The authors would like to warmly thank the reviewer for the time dedicated for reading and commenting the proposed manuscript with the aim of improving it. It is clear reading these comments that the reviewer has a strong expertise in this field.

All the comments made have been thoroughly considered and a response to each is provided in the following.

The authors would like to remind that the presented research focus on lab experiments of a realistic type of debris flows (in terms of material and Froude number) when compared to torrents encountered in the European Alps or similar settings (volume of several thousand of m3, intense rainfalls related to thunderstorms but not as intense as under typhoons, very high sediment concentration, i.e. 50-80%). Other types of debris flows exist elsewhere but we explained in our introduction the type of debris flow we restricted our study to. This type of flow has rarely been addressed in previously published research and, for this reason, current knowledge may not be relevant to real debris flows occurring in Alpine environments, in terms of flow-barrier interaction in particular. Because the type of flow considered in this research significantly differs from that in most of other studies, choice was made to keep minimum the number of references to other studies, and to refer to works from research teams all over the world.

C1. While there are numerous experimental and numerical studies on debris flows impacting flexible barriers, the specific research question addressed by this work is unclear. Please clarify the novelty of this study at the very beginning of the introduction.

R1. As mentioned in the introduction, the first novelty in this research lies in the fact that it focuses on the interaction of near critical debris flows (i.e. with F r = 0.9 – 2) with a flexible barrier while the vast majority of previous research addressed flows at much wider range of Froude numbers toward high values. Froude numbers lower than 2 are typically uncovered or just the lower end of a spectrum and covered only by a few simulations. This is clearly highlighted in the introduction. Addressing a wide range of Froude number is interesting but because it covers a wide range of regimes of impact but also consequently does not allow to comprehensively cover each regime. Here we focus on near critical debris flows. Another novelty relates to the use of a flexible barrier close to perfect mechanical similitude with the real scale. It is also important highlighting that, by contrast with previously published studies, this one considered a high solid fraction flow which contained a large amount of coarse material, as usually observed in nature. The novelty also lies in some of the main conclusions drawn from this work and in particular: (i) Four different interaction modes between the flow and the barrier are identified when the flow kinematic is varied, while two are generally considered based on studies at higher Froude numbers and (ii) the total force exerted on the barrier when all the released material is at rest is doubled in case barrier overflow occurred. All these points are mentioned in the abstract and/or the introduction. There is no doubt all this is novel and of great interest to academics and engineers.

C2. Page 12, Line 230: The two impact modes are crucial for theoretical work and engineering practice. It is recommended to include the following statement: "Kong et al. (2021, Engineering Geology, 289: 106188; 2022a, JGR Earth Surface 127(6): e2021JF006587) provide systematic investigations and a unique dataset on flow and flexible barrier behavior in pile-up and run-up modes and their transitions. This is highly relevant to this study and may offer valuable insights to readers."

R2: As mentioned in R1 and as detailed in the article, observations made during the experiments reveal that the flow-barrier interaction may follow four different modes. This conclusion specifically concerns this type of flowing material and this realistic range of Froude numbers, which both differ from that in previously published studies. See Line 281 where one can read “It also revealed it could hardly be described in a binary way as often done in the literature, where pile-up and run-up are proposed as the two processes by which an obstacle modifies the flow kinematics.” In addition, the detailed description of what was observed (i) do not allow asserting that ‘pile up’ occurred strictly speaking (in particular read the comments in Line256 and Line 265) and (ii) run-up was observed in one case only and it was considered as not representative as explained in the text (read Lines 269-277).  The two references of Kong et al. are relevant numerical studies and the first one was actually yet cited in our paper, Line 227.

