The 12th International Conference on Scour and Erosion (ICSE 2025)

In the assessment of scour process at bridge foundations, it is observed that the riverbed shear decays with the development of the scour hole as the strength and velocity of the flow vortices in the scour hole decrease. The maximum scour depth is achieved when the bed shear stress equals the critical shear of the bed material. This phenomenon forms the basis for the decay function of hydraulic loading. Parallel research from Federal Highway Administration (FHWA) developed a framework to study the probabilistic decay functions based on temporal experimental data. The challenge of using the framework is that the approach relies on the data collection of sufficient scour depth time history in the flume tests or in the field. However, most experiments found in literature only measured the equilibrium scour depth without recording the complete time history. Research from FHWA showed that using a two-parameter exponential function, determined by the initial shear stress and the equilibrium scour depth, would provide a more conservative shear decay trend than one obtained from temporal data and a pick-up function. Therefore, a method to develop the probabilistic decay function based on the equilibrium scour depth is proposed in this paper. The proposed method only requires the data of initial shear stress and the equilibrium scour depth. Design scour depths and the reference bed shear stresses were calculated with design equations from Hydraulic Engineering Circular No. 18 (HEC-18) to normalize scour depth and shear stress. In order to build a robust database and incorporate the results of full-scale computational fluid dynamics (CFD) simulations of bridge pier and abutment scour, a probabilistic ratio of measured scour depth and design scour depth was applied to the CFD simulations. A bin method was adopted to determine the representative value for selected exceedance probability in each bin. Both best-fit and envelope results were provided for comparison purpose. The proposed decay functions were validated using experimental data, which pave the way for achieving a more reliable, probabilistic scour depth assessment.