Evolution of low-karstified rock-blocks and their influence on reservoir leakage: a modelling perspective

Jiao, Youjun; Gabrovšek, Franci; Wang, Xusheng; Yu, Qingchun

doi:10.5194/egusphere-2025-1320

Preprints

https://doi.org/10.5194/egusphere-2025-1320

Preprints

03 Apr 2025

| 03 Apr 2025

Evolution of low-karstified rock-blocks and their influence on reservoir leakage: a modelling perspective

Youjun Jiao, Franci Gabrovšek, Xusheng Wang, and Qingchun Yu

Abstract. Hydraulic structures such as dams and reservoirs pose significant construction challenges in karst areas due to severe and costly leakage issues. In this study, we apply a numerical model to test the hypothesis that karst aquifers in water divide areas may contain an intrinsically low-karstified rock-blocks (LKB), which form due to the specific evolution of unconfined aquifer with recharge distributed to the water table. We develop, test, and apply a model of flow, transport, and dissolution in a 2D fracture network with a fluctuating water table. The model's structure and boundary conditions are based on the conceptualization of the Luojiaao (China) interfluve aquifer. First, we simulate the evolution of an unconfined network, representing the interfluve, up to a stage resembling the present conditions in Luojiaao. We then analyze leakage through the evolved aquifer from a reservoir at different water levels and simulate further aquifer evolution under reservoir conditions. Our results demonstrate the formation of the LKB and highlight its role in mitigating leakage.

Received: 20 Mar 2025 – Discussion started: 03 Apr 2025

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Journal article(s) based on this preprint

25 Nov 2025

Evolution of low-karstified rock-blocks and their influence on reservoir leakage: a modelling perspective

Youjun Jiao, Qingchun Yu, Xusheng Wang, and Franci Gabrovšek

Hydrol. Earth Syst. Sci., 29, 6685–6702, https://doi.org/10.5194/hess-29-6685-2025,https://doi.org/10.5194/hess-29-6685-2025, 2025

Short summary

Youjun Jiao, Franci Gabrovšek, Xusheng Wang, and Qingchun Yu

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-1320', Anonymous Referee #1, 20 May 2025
This is a very interesting paper presenting a modeling approach aimed at showing how the coupling between dissolution, transport in fracture formations, and horizontal head forms a low-karstified rock-blocks which prevent water seepage, up to a threshold of head difference between reservoirs. I very much like the approach, the results, and the layout of the article, and I can see how it will be well suited to HESS. However, three aspects require attention in this study:
The authors heavily rely on jargon and assume that specific terms and mechanisms are known to the reader. This limits the impact of this study as it targets a narrow readership while overlooking HESS's broad readership. I outlined a few examples and ways to rectify this aspect in the detailed review below.

This work lacks some crucial aspects of the model. This complex model involves multiple processes over extended spatial and temporal scales, yet fundamental elements of this model are absent. What is the grid size and layout, and what is its sensitivity? Was there a convergence test for it? Was the model's sensitivity to key parameters assessed? The authors mention the stability of the solution but provide no data on it. The modeling aspect requires more than just the equations used and their sequence; a clear section in the paper or an appendix should present these essential components of the model.

The authors take an engineering approach to the results of their model, which is noteworthy as they draw a specific and tangible conclusion from it. However, the coupling between the transport and reactive mechanisms is a fundamental nucleation phenomenon, where the boundaries lead to an anisotropic, directional change. This phenomenon is observed in other experimental and numerical dissolution processes, where fingers or preferential flows emerge by this coupling (partial list: (Detwiler & Rajaram, 2007; Dijk et al., 2002; Edery et al., 2021; Kang et al., 2003; Molins et al., 2014; Nogues et al., 2013; Rege & Fogler, 1989; Shavelzon & Edery, 2022; Singurindy & Berkowitz, 2003)). Yet this is not referred to in this work, limiting its potential to draw a more general audience and a more general conclusion. These three aspects are echoed in the specific comments below, and I believe that while the last aspect may improve the paper, the first two are essential. Specific comments are outlined as follows:

Introduction: The authors make an excellent case supporting their approach in the introduction, yet it will be beneficial to relate each aspect that is either added or missing in previous studies to the figure 1 illustration, thus providing a conceptual picture of the processes at hand.

