Laboratory Investigation on the Impact Force of Large Boulders in Debris Flows

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript presents a dimensionless impact-force model for large boulders in debris flows, derived using dimensional analysis and validated through controlled laboratory experiments and field monitoring data from Jiangjiagou, China. The authors introduce a correction coefficient to account for rheological effects and suspended particle size and propose the final predictive model.  However, several conceptual, methodological, and presentation issues must be addressed before publication. In its current form, the manuscript requires major revision.

1. The derivation of the proposed model requires a clearer and more systematic presentation. In particular, the application of Buckingham Π theory should be explained step by step. The authors are encouraged to explicitly list the governing variables, construct the dimensional matrix, and demonstrate how the final dimensionless groups were obtained. A more rigorous derivation would improve transparency and theoretical credibility.

2. To better position the contribution of this study, it would be helpful to compare the proposed formulation with existing approaches, such as momentum-based or energy-based impact models. A quantitative comparison would clarify the relative advantages, limitations, and engineering implications of the present model.

3. The manuscript assumes a constant value for the rotational energy ratio β. It is unclear whether β remains constant across different media and flow conditions. The authors should provide a clearer justification for the selected value and, if possible, conduct a sensitivity analysis. More generally, the physical origin and robustness of empirical coefficients in the model should be better explained.

4. The experimental setup would benefit from a more detailed description of the hydraulic conditions. Key parameters such as flow velocity, water depth, discharge, and flow regime should be reported. These details are essential for evaluating reproducibility and assessing similarity to field-scale debris flows.

5. Additional information regarding the force sensors should be provided, including sensor model/series, calibration procedure, sampling frequency, and measurement accuracy. Including error bars in the figures would also strengthen the analysis. Given the relatively small empirical exponents in the proposed relationships, measurement noise could significantly influence the results. A more thorough discussion of uncertainty and error propagation is therefore recommended.

6. The manuscript states that a camera operating at 25 frames per second was used to record the impact process. However, 25 fps is relatively low for capturing high-speed impact events. Please clarify whether this temporal resolution is sufficient to accurately resolve impact velocities and distinguish small differences in speed. In addition, the manuscript does not present a clear analysis of the recorded video data. The authors should describe the image-processing procedure in detail, including spatial calibration, frame selection, velocity calculation methodology, and uncertainty estimation. If the camera data significantly contributed to the results, this role should be explicitly demonstrated.

7. Although Froude similarity is mentioned in the introduction, it is not further discussed or applied in the experimental analysis. The authors are encouraged to introduce and evaluate additional relevant dimensionless numbers (e.g., Reynolds number, Bingham number) to better characterize the flow regime. Since turbulence intensity in field-scale debris flows may differ substantially from laboratory conditions, the implications of these scale effects on model applicability should be discussed more thoroughly.

8. The manuscript does not clearly state whether experiments were repeated. Please provide information on the number of repetitions, variability of the results, and statistical measures such as standard deviation or coefficient of variation. Demonstrating repeatability would increase confidence in the robustness of the findings.

9. The field validation is based on back-calculating boulder diameters from measured impact forces. While this provides qualitative support, a more direct evaluation of predictive performance would strengthen the manuscript. For example, comparing predicted and measured forces directly, or reporting statistical indicators such as RMSE, mean absolute error, or prediction intervals, would allow a clearer assessment of model accuracy.

10. The estimation of yield stress appears to rely on indirect calculations rather than direct rheometric measurements. Since yield stress plays a central role in the dimensionless parameter, uncertainty in its estimation may significantly influence the derived empirical relationships. The authors should clarify the assumptions involved and discuss potential limitations and sensitivity.

11. The manuscript would benefit from a clearer discussion of the applicability range of the proposed model. The valid ranges of particle size, yield stress, impact velocity, and flow regime should be specified. Additionally, practical guidance for engineering implementation—such as parameter selection procedures or safety considerations—would enhance the usefulness of the model.

12. The authors state that this is the first model to simultaneously incorporate yield stress and suspended particle size. However, previous studies (e.g., Cui et al., 2015; Scheidl et al., 2013; Proske et al., 2018) have already considered rheological and granular effects. The authors should more clearly articulate what is fundamentally novel in their approach and how it advances beyond existing models.

13. There appear to be inconsistencies in the reference list and in-text citations. For example, Zhang et al. (2007) and Shieh et al. (2008) are mentioned but not included in the reference list. Additionally, the citation number in Line 222 appears incorrect. Please carefully check all references and citations for completeness and accuracy.

14. Given that this manuscript is submitted to Sensors, the authors should more clearly articulate the contribution of the sensing technology itself. At present, the study primarily focuses on impact mechanics and debris-flow modeling, while the sensing system appears to function mainly as a measurement tool.

To better align with the scope of the journal, the authors should clarify whether the sensing technology, measurement methodology, calibration strategy, or signal-processing approach is novel or significantly advanced compared to existing systems. Strengthening the discussion on sensing performance, dynamic response characteristics, uncertainty analysis, or instrumentation improvements would improve the manuscript’s fit with the journal.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript presents a dimensionless model for predicting the impact force of large boulders in debris flows, derived using Buckingham π theorem and validated through laboratory experiments and field monitoring data from Jiangjiagou, China.The study combines theoretical modeling, controlled flume experiments (water, slurry, and debris-flow mixtures), and field back-calculation. The integration of yield stress and suspended particle size into the impact coefficient c is an interesting contribution.

However, although the topic is relevant and potentially valuable for debris-flow mitigation engineering, the manuscript requires substantial revision before it can be considered for publication in Sensors. The main issues relate to:

• Insufficient clarity in theoretical derivation

• Limited experimental rigor and uncertainty analysis

• Weak connection to the “Sensors” scope

• Language and formatting problems

• Overstated claims regarding novelty

 

• The manuscript claims this is the “first” model incorporating both rheology and solid-phase effects (p.16) This claim appears overstated, as previous works (e.g., Iverson 1997; Cui et al. 2015; Scheidl et al. 2013) have already considered rheological effects in debris-flow impacts.

• The exponent values (–0.1 and 0.05) appear fully empirical and lack physical interpretation.

The authors must:

• Clearly distinguish their contribution from prior models.

• Avoid absolute novelty claims unless rigorously justified.

The manuscript focuses primarily on:

• Debris-flow mechanics

• Impact-force modeling

• Rheological effects

The sensor system is described but not deeply analyzed:

• No calibration curve shown.

• No frequency response analysis.

• No discussion of dynamic response.

• No signal processing analysis.

For Sensors, the manuscript must strengthen:

• Measurement methodology

• Sensor performance evaluation

• Data acquisition validation

• Signal-processing details

Comments for author File: Comments.pdf

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Authors adressed my comments, the article is improved

Comments on the Quality of English Language

can be improved 

Author Response

Comments:Comments on the Quality of English Language can be improved
Response: The English language quality has been polished through the MDPI Author Services, and Figures 10–12 have been redrawn.

Author Response File: Author Response.pdf