Mohr–Coulomb and Modified Hoek–Brown Strength Criteria of Layered Sandstone Considering the Unloading Effect and Anisotropy

Round 1

Reviewer 1 Report

The research addresses responses of rocks to loading and unloading especially during and post mining.

The topic is not original as some research have been done in the area

before. I do however consider it relevant and does provide insights into

investigation different variant parameters and proving the responses of the

different rocks.

It provides information of rocks test under different and varying conditions. This is a great addition to knowledge.

The methodology is ok and sound.

The language and presentation need to be greatly improved in other for me to be able to judge the evidence and conclusions. As it is now, I am having trouble judging the evidence and conclusions.

The references are appropriate and ok

The figures and tables are of good quality and are addressed in the text of the article.

The article requires extensive English editing. As currently written, it is difficult to read and follow. 

The English need to be improved. As it is currently written, it is difficult to follow and fully appreciate the results of the findings by the researchers

Author Response

1. The research addresses responses of rocks to loading and unloading especially during and post mining. The topic is not original as some research have been done in the area before. I do however consider it relevant and does provide insights into investigation different variant parameters and proving the responses of the different rocks. It provides information of rocks test under different and varying conditions. This is a great addition to knowledge.

Response: Thanks for your comments. Additionally, thank you for your recognition and praise of this research again, we will conduct more in-depth research on this research direction in the future.

 

2. The methodology is ok and sound.

Response: Thanks for your comments. Additionally, thank you for your recognition and praise of this methodology used in our paper again.

 

3. The language and presentation need to be greatly improved in other for me to be able to judge the evidence and conclusions. As it is now, I am having trouble judging the evidence and conclusions.

Response: Thanks for your comments. We have carefully checked and corrected the typos and sentences during the full text in the revised manuscript, and we have conducted the proof-reading for the whole revised manuscript. Therefore, it should be easy to judge the evidence and conclusions. Thank you very much again.

 

4. The references are appropriate and ok.

Response: Thanks for your comments. We have carefully checked the format of references, and it is OK. Thank you very much again.

 

5. The figures and tables are of good quality and are addressed in the text of the article.

Response: Thanks for your comments. thank you for your recognition and praise of our figures and tables addressed in the text of the article. Thank you very much again.

 

6. The article requires extensive English editing. As currently written, it is difficult to read and follow. The English need to be improved. As it is currently written, it is difficult to follow and fully appreciate the results of the findings by the researchers.

Response: Thanks for your comments. We have carefully checked and corrected the typos and sentences during the full text in the revised manuscript, and we have conducted the proof-reading for the whole revised manuscript. Additionally, we have found a native English-speaking colleague for help to check and correcte our revised manuscript. Therefore, it should be easy to read, follow and fully appreciate the results of the findings by us.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper evaluates Mohr-Coulomb and modified Hoek-Brown strength criterion of layered sandstone considering the unloading effect and anisotropy. Overall, there are numerous typos and the quality of English needs to be enhanced.

1) Correct typo on the title: Hook Brown -- Hoek Brown

2) "Experimental system and scheme" needs to be rewritten in details. Looks like a brochure. You need to elaborate how to conduct each test for this study in order to incorporate unloading effect.

3) Please define the bedding angle.

4) In conclusion part, (2) part need to rewritten. 

There are several typos and sentences need to be corrected. Please conduct proof-reading. 

Author Response

This paper evaluates Mohr-Coulomb and modified Hoek-Brown strength criterion of layered sandstone considering the unloading effect and anisotropy. Overall, there are numerous typos and the quality of English needs to be enhanced.

1) Correct typo on the title: Hook Brown -- Hoek Brown

Response: Thanks for your comments. We have corrected the typo on the title. And the corrected title is that "Mohr-Coulomb and modified Hoek-Brown strength criterion of layered sandstone considering the unloading effect and anisotropy".

 

2) "Experimental system and scheme" needs to be rewritten in details. Looks like a brochure. You need to elaborate how to conduct each test for this study in order to incorporate unloading effect.

Response: Thanks for your comments. We have rewritten the Section of "Experimental system and scheme" in details. And the details are as follows:

“…”

Besides, there was significant anisotropy in the deep strata itself (see Fig. 1 (a)). Furthermore, there existed the obvious evolution process of the stress state of roadway surrounding rocks before excavation, excavating and after excavation (see Fig. 1 (b)). Therefore, the stress path TLUT considering the unloading effect was proposed [36-38]. Furthermore, it was expected to improving the accuracy of the applicability of the strength criterion.

Note: H, σ₁ and σ₃ represent the buried depth, axial stress and confining pressure, respectively; σ_x, σ_y, σ_z, σ_x’ and σ_z’ represent the minimum principal stress, the intermediate principal stress, the maximum principal stress, the minimum principal stress after unloading, and the maximum principal stress after re-loading.

Fig. 1. Engineering background [36-38]

“…”

2 Experimental system and scheme

MTS-815.02 electro-hydraulic servo rock mechanics test system was used in the tests. And the specific upper thresholds of basic parameters of the system were as follows:

1. The upper threshold of axial pressure is 1700 kN;
2. The upper threshold of confining pressure is 45 MPa;
3. The upper threshold of pore pressure is 45 MPa;
4. The upper threshold of osmotic water pressure difference is 2 MPa;
5. The upper threshold of osmotic gas pressure difference is 6 MPa;
6. The upper threshold of temperature is 200 ℃;
7. The upper limit of specimen size for applicable tests is 100 mm in diameter and 200 mm in height.

Besides, fully considering the excavation unloading effect of deep roadway surrounding rocks (see Fig. 1), the stress path TLUT was designed and proposed, which broke through the embarrassment of the conventional triaxial loading stress path CTLT from zero loading to rock failure. The specific stress paths of uniaxial loading (UCT), conventional triaxial loading (CTLT) and triaxial loading and unloading (TLUT) were shown in Fig. 2. And the detailed parameters setting of each stage of each sub-experiments were included. Among them, the stress state corresponding to the buried depth of 1010 m is the initial high in-situ stress at the sampling site, and the specific detail of in-situ stress measurement could be referred to [39].

Note: c represents different pre-set confining pressures;  represent uniaxial compressive strength of layered sandstones;  represent triaxial compressive strength of layered sandstones under CTLT;  represent triaxial compressive strength of layered sandstones under TLUT.

Fig. 2. Stress paths and corresponding detailed parameters [39-40]

 

3) Please define the bedding angle.

Response: Thanks for your comments. We have defined the bedding angle. And the details are as follows: There was significant anisotropy in the deep strata itself. Therefore, the bedding angle was defined that it is the intersection angle between the weak structural plans in the layered sandstone and the horizontal plane. Due to there are different angles in the layered sandstone. Therefore, there are various bedding angles in the layered sandstone.

 

4) In conclusion part, (2) part need to rewritten.

Response: Thanks for your comments. We have rewritten the part (2) of Conclusion in the revised manuscript. And the details are as follows:

Conclusions

(1) With increasing bedding angle, the peak strength first decreased and then increased. When the bedding angle was 45°, the peak strength was the smallest. Besides, with increasing confining pressure, the peak strength also showed the continuous increasing nonlinear evolution trend. Additionally, the peak strength under TLUT was significantly lower than that under CTLT.

