2Flow Redistribution at Bridge Contractions in
3Compound Channel for Extreme Hydrological
4Events and Implications for1Sediment Scour
5Yifan Yang, A.M.ASCE1; Xiaozhou Xiong2; Bruce W. Melville, M.ASCE3;
6and Terry W. Sturm, F.ASCE4
7Abstract: This study investigates the flood flow characteristics in a compound channel subject to both lateral contraction (caused by bridge
8abutment/embankment) and vertical contraction (caused by bridge deck submergence) at bridge sites. Three abutment setback distances and
9three pressure flow types [free surface (FS), submerged orifice (SO) and overtopping (OT)] are tested. The results show that turbulence
10 structures in the approach channel remained the same irrespective of downstream obstruction. However, lesser abutment setback from
11 the main channel led to greater flow acceleration as the flow approached the bridge section, where SO flow had the highest flow intensity
12 and FS flow had the lowest. At a bridge contraction, the distributions of flow velocity, turbulence intensity, and Reynolds shear stress are
13 significantly affected by the type of pressure flow and the extent of contraction. Enclosed counterclockwise secondary circulating flows in the
14 main channel may occur for a combination of long or medium setback abutments and a FS flow, while other conditions usually feature open-
15 ended upward flows due to flow relief. The strong downslope flow component detected at the main channel bank has a noticeable bank
16 erosion capability. The bed shear stress, which is an indicator of sediment scour, is highlighted by apparent peak zones at the main channel
17 bank and abutment toe. Finally, clear relationships between turbulence intensity, unit discharge ratio, and lateral contraction length are found.
18 In general, normalized turbulence intensities on the floodplain and in the main channel can be used to assess the contribution of macro-
19 turbulence to the final bed topography after scour. DOI: 10.1061/(ASCE)HY.1943-7900.0001861.© 2020 American Society of Civil
3have compound cross-sectional shapes with
23 wide (and sometimes vegetated) floodplains adjoining narrow but
24 deep main channels. During dry seasons, river flow is usually con-
25 fined in the main channel with a water level much lower than the
26 floodplain. However, for extreme hydrological events (e.g., floods),
27 the entire compound channel, including both the floodplain and
28 main channel, may be submerged, leading to significant nonuni-
29 form flow distribution. The flow field and turbulence features
30 (e.g., secondary flow, transverse momentum exchange, etc.) in
31 straight compound channels with both rectangular and trapezoidal
32 main channels have been extensively studied in the past two dec-
33 ades (Babaeyan-Koopaei et al. 2002;van Prooijen et al. 2005;
34 Vermaas et al. 2011;Yang et al. 2013;Koziol 2013;Proust
et al. 2017;Proust and Nikora 2020). In contrast, very little atten-
tion has been paid to the existence and effect of nonvegetation
structures/obstructions on the floodplain. Proust et al. (2006) stud-
ied the influence of abrupt floodplain contraction. Peltier et al.
(2013) investigated the turbulence around embankments on the
floodplain. However, more systematic research is still urgently
needed to build a profound understanding of compound channel
flow with different contraction types, which can usually be ob-
43served during flood events.
When approaching a bridge section, flood flow may be subject
to significant redistribution due to both lateral and vertical contrac-
tion. The former is usually found at a bridge abutment, an essential
part of the bridge foundation supporting the bridge deck and other
superstructures, together with embankments. A large number of
abutments are built on the floodplain and set back from the main
channel to avoid excessive disturbance to the flow. Vertical contrac-
tion usually occurs in the form of either submerged orifice (SO)
flow (when the bridge deck girders are submerged) or overtopping
(OT) flow (when the bridge superstructure is submerged) at the
bridge section. In contrast, free surface (FS) flow features only lat-
eral contraction when the bridge deck stays clear of flow impact.
Different bridge flow conditions are shown in Fig. 1. A major con-
sequence of the altered flow distribution at a bridge contraction
is the enhanced bed mobility and gradual formation of a scour
hole caused by the combined influence of local turbulence struc-
tures and flow pressurization. Scour induced by flow redistribution
is responsible for many bridge abutment failures (Morris and
Pagan-Ortiz 1999;Melville and Coleman 2000;Arneson et al.
2012). Being insufficiently studied, scour caused by vertical con-
traction is a common scene during flood events with a significant
threat to bridge abutments. In 2009, floods with more than 500-year
66recurrence magnitudes occurred in the Atlanta area, Georgia, US.