C3. Page 13, Line 285: The authors identify critical Fr and energy thresholds for different impact modes. However, real-world scenarios are highly complex. To avoid misleading conclusions, consider adding: "Flow-flexible barrier interaction modes are too complex to be quantitatively distinguished by simple signatures. For example, Kong et al. (2021, Engineering Geology, 289: 106188; 2022a, JGR Earth Surface, 127(6): e2021JF006587; 2022b, JGR Earth Surface, 127(11): e2022JF006870; 2024, Géotechnique, 74(5): 486-498) reported that factors such as flow dynamics, solid fractions, flow types, barrier types, and geometry, including flow-barrier height ratios, significantly influence interaction modes and are key considerations in flexible barrier design. This is directly relevant to this study."

R3: We agree with the general statement made by the reviewer, but we believe that these elements are yet partially, explicitly or implicitly stated in the introduction. In addition, we do not claim that our findings are relevant to other situations (in terms of flowing material and Froude numbers), actually we suspect that these findings differ in relation with the increase of kinetic energy or the other parameters listed by the reviewer. Besides, it is definitely true that the flow-barrier interaction is extremely complex and depends on many parameters. To some extent, the differences between the results derived from this research and that from other studies emphasize this complexity! Nevertheless, the reviewer points on Section 3 which concerns the results presentation and where all comments made relate to the specific material and Froude number range we addressed. For this reason, the authors prefer not to include any reference to some specific works dealing with other cases in this Section.

C4. Page 18, Line 340: The author presents the 'force within the barrier Fw' in Figures 12 and 13, defined as the sum of forces in three cables at rest. Please clarify why this force is considered more critical than their peak values. If not, please provide the peak values. Additionally, it is expected that Fw would initially increase and then decrease with increasing inclination. The observed negative trend is likely due to the limited inclination range (11 to 15 degrees).

R4: Fw is the sum of the forces in the three cables when at rest. Indeed, it was not possible to give a precise value at peak, as explained from Line 167 “The force sensors were mainly used to determine the force at rest, after the material has stopped flowing. Indeed, obtaining a precise measurement of the force during the event was not possible due to some technical limitations with the system.”. Besides, we do not see any negative trend in figure 12 and 13 of Fw vs inclination.

C5. Equation for Fb: I could not locate the equation for Fb. Is it simply 3*Fs? Fb is crucial for designing flexible barriers, but this assumption is quite strong. Please provide more details. Kong et al. (2022b, JGR: Earth Surface, 127(11): e2022JF006870) conducted a comprehensive study on analytical models for estimating total impact loads on flexible barriers. They found that the ratio between peak impact load and static load (at rest) varies with barrier types, flow materials, and dynamics. For example, Kong (2022b) reported peak-static load ratios of approximately 4 for debris flows and 1.5 for rock avalanches at a pre-impact Fr of around 4. This ratio also changes with different flow materials and barrier types (Kong et al., 2021, Engineering Geology, 289: 106188; 2022a, JGR Earth Surface, 127(6): e2021JF006587). Including these insights could prevent misunderstandings.

R5: Please see the appendix for the computation, of Fb. This is mentioned from Line 365: “As detailed in Appendix A, the model used for computing the barrier loading assumed an uniform load distribution and considered both the circular and parabolic barrier deformation assumptions. These models were used to compute the total force exerted at rest on the barrier, Fb.”. Even though the comment by the reviewer is highly relevant and based on very nice research, the fact is that it is out of purpose here, as the mentioned ratio compares the residual force with the peak force, which is not computed here.

C6. Appendix A: Note that Kong et al. (2022b, JGR: Earth Surface, 127(11): e2022JF006870) reported that cable-based solutions might introduce significant errors in estimating total impact loads on flexible barriers. This finding is relevant to the analytical model discussed and may benefit readers.

R6: The reviewer suggests referring to an excellent article where the raised issue is mentioned in one of the conclusions. More precisely, this conclusion mentions that this problem mainly concerns fast impact dynamics while in the presented research, the analytical solutions are used for slow impact dynamics and focus on the load at rest, and not at peak. In spite of this, the reviewer is true: the analytical computation of the loading exerted on the barrier based on other measurements (deflection, force in the cables) relies on many assumptions which may biases the computed result. This is also demonstrated by the proposed manuscript where two assumptions as for the barrier shape are accounted for, resulting in a ratio of 1:2 in terms of loading exerted on the barrier. Because an appendix is expected to be concise to the point and it is generally not the place where comments are required a reference to this article will be made in section 3.3.3.