Line 22: “One of the primary issues is the intensification of the natural karstification process due to artificial hydraulic gradients, which can result in persistent and uncontrollable leakage throughout the structure's lifespan”
This sentence exemplifies the narrow focus of the paper. In the second sentence of the introduction, we encounter jargon that is not properly explained. We have no idea what the artificial part is in these hydraulic gradients and why it leads to “persistent and uncontrollable leakage.” I suspect that not all potential readers remember exactly what the “karstification process” is. HESS aims at a broad readership; therefore, an effort should be made to address this broad readership by thoroughly explaining the terms and concepts.
Introducing Figure 1 earlier and including additional features, such as the permeability linked to fracture aperture changes and the chemical gradients that shape the LKB zone, can help rectify this. The latter will significantly aid in clarifying the cause-and-effect relationship that the authors seek to establish in their work. This approach will give readers a conceptual framework from the outset and elucidate the terms and concepts of the study.

Line 69: Explain what epikarst is.
Line 71: Not sure “aggressive” is clear in this context.
Line 87: Explain what “speleogenesis” is.
Line 95: add a space after “(4)”

While the criteria for transitioning between equations 1 and 2 are clear, the actual continuous transition between equations 1 and 2 or vice versa is not clear. How do we continuously transition from the laminar to the turbulent approximation without discontinuities in the flux? The flux mass balance presented in Eq. 4 should also be addressed in this context.
Addendum: at the end of the paper, we learn that equation 2 was not used throughout the simulations (or so I understood from the following sentence: “Turbulent flow did not occur throughout the simulations initiated with natural, original fractures.”). If that is the case, why present it?

Line 121: Is Figure 2 an illustration, actual layout, or sub-layout of the fractured domain? Also, the dimensions are critical in understanding the model framework (Reynolds number, head differences, etc.). Referring to boundary, seepage, and head without their dimensions seems inadequate.

Section 2.2.2: Please refer to Figure 2 when explaining the necessary steps in finding the water table.

Section 2.3: The “H₂O-CO₂-CaCO₃” system is heavily influenced by pH. Although the CO₂ concentration can provide an approximation, this is only valid within a limited range of pH values. Please address this aspect.
Furthermore, a convective approach for the laminar case must approximate the reactant depletion as it reaches the fracture surface by some rate law. Since eq. 9-11 do not consider the fracture thickness b_{ij} while the illustration in figure 3 does, I am a bit confused about this matter. Please provide clarity on this aspect.

Line 182: Is the mass removal term converted to a volume change from which the b_{ij} is updated? If so, what is the conversion constant from moles to volume?

Line 204: Correct grammar in “These analyses”

Figure 4: While we agree on the analytical solution deviation, the magnitude of the deviation between the numerical value and the analytical solution is around 50%, which necessitates further elaboration on why it is so large.

Section 2.4.2: It’s hard to understand how well the model performs since we do not have any specific case to compare it to, aside from the analytical solution, which we established as inadequate. How can we be sure that the model works as it should? In terms of numerical analysis, there is no mention of grid size sensitivity, convergence, or stability of the numerical code, which are standard practices. The authors should present these aspects of the code so that we can appreciate it accordingly.

Line 218: “on the both sides” should be “on both sides”

Line 219: “…the algorithm performed well in modeling the water table in heterogeneous network.” Well, compared to what? These statements appear throughout the paper, yet they are not supported by any comparison or measurement that helps us understand what “well” means. The only reference is to the ill-fitted analytical solution.

Table 1: What are the dimensions of the directional term? Angle?
Additionally, the mean length of the fractures is quite large. Is this realistic? Why was this length chosen? It appears that ten well-connected fractures may dominate the simulation.

Line 252: Please clarify the term “evolution time step.”

Line 255, figure 8 caption: What does “ka” stand for? I’m assuming it refers to time, but no dimensions have been provided. This should be clarified in Figure 8, not Figure 10. Additionally, the heat map for the aperture could be confused with the head heat map. It is unclear whether it is necessary.

