Submerged-Flow Bridge Scour under Maximum Clear- Water Conditions (I): Experiment

Submerged-flow bridge scour at clear water threshold condition has been studied experimentally. The experiments were conducted in a self contained recirculating tilting flume where two uniform sediment sizes and two model bridge decks with eight different inundation levels were tested for scour morphology. The experiments showed that the longitudinal scour profiles before the ma,\:imum scour depth can be approximated by a 2-D similarity profile, while the scour morphology after the maximum scour depth is 3-D. Finally, two empirical similarity equations for scour profiles were proposed for design purpose, and the collected data set could be used for analytical studies of bridge scour. INTRODUCTION Bridges are a vital component of the transportation network. Evaluating their stability and structural response to hydrodynamic loading is critical to highway safety in design phase and after flooding. The studies of bridge scour usually assume an unsubmerged bridge flow, but the flow regime can switch to submerged flow when the downstream edge of a bridge deck is partially or totally inundated during large flood events. For example, a submerged bridge flow occurred in the Cedar River in Iowa after heavy rains in June 2008 (Figure 1), which interrupted traffic on 1-80. Submerged flow most likely creates a severe scouring capability because to pass a given discharge, the flow under a bridge can only scour the channel bed to dissipate its energy. Investigations on submerged-flow bridge scour have been reported by Arneson and Abt (1998), Umbrell et al. (1998), and Lyn (2008) . Arneson and Abt (1998) did a series of flume tests and proFigure 1: Bridge-submerged flow in Iowa in 2008 posed the following regression equation "!!.!... = -0.93 + 0.23 (hu) + 0.82 (Ys + hb) + 0.03 ( Vb) (1) hu hb hu Vue


INTRODUCTION
Bridges are a vital component of the transportation network. Evaluating their stability and structural response to hydrodynamic loading is critical to highway safety in design phase and after flooding. The studies of bridge scour usually assume an unsubmerged bridge flow , but the flow regime can switch to submerged flow when the downstream edge of a bridge deck is partially or totally inundated during large flood events. For example, a submerged bridge flow occurred in the Cedar River in Iowa after heavy rains in June 2008 (Figure 1), which interrupted traffic on 1-80 . Submerged flow most likely creates a severe scouring capability because to pass a given discharge, the flow under a bridge can only scour the channel bed to dissipate its energy.
(1) has been adopted in the FHWA manual (Richardson and Davis 2001) , it suffers from a spurious correlation where both sides of the equation include Ys/hu' In the meanwhile, Umbrell et al. (1998) also conducted a series of flume tests in the FHWA J. Sterling Jones Hydraulics Laboratory. Using the mass conservation law and assuming that the velocity under a bridge at scour equilibrium is equal to the critical velocity of the upstream flow, they presented the following equation (3) where Vu = approach flow velocity that is less than or equal to the critical velocity Vue, and w = depth of weir flow when flow overtops a bridge deck and w = 0 for partially submerged flow. By comparing Eq. (3)  where the critical velocity is estimated by Eq.
(2) except that the coefficient, 1.52 , is replaced by 1.58. Eq. (3) or (4) was based on the mass conservation law, but the dynamic law of momentum or energy was overlooked, which weakens the foundation of predictions because scour is a dynamic process. Besides, Umbrell's tests were run only for 3.5 hours which is not enough time for equilibrium scour to develop although they extrapolated their results to equilibrium states. The latest study was reported by Lyn (2008) , who reanalyzed Arneson's and Umbrell 's data sets and proposed the following power law where Vi, and Vue are the same as in Eq. (1). Lyn's equation is empirical, but he identified the spurious regression ofEq.
(1) and the low quality ofUmbrell's data. In brief, the two existing data sets are insufficient to develop a general description of submerged-flow scour, especially for a scour profile. Moreover, all the existing methods lack understanding of the physical mechanism of submerged flow scour. Therefore, the objectives of this study were to collect a detailed data set of submerged-flow scour at a model bridge in a flume, and to develop a theoretical model for the maximum scour depth under threshold clear water conditions. This paper emphasizes the experimental study that includes the experimental setup, results, discussion, and conclusions. A theoretical model for equilibrium scour depth is discussed in a separate paper.

EXPERIMENTAL SETUP
The experiments aimed to understand the flow and scour phenomena of submerged bridge flow by collecting scour data at a model bridge in a flume under controlled flow conditions. Specifically, the experiments tried to answer how sediment size, bridge girders and bridge inundation affect the longit udinal scour profile and maximum scour depth of submerged bridge flow .
The experiments were conducted in the FHWA J. Sterling Jones Hydraulics Laboratory, located at the Turner-Fairbank Highway Research Center in McLean, VA. The experimental flume ( Figure 2) had a length of 21.35 m, width of 1.83 m, and depth of 0.55 m, with clear sides and a stainless steel bottom whose slope was about horizontal. In the middle of the flume was installed a test section that consists of a narrowed channel with length of 3.04 m and width of 0.63 m , a 40-cm sediment recess, and a model bridge above the recess . A honeycomb flow straightener and a trumpet-shaped inlet were carefully designed to smoothly guide the flow into the test channel. The water in the flume was supplied by a circulation system with a sump of 210 m 3 and a pump wit h capacity of 0.3 m 3 / s; the depth of flow was controlled by a tailgate; and the experimental discharge was controlled by a Lab View program and checked by an electromagnetic flowmet er.
To test the effect of sediment size on scour morphology, two uniform sands (the coefficient of gradation C g < 1.5 , and the coefficient of uniformity Cu < 5) were used in the experiments: a median diameter ,.,,,,,, ... ,,,,,,,,,,,,,,,, d 5G = 1.14 mm with C g = 1.45 and C u = 1.77, and a median diameter d 5G = 2.18 mm with C g = 1.35 and C u = 1.59 . The effect of bridge girders was examined by a three-girder deck and a six-girder deck (Figure 3). Both decks had rails at the edges (Figure 3c) that could pass over-.""'" • .",, ".,,,,,,, flow on the deck surface whose elevation was adjustable, permitting the deck to have eight different inundation levels. A Lab View program was used to control an automated flume carriage that was equipped with MicroADV for records of ve-","', .  Table 1 where the Froude and Reynolds numbers mean the approach flows were sub critical turbulent flows.
The experiments proceeded as follows: 1) Filled the sediment recess with sand and evenly distributed sand on the bottom of the flume until the depth of sand was 60 cm in the sediment recess and 20 cm in the test channel. 2) Installed a bridge deck at a designated elevation and positioned it perpendicular to the direction of flow. 3) Pumped water gradually from the sump to the flume to the experimental discharge that was checked with the electromagnetic flowmeter. 4) Ran each test for 36-48 hours and monitored scour processes by grades in a clear side wall; an equilibrium state was attained when scour changes at a reference point were less than 1 mm for three continuous hours. 5) Gradually emptied water from the flume and scanned the 3-D scour morphology using the laser distance sensor with a grid size of 5 cm x 5 cm.

