Hydraulic conditions for the propagation of pre-existing fracture in river bedrock and implication for landscape evolution

The growth of pre-existing bedrock fractures in running water plays an important role in landscape evolution. How fractures, formed by other geological processes, can be extended further by moderate water pressure to create blocks that can then be plucked by the flowing water is an open question. In this paper, the effect of hydrodynamic forcing on fracture growth that results in bedrock erosion is studied quantitatively to address this question. The fracturing process depends on the pre-existing fracture geometry, bedrock surface topology, local stresses, water flow rates and rock properties. A fracture-mechanics model coupling rock deformation and fluid flow is used to investigate the hydraulic conditions for propagation of a single pre-existing bedrock fracture. The numerical results show that fracture growth can occur and create fragments under the pressure levels for flow velocity of a few meters per second, which are comparable to those predicted by an empirical formula generated from the experiments of turbulent flow along a rough surface. The non-planar eroded blocks can be generated in the bedforms that have a reduced rock stiffness from weathering and are of an undulating morphology. The eroded block shapes are insensitive to slope angle, but depend on pre-existing fracture length and orientation, and rock fracture toughness. Under some conditions, the model predicts the fracture paths that extend deeply into massive rock. The fracture behaviors presented are useful for quantitative estimates of water-driven bedrock erosion rates.