Articles | Volume 17, issue 4
https://doi.org/10.5194/tc-17-1475-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/tc-17-1475-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A closed-form model for layered snow slabs
Philipp Weißgraeber
Faculty of Mechanical Engineering and Marine Technology, Chair of Lightweight Design, University of Rostock, Rostock, Germany
Department of Civil and Environmental Engineering,
Institute of Structural Mechanics and Design, Technical University of Darmstadt, Darmstadt,
Germany
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Melin Walet, Jakob Schöttner, Valentin Adam, Florian Rheinschmidt, Philipp Rosendahl, Philipp Weißgraeber, Jürg Schweizer, and Alec van Herwijnen
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Dry snow avalanches start when a weak snow layer fails and a crack spreads through the snowpack, but field data is limited. We tested a weak layer of coarse snow grains in field fracture experiments. Using videos of snow movement, we derived the stiffness of the weak layer and calculated the resistance to crack growth. Crack resistance increased during the season as the grains in the weak layer grew and bonded more strongly. This data can be used to improve avalanche release models.
Philipp L. Rosendahl, Johannes Schneider, Grégoire Bobillier, Florian Rheinschmidt, Bastian Bergfeld, Alec van Herwijnen, and Philipp Weißgraeber
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Avalanche formation depends on crack propagation in weak snow layers, but the conditions that stop a crack remain unclear. We show that slab touchdown reduces the energy driving crack growth, which can halt propagation even under static conditions. This suggests that crack arrest is influenced not only by snowpack variability or dynamics but also by mechanical interactions within the snowpack. Our findings refine avalanche prediction models and improve hazard assessment.
Bastian Bergfeld, Alec van Herwijnen, Grégoire Bobillier, Philipp L. Rosendahl, Philipp Weißgraeber, Valentin Adam, Jürg Dual, and Jürg Schweizer
Nat. Hazards Earth Syst. Sci., 23, 293–315, https://doi.org/10.5194/nhess-23-293-2023, https://doi.org/10.5194/nhess-23-293-2023, 2023
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For a slab avalanche to release, the snowpack must facilitate crack propagation over large distances. Field measurements on crack propagation at this scale are very scarce. We performed a series of experiments, up to 10 m long, over a period of 10 weeks. Beside the temporal evolution of the mechanical properties of the snowpack, we found that crack speeds were highest for tests resulting in full propagation. Based on these findings, an index for self-sustained crack propagation is proposed.
Mary Kate Connelly, Philipp Laurens Rosendahl, Valentin Adam, and Samuel V. Verplanck
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Avalanche models need snow properties that field teams rarely measure directly. We created a flexible framework that combines snowpit observations with published methods, tracks uncertainty, and shows where calculations fail. Applied to 14,776 snow slabs, simple weight estimates worked for up to 37%, but richer estimates including snow stiffness worked for only 4.6%. Stiffness estimates also varied widely, showing that missing observations and method choice strongly affect avalanche predictions.
Melin Walet, Jakob Schöttner, Valentin Adam, Florian Rheinschmidt, Philipp Rosendahl, Philipp Weißgraeber, Jürg Schweizer, and Alec van Herwijnen
EGUsphere, https://doi.org/10.5194/egusphere-2026-3554, https://doi.org/10.5194/egusphere-2026-3554, 2026
This preprint is open for discussion and under review for The Cryosphere (TC).
Short summary
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Dry snow avalanches start when a weak snow layer fails and a crack spreads through the snowpack, but field data is limited. We tested a weak layer of coarse snow grains in field fracture experiments. Using videos of snow movement, we derived the stiffness of the weak layer and calculated the resistance to crack growth. Crack resistance increased during the season as the grains in the weak layer grew and bonded more strongly. This data can be used to improve avalanche release models.
Philipp L. Rosendahl, Johannes Schneider, Grégoire Bobillier, Florian Rheinschmidt, Bastian Bergfeld, Alec van Herwijnen, and Philipp Weißgraeber
Nat. Hazards Earth Syst. Sci., 25, 1975–1991, https://doi.org/10.5194/nhess-25-1975-2025, https://doi.org/10.5194/nhess-25-1975-2025, 2025
Short summary
Short summary
Avalanche formation depends on crack propagation in weak snow layers, but the conditions that stop a crack remain unclear. We show that slab touchdown reduces the energy driving crack growth, which can halt propagation even under static conditions. This suggests that crack arrest is influenced not only by snowpack variability or dynamics but also by mechanical interactions within the snowpack. Our findings refine avalanche prediction models and improve hazard assessment.
