Experimental investigation of the effect of transverse waves 1, 2 and 3 modes caused by cylindrical pier groups of the bridge on local scour

IIntroduction
The passage of water through obstacles such as bridge piers in the river, dock piers in the sea, and piers of any other hydraulic structures located in an open channel causes the formation of a boundary layer upstream of the obstacles and the separation of flow lines in the downstream obstacles, leading to the formation of vortex flows. The overlap of the vortices created by each of the obstacles leads to the formation of surface waves whose propagation direction is perpendicular to the flow direction. Under special circumstances when the frequency caused by the vortex of the obstacles is equal to the natural frequency of the structure's oscillation, a resonance mode is created and transverse waves with maximum amplitude are formed along the flume width. The formation of transverse waves with maximum amplitude can affect the safety and stability of hydraulic structures including bridge piers. To this end, recognizing transverse waves can reveal the reasons for the occurrence of some phenomena. Most studies on transverse waves have been conducted in a flume with limited width and a few waves. Thus, by conducting experiments in a wide flume and creating more waves, this study aimed to investigate the effect of waves in different modes on the local scour around the cylindrical piers of bridge.

Methodology
The experiments were carried out in the Physical and Hydraulic Modeling Laboratory of the Faculty of Water and Environmental Engineering, Shahid Chamran University, Ahvaz, using a rectangular flume with a length of 16 m, a width of 1.25 m, a height of 0.6 m, and a zero slope with glass walls. The flume bed was covered with sediments with an average size of d50 = 0.7 mm. The experiments were conducted with cylindrical pier groups in three stages. The experiments in the first stage were carried out without sediments and the cylindrical piers were placed on a fixed bed without sediments. The first stage experiments aimed to measure the wave parameters (wave amplitude, wave frequency, and flow depth) in the resonance. In the second stage, the sediment experiments were conducted with the formation of transverse waves. After adjusting the water level and forming the desired wave, 4 hours of equilibrium time was considered. Then, the pump was turned off and the end weir was slowly opened. After the complete discharge of the flow, the topography of the bed was measured using a laser meter with an accuracy of 1 mm as 1×1 cm2. The sediment experiments were in the third stage with the removal of transverse waves (control experiments) which were performed to compare with the results of the second stage experiments. A glass sheet was used for this purpose. The glass sheet prevented matching the natural frequency of the channel and the frequency caused by the tier vortex.

Results and Discussion
To investigate the effect of transverse waves caused by cylindrical piers on the maximum scour depth, each scour in the experiment with transverse waves was compared with the corresponding experiment conducted without transverse waves. The results showed that in wave modes 1, 2, and 3, the maximum scour depth was greater in the case with waves than in the case without waves. The maximum scour depth in wave mode 1 experiments at Froude numbers 0.059, 0.057, and 0.055 was 71, 55, and 54 percent higher than the scour depth in the experiments without waves, and for wave mode 2, the maximum scour depth in the experiments with waves at Froude numbers of 0.117, 0.110 and 0.106 was 90, 76 and 66 percent higher than the maximum scour depth in the experiments conducted without waves. The maximum scour depth in the wave mode 3 experiments with waves at Froude numbers of 0.156 and 0.151 was 70 and 68 percent was higher than the scour depth in the experiments without waves. This study also examined the effect of wave mode on the maximum scour depth. The results indicated that with an increase in the wave number, the maximum scour depth increased in each discharge. On average, the maximum scour depth in wave mode 3 increased by 130 percent compared to wave mode 1 and by 43 percent compared to wave mode 2, and the maximum scour depth in wave mode 2 increased by 60 percent compared to wave mode 1. Also, the maximum scour depth in each wave mode increased with an increase in the wave amplitude, indicating the existence of a direct relationship between the wave amplitude and the maximum scour depth. In addition to the maximum scour depth, transverse waves also affected the scour volume, which was greater in the experiments conducted with waves than in the experiments without waves. On average, the scour volume was 4.3 times in wave mode 1, 3.5 times in wave mode 2, and 9 times in wave mode 3 compared to the wave-free mode.

Conclusion
The present study examined the effect of transverse waves mode 1, 2, and 3 on the local scour around the cylindrical piers of the bridge. The formation of transverse waves affected the scouring of cylindrical piers, and the maximum scour depth in the experiments conducted with waves was greater than in the experiments without waves. On average, the maximum scour depth increased by 60 percent, 78 percent, and 69 percent in the wave modes 1, 2, and 3 compared to the wave-free mode respectively. Moreover, with an increase in the wave number, the maximum scour depth increased in each discharge, with the maximum and minimum scour depths being found in wave modes 3 and 1, respectively. Overall, the changes in the scour volume followed the same trend as the changes in the maximum scouring depth. On average, the scour volume was 4.3 times in wave mode 1, 3.5 times in wave mode 2, and 9 times in wave mode 3 compared to the wave-free mode.