Section 3.3: In this section, the authors relate the change in aperture to the location of the aquifer, as evident in Figure 11, and also relate the change in flux in a similar manner. However, the cause and effect suggest that the higher potential near the boundaries dictates higher fluxes, and as the flux increases, so does the reaction rate, which widens the aperture. This is a nucleation phenomenon observed in many studies on dissolution, specifically in the context of permeable structures.

Line 295: I find the K calculation very interesting. To begin with, the fact that there is only dissolution in this setup means that the LKB is a “residual” permeability, indicating that while some permeabilities have increased, the LKB remained unchanged. However, the K is calculated directly for a subsection, and figure 12, as well as a close examination of figure 8, shows that there is an anisotropic change in the aperture, where horizontal fractures experience more dissolution than the vertical fractures. This also leads to the formation of the LKB and the observed changes in flux. However, this structural anisotropy is not discussed or quantified in this context, although it is clear that the horizontal head difference drives the anisotropy. This emergence of anisotropy can be found in many studies on rock dissolution, where preferential flows arise due to these boundary conditions coupled with reactive transport. As this emergent behavior appears in similar fields, the connection should be made among them.

Detwiler, L. R., & Rajaram, H. (2007). Predicting dissolution patterns in variable aperture fractures: Evaluation of an enhanced depth-averaged computational model. Water Resour. Res., 43, W04403, doi:10.1029/2006WR005147.
Dijk, P. E., Berkowitz, B., & Yechieli, Y. (2002). Measurement and analysis of dissolution patterns in rock fractures. Water Resour. Res., 38, doi:10.1029/2001WR000246.
Edery, Y., Stolar, M., Porta, G., & Guadagnini, A. (2021). Feedback mechanisms between precipitation and dissolution reactions across randomly heterogeneous conductivity fields. Hydrology and Earth System Sciences Discussions, 1–14.
Kang, Q., Zhang, D., & Chen, S. (2003). Simulation of dissolution and precipitation in porous media. Journal of Geophysical Research: Solid Earth, 108(B10).
Molins, S., Trebotich, D., Yang, L., Ajo-Franklin, J. B., Ligocki, T. J., Shen, C., & Steefel, C. I. (2014). Pore-scale controls on calcite dissolution rates from flow-through laboratory and numerical experiments. Environmental Science & Technology, 48(13), 7453–7460.
Nogues, J. P., Fitts, J. P., Celia, M. A., & Peters, C. A. (2013). Permeability evolution due to dissolution and precipitation of carbonates using reactive transport modeling in pore networks. Water Resources Research, 49(9), 6006–6021.
Rege, S. D., & Fogler, H. S. (1989). Competition among flow, dissolution, and precipitation in porous media. Am. In. Chem. Eng., 35(7), 1177� – 1185.
Shavelzon, E., & Edery, Y. (2022). Modeling of Reactive Transport in Porous Rock: Influence of Peclet Number, EGU22-8059. https://doi.org/10.5194/egusphere-egu22-8059
Singurindy, O., & Berkowitz, B. (2003). Evolution of hydraulic conductivity by precipitation and dissolution in carbonate rock. Water Resour. Res., 39(1), W1016, doi:10.1029/2001WR001055.
Citation: https://doi.org/10.5194/egusphere-2025-1320-RC1
- AC1: 'Reply on RC1', Youjun Jiao, 02 Jul 2025
  
  We sincerely appreciate your thorough and thoughtful review. Many of the comments and suggestions required careful consideration and prompted substantial revisions to the manuscript. With your help we have managed to resolve several inconsistencies in the manuscript and clear out many critical points, which hindered readability. We have made every effort to address all remarks. We hope you will recognize the extent of our efforts and find our responses satisfactory. Please find all replies in attached supplement.
  
  Thank you very much again for your review.
  
  The Authors
  
  Citation: https://doi.org/10.5194/egusphere-2025-1320-AC1
RC2:
'Comment on egusphere-2025-1320', Anonymous Referee #2, 26 May 2025

The authors present an interesting methodology to model karst evolution due to flow, transport and the dissolution within a fracture network, below a fluctuating water table. Although the approach is mainly presented within a limited context of dams and reservoirs, such modeling approach could be useful in a much wider context as well. I think the paper could be a valuable contribution to the journal, it is well written and easy to follow.
I have a few recommendations that would improve the text:
General comments:

- While the individual steps of the modeling are mostly well presented, I would find useful to have an overview of the whole modeling process. In my opinion a flowchart would greatly help the methodology section.