The authors would like to warmly thank the reviewer for the time dedicated for reading and commenting the proposed manuscript with the aim of improving it. It is clear reading these comments that the reviewer has a strong expertise in this field.

All the comments made have been thoroughly considered and a response to each is provided in the following.

The authors would like to remind that the presented research focus on lab experiments of a realistic type of debris flows (in terms of material and Froude number) when compared to torrents encountered in the European Alps or similar settings (volume of several thousand of m3, intense rainfalls related to thunderstorms but not as intense as under typhoons, very high sediment concentration, i.e. 50-80%). Other types of debris flows exist elsewhere but we explained in our introduction the type of debris flow we restricted our study to. This type of flow has rarely been addressed in previously published research and, for this reason, current knowledge may not be relevant to real debris flows occurring in Alpine environments, in terms of flow-barrier interaction in particular. Because the type of flow considered in this research significantly differs from that in most of other studies, choice was made to keep minimum the number of references to other studies, and to refer to works from research teams all over the world.

C1. While there are numerous experimental and numerical studies on debris flows impacting flexible barriers, the specific research question addressed by this work is unclear. Please clarify the novelty of this study at the very beginning of the introduction.

R1. As mentioned in the introduction, the first novelty in this research lies in the fact that it focuses on the interaction of near critical debris flows (i.e. with F r = 0.9 – 2) with a flexible barrier while the vast majority of previous research addressed flows at much wider range of Froude numbers toward high values. Froude numbers lower than 2 are typically uncovered or just the lower end of a spectrum and covered only by a few simulations. This is clearly highlighted in the introduction. Addressing a wide range of Froude number is interesting but because it covers a wide range of regimes of impact but also consequently does not allow to comprehensively cover each regime. Here we focus on near critical debris flows. Another novelty relates to the use of a flexible barrier close to perfect mechanical similitude with the real scale. It is also important highlighting that, by contrast with previously published studies, this one considered a high solid fraction flow which contained a large amount of coarse material, as usually observed in nature. The novelty also lies in some of the main conclusions drawn from this work and in particular: (i) Four different interaction modes between the flow and the barrier are identified when the flow kinematic is varied, while two are generally considered based on studies at higher Froude numbers and (ii) the total force exerted on the barrier when all the released material is at rest is doubled in case barrier overflow occurred. All these points are mentioned in the abstract and/or the introduction. There is no doubt all this is novel and of great interest to academics and engineers.

C2. Page 12, Line 230: The two impact modes are crucial for theoretical work and engineering practice. It is recommended to include the following statement: "Kong et al. (2021, Engineering Geology, 289: 106188; 2022a, JGR Earth Surface 127(6): e2021JF006587) provide systematic investigations and a unique dataset on flow and flexible barrier behavior in pile-up and run-up modes and their transitions. This is highly relevant to this study and may offer valuable insights to readers."

R2: As mentioned in R1 and as detailed in the article, observations made during the experiments reveal that the flow-barrier interaction may follow four different modes. This conclusion specifically concerns this type of flowing material and this realistic range of Froude numbers, which both differ from that in previously published studies. See Line 281 where one can read “It also revealed it could hardly be described in a binary way as often done in the literature, where pile-up and run-up are proposed as the two processes by which an obstacle modifies the flow kinematics.” In addition, the detailed description of what was observed (i) do not allow asserting that ‘pile up’ occurred strictly speaking (in particular read the comments in Line256 and Line 265) and (ii) run-up was observed in one case only and it was considered as not representative as explained in the text (read Lines 269-277).  The two references of Kong et al. are relevant numerical studies and the first one was actually yet cited in our paper, Line 227.

