Salt Cavern Thermal Damage Evolution Investigation Based on a Hybrid Continuum-Discrete Coupled Modeling

Round 1

Reviewer 1 Report

here are some suggestions for improvement:

 

Clarity: Although the writing is technically precise, it may be beneficial to rephrase some sentences to make them clearer for the average reader. For example, the sentence "The dynamic responses of rock salt, including temperature spatiotemporal variation, microscopic cracking patterns, and energy evolution, exhibit spatial and confinement dependence" could be simplified to say "Changes in temperature and pressure cause the salt cavern to crack in specific ways."

 

Sentence Structure: Some of the sentences are long and difficult to read. Breaking them down into shorter sentences may improve readability and comprehension.

 

Simplify Technical Jargon: Although specialized language is necessary, it could be helpful to simplify some of the technical jargon, particularly for non-experts. For instance, instead of "continuum-discrete model accounting for the thermal-mechanical process," you could say "a model that considers how temperature and pressure affect the salt cavern."

 

Introduction and Conclusion: The writing could benefit from a clear introduction and conclusion that briefly summarizes the purpose and findings of the study. This would provide readers with a quick overview of what to expect and help them understand the relevance of the study.

 

Visual Aids: Including visual aids such as diagrams or graphs may also help readers understand the concepts more easily. This would also break up the text and make it more visually appealing.

 

In summary, while the writing appears technically sound, simplifying language, breaking down complex sentences, and providing visual aids could improve readability and comprehension. Additionally, a clear introduction and conclusion could help readers understand the relevance of the study.

 

Comments for author File: Comments.pdf

Author Response

 

1. Article Title (Line 4) - highlight the innovative part in the paper?

Response: Thanks a lot for the suggestion. We demonstrated the innovative part in the Highlight document. In this study, a hybrid continuum-discrete model accounting for the thermal-mechanical process is proposed to investigate thermal damage evolution mechanism towards a field case, which is the most innovative part in this paper.

 

2. Line 16- add key specific results.

Response: Thanks a lot for the suggestion. The key specific results are: the evolution of cracks is controlled by: (1) the thermal-mechanical process (i.e. depressurization and retain at low pressure) (2) the anomalous zone close to the brim of salt cavity surrounding wall. We added another one: “The zone far away from marginal surrounding wall is less affected by temperature, and only the mechanical conditions control the development of cracks.”  in the revision manuscript.

 

3. Line 40- add a detailed background of problem studied before presenting problem statement.

 

Response: Thanks a lot for the suggestion. We added a detailed background of the problem in the Introduction part in the revision manuscript.

 

4. Line 54- what is the basis of this assumption?

Response: Thanks a lot for the very professional comment. In the stage of salt cavern gas injection and gas withdrawal, there are not only pressure but also temperature changes in salt cavern. Especially in the stage of gas withdrawal, too fast rate of gas withdrawal process will make the temperature of the cavity drop significantly, resulting in thermal effect in the surrounding rock of the cavity wall, which leads to the tensile stress concentration. Considering the rock salt has very low tensile strength, it is easy to cause tensile damage.

 

 

5. Line 59- why flac3d?

Response: Thanks a lot for the very professional comment. FLAC3D adopts explicit Lagrangian algorithm and mixed discrete partitioning technology, which can accurately simulate the plastic failure and flow of materials. Due to the need to form a stiffness matrix and the ability to solve large-scale three-dimensional problems based on a small memory space, it is more suitable for analyzing underground salt cavities with burial depths of over a kilometer and cavity heights close to the height of the Eiffel Tower. In terms of software functionality, this software has unique advantages in solving problems such as large deformation and failure of rock masses that cannot be solved by general finite element methods, and is particularly suitable for analyzing asymptotic and instability; At the same time, research and multi field coupling can be carried out on seepage, creep, thermal calculation, dynamic analysis, and other issues, and the operation is simple, and the mapping effect is good.

 

 

6. Line 69- add captions for sub figures and add a) and b) in figures.

Response: Thanks a lot for the very professional comment. We have added sub-titles to both figures.

