discrepancy between the changes in the elastic modulus and the P-wave velocity. We appreciate your careful review. The observed difference between the variations in elastic modulus and P-wave velocity can be attributed to the distinct nature of these two parameters. The elastic modulus reflects the stiffness of the specimen, which is influenced by the overall structure and mineral composition of the sandstone. When the sandstone is subjected to increasing loading, the inter-granular contacts are compacted, leading to an increase in stiffness, and consequently, the elastic modulus increases significantly. On the other hand, the P-wave velocity is more sensitive to the specimen’s internal meso-structure, particularly the porosity and the presence of cracks. While the compaction of the specimen under stress may result in a slight increase in P-wave velocity, it is not as drastically affected as the elastic modulus. The relatively small change in P-wave velocity could be due to the fact that, while microdefects are compacted, the overall structure still retains some degree of porosity, which limits the change in wave propagation speed.

We hope this explanation clarifies the observed discrepancy. Thank you again for your valuable feedback.

Comment #1.6:

It was stated in the text that 'the specimens subjected to 5 MPa loading stress shows an increase in micro-pores and a decrease in small-pores in terms of porosity, while the porosity of medium-pores and large-pores remains largely unchanged'. However, it was noticed form the Table 5 that the porosity of micro-pores changed from 4.294% to 4.305% and the porosity of medium-pores changed from 1.18% to 1.156%. Why was the porosity of micro-pores considered as increased while the porosity of medium-pores considered as largely unchanged? Please double check the statements in this paragraph and make sure they are consistent with the data in the Table 5.

Reply: Thank you for your valuable suggestion and for pointing out the discrepancy between the description in the manuscript and the data presented in Table 5. We apologize for the inconsistency appreciate your attention to detail in bringing this to our attention.

Upon reviewing data, we reanalyzed the pore classification and made revisions to ensure greater accuracy in the analysis. Specifically, we have updated the pore classification standards. To original classification of micro-pores (0-0.06μm), small-pores (0.06-1μm), medium-pores (1-8μm), and large-pores (above 8μm) has been revised to micro-pores (0-0.08μm), small-pores (0.08-1μm), medium-pores (1-8μm), and large-pores (above 8μm). In addition, we placed more emphasis on the changes in the peaks of the pore size distribution (Fig 6) during our subsequent analysis.

To address your concern and ensure the accuracy of the data interpretation, we have revised the manuscript to better reflect the data in Table 5 and Fig 6: As shown in Fig 6a, compared with the specimens without loading stress (0 MPa), the specimens subjected to 5 MPa loading stress show a significant increase in the first peak (0.02μm) and second peak (0.25μm), while the third peak (2μm) and fourth peak (10μm) remain largely unchanged. Additionally, within the micro-pores range (0-0.08μm), there is a notable reduction in pore sizes between 0.03-0.08μm, while the pore sizes between 0-0.03μm increase. This result directly demonstrates that under uniaxial loading, larger pores in the specimens are compressed and transformed into smaller pores during the early stage of crack closure. On the other hand, the specimens subjected to 15 MPa loading stress show a slight increase and a rightward shift in the first peak, while the second peak (0.25μm), third peak (2μm), and four peak (10μm) all show a noticeable increase (Fig 6a). More significantly, the porosity of micro-pores (0-0.08μm) shows a slight increase, while the porosity of small-pores (0.08-1μm) shows a slight decrease (Table 5). Additionally, the porosity of medium-pores (1-8μm) and large-pores (>8μm) increases significantly (Table 5). (Lines 272-285)

Table 5. Pore size distribution of specimens under different loading stresses

Loading

stress

Pore size 0MPa 5MPa 15MPa 30MPa 40MPa

Porosity

n0/% Porosity

n0/% Porosity

n0/% Porosity

n0/% Porosity

n0/%

Micro-pores

(0-0.08μm) 4.631 4.580 4.671 5.178 5.465

Small-pores

(0.08-1μm) 4.022 3.951 3.955 4.327 4.634

Medium-pores

(1-8μm) 1.180 1.156 1.687 1.723 1.553

Large-pores

(8μm) 0.001 0.009 0.058 0.024 0.068

Total porosity n/% 9.834 9.696 10.371 11.252 11.720

Fig 6. NMR characteristics of specimens under different loading stresses: (a) pore size distribution of specimens without loading stress (0 MPa) and with 5 and 15 MPa loading stresses; and (b) pore size distribution of specimens subjected to 15, 30, and 40 MPa loading stresses.

