A scale-invariant model for snow slab avalanches

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2009, Issue 2, 2009, Pages

  Chiaia, B ^a   Frigo, B ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Avalanches (theory); Renormalization group

Indexed keywords

EID: 65449155540     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2009/02/P02056     Document Type: Article

References (54)

1. Allègre C J, Le Mouel J L and Provost A 1982 Scaling rules in rock fracture and possible implications for earthquake prediction Nature 297 47 (Pubitemid 12279400)
2. Bader H and Salm B 1990 On the mechanics of snow slab release Cold Reg. Sci. Technol. 17 287 (Pubitemid 20674304)
3. Barpi F, Borri-Brunetto M and Delli Veneri L 2007 Cellular-automata model for dense-snow avalanches J. Cold Reg. Eng. 21 121 (Pubitemid 350162730)
4. Bažant Z P, Zi G and McClung D M 2003 Size effect law and fracture mechanics of the triggering of dry snow slab avalanche J. Geophys. Res. 108 2119 (Pubitemid 36821826)
5. Birkeland K W 2001 Spatial patterns of snow stability throughout a small mountain range J. Glaciol. 47 176
6. Birkeland K W and Landry C C 2002 Power-laws and snow avalanches Geophys. Res. Lett. 29 49 (Pubitemid 35274148)
7. Birkeland K, Kronholm K, Schneebeli M and Pielemeier C 2004 Changes in the shear strength and micro-penetration hardness of a buried surface hoar layer Ann. Glaciol. 38 223 (Pubitemid 40398528)
8. Carpinteri A 1994 Scaling laws and renormalization groups for strength and toughness of disordered materials Int. J. Solids Struct. 31 291
9. Carpinteri A and Chiaia B 1996 Size effects on concrete fracture energy: dimensional transition from order to disorder Mater. Struct. 29 259
10. Carpinteri A, Chiaia B and Invernizzi S 1999 Three-dimensional fractal analysis of concrete fracture at the meso-level Theor. Appl. Fract. Mech. 31 163
11. Chiaia B 2002 On the sliding instabilities at rough surfaces J. Mech. Phys. Solids 50 895 (Pubitemid 34201326)
12. Chiaia B, Cornetti P, Frigo B and Luisi A 2005 Triggering of dry snow slab avalanches and a new concept of active defence Proc. XVII Congresso Nazionale dell'Associazione Italiana di Meccanica Teorica ed Applicata (AIMETA) (Firenze (IT), Firenze University Press) CD-ROM
13. Chiaia B, Cornetti P and Frigo B 2008 Triggering of dry snow slab avalanches: stress versus fracture mechanical approach Cold Reg. Sci. Technol. 53 170
14. Chiaia B and Frigo B 2007 Fractal and RG model for snow avalanche release Proc. XVIII Congresso Nazionale dell'Associazione Italiana di Meccanica Teorica ed Applicata (AIMETA) (Brescia (IT), Starrylink Editrice) CD-ROM
15. Conway H and Abrahamson J 1988 Snowslope stability-a probabilistic approach J. Glaciol. 34 170
16. Faillettaz J 2003 Le déclenchement des avalanches de plaque de neige: de l'approche mécanique l'approche statistique PhD Thesis Université Joseph Fourier (Grenoble I) p 216
17. Faillettaz J, Louchet F and Grasso J R 2004 Two-threshold model for scaling laws of non-interacting snow avalanches Phys. Rev. Lett. 93 208001
18. Faillettaz J, Louchet F, Grasso J R, Daudon D and Dendievel R 2002 Scale invariance of snow triggering mechanisms Proc. of Int. Snow Science Workshop (Penticton, BC) pp528-31
19. Faillettaz J, Louchet F and Grasso J R 2003 Possible self-organised criticality of snow avalanches Proc. Jornadas SAM/CONAMET/MATERIA (San Carlos de Bariloche)
20. Falconer K 1990 Fractal Geometry Mathematical Foundations and Applications (New York: Wiley)
21. Föhn P M B 2000 Snowpack stability and avalanche forecasting European Summer University on Natural Hazard: Snow and Avalanches (Salardu (Val d'Aran)) (Grenoble: Ple Grenoblois d'Etudes et de Recherche pour la Prévention des Risques Naturels)
22. Harlow D G and Phoenix S L 1991 Approximations for the strength distribution and size effect in an idealized lattice model of material breakdown J. Mech. Phys. Solids 39 173
23. Heierli J and Zaiser M 2006 An analytical model for fracture nucleation in collapsible stratifications Geophys. Res. Lett. 33 L06501
24. Heierli J and Zaiser M 2008 Failure initiation in snow stratifications containing weak layers: nucleation of whumpfs and slab avalanches Cold Reg. Sci. Technol. 52 385