(2) With increasing bedding angle, the cohesion with CTLT decreased first and then increased, while the evolution trend of internal friction angle with CTLT was opposite. Additionally, with increasing bedding angle, the cohesion with TLUT also decreased first and then increased, but the cohesion with TLUT increased first, then decreased, and finally increased again.

(3) The cohesion, internal friction angle, parameter (n) and (γ) were not constants, and would change with increasing bedding angle. Compared with CTLT, the variation degree of the cohesion and internal friction angle under TLUT was more significantly with increasing bedding angle.

(4) Compared with the M-C strength criteria, the modified H-B strength criteria was more suitable to estimate the peak strength of layered sandstones.

 

5) There are several typos and sentences need to be corrected. Please conduct proof-reading.

Response: Thanks for your comments. We have carefully checked and corrected the typos and sentences during the full text in the revised manuscript, and we have conducted the proof-reading for the whole revised manuscript. Additionally, we have found a native English-speaking colleague for help to check and correcte our revised manuscript.

Author Response File: Author Response.pdf

Reviewer 3 Report

The M-C and H-B strength criterion are used widely in various engineering fields, including mining engineering, slope engineering, tunnel engineering, geothermal engineering, nuclear waste and CO₂ storage engineering. It can visually represent the relationship between the stress state and rock strength. Therefore, the M-C and modified H-B strength criterion were established considering the unloading effect and anisotropy. Then, according to the strength criterion established, the peak strength could be estimated theoretically. Furthermore, compared to the M-C strength criterion, the modified H-B strength criterion was more appropriate. It is a very good study. Meanwhile, the authors have conducted an extensive experimental analysis of this work, which may be of interest to readers. Therefore, this manuscript can be accepted in Sustainability after minor revision. Here are some comments:

 

1. Language should be carefully checked. There are still some grammar errors.

 

2. The literature citation is insufficient, and the relevant references should be supplemented.

 

3.Some mistakes appear in the study. The figure should appear after the text.

 

4. Did the authors conducted repeated conditions under?

 

5. There are obvious problems with the format of the literature citation, such as [33], [34], [48].

 

6. The conclusions need to be further refined and improved.

 

7. The part of Abstract was too repetitive and burdensome. Therefore, it is suggested that the authors refine the part of Abstract.

 

8. The formulas in the text should be carefully proofread to avoid errors.

The M-C and H-B strength criterion are used widely in various engineering fields, including mining engineering, slope engineering, tunnel engineering, geothermal engineering, nuclear waste and CO₂ storage engineering. It can visually represent the relationship between the stress state and rock strength. Therefore, the M-C and modified H-B strength criterion were established considering the unloading effect and anisotropy. Then, according to the strength criterion established, the peak strength could be estimated theoretically. Furthermore, compared to the M-C strength criterion, the modified H-B strength criterion was more appropriate. It is a very good study. Meanwhile, the authors have conducted an extensive experimental analysis of this work, which may be of interest to readers. Therefore, this manuscript can be accepted in Sustainability after minor revision. Here are some comments:

 

1. Language should be carefully checked. There are still some grammar errors.

 

2. The literature citation is insufficient, and the relevant references should be supplemented.

 

3.Some mistakes appear in the study. The figure should appear after the text.

 

4. Did the authors conducted repeated conditions under?

 

5. There are obvious problems with the format of the literature citation, such as [33], [34], [48].

 

6. The conclusions need to be further refined and improved.

 

7. The part of Abstract was too repetitive and burdensome. Therefore, it is suggested that the authors refine the part of Abstract.

 

8. The formulas in the text should be carefully proofread to avoid errors.

Author Response

The M-C and H-B strength criterion are used widely in various engineering fields, including mining engineering, slope engineering, tunnel engineering, geothermal engineering, nuclear waste and CO₂ storage engineering. It can visually represent the relationship between the stress state and rock strength. Therefore, the M-C and modified H-B strength criterion were established considering the unloading effect and anisotropy. Then, according to the strength criterion established, the peak strength could be estimated theoretically. Furthermore, compared to the M-C strength criterion, the modified H-B strength criterion was more appropriate. It is a very good study. Meanwhile, the authors have conducted an extensive experimental analysis of this work, which may be of interest to readers. Therefore, this manuscript can be accepted in Sustainability after minor revision. Here are some comments:

1. Language should be carefully checked. There are still some grammar errors.

Response: Thanks for your comments. We have carefully checked and corrected the the full text in the revised manuscript. Additionally, we have found a native English-speaking colleague for help to check and correcte our revised manuscript.

 

2. The literature citation is insufficient, and the relevant references should be supplemented.

Response: Thanks for your comments. We have added more references about the establishment of M-C and H-B strength criterion of rocks in Introduction. And the corresponding details are as follows:

1. Introduction

“...”

Additionally, numerous scholars obtained certain innovative conclusions according to the rock strength criteria established from the multiple perspectives with the strain rate effect, the effect of intermediate principal stress (including the effect of Lord's angle), the thermal effect, the bedding effect and the effect of hydrostatic pressure [16-35].

“...”

• Lee, Y.K., Bobet, A. Instantaneous friction angle and cohesion of 2-D and 3-D Hoek-Brown rock failure criteria in terms of stress invariants. Rock Mech. Rock Eng. 2014, 47(2), 371-385.
• Yin, Q., Liu, R.C., Jing, H.W., Su, H.J., Yu, L.Y., He, L.X. Experimental study of nonlinear flow behaviors through fractured rock samples after high-temperature exposure. Rock Mech. Rock Eng. 2019, 52, 2963-2983.
• Yin, Q., Wu, J.Y., Zhu, C., He, M.C., Meng, Q.X., Jing, H.W. Shear mechanical responses of sandstone exposed to high temperature under constant normal stiffness boundary conditions. Geophysics. Geo. 2021, 7(2), 1-17.
• Yin, Q., Wu, J.Y., Zhu, C., Wang, Q., Xie, J.Y. The role of multiple heating and water cooling cycles on physical and mechanical responses of granite rocks. Geophysics. Geo. 2021, 7, 69.
• Pan, J.L., Zhang, Y., Li, P., Wu, X., Xi, X. Mechanical properties and thermo-chemical damage constitutive model of granite subjected to thermal and chemical treatments under uniaxial compression. Constr. Build. Mater. 2023, 390, 131755.
• Pan, J.L., Cai, M.F., Li, P., Guo, Q.F. A damage constitutive model of rock-like materials containing a single crack under the action of chemical corrosion and uniaxial compression. J. Cent. South. Univ. 2022, 29(2), 486-498.

 

3.Some mistakes appear in the study. The figure should appear after the text.

Response: Thanks for your comments. We have modified the mistakes in Fig. 1 in the revised manuscript. And the Figures were appeared after the text.

 

4. Did the authors conducted repeated conditions under?

Response: Thanks for your comments. Yes, we have conducted the corresponding repeated three tests under each same conditions. Then, we have selected the most representative group to present the results for in-depth analysis.

