Ned Bair US Army Corps of Engineers Cold Regions Research and Engineering Laboratory Earth Research Institute, UC - Santa Barbara AVPRO 9-10AM 2/27/14.

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Ned Bair US Army Corps of Engineers Cold Regions Research and Engineering LaboratoryEarth Research Institute, UC - Santa BarbaraAVPRO9-10AM 2/27/14

Fracture mechanics

Snow as a material

Sigrist, C., 2006: Measurement of fracture mechanical properties of snow and application to dry snow slab avalanche release, doi:10.3929/ethz-a-005282374.

2The Weibull modulus of snowMaterialmSnow1-2Freshwater ice3-5Concrete12Steel25

Kirchner, H. O., H. Peterlik, and G. Michot, 2004: Size independence of the strength of snow. Phys. Rev. E, 69, 011306.

3Snow is weak, full of flaws, and unreliable.The extremely low Weibull modulus means that the failure of snow is highly unpredictable.

Jamieson, B. Regional Danger Ratings and the Odds of Triggering a Potentially Fatal Avalanche , The Avalanche Review, Vol 28, No. 1, October 2009, p. 15.If you are trying to find an avalanche expert, look under the avalanche debris. Jim Kanzler, 1949-20114Snow slope stability (SNOSS) model Strength/stress (stability index)Shear strength fx: Shear stress Density A=1.8-2.2104 Pa; b = 1.55-2.07 (Perla et al., 1982; Jamieson, 1995)P=SWE over some time interval tg and gravity and slope angle5

Perla, R., Beck, T., and Cheng, T.: The shear strength index of alpine snow, Cold Regions Science and Technology, 11-20, 10.1016/0165-232X(82)90040-4, 1982.Jamieson, J. B.: Avalanche prediction for persistent snow slabs, Department of Civil Engineering, University of Calgary, Calgary, AB, Canada, 258 pp., 1995.Conway, H., and Wilbour, C.: Evolution of slope stability during storms, Cold Regions Science and Technology, 30, 67-77, 10.1016/S0165-232X(99)00009-9, 1999.Shortcomings of SNOSSSnoss does not account account for fracture mechanical concepts, e.g. crack length and slab stiffness.In a fracture mechanical model, the concept of strength depends on these parameters.6What is fracture mechanics?In the 1920s it was known that glass fractured at stresses one or two orders of magnitude lower than its theoretical strength, computed based on breaking molecular bonds.

For his Ph.D. work, A.A. Griffith hypothesized this discrepancy was caused by many flaws (he called them scratches) that weakened the material.7Griffiths CriterionThe stress f at fracture decreases with increasing crack length a. C is a constant.8

Fundamental properties stress (Pa), internal forces, often separated into shear (yy) and compressive stress (xx)

strain (%), deformation

E (Effective) Elastic Modulus (MPa), slope of stress:strain curve; a measure of slab stiffness

wf - specific fracture energy or critical energy release rate (J m-2), energy release rate required for fracture; a measure of failure layer strength

9Linear elastic fracture mechanicsThe simplest form of fracture mechanicsStress is linearly proportional to strain . / is the Elastic Modulus E.Snow is not a linear elastic material, but it seems to be a reasonable approximation.

p. 76 of Sigrist (2006)5.5 MPa6.5 MPa10Brittle, ductile, and quasi-brittle

p. 21 of Sigrist (2006)11Brittle to ductile transition12Narita, H., 1980: Mechanical behavior and structure of snow under uniaxial tensile stress. Journal of Glaciology, 26, 275-282.Snow is ductile at low strain rates (< 10-5 s-1) and brittle at high strain rates (> 10-3 s-1, Narita 1980)

Photo courtesy of John McGrathAtomic level fracture13

Grain scale fracture14

Slope scale fracture15Fractures and cracksFracture is a process that creates a crack.

A crack is a flaw or discontinuity.

As long as there is more energy to feed the crack (i.e. bending and collapse of the slab) than resistance (i.e. strength of the failure layer), the crack will propagate.