 

7. Line 78- but this is not much relevant.

Response: Thanks a lot for the very professional comment. What we simulated this time was the actual working condition of 3.14 years, in which both the pressure and temperature decreased, namely, the process of rapid cooling of salt cavern.

 

8. Line 166- FLAC Finite difference while DEM is better for solving this kind of problem - justify your choice.

Response: Thanks a lot for the very professional comment. The discrete element method is not limited by the amount of deformation, can conveniently deal with the mechanics of discontinuous media, reflect the different physical relations of heterogeneous media, can effectively simulate the discontinuous phenomena such as cracking and separation of media, and can reflect the micro-mechanism, process and result.

 

9. Line 170- how? flac is not discrete element.

Response: Thanks a lot for the very professional comment. For the example of cavity collapse in engineering, it is necessary to conduct dynamic analysis of the failure process of surrounding rock peeling. Because the finite difference algorithm adopted by FLAC3D for continuous media makes it unable to simulate the phenomenon of rock mass fracture, sliding and collapse, so for thermal damage, this paper uses PFC3D with excellent discontinuous problem analysis ability to conduct continuous and discrete coupling.

 

10. Line 185- this should be a dynamic model. Add details.

Response: Thanks a lot for the very professional comment. The geometric conditions of the model are shown in Figure 3. The physical process of the cavity in the model is shown in Figure 6. The boundary conditions of the model are shown in Figure 7 (a).

 

 

11. Line 192- why a hybrid model is used, why not PFC alone?

Response: Thanks a lot for the very professional comment. Generally speaking, we use FLAC3D to apply boundary conditions towards the field case, while use PFC to study the micro-mechanism of thermal damage evolution. Continuous numerical simulation methods, such as finite difference method and finite element method, rely on elements for calculation and share nodes between elements to reasonably describe the transfer of load force. The amount of deformation that can be simulated is limited. When the deformation increases to a certain extent, the element will be deformed and the stiffness matrix cannot be solved, resulting in the termination of calculation. The discrete element method is based on the block or particle, which can be separated, and the motion equation of the block or particle is updated by constant contact judgment at each time step, which is not limited by the amount of deformation. However, a large number of contact judgment will lead to the reduction of the calculation speed. The continuous-discontinuous coupling numerical simulation method can not only meet the requirements of computational efficiency, but also be free from the deformation limit, which can promote the development of numerical simulation to a deeper level.

 

12. Line 197- add sub captions a) b) and c), Also show dimensions of PFC zones and balls.

Response: Thanks a lot for the very professional comment. We have added the title and the size of the ball.

 

13. Line 225- you should use rock mass properties instead of intact rock properties.

Response: Thanks a lot for the very professional comment. We have modified it on the top of the table.

 

14. Line 226- add to column of units.

Response: Thanks a lot for the very professional comment. We have modified it.

 

15. Line 229- what is new?

Response: Thanks a lot for the very professional comment. According to the literature research, the previous scholars only applied mechanical force in the continuous - discrete coupling simulation, while we applied the thermal attribute to the coupling scheme for the very first time.

 

16. Line 279- a) is poor quality.

Response: Thanks a lot for the very professional comment. The flow chart in FIG. 4(a) represents the transfer relationship between mechanical force and heat properties in the coupling model in the continuous-discrete coupling model. Important parameters of the transfer relationship between the left and right sides can be easily seen. Continuity and dispersion can only be transmitted in the intermediate medium of the coupling wall, and the temperature needs to be transmitted to the coupling wall by the fish function.

 

17. Line 285- numbering is incorrect.

Response: Thanks a lot for the very professional comment. We have modified it.

 

 

18. Line 289- why 5?

Response: Thanks a lot for the very professional comment. This process is a practical engineering case. The cavity construction began in May 2005, and a sonar cavity measurement operation was carried out in July 2009, with the measured volume reaching 116815.5m³. After that, the cavity completed gas injection and halogen drainage, and began gas injection and production in November 2010. At that time, according to the traditional stability analysis, the cavity would maintain limited shrinkage during the stable operation, with no obvious risk to the surrounding rock as a whole. However, in November 2015, five years after the operation, the cavity was tested again with sonar belt pressure, and it was found that the shoulder of the cavity collapsed about 4 meters.

