Predictors for clear-water and live-bed scour at circular piers

In this work, we propose a new predictor for estimating the local scour at circular piers in live-bed conditions, explicitly accounting for the dependence of the time-averaged equilibrium scour depth on dimensionless factors for pier slenderness, sediment coarseness, sediment gradation, and flow intensity. The empirical model is constructed as the product of four independent subfunctions, a modular formulation that simplifies the normalization of experimental data and enables a clear interpretation of the individual effects of these parameters. The presented equation outperforms other approaches proposed in the literature.We also present a full trend of the equilibrium scour depth as a function of the flow intensity for both clear-water and live-bed regimes (for flow velocity up to 4.5 times the threshold for sediment motion in the unobstructed reach). For the estimation of the scour depth in clear-water condition we slightly modified a predictor that we recently proposed. Our formulae are supported by an extensive data set comprising 1,175 experimental data points, underscoring the robustness and applicability of the proposed model. For uniform sediment, the maximum scour occurs in the clear-water regime. By contrast, in flows with nonuniform sediment, the worstcase scenario occurs in the live-bed regime.