 

5. There are obvious problems with the format of the literature citation, such as [33], [34], [48].

Response: Thanks for your comments. We have carefully checked again and corrected the reference format in the revised manuscript, including the Journal title, volume number, issue number, page number, author names and orders. And the details are as follows:

• Genis, M., Basarir, H., Ozarslan, A., Bilir, E., Balaban, E. Engineering geological appraisal of the rock masses and preliminary support design, Dorukhan Tunnel, Zonguldak, Turkey. Geol. 2007, 92(1-2), 14-26.
• Xue, Y.G., Zhang, X.L., Li, S.C., Qiu, D.H., Su, M.X., Li, L.P., Li, Z.Q., Tao, Y.F. Analysis of factors influencing tunnel deformation in loess deposits by data mining: A deformation prediction model. Geol. 2018, 232, 94-103.
• Feng, S.J., Zhao, Y., Zhang, X.L., Bai, Z.B. Leachate leakage investigation, assessment and engineering countermeasures for tunneling underneath a MSW landfill. Geol. 2020, 265, 105447.
• Liu, D.Q., Ling, K., Guo, C.B., He, P.F., He, M.C., Sun, J., Yan, X.H. Experimental simulation study of rockburst characteristics of Sichuan-Tibet granite: A case study of the Zheduoshan tunnel. Geol. 2022, 305, 106701.
• Tao, J., Yang, X.G., Ding, P.P., Li, X.L., Zhou, J.W., Lu, G.D. A fully coupled thermo-hydro-mechanical-chemical model for cemented backfill application in geothermal conditions. Geol. 2022, 302, 106643.
• Benavente, D., Garcia, D., Cura, M.A., Fort, R., Ordonez, S. Durability estimation of porous building stones from pore structure and strength. Geol. 2004, 74, 113-127.
• Hecht, C.A., Bonsch, C., Bauch, E. Relations of rock structure and composition to petrophysical and geomechanical rock properties: examples from permocarboniferou red-beds. Mech. Rock. Eng. 2005, 38, 197-216.
• Sabatakakis, N., Koukis, G., Tsiambaos, G., Papanakli, S. Index properties and strength variation controlled by microstructure for sedimentary rocks. Geol. 2008, 97, 80-90.
• Torok, A., Vasarhelyi, B. The influence of fabric and water content on selected rock mechanical parameters of travertine, examples from Hungary. Geol. 2010, 115, 237-245.
• Shen, J.Y., Jimenez, R., Karakus, M., Xu, C.S. A simplified failure criterion for intact rocks based on rock type and uniaxial compressive strength. Mech. Rock. Eng. 2014, 47(2), 357-369.
• Shen, J.Y., Karakus, M. Simplified method for estimating the Hoek-Brown constant for intact rocks. Geotech. Geoenviron. 2014, 140(6), 971-984.
• Rajabzadeh, M.A., Moosavinasab, Z., Rakhshandehroo, G. Effects of rock classes and porosity on the relation between uniaxial compressive strength and some rock properties for Carbonate rocks. Mech. Rock. Eng. 2012, 45(1), 113-122.
• Wang, Y.F., Cui, F. Energy evolution mechanism in process of sandstone failure and energy strength criterion. Appl. Geophys. 2018, 154, 21-28.
• Li, Z., Zhou, H., Hu, D.W., Zhang, C.Q. Yield criterion for rocklike geomaterials based on strain energy and CMP model. J. Geomech. 2020, 20(3), 04020013.
• Sari, M. An improved method of fitting experimental data to the Hoek–Brown failure criterion. Geol. 2012, 127, 27-35.
• Zhao, Applicability of Mohr–Coulomb and Hoek–Brown strength criteria to the dynamic strength of brittle rock. Int. J. Rock. Mech. Min. Sci. 2000, 37(7), 1115-1121.
• Priest, S.D. Determination of shear strength and three-dimensional yield strength for the Hoek-Brown criterion. Mech. Rock. Eng. 2005, 38(6), 299-327.
• Zhang, Q., Zhu, H.H. Collaborative 3D geological modeling analysis based on multi-source data standard. Geol. 2018, 246, 233-244.
• Saroglou, H., Tsiambaos, G. A modified Hoek-Brown failure criterion for anisotropic intact rock. J. Rock. Mech. Min. Sci. 2008, 45(2), 223-234.
• Singh, M., Raj, A., Singh, B. Modified Mohr-Coulomb criterion for non-linear triaxial and poly-axial strength of intact rocks. J. Rock. Mech. Min. Sci. 2011, 48(4), 546-555.
• Zhou, C.T., Xu, C.S., Karakus, M., Shen, J.Y. A particle mechanics approach for the dynamic strength model of the jointed rock mass considering the joint orientation. J. Numer. Anal. Met. 2019, 43(18), 2797-2815.
• Zhou, C.T., Xie, H.P., Zhu, J.B., Zhou, T. Failure criterion considering high temperature treatment for rocks from a micromechanical perspective. Appl. Fract. Mec. 2022, 118:103226.
• Wang, G.S., Lu, D.C., Du, X.L., Zhao, X. Dynamic multiaxial strength criterion for concrete based on strain rate–dependent strength parameters. Eng. Mech. 2018, 144(5), 04018018.
• Wang, G.S., Lu, D.C., Li, M., Zhao, X., Wang, J.T., Du, X.L. Static–dynamic combined multiaxial strength criterion for concrete. Eng. Mech. 2021, 147(5), 04021017.
• Yang, Q., Zan, Y.W., Xie, L.G. Comparative analysis of the nonlinear unified strength criterion for rocks and other three-dimensional Hoek-Brown strength criteria. Geophysics. Geo. 2018, 4, 29-37.
• Zhang, Q., Li, C., Jiang, B.S. New true-triaxial rock strength criteria considering intrinsic material characteristics. Acta Mech. Sinica. 2018, 34(01), 138-150.
• Song, Z.L., Li, M.H., Yin, G.Z., Ranjith, P.G., Liu, C. Rock strength criterion considering the effect of hydrostatic stress on lode angle effect. Sci. Eng. 2019, 7(4), 1166-1177.
• Song, Z.L., Yin, G.Z., Ranjith, P.G., Li, M.H., Huang, J., Liu, C. Influence of the intermediate principal stress on sandstone failure. Mech. Rock. Eng. 2019, 52(9), 3033-3046.
• Zhang, Q.G., Yao, B.W., Fan, X.Y., Li, Y., Li, M.H., Zeng, F.T., Zhao, P.F. A modified Hoek-Brown failure criterion for unsaturated intact shale considering the effects of anisotropy and hydration. Fract. Mech. 2020, 241, 107369.
• Lee, Y.K., Bobet, A. Instantaneous friction angle and cohesion of 2-D and 3-D Hoek-Brown rock failure criteria in terms of stress invariants. Mech. Rock. Eng. 2014, 47(2), 371-385.