Comment #1.7:

Please explain how to distinguish and recognize the skeleton minerals and filler minerals in SEM images as shown in Fig.9.

Reply: Thank you for your valuable comment and for raising this important point regarding the identification of skeleton minerals and filler minerals in the SEM images shown in Figure 9. In the SEM images, we distinguish skeleton minerals from filler minerals based on their distinct morphological characteristics. Skeleton minerals, such as quartz and feldspar, typically exhibit angular or sub-angular shapes with well-defined edges and a more crystalline appearance. These minerals often form the structural framework of the sandstone. In contrast, filler minerals, including clay minerals and carbonates, tend to have a more irregular and rounded morphology. These minerals fill the spaces between the skeleton minerals and are often finer in size compared to the skeleton minerals. Furthermore, we rely on the elemental composition observed through Energy Dispersive X-ray Spectroscopy (EDS) coupled with SEM, which helps confirm the mineral identity. The skeleton minerals, predominantly composed of quartz and feldspar, have distinct elemental signatures (e.g., silicon and aluminum for quartz, and silicon and potassium for feldspar). In contrast, the filler minerals, such as clay minerals and carbonates, have characteristic signatures (e.g., magnesium, calcium, and iron for clays and carbonates).

Comment #1.8:

The SEM image selected in Fig.11 seem not to totally be similar to those shown in Fig.10. Whether are the particle system model can well reflect the characteristics of sandstone meso-structure. Generally, most sandstone cannot be considered as a kind of granular materials such as sandy soil or soil-rock mixture because the minerals in sandstone are tightly bonded together. Please explain how do the minerals rotate under the constraints of surrounding matrix such as clay minerals.

Reply: Thank you for your thoughtful comment. We appreciate your careful examination of the SEM images and the particle system model presented in Figures 10 and 11. Regarding your concern about the similarity between the SEM images in Figure 11 and those in Figure 10, we acknowledge that there may appear to be some differences in the images. The SEM image selected for Figure 11 was intended to illustrate the general meso-structural characteristics of the sandstone. While there are some variations in the observed features between Figures 10 and 11, the key meso-structural components, such as the arrangement of skeleton minerals and the presence of filler minerals, remain consistent.

As for the particle system model used to represent the meso-structure of sandstone, we recognize that sandstone is indeed a more cohesive material compared to granular materials, such as sandy soils or soil-rock mixture, where the particles are loosely bonded. In the case of sandstone, the minerals are tightly bonded together by cementing materials such as clay minerals, carbonates, and other fillers. However, despite this strong bonding, under sufficient loading, the minerals can still exhibit some degree of relative movement, particularly in the form of rotation or sliding along the grain boundaries. This movement occurs at the mesoscale and is influenced by the relative stiffness of the minerals and the surrounding matrix. The surrounding matrix, which includes clay minerals and cementing agents, exerts constraints on this movement, limiting the degree of rotation but still allowing for some deformation, especially under external loading. We will elaborate on this mechanism in the revised manuscript, explaining how particle rotation is constrained by the surrounding matrix and how it contributes to the overall deformation of the sandstone under loading. (Lines 408-427)

Comment #1.9:

The samples were prepared by drying under 25℃, uniaxial l

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Submitted filename: Response_to_Reviewers_auresp_2.doc

Response Letter

Dear Editors and Reviewers:

We are very grateful for your letter and for the comments from Editors and Reviewers concerning our manuscript entitled “Meso-structural evolution of sandstone under uniaxial loading: a study on microdefect compaction and transgranular crack formation mechanisms” (ID: PONE-D-24-51359R2). These comments have been very valuable and helpful in revising and improving our manuscript, and they provide important guidance for our research. We have carefully studies the comments and made corrections that we hope will meet with your approval. All changes to the manuscript are marked in Revision Mode in the Revised Manuscript with Track Changes. The main corrections in the paper, as well as our responses to the Editors’ and Reviewers’ comments, are as follows:

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Editor Comments:

Response to Editor:

Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

Reply: Thank you for your careful and constructive comments regarding the accuracy and completeness of the reference.