One thing I found confusing is the mixing of terms inner-outer iterations, steps - it was difficult to follow which steps happen within a single timestep etc. Using a flowchart could easily alleviate this issue, and would give a good entry point to the modelling process.
- How would you validate such modeling approach? Do you see a potential to compare the results with field measurements? Or did you consider validating the individual modelled processes against other modeling approaches?

I think such validation would be an important step for presenting such new methodology.

It would also be interesting to see, how the modeling results compare against other methods (such as equivalent porous media, or a static DFN model).
- In general, I think there are too many figures in the manuscript, and many of them could be moved to the supplements. Fewer figures with less information, would better highlight the interesting results from the modeling.
Specific comments:

L30: The concept of LKB is very important for this paper, but this explanation is too short for it. Please explain it better.
L35: "The patter of groundwater flow in water divide areas also suggest the possibility of an LKB in karst aquifer." - why?
L50 onwards: this is a very good motivation for the paper
L90: all these steps happen within one timestep>
L128: Does this mean you are aiming for a steady state within the iterations?
L147: what does middle iterations mean?
L149: a flowchart would be great here
L150: What does layer-by-layer mean here? This part in general is quite confusing
L188: What does homogeneous mean here? Are you verifying against an equivalent porous media model?
L213: More details about the high-performance platform is needed (CPU type)
L227: This section is unclear to me. Are we talking about in the dam or somewhere else? What is a karst reservoir in this context?
L235: This is a very good case study site for the approach.
Table 1: How did you choose the parameters?
L251: How did you choose the simulation length?
Figure 9: These plots a bit confusing, can you rotate them so the x-y plane is vertical?
L272: "The water table..." - This sentence is unclear
Fig. 10-11-12: I see a lot of redundancy in these figures, are they all important? Consider moving some of them to the supplements.
L347: "Considering..." - elaborate this statement more

Where do you see here the link between the model and the real case? How could the model be used in this specific setting?
L366: this section title is unclear to me.

Citation: https://doi.org/10.5194/egusphere-2025-1320-RC2
- AC2: 'Reply on RC2', Youjun Jiao, 02 Jul 2025
  
  We sincerely appreciate your thorough and thoughtful review. Many of the comments and suggestions required careful consideration and prompted substantial revisions to the manuscript. With your help we have managed to resolve several inconsistencies in the manuscript and clear out many critical points, which hindered readability. We have made every effort to address all remarks. We hope you will recognize the extent of our efforts and find our responses satisfactory. Please find all replies in attached supplement.
  
  Thank you very much again for your review.
  
  The Authors
  
  Citation: https://doi.org/10.5194/egusphere-2025-1320-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-1320', Anonymous Referee #1, 20 May 2025
This is a very interesting paper presenting a modeling approach aimed at showing how the coupling between dissolution, transport in fracture formations, and horizontal head forms a low-karstified rock-blocks which prevent water seepage, up to a threshold of head difference between reservoirs. I very much like the approach, the results, and the layout of the article, and I can see how it will be well suited to HESS. However, three aspects require attention in this study:
The authors heavily rely on jargon and assume that specific terms and mechanisms are known to the reader. This limits the impact of this study as it targets a narrow readership while overlooking HESS's broad readership. I outlined a few examples and ways to rectify this aspect in the detailed review below.

This work lacks some crucial aspects of the model. This complex model involves multiple processes over extended spatial and temporal scales, yet fundamental elements of this model are absent. What is the grid size and layout, and what is its sensitivity? Was there a convergence test for it? Was the model's sensitivity to key parameters assessed? The authors mention the stability of the solution but provide no data on it. The modeling aspect requires more than just the equations used and their sequence; a clear section in the paper or an appendix should present these essential components of the model.