 

 

19. Line 354- show all modeling regime.

Response: Thanks a lot for the very professional comment. The physical process of the cavity in the model is shown in Figure 6. The boundary conditions of the model are shown in Figure 7 (a). From the model regime, the variables of each process cannot be effectively seen, so we draw the figure of each parameter to indicate the variables of each parameter.

 

 

20. Line 358- figure should be presented after discussion in text.

Response: Thanks a lot for the very professional comment. We have adjusted.

 

21. Line 383- add a legend. Add a), b) and c) with figures and their captions.

Response: Thanks a lot for the very professional comment. The “1, 2, 3” indicates the selected locations.

 

 

22. Line 383- How to know if crack is propagating, maybe its fluid or stress.

Response: Thanks a lot for the very professional comment. After 5 years of injection and withdrawal operation, a certain cavity of the Jintan Salt Cave Gas Storage Tank underwent sonar pressure measurement on November 25, 2015. Comparing the measurement results with the results of the completed cavity sonar measurement at the end of 2008, it was found that a large area of collapse occurred at the top of the cavity, with a displacement difference of 4 meters, and a local collapse also occurred in the middle of the salt cavity. In response to this issue in engineering, in-depth analysis was conducted, fully considering the influence of thermal effects during gas injection and production. The finite element numerical simulation method was used to couple the temperature field and stress field of the surrounding rock to establish a cavity thermal model. The distribution of thermal stress in the cavity surrounding rock was analyzed, and the cavity thermal model was compared with the conventional mechanical model previously used for cavity stability analysis, The research results found that in some areas that exhibit stability in conventional mechanical models, collapse occurs in thermal models. The calculated results of the thermal model are consistent with the results of sonar pressure measurement of the cavity after 5 years of injection and production operation. Therefore, it is inferred that the thermal stress generated by temperature changes is an important factor affecting the stability of the cavity, and in severe cases, it may lead to cavity collapse. Especially in the gas production stage, if the gas production rate is too fast, the temperature of the cavity will significantly decrease, causing a thermal effect on the surrounding rock of the cavity wall, leading to the occurrence of tensile stress; The tensile strength of salt rock is very low, which is prone to tensile damage and failure.

 

23. Line 425- the model has deleted the balls?

Response: Thanks a lot for the very professional comment. Figure 11 shows the crack density form of fracture between particles, with no balls anymore, indicating the differences in crack density at different positions.

 

 

24. Line 434- what is the significance of rossette chart?

Response: Thanks a lot for the very professional comment. In order to explore the non-uniformity of cracks under the action of thermodynamic coupling, which tensile or shear cracks are more affected by temperature changes in different positions. Blanc-martin et al. conducted thermal stress experiments in salt caverns to observe the macro-mechanical property response of rocks, and found that salt rock with rapid cooling would have tensile cracks.

Blanco-Martín, L., Rouabhi, A., Billiotte, J., Hadj-Hassen, F., Tessier, B., Hévin, G., ... & Hertz, E. (2018). Experimental and numerical investigation into rapid cooling of rock salt related to high frequency cycling of storage caverns. International Journal of Rock Mechanics and Mining Sciences, 102, 120-130.

 

 

25. Line 463- add a legend. The text is not readable. Also make it compatible for printing in B&W.

Response: Thanks a lot for the very professional comment. We have modified it.

 

 

26. Line 503- numbering must be corrected.

Response: Thanks a lot for the very professional comment. We have modified it.

 

 

27. Line 537- what is the reason and significance.

Response: Thanks a lot for the very professional comment. Blanc-martin et al. conducted thermal stress experiments in salt caverns to observe the macro-mechanical property response of rocks, and found that salt rock with rapid cooling would have tensile cracks. Salt rock is prone to tensile cracks under the influence of temperature, and the reduction of tensile cracks indicates that the effect of temperature on salt rock in the later stage is relatively small.

