Fracture mechanics approach to penetration of surface crevasses on glaciers

Abstract

In linear elastic fracture mechanics, the stress intensity factor is used to describe elastic stresses near the tip of a crack. Crack growth occurs when the stress intensity factor is larger than a critical value, the fracture toughness, which is a material parameter that applies to cracks of any size. For surface crevasses on glaciers, the net stress intensity factor can be calculated by superimposing the effects of a tensile stress, the weight of the ice, and water pressure if the crevasse is filled with water. The analysis is applied to individual and multiple crevasses to investigate the important factors determining crevasse depth. The model indicates that a single crevasse can only exist if the tensile stress is larger than 30–80 kPa, depending on the fracture toughness of glacier ice. Multiple crevasses result in a decrease in stress intensity factor for any crevasse, thus reducing their depth (all other factors being equal). Consequently, in a field of crevasses, a larger tensile stress is needed compared to an individual crevasse, to allow crevasse formation. Further, a water-filled crevasse or field of crevasses can reach the bottom of a glacier provided that the water level is about 15 m below the surface, or higher, and the tensile stress is larger than ∼150 kPa. Compared to earlier studies, it is shown that accounting for the finite thickness of the glacier has a small effect on the calculated stress intensity factor only if the ratio of crevasse depth to ice thickness is larger than ∼0.3. However, such deep crevasses can only exist if filled with water, in which case the crevasse may penetrate the ice completely and the small error introduced by approximating the glacier as a semi-infinite plane is unimportant. It is more important to account for the lower density of the upper firn layers: this effect increases the maximum depth of crevasses by almost a factor of two compared to the solution of Weertman (1973) [Weertman, J., 1973. Can a water-filled crevasse reach the bottom surface of a glacier? IASH Publ. 95, 139–145.].