The authors take an engineering approach to the results of their model, which is noteworthy as they draw a specific and tangible conclusion from it. However, the coupling between the transport and reactive mechanisms is a fundamental nucleation phenomenon, where the boundaries lead to an anisotropic, directional change. This phenomenon is observed in other experimental and numerical dissolution processes, where fingers or preferential flows emerge by this coupling (partial list: (Detwiler & Rajaram, 2007; Dijk et al., 2002; Edery et al., 2021; Kang et al., 2003; Molins et al., 2014; Nogues et al., 2013; Rege & Fogler, 1989; Shavelzon & Edery, 2022; Singurindy & Berkowitz, 2003)). Yet this is not referred to in this work, limiting its potential to draw a more general audience and a more general conclusion. These three aspects are echoed in the specific comments below, and I believe that while the last aspect may improve the paper, the first two are essential. Specific comments are outlined as follows:

Introduction: The authors make an excellent case supporting their approach in the introduction, yet it will be beneficial to relate each aspect that is either added or missing in previous studies to the figure 1 illustration, thus providing a conceptual picture of the processes at hand.

Line 22: “One of the primary issues is the intensification of the natural karstification process due to artificial hydraulic gradients, which can result in persistent and uncontrollable leakage throughout the structure's lifespan”
This sentence exemplifies the narrow focus of the paper. In the second sentence of the introduction, we encounter jargon that is not properly explained. We have no idea what the artificial part is in these hydraulic gradients and why it leads to “persistent and uncontrollable leakage.” I suspect that not all potential readers remember exactly what the “karstification process” is. HESS aims at a broad readership; therefore, an effort should be made to address this broad readership by thoroughly explaining the terms and concepts.
Introducing Figure 1 earlier and including additional features, such as the permeability linked to fracture aperture changes and the chemical gradients that shape the LKB zone, can help rectify this. The latter will significantly aid in clarifying the cause-and-effect relationship that the authors seek to establish in their work. This approach will give readers a conceptual framework from the outset and elucidate the terms and concepts of the study.

Line 69: Explain what epikarst is.
Line 71: Not sure “aggressive” is clear in this context.
Line 87: Explain what “speleogenesis” is.
Line 95: add a space after “(4)”

While the criteria for transitioning between equations 1 and 2 are clear, the actual continuous transition between equations 1 and 2 or vice versa is not clear. How do we continuously transition from the laminar to the turbulent approximation without discontinuities in the flux? The flux mass balance presented in Eq. 4 should also be addressed in this context.
Addendum: at the end of the paper, we learn that equation 2 was not used throughout the simulations (or so I understood from the following sentence: “Turbulent flow did not occur throughout the simulations initiated with natural, original fractures.”). If that is the case, why present it?

Line 121: Is Figure 2 an illustration, actual layout, or sub-layout of the fractured domain? Also, the dimensions are critical in understanding the model framework (Reynolds number, head differences, etc.). Referring to boundary, seepage, and head without their dimensions seems inadequate.

Section 2.2.2: Please refer to Figure 2 when explaining the necessary steps in finding the water table.

Section 2.3: The “H₂O-CO₂-CaCO₃” system is heavily influenced by pH. Although the CO₂ concentration can provide an approximation, this is only valid within a limited range of pH values. Please address this aspect.
Furthermore, a convective approach for the laminar case must approximate the reactant depletion as it reaches the fracture surface by some rate law. Since eq. 9-11 do not consider the fracture thickness b_{ij} while the illustration in figure 3 does, I am a bit confused about this matter. Please provide clarity on this aspect.

Line 182: Is the mass removal term converted to a volume change from which the b_{ij} is updated? If so, what is the conversion constant from moles to volume?

Line 204: Correct grammar in “These analyses”

Figure 4: While we agree on the analytical solution deviation, the magnitude of the deviation between the numerical value and the analytical solution is around 50%, which necessitates further elaboration on why it is so large.

Section 2.4.2: It’s hard to understand how well the model performs since we do not have any specific case to compare it to, aside from the analytical solution, which we established as inadequate. How can we be sure that the model works as it should? In terms of numerical analysis, there is no mention of grid size sensitivity, convergence, or stability of the numerical code, which are standard practices. The authors should present these aspects of the code so that we can appreciate it accordingly.