In response to your comment, I have thoroughly checked all references cited in the manuscript. I confirm that none of the referenced articles have been retracted. Additionally, to improve the precision and compliance with journal formatting guidelines, I have made following specific revisions to the reference list (all changes are marked using Track Changes in the revised manuscript):

Reference 5: The journal name has been changed from Tunnelling Underground Space Technol to the proper abbreviation Tunn Undergr Sp Tech. (please see Lines 646-648)

Reference 8: The journal name has been updated from Fatigue & Fracture of Engineering Materials & Structures to its abbreviation Fatigue Fract Eng M. (please see Lines 654-656)

Reference 28: The publication year and page numbers have been updated from 2023; 1-17 to 2024;19: 2975-2991. (please see Lines 709-711)

Reference 36: The publication year has been corrected from 2020 to 2021. (please see Lines 731-733)

Reference 53: The sixth author was mistakenly listed as the fifth author, and this has been corrected (updated from Yu L to Wang WM). In addition, the journal name has been revised form uppercase ACTA PETROLEI SINICA to sentence case Acta Petrolei Sinica. (please see Lines 778-781)

Reference 54: The journal name has been changed from Engineering Fracture Mechanics to its standard abbreviation Eng Fract Mech. (please see Lines 782-784)

Reference 56: The journal name has been changed from Journal of Geophysical Research: Planets to its abbreviation J Geophys Res. (please see Lines 788-791)

These modifications ensure that all references are up to date, correctly formatted, and consistent with citation standards. I hope these revisions meet with your approval.

Reviewer Comments:

Response to reviewer #1:

The authors have revised the manuscript and explained most concerns from the reviewers.

Reply: Thank you for your thoughtful and constructive feedback on the revised manuscript. I sincerely appreciate the time and effort you have dedicated to reviewing the manuscript to reviewing the manuscript and acknowledging that most of your concerns have been addressed.

Regarding the remaining questions your raised about some aspects of the test procedure, I fully understand your concerns and will carefully address them in the following sections. I will provide a detailed explanation and clarification for each point to ensure that all aspects of the methodology are clear and transparent.

Thank you once again for your valuable comments. I look forward to your further thoughts after reviewing the revised responses.

But I'm still wondering about some test procedure:

Comment #1.1:

Since the samples had been dried before compression test as described in the 1st step, why were they still dried again after compression test and P-wave velocity test as described in the 5th step?

Reply: Thank you for your thoughtful comment regarding the drying steps in the experimental process. The experimental procedure includes two drying steps, each with a distinct purpose.

To address your concern about the drying steps, I will focus on explaining the purpose of each drying step:

Initial Drying (Step 1): The first drying step is performed to ensure that all specimens begin under the same anhydrous conditions, thereby eliminating any discrepancies caused by the natural moisture content of the specimens. This ensures consistency across all the specimens and eliminates the risk of errors related to varying moisture levels.

Re-drying after compression and P-wave velocity tests (Step 5): After completing the compression test (Step 2) and P-wave velocity test (Step 3), the specimens may absorb moisture from the surrounding air. This necessitates a second drying step before the Scanning Electron Microscopy (SEM) test for the following two primary reasons:

Vacuum treatment for SEM: The SEM test requires the specimens to be subjected to a vacuum process. If the specimens contain moisture, it may be drawn into the equipment, potentially damage the SEM equipment.

Clear imaging of clay minerals: Sandstone specimens typically contain clay minerals that have the ability to absorb water and expand. If the specimens retains moisture, this can cause the clay minerals to swell, potentially leading to misinterpretation of meso-structure, which may affect the accuracy of the results.

