the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 Aug 2024
The effect of slab touchdown on anticrack arrest in propagation saw tests
Abstract. Understanding crack phenomena in the snowpack and their role in avalanche formation is imperative for hazard prediction and mitigation. Many studies have explored how structural properties of snow contribute to the initial instability of the snowpack, focusing particularly on failure initiation within weak snow layers and the onset of crack propagation. This work addresses the subsequent stage, the effect of slab touchdown after weak layer failure in mixed-mode loading (compresive anticrack (mode I) and shear (mode II) loading). Here we show that slab touchdown reduces the energy release rate, potentially leading to crack arrest, even in static considerations. This finding challenges the notion that dynamic properties of snow layers and spatial snowpack changes alone dictate arrest, highlighting the critical role of mechanical interactions between the slab, weak layer, and base layer. By integrating these findings into the broader context of snowpack stability analysis, we contribute to a more nuanced understanding of avalanche initiation mechanisms. By offering a comprehensive model that can be applied in diverse geophysical settings (https://github.com/2phi/weac), this work extends the scope of avalanche science, promising new strategies for hazard assessment and mitigation.
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RC1: 'Comment on nhess-2024-122', Ron Simenhois, 11 Sep 2024
The authors present a novel method for analyzing slab touchdown in a Propagation Saw Test (PST) by developing a closed-form analytical model that incorporates mixed-mode loading (compression and shear) to calculate the Energy Release Rate (ERR) from slab deformation and the resulting crack arrest. To streamline the mathematical framework, they divide the slab touchdown progression into three distinct stages, each characterized by linear behavior and representing different phases of crack propagation and interaction with the collapsed weak layer. The model is validated using finite-element and discrete-element methods, providing a more nuanced understanding of avalanche initiation mechanisms.
I enjoyed reading this article. It is well-written, the model is clearly explained, and sensitivity analyses clearly illustrate its contribution to the avalanche field. While I have very few specific comments on the article's content, minor additions could enhance the manuscript. Below is a list of general comments.
- Sensitivity Analysis: The article provides a thorough sensitivity analysis examining the impact of various parameters—such as slab thickness, density, weak layer properties, and slope angle—on crack propagation and arrest. Including a summarized list or table of these findings would enhance their accessibility and value to a broader audience.
- Model Limitations in Capturing Dynamic Processes: Although the study's static model effectively illustrates the effects of slab touchdown, it fails to capture the dynamic processes involved in slope-scale crack propagation during real-world avalanches. While the authors acknowledge that the model does not account for dynamic stages of crack propagation, this limitation should be explicitly emphasized in the discussion or conclusions. In practical terms, crack arrest in real-world avalanches, occurring after the weak layer crack transitions to a dynamic stage, differs significantly from crack arrest that prevents the transition to a dynamic stage. Addressing this distinction is crucial for clarifying the model's applicability and limitations.
- Limited Experimental Validation: While the authors validate the model using numerical simulations, there is limited reliance on direct experimental data to substantiate the model's predictions. The use of experimental data from natural winter snowpack (Bergfeld et al., 2023a, b) is only briefly mentioned in the "Practical Implications" section. To strengthen the manuscript, I recommend relocating the sections that compare the model to data from Bergfeld et al., 2023a, b to the "Methods" and "Results" sections, as this comparison provides the most compelling validation of the proposed model.
- Complexity and Accessibility: The article's technical language and in-depth mathematical modeling may limit its accessibility to a broader audience, such as those involved in developing "best practice" guidelines for snowpack observation and avalanche testing who could benefit from its insights. To increase its impact, the authors could provide a concise summary of the key results and a more accessible overview, highlighting practical implications and recommendations for application in the field.
- Practical Implications Not Fully Explored: While the study offers theoretical insights into crack arrest mechanisms, its practical implications are mostly confined to tentative recommendations for PST geometry. However, as the authors suggest by listing these recommendations, even the optimal geometry for PST remains uncertain, and there is still a lack of understanding of how to interpret test results concerning actual avalanche occurrences. The article would benefit from leveraging its rigorous sensitivity analysis to discuss further how these findings could inform practical avalanche safety strategies and improve real-world decision-making for avalanche risk management.
- Simplification and Assumptions: As noted in the article, the model does not consider frictional sliding during slab touchdown and assumes full contact and stress transfer. In real-world scenarios, frictional effects can be significant, particularly at high slope angles, potentially affecting the ERR and the probability of crack arrest. Although this limitation comes into play at the extreme upper end of the avalanche release slope angle, this and other limitations should be clearly outlined in the discussion or conclusion sections to provide a more comprehensive understanding of the model's constraints and applicability to real avalanche conditions.
