Glacial quarrying: a simple theoretical model

Abstract

Glacial quarrying remains enigmatic despite being long recognized as a primary, perhaps the dominant, process by which glaciers erode bedrock. The rate-limiting process appears to be subglacial rock fracture due to ice-induced mechanical stresses. To study this erosional process, a simple model of quarrying is developed for a glacier sliding over a periodic series of bedrock steps. Consideration of the balance of forces at the ice/rock interface and of the rate of cavity closure permits evaluation of ice-induced stresses on bedrock surfaces. The resulting stress distribution where ice loads are most concentrated near the corner of bedrock steps is evaluated using a simple elastic solution for the state of stress in a loaded quarter-plane. It is then used to determine whether fractures in the rock will grow, and to estimate the rate of progressive crack growth. Based on these crack-growth rates, an index of the quarrying rate is then calculated as a function of glaciological variables effective pressure and sliding velocity—and various bed parameteres. Considerable incentive exists for further analysis of quarrying, and for seeking field data to test the model.