Experimental investigation of the effect of hydrographs with different skewness and duration time on temporal variations of scour around a single cylindrical pier

Introduction
For a bridge pier in the flow path, a three-dimensional and complex flow pattern is formed around the pier leading to the formation of a scour hole around it. The development of the scour hole will cause the instability of the bridge pier and ultimately the destruction of the pier and the bridge. This problem becomes very important during the floods, when the flow in the river increases rapidly and has the highest potential of destruction. Most studies have investigated scouring in steady flow conditions. The maximum scour depth that occurs under a flood hydrograph can be much smaller than the equilibrium depth resulting from steady flow under peak discharge conditions (Kothyari et al., 1992; Lai et al., 2009). Therefore, the use of flood peak discharge for design can greatly overestimate the maximum scour depth compared to the actual flood conditions (Chang et al., 2004). Considering the importance of scouring investigation in the conditions of unsteady flow and the limited available studies in this regard, more research in this field is necessary. The purpose of this research is to investigate the effect of the time of the rising and falling limbs of the hydrograph, as well as the duration of the hydrograph on the temporal variations of scour depth and its maximum value around the cylindrical pier.

Methodology
The experiments were carried out in a rectangular flume with glass walls and a straight length of 10 m, a width of 0.74 m and a depth of 0.6 m in the Physical and Hydraulic Modeling Laboratory of Shahid Chamran University, Ahvaz. The test section in the flume was covered with uniform sand with an average size of d50=0.7 mm and geometric standard deviation σ=1.3. In order to achieve the goals of this study, a total of 13 experiments were examined. In order to investigate the effect of the time of the rising and falling limbs of the hydrograph on the temporal variation and the maximum scour depth, a number of 6 hydrographs with a constant duration of 100 minutes and the ratio of the time to reach the peak (Tp) to the duration time (Td) of the hydrograph (skewness) equal to 0.1, 0.2, 0.4, 0.6, 0.8 and 0.9 were designed. Also, 7 hydrographs with Gaussian distribution and duration times (Td) of 10, 20, 45, 80, 100, 120 and 160 were simulated to investigate the effect of flood duration on scouring (Fig. 3 and Table 1). A hydrograph generation system was used to create unsteady flow in the flume. This system included a programmed inverter that was used to adjust the variable flow rate of the hydrograph. The inverter was connected to the pump on one side and to the electromagnetic flow meter on the other side and was run by a computer through a software.

Results and discussion
The results of the temporal variations of scouring showed that scouring starts from the sides of the pier and reaches the nose of the pier over time, and finally, the maximum depth of scouring occurs in the nose of the pier. The results showed that the maximum scour depth in the hydrograph with a Gaussian distribution occurs after the peak time (about 10% of duration time) (Fig. 5). Investigating of the effect of the rising limb of the hydrograph showed that in hydrographs with similar duration, the time to reach the peak of the hydrograph has no effect on the maximum scour depth, but it has a significant effect on the temporal changes of shear stress and scour depth. By reducing the time of the rising limb of the hydrograph from 90 minutes to 10 minutes, the shear stress change rate increases 9 times and the scouring rate increases about 6 times. Investigating the effect of the falling limb of the hydrograph on the maximum scour depth showed that the effect of the falling limb on the maximum scour depth increases with the decrease of the time of the rising limb of the hydrograph. The results also showed that the maximum scour depth in hydrographs with skewness of 0.1, 0.2, 0.4, 0.6 and 0.8 is 51.35, 21.28, 12, 5.56 and 1.79 percent more than the scour depth at peak discharge, respectively (Fig. 6). It was also observed that in hydrographs with the same peak time but different duration time, the time of the falling limb is effective on the value of the maximum scour depth. With the increase of 9, 4, and 1.5 times the time of the falling limb of the hydrograph, the maximum scour depth increases by 30.23, 14, and 1.82 percent, respectively. Investigating the duration time of the hydrograph showed that the increase in the duration time increases the depth and dimensions of the scour hole around the pier. It was observed that the maximum scour depth for hydrographs with a duration of 20, 45, 80, 100, 120 and 160 minutes were 19.44, 38.89, 52.78, 58.33, 66.67 and 69.44% more than a hydrograph with a duration of 10 minutes, respectively (Fig. 7). In addition, the slope of the time variations of the scour depth decreases with the increase of the duration time due to the lengthening of the flow rate changes interval along the rising limb of the hydrograph (Fig. 8).

Conclusion
In this study, scouring around a cylindrical pier was investigated under unsteady flow conditions. The results showed that for hydrographs with similar peak discharge and duration time, the time of the rising limb of the hydrograph has a significant effect on the temporal variation of shear stress and scour depth, but it has almost no effect on the maximum scour depth. In addition, it was found that by reducing the time of the rising limb, the influence of the falling limb of the hydrograph on the maximum scour depth increases. Investigating the results of the effect of hydrograph duration time on local scour showed that with the increase of hydrograph duration time, the maximum scour depth increases and the slope of temporal variations of scour depth decreases.