Estimating sediment entrainment thresholds in gravel-bed rivers with the force balance model: Developing location-general relations for predicting grain pivoting angle, projection and exposure

Conditions for bedload movement are most often described in terms of dimensionless critical shear stress (τc∗), however a key difficulty is accurately estimating τc∗, leading to significant uncertainties with entrainment threshold predictions. One approach to predicting τc∗ is with a force balance which considers the relative magnitude of the forces acting to entrain a particle and those acting to keep it in on the river bed. The key sedimentological parameters of the force balance are grain pivoting angle (ϕ), projection (𝑝𝑝) and exposure (𝑒𝑒), with ϕ representing a particle’s resistance to motion and p and e determining the drag and lift forces acting on a grain. Grain pivoting angle, projection and exposure are known to vary with the properties of the bed, although the exact co-dependencies have not been fully investigated. Previous studies into the factors controlling ϕ are thought to be limited as they sampled beds with a narrow range of sediment characteristics, and little work has been carried out to determine the bed sediment and elevation characteristics that determine grain projection and exposure. Through the measurement of over 10,300 pivoting angle values and 9,600 estimates of projection and exposure across a broad range of sediment mixtures from different gravel-bed river environments (humid-temperate perennial in the UK and dryland ephemeral rivers in Israel), this novel study has led to an improved understanding of how bed sediment character affects the key parameters of the force balance model, and thus sediment entrainment thresholds. Relative grain size, bed sediment sorting and grain shape were shown to be significant determinants of ϕ, 𝑝𝑝 and 𝑒𝑒 at a site. Additionally, bed roughness and angularity were significant determinants of ϕ and median grain size and kurtosis were significant determinants of 𝑝𝑝 and 𝑒𝑒. From this, empirical relations for predicting ϕ, 𝑝𝑝 and 𝑒𝑒 as a function of bed sediment characteristics alone (location-general relations) have been derived.