In conclusion, both drying steps serve important but different purposes. The initial drying ensures uniform starting conditions, while the second drying ensures the specimens are prepared for SEM imaging with moisture-related issues.

I hope this clarification addresses your concern. Tank you again for your constructive comment.

Comment #1.2:

The NMR data were compared among different samples that had been compressed to a certain stress. It would be more convincible if the comparison focused on the same sample. I mean the NMR results from an initial sample were first obtained and compared to the NMR results from this sample after it was compressed, and then such variation corresponding to different loading stress were compared so as to discuss the effect of different loading stress.

Reply: Thank you very much for your insightful comment regarding the comparability of the NMR data. We would like to first acknowledge that your suggestion is extremely constructive. Indeed, obtaining results from the same specimen under different loading stress conditions to observe the variations in meso-structure features would certainly provide a more direct and convincing way to evaluate the effect of loading stress.

We fully agree that such an approach would yield even more reliable and convincing results, and we recognize its value in enhancing the robustness of the analysis. We must also note that this study represents only a preliminary exploration into the effects of loading stress on meso-structure changes in sandstone.

Currently, we are conducting further research to address the very point you raised. For instance, we are using both loading NMR and loading CT techniques to study how the pore structure and 3D morphology of the same specimen change under different loading stress. Preliminary results from these ongoing experiments have shown promising insights, and we are excited to expand on these findings in future publications.

Your constructive suggestion has greatly motivated us, and we are now even more eager to continue our exploration in this area. We will make sure to incorporate such a within-specimen comparison method in our future studies, as it will undoubtedly provide stronger evidence for the effects of different loading stresses on meso-structure behavior.

Thank you again for your valuable suggestion, which will help guide our future research efforts.

Comment #1.3:

The data point at 5 MPa in Fig.10(d) should be a negative value but not positive value. The differences defined in Eq.1-3 were set as an absolute value. It's not reasonable. Since the damage deterioration always cause the decreasing of strength and P-wave velocity or the increasing of porosity, an inverse change should be taken as an opposite sign or eliminated. In addition, the various failure strains could also be discussed together.

Reply: Thank you for your thoughtful and constructive comments regarding the inconsistencies in Eq. 1-3 and your suggestion to address the different failure strains under different loading stresses.

We fully acknowledge the validity of your observation regarding the use of absolute values in these equations, which may not appropriately reflect the expected physical behavior. In response, we have revised Eq. 1-3 to better capture the direction changes of failure strength, P-wave velocity, and total porosity under different loading stresses. The revised formulas are as follows:

S_σ=(σ_cs-σ_cs')/σ_cs'×100% (1)

S_v=(σ_v-σ_v')/σ_v'×100% (2)

S_n=(σ_n-σ_n')/σ_n'×100% (3)

Additionally, we have updated Figure 10(d) to reflect these changes. The revised Figure 10 are as follows:

Fig 10. Damage parameters based on mechanical data: (a) degree of deterioration in failure strength; (b) degree of deterioration in P-wave velocity; (c) degree of deterioration in total porosity; and (d) comparison of the degrees of deterioration in failure strength, P-wave velocity, and total porosity. (please see Lines 416-419)

Meanwhile, corresponding modifications were made to the manuscript as follows:

Compared with the S_σ of the specimens without loading stress (0 MPa), the decrease in S_σ for the specimens subjected to different loading stresses is approximately -2.20%, 4.74%, 19.96%, and 26.36% (Fig 10a). (please see Lines 413-415)

Compared with the S_v of the specimens without loading stress (0 MPa), the decrease in S_v of the specimens subjected to different loading stresses is approximately -1.22%, 2.08%, 4.72%, and 9.04% (Fig 10b). (please see Lines 425-427)

Meanwhile, with the increase in loading stresses (5, 15, 30, and 40 MPa), the increase in S_n of the specimens is approximately -1.40%, 5.46%, 14.42%, and 19.18% (Fig 10c). (please see Lines 427-428)

