Algorithm Implementation and Statistical Evaluation of a Novel Failure Criterion Governing the Release of Slab Avalanches

Abstract

Fracture-mechanics-based avalanche failure modeling offers a promising approach for predicting slope-specific snow stability, as opposed to broader regional avalanche danger levels. Understanding slab avalanche failure through weak layer collapse, governed by both material strength and toughness, is rooted in the coupled criterion proposed by Leguillion. This thesis implements a novel algorithm to evaluate the failure criterion originally developed by Rosendahl and Weißgraeber, leveraging the newly published fracture toughness envelope by Adam. For the first time, crack initiation in weak snow layers can be conclusively described from the fracture mechanical point of view, forming a practical implementation for avalanche initiation using the original coupled criterion proposed by Leguillion.

The algorithm implementation of the coupled criterion displayed robust performance, as the standard snow profile parameter studies matched expectations from practitioner experience well. The predictive capabilities of the mechanical model were evaluated for 748 snow profiles and associated Rutschblock (RB) tests performed in Switzerland over 18 winter seasons from 2001/02 to 2018/19. To establish a baseline, traditional statistical models, including ordinary least squares (OLS), Huber regression, and Random Forest (RF), were applied to predict snow stability from raw snow profile data. Consistent with previous research, regression techniques struggled to predict stability across the full range of RB scores, though classification of extreme stability conditions was in general possible. No benchmark model could predict the full RB range, while binary classification was possible when using only snow profile raw data, and accurate when allowing local avalanche danger as an additional input parameter. The best performing RF classifier achieved accuracy of 0.920, precision of 0.911, recall of 0.901, F1 score of 0.905, ROC AUC of 0.959, and specificity of 0.934 on average.

The mechanical model showed a positive correlation between critical skier weight and RB scores. However, its predictive capability could not be statistically validated. Due to large variance in the observed relationship between critical skier weight and RB scores, full-range prediction was not possible, though classification of stability extremes was comparable to the best-performing RF classifier using raw snow profile data.

Compared to the stability index SK₃₈ᴹᴸ, the mechanical model demonstrated improved performance, though it was outperformed by the Random Forest classifier of Mayer et al. From a strictly statistical perspective, the mechanical model does not provide a significant predictive advantage. This may indicate either a fundamental limitation in its ability to model micro-scale failure mechanics or an insufficient dataset for proper validation.

Dataset limitations are primarily attributed to variability in manually collected snow profile data and inconsistencies in RB test conditions. To validate the mechanical model effectively, future research should prioritize controlled laboratory experiments with high-precision snow profile measurements and well-defined force-loading conditions.

Popular Abstract

Avalanches remain a persistent hazard to skiers and mountaineers. Of the different avalanche types, slab avalanches cause more than 90% of fatalities. Physically, slab avalanche release is explained by the interaction of a weak layer with a well-bonded cohesive snow slab. With sufficient force, either from the slab itself or from additional skier weights, the weak layer collapses, and the slab mass slides downhill rapidly. Essentially, slab avalanche release is a fracture process. The research field of fracture mechanics provides the most promising method to describe, and subsequently predict, when slab avalanches occur. This thesis has implemented and evaluated a novel fracture-mechanics-based failure criterion.

The avalanche danger is a five-step scale and is published daily by the responsible national agencies in the Alps, the Nordics, and North America. The issued warnings often cover several square kilometers, giving backcountry skiers an overview of the existing problems in the snowpack. Slab avalanche release, as described using fracture mechanics, has the potential to enable slope-specific predictions of snow stability. By digging a snow profile and noting the structure of the snowpack, one could receive exact predictions of the critical additional loads the snowpack could sustain before a weak layer collapse.

Slab avalanche release can be described as a sequence of two fracture processes. The first involves the formation of an anticrack, which is a sudden, collective loss of volume in a porous layer, corresponding to a partial collapse of the weak layer. A weak layer in the snowpack is made up of loosely bonded, low-density snow, with snow grains that have irregular shapes. If the energy release of the initial collapse is sufficiently high, it can propagate into a full-scale avalanche. The initial collapse, often referred to as a *whumpf*, is named after the distinctive sound of the snowpack settling.

The key question, which remained unanswered until recently, concerns the boundary conditions of the critical force to trigger a whumpf. The size of the anticrack depends on a coupled criterion of both strength and toughness of the weak layer. Strength refers to a material's ability to resist breaking under stress, while toughness describes its capacity to absorb energy and withstand deformation before fracturing. The boundary conditions for fracture toughness were published in September of 2024 by Adam, forming the final piece of the puzzle.

After having developed a robust algorithm, which finds the exact solution of the critical force and corresponding anticrack length for a given snow profile, the performance was evaluated on a range of standard snow profiles. The studies were promising, as results aligned with expectations based on existing knowledge and practitioner experience. To attempt validation of the mechanical model, its predictive performance was tested on a dataset of 748 Rutschblock (RB) tests, collected over eighteen winter seasons in Switzerland. The Rutschblock test is the most well-established snow stability test and involves a skier jumping onto a 2 x 1.5 x h block of snow to determine the additional force the snowpack can sustain before fracture. As the mechanical model finds the critical skier weight for initial collapse, the comparison with a snow stability test based on skier weight loading should, in theory, be fair. When evaluating the mechanical model on the 748 RB tests, the suggested relationship, however, is not sufficient to enable prediction of the full RB range. The mechanical model parameters also fail to improve binary classification, compared to established benchmark models using only snow profile raw data.

Comparison against the established stability index SK₃₈ᴹᴸ suggests that performance is better for the mechanical model, while the Random Forest classifier of Mayer et al. outperforms the mechanical model. From a strictly statistical point of view, the use of the mechanical model is redundant, and improved prediction cannot be proven. This suggests two primary explanations: either the model lacks the capability to accurately predict failure mechanics at the micro level, or the dataset is insufficient for proper validation.

The dataset insufficiency conclusion is fundamentally supported by the variance introduced by manually collected snow profile data and the ambiguity in the RB test setup. To validate the mechanical model effectively, future research should prioritize controlled laboratory experiments with greater precision in snow profile parameter measurements and force-loading conditions.

• author: Nauclér, Carl
• supervisor: Andreas Jakobsson
• organization: Mathematical Statistics
• course: FMSM01 20242
• year: 2025
• type: H2 - Master's Degree (Two Years)
• subject: Mathematics and Statistics
• keywords: slab avalanche release, fracture mechanics, anticrack nucleation, coupled criterion, fracture toughness, random forest classifier, Rutschblock
• publication/series: Master’s Theses in Mathematical Sciences
• report number: LUTFMS-3511-2025
• ISSN: 1404-6342
• other publication id: 2025:E7
• language: English
• id: 9185357
• date added to LUP: 2025-02-19 13:38:23
• date last changed: 2025-02-20 08:13:35