Cj. Vanderveen, FRACTURE-MECHANICS APPROACH TO PENETRATION OF SURFACE CREVASSES ON GLACIERS, Cold regions science and technology, 27(1), 1998, pp. 31-47
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.