A damage mechanics assessment of the Larsen B ice shelf prior to collapse: Toward a physically‐based calving law

Abstract

[1] Calving is a primary process of mass ablation for glaciers and ice sheets, though it still eludes a general physical law. Here, we propose a calving framework based on continuum damage mechanics coupled with the equations of viscous deformation of glacier ice. We introduce a scalar damage variable that quantifies the loss of load-bearing surface area due to fractures and that feeds back with ice viscosity to represent fracture-induced softening. The calving law is a standard failure criterion for viscous damaging materials and represents a macroscopic brittle instability quantified by a critical or threshold damage. We constrain this threshold using the Ice Sheet System Model (ISSM) by inverting for damage on the Larsen B ice shelf prior to its 2002 collapse. By analyzing the damage distribution in areas that subsequently calved, we conclude that calving occurs after fractures have reduced the load-bearing capacity of the ice by 60 AE 10%. Citation: Borstad, C. P., A. Khazendar, E. Larour, M. Morlighem, E. Rignot, M. P. Schodlok, and H. Seroussi (2012), A damage mechanics assessment of the Larsen B ice shelf prior to collapse: Toward a physically-based calving law, Geophys.

Combining damage and fracture mechanics to model calving

“…When the damage increases (D > 0), E > 1, the viscosity of the ice is reduced, and the velocity of the flow consequently increases. This formulation of the enhancement factor is consistent with the expected behaviour, and has already been used in previous studies, such as Borstad et al (2012). The damage then evolves under the effect of the stress field, where the ice undergoes a critical tensile stress σ th in the direction of the principal stress, and exerts positive feedback on the velocity field.…”

“…Slow deformation is typically encountered in glaciology, when ice flows slowly under its own weight following the surface slope. CDM has been successfully used in ice-flow models to deal with some glaciological problems such as the flow acceleration of large damaged areas or the opening of crevasses in hanging glaciers (Xiao and Jordaan, 1996;Pralong et al, 2003;Pralong and Funk, 2005;Jouvet et al, 2011;Borstad et al, 2012).…”

“…In the last few years, some authors have used continuum damage mechanics to represent both the development from micro-defects in the ice to the development of macro-scale crevasses, and their effects on the viscous behaviour of the ice while keeping a continuum approach (Duddu and Waisman, 2012;Borstad et al, 2012;Albrecht and Levermann, 2014). Initially developed for metal deformation (Kachanov, 1958), damage mechanics has recently been applied to ice dynamics to study the appearance of a single crevasse (Pralong et al, 2003;Pralong and Funk, 2005;Duddu and Waisman, 2013) or to average crevasse fields (Borstad et al, 2012).…”

“…Initially developed for metal deformation (Kachanov, 1958), damage mechanics has recently been applied to ice dynamics to study the appearance of a single crevasse (Pralong et al, 2003;Pralong and Funk, 2005;Duddu and Waisman, 2013) or to average crevasse fields (Borstad et al, 2012). Linear elastic fracture mechanics (van der Veen, 1998a, b) has been used to describe the rapid propagation of surface and bottom crevasses through the ice.…”

Modeling the instantaneous response of glaciers after the collapse of the Larsen B Ice Shelf

“…Adjoint methods have been used perviously to obtain information about the rheology of the LBIS before its disintegration [Vieli et al, 2006;Khazendar et al, 2007;Borstad et al, 2012], but an inversion for both slipperiness and rheology of the region, including the tributary glaciers, has not been attempted before. Our analysis simulates the important flow features with high surface velocities in the valleys and close-to-stagnant ice on the steep slopes and toward the Bruce Plateau.…”