A new mathematical model to calculate the equilibrium scour depth around a pier

The Equilibrium Scour Depth around a Pier under the Action of Collinear Waves and Current

“…Assuming that the current velocity profile obeys the power law, the combined velocity for the collinear waves and current is obtained by adding the wave velocity and the current velocity, respectively. The present model is an extension to the model developed by Gazi and Afzal [38] and has the ability of capturing any arbitrary scour profile under collinear waves and current. The results obtained using the proposed equation show very good agreement with the results of Sumer and Fredsøe [30] and Quezada et al [39], respectively.…”

“…In this section, an analytical equation capable of estimating the scour depth around a pier under the action of collinear waves and current is developed. The equation is obtained assuming the energy balance approach as outlined by Gazi and Afzal [38], Hafez [46] but incorporating the effect of waves, which was not considered in the previously mentioned works. When a pier is placed in a flowing fluid (case of oceans and/or river) the flow gets disturbed, and the fluid does work on the surface of the pier.…”

“…where, ζ = B is the channel width or distance between two piers, ρ is the density of flowing fluid, and Γ is the gamma function. Following Gazi and Afzal [38], the scour profiles at the front and the rear side of the pier are expressed by Equations (9) and (10) given below.…”

“…In the present study, the authors propose an analytical model of the equilibrium scour depth under the action of the collinear waves and current. This model is a significant development over the previous model by Gazi and Afzal [38], where the action of the waves were not considered. Here, the equilibrium scour depth is obtained by equating the work done by the flowing fluid while interacting with the pier under the action of the collinear waves and current and the work done by the total volume of the sediment particles removed from the scour hole, respectively.…”

Hybrid Scour Depth Prediction Equations for Reliable Design of Bridge Piers

“…Validation of the available formulas under different conditions is required for a more accurate estimation of the maximum scour depth around bridge piers. This can lead to more accurate scouring predictions, save unnecessary costs for protection around the pier, increase safety, and make the bridge design process more efficient [24,25]. Some of the relationships have been reviewed and modified by other researchers to increase their reliability.…”