• Yin, Q., Liu, R.C., Jing, H.W., Su, H.J., Yu, L.Y., He, L.X. Experimental study of nonlinear flow behaviors through fractured rock samples after high-temperature exposure. Mech. Rock. Eng. 2019, 52, 2963-2983.
• Yin, Q., Wu, J.Y., Zhu, C., He, M.C., Meng, Q.X., Jing, H.W. Shear mechanical responses of sandstone exposed to high temperature under constant normal stiffness boundary conditions. Geophysics. Geo. 2021, 7(2), 1-17.
• Yin, Q., Wu, J.Y., Zhu, C., Wang, Q., Xie, J.Y. The role of multiple heating and water cooling cycles on physical and mechanical responses of granite rocks. Geophysics. Geo. 2021, 7, 69.
• Pan, J.L., Zhang, Y., Li, P., Wu, X., Xi, X. Mechanical properties and thermo-chemical damage constitutive model of granite subjected to thermal and chemical treatments under uniaxial compression. Build. Mater. 2023, 390, 131755.
• Pan, J.L., Cai, M.F., Li, P., Guo, Q.F. A damage constitutive model of rock-like materials containing a single crack under the action of chemical corrosion and uniaxial compression. Cent. South. Univ. 2022, 29(2), 486-498.
• Zhang, J.W., Song, Z.X., Wang, S.Y. Experimental investigation on permeability and energy evolution characteristics of deep sandstone along a three-stage loading path. Eng. Geol. Environ. 2020, 80(2), 1571-1584.
• Zhang, J.W., Song, Z.X., Wang, S.Y. Mechanical behavior of deep sandstone under high stress-seepage coupling. Cent. South. U. 2021, 28(10), 3190-3206.
• Song, Z.X., Zhang, J.W., Zhang, L.C., Dong, X.K., Niu, W.M., Zhang, Y. The permeability properties of bedded coal and rock: Review and new insights. Sci. Eng. 2022, 10(4), 1544-1565.
• Song, Z.X., Zhang, J.W., Wang, S.Y., Dong, X.K., Zhang, Y. Energy evolution characteristics and weak structure - “Energy Flow” impact damaged mechanism of deep-bedded sandstone. Rock Mech. Rock Eng. 2023, 56, 2017–2047.
• Song, Z.X., Zhang, J.W., Zhang, Y., Dong, X.K., Wang, S.Y. Characterization and evaluation of brittleness of deep bedded sandstone from the perspective of the whole life-cycle evolution process. J. Min. Sci. Technol. 2023, 33, 481–502.
• Erener, A., Mutlu, A., Düzgün, H.S. A comparative study for landslide susceptibility mapping using GIS-based multi-criteria decision analysis (MCDA), logistic regression (LR) and association rule mining (ARM). Geol. 2016, 203, 45-55.
• Sepehri, M., Apel, D.B., Adeeb, S., Leveille, P., Hall, R.A. Evaluation of mining-induced energy and rockburst prediction at a diamond mine in Canada using a full 3D elastoplastic finite element model. Geol. 2020, 266, 105457.
• Kokkala, A., Marinos, V. An engineering geological database for managing, planning and protecting intelligent cities: The case of Thessaloniki city in Northern Greece. Geol. 2022, 301, 106617.
• He, M.C. Physical modeling of an underground roadway excavation in geologically 45° inclined rock using infrared thermography. Geol. 2011, 121(3-4), 165-176.
• Torresa, F., Piccinini, L., Pola, Marco., Zampieri, D., Fabbri, P.3D hydrogeological reconstruction of the fault-controlled Euganean Geothermal System (NE Italy). Geol. 2020, 274, 105740.
• Song, Z.X., Zhang, J.W. Research on the progressive failure process and fracture mechanism of rocks with the structural evolution perspective. Struct. Geol. 2022, 154, 104484.
• Zhao, J. Applicability of Mohr–Coulomb and Hoek–Brown strength criteria to the dynamic strength of brittle rock. J. Rock. Mech. Min. Sci. 2000, 37(7), 1115-1121.
• Song, Z.X., Zhang, J.W. The effect of confining pressure on mechanical properties in coal and rock: review and new insights. J. Geosci. 2021, 14(23), 2564.
• Hoek, E., Brown, E.T. Underground Excavation in Rock. London: Institution of Mining and Metallurgy, 1980.
• Hoek, E., Brown, E.T. Practical estimates of rock mass strength. J. Rock. Mech. Min. Sci. 1997, 34(8), 1165-1186.
• Hoek, E., Brown, E.T. The Hoek-Brown failure criterion and GSI-2018 edition. Rock. Mech. Geotech. Eng. 2018, 37,1-28.
• Peng, J., Cai, M.F. A cohesion loss model for determining residual strength of intact rocks. J. Rock. Mech. Min. Sci. 2019, 119, 131-139.
• Alejano, L.A., Walton, G., Gaines, S. Residual strength of granitic rocks. Undergr. Sp. Tech. 2021, 118, 104189.
• Shi, X.C., Yang, X., Meng, Y.F., Li, G. Modified Hoek-Brown failure criterion for anisotropic rocks. Earth. Sci. 2016, 75(11), 995.1-995.11.
• He, M.M., Zhang, Z.Q., Zhu, J.W., Li, N. Correlation between the constant mi of Hoek-Brown criterion and porosity of intact rock. Mech. Rock. Eng. 2022, 55(2), 923-936.
• Luo, B.Y., Ye, Y.C., Hu, N.Y., Wang, W.Q. Investigation of dip effect on uniaxial compressive strength of inclined rock sample by experimental and theoretical models. Mech. Rock. Eng. 2020, 53(4), 1-17.
• Shen, B.T., Shi, J.Y., Barton, N. Graphic examples of a logical nonlinear strength criterion for intact rock. Mech. Rock. Eng. 2019, 53(1), 71-75.
• Singh, M., Singh, B. Modified Mohr-Coulomb criterion for non-linear triaxial and poly-axial strength of jointed rocks. J. Rock. Mech. Min. Sci. 2012, 51, 43-52.
• Barton, N. Shear strength criteria for rock, rock joints, rockfill and rock masses: problems and some solutions. Rock. Mech. Geotech. Eng. 2013, 5(4), 249-261.
• Poulsen, B.A., Adhikary, D.P., Elmouttie, M.K., Wilkins, A. Convergence of synthetic rock mass modelling and the Hoek-Brown strength criterion. J. Rock. Mech. Min. Sci. 2015, 80, 171-180.
• Tsiambaos, G., Saroglou, H. Excavatability assessment of rock masses using the geological strength index (GSI). Eng. Geol. Environ. 2010, 69(1), 13-27.
• Kang H.P. Temporal scale analysis on coal mining and strata control technologies. Min. Strata. Control. Eng. 2021, 3(1), 5-27.

