Experimental study of the effect of transverse distance between the rectangular piers on local scour around them

Introduction
Bridges are built to connect the two sides of rivers. As a result of the flows hitting the piers of bridges, scour occurs around them, especially during floods. Sometimes the degree of the score is so high that it destroys the pier and eventually the bridge. Every year, many bridges around the world are destroyed due to scour around their piers and abutments (Ghodsi et al. 2015). Various studies have addressed the scour formed around bridge piers, mostly single piers, and the factors affecting it. However, some studies have examined pier groups, but the number of such studies is smaller than the studies conducted on single piers. Cylindrical piers are mostly used in the mentioned studies. A few studies
have addressed the effect of the transverse distance between the piers in the group of piers, especially rectangular piers. The present study hypothesized that the changes in the transverse distance between the piers are effective on the intensity of scour around them in the pier group. To this end, the present study sought to investigate the effect of changes in the transverse distance between rectangular piers on the local scour around them in the group of piers with a 2×2 arrangement.

Methodology
The experiments of this study were carried out in Flume with a rectangular cross-section and length and width equal to 6 and 0.73 meters, respectively. The sediments used in this study were sand with a relative density of 2.65. The average size of the sediment particles (d50) was equal to 0.73 mm and the standard deviation coefficient of bed sediments  was equal to 1.22, which indicates the uniformity of the sediment grading. The piers used in this study were rectangular 2.5 cm wide and 3.5 cm long. In all experiments, the pier group was used with a 2×2 arrangement. The longitudinal distance between the piers was fixed and 4 times the width of the pier (10 cm). The transverse distance between the piers was chosen as 1, 3, 5, and 8 times the width of the pier equivalent to 2.5, 7.5, 12.5, and 20 cm. In this study, the flow depth was equal to 14 cm with discharge rates of 19, 22, 25, and 29 L/s (Froude numbers 0.16, 0.186, 0.211, and 0.245). All the experiments were conducted in clear water.

Results and discussion
The scour rate around the piers is a function of the flow Froude number, the distance of the piers from each other, and the row of the pier placement (the first or second row). With an increase in the Froude number, the scour depth also increased due to an increase in the strength of the erosive eddies and the bed shear stress around the piers.

Conclusion
In all the experiments, the maximum depth of the scour hole was observed around the piers of the first row. Figure 1 displays the trend of changes in the maximum relative scour depth (ds1/w) for different distances and Froude numbers. As can be seen, with an increase in the transverse distance between the piers, the maximum scour depth first started a downward trend and reached the minimum value at a distance three times the width of the pier, then the trend of changes in the maximum scour depth increased and reached its maximum value at a distance of 8 times the pier width. The data showed that the maximum scour depth at a distance of 8 times the width of the pier with Froude numbers
0.16, 0.186, 0.211, and 0.245, was 39.5, 35, 35, and 28% greater than the distance 3 times the pier width, 37, 37, 32 and 14% greater than the distance 5 times the pier width, and 30, 25, 20 and 10% greater than the distance 1 time the pier width. In all the experiments, the maximum scour depth around the piers in the first row was greater than that of the piers in the second row. The data revealed that the maximum scour depth around the piers in the second row at transverse distances of 1, 3, 5, and 8 times the pier width was on average 35, 48, 40, and 42% smaller than the maximum scour depth around the piers in the first row.