Predictive modelling of time-dependent scour around inclined and vertical piles under steady and combined wave-current flows

Understanding the time-dependent development of scour is essential for the reliable design of hydraulic and offshore foundations. This study examines the temporal evolution of local scour around vertical and inclined piles under steady currents and combined wave-current conditions in both clear-water and live-bed regimes. A generalised time-scaling formulation is developed for vertical piles and shown to perform well under varying sediment mobility conditions. The model is then extended to incorporate pile inclination under steady currents. Temporal scour behaviour under combined wave-current interaction is also analysed for both configurations, and predictive expressions are proposed, primarily calibrated for live-bed conditions but validated for clear-water cases as well. The equations are developed using 60% of a compiled dataset (including published and present experimental data), with the remaining 40% used for independent validation. The empirical coefficients ( n , z , m ) are parameterised in terms of sediment size ( d 50 ), pile diameter ( D ), Keulegan-Carpenter number ( KC ), flow depth ( h ), and inclination angle ( α ). The formulation captures the influence of KC in intensifying oscillatory sediment motion and accelerating scour stabilization under combined loading. For inclined piles, geometric effects associated with inclination are found to dominate over wave-related parameters in controlling temporal scour evolution.