An analytical model for fracture nucleation in collapsible stratifications

Abstract

In collapsible stratifications a particular type of fracture can develop for which nucleation and propagation are governed by the transformation of gravitational energy into fracture energy. The associated nucleation problem is studied for a stratification consisting of an elastic surface layer, a collapsible intermediate layer and a rigid basal layer. An analytical model for fracture nucleation is obtained by calculating the energy ('crack energy') associated with a localized collapse of the intermediate layer. The size and energy of a critical crack are evaluated as functions of continuum properties of the strata. The theory is illustrated by an application to the case of whumpfs in collapsible snow stratifications. Citation: Heierli, J., and M. Zaiser

Critical energy release rates of weak snowpack layers determined in field experiments

“…The FEM results showed that bending contributed a considerable amount of energy to the available energy for crack propagation. These findings correspond well with the analytical model of Heierli and Zaiser [2006]. In order to replace the FE simulations by an analytical solution in the future, it should be considered that a potential analytical solution [such as Heierli and Zaiser , 2006] is easier to adapt to a rectangular test geometry, similar to Figure 2b.…”

“…These findings correspond well with the analytical model of Heierli and Zaiser [2006]. In order to replace the FE simulations by an analytical solution in the future, it should be considered that a potential analytical solution [such as Heierli and Zaiser, 2006] is easier to adapt to a rectangular test geometry, similar to Figure 2b. [19] Figure 4 shows that for slope angles lower than about 45°, i.e. in the relevant slope angle range for snow avalanche release, more than 50% of the energy was contributed by slope normal bending in our test setup.…”

Fracture propagation propensity in relation to snow slab avalanche release: Validating the Propagation Saw Test

“…This is not entirely unexpected, since both the FM and WLC models emphasize the physical process by which a fracture may start to propagate in an unstable snowpack configuration, and the conditions required to achieve that state. Heierli's [2005] and Heierli and Zaiser's [2006, 2008] analytical models do describe propagation process beyond initiation physically, but do not address the ability of the slab to transfer the disturbance. The emphasis of the recent approaches to describing propagation remains on the propensity of a slab‐weak layer system for the initiation of fracture propagation, rather than its ability to sustain it.…”

“…Fracture in a weak snowpack layer is known to be the primary failure in the sequence that leads to dry slab avalanche release [ Perla , 1975]; this weak layer fracture must first initiate, and then propagate up, down, and across a slope. This study was designed to validate the predictions of a new field‐test for weak snowpack layer fracture propagation propensity, which employs a method of initiating and observing fractures that is consistent with fracture propagation theories, including both slope parallel shear fracture mechanics (FM) [ McClung , 1979, 1981; Bazant et al , 2003; Louchet , 2001a, 2001b] and weak layer collapse (WLC) [ Heierli , 2005; Heierli and Zaiser , 2006, 2008], as well as emerging syntheses of FM and WLC concepts [ Sigrist , 2006; Sigrist and Schweizer , 2007; Heierli and Zaiser , 2008].…”

On the evolution of the snow surface during snowfall

“…[2] The physical properties of the natural snowpack are of great importance for many geophysical processes such as heat transfer [Kaempfer et al, 2005;Sturm et al, 2002], interaction with the turbulent boundary layer [Lehning et al, 2002], wind erosion [Clifton et al, 2006], failure and crack propagation [Sigrist and Schweizer, 2007;Heierli and Zaiser, 2006]. However, the ice structure within a natural snowpack is a non-equilibrium system which undergoes metamorphic changes induced by many physical and chemical processes [see, e.g., Arons and Colbeck, 1995;Schweizer et al, 2003, and references therein].…”