f, has been reduced to some small finite residual value, r.JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. B2, 2119, doi:10.1029/2002JB001884, 2003
[2] There are two types of dry snow avalanches: (1) loose avalanches characterized by surface failures in snow that lacks cohesion and (2) slab avalanches characterized by snow which is cohesive enough to form a slab. Dry slab avalanches (the subject of this paper) are much larger and more destructive than loose snow avalanches [McClung and Schaerer, 1993; Daerr and Douady, 1999], and are responsible for most of the damage from avalanches.
[3] Dry snow slab avalanches initiate as brittle fractures in which the failure process becomes dynamic as soon as it is triggered. A drop of friction at the base after the layer of snow begins to slide is a common characteristic. As a result, the failure cannot be described in terms of plasticity, but fracture mechanics must be used. The sliding surface behaves as a shear (mode II) crack in which the initial frictional stress, f, has been reduced to some small finite residual value, r.
[4] Slides in overconsolidated clay are a similar phenomenon. Their fracture character was postulated by Palmer and Rice [1973]. They considered the fracture process zone at the front of a sliding crack to have some nonnegligible finite length (denoted here as 2cf) and formulated the failure condition in terms of Rice's J integral.
[5] In plasticity, the mechanical failure criterion is expressed in terms of the stress and strain tensors and their invariants. Such a criterion in general implies that there is no size effect, i.e., geometrically similar small and large structures fail at the same maximum stress, or at the same nominal stress 
N, defined as the average stress in a cross section of the structure. In fracture mechanics, by contrast, the material failure criterion is expressed in terms of either the energy release rate or the stress-displacement relation of the opening crack. This is now known to automatically imply a size effect on the nominal strength of the structure.
[6] The necessity of a size effect on clay slides was recognized, and its form discussed, by Palmer and Rice [1973], although without attempting to obtain an approximate general formula. A size effect in dry slab avalanches has been inferred from observations of avalanche fracture lines [Perla, 1971; McClung, 1979]. The study of Palmer and Rice [1973] was applied to the dry slab avalanches to formulate the crack propagation criteria for a dry snow slab [McClung, 1979, 1981].
[7] This study is aimed at obtaining a simple general analytical formula of asymptotic matching type through the use of equivalent linear elastic fracture mechanics (LEFM) and verifying it numerically by a two-dimensional cohesive crack model. The asymptotic analysis is based on a simplified model of one-dimensional sliding of a layer of snow of constant thickness, D, on a base of constant slope, 
.
[8] The stratigraphy of the dry snow slab always consists of a relatively thick strong (and stiff) slab on top of a weaker thin layer which fails in shear. Normally, the material below the weak layer is stronger (and stiffer) than that in the weak layer. In this paper, it is assumed that the snow below the weak layer is rigid, to simplify the analysis. In some cases, this is a very good assumption. This is especially true when the fracture develops over a stiff crust or ice layer.
[9] This simplifying assumption is not always completely justified but the general conclusions of the paper will not be affected by it. Thus, in general, the snow slab stratigraphy is such that shear failure initiates in the weak layer beneath the slab and then ultimately the failure becomes a rapid self-propagating shear fracture (modes II and III) within the weak layer [McClung, 1981]. In this paper, we consider slab avalanche initiation from the perspective of mode II fracture propagation, but extension to include mode III would be possible.
[10] For cohesive snow failing in shear, the snow is characterized as a pressure sensitive, dilatant, strain-softening material with significant rate- and temperature-dependent characteristics. In this paper, shear failure and shear fracture within the weak layer are analyzed from the perspective of LEFM assuming the slab above is elastic. However, these assumptions (elastic slab and strain-softening failure of a weak layer) require qualifiers for both the slab deformation model and weak layer failure, as explained in the following.
Citation: Ba
ant, 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.