Overall, these suggestions could help enhance the manuscript's clarity, relevance, and applicability for researchers and practitioners in avalanche science.
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RC2: 'Comment on nhess-2024-122', Anonymous Referee #2, 02 Oct 2024
The paper is well-written and presents solid research, though its contribution is somewhat incremental compared to existing literature, particularly with respect to previous work by both the authors and other scholars in the field. Despite this, I believe the study introduces enough novel insights to warrant publication in NHESS after a few major revisions detailed below together with more specific minor comments.
Novelty and contribution:
As briefly mentioned above, although the paper builds upon previous work by the authors and others in the field (especially Benedetti et al.), it does introduce enough novel elements to warrant consideration for publication in NHESS. A significant portion of the mechanical model has already been presented in Weissgraber and Rosendahl (2023) and applied in Bergfeld et al. (2023). Moreover, the concept of touch-down distance in a static slab-weak layer model was introduced by Benedetii et al., although without incorporating slab shear (Euler-Bernoulli beam theory) nor slab layering. The important contribution of this paper lies in combining these two elements, leading to a more robust model, performing detailed sensitivity analysis, validation with FEM and DEM, and applying it to field data. I believe this combination is very solid and represents excellent work.
However, I encourage the authors to be more explicit about the overlap with prior work and to clearly articulate the unique contributions of this paper. Suggestions below.
Some overstatements and comparison / discussion with Benedetti:
I noted a few overstatements throughout the paper that are I believe unnecessary. Additionally it would be good to add a comparison with Benedetti's "twin" model, or at least a deeper discussion. For instance, the paper introduces the different phases during collapse, which were already presented in greater detail (with additional steps) by Benedetti et al. It appears from the methods section that the authors are positioning themselves as the first to introduce these phases, but they were previously discussed by Heierli (though in less detail), Benedettii et al., and more recently by Siron et al., who also included dynamics. While this is briefly acknowledged in the discussion, it should be much clearer earlier in the paper.
Model comparison: I would suggest to compare with Beneddetti's analytical model in various configurations (obvioulsy without layering), particularly regarding unsupported length and touch-down distance. It seems to me that the results could be quite different. This would illustrate better the necessity to introduce slab shear if the discrepancy arises from the lack of this process in Benedetti. For instance, the slab stress in Benedetti has very similar characteristics has the ERR in your paper, however, this trend is not well reflected on the weak layer stresses in Benedetti et al. (probably too strong stress increase). I believe your model is very likely more accurate and it would be great to elaborate on the differences: is the problem due to incorrect assumption (e.g. lack of slab shear) or is there another problem (quite likely as I don't think the lack of shear in the slab would make such a big difference on the weak layer stresses, to be checked)?
In the discussion, the claim that Benedetti's model is not continuous needs clarification, as distance and stresses appear continuous and the model seem to be developed with continuity conditions. The issue seems to be with the derivatives, which are often discontinuous in problems involving contact and friction, so a more precise statement is required.
Crack arrest and model relevance: The link to crack arrest is only introduced late in the discussion, which is somewhat confusing. In addition, while I appreciate the use of fracture mechanics, the paper introduces the critical energy release rate (Gc), essentially stress (a)^2 divided by weak layer stiffness, adding another layer of uncertainty as one needs to know kn and kt as well, properties which are very hard to measure. I recommend instead, or at least additionally to present results in a stress-strength framework to avoid this additional uncertainty and offer further insights into crack arrest.
For instance, including metrics like τc/τs and σc/σs, alongside Gc/Gs, would be beneficial, as these are commonly used in engineering and avalanche science to assess stability and also in many strength-of-material oriented models. This would be a very interesting additional outcome that could give insights for researchers using different frameworks (fracture or strength of materials). In fact the sentence "As shown in Table 3, the quotient of both Gc/Gs is therefore a reasonable metric to map the propensity for wide-spread crack propagation of a given snowpack/PST” suggests that one can only get this information through toughness. You would essentially get the same type of information by looking at stress and strength. Additionally, this would make a better link to Figure 5 (DEM comparison) which is only one with stress instead of energy... I think this would be very valuable and interesting addition.