Compared with the points of deterioration in P-wave velocity (S_v), the points of deterioration in total porosity (S_n) closely align with the points of deterioration in failure strength (S_σ), while the points of deterioration in P-wave velocity (S_v) deviate more from this trend (Fig 10d). This result confirms that total porosity provides a stronger correlation with failure strength than P-wave velocity, making it a more sensitive indicator of rock deterioration. (please see Lines 435-440)

Regarding your suggestion to discuss the various failure strains under different loading stresses, we have taken your valuable advice into revised manuscript. In the Discussion section, we have added a new subsection title “Quantitative analysis of the mechanical properties of the sandstone” (please see Lines 360-402), where we perform an Single-factor Analysis of Variance (ANOVA) and Pearson correlation coefficients to examine the relationships between mechanical properties (failure strength, failure strain, and elastic modulus) and their correlation with P-wave velocity and total porosity under different loading stresses. This section includes a detailed discussion on failure strain as you suggested, and we hope this addition addresses your concern and provides a more comprehensive analysis.

We sincerely hope that the revisions made in response to your feedback meet your expectations and contribute to the clarity and quality of the revised manuscript. We greatly appreciate your constructive suggestion, which has significantly enhanced our research.

Nevertheless, this study illustrates some interesting phenomenon about the damage effect of early loading before peak stress. The current experimental results can provide some valuable information and creative ideas.

Reply: Thank you for your positive and encouraging comments regarding the findings of our study.

We are grateful for your interest in the findings of our study, particularly your recognition of the significance of early loading damage effects prior to peak stress. We agree that understanding the behavior of materials under early loading conditions is crucial, and we are glad that our results offer valuable insights and potentially creative ideas for future research in this area.

As we continue to explore the damage evolution of sandstone under different loading conditions, we are confident that this early loading stage will provide a deeper understanding of material behavior before peak stress, which can be instrumental for practical application in rock mechanics and engineering.

Once again, thank you for recognizing the significance of these findings, and we appreciate your feedback, which encourages us to further investigate theses interesting phenomena.

Response to reviewer #2:

You have really done many works in handling the manuscript, and the paper is very much improved, however, there are still several questions that have not been dealt with.

Reply: Thank you very much for your kind words regarding the improvements made to the manuscript and for your continued constructive comments. We greatly appreciate the time and effort you have invested in reviewing our study.

We acknowledge that despite the significant improvements, there are still several issues that need to be addressed. We are fully committed to resolving these remaining concerns and have carefully reviewed your comments to ensure that all outstanding questions are properly dealt with.

We will go over each of the issues you raised and provide thorough responses or revisions where necessary to further improve the clarity and quality of the manuscript. Your feedback is invaluable in helping us refine and enhance the content, and we hope to meet your expectations with the revised manuscript.

Thank you once again for your detailed review and for pointing out these remaining concerns. We look forward to addressing them fully and submitting the revised manuscript for your consideration.

Comment #2.1:

Revise the abstract to highlight the research significance and main conclusions of the paper.

Reply: Thank you for your valuable suggestion to revise the abstract in order to better highlight the research significance and main conclusions of the paper.

In response to your feedback, we have revised the Abstract to more effectively convey the significance of the research and to clearly outline the main conclusions. Specifically, we have modified the first part of the abstract to emphasize the importance of understanding how meso-structure influences rock deterioration and how different loading stresses affect the evolution of meso-structure. The revised version is as follows:

Original version: Rock deterioration under uniaxial compression is strongly influenced by changes in meso-structure. However, the evolution of rock meso-structures under different uniaxial loading stresses remains enigmatic.

Revised version: Rock deterioration under uniaxial compression is significantly influenced by changes in meso-structure, which plays a key role in determining the mechanical behavior and stability of rock materials. Understanding how different loading stresses affect the evolution of meso-structure is crucial for assessing rock stability in engineering application, such as tunneling and landslide prevention. (please see Lines 17-21)

Additionally, we have enhanced the last section of the abstract to emphasize the broader implications of the research findings for engineering practices, particularly in the context of rock stabil

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