Geotechnical controls on erodibility in fluvial impact erosion

Bedrock incision by rivers is commonly driven by the impacts of moving bedload particles. The speed of incision is modulated by rock properties, which is quantified within a parameter known as erodibility that scales the erosion rate to the erosive action of the flow. Although basic models for the geotechnical controls on rock erodibility have been suggested, large scatter and trends in the remaining relationships indicate that they are incompletely understood. Here, we conducted dedicated laboratory experiments measuring erodibility using erosion mills. In parallel, we measured uniaxial compressive strength, tensile strength, Young's modulus, bulk density, and the Poisson's ratio for the tested lithologies. We find that under the same flow conditions, erosion rates of samples from the same lithology can vary by a factor of up to 60. This indicates that rock properties that may vary over short distances within the same rock can exert a strong control on its erosional properties. The geotechnical properties of the tested lithologies are strongly cross-correlated, preventing a purely empirical determination of their controls on erodibility. The currently prevailing model predicts that erosion rates should scale linearly with Young's modulus and inversely with the square of the tensile strength. We extend this model using first-principle physical arguments, taking into account the geotechnical properties of the impactor. The extended model provides a better description of the data than the existing model. Yet, the fit is far from satisfactory. We suggest that the ratio of mineral grain size to the impactor diameter presents a strong control on erodibility that has not been quantified so far. We also discuss how our laboratory results upscale to real landscapes and long timescales. For both a revised stream power incision model and a sediment-flux-dependent incision model, we suggest that long-term erosion rates scale linearly with erodibility and that, within this theoretical framework, relative laboratory measurements of erodibility can be applied at the landscape scale.