Bastian Bergfeld, Karl W. Birkeland, Valentin Adam, Philipp L. Rosendahl, and Alec van Herwijnen
Nat. Hazards Earth Syst. Sci., 25, 321–334, https://doi.org/10.5194/nhess-25-321-2025, https://doi.org/10.5194/nhess-25-321-2025, 2025
Short summary
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To release a slab avalanche, a crack in a weak snow layer beneath a cohesive slab has to propagate. Information on that is essential for assessing avalanche risk. In the field, information can be gathered with the propagation saw test (PST). However, there are different standards on how to cut the PST. In this study, we experimentally investigate the effect of these different column geometries and provide models to correct for imprecise field test geometry effects on the critical cut length.
Bastian Bergfeld, Alec van Herwijnen, Grégoire Bobillier, Philipp L. Rosendahl, Philipp Weißgraeber, Valentin Adam, Jürg Dual, and Jürg Schweizer
Nat. Hazards Earth Syst. Sci., 23, 293–315, https://doi.org/10.5194/nhess-23-293-2023, https://doi.org/10.5194/nhess-23-293-2023, 2023
Short summary
Short summary
For a slab avalanche to release, the snowpack must facilitate crack propagation over large distances. Field measurements on crack propagation at this scale are very scarce. We performed a series of experiments, up to 10 m long, over a period of 10 weeks. Beside the temporal evolution of the mechanical properties of the snowpack, we found that crack speeds were highest for tests resulting in full propagation. Based on these findings, an index for self-sustained crack propagation is proposed.
Cited articles
Bair, E. H.: Forecasting artificially-triggered avalanches in storm snow at a
large ski area, Cold Reg. Sci. Technol., 85, 261–269,
https://doi.org/10.1016/j.coldregions.2012.10.003, 2013. a
Bergfeld, B., van Herwijnen, A., Reuter, B., Bobillier, G., Dual, J., and Schweizer, J.: Dynamic crack propagation in weak snowpack layers: insights from high-resolution, high-speed photography, The Cryosphere, 15, 3539–3553, https://doi.org/10.5194/tc-15-3539-2021, 2021a. a
Bergfeld, B., van Herwijnen, A., Reuter, B., Bobillier, G., Dual, J., and
Schweizer, J.: Dynamic crack propagation in weak snowpack layers: Insights
from high-resolution, high-speed photography, The Cryosphere Discuss. [preprint],
https://doi.org/10.5194/tc-2020-360,
2021b. a, b
Bergfeld, B., van Herwijnen, A., Bobillier, G., Rosendahl, P. L., Weißgraeber, P., Adam, V., Dual, J., and Schweizer, J.: Temporal evolution of crack propagation characteristics in a weak snowpack layer: conditions of crack arrest and sustained propagation, Nat. Hazards Earth Syst. Sci., 23, 293–315, https://doi.org/10.5194/nhess-23-293-2023, 2023a. a, b, c, d
Bergfeld, B., van Herwijnen, A., and Schweizer, J.: Time series data on
dynamic crack propagation in long propagation saw tests, EnviDat [data set],
https://doi.org/10.16904/envidat.365, 2023b. a, b, c
Birkeland, K. W., van Herwijnen, A., Reuter, B., and Bergfeld, B.: Temporal
changes in the mechanical properties of snow related to crack propagation
after loading, Cold Reg. Sci. Technol., 159, 142–152,
https://doi.org/10.1016/j.coldregions.2018.11.007, 2019. a
Bobillier, G., Gaume, J., van Herwijnen, A., Dual, J., and Schweizer, J.:
Modeling the propagation saw test with discrete elements, in: Proceedings
of the International Snow Science Workshop ISSW 2018, edited by: Fischer,
J.-T., Adams, M., Dobesberger, P., Fromm, R., Gobiet, A., Granig, M.,
Mitterer, C., Nairz, P., Tollinger, C., and Walcher, M.,
Innsbruck, Austria, 976–980, http://arc.lib.montana.edu/snow-science/item/2690 (last access: 29 March 2023), 2018. a
Broberg, K. B.: The near-tip field at high crack velocities, International
J. Fract., 39, 1–13, https://doi.org/10.1007/BF00047435, 1989. a, b
Camponovo, C. and Schweizer, J.: Measurements on skier triggering, in:
Proceedings of the International Snow Science Workshop 1996, 100–103, http://arc.lib.montana.edu/snow-science/item/1415 (last access: 29 March 2023),
