| 04 Aug 2026
Seasonal increase of the mixed-mode fracture toughness of faceted-crystal weak layers
Abstract. Mixed-mode fracture toughness of natural snow weak layers has rarely been measured directly, yet it is a key parameter governing dry-snow slab avalanche release on inclined, snow-covered slopes. Most prior estimates relied on assumed elastic properties of slab and weak layer rather than direct measurements. Here, we present field-based fracture experiments investigating the seasonal evolution of the mixed-mode fracture toughness of a natural weak layer composed of faceted crystals. We introduce a novel method that combines digital image correlation of snow displacement fields with inverse modeling to derive effective elastic properties of both the weak layer and the overlying slab. These experimentally constrained elastic properties provided more robust estimates of weak layer fracture toughness than previously possible. Results show a clear increase in fracture toughness over the season from 0.29 ± 0.042 J m-2 to 0.67 ± 0.06 J m-2 in mode I and from 0.10 ± 0.022 J m-2 to 1.0 ± 0.1 J m-2 in mode II. The effective elastic modulus of the weak layer evolved from approximately 0.63 ± 0.094 MPa at the beginning of the measurement period to 0.40 ± 0.046 MPa later in the season, while slab elasticity increased from 16 ± 1 MPa at the start to 40 ± 2 MPa. Furthermore, micro-computed tomography and manual snow profiles revealed that, although the weak layer density remained nearly constant, the specific surface area decreased and the mean local ice and pore thickness increased, as did the grain size. These findings suggest that the increases in both mode I and mode II fracture toughness are associated with grain size growth and growth of the bonds between the grains. The study further demonstrates that displacement-constrained inverse modeling provides robust snow elastic properties, improving fracture-mechanical estimates of avalanche release processes.
Competing interests: At least one of the (co-)authors is a member of the editorial board of The Cryosphere.
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This study presents field-based mixed-mode fracture experiments on a natural faceted-crystal weak layer, combining a mixed-mode fracture test with digital image correlation (DIC). They combined the displacement field of the experiment with inverse modeling to derive effective elastic properties of both the slab and the weak layer as well fracture toughness in mode I and II. The authors document a clear seasonal increase in mixed-mode fracture toughness over a three-week measurement period, supported by microstructural characterization using micro-computed tomography.
The main novelty and contribution of this paper reside in its experimental methodology and the dataset it provides. By constraining elastic properties directly from displacement fields rather than relying on assumed values, the authors reduce a key source of uncertainty in fracture toughness estimates — an important methodological advance for the field. The resulting dataset constitutes, to my knowledge, the first mixed-mode fracture toughness envelope for a faceted-crystal weak layer, and will serve as a valuable benchmark for future modeling studies.
The manuscript is well-written and the methodology is sound. My main revision is to add a bit of comparison with previous snow mechanical studies to strengthen the discussion. I recommend minor revisions, with the following specific comments to be addressed by the authors.
Specific comments
Line 97: Consider adding to the sentence :” the weak layer was cut, either in the downslope or upslope direction”
Line 139: I would add the symbol E_wl after introducing the weak layer elastic modulus for clarity.
Line 153: Specifying the version package of Scipy and Weac version is enough for scientific reproducibility.
Line 169: It would be helpful to clarify whether the type of distributions (uniform or gaussian) used in the Monte Carlo sampling. This will affect if the sampling is center around the initial guess or explore across the whole range of values. Since the choice of sampling distribution can influence the resulting parameter distribution and the derived confidence intervals, I suggest the authors clarify this point. and would improve the reproducibility of the method.
Line 174: Propagating measurement uncertainties into the physical model is important but I’m wondering where are these uncertainties range come from? Maybe add details on how they were derived.
Line 175: The Poisson’s ratio of the weak layer is stated to be 0.25, but it is unclear whether the same value was assumed for the slab. I suggest clarifying whether the slab Poisson’s ratio was also fixed at 0.25 in Eq.3.
Figure 8: The figure caption refers to “Bergfeld’s density parametrization” for the slab elastic moduli. But it was stated in the methods that the density values shown are derived from the Gerling et al. (2017) scaling law.
Figure 13: Given that the information conveyed by this figure is less significant and well described in the text at Lines 246–248, I question whether it is necessary to include it as a main-text figure. I could also argue that the reduction in SSA is rather small between the Series, maybe tone down a bit the statement in conclusion. However, I do acknowledge a more significant effect on the mean ice thickness between bonds.
The authors may wish to consider whether it could be moved to the Appendix, unless the visual representation provides additional insight beyond what is stated in the text.
Lines 301–302: The statement that the weak layer strengthens progressively over time would benefit from additional references. While the present study focuses on fracture toughness rather than strength, the temporal evolution of weak layer mechanical resistance is well-documented in the snow science literature. Adding references to studies on the strengthening of weak layers over time — for instance, through bond growth — would lend more weight to this claim and could potentially allow the authors to remove the final cautionary sentence of the paragraph, which currently somewhat undermines an otherwise well-supported conclusion.
Line 314: I suggest adding a statement noting that the elastic property values derived in this study are consistent with previously reported values in the literature using different methods. Estimating elastic properties, especially the weak layer, is rather difficult and a comparison will add support to the values reported in this study. This would help contextualize the results and further support the validity of the proposed methodology.