05 Sep 2022
05 Sep 2022
Status: this preprint is currently under review for the journal TC.

A closed-form model for layered snow slabs

Philipp Weißgraeber1, and Philipp Laurens Rosendahl2, Philipp Weißgraeber and Philipp Laurens Rosendahl
  • 1University of Rostock, Chair of Lightweight Design, Germany
  • 2Technical University of Darmstadt, Department of Civil and Environmental Engineering, Institute of Structural Mechanics and Design, Germany
  • These authors contributed equally to this work.

Abstract. 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 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 and

Philipp Weißgraeber and Philipp Laurens Rosendahl

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on tc-2022-140', Anonymous Referee #1, 02 Nov 2022
    • AC3: 'Reply on RC1', Philipp Rosendahl, 04 Feb 2023
  • CC1: 'Comment on tc-2022-140', Xingyue Li, 08 Nov 2022
    • AC1: 'Reply on RC2', Philipp Rosendahl, 04 Feb 2023
    • AC4: 'Reply on CC1', Philipp Rosendahl, 04 Feb 2023
  • RC2: 'Comment on tc-2022-140', Anonymous Referee #2, 09 Nov 2022
    • AC1: 'Reply on RC2', Philipp Rosendahl, 04 Feb 2023
  • RC3: 'Comment on tc-2022-140', Anonymous Referee #3, 28 Nov 2022
    • AC2: 'Reply on RC3', Philipp Rosendahl, 04 Feb 2023

Philipp Weißgraeber and Philipp Laurens Rosendahl

Philipp Weißgraeber and Philipp Laurens Rosendahl


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Short summary
The work presents a mathematical model that calculates the behavior of layered snow covers in response to loadings. The information is necessary to predict the formation of snow slab avalanches. While sophisticated computer simulations may achieve the same goal, they can require weeks to run. By using mathematical simplifications commonly used by structural engineers, the present model can provide hazard assessments in milliseconds, even for snowpacks with many layers of different types of snow.