Time development of clear-water scour around a pile foundation: Phenomenological theory of turbulence-based approach

Existing prediction formulas for clear-water scour development are typically empirical fittings of lab-scale results. However, it is unreasonable to evaluate the in-situ clear-water scour process around a pile based on smallscale flume tests due to inherent scale effect. This study proposes a time-dependent model of clear-water scour development around a pile foundation under steady currents. A scaling expression of shear stress acting on sediment particles at the front of a circular pile is established based on the phenomenological theory of turbulence. By applying the sediment transport model of flat-bed to local scour around a circular pile, a physics-based ordinary differential equation for predicting the scour depth development is derived. The analytical solution of scour depth development is generally more consistent with the experimental data compared with previous models. The probability density function distribution of the proposed model's error mainly concentrates within the range of +/- 10%, which is significantly superior to previous models. The proposed model integrates all pertinent parameters that govern the scour process using fundamental principles, rendering it free from scale issues and applicable to prototype conditions. The present model is applied to evaluating clear-water scour development around typical prototype piles with diameters ranging from 2.0 m to 10.0 m. The predicted variations of equilibrium scour time with pile diameter, flow velocity and sediment particle size aligns closely with previous experimental observations.