A closed-form model for layered snow slabs

• Published in: The cryosphere 2023-04, Vol.17 (4), p.1475-1496
• Main Authors: Weißgraeber, Philipp, Rosendahl, Philipp L
• Format: Article
• Language: English
• Subjects: Avalanches; Closed form solutions; Crack initiation; Crack propagation; Deformation; Elastic anisotropy; Elastic foundations; Energy; Exact solutions; Finite element method; Gravity; Interfaces; Kinematics; Laminates; Landslides; Layering; Load; Mathematical analysis; Mathematical models; Mechanical properties; Mechanics; Modelling; Normal stress; Nucleation; Plane strain; Propagation; Slabs; Snow; Snow avalanches; Stress analysis; Stress propagation; Two dimensional models
• ISSN: 1994-0424; 1994-0416; 1994-0424; 1994-0416
• DOI: 10.5194/tc-17-1475-2023

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).