A novel formula to determine the time to achieve quasi-equilibrium scour around a circular pier

The actual occurrence of equilibrium scour depth near the bridge piers is theoretically infinitely long. However, the quasi-equilibrium state can be reached in a certain period, which is useful for designing cost-effective bridge piers. Previous studies have developed formulas for predicting the time to reach equilibrium scour at bridge piers. These equilibrium time formulas match well with the datasets they were originally based on, but they often produce significant deviations when applied to a wider range of datasets. This serves as the basis for the present study by proposing a new formula to calculate the quasi-state of equilibrium scour time (<i>T</i>_<i>E</i>) using dimensional analysis and functional relationships. Using this <i>T</i>_<i>E</i> both quasi-equilibrium and time-dependent scour can be more accurately predicted around circular bridge piers in clear-water conditions compared to literature formulas. This new formula has been developed to synthesize clearwater metadata from literatures published over six decades. It considers five hydraulic characteristics like pier slenderness, flow intensity, sediment coarseness, sediment uniformity and constriction ratio. This novel formula has good predictive ability, outperforming five literature formulas comparing the statistical parameters. The present formula is 44% more accurate in validation than the best literature formula compared to datapoints within the ± 20% error range.