Extrapolating time development curves of clear-water scour around piles: From empirical fitting to physics-based approach

Abstract

The currently available prediction formulas for the scour development around a pile predominantly rely on empirical fittings, lacking clear physical mechanisms. This study integrates the principle of sediment mass conservation, the flat-bed sediment transport model, and the phenomenological theory of turbulence to propose a semi-analytical model for predicting clear-water scour development around circular piles. This model overcomes scale-related issues and is governed by three fundamental parameters: the equilibrium scour depth, the characteristic time, and the ratio of the scour depth coefficient to the primary horseshoe vortex coefficient. The results demonstrate that the proposed model is consistent with experimental data. The proposed model offers significant improvements by addressing two critical issues observed in existing models: (i) empirical formulas expressed purely in mathematical terms exhibit low prediction accuracy for long-term scour, resulting in underestimation of the extrapolated equilibrium scour depth and premature attainment of equilibrium conditions; (ii) other models exhibit a divergence phenomenon, where the extrapolated equilibrium scour depth greatly exceeds the pile diameter, contradicting prevailing understanding. Applying the proposed model allows for a substantial reduction in test duration while accurately capturing the subsequent scour development process.