Another important aspect is the lack of discussion regarding the model’s relevance to real-scale avalanches. The paper focuses on arrest conditions at the PST scale, not the slope scale. Although arrest can indeed be induced by slab and weak layer properties at the PST scale, as demonstrated here and by others, once crack propagation occurs at the slope scale, touch-down distance does not have the same impact (it actually becomes much larger in a dynamic setting). Arrest at this stage is likely driven by slab tensile failure, spatial variability (see Meloche et al. https://arxiv.org/abs/2406.01360), and topography (Gaume et al. 2019 Cold Reg.). This scale is reflected very well in the title of the paper, but the text needs further elaboration in the introduction and discussion sections in my opinion.
Crack arrest explanation: Moreover, the current paper does not completely explain why crack arrest occurs; it suggests that it could be related to Gc/Gs, but the ratios remain below one, meaning energy release still exceeds toughness. This is fine but I think it should be further discussed. Additional research is needed to fully understand this process, especially at the slope scale, where other factors like slab tensile failure, spatial variability, and topography play crucial roles.
Frictional sliding: It is both surprising and a bit disappointing that the current study does not account for frictional sliding, an essential factor, particularly for cases on steep slopes. Why was this omitted? Including friction seems quite straightforward and would provide a more comprehensive understanding of the crack arrest phenomena. I understand that at a scale of a classical PST (1m) it won't affect the results much, but at the larger scale it will have crucial consequences on the results. There must be a clear and objective rationale for excluding it, though I find it difficult to grasp the complexity behind this decision, especially since similar modeling has included friction before. How complex it is to add the friction term into the equations?
Equations: I suggest to add more details on the stress calculations.
Experimental validation: At the moment the validation is performed using DEM and FEM and the model is then applied to experimental cases. I wonder if it would be feasible to extend the validation to a much broader database of PSTs which include snowpack information and PST outcome, even if this validation is at a lower level of details. Once does not always have such precise data as those presented here but I still think such data could give important general insughts on the model applicability. For instance, one could use a threshold-based approach to check whether you are able to "predict" ARR and END cases.
Suggested limitations and outlook section: A section on limitations and outlook would greatly enhance the paper. It could include topics such as the effects of slab fracture (which could be modeled similarly to Benedetii but here including layering model) and discuss skier triggering, spatial variability, and slab fracture dynamics, especially since slab fracture may be difficult to observe in PSTs.
More detailed comments:
- Relevant literature: The paper by Jamieson and Johnston (1992) "A fracture-arrest model for unconfined dry slab avalanches," could be relevant for this paper.
- Abstract: The last sentence should either be removed or elaborated in the main text. Specify which geophysical settings are referred to?
- Introduction, page 1: Define "anticrack" before discussing its importance, as it may not be clear to all readers.
- Introduction, line 29: Include a discussion on dynamic and slope scale studies.
- Introduction, line 36: Trottet et al and Gaume et al. (2019) also discuss slab fracture and arrest.
- Introduction, line 44: The statement about physical mechanisms behind crack propagation and arrest should be reworded. Benedetti showed similar results, even without considering slab shear and layering, but framed them differently. Moreover, this paper gives very important insights but does not fully explain crack arrest, instead linking experimental results to metrics from the model. Gc > G at arrest suggests more work is required to understand this process.
- Methods: I think it would be fair to reference Benedetti at least and perhpas Siron when introducing PST stages, as the stages here are essentially a subset of those proposed by Benedetti.
- Figures 6, 7, 8, equation 14: Discussion / comparison with Benedetti would be interesting.
- Figures: can the authors explain the second peak in the ERR curves which is not observed in FEA?
- Figure 5: I suggest to show the DEM simulation and elaborate in an appendix.
- Section 4.6: The link to crack arrest is only made here, despite the focus of the paper. I think the end of the introduction could somewhat elaborate on that and tell the reader that the link to crack arrest will only be made in a final section introducing field data with different PST outcomes..
- Line 323: Clarify the claim regarding Benedetti's model and provide more precise reasoning.
- Table 3: Add missing units.
- Line 362: Specify how steady-state or plateau values were chosen in cases with no apparent steady state.
- Line 385: Consider adding a section on limitations and outlook, discussing crack propagation dynamics, spatial variability, skier triggering (quid of skier motion and progressive weak layer damage), and slab fracture (slab fracture may be hard to see in PSTs and ARR could in fact be unseen SF, of slab damage preventing further increase in tension), etc. Slab fracture can be easily added in this model... I also suppose the authors have access to SF data, it would have really nice to extend and see if the present model can reproduce SF through a very simple tensile strength threshold for instance.
Citation: https://doi.org/10.5194/nhess-2024-122-RC2
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