Blanco-Martín, L., Rouabhi, A., Billiotte, J., Hadj-Hassen, F., Tessier, B., Hévin, G., ... & Hertz, E. (2018). Experimental and numerical investigation into rapid cooling of rock salt related to high frequency cycling of storage caverns. International Journal of Rock Mechanics and Mining Sciences, 102, 120-130.

 

 

28. Line 560- discuss the figure in text before presenting the figure.

Response: Thanks a lot for the very professional comment. We have modified it.

 

 

29. Line 563- not much difference though.

Response: Thanks a lot for the very professional comment. The figure also shows that the influence of friction coefficient is not obvious.

30. Line 577- add recommendations and future work.

Response: Thanks a lot for the suggestion. We added a future work in the Conclusion part in the revision manuscript.

Reviewer 2 Report

This paper discusses a hybrid continuum-discrete model accounting for the thermal-mechanical process proposed to investigate the thermal damage evolution mechanism towards a field case with blocks falling off the salt cavity. The following comments and suggestions are provided for further improving the manuscript.

(1) In this simulation, is the direction of temperature transfer unidirectional or bidirectional, from discrete body to continuum, or continuum to discrete body?

(2) As stated in this study, the thermal effect induced the falling of the cap rock, is there any other reasons may act as a trigger for this?

(3) How does heat and mechanical force transferred on the continuum zones? Does it have to be updated every time step?

(4) The author selected three parts in the rock salt surrounding rock. What is the significance of selecting these three parts? Why not select more parts and why not select the parts on the surface of the rock salt cavity? Please make necessary explanation.

Author Response

Thank you  very much for the careful reading, review, affirming of our work, and many constructive suggestions. The detailed replies to the reviewers’ comments are as the followings: 

1. In this simulation, is the direction of temperature transfer unidirectional or bidirectional, from discrete body to continuum, or continuum to discrete body?

Response: Thanks a lot for the very professional comment. In this simulation, we changed the temperature of the salt cavern cavity; that is, the temperature change is transmitted from the wall surface of the salt cavern to the deep beneath the surrounding wall surface. The surrounding wall rock farther away from the salt cavity surface is less affected by the temperature variation, and the rock closer to the salt cavern is more affected by the temperature change. The direction of temperature transfer is unidirectional, from the continuous zones to the discrete particles, and then observe the development of cracks in the discontinuous assembly which is breakable and detachable.

 

 

 

 

2. As stated in this study, the thermal effect induced the falling of the cap rock, is there any other reasons may act as a trigger for this?

Response: Thanks a lot for the very professional comment. In general, the falling of cap rock is associated with many various influencing factors. The main aspects we concluded as followings:

• The in-situ stress

The very first influencing factor is the in-situ stress. The effect of change in  (the ratio of horizontal to vertical in-situ stress) value, as an important boundary condition, has been analyzed. Generally, with decrease  ratio, the less convergence in cavern wall, and the stability of salt cavern will increase.  With decrease  ratio, the tension stress occurs in upper cap rock, while increase  ratio, the tension stress occurs in surrounding of cavern wall. The in-situ stress, depending on the governing tectonic regime of the rock salt formation, is one of the inducing factors for collapse.

• Shape of the cavern

It is widely accepted that the stable shapes of salt cavern used for gas storage is pear-shape, oval shape or called ellipsoids. When the upper cap is wider at the top with a gentle incline, it will cause the instability of the salt cavern, and possibility of cap rock failure. It associated with the consequence of solution mining of rock salt formation. Before the operation of solution mining, the in-situ stress field is in equilibrium state; when the leaching is completed, the upper cap rock in unloading process hardly reach equilibrium state, resulting in large deformation and instability.  

• The fractures
• The fractures are pre-existing the in salt cavern wall. In the process of leaching, and gas injection-and-withdrawal, the fractures might propagate due to erosion of brine and gas.
• With the influence of interlayer and impurities, the cracks primarily initiate near the interface region, and then propagate to the interlayer. (Li, et al., 2014). The gas loading and unloading operation induces the repeated loads. Its cracking behavior is also controlled by the microscopic heterogeneity of composite rock salt coupling with the external stress acting on cavern wall. 
• In this study, we mainly study the thermal stress on cavern wall induced by thermal effect of gas cycling operation. The thermal cracking and the thermal damage evolution are our concerns.