 

6. The conclusions need to be further refined and improved.

Response: Thanks for your comments. We have further refined and improved the  Conclusions in the revised manuscript. And the details are as follows:

Conclusions

(1) With increasing bedding angle, the peak strength first decreased and then increased. When the bedding angle was 45°, the peak strength was the smallest. Besides, with increasing confining pressure, the peak strength also showed the continuous increasing nonlinear evolution trend. Additionally, the peak strength under TLUT was significantly lower than that under CTLT.

(2) With increasing bedding angle, the cohesion with CTLT decreased first and then increased, while the evolution trend of internal friction angle with CTLT was opposite. Additionally, with increasing bedding angle, the cohesion with TLUT also decreased first and then increased, but the cohesion with TLUT increased first, then decreased, and finally increased again.

(3) The cohesion, internal friction angle, parameter (n) and (γ) were not constants, and would change with increasing bedding angle. Compared with CTLT, the variation degree of the cohesion and internal friction angle under TLUT was more significantly with increasing bedding angle.

(4) Compared with the M-C strength criteria, the modified H-B strength criteria was more suitable to estimate the peak strength of layered sandstones.

 

7. The part of Abstract was too repetitive and burdensome. Therefore, it is suggested that the authors refine the part of Abstract.

Response: Thanks for your comments. We have simpled the Abstract in the revised manuscript. And the details are as follows:

Abstract

The Mohr-Coulomb (M-C) and Hoek-Brown (H-B) strength criteria are widely used in various engineering fields, such as mining engineering, tunnel engineering and so on. To investigate the M-C and H-B strength criteria considering the unloading effect and anisotropy, series of triaxial loading (unloading) tests on layered sandstone were conducted. The results revealed that the peak strength was significantly affected by the unloading effect. Moreover, the cohesion and internal friction angle had the significant nonlinear relationship with the bedding angle. Besides, the M-C and modified H-B strength criteria were established considering the unloading effect and anisotropy. Then, according to the strength criterion established, the peak strength could be estimated theoretically. Furthermore, compared to the M-C strength criteria, the modified H-B strength criteria was more appropriate for accurately estimating the triaxial compressive strength of layered sandstones. The conclusions obtained could provide certain of references for the stability control of deep excavation engineering.

 

8. The formulas in the text should be carefully proofread to avoid errors.

Response: Thanks for your comments. We have carefully check and corrected the formulas in the text, including the meanings of parameters in the Eqs. in the text.

Author Response File: Author Response.pdf

Reviewer 4 Report

See my comments in the attachment.

Comments for author File: Comments.pdf

The language of the manuscript should be double-checked and improved.

Author Response

The paper entitled “Mohr-Coulomb and modified Hook-Brown strength criterion of layered sandstone considering the unloading effect and anisotropy” tried to extended the classical failure criteria to capture the unloading effect together with ansitotropy. The content seems to be interesting to the research on the rock mechancis. From my evalutaiton, this study could insipire the relevant research. However, there is still some issues for improvement before publication. My comments and suggestions are given as follows:

1. Although the whole paper is well-prepared, there are still some grammatical issues in the current version. Please check the whole paper by a native speaker or a professional service. For example, the “Mohr-Coulomb and modified Hook-Brown strength criterion” should be Mohr-Coulomb and modified Hook-Brown strength criteria”.

Response: Thanks for your comments. We have carefully checked and corrected the typos and sentences during the full text in the revised manuscript, and we have conducted the proof-reading for the whole revised manuscript. Additionally, we have found a native English-speaking colleague for help to check and correcte our revised manuscript. Therefore, it should be easy to read, follow and fully appreciate the results of the findings by us. Besides, we have corrected the “Mohr-Coulomb and modified Hook-Brown strength criterion” to the “Mohr-Coulomb and modified Hook-Brown strength criteria” in the revised manuscript.

 

2. Many typos are still found in the current version of this manuscript, please double-check the manuscript and correct them. For example, in line 16, the “C” cohesion (C) should in lower case. The word “Where” next to a function should also be in lower case.

Response: Thanks for your comments. We have carefully checked and corrected the typos in the revised manuscript. Additionally, we have corrected the “C” cohesion (C) to the (c) with lower case. And the word “Where” has been corrected to the “where”.

 

3. In section 2, the experiment should be briefly introduced.

Response: Thanks for your comments. We have rewritten the Section of "Experimental system and scheme" in details. And the details are as follows:

2 Experimental system and scheme

MTS-815.02 electro-hydraulic servo rock mechanics test system was used in the tests. And the specific upper thresholds of basic parameters of the system were as follows:

1. The upper threshold of axial pressure is 1700 kN;
2. The upper threshold of confining pressure is 45 MPa;
3. The upper threshold of pore pressure is 45 MPa;
4. The upper threshold of osmotic water pressure difference is 2 MPa;
5. The upper threshold of osmotic gas pressure difference is 6 MPa;
6. The upper threshold of temperature is 200 ℃;
7. The upper limit of specimen size for applicable tests is 100 mm in diameter and 200 mm in height.

Note: c represents different pre-set confining pressures;  represent uniaxial compressive strength of layered sandstones;  represent triaxial compressive strength of layered sandstones under CTLT;  represent triaxial compressive strength of layered sandstones under TLUT.

Fig. 2. Stress paths and corresponding detailed parameters [39-40]

Besides, fully considering the excavation unloading effect of deep roadway surrounding rocks (see Fig. 1), the stress path TLUT was designed and proposed, which broke through the embarrassment of the conventional triaxial loading stress path CTLT from zero loading to rock failure. The specific stress paths of uniaxial loading (UCT), conventional triaxial loading (CTLT) and triaxial loading and unloading (TLUT) were shown in Fig. 2. And the detailed parameters setting of each stage of each sub-experiments were included. Among them, the stress state corresponding to the buried depth of 1010 m is the initial high in-situ stress at the sampling site, and the specific detail of in-situ stress measurement could be referred to [39].

 

4. The abbreviation in the manuscript should be explained.

Response: Thanks for your comments. We have explained the abbreviation in the revised manuscript in details.

 

5. For the M-C failure criterion, the author used the nonlinear polynomial fitting method to derive the expression of cohesion and internal friction angle, which can be arbitrary. Furthermore, how can the modified failure criterion reflect the unloading effect?

Response: Thanks for your comments. According to the analysis in Section 3.1, under identical working condition, the peak strength under TLUT was significantly lower than that under CTLT (see Fig. 16). Meanwhile, the unloading effect could be demonstrated by combining the Mohr stress circle and its envelope under TLUT. In this study, the influences of excavation unloading effect on the bearing ability of deep roadway surrounding rocks was fully considered, and the construction of strength criteria is mainly to provide a more accurate quantitative idea to obtain its peak strength. Therefore, the modified failure criterion reflect the unloading effect just according to the measured and predicted peak strength values.

   

Fig. 16 Variations in peak strength evolution characteristics under CTLT and TLUT. (Song et al. 2023)

Song, Z.X., Zhang, J.W., Wang, S.Y., Dong, X.K., Zhang, Y. Energy evolution characteristics and weak structure - “Energy Flow” impact damaged mechanism of deep-bedded sandstone. Rock Mech. Rock Eng. 2023, 56, 2017–2047.

 

6. In Figs. 9 and10, the prediction performance of proposed failure criterion is poor. explain it, especially compared with those predicted by modified H-B failure criterion.

Response: Thanks for your comments. Due to the combined influences of bedding effect and unloading effect, the cohesion and internal friction angle of layereded sandstones obtained were greatly deviated. Meanwhile, the cohesion and internal friction angle of layereded sandstones had significant nonlinear evolution characteristics with the bedding angle. Therefore, there were poor prediction performance of proposed Mohr-Coulomb strength criteria considered the anisotropy of layeed sandstones and unloading effect was used to calculating the theoretical peak strength compared with the measured peak strength. However, the parameters of modified H-B strength criteria were less affected by the bedding effect, and the peak strength and confining pressure of layered sandstone with various bedding angles have significant nonlinear evolution characteristics, and the fitting correlation coefficient were higher. Therefore, the prediction performances of the modified H-B strength criteria for the peak strength of layered sandstones was higher than that of M-C strength criteria.

 

7. In Equation, rewrite the H-B failure criterion using the classical formation.

Response: Thanks for your comments. We have corrected the Equation of the H-B failure criteria to the classical formation in the revised manuscript.

 

8. The references in the manuscript should be reformed.

Response: Thanks for your comments. We have reformed the references in the revised manuscript.

