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
Related authors
Philipp L. Rosendahl, Johannes Schneider, Grégoire Bobillier, Florian Rheinschmidt, Bastian Bergfeld, Alec van Herwijnen, and Philipp Weißgraeber
Nat. Hazards Earth Syst. Sci. Discuss., https://doi.org/10.5194/nhess-2024-122, https://doi.org/10.5194/nhess-2024-122, 2024
Revised manuscript under review for NHESS
Short summary
Short summary
Our research investigates the role of anticracks in snowpacks and their impact on avalanche formation, focusing on anticracks due to weak layer collapse. We discovered that slab touchdown on the snow below the weak layer decreases the energy available for crack propagation, potentially leading to a stop of crack propagation. This underscores the importance of mechanical interactions in snowpack stability. Our work offers new insights for enhancing avalanche prediction and mitigation strategies.
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.
Philipp L. Rosendahl and Philipp Weißgraeber
The Cryosphere, 14, 115–130, https://doi.org/10.5194/tc-14-115-2020, https://doi.org/10.5194/tc-14-115-2020, 2020
Short summary
Short summary
Dry-snow slab avalanche release is preceded by a fracture process within the snowpack. Recognizing weak layer collapse as an integral part of the fracture process is crucial and explains phenomena such as whumpf sounds and remote triggering of avalanches from low-angle terrain. In this first part of the two-part work we propose a novel closed-form analytical model for a snowpack that provides a highly efficient and precise analysis of the mechanical response of a loaded snowpack.
Philipp L. Rosendahl and Philipp Weißgraeber
The Cryosphere, 14, 131–145, https://doi.org/10.5194/tc-14-131-2020, https://doi.org/10.5194/tc-14-131-2020, 2020
Short summary
Short summary
Dry-snow slab avalanche release is preceded by a fracture process within the snowpack. Recognizing weak layer collapse as an integral part of the fracture process is crucial and explains phenomena such as whumpf sounds and remote triggering of avalanches from low-angle terrain. In this second part of the two-part work we propose a novel mixed-mode coupled stress and energy failure criterion for nucleation of weak layer failure due to external loading of the snowpack.
Philipp L. Rosendahl, Johannes Schneider, Grégoire Bobillier, Florian Rheinschmidt, Bastian Bergfeld, Alec van Herwijnen, and Philipp Weißgraeber
Nat. Hazards Earth Syst. Sci. Discuss., https://doi.org/10.5194/nhess-2024-122, https://doi.org/10.5194/nhess-2024-122, 2024
Revised manuscript under review for NHESS
Short summary
Short summary
Our research investigates the role of anticracks in snowpacks and their impact on avalanche formation, focusing on anticracks due to weak layer collapse. We discovered that slab touchdown on the snow below the weak layer decreases the energy available for crack propagation, potentially leading to a stop of crack propagation. This underscores the importance of mechanical interactions in snowpack stability. Our work offers new insights for enhancing avalanche prediction and mitigation strategies.
Bastian Bergfeld, Karl W. Birkeland, Valentin Adam, Philipp L. Rosendahl, and Alec van Herwijnen
EGUsphere, https://doi.org/10.5194/egusphere-2024-690, https://doi.org/10.5194/egusphere-2024-690, 2024
Short summary
Short summary
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.
Philipp L. Rosendahl and Philipp Weißgraeber
The Cryosphere, 14, 115–130, https://doi.org/10.5194/tc-14-115-2020, https://doi.org/10.5194/tc-14-115-2020, 2020
Short summary
Short summary
Dry-snow slab avalanche release is preceded by a fracture process within the snowpack. Recognizing weak layer collapse as an integral part of the fracture process is crucial and explains phenomena such as whumpf sounds and remote triggering of avalanches from low-angle terrain. In this first part of the two-part work we propose a novel closed-form analytical model for a snowpack that provides a highly efficient and precise analysis of the mechanical response of a loaded snowpack.
Philipp L. Rosendahl and Philipp Weißgraeber
The Cryosphere, 14, 131–145, https://doi.org/10.5194/tc-14-131-2020, https://doi.org/10.5194/tc-14-131-2020, 2020
Short summary
Short summary
Dry-snow slab avalanche release is preceded by a fracture process within the snowpack. Recognizing weak layer collapse as an integral part of the fracture process is crucial and explains phenomena such as whumpf sounds and remote triggering of avalanches from low-angle terrain. In this second part of the two-part work we propose a novel mixed-mode coupled stress and energy failure criterion for nucleation of weak layer failure due to external loading of the snowpack.