RESULTS
The results include the records of 3-D scour morphology, the widthaveraged 2-D longitudinal scour profiles, and the width-averaged m&'Cimum scour depths. A representative 3-D scour morphology is shown in Figure 4 Figure 5 where x = 0 is at the maximum scour point that is 4 cm from the downstream deck edge, and y = 0 is at the channel bed before scour. The most important results, the width-averaged m&ximum scour depths, are shown in Figure 5 and will be detailed in Guo et al. (2010) . Figure 4 shows that the scour morphology before the maximum point is approximately 2-D , after the maximum scour point it is 3-D. Furthermore, it is found that the 2-D scour morphology is subjected to pressurized flow while the 3-D scour morphology corresponds to free surface flow where the flow just exits the bridge, as shown in Figure 5, which plots 26 measured width-averaged longitudinal scour profiles. From F igure 5 one can see that: (1) The measured data are reproducible, as shown in subplot (a) where the data of two tests with hb = 15 cm almost collapse into a single curve; similarly, a reproduction for two tests with hb = 20.5 cm in subplot (b) can also be found before the maximum scour point, the difference after the ma..'Cimum scour point is due to the effect of free surface. (2) The longitudinal scour profiles are bell-shaped curves, but not symmetrical because the eroded materials deposit approximately two to three times the deck width downstream of the bridge. (3) The scour decreases with increasing sediment size, though the approach velocity in subplot (c) is larger than that in subplo t (b).

DISCUSSION
(4) The number of bridge girders has little effect on scour, as shown in subplots (a) and (b), but further test of this hypothesis is needed later since t he values of hb in the two plots are not the same.
where x :S O. The corresponding correlation coefficient is R2 = 0.995 and the standard deviation is 0"1 = 0.032, which implies t hat 68% of the data can be described by Eq. (6) with an error of ±0.032, and 95% of the data with an error of ±0.064. Accordingly, the scour depth at the upstream edge of a bridge deck where . 1:/W = -0.846 is approximately Jf.... = -0.479 ± 0.064 (7) Ys with 95 % confidence interval. Eq. (7) may be used for fie ld scour evaluation. Considering that a significant scour starts at y/Ys = -0.1, from Eq. (6) and considering 95% confidence interval the x-coordinate of the initiation of scour is between -1.58 :S x/vV :S -1.23.
which is plotted in Figure 6 and denoted by the dashed line. Note that although the width of deck in the experiments was constant, it was the only length in the flow direction so that it is natural to be the horizontal length scale. It is expected that Eqs. (6) -(8) are valid for similar bridge decks that are neither very thin like a sluice gate nor very wide like a water tunnel where a uniform scour profile may be developed after an entrance region.
Briefly, the horizontal scour range of a submerged flow depends on the width of bridge deck, but the design of a scour profile by Eqs. (6) and (8) needs the ma,'Cimum scour depth y" which may be calculated by the methods reviewed in the introduction.
Comparisons between the existing methods and the ma,'Cimum scour depths in Figure 5 are plotted in Figure 7, which shows that: (1) the Arneson and Abt method has an adverse tendency with the test data, which means the functional structure of the equation is not correct; (2) the Umbrell et al.
method, in general, agTees with the present data, in particular for sediment d 50 = 1.14 mm; and (3) the Lyn method underestimates most of the present data. For a better estimation of YSJ a theoretical model, based on the mass and energy conservations, will be proposed in Guo et al. (2010).

CONCLUSIONS
The experiments showed that under threshold clear water conditions: (1) a similarity longitudinal scour profile, Eq. (6) , for submerged flows exists before the maximum scour point that is approximately 15% of deck width to the downstream bridge edge; (2) after the maximum scour point, scour morphology is 3-D and the lower envelope of scour can be empirically described by Eq. (8); (3) the maximum scour depth increases with deck inundation level, but decreases with increasing sediment size; and (4) the maximum scour depth is independent of the number of deck girders.

ACKNOWLEDGMENT
This study was financially supported by the FHWA Hydraulics R&D Program with Contract No. DTFH61-04-C-00037. T he writers would like to thank Mr. Oscar Berrios for running the tests and preparing some of the figures. The writers are also thankful to Mr. Bart Bergendahl at FHWA for his constructive comments and suggestions.