Quarrying is a significant, locally dominant glacial erosion process. For settings where glaciers cut into partially intact bedrock, prior work has hypothesized that it occurs when glaciers impose spatially concentrated loads to drive fracture growth in the underlying rock, linking pre-existing fractures to complete dislodgment. This prior work, however, has not rigorously explained how most of this process occurs or whether it can leave the bed with a form susceptible to subsequent quarrying. We use a numerical model that combines finite element and discrete element capabilities to calculate the co-evolution of stress, elastic deformation, and fracturing in a granite and a weak sandstone containing discontinuous prior fractures. We find that quarrying is achievable in situations with rapid glacier sliding, as expected from prior work, but only if additional factors contribute. These include, especially, transient episodes when loading increasingly concentrates on the lips of bedrock steps, imposition of shear traction by friction between entrained clasts and the bed, and exploitation of anisotropic structural weaknesses in the bedrock. Hydraulic fracturing can significantly reduce the loads needed for quarrying if low hydraulic transmissivity allows for large water pressure differences between saturated fractures and the adjacent subglacial water system.