C3. Page 13, Line 285: The authors identify critical Fr and energy thresholds for different impact modes. However, real-world scenarios are highly complex. To avoid misleading conclusions, consider adding: "Flow-flexible barrier interaction modes are too complex to be quantitatively distinguished by simple signatures. For example, Kong et al. (2021, Engineering Geology, 289: 106188; 2022a, JGR Earth Surface, 127(6): e2021JF006587; 2022b, JGR Earth Surface, 127(11): e2022JF006870; 2024, Géotechnique, 74(5): 486-498) reported that factors such as flow dynamics, solid fractions, flow types, barrier types, and geometry, including flow-barrier height ratios, significantly influence interaction modes and are key considerations in flexible barrier design. This is directly relevant to this study."

R3: We agree with the general statement made by the reviewer, but we believe that these elements are yet partially, explicitly or implicitly stated in the introduction. In addition, we do not claim that our findings are relevant to other situations (in terms of flowing material and Froude numbers), actually we suspect that these findings differ in relation with the increase of kinetic energy or the other parameters listed by the reviewer. Besides, it is definitely true that the flow-barrier interaction is extremely complex and depends on many parameters. To some extent, the differences between the results derived from this research and that from other studies emphasize this complexity! Nevertheless, the reviewer points on Section 3 which concerns the results presentation and where all comments made relate to the specific material and Froude number range we addressed. For this reason, the authors prefer not to include any reference to some specific works dealing with other cases in this Section.

C4. Page 18, Line 340: The author presents the 'force within the barrier Fw' in Figures 12 and 13, defined as the sum of forces in three cables at rest. Please clarify why this force is considered more critical than their peak values. If not, please provide the peak values. Additionally, it is expected that Fw would initially increase and then decrease with increasing inclination. The observed negative trend is likely due to the limited inclination range (11 to 15 degrees).

R4: Fw is the sum of the forces in the three cables when at rest. Indeed, it was not possible to give a precise value at peak, as explained from Line 167 “The force sensors were mainly used to determine the force at rest, after the material has stopped flowing. Indeed, obtaining a precise measurement of the force during the event was not possible due to some technical limitations with the system.”. Besides, we do not see any negative trend in figure 12 and 13 of Fw vs inclination.

C5. Equation for Fb: I could not locate the equation for Fb. Is it simply 3*Fs? Fb is crucial for designing flexible barriers, but this assumption is quite strong. Please provide more details. Kong et al. (2022b, JGR: Earth Surface, 127(11): e2022JF006870) conducted a comprehensive study on analytical models for estimating total impact loads on flexible barriers. They found that the ratio between peak impact load and static load (at rest) varies with barrier types, flow materials, and dynamics. For example, Kong (2022b) reported peak-static load ratios of approximately 4 for debris flows and 1.5 for rock avalanches at a pre-impact Fr of around 4. This ratio also changes with different flow materials and barrier types (Kong et al., 2021, Engineering Geology, 289: 106188; 2022a, JGR Earth Surface, 127(6): e2021JF006587). Including these insights could prevent misunderstandings.

R5: Please see the appendix for the computation, of Fb. This is mentioned from Line 365: “As detailed in Appendix A, the model used for computing the barrier loading assumed an uniform load distribution and considered both the circular and parabolic barrier deformation assumptions. These models were used to compute the total force exerted at rest on the barrier, Fb.”. Even though the comment by the reviewer is highly relevant and based on very nice research, the fact is that it is out of purpose here, as the mentioned ratio compares the residual force with the peak force, which is not computed here.

C6. Appendix A: Note that Kong et al. (2022b, JGR: Earth Surface, 127(11): e2022JF006870) reported that cable-based solutions might introduce significant errors in estimating total impact loads on flexible barriers. This finding is relevant to the analytical model discussed and may benefit readers.

R6: The reviewer suggests referring to an excellent article where the raised issue is mentioned in one of the conclusions. More precisely, this conclusion mentions that this problem mainly concerns fast impact dynamics while in the presented research, the analytical solutions are used for slow impact dynamics and focus on the load at rest, and not at peak. In spite of this, the reviewer is true: the analytical computation of the loading exerted on the barrier based on other measurements (deflection, force in the cables) relies on many assumptions which may biases the computed result. This is also demonstrated by the proposed manuscript where two assumptions as for the barrier shape are accounted for, resulting in a ratio of 1:2 in terms of loading exerted on the barrier. Because an appendix is expected to be concise to the point and it is generally not the place where comments are required a reference to this article will be made in section 3.3.3.