1997. a
De Barros, S. T.: Deflection factor charts for two-and three-layer elastic
systems, Highway Research Record, 145, 83–108, http://onlinepubs.trb.org/Onlinepubs/hrr/1966/145/145-005.pdf (last access: 29 March 2023), 1966. a
Föhn, P. M. B.: Simulation of surface-hoar layers for snow-cover
models, Ann. Glaciol., 32, 19–26, https://doi.org/10.3189/172756401781819490,
2001. a
Fraisse, P. and Schmit, F.: Use of J-integral as fracture parameter in
simplified analysis of bonded joints, Int. J. Fract., 63,
59–73, 1993. a
Gaume, J. and Reuter, B.: Assessing snow instability in skier-triggered snow
slab avalanches by combining failure initiation and crack propagation, Cold
Reg. Sci. Technol., 144, 6–15,
https://doi.org/10.1016/j.coldregions.2017.05.011, 2017. a, b
Gaume, J., van Herwijnen, A., Chambon, G., Birkeland, K. W., and Schweizer, J.: Modeling of crack propagation in weak snowpack layers using the discrete element method, The Cryosphere, 9, 1915–1932, https://doi.org/10.5194/tc-9-1915-2015, 2015. a
Gaume, J., van Herwijnen, A., Chambon, G., Wever, N., and Schweizer, J.: Snow fracture in relation to slab avalanche release: critical state for the onset of crack propagation, The Cryosphere, 11, 217–228, https://doi.org/10.5194/tc-11-217-2017, 2017. a
Gaume, J., Gast, T., Teran, J., van Herwijnen, A., and Jiang, C.: Dynamic
anticrack propagation in snow, Nat. Commun., 9, 3047,
https://doi.org/10.1038/s41467-018-05181-w, 2018. a
Gauthier, D. and Jamieson, B.: Evaluation of a prototype field test for
fracture and failure propagation propensity in weak snowpack layers, Cold
Reg. Sci. Technol., 51, 87–97,
https://doi.org/10.1016/j.coldregions.2007.04.005,
2008. a
Geldsetzer, T. and Jamieson, B.: Estimating dry snow density from grain form
and hand hardness, in: International Snow Science Workshop, 121–127, https://arc.lib.montana.edu/snow-science/item/717 (last access: 29 March 2023),
2000. a
Gerling, B., Löwe, H., and van Herwijnen, A.: Measuring the Elastic
Modulus of Snow, Geophys. Res. Lett., 44, 11088–11096,
https://doi.org/10.1002/2017GL075110, 2017. a
Goland, M. and Reissner, E.: The stresses in cemented joints, J.
Appl. Mech., 11, A17–A27, 1944. a
Heierli, J.: Anticrack model for slab avalanche release, PhD thesis,
Universität Karlsruhe, https://doi.org/10.5445/IR/1000011033, 2008. a
Heierli, J. and Zaiser, M.: An analytical model for fracture nucleation in
collapsible stratifications, Geophys. Res. Lett., 33, L06501,
https://doi.org/10.1029/2005GL025311, 2006. a
Heierli, J. and Zaiser, M.: Failure initiation in snow stratifications
containing weak layers: Nucleation of whumpfs and slab avalanches, Cold
Reg. Sci. Technol., 52, 385–400,
https://doi.org/10.1016/j.coldregions.2007.02.007, 2008. a
Huang, Y. H.: Slope Stability Analysis by the Limit Equilibrium, American
Society of Civil Engineers, ISBN 978-0-7844-1288-6, 2014. a
Hübsch, J. D., Rosendahl, P. L., and Mittelstedt, C.: An analytical
failure model for pressurized blister tests of thermally loaded composite
laminates, Compos. Part B-Eng., 214, 108588,
https://doi.org/10.1016/j.compositesb.2020.108588, 2021. a
Jamieson, B. and Schweizer, J.: Texture and strength changes of buried
surface-hoar layers with implications for dry snow-slab avalanche release,
J. Glaciol., 46, 151–160, https://doi.org/10.3189/172756500781833278, 2000. a
Jamieson, J. and Johnston, C.: Refinements to the stability index for
skier-triggered dry-slab avalanches, Ann. Glaciol., 26, 296–302,
1998. a
Jones, R. M.: Mechanics of composite materials, 2nd Edn., CRC press, ISBN 9781315272986, https://doi.org/10.1201/9781498711067, 1998. a
Klarmann, R. and Schweizerhof, K.: A Priori Verbesserung von
Schubkorrekturfaktoren zur Berechnung von geschichteten anisotropen
Schalentragwerken, Arch. Appl. Mech., 63, 73–85,
https://doi.org/10.1007/BF00788914, 1993. a
Krenk, S.: Energy release rate of symmetric adhesive joints, Eng.
