Numerical bed response around a circular bridge pier under short hydrographs with equal time-integrated inlet velocity and different peak times

Three-dimensional water–sediment Euler–Euler RANS calculations were re-examined to distinguish hydrograph timing effects from initialization transients and background bed lowering. A circular pier of diameter 0.060 m was embedded in 0.86 mm sediment beneath a 0.114 m water column with a rigid-lid top boundary. Three 0.60 s triangular velocity histories shared base and peak velocities of 0.3205 and 0.4800 m s −1 and identical time-integrated input, with peak-time ratios of 0.30, 0.50, and 0.70. The 0.10 s common preconditioning interval was not demonstrated to produce an equilibrium bed or developed approach flow. A new approach-bed reference, evaluated 6–10 pier diameters upstream, removed 77.4%–78.8% of the original fixed-reference deficit volume at the principal time step. Corrected terminal local volumes were 1.178, 1.131, and 1.088 × 10 −4 m 3 at a maximum time step of 0.25 m, and 1.135, 1.082, and 1.045 × 10 −4 m 3 at 0.125 m. Their ordering persisted, but corrected within-case temporal changes of 3.81%–4.59% and unquantified spatial error prevent a validated physical ranking. Corrected pre-peak depth fractions were 23.6%, 47.2%, and 71.8%, compared with null expectations of 30%, 50%, and 70%; corrected volume fractions were 37.4%, 64.1%, and 80.2%. Thus, the original stage fractions and clockwise loops alone do not establish hydrograph-specific memory. The mesh had 12 mm vertical spacing, approximately 14 grain diameters, and no formal grid-convergence or benchmark validation was available. These calculations provide a diagnostic comparison of short numerical bed-response histories; physically representative flood-scour rates and design implications remain unresolved.