Li, Y., Liu, W., Yang, C., & Daemen, J. J. (2014). Experimental investigation of mechanical behavior of bedded rock salt containing inclined interlayer. International Journal of Rock Mechanics & Mining Sciences, 69, 39-49.

 

 

3. How does heat and mechanical force transferred on the continuum zones? Does it have to be updated every time step?

Response: Thanks a lot for the very professional comment. In the continuum, the transfer of mechanical forces is transmitted governing by the constitutive equation, and the relationship between stress and strain is transferred from the deformation behavior of one zone to another. Heat is transferred governing by the formula of Fourier's law of heat conduction, according to the differential equation of heat conduction. Each time step is calculated once; that is, each step is iteratively updated.

 

 

4. The author selected three parts in the rock salt surrounding rock. What is the significance of selecting these three parts? Why not select more parts and why not select the parts on the surface of the rock salt cavity? Please make necessary explanation.

Response: Thanks a lot for the very professional comment. Towards to the field case, in this study, we selected three sections in the shoulder part of the salt cavern to explore the thermal sensitivity to temperature variation. These three sections are the corner of the salt cavern shoulder, the right side of the salt cavern shoulder, and the depth of the surrounding rock of the salt cavern shoulder. These three sections are very representative in the thermal damage evolution of the salt cavity. In the coupling process between the continuum and discrete medium, an interface (wall-zone) must be constructed to transfer force and displacement. However, the coupling wall should not be affected by any additional external force, so the selected part cannot be a rock salt wall surface.

Reviewer 3 Report

Please send this PDF file (with comments included) to the author for compliance.

Comments for author File: Comments.pdf

Some minor editing of the English language is required.

Author Response

Thank you very much for the careful reading, review, affirming of our work, and many constructive suggestions. We have carefully revised the manuscript following the reviewers’ comments in track-changes mode and a clean finalised version of the manuscript has also been appended. We hope that this revised manuscript fully addresses the issues raised by the reviewers.

Reviewer 4 Report

Comment in attachment

Comments for author File: Comments.pdf

Minor editing of English language required

Author Response

Thank you very much for the careful reading, review, affirming of our work, and many constructive suggestions. The detailed replies to the reviewers’ comments are as the followings: 

Some issues should be addressed before publication:

1. The choice of model parameters should be justified in more detail.

Response: Thank you so much for the comments. The simulation based on hybrid continuum-discrete model is operated towards a field case (Li et al., 2021). The parameters in continuum medium (FLAC3D) of the hybrid model are selected according to the parameters used in the field case; the parameters in discrete medium are selected from the recommendations from the PFC manual.

Li, W., Nan, X., Chen, J., & Yang, C. (2021). Investigation of thermal-mechanical effects on salt cavern during cyclying loading. Energy, 232:120969.

Itasca Consulting Group, Inc. (2019). Particle Flow Code 6.0 User's Manual. Minneapolis, Minnesota, USA: Itasca Consulting Group, Inc.

 

2. The equations used are insufficiently described to allow understanding by non-experts in the field.

Response: Thank you so much for the comments. In this study, we focus on the application of the hybrid model a field case with blocks fall off from the salt cavern roof, the necessary equations for explanation of Energy Tracking of particles in DEM.

 

3. Figures 7, 8, 10, 15, 16 are missing a color scale.

Response: Thank you for the advice. The color scale means nothing but representation of different detached broken particles formed as a result of cracking. We added an explanation in the revision manuscript.

 

4. Figures 9 and 16 - what does the % on the axis mean?

Response: Thanks a lot for the very professional comment. “%” in Fig. 9 represents the ratio of tensile cracks to total cracks. “%”in Figure 16 represents the ratio of tensile cracks to total cracks and shear cracks to total cracks.

 

5. Figure 14 - axis descriptions are illegible.

Response: Thanks a lot for your reminder. We added the axis descriptions for that figure.

