The importance of bending in the formation of basal crevasses on ice shelves

Abstract:

Radar images of show that basal crevasses exist under most ice shelves and their role in the breakup of these shelves is much discussed. The spacing of basal crevasses in a particular region are relatively uniform. We report data showing that for basal crevasses with heights less than about half the ice layer thickness the distance between crevasses is close to the layer thickness. For crevasses with greater heights the distance between crevasses is several times the layer thickness. Previous analyses suggest that basal crevasse height in an elastic half space should depend linearly on the extensional stress, Sxx, applied to an ice layer. The buttressing stresses at the ice-shelf margins should act to reduce Sxx and so should affect the height of basal crevasses.

Given that standard linear-elastic-fracture-mechanics (LEFM) analyses of basal crevasse opening (e.g. Weertman, 1973) do not fully account for the bending of a floating elastic layer with a free surface, we applied a fully two-dimensional numerical model this problem. The boundary conditions are identical to the earlier studies with the maximum extensional deviatoric stress, Sxxmax, equal to the pressure applied by water on which ice layer floats. A series of cases were run with different values of R = Sxx/Sxxmax.

When the applied extensional stress is much lower than Sxxmax (i.e R<<1) new model resultsmatch predictions of the standard LEFM analysis in an elastic half-space. As the stress approaches the maximum stress the model ice layer bends significantly and the new results diverge markedly from the previous results. For Sxx = Sxxmax the calculated height of water filled basal crevasses is about 20% greater than that estimated in the standard analysis. In that case the width of basal crevasses is found to be more than twice that of the standard LEFM model. Also, for small values of R the width of the region of deviatoric stress reduction around a basal crevasse (the “stress shadow”) scales with the height of the crevasses. However, for R>~0.5 the width of the stress shadow is can approach several times the layer thickness.

We suggest that the width of the stress shadow may control the spacing of basal crevasses. Given that the height, opening width and stress shadow width of basal crevasses is a strong function of the stress experienced by an ice shelf the new model results may enable better estimation of buttressing stresses for different parts of ice shelves.