Integrated Turbulence and Machine Learning Models Explain Pier Scour in Erodible Channels

Abstract Pier scour, a primary cause of bridge failures, stems from turbulent erosion at the pier's approach surface, jeopardizing bridge stability and influencing both river morphology and interactions between aquatic and terrestrial ecosystems. The scouring process, initiated by turbulent eddies interacting with sediments over erodible channels, leads to the formation of scour holes—a phenomenon that remains to be scientifically investigated. Traditionally, scour depth estimation ‐ relies on empirical formulas that lack a robust physical basis. This study introduces a novel approach grounded in turbulence physics, elucidating the scouring process through interactions between energetic turbulent eddies and pier drag and correlating equilibrium scour depth with the size of the largest channel eddies. By coupling a turbulent kinetic energy budget, which describes the energy transitions between eddies and pier‐induced drag, with a shear stress covariance budget, formed by the mean velocity gradient, vertical velocity spectrum, and a pressure‐velocity interaction destruction term, this research establishes a direct bridge between flow properties and pier scour. Further integrating a well‐established velocity spectrum with symbolic regression, a concise approximate solution for bulk‐scale variables is derived from complex micro‐scale prognostic equations, resulting in an explicit expression for scour depth. Consequently, a general predictive framework is derived, unifying scour depth data across two orders of magnitude. Those predictions align closely with measurements from multiple sources, demonstrating its robustness and potential for broad applicability in hydraulic engineering.