Line 218: “on the both sides” should be “on both sides”

Line 219: “…the algorithm performed well in modeling the water table in heterogeneous network.” Well, compared to what? These statements appear throughout the paper, yet they are not supported by any comparison or measurement that helps us understand what “well” means. The only reference is to the ill-fitted analytical solution.

Table 1: What are the dimensions of the directional term? Angle?
Additionally, the mean length of the fractures is quite large. Is this realistic? Why was this length chosen? It appears that ten well-connected fractures may dominate the simulation.

Line 252: Please clarify the term “evolution time step.”

Line 255, figure 8 caption: What does “ka” stand for? I’m assuming it refers to time, but no dimensions have been provided. This should be clarified in Figure 8, not Figure 10. Additionally, the heat map for the aperture could be confused with the head heat map. It is unclear whether it is necessary.

Section 3.3: In this section, the authors relate the change in aperture to the location of the aquifer, as evident in Figure 11, and also relate the change in flux in a similar manner. However, the cause and effect suggest that the higher potential near the boundaries dictates higher fluxes, and as the flux increases, so does the reaction rate, which widens the aperture. This is a nucleation phenomenon observed in many studies on dissolution, specifically in the context of permeable structures.

Line 295: I find the K calculation very interesting. To begin with, the fact that there is only dissolution in this setup means that the LKB is a “residual” permeability, indicating that while some permeabilities have increased, the LKB remained unchanged. However, the K is calculated directly for a subsection, and figure 12, as well as a close examination of figure 8, shows that there is an anisotropic change in the aperture, where horizontal fractures experience more dissolution than the vertical fractures. This also leads to the formation of the LKB and the observed changes in flux. However, this structural anisotropy is not discussed or quantified in this context, although it is clear that the horizontal head difference drives the anisotropy. This emergence of anisotropy can be found in many studies on rock dissolution, where preferential flows arise due to these boundary conditions coupled with reactive transport. As this emergent behavior appears in similar fields, the connection should be made among them.

Detwiler, L. R., & Rajaram, H. (2007). Predicting dissolution patterns in variable aperture fractures: Evaluation of an enhanced depth-averaged computational model. Water Resour. Res., 43, W04403, doi:10.1029/2006WR005147.
Dijk, P. E., Berkowitz, B., & Yechieli, Y. (2002). Measurement and analysis of dissolution patterns in rock fractures. Water Resour. Res., 38, doi:10.1029/2001WR000246.
Edery, Y., Stolar, M., Porta, G., & Guadagnini, A. (2021). Feedback mechanisms between precipitation and dissolution reactions across randomly heterogeneous conductivity fields. Hydrology and Earth System Sciences Discussions, 1–14.
Kang, Q., Zhang, D., & Chen, S. (2003). Simulation of dissolution and precipitation in porous media. Journal of Geophysical Research: Solid Earth, 108(B10).
Molins, S., Trebotich, D., Yang, L., Ajo-Franklin, J. B., Ligocki, T. J., Shen, C., & Steefel, C. I. (2014). Pore-scale controls on calcite dissolution rates from flow-through laboratory and numerical experiments. Environmental Science & Technology, 48(13), 7453–7460.
Nogues, J. P., Fitts, J. P., Celia, M. A., & Peters, C. A. (2013). Permeability evolution due to dissolution and precipitation of carbonates using reactive transport modeling in pore networks. Water Resources Research, 49(9), 6006–6021.
Rege, S. D., & Fogler, H. S. (1989). Competition among flow, dissolution, and precipitation in porous media. Am. In. Chem. Eng., 35(7), 1177� – 1185.
Shavelzon, E., & Edery, Y. (2022). Modeling of Reactive Transport in Porous Rock: Influence of Peclet Number, EGU22-8059. https://doi.org/10.5194/egusphere-egu22-8059
Singurindy, O., & Berkowitz, B. (2003). Evolution of hydraulic conductivity by precipitation and dissolution in carbonate rock. Water Resour. Res., 39(1), W1016, doi:10.1029/2001WR001055.
Citation: https://doi.org/10.5194/egusphere-2025-1320-RC1
- AC1: 'Reply on RC1', Youjun Jiao, 02 Jul 2025
  
  We sincerely appreciate your thorough and thoughtful review. Many of the comments and suggestions required careful consideration and prompted substantial revisions to the manuscript. With your help we have managed to resolve several inconsistencies in the manuscript and clear out many critical points, which hindered readability. We have made every effort to address all remarks. We hope you will recognize the extent of our efforts and find our responses satisfactory. Please find all replies in attached supplement.
  