1Honarory Research Fellow, Dept. of Civil and Environmental
Engineering, Univ. of Auckland, Private Bag 92019, Auckland 1142,
New Zealand (corresponding author). ORCID: https://orcid.org/0000
-0002-8205-9617. Email: firstname.lastname@example.org
2Formerly, Ph.D. Researcher, Dept. of Civil and Environmental
Engineering, Univ. of Auckland, Private Bag 92019, Auckland 1142,
New Zealand. Email: email@example.com
3Professor, Dept. of Civil and Environmental Engineering, Univ.
of Auckland, Private Bag 92019, Auckland 1142, New Zealand. Email:
4Professor, School of Civil and Environmental Engineering, Georgia
Institute of Technology, Atlanta, GA 30332. Email: terry.sturm@ce
Note. This manuscript was submitted on May 4, 2020; approved on
October 12, 2020No Epub Date. Discussion period open until 0, 0;
separate discussions must be submitted for individual papers. This paper
is part of the Journal of Hydraulic Engineering, © ASCE, ISSN 0733-
© ASCE 1 J. Hydraul. Eng.
67 The peak stage of the floods reached up to nearly 6.1m higher than
68 the estimated peak stage of the 500-year flood, causing widespread
69 damage to bridge embankments and abutments with overtopping
70 flows and resulting in more than $193 million in damages and
71 ten deaths (Gotvald and McCallum 2010).
72 The complexity of abutment scour in a compound channel is
73 represented by the existence of pressure flow, the nonuniform
74 cross-sectional flow distribution (i.e., usually clear-water flow
75 on the floodplain and live-bed flow in the main channel), and
76 the difficulty in separating each scour component from the com-
77 bined final bed topography (Sturm et al. 2011). This dilemma ne-
78 cessitates a better understanding of the flow field at bridge
79 contractions as well as a thorough evaluation of erosive flow
81 Over the last 20 years, particular attention has been paid to the
82 flow field around unprotected abutments in simple rectangular
83 channels with FS flow, by both physical experiments (Kwan
84 and Melville 1994;Melville and Coleman 2000;Dey and
85 Barbhuiya 2005,2006a,b) and numerical modeling (Koken and
86 Constantinescu 2008a,b,2014;Koken 2018;Vui Chua et al.
87 2019). However, for an erodible abutment with protection under
88 the influence of pressure flow, sediment erosion processes feature
89 a gradual displacement of the scour hole to the downstream side
90 of the bridge, dynamic armoring when launching apron rocks
91 are used, and even the wash-out of embankment fill material
92 (Ettema et al. 2016;Idil-Bektur and Ettema 2017), which introdu-
93 ces uncertainty beyond the scope of an oversimplified model study.
94 To address this problem, research by Hong et al. (2015) has already
95 shown that, for a setback bridge abutment with a launching apron as
96 protection under pressure flows, the near-bottom turbulence inten-
97 sities prior to scour could be used as a scour indicator under clear-
98 water flow conditions. Under live-bed conditions, the relationship
99 between the initial flow field and the final bed topography are more
100 complicated because of the differential bed mobility in the main
101 channel and on the floodplain, which entails more sophisticated
102 flow measurement and analysis. This obvious research gap moti-
103 vated the present study, which was an offshoot of a much larger
104 study on the interaction of different bridge scour components in
105 both clear-water and live-bed scour (Sturm et al. 2018).
106 Currently, flow measurement in physical experiments is the
107 most reliable and practical approach to investigating flow fields.
108 In the past decades, techniques of flow measurement using acoustic
109 Doppler velocimeter (ADV) have developed tremendously (Nikora
110 and Goring 1998;Wahl 2000;Hurther and Lemmin 2001,2008;
111 Goring and Nikora 2002;Garcia et al. 2005;Blanckaert and
112 Lemmin 2006;Garcia et al. 2007;Dombroski and Crimaldi 2007;
113 Chanson 2008;Doroudian et al. 2010;Khorsandi et al. 2012).
114To deal with the inherent Doppler noise (Garbini et al. 1982), a
115series of procedures set by some of the aforementioned studies
116for noise reduction and signal despiking were strictly followed
117in this study, which will be detailed in the methodology section.
118The scope of this paper includes: (1) examining the appropri-
119ateness of using ADV for flow measurement with complex model
120configurations; (2) investigating the flow and turbulence features at
121bridge contractions in a compound channel with setback abut-
122ments; (3) investigating the effect of bridge deck submergence
123under FS, SO, and OT flow conditions; and (4) providing insights
124for evaluating the potential sediment scour damage that may occur
125during extreme flood events.
