FRACTURE-MECHANICS APPROACH TO PENETRATION OF SURFACE CREVASSES ON GLACIERS

In linear elastic fracture mechanics, the stress intensity factor is u sed to describe elastic stresses near the tip of a crack. Crack growth occurs when the stress intensity factor is larger than a critical val ue, the fracture toughness, which is a material parameter that applies to cracks of any size. For surface crevasses on glaciers, the net str ess intensity factor can be calculated by superimposing the effects of a tensile stress, the weight of the ice, and water pressure if the cr evasse is filled with water. The analysis is applied to individual and multiple crevasses to investigate the important factors determining c revasse depth. The model indicates that a single crevasse can only exi st if the tensile stress is larger than 30-80 kPa, depending on the fr acture toughness of glacier ice. Multiple crevasses result in a decrea se in stress intensity factor for any crevasse, thus reducing their de pth (all other factors being equal). Consequently, in a field of creva sses, a larger tensile stress is needed compared to an individual crev asse, to allow crevasse formation. Further, a water-filled crevasse or field of crevasses can reach the bottom of a glacier provided that th e water level is about 15 m below the surface, or higher, and the tens ile stress is larger than similar to 150 kPa. Compared to earlier stud ies, it is shown that accounting for the finite thickness of the glaci er has a small effect on the calculated stress intensity factor only i f the ratio of crevasse depth to ice thickness is larger than similar to 0.3. However, such deep crevasses can only exist if filled with wat er, in which case the crevasse may penetrate the ice completely and th e small error introduced by approximating the glacier as a semi-infini te plane is unimportant. It is more important to account for the lower density of the upper firn layers: this effect increases the maximum d epth of crevasses by almost a factor of two compared to the solution o f Weertman (1973) [Weertman, J., 1973. Can a water-filled crevasse rea ch the bottom surface of a glacier? IASH Publ. 95, 139-145.]. (C) 1998 Elsevier Science B.V.