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Anticrack Model for Slab Avalanche Release

Anticrack Model for Slab Avalanche Release

J Heierli


Dissertation, Universität Karlsruhe (TH), 19.12.2008

The aim of this thesis is to lay the groundwork for a new and comprehensive theory of slab avalanche release in dry snow. Simple shear fracture models have long been considered as standard explanation of slab avalanche formation. These models assume brittle fracture to take place in a slip plane of zero thickness. The change in strain energy in response to crack formation then depends only on the shear loading of the slip plane, but not on the compressive loading. In reality, the fracture process takes place in a weak layer composed of sparsely packed ice grains. When such a granular aggregate fails, the debris pack tighter and the weak layer undergoes a reduction in volume, resulting in the subsidence of overlying snowpack layers. As a consequence, the change in strain energy also depends on the compressive loading of the weak layer. It is shown that subsidence significantly contributes to the driving force for crack nucleation and crack propagation, and that failure nucleates as a mixed-mode anticrack and propagates as a non-linear wave which progressively delaminates the slab over a large area. In the first part of the work the mechanical energy of an anticrack resulting from a collapsed section in the weak layer is calculated. The anticrack experiences gravity-induced shear stress t and compressive stress s. It is shown that anticrack energy can be partitioned into a contribution proportional to tt and one proportional to ss. The energy of a notch can be partitioned into contributions proportional to tt, ts and ss. From the expressions for crack and notch energies, criteria for fracture propagation are deduced, in particular for cracks of size zero (spontaneous crack nucleation). It is found that skiers and gaps in the snowpack can nucleate slab avalanches even if there are no pre-cracked areas in the weak layer. In the second part of this work an asymptotic solution describing the propagation of fracture in weak layers is proposed. The corresponding action functional is formulated and non-linear wave solutions with velocity below the shear wave speed are analysed. Expressions for the propagation velocity, wavelength, deformation profile and dispersion of the non-linear collapse waves are obtained. Experimental evidence from field tests confirms the developed criterion for fracture propagation in weak layers. Experiments on long snow samples, in which the deformation field during fracture propagation is measured with high precision, confirm the calculated properties of the collapse waves. The anticrack model explains instabilities known as whumpfs, their connection with avalanche hazard, as well as the remote triggering of avalanches. The calculation leads to a two-stage scenario of slope failure. In the first stage, nucleation and propagation of a mixedmode anticrack delaminates the slab from the snow below. This process can occur with or without shear loading and for arbitrary amounts of crack-face friction. In the second stage frictional forces between the crack faces decide whether the slab will slide, causing an avalanche, or subside, causing a whumpf.