The critical crack size is comparable to the critical length in a PST.

Cracks in failure layers travel at 10-45 m/s (22-101 mph, van Herwijnen and Birkeland, 2012).

16Birkeland, K. W., and A. van Herwijnen, 2012: Using High-speed Video to Better Understand Extended Column Tests. Proceedings of the 2012 International Snow Science Workshop, 98-103.Crack arrestG(a) is the driving force (energy release rate) of the crack. R is the material resistance. It can be constant, or it can change.17

Anderson, T. L.: Fracture Mechanics: Fundamentals and Applications, Taylor and Francis, Boca Raton, FL, 2005, p 38.Fracture modes18

Anderson, T. L.: Fracture Mechanics: Fundamentals and Applications, Taylor and Francis, Boca Raton, FL, 2005, p 43.19Simple shear model (McClung, 1979)Fractures propagate in shear wavesTriggering depends on slope angleFractures cannot propagate on flat ground

Anticrack model (Heierli et al., 2008)Fractures propagate as collapse wavesInitiation does not depend on slope angle, but whether a slab slides after collapse does.Explains whoompfing and remote triggering.

Fracture models

p 96 of The Avalanche Handbook, 3rd editionHeierli, J., Gumbsch, P., & Zaiser, M. (2008). Anticrack nucleation as triggering mechanism for snow slab avalanches. Science, 321, 240-243, doi: 10.1126/science.1153948.McClung, D.M. (1979). Shear fracture precipitated by strain softening as a mechanism of dry slab avalanche release. Journal of Geophysical Research, 84, 3519-3526, doi: 10.1029/JB084iB07p03519.Heierli et al. (2008)Critical lengths for shear and anticrack modelsMcClung (1979)Heierli et al. (2008)20

The anticrack model21An anticrack is collapse.

The model envisions fractures traveling in a mixed-mode collapse wave.

Triggering does not depend on slope angle.

Whether the slab whoompfs or whether it whoompfs and releases depends on the slope angle.Heierli, J., 2008: Anticrack model for slab avalanche release. Institut fr Zuverlaessigkeit von Bauteilen und Systemen, 113.22

Heierli, J., 2008: Anticrack model for slab avalanche release. Institut fr Zuverlaessigkeit von Bauteilen und Systemen, 113.Crack energy V

123456r, m

723Heierli, J., 2008: Anticrack model for slab avalanche release. Institut fr Zuverlaessigkeit von Bauteilen und Systemen, 113.Testing the anticrack modelECT and PST triggering shows slope angle invariance on persistent weak layers

Heierli, J., P. Gumbsch, and M. Zaiser, 2008: Anticrack nucleation as triggering mechanism for snow slab avalanches. Science, 321, 240-243, doi:10.1126/science.1153948.

Heierli, J., K. W. Birkeland, R. Simenhois, and P. Gumbsch, 2011: Anticrack model for skier triggering of slab avalanches. Cold Regions Science and Technology, 65, 372-381, doi:10.1016/j.coldregions.2010.10.008.24Implications of the anticrack modelYou can remotely trigger avalanches on all types of failure layers (e.g. precipitation particles, faceted crystals, and surface hoar).

You can dig pits in flat terrain, away from hazardous avalanche areas.25

Z. Guy, Colorado Avalanche Information CenterCollapse wave speed

26Field measurements of the elastic modulus E and specific fracture energy wfvan Herwijnen, A., E. H. Bair, B. Reuter, K. W. Birkeland, and J. Heierli, in preparation: Energy-based method for deriving fracture energy and elastic properties of snowpack layers. Journal of Glaciology.27

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van Herwijnen, A., E. H. Bair, B. Reuter, K. W. Birkeland, and J. Heierli, in preparation: Energy-based method for deriving fracture energy and elastic properties of snowpack layers. Journal of Glaciology.The expression is the shear stress at the weak layer reduced by residual crack-face friction . ghsin and r = min [ ghcos]. wf is the fracture energy, is slab density, E is the elastic modulus, is slope angle, and is the coefficient of friction.