A NEW MODEL OF BEDROCK QUARRYING BY GLACIERS

Owing to climate as a potential driver for tectonic change, effects of glacial erosion on topographic relief and uplift of mountain belts have been widely debated. Increasingly this debate and related discussion of the genesis of distinctive glacial landforms, such as U-shaped valleys and overdeepened bedrock basins, is informed by results of landscape evolution models. They are grounded on a power-law rule that relates bedrock erosion rate to either glacier sliding speed or discharge. This rule is poorly linked to the principal process of glacial erosion: quarrying, in which bedrock blocks are dislodged from the bed by sliding ice.

A new model of quarrying allows this erosion rule to be evaluated. As in past quarrying models, increasing ice-bed separation is assumed to increase deviatoric stresses in the rock that cause subcritical crack growth. Unlike past quarrying models, bedrock strength heterogeneity resulting from pre-glacial fractures is included using a Weibull statistical distribution of rock strength. This strength distribution is predicated on a fundamental but neglected precept of rock mechanics: larger rock bodies have lower strengths because they have a greater probability of containing a large fracture. Including this effect in the model has a profound influence on the role of ice-bed separation in quarrying. Model results can, indeed, be closely fitted with a power-law erosion rule, but its nonlinearity, the range of sliding speed over which it applies, and erosion rates depend sensitively on bedrock strength heterogeneity and effective pressure. The model provides a vehicle for including rock strength variability in landscape evolution models and reinforces recent emphasis on the role of bedrock fractures in accelerating geomorphic processes.