88 / 2025-04-24 12:55:55

A Framework of Probabilistic Decay Function Development for Assessing Bridge Scour

Scour around bridge piers and abutments occur when these structures are subjected to hydraulic loading from flood events. The progressive scour can undermine foundation stability and significantly impact the safety and reliability of highway bridges during their design life. A proper scour depth estimation is critical for achieving efficient design of new bridges or a robust retrofit of existing bridges.

Hydraulic Engineering Circular No. 18 (HEC-18) is the most widely used scour design guidance in the United States, which addresses the bridge design by predicting a maximum scour depth. HEC-18 has implicitly implemented the shear decay function (or decay function) concepts in various sections. The concept of decay function is as follows: scour will proceed when the bed shear stress on the riverbed is greater than the erosion resistance of the materials at the bridge pier or abutment. As the scour hole progresses around the bridge, the velocity and strength of the flow vortices reduce due to the increasing scour depth, which results in a decay trend of the riverbed shear stress, i.e., hydraulic loading. When the hydraulic loading decreases to the level that is equal to the erosion resistance of the material, the scour stops and reaches the maximum scour depth.

This paper introduced a framework to develop decoupled and coupled decay functions proposed by the FHWA researchers. The proposed decay functions contain two parameters: an amplification factor and a decay factor. The amplification factor reflects the ratio of the initial bed shear to a reference shear stress which could be the bed shear stress at the approach cross section, the bed shear stress at the opening cross section, or the critical shear stress of the bed material. The decay factor reflects the decay rate of the bed shear as the scour hole proceeds.

The proposed decay functions were developed based on the temporal scour depth data obtained from flume experiments found in literature. Jones’ equation was used for temporal scour depth regression. A modified Van Rijn pick-up function was adopted to convert scour rate to bed shear stress in the scour hole. 6,000 computational fluid dynamics (CFD) simulations were conducted to compute the reference shear stress and determine the amplification factor. The uncertainties on temporal data regression, Van Rijn pick-up function, and amplification factor were considered in the probabilistic decay function analysis. As a result, general decay functions were proposed for assessment of scour depths around bridge piers and abutments.