 

9. In section 1, the author should improve the introduction to clarify the research gap of this study. It is suggested to review the existing criteria to cope with anisotropy, loading rate, thermal effect, and etc. for example: DOI:10.1016/S1365-1609(00)00049-6, DOI: 10.1002/nag.3002, DOI: 10.1016/j.tafmec.2021.103226.

Response: Thanks for your comments. We have reviewed the existing criteria to cope with anisotropy, loading rate, thermal effect, and etc. to improve the Introduction to clarify the research gap of this study. And the references of DOI:10.1016/S1365-1609(00)00049-6 [16], DOI: 10.1002/nag.3002 [21], DOI: 10.1016/j.tafmec.2021.103226 [22] were added in the revised manuscript.

• Genis, M., Basarir, H., Ozarslan, A., Bilir, E., Balaban, E. Engineering geological appraisal of the rock masses and preliminary support design, Dorukhan Tunnel, Zonguldak, Turkey. Geol. 2007, 92(1-2), 14-26.
• Xue, Y.G., Zhang, X.L., Li, S.C., Qiu, D.H., Su, M.X., Li, L.P., Li, Z.Q., Tao, Y.F. Analysis of factors influencing tunnel deformation in loess deposits by data mining: A deformation prediction model. Geol. 2018, 232, 94-103.
• Feng, S.J., Zhao, Y., Zhang, X.L., Bai, Z.B. Leachate leakage investigation, assessment and engineering countermeasures for tunneling underneath a MSW landfill. Geol. 2020, 265, 105447.
• Liu, D.Q., Ling, K., Guo, C.B., He, P.F., He, M.C., Sun, J., Yan, X.H. Experimental simulation study of rockburst characteristics of Sichuan-Tibet granite: A case study of the Zheduoshan tunnel. Geol. 2022, 305, 106701.
• Tao, J., Yang, X.G., Ding, P.P., Li, X.L., Zhou, J.W., Lu, G.D. A fully coupled thermo-hydro-mechanical-chemical model for cemented backfill application in geothermal conditions. Geol. 2022, 302, 106643.
• Benavente, D., Garcia, D., Cura, M.A., Fort, R., Ordonez, S. Durability estimation of porous building stones from pore structure and strength. Geol. 2004, 74, 113-127.
• Hecht, C.A., Bonsch, C., Bauch, E. Relations of rock structure and composition to petrophysical and geomechanical rock properties: examples from permocarboniferou red-beds. Mech. Rock. Eng. 2005, 38, 197-216.
• Sabatakakis, N., Koukis, G., Tsiambaos, G., Papanakli, S. Index properties and strength variation controlled by microstructure for sedimentary rocks. Geol. 2008, 97, 80-90.
• Torok, A., Vasarhelyi, B. The influence of fabric and water content on selected rock mechanical parameters of travertine, examples from Hungary. Geol. 2010, 115, 237-245.
• Shen, J.Y., Jimenez, R., Karakus, M., Xu, C.S. A simplified failure criterion for intact rocks based on rock type and uniaxial compressive strength. Mech. Rock. Eng. 2014, 47(2), 357-369.
• Shen, J.Y., Karakus, M. Simplified method for estimating the Hoek-Brown constant for intact rocks. Geotech. Geoenviron. 2014, 140(6), 971-984.
• Rajabzadeh, M.A., Moosavinasab, Z., Rakhshandehroo, G. Effects of rock classes and porosity on the relation between uniaxial compressive strength and some rock properties for Carbonate rocks. Mech. Rock. Eng. 2012, 45(1), 113-122.
• Wang, Y.F., Cui, F. Energy evolution mechanism in process of sandstone failure and energy strength criterion. Appl. Geophys. 2018, 154, 21-28.
• Li, Z., Zhou, H., Hu, D.W., Zhang, C.Q. Yield criterion for rocklike geomaterials based on strain energy and CMP model. J. Geomech. 2020, 20(3), 04020013.
• Sari, M. An improved method of fitting experimental data to the Hoek–Brown failure criterion. Geol. 2012, 127, 27-35.
• Zhao, Applicability of Mohr–Coulomb and Hoek–Brown strength criteria to the dynamic strength of brittle rock. Int. J. Rock. Mech. Min. Sci. 2000, 37(7), 1115-1121.
• Priest, S.D. Determination of shear strength and three-dimensional yield strength for the Hoek-Brown criterion. Mech. Rock. Eng. 2005, 38(6), 299-327.
• Zhang, Q., Zhu, H.H. Collaborative 3D geological modeling analysis based on multi-source data standard. Geol. 2018, 246, 233-244.
• Saroglou, H., Tsiambaos, G. A modified Hoek-Brown failure criterion for anisotropic intact rock. J. Rock. Mech. Min. Sci. 2008, 45(2), 223-234.
• Singh, M., Raj, A., Singh, B. Modified Mohr-Coulomb criterion for non-linear triaxial and poly-axial strength of intact rocks. J. Rock. Mech. Min. Sci. 2011, 48(4), 546-555.
• Zhou, C.T., Xu, C.S., Karakus, M., Shen, J.Y. A particle mechanics approach for the dynamic strength model of the jointed rock mass considering the joint orientation. J. Numer. Anal. Met. 2019, 43(18), 2797-2815.
• Zhou, C.T., Xie, H.P., Zhu, J.B., Zhou, T. Failure criterion considering high temperature treatment for rocks from a micromechanical perspective. Appl. Fract. Mec. 2022, 118:103226.
• Wang, G.S., Lu, D.C., Du, X.L., Zhao, X. Dynamic multiaxial strength criterion for concrete based on strain rate–dependent strength parameters. Eng. Mech. 2018, 144(5), 04018018.
• Wang, G.S., Lu, D.C., Li, M., Zhao, X., Wang, J.T., Du, X.L. Static–dynamic combined multiaxial strength criterion for concrete. Eng. Mech. 2021, 147(5), 04021017.
• Yang, Q., Zan, Y.W., Xie, L.G. Comparative analysis of the nonlinear unified strength criterion for rocks and other three-dimensional Hoek-Brown strength criteria. Geophysics. Geo. 2018, 4, 29-37.
• Zhang, Q., Li, C., Jiang, B.S. New true-triaxial rock strength criteria considering intrinsic material characteristics. Acta Mech. Sinica. 2018, 34(01), 138-150.
• Song, Z.L., Li, M.H., Yin, G.Z., Ranjith, P.G., Liu, C. Rock strength criterion considering the effect of hydrostatic stress on lode angle effect. Sci. Eng. 2019, 7(4), 1166-1177.
• Song, Z.L., Yin, G.Z., Ranjith, P.G., Li, M.H., Huang, J., Liu, C. Influence of the intermediate principal stress on sandstone failure. Mech. Rock. Eng. 2019, 52(9), 3033-3046.
• Zhang, Q.G., Yao, B.W., Fan, X.Y., Li, Y., Li, M.H., Zeng, F.T., Zhao, P.F. A modified Hoek-Brown failure criterion for unsaturated intact shale considering the effects of anisotropy and hydration. Fract. Mech. 2020, 241, 107369.