Related subject area
Discipline: Snow | Subject: Natural Hazards
Impact of climate change on snow avalanche activity in the Swiss Alps
Interactive snow avalanche segmentation from webcam imagery: results, potential, and limitations
Snow mechanical property variability at the slope scale – implication for snow mechanical modelling
Combining modelled snowpack stability with machine learning to predict avalanche activity
Can Saharan dust deposition impact snowpack stability in the French Alps?
A random forest model to assess snow instability from simulated snow stratigraphy
Using snow depth observations to provide insight into the quality of snowpack simulations for regional-scale avalanche forecasting
Snow Avalanche Frequency Estimation (SAFE): 32 years of monitoring remote avalanche depositional zones in high mountains of Afghanistan
Brief communication: Weak control of snow avalanche deposit volumes by avalanche path morphology
Elevation-dependent trends in extreme snowfall in the French Alps from 1959 to 2019
Dynamic crack propagation in weak snowpack layers: insights from high-resolution, high-speed photography
Avalanche danger level characteristics from field observations of snow instability
Using avalanche problems to examine the effect of large-scale atmosphere–ocean oscillations on avalanche hazard in western Canada
On the importance of snowpack stability, the frequency distribution of snowpack stability, and avalanche size in assessing the avalanche danger level
The mechanical origin of snow avalanche dynamics and flow regime transitions
On the relation between avalanche occurrence and avalanche danger level
Validating modeled critical crack length for crack propagation in the snow cover model SNOWPACK
Where are the avalanches? Rapid SPOT6 satellite data acquisition to map an extreme avalanche period over the Swiss Alps
Cold-to-warm flow regime transition in snow avalanches
Stephanie Mayer, Martin Hendrick, Adrien Michel, Bettina Richter, Jürg Schweizer, Heini Wernli, and Alec van Herwijnen
The Cryosphere, 18, 5495–5517, https://doi.org/10.5194/tc-18-5495-2024, https://doi.org/10.5194/tc-18-5495-2024, 2024
Short summary
Short summary
Understanding the impact of climate change on snow avalanche activity is crucial for safeguarding lives and infrastructure. Here, we project changes in avalanche activity in the Swiss Alps throughout the 21st century. Our findings reveal elevation-dependent patterns of change, indicating a decrease in dry-snow avalanches alongside an increase in wet-snow avalanches at elevations above the current treeline. These results underscore the necessity to revisit measures for avalanche risk mitigation.
Elisabeth D. Hafner, Theodora Kontogianni, Rodrigo Caye Daudt, Lucien Oberson, Jan Dirk Wegner, Konrad Schindler, and Yves Bühler
The Cryosphere, 18, 3807–3823, https://doi.org/10.5194/tc-18-3807-2024, https://doi.org/10.5194/tc-18-3807-2024, 2024
Short summary
Short summary
For many safety-related applications such as road management, well-documented avalanches are important. To enlarge the information, webcams may be used. We propose supporting the mapping of avalanches from webcams with a machine learning model that interactively works together with the human. Relying on that model, there is a 90% saving of time compared to the "traditional" mapping. This gives a better base for safety-critical decisions and planning in avalanche-prone mountain regions.
Francis Meloche, Francis Gauthier, and Alexandre Langlois
The Cryosphere, 18, 1359–1380, https://doi.org/10.5194/tc-18-1359-2024, https://doi.org/10.5194/tc-18-1359-2024, 2024
Short summary
Short summary
Snow avalanches are a dangerous natural hazard. Backcountry recreationists and avalanche practitioners try to predict avalanche hazard based on the stability of snow cover. However, snow cover is variable in space, and snow stability observations can vary within several meters. We measure the snow stability several times on a small slope to create high-resolution maps of snow cover stability. These results help us to understand the snow variation for scientists and practitioners.
Léo Viallon-Galinier, Pascal Hagenmuller, and Nicolas Eckert
The Cryosphere, 17, 2245–2260, https://doi.org/10.5194/tc-17-2245-2023, https://doi.org/10.5194/tc-17-2245-2023, 2023
Short summary
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Avalanches are a significant issue in mountain areas where they threaten recreationists and human infrastructure. Assessments of avalanche hazards and the related risks are therefore an important challenge for local authorities. Meteorological and snow cover simulations are thus important to support operational forecasting. In this study we combine it with mechanical analysis of snow profiles and find that observed avalanche data improve avalanche activity prediction through statistical methods.
Oscar Dick, Léo Viallon-Galinier, François Tuzet, Pascal Hagenmuller, Mathieu Fructus, Benjamin Reuter, Matthieu Lafaysse, and Marie Dumont
The Cryosphere, 17, 1755–1773, https://doi.org/10.5194/tc-17-1755-2023, https://doi.org/10.5194/tc-17-1755-2023, 2023
Short summary
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Saharan dust deposition can drastically change the snow color, turning mountain landscapes into sepia scenes. Dust increases the absorption of solar energy by the snow cover and thus modifies the snow evolution and potentially the avalanche risk. Here we show that dust can lead to increased or decreased snowpack stability depending on the snow and meteorological conditions after the deposition event. We also show that wet-snow avalanches happen earlier in the season due to the presence of dust.