127Experimental Setup and Conditions
128The experiments were conducted in a 1.54-m-wide, 1.2-m-deep,
129and 45-m-long recirculating flume with adjustable slope. A 1.08-
130m-wide floodplain, a 0.26-m-wide main channel bank (2∶1), and
131a 0.2-m-wide main channel were built along the flume. A 4.6-m-
132long test section was located 30 m downstream from the inlet sec-
133tion. To measure the flow fields prior to scour, the test section was
134immobilized and coated with uniform quartz sand with a median
135diameter d50 ¼0.84 mm and a geometric standard deviation
136σg¼1.3. Outside the test section, the floodplain was roughened
137using uniform rocks, and the main channel was immobilized and
138coated using the sand as previously discussed. Fig. 2shows the
139schematic drawings of the flume and the model configurations.
140The test models were designed to represent a prototype, two-
141lane bridge at a 1∶45 geometric scale. The abutment models were
142in spill-through form with 2∶1side slopes (around 27° to the hori-
143zontal plane). An immobilized launching apron was used as a scour
144countermeasure around the abutment to simulate close-to-reality
145situations. The apron dimensions and the apron-rock size were de-
146termined based on the recommendations in HEC-23 (Lagasse et al.
1472009). The extent of the apron was 170 mm from the abutment toe
148toward the bridge waterway, and 170 mm from the abutment back
149along the embankment at the downstream side. The size of riprap
150rocks depended on abutment shape, channel Froude number, and
151flow depth and was calculated accordingly. After adjusting the
152flume slope for each case, preliminary velocity measurements were
153conducted along the flume to check that uniform flow was
155The experimental conditions in the present study, as summa-
156rized in Table 1, comprise a matrix of flow conditions, abutment
157lengths, and flow intensities, as described below:
F1:1 Fig. 1. Classification of bridge flow during flood events: (a) FS; (b) SO; and (c) OT. (Images courtesy of th4e USGS.)
© ASCE 2 J. Hydraul. Eng.
158 •Three flow conditions—FS, SO, and OT: These three conditions
159 cover the typical situations that usually occur during flood
161 •Three abutment lengths—long setback abutment (LSA, La=
162 Bf¼0.5), medium setback abutment (MSA, La=Bf¼0.65),
163 and short setback abutment (SSA, La=Bf¼0.8): Specifically,
164 Lais the abutment length from the tip to the flume wall, and Bf
165 is the width of the floodplain.
166 •Flow intensity in the main channel: The flow in the main chan-
167 nel was under live-bed conditions while not eroding the immo-
168 bilized bed, and the flow intensity ratio can be categorized into
169 two groups by its magnitude. The first group has relatively small
170 flow intensity (1.00 ≪Um=Um c ≤1.15) and is denoted by q
171 hereafter. The other group has relatively large flow intensity
172 (1.34 ≪Um=Um c ≤1.71) and is denoted by Qhereafter. Spe-
173 cifically, Umis the mean flow velocity in the upstream main
174channel, and Um c is the critical velocity for sediment incipient
175motion in the main channel.
176•Flow intensity on the floodplain: The flow on the floodplain
177was under clear-water condition (Ufl=Uflc≤1.0), where Ufl
178is the mean flow velocity on the upstream floodplain, and
179Ufl cis the critical velocity for sediment incipient motion on
181Data Acquisition and Processing
182A four-receiver Vectrino+ down-looking ADV (Nortek AS) wa 5s
183used to measure the flow field around the abutment. Measurements
184were conducted at three cross sections: the approach section
185(C.S.1), the downstream end of the bridge deck (C.S.4), and the
186downstream toe of the abutment (C.S.5), as shown in Fig. 2(a).
187The ADV was attached to a very rigid carriage and no noticeable
Long setback abutment
Medium setback abutment
Short setback abutment
Main channel bank
Section A - A
Main channelFlood plain Launching apron
LSA MSA SSA
C.S.1 C.S.4 C.S.5
F2:1 Fig. 2. Experimental setup and model configurations (unit: millimeters).
© ASCE 3 J. Hydraul. Eng.