• Lee, Y.K., Bobet, A. Instantaneous friction angle and cohesion of 2-D and 3-D Hoek-Brown rock failure criteria in terms of stress invariants. Mech. Rock. Eng. 2014, 47(2), 371-385.
• Yin, Q., Liu, R.C., Jing, H.W., Su, H.J., Yu, L.Y., He, L.X. Experimental study of nonlinear flow behaviors through fractured rock samples after high-temperature exposure. Mech. Rock. Eng. 2019, 52, 2963-2983.
• Yin, Q., Wu, J.Y., Zhu, C., He, M.C., Meng, Q.X., Jing, H.W. Shear mechanical responses of sandstone exposed to high temperature under constant normal stiffness boundary conditions. Geophysics. Geo. 2021, 7(2), 1-17.
• Yin, Q., Wu, J.Y., Zhu, C., Wang, Q., Xie, J.Y. The role of multiple heating and water cooling cycles on physical and mechanical responses of granite rocks. Geophysics. Geo. 2021, 7, 69.
• Pan, J.L., Zhang, Y., Li, P., Wu, X., Xi, X. Mechanical properties and thermo-chemical damage constitutive model of granite subjected to thermal and chemical treatments under uniaxial compression. Build. Mater. 2023, 390, 131755.
• Pan, J.L., Cai, M.F., Li, P., Guo, Q.F. A damage constitutive model of rock-like materials containing a single crack under the action of chemical corrosion and uniaxial compression. Cent. South. Univ. 2022, 29(2), 486-498.
• Zhang, J.W., Song, Z.X., Wang, S.Y. Experimental investigation on permeability and energy evolution characteristics of deep sandstone along a three-stage loading path. Eng. Geol. Environ. 2020, 80(2), 1571-1584.
• Zhang, J.W., Song, Z.X., Wang, S.Y. Mechanical behavior of deep sandstone under high stress-seepage coupling. Cent. South. U. 2021, 28(10), 3190-3206.
• Song, Z.X., Zhang, J.W., Zhang, L.C., Dong, X.K., Niu, W.M., Zhang, Y. The permeability properties of bedded coal and rock: Review and new insights. Sci. Eng. 2022, 10(4), 1544-1565.
• Song, Z.X., Zhang, J.W., Wang, S.Y., Dong, X.K., Zhang, Y. Energy evolution characteristics and weak structure - “Energy Flow” impact damaged mechanism of deep-bedded sandstone. Rock Mech. Rock Eng. 2023, 56, 2017–2047.
• Song, Z.X., Zhang, J.W., Zhang, Y., Dong, X.K., Wang, S.Y. Characterization and evaluation of brittleness of deep bedded sandstone from the perspective of the whole life-cycle evolution process. J. Min. Sci. Technol. 2023, 33, 481–502.
• Erener, A., Mutlu, A., Düzgün, H.S. A comparative study for landslide susceptibility mapping using GIS-based multi-criteria decision analysis (MCDA), logistic regression (LR) and association rule mining (ARM). Geol. 2016, 203, 45-55.
• Sepehri, M., Apel, D.B., Adeeb, S., Leveille, P., Hall, R.A. Evaluation of mining-induced energy and rockburst prediction at a diamond mine in Canada using a full 3D elastoplastic finite element model. Geol. 2020, 266, 105457.
• Kokkala, A., Marinos, V. An engineering geological database for managing, planning and protecting intelligent cities: The case of Thessaloniki city in Northern Greece. Geol. 2022, 301, 106617.
• He, M.C. Physical modeling of an underground roadway excavation in geologically 45° inclined rock using infrared thermography. Geol. 2011, 121(3-4), 165-176.
• Torresa, F., Piccinini, L., Pola, Marco., Zampieri, D., Fabbri, P.3D hydrogeological reconstruction of the fault-controlled Euganean Geothermal System (NE Italy). Geol. 2020, 274, 105740.
• Song, Z.X., Zhang, J.W. Research on the progressive failure process and fracture mechanism of rocks with the structural evolution perspective. Struct. Geol. 2022, 154, 104484.
• Zhao, J. Applicability of Mohr–Coulomb and Hoek–Brown strength criteria to the dynamic strength of brittle rock. J. Rock. Mech. Min. Sci. 2000, 37(7), 1115-1121.
• Song, Z.X., Zhang, J.W. The effect of confining pressure on mechanical properties in coal and rock: review and new insights. J. Geosci. 2021, 14(23), 2564.
• Hoek, E., Brown, E.T. Underground Excavation in Rock. London: Institution of Mining and Metallurgy, 1980.
• Hoek, E., Brown, E.T. Practical estimates of rock mass strength. J. Rock. Mech. Min. Sci. 1997, 34(8), 1165-1186.
• Hoek, E., Brown, E.T. The Hoek-Brown failure criterion and GSI-2018 edition. Rock. Mech. Geotech. Eng. 2018, 37,1-28.
• Peng, J., Cai, M.F. A cohesion loss model for determining residual strength of intact rocks. J. Rock. Mech. Min. Sci. 2019, 119, 131-139.
• Alejano, L.A., Walton, G., Gaines, S. Residual strength of granitic rocks. Undergr. Sp. Tech. 2021, 118, 104189.
• Shi, X.C., Yang, X., Meng, Y.F., Li, G. Modified Hoek-Brown failure criterion for anisotropic rocks. Earth. Sci. 2016, 75(11), 995.1-995.11.
• He, M.M., Zhang, Z.Q., Zhu, J.W., Li, N. Correlation between the constant mi of Hoek-Brown criterion and porosity of intact rock. Mech. Rock. Eng. 2022, 55(2), 923-936.
• Luo, B.Y., Ye, Y.C., Hu, N.Y., Wang, W.Q. Investigation of dip effect on uniaxial compressive strength of inclined rock sample by experimental and theoretical models. Mech. Rock. Eng. 2020, 53(4), 1-17.
• Shen, B.T., Shi, J.Y., Barton, N. Graphic examples of a logical nonlinear strength criterion for intact rock. Mech. Rock. Eng. 2019, 53(1), 71-75.
• Singh, M., Singh, B. Modified Mohr-Coulomb criterion for non-linear triaxial and poly-axial strength of jointed rocks. J. Rock. Mech. Min. Sci. 2012, 51, 43-52.
• Barton, N. Shear strength criteria for rock, rock joints, rockfill and rock masses: problems and some solutions. Rock. Mech. Geotech. Eng. 2013, 5(4), 249-261.
• Poulsen, B.A., Adhikary, D.P., Elmouttie, M.K., Wilkins, A. Convergence of synthetic rock mass modelling and the Hoek-Brown strength criterion. J. Rock. Mech. Min. Sci. 2015, 80, 171-180.
• Tsiambaos, G., Saroglou, H. Excavatability assessment of rock masses using the geological strength index (GSI). Eng. Geol. Environ. 2010, 69(1), 13-27.
• Kang H.P. Temporal scale analysis on coal mining and strata control technologies. Min. Strata. Control. Eng. 2021, 3(1), 5-27.