Stephanie Mayer, Alec van Herwijnen, Frank Techel, and Jürg Schweizer
The Cryosphere, 16, 4593–4615, https://doi.org/10.5194/tc-16-4593-2022, https://doi.org/10.5194/tc-16-4593-2022, 2022
Short summary
Short summary
Information on snow instability is crucial for avalanche forecasting. We introduce a novel machine-learning-based method to assess snow instability from snow stratigraphy simulated with the snow cover model SNOWPACK. To develop the model, we compared observed and simulated snow profiles. Our model provides a probability of instability for every layer of a simulated snow profile, which allows detection of the weakest layer and assessment of its degree of instability with one single index.
Simon Horton and Pascal Haegeli
The Cryosphere, 16, 3393–3411, https://doi.org/10.5194/tc-16-3393-2022, https://doi.org/10.5194/tc-16-3393-2022, 2022
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Snowpack models can help avalanche forecasters but are difficult to verify. We present a method for evaluating the accuracy of simulated snow profiles using readily available observations of snow depth. This method could be easily applied to understand the representativeness of available observations, the agreement between modelled and observed snow depths, and the implications for interpreting avalanche conditions.
Arnaud Caiserman, Roy C. Sidle, and Deo Raj Gurung
The Cryosphere, 16, 3295–3312, https://doi.org/10.5194/tc-16-3295-2022, https://doi.org/10.5194/tc-16-3295-2022, 2022
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Snow avalanches cause considerable material and human damage in all mountain regions of the world. We present the first model to automatically inventory avalanche deposits at the scale of a catchment area – here the Amu Panj in Afghanistan – every year since 1990. This model called Snow Avalanche Frequency Estimation (SAFE) is available online on the Google Engine. SAFE has been designed to be simple and universal to use. Nearly 810 000 avalanches were detected over the 32 years studied.
Hippolyte Kern, Nicolas Eckert, Vincent Jomelli, Delphine Grancher, Michael Deschatres, and Gilles Arnaud-Fassetta
The Cryosphere, 15, 4845–4852, https://doi.org/10.5194/tc-15-4845-2021, https://doi.org/10.5194/tc-15-4845-2021, 2021
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Snow avalanches are a major component of the mountain cryosphere that often put people, settlements, and infrastructures at risk. This study investigated avalanche path morphological factors controlling snow deposit volumes, a critical aspect of snow avalanche dynamics that remains poorly known. Different statistical techniques show a slight but significant link between deposit volumes and avalanche path morphology.
Erwan Le Roux, Guillaume Evin, Nicolas Eckert, Juliette Blanchet, and Samuel Morin
The Cryosphere, 15, 4335–4356, https://doi.org/10.5194/tc-15-4335-2021, https://doi.org/10.5194/tc-15-4335-2021, 2021
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Extreme snowfall can cause major natural hazards (avalanches, winter storms) that can generate casualties and economic damage. In the French Alps, we show that between 1959 and 2019 extreme snowfall mainly decreased below 2000 m of elevation and increased above 2000 m. At 2500 m, we find a contrasting pattern: extreme snowfall decreased in the north, while it increased in the south. This pattern might be related to increasing trends in extreme snowfall observed near the Mediterranean Sea.
Bastian Bergfeld, Alec van Herwijnen, Benjamin Reuter, Grégoire Bobillier, Jürg Dual, and Jürg Schweizer
The Cryosphere, 15, 3539–3553, https://doi.org/10.5194/tc-15-3539-2021, https://doi.org/10.5194/tc-15-3539-2021, 2021
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The modern picture of the snow slab avalanche release process involves a
dynamic crack propagation phasein which a whole slope becomes detached. The present work contains the first field methodology which provides the temporal and spatial resolution necessary to study this phase. We demonstrate the versatile capabilities and accuracy of our method by revealing intricate dynamics and present how to determine relevant characteristics of crack propagation such as crack speed.
Jürg Schweizer, Christoph Mitterer, Benjamin Reuter, and Frank Techel
The Cryosphere, 15, 3293–3315, https://doi.org/10.5194/tc-15-3293-2021, https://doi.org/10.5194/tc-15-3293-2021, 2021
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Snow avalanches threaten people and infrastructure in snow-covered mountain regions. To mitigate the effects of avalanches, warnings are issued by public forecasting services. Presently, the five danger levels are described in qualitative terms. We aim to characterize the avalanche danger levels based on expert field observations of snow instability. Our findings contribute to an evidence-based description of danger levels and to improve consistency and accuracy of avalanche forecasts.