 

6. Figure 15 - barely visible line for 16 MPa.

Response: Thanks a lot for your reminder. We made the line more visible and clearly in Fig. 16.

 

7. Lines 444-470 - duplicated symbols and careless formatting, including Figure 14.

Response: Thanks a lot for your reminder. We deleted the duplicated symbols and examined the formatting.

 

8. I consider the use of the same symbols for the definitions of TMK, TML, TMS to be quite a bad idea.

Response: Thank you for the advice. We made the improvement for the indicators.

 

9. The results presented are discussed quite superficially.

Response: Thank you for the advice. The authors have rewritten the conclusions, and added supplementary discussions for the results. Please refer to the Conclusions section of manuscript for revision.

Round 2

Reviewer 4 Report

The authors made the necessary corrections to the manuscript, so I have no further objections to publication.

Author Response

 

1. Article Title (Line 4) - highlight the innovative part in the paper?

Response: Thanks a lot for the suggestion. We demonstrated the innovative part in the Highlight document. In this study, a hybrid continuum-discrete model accounting for the thermal-mechanical process is proposed to investigate thermal damage evolution mechanism towards a field case, which is the most innovative part in this paper.

 

2. Line 16- add key specific results.

Response: Thanks a lot for the suggestion. The key specific results are: the evolution of cracks is controlled by: (1) the thermal-mechanical process (i.e. depressurization and retain at low pressure) (2) the anomalous zone close to the brim of salt cavity surrounding wall. We added another one: “The zone far away from marginal surrounding wall is less affected by temperature, and only the mechanical conditions control the development of cracks.”  in the revision manuscript.

 

3. Line 40- add a detailed background of problem studied before presenting problem statement.

 

Response: Thanks a lot for the suggestion. We added a detailed background of the problem in the Introduction part in the revision manuscript.

 

4. Line 54- what is the basis of this assumption?

Response: Thanks a lot for the very professional comment. In the stage of salt cavern gas injection and gas withdrawal, there are not only pressure but also temperature changes in salt cavern. Especially in the stage of gas withdrawal, too fast rate of gas withdrawal process will make the temperature of the cavity drop significantly, resulting in thermal effect in the surrounding rock of the cavity wall, which leads to the tensile stress concentration. Considering the rock salt has very low tensile strength, it is easy to cause tensile damage.

 

 

5. Line 59- why flac3d?

Response: Thanks a lot for the very professional comment. FLAC3D adopts explicit Lagrangian algorithm and mixed discrete partitioning technology, which can accurately simulate the plastic failure and flow of materials. Due to the need to form a stiffness matrix and the ability to solve large-scale three-dimensional problems based on a small memory space, it is more suitable for analyzing underground salt cavities with burial depths of over a kilometer and cavity heights close to the height of the Eiffel Tower. In terms of software functionality, this software has unique advantages in solving problems such as large deformation and failure of rock masses that cannot be solved by general finite element methods, and is particularly suitable for analyzing asymptotic and instability; At the same time, research and multi field coupling can be carried out on seepage, creep, thermal calculation, dynamic analysis, and other issues, and the operation is simple, and the mapping effect is good.

 

 

6. Line 69- add captions for sub figures and add a) and b) in figures.

Response: Thanks a lot for the very professional comment. We have added sub-titles to both figures.

 

7. Line 78- but this is not much relevant.

Response: Thanks a lot for the very professional comment. What we simulated this time was the actual working condition of 3.14 years, in which both the pressure and temperature decreased, namely, the process of rapid cooling of salt cavern.

 

8. Line 166- FLAC Finite difference while DEM is better for solving this kind of problem - justify your choice.

Response: Thanks a lot for the very professional comment. The discrete element method is not limited by the amount of deformation, can conveniently deal with the mechanics of discontinuous media, reflect the different physical relations of heterogeneous media, can effectively simulate the discontinuous phenomena such as cracking and separation of media, and can reflect the micro-mechanism, process and result.

