Numerical models are used commonly to study the topographic evolution of glacially eroded landscapes. These models are grounded on a power-law rule that relates bedrock erosion rate to either the sliding speed or discharge of glaciers. This rule, however, 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, ice-bed separation during sliding controls deviatoric stresses in the rock that cause crack growth. Unlike past models, bedrock strength heterogeneity resulting from preglacial fractures is included using a Weibull statistical distribution of rock strength. This strength distribution is predicated on the observation that larger rock bodies have lower strengths because they have a greater probability of containing a large fracture. 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. This theory anchors large-scale models of glacial erosion to the primary small-scale process that these models hope to simulate and reinforces recent emphasis on the role of bedrock fractures in accelerating geomorphic processes. Moreover, by linking basal water pressure to erosion rate, the theory can improve efforts with numerical models to study feedbacks between subglacial hydrology and landscape evolution.