Pascal Haegeli, Bret Shandro, and Patrick Mair
The Cryosphere, 15, 1567–1586, https://doi.org/10.5194/tc-15-1567-2021, https://doi.org/10.5194/tc-15-1567-2021, 2021
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Numerous large-scale atmosphere–ocean oscillations including the El Niño–Southern Oscillation, the Pacific Decadal Oscillation, the Pacific North American Teleconnection Pattern, and the Arctic Oscillation are known to substantially affect winter weather patterns in western Canada. Using avalanche problem information from public avalanche bulletins, this study presents a new approach for examining the effect of these atmospheric oscillations on the nature of avalanche hazard in western Canada.
Frank Techel, Karsten Müller, and Jürg Schweizer
The Cryosphere, 14, 3503–3521, https://doi.org/10.5194/tc-14-3503-2020, https://doi.org/10.5194/tc-14-3503-2020, 2020
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Exploring a large data set of snow stability tests and avalanche observations, we quantitatively describe the three key elements that characterize avalanche danger: snowpack stability, the frequency distribution of snowpack stability, and avalanche size. The findings will aid in refining the definitions of the avalanche danger scale and in fostering its consistent usage.
Xingyue Li, Betty Sovilla, Chenfanfu Jiang, and Johan Gaume
The Cryosphere, 14, 3381–3398, https://doi.org/10.5194/tc-14-3381-2020, https://doi.org/10.5194/tc-14-3381-2020, 2020
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This numerical study investigates how different types of snow avalanches behave, how key factors affect their dynamics and flow regime transitions, and what are the underpinning rules. According to the unified trends obtained from the simulations, we are able to quantify the complex interplay between bed friction, slope geometry and snow mechanical properties (cohesion and friction) on the maximum velocity, runout distance and deposit height of the avalanches.
Jürg Schweizer, Christoph Mitterer, Frank Techel, Andreas Stoffel, and Benjamin Reuter
The Cryosphere, 14, 737–750, https://doi.org/10.5194/tc-14-737-2020, https://doi.org/10.5194/tc-14-737-2020, 2020
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Snow avalanches represent a major natural hazard in seasonally snow-covered mountain regions around the world. To avoid periods and locations of high hazard, avalanche warnings are issued by public authorities. In these bulletins, the hazard is characterized by a danger level. Since the danger levels are not well defined, we analyzed a large data set of avalanches to improve the description. Our findings show discrepancies in present usage of the danger scale and show ways to improve the scale.
Bettina Richter, Jürg Schweizer, Mathias W. Rotach, and Alec van Herwijnen
The Cryosphere, 13, 3353–3366, https://doi.org/10.5194/tc-13-3353-2019, https://doi.org/10.5194/tc-13-3353-2019, 2019
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Information on snow stability is important for avalanche forecasting. To improve the stability estimation in the snow cover model SNOWPACK, we suggested an improved parameterization for the critical crack length. We compared 3 years of field data to SNOWPACK simulations. The match between observed and modeled critical crack lengths greatly improved, and critical weak layers appear more prominently in the modeled vertical profile of critical crack length.
Yves Bühler, Elisabeth D. Hafner, Benjamin Zweifel, Mathias Zesiger, and Holger Heisig
The Cryosphere, 13, 3225–3238, https://doi.org/10.5194/tc-13-3225-2019, https://doi.org/10.5194/tc-13-3225-2019, 2019
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We manually map 18 737 avalanche outlines based on SPOT6 optical satellite imagery acquired in January 2018. This is the most complete and accurate avalanche documentation of a large avalanche period covering a big part of the Swiss Alps. This unique dataset can be applied for the validation of other remote-sensing-based avalanche-mapping procedures and for updating avalanche databases to improve hazard maps.
Anselm Köhler, Jan-Thomas Fischer, Riccardo Scandroglio, Mathias Bavay, Jim McElwaine, and Betty Sovilla
The Cryosphere, 12, 3759–3774, https://doi.org/10.5194/tc-12-3759-2018, https://doi.org/10.5194/tc-12-3759-2018, 2018
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Snow avalanches show complicated flow behaviour, characterized by several flow regimes which coexist in one avalanche. In this work, we analyse flow regime transitions where a powder snow avalanche transforms into a plug flow avalanche by incorporating warm snow due to entrainment. Prediction of such a transition is very important for hazard mitigation, as the efficiency of protection dams are strongly dependent on the flow regime, and our results should be incorporated into avalanche models.
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...