 

9. Line 170- how? flac is not discrete element.

Response: Thanks a lot for the very professional comment. For the example of cavity collapse in engineering, it is necessary to conduct dynamic analysis of the failure process of surrounding rock peeling. Because the finite difference algorithm adopted by FLAC3D for continuous media makes it unable to simulate the phenomenon of rock mass fracture, sliding and collapse, so for thermal damage, this paper uses PFC3D with excellent discontinuous problem analysis ability to conduct continuous and discrete coupling.

 

10. Line 185- this should be a dynamic model. Add details.

Response: Thanks a lot for the very professional comment. The geometric conditions of the model are shown in Figure 3. The physical process of the cavity in the model is shown in Figure 6. The boundary conditions of the model are shown in Figure 7 (a).

 

 

11. Line 192- why a hybrid model is used, why not PFC alone?

Response: Thanks a lot for the very professional comment. Generally speaking, we use FLAC3D to apply boundary conditions towards the field case, while use PFC to study the micro-mechanism of thermal damage evolution. Continuous numerical simulation methods, such as finite difference method and finite element method, rely on elements for calculation and share nodes between elements to reasonably describe the transfer of load force. The amount of deformation that can be simulated is limited. When the deformation increases to a certain extent, the element will be deformed and the stiffness matrix cannot be solved, resulting in the termination of calculation. The discrete element method is based on the block or particle, which can be separated, and the motion equation of the block or particle is updated by constant contact judgment at each time step, which is not limited by the amount of deformation. However, a large number of contact judgment will lead to the reduction of the calculation speed. The continuous-discontinuous coupling numerical simulation method can not only meet the requirements of computational efficiency, but also be free from the deformation limit, which can promote the development of numerical simulation to a deeper level.

 

12. Line 197- add sub captions a) b) and c), Also show dimensions of PFC zones and balls.

Response: Thanks a lot for the very professional comment. We have added the title and the size of the ball.

 

13. Line 225- you should use rock mass properties instead of intact rock properties.

Response: Thanks a lot for the very professional comment. We have modified it on the top of the table.

 

14. Line 226- add to column of units.

Response: Thanks a lot for the very professional comment. We have modified it.

 

15. Line 229- what is new?

Response: Thanks a lot for the very professional comment. According to the literature research, the previous scholars only applied mechanical force in the continuous - discrete coupling simulation, while we applied the thermal attribute to the coupling scheme for the very first time.

 

16. Line 279- a) is poor quality.

Response: Thanks a lot for the very professional comment. The flow chart in FIG. 4(a) represents the transfer relationship between mechanical force and heat properties in the coupling model in the continuous-discrete coupling model. Important parameters of the transfer relationship between the left and right sides can be easily seen. Continuity and dispersion can only be transmitted in the intermediate medium of the coupling wall, and the temperature needs to be transmitted to the coupling wall by the fish function.

 

17. Line 285- numbering is incorrect.

Response: Thanks a lot for the very professional comment. We have modified it.

 

 

18. Line 289- why 5?

Response: Thanks a lot for the very professional comment. This process is a practical engineering case. The cavity construction began in May 2005, and a sonar cavity measurement operation was carried out in July 2009, with the measured volume reaching 116815.5m³. After that, the cavity completed gas injection and halogen drainage, and began gas injection and production in November 2010. At that time, according to the traditional stability analysis, the cavity would maintain limited shrinkage during the stable operation, with no obvious risk to the surrounding rock as a whole. However, in November 2015, five years after the operation, the cavity was tested again with sonar belt pressure, and it was found that the shoulder of the cavity collapsed about 4 meters.

 

 

19. Line 354- show all modeling regime.

Response: Thanks a lot for the very professional comment. The physical process of the cavity in the model is shown in Figure 6. The boundary conditions of the model are shown in Figure 7 (a). From the model regime, the variables of each process cannot be effectively seen, so we draw the figure of each parameter to indicate the variables of each parameter.

 

 

20. Line 358- figure should be presented after discussion in text.

Response: Thanks a lot for the very professional comment. We have adjusted.

 

21. Line 383- add a legend. Add a), b) and c) with figures and their captions.

Response: Thanks a lot for the very professional comment. The “1, 2, 3” indicates the selected locations.

