Simulation and characterization of fracture patterns in glaciers

During drainage of subglacial lakes the surface of the glacier subsides and fractures, generating a homogeneous, circular fracture pattern on the rim of the resulting depression. We have analyzed several fracture patterns aro und the Skafta cauldron on Iceland, A regular fracture spacing was observed on the cauldron rim, indicating that the region was subjected to a uniform strain. In this region, standard image analysis techniques were applied to find the lengths L and open areas A of the fractures. We demonstrate that an understanding of sampling biases allows a scaling relation L proportiona l to A(beta) to be established and the exponent beta to be determined. This relation provides a quantitative characterization of interactions between fractures in the population. The value of beta is higher for that observed for laboratory experiments on clay, but the uncertainties do not rule out a universal behavior, which applies to ice, rock, and all other solids. The size distribution bf fractures did not display a similarly simple crossover behavior, and a power law scaling relation could not be established withou t a better understanding of the crossovers for large fractures. We introduc e a simple simulation model that reproduces the most important visual and s tatistical properties of the glacier fracture pattern. The direct compariso n validates the use of the model to simulate geological fracturing processe s.