Modeling of the Destabilization of Ice Chunks in Hanging Glaciers.

The prediction of large ice falls from hanging glaciers can reduce loss of live and damage to settlements. A common predictive method is based on the regular acceleration observed on large ice masses prior to the collapse. The failure time of a large ice chunk was forecasted quite accurately by Flotron (1977, Journal of Glaciology, 19(81), 671-672) for a hanging glacier located on the east face of the Weisshorn (Valais, Switzerland). On the basis of the velocity measured on the unstable part of this glacier, Flotron extrapolated the value of the velocity until the time of failure. The extrapolation was performed according to the equation

v(t)=v₀+a/(t_f-t)^m

which describes the increasing velocity v(t) of the unstable ice mass before breaking-off. t_f, a, m and v₀ are parameters. t_f corresponds to the failure time. This equation is widespread. It describes the fracture of materials like rock, soil and high-performance metal alloys and allows to predict high magnitude earthquakes with an uncertainty of 2 years. To improve this approach for hanging glaciers, a numerical model is developed to describe breaking-off processes.

The material discontinuities due to crevasses require a complex, time-depending model geometry. To avoid the description and the continuous adaptation of the glacier geometry, the ice and the crevasses are treated in a continuum approach as a unique domain composed of regions with distinct material properties. The difficulty of interface location can then be solved using a level set method.

The description of crevasse opening based on fracture mechanics implies a non-trivial criterion (C*-Integral) for crack propagation in a viscoelastic medium or assumes a linear elastic description of the fracture in ice. Furthermore, the sub-critical crack growth process, which is crucial to describe the dynamics of crack opening at low stress, has not been studied for ice so far. If multiple interacting crevasses or macro-fractured ice domains are considered, further difficulties emerge from fracture mechanics. To describe the progressive fracturing of a hanging glacier, continuum damage mechanics is an efficient alternative to fracture mechanics.

Numerical results show (see Figure) that the crevasse formation in glaciers can be well described using continuum damage mechanics. Furthermore, the crevassed surface can be easily computed with a level set method. In addition to the traditional ice flow equations, two field variables (level set and damage variables) as well as two differential equations (evolution of the damage variable and advection of the level set variable) need to be added to the flow model.