  Thank you very much again for your review.
  
  The Authors
  
  Citation: https://doi.org/10.5194/egusphere-2025-1320-AC1
RC2:
'Comment on egusphere-2025-1320', Anonymous Referee #2, 26 May 2025

The authors present an interesting methodology to model karst evolution due to flow, transport and the dissolution within a fracture network, below a fluctuating water table. Although the approach is mainly presented within a limited context of dams and reservoirs, such modeling approach could be useful in a much wider context as well. I think the paper could be a valuable contribution to the journal, it is well written and easy to follow.
I have a few recommendations that would improve the text:
General comments:

- While the individual steps of the modeling are mostly well presented, I would find useful to have an overview of the whole modeling process. In my opinion a flowchart would greatly help the methodology section.

One thing I found confusing is the mixing of terms inner-outer iterations, steps - it was difficult to follow which steps happen within a single timestep etc. Using a flowchart could easily alleviate this issue, and would give a good entry point to the modelling process.
- How would you validate such modeling approach? Do you see a potential to compare the results with field measurements? Or did you consider validating the individual modelled processes against other modeling approaches?

I think such validation would be an important step for presenting such new methodology.

It would also be interesting to see, how the modeling results compare against other methods (such as equivalent porous media, or a static DFN model).
- In general, I think there are too many figures in the manuscript, and many of them could be moved to the supplements. Fewer figures with less information, would better highlight the interesting results from the modeling.
Specific comments:

L30: The concept of LKB is very important for this paper, but this explanation is too short for it. Please explain it better.
L35: "The patter of groundwater flow in water divide areas also suggest the possibility of an LKB in karst aquifer." - why?
L50 onwards: this is a very good motivation for the paper
L90: all these steps happen within one timestep>
L128: Does this mean you are aiming for a steady state within the iterations?
L147: what does middle iterations mean?
L149: a flowchart would be great here
L150: What does layer-by-layer mean here? This part in general is quite confusing
L188: What does homogeneous mean here? Are you verifying against an equivalent porous media model?
L213: More details about the high-performance platform is needed (CPU type)
L227: This section is unclear to me. Are we talking about in the dam or somewhere else? What is a karst reservoir in this context?
L235: This is a very good case study site for the approach.
Table 1: How did you choose the parameters?
L251: How did you choose the simulation length?
Figure 9: These plots a bit confusing, can you rotate them so the x-y plane is vertical?
L272: "The water table..." - This sentence is unclear
Fig. 10-11-12: I see a lot of redundancy in these figures, are they all important? Consider moving some of them to the supplements.
L347: "Considering..." - elaborate this statement more

Where do you see here the link between the model and the real case? How could the model be used in this specific setting?
L366: this section title is unclear to me.

Citation: https://doi.org/10.5194/egusphere-2025-1320-RC2
- AC2: 'Reply on RC2', Youjun Jiao, 02 Jul 2025
  
  We sincerely appreciate your thorough and thoughtful review. Many of the comments and suggestions required careful consideration and prompted substantial revisions to the manuscript. With your help we have managed to resolve several inconsistencies in the manuscript and clear out many critical points, which hindered readability. We have made every effort to address all remarks. We hope you will recognize the extent of our efforts and find our responses satisfactory. Please find all replies in attached supplement.
  
  Thank you very much again for your review.
  