Fract. Mech., 43, 549–559, https://doi.org/10.1016/0013-7944(92)90198-N, 1992. a, b
Leguillon, D.: Strength or toughness? A criterion for crack onset at a notch,
Eur. J. Mech. A-Solid., 21, 61–72,
https://doi.org/10.1016/S0997-7538(01)01184-6, 2002. a
Lehning, M., Fierz, C., Brown, B., and Jamieson, B.: Modeling snow instability
with the snow-cover model SNOWPACK, Ann. Glaciol., 38, 331–338, 2004. a
McClung, D.: Fracture energy applicable to dry snow slab avalanche release,
Geophys. Res. Lett., 34, L02503, https://doi.org/10.1029/2006GL028238, 2007. a
McClung, D. and Schweizer, J.: Fracture toughness of dry snow slab avalanches
from field measurements, J. Geophys. Res.-Earth, 111, F04008, https://doi.org/10.1029/2005JF000403,
2006. a
McClung, D. M.: Shear Fracture Precipated by Strain Softening as a Mechanism
of Dry Slab Avalanche Release, J. Geophys. Res., 84,
3519–3526, 1979. a
McClung, D. M.: Fracture mechanical models of dry slab avalanche release,
J. Geophys. Res.-Sol. Ea., 86, 10783–10790,
https://doi.org/10.1029/JB086iB11p10783, 1981. a
McClung, D. M. and Schweizer, J.: Skier triggering, snow temperatures and the
stability index for dry-slab avalanche initiation, J. Glaciol.,
45, 190–200, https://doi.org/10.3189/002214399793377121, 1999. a
Morin, S., Horton, S., Techel, F., Bavay, M., Coléou, C., Fierz, C.,
Gobiet, A., Hagenmuller, P., Lafaysse, M., Ližar, M., Matjaž Ližar, Mitterer, C., Monti, F., Müller, K., Olefs, M., Snook, J. S., van Herwijnen, A., and Vionnet, V.:
Application of physical snowpack models in support of operational avalanche
hazard forecasting: A status report on current implementations and prospects
for the future, Cold Reg. Sci. Technol., 170, 102910, https://doi.org/10.1016/j.coldregions.2019.102910, 2020. a, b
Neuber, H.: Theorie der technischen Formzahl, Forschung auf dem Gebiete des
Ingenieurwesens, 7, 271–274, https://doi.org/10.1007/BF02584908, 1936. a
Peterson, R. E.: Methods of correlating data from fatigue tests of stress
concentration specimens, in: Stephen Timoshenko Anniversary Volume,
Macmillan, New York, 179–183, 1938. a
Reddy, J. N.: Mechanics of Laminated Composite Plates and Shells: Theory and
Analysis, 2nd Edn., CRC Press, Boca Raton, https://doi.org/10.1201/b12409, 2003. a, b, c
Reiweger, I., Gaume, J., and Schweizer, J.: A new mixed-mode failure criterion
for weak snowpack layers, Geophys. Res. Lett., 42, 1427–1432,
https://doi.org/10.1002/2014GL062780,
2015. a
Reuter, B., Schweizer, J., and van Herwijnen, A.: A process-based approach to estimate point snow instability, The Cryosphere, 9, 837–847, https://doi.org/10.5194/tc-9-837-2015, 2015. a
Richter, B., van Herwijnen, A., Rotach, M. W., and Schweizer, J.: Sensitivity of modeled snow stability data to meteorological input uncertainty, Nat. Hazards Earth Syst. Sci., 20, 2873–2888, https://doi.org/10.5194/nhess-20-2873-2020, 2020. a
Rosendahl, P. L. and Weißgraeber, P.: Modeling snow slab avalanches caused by weak-layer failure – Part 2: Coupled mixed-mode criterion for skier-triggered anticracks, The Cryosphere, 14, 131–145, https://doi.org/10.5194/tc-14-131-2020, 2020b. a, b, c, d
Rosendahl, P. L. and Weißgraeber, P.: Weak Layer Anticrack Nucleation
Model (WEAC), Zenodo [code], https://doi.org/10.5281/zenodo.5810763, 2022. a, b
Rosendahl, P. L. and Weißgraeber, P.: Weak Layer Anticrack Nucleation Model, https://pypi.org/project/weac/, last access: 28 March 2023. a
Rosendahl, P. L., Staudt, Y., Schneider, A. P., Schneider, J., and Becker, W.:
Nonlinear elastic finite fracture mechanics: Modeling mixed-mode crack