25. Herrmann H J and Roux S 1990 Statistical Models for the Fracture of Disordered Media (Amsterdam: Elsevier)
26. Kirchner H O K, Michot G, Narita H and Suzuki T 2001 Snow as a foam of ice: plasticity, fracture and the brittle-to-ductile transition Phil. Mag. A 81 2161
27. Kirchner H O, Peterlik H and Michot G 2004 Size independence of the strength of snow Phys. Rev. E 69 011306
28. Kronholm K and Birkeland K W 2004 Relating spatial variability to snow stability using a cellular automaton model initialized with field data Proc. 2004 Int. Snow Science Workshop (Jackson Hole, Wyoming)
29. Kronholm K and Schweizer J 2003 Snow stability variation on small slopes Cold Reg. Sci. Technol 37 453 (Pubitemid 37312650)
30. Kronholm K, Schweizer J, Schneebeli M and Pielmeier C 2001 Spatial variability of snowpack stability on small slopes studied with the Stuffblock test Proc. 2nd Int. Conf. Avalanches and Related Subjects (Kirovsk, Murmansk)
31. Lemaitre J and Chaboche J L 1990 Mechanics of Solid Materials (Cambridge: Cambridge University Press)
32. Logan S 2005 Temporal changes in the spatial patterns of weak layer shear strength and stability on uniform slopes MS Thesis Department of Earth Sciences, Montana State University p 157
33. Loreto V V, Pietronero L, Vespignani A and Zapperi S 1995 Renormalization group approach to the critical behaviour of the forest-fire model Phys. Rev. Lett. 75 465
34. Louchet F 2001 Creep instability of the weak layer and natural slab avalanche triggerings Cold Reg. Sci. Technol. 33 141 (Pubitemid 34002471)
35. Louchet F, Faillettaz J, Daudon D, Bédouin N, Collet E, Lhuissier J and Portal A M 2002 Possible deviations from Griffith's criterion in shallow slabs and consequences on slab avalanche release Nat. Hazards Earth Syst. Sci. 2 157
36. McClung D M 1979 Shear fracture precipitated by strain softening as a mechanism of dry slab avalanche release J. Geophys. Res. 84 3519
37. McClung D M 1981 Fracture mechanical models of dry slab avalanche release J. Geophys. Res. 86 10783
38. McClung D M 1987 Mechanics of snow slab failure from a geotechnical perspective IAHS Publication 162 475
39. McClung D and Schaerer P 1993 Manuale delle Valanghe Zanichelli Editore p248
40. Perla R 1982 Preparation of section planes in snow specimens J. Glaciol. 28 199
41. Perla R I and LaChapelle E R 1970 A theory of snow slab failure J. Geophys. Res. 75 7619
42. Plischke M and Bergersen B 1994 Equilibrium Statistical Physics 2nd edn (Singapore: World Scientific)
43. Roch A 1966 Les declenchements d'avalanches Symp. Int. Sur Les Aspects Scientifiques des Avalanches de Neige (Davos (CH)) pp182-95
44. Rosenthal W and Elder K 2003 Evidence of chaos in slab avalanching Cold Reg. Sci. Technol. 37 243 (Pubitemid 37312634)
45. Schweizer J 1999 Review of dry snow avalanche release Cold Reg. Sci. Technol. 30 43 (Pubitemid 30113149)
46. Schweizer J and Jamieson B 2003 Snow stability measurements Proc. Int. Seminar on Snow and Avalanche Test Sites (Grenoble) (Grenoble: CEMAGREF) pp317-31
47. Schweizer J, Kronholm K, Jamieson J B and Birkeland K W 2008 Review of spatial variability of snowpack properties and its importance for avalanche formation Cold Reg. Sci. Technol. 51 253
48. Smalley R F, Turcotte D L and Sola S A 1985 A renormalisation group approach to the stick-slip behaviour of faults J. Geophys. Res. 90 84-1900 (Pubitemid 15465810)
49. Turcotte D L 1992 Fractals and Chaos in Geology and Geophysics (Cambridge: Cambridge University Press)
50. Van Mier J G M, Chiaia B and Vervuurt A 1997 Numerical simulation of chaotic and self-organizing damage in brittle disordered materials Comput. Methods Appl. Mech. Eng. 42 189
51. Wilson K G 1971 Renormalization group and critical phenomena Phys. Rev. B 4 3174
52. Zaiser M 2004 Slab avalanche release viewed as interface fracture in a random medium Ann. Glaciol. 38 9 (Pubitemid 40398495)
53. Zeidler A and Jamieson B 2006 Refinements of empirical models to forecast the shear strength of persistent weak snow layers part A: layers of faceted crystals Cold Reg. Sci. Technol. 44 194
54. Zeidler A and Jamieson B 2006 Refinements of empirical models to forecast the shear strength of persistent weak snow layers. Part B: layers of surface hoar crystals Cold Reg. Sci. Technol. 44 184