  The Authors
  
  Citation: https://doi.org/10.5194/egusphere-2025-1320-AC2

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

ED: Reconsider after major revisions (further review by editor and referees) (02 Jul 2025) by Heng Dai

AR by Youjun Jiao on behalf of the Authors (16 Jul 2025) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (18 Jul 2025) by Heng Dai

RR by Anonymous Referee #1 (25 Jul 2025)

Suggestions for revision or reasons for rejection

The authors have made significant revisions to the paper, and the new version is significantly better; however, I still feel that several comments were not fully addressed. Although there is a “good agreement” between MODFLOW and the authors’ solver, details are needed regarding the grid size sensitivity, convergence, and stability of the numerical code, as these are standard practices. That is why the added S1 does not address my comment. Stating that “We also explored the model's behavior under different flow regimes by simulating the coexistence of turbulent and laminar flows” is not sufficient; one should show the outcome of this exploration in a quantitative way, how many iterations were required to solve the flow equation? How well did they reproduce the benchmark of MODFLOW?, etc.,
In the same sense, stating that this is just one realization out of many other possibilities in response to my comment on the relatively high fracture length does not really address my comment. Every realization is one out of many possibilities, which is what makes it a realization from a statistical standpoint. That is why we aim to simulate a “representative case” and justify why it is representative, which was my request. Otherwise, we deal with a toy model intended to outline a process rather than reproduce it. This is even more important when the fracture lengths clearly dominate the whole regime, in a way that may suggest that the results presented are not representative. This should be further clarified.
I believe that the Yes /No aspect is missing in the “No nodes wet?” part of the chart.
“This approximation is valid for situations where the solutions are close to equilibrium, which is mostly the case in the presented scenarios”. Can you provide a reference to this approximation?
Figure 7. It seems that the heat map range does not cover the entire range (the red color is missing from the heat map).

After addressing these revisions, the paper will be ready for publication.

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RR by Anonymous Referee #2 (23 Sep 2025)

Suggestions for revision or reasons for rejection

The authors have sufficiently address my comments and I think the manuscript improved significantly. I only have a few minor comments regarding some of the modifications.

Please check carefully the language and style of the revised new sections, as they are often read very differently compared to the original parts, and break the flow of the text.

Figure 1. - caption is a bit unclear: what do you mean here by flow solution? In b) and c) you talk about processes but here about modeling? Please clarify this.

Figure 2 - The flowchart really helps with the understanding with the methodology. It was a great idea to link the flowchart elements to the different sections, but then do it for section 2.1 as well.
The text in the figure could be a bit reduced in size. I would also recommend a more figure figure friendly font (e.g. Arial - see the new flowchart in the supplements (Fig. R2) which reads a bit nicer due to this)

section 2.2.1 - Don't forget the reference to the new supplementary figure (R2) and the inclusion of the figure to the supplements.

Section 2.4 I would reduce this part significantly, because it currently reads a bit strange. Also, because this only refers to the flow solution it could be just added to the end of section 2.2.2 - because here it is confusing as a verification to the karstification too.
A shorter version could be:
"The numerical model was verified successfully against a MODFLOW model and an analytical model using the Dupuit assumption. Please see the Supplements for details."

L394: Do you mean that different possible initial aquifer structures can be tested out using the numerical model, to see their impacts later? If so you may use the approach for scenario analysis or even assessing the uncertainties in karst evolution.

L402: "These low karstified..." - this sentence really stands out from here, I think you can delete it (too introductory to the end of the paper and also breaks the linkage between the sentences before and after)

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ED: Publish subject to minor revisions (review by editor) (11 Oct 2025) by Heng Dai

AR by Youjun Jiao on behalf of the Authors (20 Oct 2025) Author's response Author's tracked changes Manuscript

ED: Publish as is (22 Oct 2025) by Heng Dai

AR by Youjun Jiao on behalf of the Authors (28 Oct 2025)

Journal article(s) based on this preprint

25 Nov 2025

Evolution of low-karstified rock-blocks and their influence on reservoir leakage: a modelling perspective

Youjun Jiao, Qingchun Yu, Xusheng Wang, and Franci Gabrovšek

Hydrol. Earth Syst. Sci., 29, 6685–6702, https://doi.org/10.5194/hess-29-6685-2025,https://doi.org/10.5194/hess-29-6685-2025, 2025

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Youjun Jiao, Franci Gabrovšek, Xusheng Wang, and Qingchun Yu

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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.

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Dams and reservoirs in karst areas often struggle with significant leakage, making construction both challenging and costly. This study uses a numerical model to show how karst aquifers in water divide regions evolve to form low-karstified rock-blocks (LKB). It also explores how and when these LKBs can significantly reduce leakage across the water divides if a reservoir is built on one side.


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