Experimental estimation of afflux equation in circular and semicircular nose and tail shape of piers by considering effective parameters

Bridges are one of the most important river structures that have been used for many years. With the construction of bridges, the natural width of the river decreases and this results in a barrier in water flow. This causes the depth of water upstream of the bridge to exceed the normal depth and this increase in depth is called afflux, which is an important factor to consider when designing bridges. In this present study, two kinds of bridge piers of different shapes were used; circular and semicircular nose and tail. Using laboratory modeling and the two types of bridge piers, the effect of Froude number, the amount of flow path narrowing (σ), and the effect of the angle of bridge pier with respect to flow direction, pier shape, and ratio of length to thickness of the bridge pier were examined. Experiments were done in a flume with 15 m length, 30.9 cm width, and a 45 cm height. Results show that when Froude number is increased, afflux is increased as well. However, these changes are not the same in the two different bridge pier shapes. By examining Froude number in different path narrowing, it was found that generally, the amount of afflux is directly related to the Froude number. This survey also investigated the length-thickness ratio (L/t) effect of piers. For this purpose, different dimensions of piers, with widths of 3.8 cm and lengths of 15.2, 26.6, and 38 cm were investigated. For circular shape bridge piers, 3.8 cm diameter piers were used. When Froude number is constant, afflux is increased by increasing the number of piers across the channel. Results indicate that the amount of water rising is different in the two kinds of bridge piers (in circular shape and semicircular nose and tail piers). Additionally, changing the direction of piers also affects the formation of this phenomenon (afflux). Usually, piers are installed so that their mounting degree with flow direction is 90 degrees, but sometimes it is necessary to install them in another degree. Therefore, the use of skewed bridge piers with various angles can be important for the design. In this study, it was shown that , the angle of the pier, strongly affects the amount of afflux. It was illustrated that afflux increases more when changes are among higher degrees. For instance, when is changed from 15 to 20 compared to changing from 10 to 15, the increase in afflux is greater. According to results, afflux is higher in semicircular nose and tail piers than in circular shapes with the same Froude number. Also, as Froude number increases, the slope of the afflux curve of circular piers becomes smaller than that of the semicircle nose and tail piers.

Investigation of the length-thickness ratio (L/t) effect of piers on afflux shows that this parameter is negligible in (when pier direction is parallel to flow direction). However, as is increased, this parameter affects afflux more. Finally, by considering all the parameters, the experimental relationships for estimating the amount of afflux were developed for both bridge pier shapes utilized in the study.