Investigating Glacial Quarrying with Numerical Rock Fracture Simulations

Two principal processes are responsible for subglacial bedrock erosion: abrasion and quarrying, with quarrying accounting for about 75% of the overall erosion. Quarrying occurs o n the lee of bedrock obstacles as pressure exerted by the overriding ice on the bedrock causes preexisting bedrock fractures to propagate, eventually resulting in the isolation of bed rock blocks from the surrounding intact rock . The isolated blocks are then extracted by the overriding ice. Fracture propagation is considered the rate-limiting process for subglacial quarrying and thus the rate-limiting process for glacial erosion in general. Current models of quarrying rely on standard analytical approximations for fracture growth in a stepped bed (a quarter space model), though the validity of these approximations for quarrying are not known. Here, we study how the orientation of a preexisting fracture in a stepped bed geometry affects its stress intensity factor (and thus growth rate) using the finite element software (FEM) package COMSOL. We estimate the stress field for a range of crack lengths and orientations (0 to 30 degrees) and evaluate the J-integral around the crack tip to determine the fracture's mode-I stress intensity factor. Our results show that fractures exhibit divergent behavior depending on their initial orientation. Bed-perpendicular fractures demonstrate decelerating growth rates as they propagate through the bedrock step, whereas cracks angled only slightly (>8 degrees) towards the step ledge exhibit exponential growth rates. In both cases, the FEM J-integral results for estimating the stress intensity factor as a function of crack length differ fundamentally from the analytic quarter space model used in quarrying models . This indicates subglacial erosion rates estimated using the analytic fracture propagation solution could be problematic and that more sophisticated calculations from FEM are required for realistic estimates of subglacial erosion.