nucleation in structural glazing silicone sealants, Materials Design,
182, 108057, https://doi.org/10.1016/j.matdes.2019.108057, 2019. a
Schweizer, J.: The influence of the layered character of snow cover on the
triggering of slab avalanches, Ann. Glaciol., 18, 193–198,
https://doi.org/10.3189/S0260305500011496, 1993. a, b
Schweizer, J. and Camponovo, C.: The skier's zone of influence in triggering
slab avalanches, Ann. Glaciol., 32, 314–320,
https://doi.org/10.3189/172756401781819300, 2001a. a
Schweizer, J. and Camponovo, C.: The skier’s zone of influence in triggering
slab avalanches, Ann. Glaciol., 32, 314–320, 2001b. a
Schweizer, J. and Jamieson, J. B.: A threshold sum approach to stability
evaluation of manual snow profiles, Cold Reg. Sci. Technol., 47,
50–59, 2007. a
Schweizer, J. and Wiesinger, T.: Snow profile interpretation for stability
evaluation, Cold Reg. Sci. Technol., 33, 179–188, 2001. a
Schweizer, J., Schneebeli, M., Fierz, C., and Föhn, P. M.: Snow mechanics
and avalanche formation: Field experiments on the dynamic response of the
snow cover, Surv. Geophys., 16, 621–633, 1995. a
Sigrist, C.: Measurement of fracture mechanical properties of snow and
application to dry snow slab avalanche release, PhD thesis, ETH
Zürich, https://doi.org/10.3929/ethz-a-005282374, 2006.
a
Sigrist, C. and Schweizer, J.: Critical energy release rates of weak snowpack
layers determined in field experiments, Geophys. Res. Lett., 34, L03502,
https://doi.org/10.1029/2006GL028576, 2007. a, b, c
Sih, G. C.: Strain-energy-density factor applied to mixed mode crack
problems, Int. J. Fract., 10, 305–321,
https://doi.org/10.1007/BF00035493, 1974. a
Smith, F. and Curtis, J.: Stress analysis and failure prediction in avalanche
snowpacks, IAHS Publication, 114, 332–340, 1975. a
Smith, T. L. and Chu, W. H.: Ultimate tensile properties of elastomers. VII.
Effect of crosslink density on time–temperature dependence, J.
Polym. Sci. A2, 10, 133–150,
https://doi.org/10.1002/pol.1972.160100110, 1972. a
Stein, N., Weißgraeber, P., and Becker, W.: A model for brittle failure in
adhesive lap joints of arbitrary joint configuration, Compos. Struct.,
133, 707–718, 2015. a
Thumlert, S. and Jamieson, B.: Stress measurements in the snow cover below
localized dynamic loads, Cold Reg. Sci. Technol., 106-107,
28–35, https://doi.org/10.1016/j.coldregions.2014.06.002, 2014. a, b, c
van Herwijnen, A. and Jamieson, B.: Snowpack properties associated with
fracture initiation and propagation resulting in skier-triggered dry snow
slab avalanches, Cold Reg. Sci.Technol., 50, 13–22,
https://doi.org/10.1016/j.coldregions.2007.02.004, 2007. a, b, c, d
van Herwijnen, A., Gaume, J., Bair, E. H., Reuter, B., Birkeland, K. W., and
Schweizer, J.: Estimating the effective elastic modulus and specific
fracture energy of snowpack layers from field experiments, J.
Glaciol., 62, 997–1007, https://doi.org/10.1017/jog.2016.90, 2016. a, b, c
Waddoups, M. E., Eisenmann, J. R., and Kaminski, B. E.: Macroscopic Fracture
Mechanics of Advanced Composite Materials, J. Compos. Mater.,
5, 446–454, https://doi.org/10.1177/002199837100500402, 1971. a
Weißgraeber, P., Felger, J., Geipel, D., and Becker, W.: Cracks at
elliptical holes: Stress intensity factor and Finite Fracture Mechanics
solution, Eur. J. Mech. A-Solid., 55, 192–198,
https://doi.org/10.1016/j.euromechsol.2015.09.002, 2015. a
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.
The work presents a mathematical model that calculates the behavior of layered snow covers in...