RC2: This manuscript has addressed the interaction problem between debris flow and flexible barrier with a focus on the near-critical flow regimes. The physical experiments are well designed, and with the obtained data, the deformation and loading behaviors of flexible barrier are analyzed in detailed. I would recommend this manuscript after a proper revision. Several main comments are listed below.

1.The authors have emphasized the importunate of near-critical debris flows, but the main reason is that the most debris flows in nature fall into this flow regime but without enough investigations. I think this motivation cannot justify the contribution of the manuscript. There are quite many researches that try to establish impact models suitable for a wide range of Froude regimes. For such a reason, the authors are supposed to defend their contributions by declaring the fundamental differences between the near-critical and supercritical debris flow impact.

Reply: As explained at length in the paper from almost the beginning of the introduction to Line 63, it is true that this article doesn’t investigate the influence of the various impact regimes on the flow-barrier interaction and barrier maximum loading. Also, it doesn’t try to establish some laws suitable for a wide range of Froude numbers. Clearly, this is not the purpose here. This was the objective of many interesting papers that are already published and we do not intend to follow this research line.

As reviewed in the Introduction, it is a fact that there are much more articles dealing with flexible barriers exposed to high Froude numbers flows than that for near-critical debris flows. In particular, experimental data related to critical flows of materials containing a large amount of coarse and angular material mixed with fine and saturated materials are missing, while these types of flows are common in torrents encountered in the European Alps or similar settings (as clearly evidenced by the references provided lines 22-26).  There is clearly a need for a deeper investigation of the flow barrier interaction for low Froude numbers, in particular because there is a fundamental difference in impact loading between near-critical and supercritical flows as mentioned from line 55. Last, the conclusions from this study are original with respect to previous knowledge.

We hope it is acceptable not to follow exactly the line of research other teams explored and that we want to address more in detail a research gap (which is in addition closer from the reality of our steep creeks).

2.I didn’t understand why only the loading characteristics of the barrier after impact are considered in this manuscript. Now that the cable tension force has been measured, why not show the time-history data of impact force? I think at least for the Mode Ⅳ, peak force may not appear at the end of impact stage. This aspect should be better explained.

Reply: The reason for focusing on the situation at rest, and not addressing that at peak is given in the text, Line 168 where one can read “obtaining a precise measurement of the force during the event was not possible due to some technical limitations with the system.” In fact, after the test campaign we conducted a detailed analysis and concluded that there was a limitation with the acquisition system the authors were not able to correct and which made the peak value not reliable enough for being published. This also explains why no curve showing the evolution of force with time are presented. This is indeed a bit frustrating and the authors regret it as well. Nevertheless, the loading at rest, after the event, has been rarely addressed up to now. Focusing on this makes sense, in particular in the case where debris flows consist of successive surges. In such cases, the total load accounts for a dynamic component associated with the subsequent surge and a static loading, associated with the material intercepted during the previous surge. Also, design practices generally consider that, during the progressive filling by a single surge, the loading is also the sum of dynamic and a static component. So, it clearly makes sense focusing on the static loading. And, in the end, the conclusions drawn from these experiments appear to be of interest for design engineers as for the static component evaluation.

3.It is questionable that whether the barrier model could represent the dynamic responses of prototype flexible barriers. At least, without the energy dissipators the deformation of flexible barriers has been fundamentally changed. Because the loading and deformation response of barrier are the main points of this manuscript, it is necessary to explain this discrepancy.

Reply: This comment is relevant and it holds too for all the small-scale experiments conducted up-to-now on flexible barriers (among which some served as basis for proposing design guidelines). Indeed, we are not aware of existing experiments using rigorously downscaled energy dissipators, cables and nets. To the best of our knowledge, we are presenting here the first small scale experiments with cables and net being designed accounting for mechanical similitude with actual steel material. 

