A closed-form model for layered snow slabs

• Published in: The Cryosphere
• Main Authors: Weißgraeber, Philipp, Rosendahl, Philipp L.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Copernicus Publications 2023
• Subjects: article; Verlagsveröffentlichung; The Cryosphere
• Online Access: https://doi.org/10.5194/tc-17-1475-2023; https://noa.gwlb.de/receive/cop_mods_00065799; https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00064310/tc-17-1475-2023.pdf; https://tc.copernicus.org/articles/17/1475/2023/tc-17-1475-2023.pdf

We propose a closed-form analytical model for the mechanical behavior of stratified snow covers for the purpose of investigating and predicting the physical processes that lead to the formation of dry-snow slab avalanches. We represent the system of a stratified snow slab covering a collapsible weak layer by a beam composed of an arbitrary number of layers supported by an anisotropic elastic foundation in a two-dimensional plane-strain model. The model makes use of laminate mechanics and provides slab deformations, stresses in the weak layer, and energy release rates of weak-layer anticracks in real time. The quantities can be used in failure models of avalanche release. The closed-form solution accounts for the layering-induced coupling of bending and extension in the slab and of shear and normal stresses in the weak layer. It is validated against experimentally recorded displacement fields and a comprehensive finite-element model indicating very good agreement. We show that layered slabs cannot be homogenized into equivalent isotropic bodies and reveal the impact of layering on bridging with respect to weak-layer stresses and energy release rates. It is demonstrated that inclined propagation saw tests allow for the determination of mixed-mode weak-layer fracture toughnesses. Our results suggest that such tests are dominated by mode I when cut upslope and comprise significant mode II contributions when cut downslope. A Python implementation of the presented model is publicly available as part of the Weak Layer Anticrack Nucleation Model (WEAC) software package under https://github.com/2phi/weac (last access: 28 March 2023) and https://pypi.org/project/weac (last access: 28 March 2023, Rosendahl and Weißgraeber, 2022).