JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. B2, 2119, doi:10.1029/2002JB001884, 2003
[11] Under most conditions for which snow slabs get released (excluding application of explosives), the snow slab (as distinct from the weak layer) will be undergoing viscoelastic deformation. The viscoelastic behavior per se nevertheless cannot be the cause of fracture because, in the field, the rates of creep deformation leading to failure are typically 2 orders of magnitude lower than necessary to achieve strain-softening behavior.
[12] Striving for simplicity, we assume in this study that the slab behaves elastically when it is failing. Since, during failure, the slab rapidly releases energy and thus undergoes fast unloading, this seems not to be a bad assumption. The problem seems similar to what is obtained in concrete which, too, exhibits strong creep yet the creep effect in fracture is not major [Ba
ant and Li, 1997]. An extension to viscoelastic behavior, probably similar to that presented for concrete, might nevertheless be needed in future studies, for a completely realistic model. In this extension, one would need to take into account the fact that aside from viscoelasticity in the bulk of snow, the fracture in the weak layer must also be rate-sensitive and that this rate sensitivity is of a different kind than the bulk viscoelasticity [Baant and Li, 1997].
[13] Alpine snow, in similarity to other geomaterials, displays different shear failure characteristics, depending on the precise loading and deformation [e.g., McClung, 1981, 1987]. In the literature, one finds distinctions between the “load-controlled” and the so-called “strain-controlled” conditions. The former, which is also called the “direct action,” refers to fracture during progressive snow accumulation. The latter of course does not mean that the strain would actually be controlled (which is impossible) but simply refers to “delayed action,” meaning fracture after a storm. From the fracture mechanics viewpoint, the only distinction can be between load-controlled and displacement-controlled fractures, however, the difference between them occurs only for the postpeak load-softening response, while the triggering of an avalanche must occur at the peak of the load-displacement curve. As long as the avalanche is driven by the gravity of snow, whether or not accumulating, the failure is always load controlled, while a displacement control of an avalanche is hard to imagine. As for the snow properties for fracture at snow accumulation and for delayed fracture, they can of course be quite different.
[14] It must be emphasized, however, that both types of behavior are governed by the same material laws, the only difference being in the age effect on snow properties, and probably in the deformation rates produced by the different types of loading and in the conditions of stability of equilibrium of the whole specimen or structure [Ba
ant and Cedolin, 1991]. The gradual strain-softening with dilatancy in the weak zone of course takes place under load control as well, but only after stability has been lost and the failure has become dynamic. Assuming that no prescribed displacements are applied to the snow slab, all the loading is by gravity, i.e., by the accumulated weight of the snow slab. This corresponds to the load control conditions, for which the load during failure remains approximately constant. Such conditions, along with an approximately constant deformation rate, were implicitly assumed in the classical cohesive fracture analysis of Palmer and Rice [1973] and will be also assumed in this study. It is further assumed that the effects of inhomogeneity and anisotropy of the snow slab can be neglected in elastic fracture analysis, and that the strain can be considered small.
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.