Meanwhile, we perfectly agree with Reviewer #2 that energy dissipators have a very strong influence on the barrier response and result in a higher barrier deformation, with consequence on the flow-barrier interaction, as well as on the force within the barrier (one of the authors worked on this one decade ago – see Albaba et al, 2015, Doi/10.1007/s10035-015-0579-8). The point is that energy dissipators have a threshold resistance and influence the barrier deformation only above this threshold force. Their function is in essence to distribute the force within the barrier to safeguard an anchor.

Not integrating energy dissipators was deliberate choice with two main reasons: (i) to measure as accurately as possible the actual force in the cables, i.e. before the energy dissipators would be triggered, and (ii) because of the complexity of designing, manufacturing and installing a downscaled equivalent of an energy dissipator. At the small-scale, manufacturing downscaled cables and net was a challenge that we were the first to address (none existing references did it). We acknowledge that we did not downscaled the energy dissipators, that is beyond the scope of the paper but it is not an issue to produce the analysis we wanted to perform. In the end, this constitutes a limitation with respect to prototype barriers equipped with energy dissipators but it enables to perform more accurate measurements of the forces. The absence of energy dissipators will be reminded in the Material and Methods as well as in the Conclusion.

4.The proposed impact model would be quite site-specific, e.g., the Illgraben torrent (Switzerland), because only the data of near-critical debris flows is included. It would be more interesting and useful to develop a more unified load model by incorporating the data cross a wide range of Froude regimes.

Reply: We disagree with this statement as explained in the Introduction where the working context is clearly defined. We rather believe that experimenters and numerical modelers, insufficiently aware of field reality, cautiously explored wide ranges of Froude numbers. Field monitoring data are however now more and more numerous and it seems crucial that experiments and simulations sometime try to focus on field reality. As explained in the Introduction, almost all of field measurements are consistent with Froude numbers in the range 0.5 – 2; a few peculiar creeks experience faster debris flows with Fr up to 3 or 4 and a couple of references describe single events in specific locations that were faster. Meanwhile, many recent papers focus on the upper range, typically Fr = 3 – 10. This study focuses on a certain range of Froude numbers as this was less addressed up to now. The aim was not to cover a wide range and propose a unified model, but rather to describe in detail what is observed for this specific range. This type of flow corresponds rather well to that presented in various footages available on the internet or shared via some professional social media and showing natural debris flows that occurred in the Alps and in different places in the world. 

5.The flexible barrier is open-type with the net allowing the pass of debris flow materials. But this part has not been discussed. I think it is also important for loading response of barrier in addition to the overflow process.

Reply: The considered barrier is similar to that used in torrents. Nevertheless, it is true that there exist different types of flexible barriers, including barriers with basal clearance, etc. And, of course, the barrier design has an influence on the loading response.  In our case, the large grains had a dimension larger than the mesh size, to increase the ratio of intercepted material and let fluid through, which is a common practice. We focused on a specific barrier type and the results we present concern this barrier type only and we do not claim the conclusions are valid for all types of barriers.

6.Some minor comments also are provided for reference: 1) the details about the used cameras, e.g., the frame rate and resolution; 2) the strength similarity design of model barrier; 3) the figure quality; 4) the specific value of the solid fraction of the modelled debris flows.

Reply: (1) We decided not to give any information about the cameras. These were very simple and the obtained images were primarily used for description purpose. Some measurements were derived from the images but the obtained data are considered as indicative (all values derived have a low precision). In such a context, detailing the camera’s characteristics didn’t seem necessary to us. (2) similitude is addressed in detail in Lambert et al.  2024, as mentioned line 119) (3) we will improve the quality of the presented figures (4) the flowing material is described line 96. We will complement it with the solid fraction.

We thank very well Reviewer #2 for his/her comments that helped us to improve the clarity and quality of the paper.