Author Response File: Author Response.pdf

Reviewer 5 Report

In this manuscript, the specific expressions of the M-C and modified H-B strength criterion considering the unloading effect and anisotropy were established. And the applicability of the M-C and modified H-B strength criterion were verified by comparing the theoretical strengths with the actual experimental strengths. It is a very good study. Therefore, this manuscript can be accepted in Sustainability after minor revision. Here are some comments:

1. “Especially, Shen et al. proposed a simple empirical strength criterion based on the uniaxial compressive strength of eight types of rocks and confining stress in the absence of triaxial strength parameters [12]. Sabatakakis et al. evaluated and modified the rock parameter of (mi) in Hoek-Brown strength criterion from the perspective of basic physical properties factors of marlstones, sandstones and limestones [8]. From the energy evolution perspective, Wang and Cui deeply revealed the energy evolution mechanism of sandstone based on the effect of confining pressure [14]. Meanwhile, the corresponding energy-strength criterion was established. Besides, Li et al. constructed the yield criterion with the perspectives of strain energy and modified compounded mobilized planes model [15]. Meanwhile, the corresponding strength-energy criterion under different stress conditions were established.” This part suggests that it is more reasonable to change the author to passive statement.

2. “Similarly, Singh et al. constructed the nonlinear triaxial and poly-axial strength criterion for isotropic intact rocks considering the effect of intermediate principal stress, and verified the applicability and accuracy of the criterion [20]. Correspondingly, though introducing the weighting factor of the intermediate principal stress, Priest S.D. simplified and established the three-dimensional yield criterion, which could effectively simulate the true triaxial test of rocks under different stress levels [17].” This part suggests that it is more reasonable to change the author to passive statement.

 3. “MTS-815.02 electro-hydraulic servo rock mechanics test system was used in the tests. The test system could be used for various types of rock mechanics tests, including the uniaxial or triaxial compression tests, the triaxial fatigue loading (unloading) tests, the uniaxial or triaxial rheological tests, the gas-seepage tests, and the thermo-hydro-mechanical coupling tests.” This section is suggested to be simplified and does not need to be detailed.

4. “For example, before excavation, modern geophysical detection technology, geological Big-data, 5G communications, artificial intelligence and other technologies could be utilized to build a visual mine with high accuracy and real-time [39-41];”. The semicolon here should be replaced by a period.

5. “In this way, the effect of "precise strengthening and overall improvement" could be achieved.” This sentence is too Chinese expression, suggest deletion. 

6. The title of Section 3.2, 3.2.2, 3.3 and 3.3.2 should deleted the “considering anisotropy”.

7. The expressions of the full text needs to be carefully checked and corrected, including the word spelling ect.

Author Response

In this manuscript, the specific expressions of the M-C and modified H-B strength criterion considering the unloading effect and anisotropy were established. And the applicability of the M-C and modified H-B strength criterion were verified by comparing the theoretical strengths with the actual experimental strengths. It is a very good study. Therefore, this manuscript can be accepted in Sustainability after minor revision. Here are some comments:

1. “Especially, Shen et al. proposed a simple empirical strength criterion based on the uniaxial compressive strength of eight types of rocks and confining stress in the absence of triaxial strength parameters [12]. Sabatakakis et al. evaluated and modified the rock parameter of (mi) in Hoek-Brown strength criterion from the perspective of basic physical properties factors of marlstones, sandstones and limestones [8]. From the energy evolution perspective, Wang and Cui deeply revealed the energy evolution mechanism of sandstone based on the effect of confining pressure [14]. Meanwhile, the corresponding energy-strength criterion was established. Besides, Li et al. constructed the yield criterion with the perspectives of strain energy and modified compounded mobilized planes model [15]. Meanwhile, the corresponding strength-energy criterion under different stress conditions were established.” This part suggests that it is more reasonable to change the author to passive statement.

Response: Thanks for your comments. We have corrected the statement with the passive format. And the details are as follows:

Especially, a simple empirical strength criterion based on the uniaxial compressive strength of eight types of rocks and confining stress based on triaxial strength parameters was proposed [12]. Besides, the rock parameter of (m_i) in Hoek-Brown strength criterion from the perspective of basic physical properties factors of marlstones, sandstones and limestones were evaluated and modified [8]. From the energy evolution perspective, the energy evolution mechanism of sandstone was deeply revealed based on the effect of confining pressure [14]. Meanwhile, the corresponding energy-strength criterion was established. Besides, the yield criterion and modified compounded mobilized planes model was also constructed with the perspectives of strain energy [15]. Meanwhile, the corresponding strength-energy criterion under different stress conditions were established.

 

2. “Similarly, Singh et al. constructed the nonlinear triaxial and poly-axial strength criterion for isotropic intact rocks considering the effect of intermediate principal stress, and verified the applicability and accuracy of the criterion [20]. Correspondingly, though introducing the weighting factor of the intermediate principal stress, Priest S.D. simplified and established the three-dimensional yield criterion, which could effectively simulate the true triaxial test of rocks under different stress levels [17].” This part suggests that it is more reasonable to change the author to passive statement.

Response: Thanks for your comments. We have corrected the statement with the passive format. And the details are as follows:

Similarly, the nonlinear triaxial and poly-axial strength criterion for isotropic intact rocks considering the effect of intermediate principal stress was also constructed, and the applicability and accuracy of the criterion was verified [20]. Correspondingly, though introducing the weighting factor of the intermediate principal stress, the three-dimensional yield criterion was also simplified and established, which could effectively simulate the true triaxial strength of rocks under different stress levels [17].

 

3. “MTS-815.02 electro-hydraulic servo rock mechanics test system was used in the tests. The test system could be used for various types of rock mechanics tests, including the uniaxial or triaxial compression tests, the triaxial fatigue loading (unloading) tests, the uniaxial or triaxial rheological tests, the gas-seepage tests, and the thermo-hydro-mechanical coupling tests.” This section is suggested to be simplified and does not need to be detailed.

Response: Thanks for your comments. We have moveed the introduction for the MTS-815.02 electro-hydraulic servo rock mechanics test system. And the details are as follows:

MTS-815.02 electro-hydraulic servo rock mechanics test system was used in the tests. And the specific upper thresholds of basic parameters of the system were as follows:

1. The upper threshold of axial pressure is 1700 kN;
2. The upper threshold of confining pressure is 45 MPa;
3. The upper threshold of pore pressure is 45 MPa;
4. The upper threshold of osmotic water pressure difference is 2 MPa;
5. The upper threshold of osmotic gas pressure difference is 6 MPa;
6. The upper threshold of temperature is 200 ℃;
7. The upper limit of specimen size for applicable tests is 100 mm in diameter and 200mm in height.

 

4. “For example, before excavation, modern geophysical detection technology, geological Big-data, 5G communications, artificial intelligence and other technologies could be utilized to build a visual mine with high accuracy and real-time [39-41];”. The semicolon here should be replaced by a period.

Response: Thanks for your comments. We have changed the semicolon to period.

 

5. “In this way, the effect of "precise strengthening and overall improvement" could be achieved.” This sentence is too Chinese expression, suggest deletion.

Response: Thanks for your comments. We have moved the sentence in the revised muanscript.

 

6. The title of Section 3.2, 3.2.2, 3.3 and 3.3.2 should deleted the “considering anisotropy”.

Response: Thanks for your comments. We have moved the “considering anisotropy” in the title of Section 3.2, 3.2.2, 3.3 and 3.3.2 in the revised muanscript.

 

7. The expressions of the full text needs to be carefully checked and corrected, including the word spelling ect.

Response: Thanks for your comments. We have carefully check and corrected the expressions of the whole text.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have taken the comments I made into consideration in the revision of the article. The English language has been greatly improved

Reviewer 3 Report

Authors have gone a careful revision, and it can be accepted for publication in present form.