188 vibration occurred during the measurements; the probe alignment
189 was checked after each movement. For selection of a sampling rate,
190 Nezu and Nakagawa (1993) suggested a dimensionless frequency,
191 Ff¼fRL=V>20, as the sampling frequency criterion (fRis the
192 recording frequency; Lis the energy-containing eddy length scale,
193 which can be assumed to be equal to the water depth; and Vis the
194 convective flow velocity). In this study the sampling rate was
195 chosen as 200 Hz (the upper limit of temporal resolution) for all
196 the measurements.
197 The ADV configurations, measurements, and postprocessing
198 procedures followed the general guidelines of Garcia et al.
199 (2007). In the near-bed flow zone, the sampling height was set at
200 1–2.5 mm, as suggested by Dey et al. (2011) and Guan et al.
201 (2014). Above this zone, the sampling height was set at 2.5–7 mm.
202 Because the optimum sampling time for a given turbulence level
203 is case-dependent, a sensitivity analysis to determine sampling
204 numbers was conducted prior to actual measurement, to ensure that
205 at least the second-order moment did not vary by more than 2% of
206 that from the longest sampling times. For each turbulence measure-
207 ment, typically 24,000 samples were recorded; for highly turbulent
208 zones, e.g., the near-bed flow zone at the bridge section, at least
209 60,000 samples were recorded, as suggested by Krogstad et al.
211 Generally, the raw data w
6ere first postprocessed using WinADV
212 (Wahl 2000) to remove spikes [using the phase-space threshold
213 method of Goring and Nikora (2002)] and to remove the data with
214 less than 70% signal correlation (COR) and less than 15-dB signal
215 noise ratio (SNR). Afterward, the method of Hurther and Lemmin
216 (2001) was applied to reduce the noise contained in the measure-
217 ments. The method is based on a noise spectrum reconstruction
218 using cross-correlation analysis of two simultaneous and indepen-
219 dent measurements of the same flow velocity component. Then the
220 noise spectra and variances are calculated and removed from the
221 corresponding velocity components. Kolmogorov’s−5=3law is
222 used as a criterion to examine the quality of corrected signals. It
223 should also be noted that due to the limitations of down-looking
224 ADVs, flow information for the top 50 mm of the flow is not
226Method of Analysis
227In this study, a set of turbulence properties are calculated using the
228measured data to help the analysis of flow features. Those turbu-
229lence properties include the overall turbulence intensity k, the tur-
230bulent kinetic energy (TKE), Reynolds shear stress components
231(τuv,τuw , and τvw), and the bed shear stress τ. The definitions
232and equations are detailed below.
233The overall turbulence intensity kis a differe 7nt form but related
234to the usual TKE representation, and the value can be calculated by
235in which u0,v0, and w0= streamwise, transverse, and vertical fluc-
236tuating velocity components.
237The TKE can be expressed as a function of k:
238in which ρ= density of water. The streamwise, transverse, and ver-
239tical TKE components can be obtained by replacing kin Eq. (2)
240with the corresponding fluctuating velocity components.
241Reynolds shear stress components represent turbulent fluctua-
242tions in fluid momentum in different planes and can be expressed
244Four methods are commonly used to estimate the bed shear
245stress τ(Soulsby 1981;Galperin et al. 1988;Biron et al. 2004;
246Pope et al. 2006); of these, the TKE method, formulated by Soulsby
247(1981), is used here:
Table 1. Experimental parameters
T1:1 Experiment Lα=BfQ(L=s) QOT (L=s) yf1(mm) yf2(mm) yf0(mm) qf2=qf1u%
T1:2 SSA_FS_q 0.8 36.1 —65 56 60 1.53 1.8
T1:3 SSA_SO_q 56.8 —102 85 87 1.28 1.7
T1:4 SSA_OT_q 84.4 24.4 150 147 133 1.27 1.9
T1:5 SSA_FS_Q 55.8 —71 57 59 1.44 2.5
T1:6 SSA_SO_Q 77.5 —103 64 62 1.28 2.4
T1:7 SSA_OT_Q 123.0 38.8 159 149 128 1.38 1.8
T1:8 MSA_FS_q 0.65 37.3 —69 67 68 1.65 1.9
T1:9 MSA_SO_q 57.0 —100 83 88 1.41 2.0
T1:10 MSA_OT_q 91.0 23.2 146 137 140 1.23 1.8
T1:11 MSA_FS_Q 55.6 —70 62 65 1.56 2.6
T1:12 MSA_SO_Q 78.8 —98 60 64 1.17 2.7
T1:13 MSA_OT_Q 129.9 37.9 155 145 134 1.21 2.7
T1:14 LSA_FS_q 0.5 40.4 —67 67 69 1.73 2.0
T1:15 LSA_SO_q 59.3 —101 86 93 1.37 2.0
T1:16 LSA_OT_q 92.0 24.3 147 141 142 1.24 2.0
T1:17 LSA_FS_Q 59.9 —68 63 67 1.94 2.8
T1:18 LSA_SO_Q 83.1 —99 61 74 1.19 2.7
T1:19 LSA_OT_Q 130.0 37.9 154 125 137 1.19 2.8
Note: Lα=Bf= ratio of abutment length to floodplain width; Q= total discharge; QOT = OT discharge; yf1,yf2,yf0= mean flow depth on floodplain measured
at approach (upstream) section (C.S.1), downstream end of bridge deck (C.S.4), and downstream section far from abutment, respectively; qf1,qf2= discharge
per unit width at C.S.1 and C.S.4, respectively; and u%
m1= shear velocity at C.S.1 in main channel.
