The influence of bedrock river morphology and alluvial cover on gravel entrainment: Part 2. Modelling critical shear stress

Abstract

The critical shear stress (τc) at which grains are entrained on a bedrock surface is important for determining how bedrock rivers evolve through changes in sediment cover and bedrock erosion. The difference in τc for grains on bedrock and alluvial surfaces also determines whether a channel may be susceptible to runaway alluviation. Bedrock channel beds can have a wide variety of morphologies, but we do not fully understand how this variation affects τc. Here we address how bedrock morphology alters the grain entrainment parameters of pivoting angle, grain exposure and roughness height z0, and thus τc. In our companion article we used scaled, 3D printed replicas of seven bedrock surfaces to measure grain pivoting angles for four grain sizes. For three surfaces, pivoting angles were also measured with 25–100% sediment cover. In this second article, we combine these pivot angle data with measurements of grain exposure and surface roughness (standard deviation of elevations, σz) to predict τc using a force–balance model. The bedrock topography produces substantial variation in τc; for a given grain diameter (D), a 3.6× range of σz across the surfaces without sediment cover produces up to a 5.1× variation in τc. For comparison, for any single surface, τc varies by up to 2.5× for a fourfold range in grain size. Comparison to previous models with less representation of grain-scale geometry shows that in our results grains move at lower values of dimensionless critical shear stress (τ*c), and that τ*c decreases more quickly with increasing D/σz. However, direct comparison is difficult because previous relationships are based on a hydraulic roughness length that cannot be easily predicted without hydraulic data. Our results propose a new relationship between D/σz and τ*c, but further development and testing require datasets that combine measurements of flow, τc and grain-scale geometry.