 

 

22. Line 383- How to know if crack is propagating, maybe its fluid or stress.

Response: Thanks a lot for the very professional comment. After 5 years of injection and withdrawal operation, a certain cavity of the Jintan Salt Cave Gas Storage Tank underwent sonar pressure measurement on November 25, 2015. Comparing the measurement results with the results of the completed cavity sonar measurement at the end of 2008, it was found that a large area of collapse occurred at the top of the cavity, with a displacement difference of 4 meters, and a local collapse also occurred in the middle of the salt cavity. In response to this issue in engineering, in-depth analysis was conducted, fully considering the influence of thermal effects during gas injection and production. The finite element numerical simulation method was used to couple the temperature field and stress field of the surrounding rock to establish a cavity thermal model. The distribution of thermal stress in the cavity surrounding rock was analyzed, and the cavity thermal model was compared with the conventional mechanical model previously used for cavity stability analysis, The research results found that in some areas that exhibit stability in conventional mechanical models, collapse occurs in thermal models. The calculated results of the thermal model are consistent with the results of sonar pressure measurement of the cavity after 5 years of injection and production operation. Therefore, it is inferred that the thermal stress generated by temperature changes is an important factor affecting the stability of the cavity, and in severe cases, it may lead to cavity collapse. Especially in the gas production stage, if the gas production rate is too fast, the temperature of the cavity will significantly decrease, causing a thermal effect on the surrounding rock of the cavity wall, leading to the occurrence of tensile stress; The tensile strength of salt rock is very low, which is prone to tensile damage and failure.

 

23. Line 425- the model has deleted the balls?

Response: Thanks a lot for the very professional comment. Figure 11 shows the crack density form of fracture between particles, with no balls anymore, indicating the differences in crack density at different positions.

 

 

24. Line 434- what is the significance of rossette chart?

Response: Thanks a lot for the very professional comment. In order to explore the non-uniformity of cracks under the action of thermodynamic coupling, which tensile or shear cracks are more affected by temperature changes in different positions. Blanc-martin et al. conducted thermal stress experiments in salt caverns to observe the macro-mechanical property response of rocks, and found that salt rock with rapid cooling would have tensile cracks.

Blanco-Martín, L., Rouabhi, A., Billiotte, J., Hadj-Hassen, F., Tessier, B., Hévin, G., ... & Hertz, E. (2018). Experimental and numerical investigation into rapid cooling of rock salt related to high frequency cycling of storage caverns. International Journal of Rock Mechanics and Mining Sciences, 102, 120-130.

 

 

25. Line 463- add a legend. The text is not readable. Also make it compatible for printing in B&W.

Response: Thanks a lot for the very professional comment. We have modified it.

 

 

26. Line 503- numbering must be corrected.

Response: Thanks a lot for the very professional comment. We have modified it.

 

 

27. Line 537- what is the reason and significance.

Response: Thanks a lot for the very professional comment. Blanc-martin et al. conducted thermal stress experiments in salt caverns to observe the macro-mechanical property response of rocks, and found that salt rock with rapid cooling would have tensile cracks. Salt rock is prone to tensile cracks under the influence of temperature, and the reduction of tensile cracks indicates that the effect of temperature on salt rock in the later stage is relatively small.

Blanco-Martín, L., Rouabhi, A., Billiotte, J., Hadj-Hassen, F., Tessier, B., Hévin, G., ... & Hertz, E. (2018). Experimental and numerical investigation into rapid cooling of rock salt related to high frequency cycling of storage caverns. International Journal of Rock Mechanics and Mining Sciences, 102, 120-130.

 

 

28. Line 560- discuss the figure in text before presenting the figure.

Response: Thanks a lot for the very professional comment. We have modified it.

 

 

29. Line 563- not much difference though.

Response: Thanks a lot for the very professional comment. The figure also shows that the influence of friction coefficient is not obvious.

 

30. Line 577- add recommendations and future work.

Response: Thanks a lot for the suggestion. We added a future work in the Conclusion part in the revision manuscript.