k P. Ba
ant and Goangseup ZiJOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. B2, 2119, doi:10.1029/2002JB001884, 2003
Size effect law and fracture mechanics of the triggering of dry snow slab avalanches
Zdenk P. Baant and Goangseup Zi
Department of Civil Engineering, Northwestern University,
Evanston, Illinois, USA
Department of Geography, University of British Columbia,
Vancouver, British Columbia, Canada
Abstract
[1] A size effect law for fracture triggering in dry snow slabs of high enough length-to-thickness ratio is formulated, based on simplified one-dimensional analysis by equivalent linear elastic fracture mechanics. Viscoelastic effects during fracture are neglected. The derived law, which is analogous to Ba
ant's energetic size effect law developed for concrete and later for sea ice, fiber composites, rocks, and ceramics, is shown to agree with two-dimensional finite element analysis of mode II cohesive crack model with a finite residual shear stress. Fitting the proposed size effect law to fracture data for various slab thicknesses permits identifying the material fracture parameters. The value of preexisting shear stress in a thin weak zone of finite length is shown to have significant effect. There exists a certain critical snow depth, depending on the preexisting stress value, below which the size effect disappears. Practical applications require considering that the material properties (particularly the mode II fracture toughness or fracture energy) at the snow slab base are not constant but depend strongly on the slab thickness. This means that one must distinguish the material size effect from the structural size effect, and the combined size effect law must be obtained by introducing into the structural size effect law dependence of its parameters on snow thickness. The thickness dependence of these parameters can be obtained by matching the combined law to avalanche observations. Matching Perla's field data on 116 avalanches suggests that the mode II fracture toughness is approximately proportional to 1.8 power of snow thickness.
Received 20 March 2002; revised 8 August 2002; accepted 18 November 2002; published 25 February 2003.
Keywords: snow, avalanches, scaling, size effect, fracture mechanics.
Index Terms: 1827 Hydrology: Glaciology (1863); 1863 Hydrology: Snow and ice (1827); 3210 Mathematical Geophysics: Modeling; 3220 Mathematical Geophysics: Nonlinear dynamics; 8020 Structural Geology: Mechanics.
Citation: Baant, Z. P., G. Zi, and D. McClung, Size effect law and fracture mechanics of the triggering of dry snow slab avalanches, J. Geophys. Res., 108(B2), 2119, doi:10.1029/2002JB001884, 2003.