The effect of pressure flow conditions on bridge pier scour in compound open channels with vegetation

Introduction
Bridges are one of the most important structures built on rivers and are considered as a structure connecting the two parts of the road. One of the most important reasons for the destruction of bridges is the scouring of its piers. New bridge design challenges, due to climate change and human intervention, as well as uncertainties associated with maximum events, may not adequately lead to accurate hydraulically design of bridges and may therefore as a result, in some floods, the bridge deck submerged. Under these conditions, the flow can be converted to a pressurized. This pressurized flow passes at high velocity in the region of bridge piers. As a result, it can increase the erosion potential of bed materials near bridge piers. Up to now, many studies have been performed to determine the relationship between estimating the rate of scouring of bridge piers in laboratory conditions with clear water and living bed, Such as: CSU equation.
Under pressurized flow condition, researchers such as Umbrel et al., Richardson and Davis, Zehi, and Karankina et al. Have developed relationships to determine the amount of scouring of bridge piers in simple channels. Due to the difference in flow velocity in the main channel and floodplains in the compound open channels, the important changes occur in the kinetic structure of the flow near the connection line between the main channel and floodplains. These changes also cause vortices as a result of excess energy loss in the flow. In addition, the presence of vegetation on floodplains complicates the hydraulic analysis of the flow in such sections. Up to now, many studies have been performed to explain the hydraulic conditions of the flow in compound channels with and without vegetation, including Shiono knight (1991), Rameshwaran and Shiono (2007), Zarati et al. (2008), Yu-qi Shan et al. (2016), Tanino et al. (2008). and Sonnenwald et al. (2018).

In previous studies, the amount of scouring of bridge piers in the conditions of pressurized flow under the deck in compound channels with vegetation has not been investigated.
The aim of this study was to investigate the effects of vegetation density, pressurized flow under the bridge deck with different geometric and hydraulic conditions on the scour depth of bridge piers in a compound channel.
Methodology
Experiments of this research was performed in a laboratory channel with a width of 1.5 meters and a length of 10 meters. The experiments in this study were performed with 3 geometric ratios of cross section (=B/b), 3 relative depths (Dr) and 3 vegetation densities (). It should be noted that the experiments are designed in such a way that in all of relative depths, the bridge deck is submerged and the flow pressurized.
The maximum depth of scouring under the flow pressurized passing under the bridge can be expressed as a simple and dimensionless equation (1):
( (1
Considering the control volume from the upstream of the bridge deck to the downstream of it, the momentum equation can be written to calculate the apparent shear stress as follows:
(2)

Results and Discussion
A: Depth averaged velocity
In vegetation densities used in this study, the average velocity on floodplains with vegetation is relatively constant in most cases. This shows that except in the interface of the main channel and floodplains, the flow distribution on floodplains can be considered two-dimensional. As the vegetation density increases, the depth averaged velocity difference between the main channel and the floodplain increases between 50%-80%.
B: Shear stress
Due to the presence of vegetation, the reduction of the average flow velocity on the floodplain occurred as a result of shear stress has also decreased. The transverse changes of shear stress downstream of the bridge, due to the behavior of the pressurized flow passing in the deck, have more fluctuations and are on average about 25% more than the average values upstream of the bridge.
C: Local friction factor
The Darcy–Weisbach friction factor in the floodplain area increases significantly due to the presence of vegetation elements. The pattern of variability of Darcy–Weisbach friction factor on the floodplain also causes a sinusoidal pattern due to the reduction of flow velocity and the presence of skin friction on the surface of the rods.
D: Apparent shear stress
Due to the resistance due to increasing vegetation density, the amount of apparent shear stress at higher densities increases. On the other hand, with increasing relative depth and decreasing of secondary current, the amount of apparent shear stress decreases. As the width of the floodplain increases and the secondary currents become stronger, it shows an average of 40% apparent shear stress.
E: Equation for predicting maximum scour depth
Based on determining the effective parameters in the amount of scour rate and using the data of this study, the following equation is presented to estimate the amount of scour of the bridge pier under pressurizes flow conditions.
(3)

Conclusion
- Increasing the density of vegetation increases the longitudinal velocity in the main canal and decreases it in the floodplain.
-Bridge pier scouring develops faster in pressurized flow than in free surface flow.
-With the exception of the height of the dune in the pressurized flow, the depth of scour hole on a small laboratory scale is less than 50% of the depth of the upstream of the bridge deck.
-The position of the maximum scouring depth quickly reaches its equilibrium position near the downstream edge of the bridge deck.