© ASCE 4 J. Hydraul. Eng.
248 were τ= time-averaged shear stress; C0= empirical coefficient that
249 is taken as 0.19 in this study; and E= TKE.
251 Flow at Approach Section (C.S.1)
252 The flow distribution and turbulence features at the approach sec-
253 tion are considered similar to the uniform flow in a straight and
254 unobstructed compound channel with the same flow conditions
255 (e.g., velocity and depth), as the flow contraction is located far
256 downstream and the disturbance is minor. However, it should still
257 be noted that the flow at C.S.1 is not comparable to that in a similar
258 unobstructed channel with the same discharge due to the backwater
259 effect, especially for subcritical flows. Fig. 3(a) shows the vertical
260 distribution of normalized turbulence intensity at C.S.1 for a SSA
261 with overtopping flow and large flow rate (SSA_OT_Q). Specifi-
262 cally, u0,v0, and w0are the streamwise, transverse, and vertical
263 fluctuating velocity components, which are nondimensionalized
264 by the mean cross-sectional velocity U, and his the distance from
265 the measurement point to the local bed elevation. At C.S.1, a gen-
266 eral relationship of u0=U>v0=U>w0=Uis observed, which is in
267 accord with the prediction by Nezu and Nakagawa (1993) and mea-
268 surements by Babaeyan-Koopaei et al. (2002) and Koziol (2013)
269 for turbulent open-channel flow in compound channels. Moving
270 from the floodplain to the main channel, the distributions of
271 u0=U,v0=U, and w0=Utend to merge, presenting near-isotropic
272 turbulence. This can be attributed to the three-dimensional nature
273 of the flow around the floodplain-main channel interface
274 (Babaeyan-Koopaei et al. 2002;Koziol 2013). On the floodplain
275 (Y>460 mm), w0=Uincreases from the bottom upward to
276 h=ym1¼0.2and then slightly decreases toward the water surface.
277 This w0=Udistribution is different from the corresponding equa-
278 tions for turbulence intensity distribution of Nezu and Rodi
(1986) and Nikora and Goring (2000), which were derived for
smooth flat and gravel boundaries, respectively. Those equations
can be expressed in the form of either w0=U¼A×ðh=ym1ÞBor
w0=u%¼A×expðB×h=ym1Þ, where Aand Bare constant param-
eters and u%is the shear velocity mentioned in Table 1. One reason
for the difference in this study is the presence of the vegetationlike
roughness in the upstream channel, which caused a maximum value
of w0=Uabove the height of roughness elements instead of a
smooth increase toward the water surface. A similar vertical turbu-
lence intensity distribution was found by Koziol (2013) for a veg-
etated compound channel. The increasing trend of the three
normalized turbulence intensity components from h=ym1¼0.6up-
ward in the main channel agrees with the measurements conducted
by Koziol (2013). This increasing trend is due to suppression of the
vertical movement of eddies, and to surface waves (Nezu and
Fig. 3(b) shows the vertical distributions of u0=U,v0=U, and
w0=Uat Y¼100 mm (center of the main channel) for SSA experi-
ments. From the bottom to h=ym1¼0.2, all experiments have
decreasing trends of u0=Uand v0=U. In contrast, the distribution
of w0=Uis much more uniform. For the depth range 0.3<h=
ym1<0.5, the distributions of u0=Uand v0=Uexhibit a decreasing
trend for shallower water experiments (SSA_FS_q and SSA_
FS_Q) and are approximately constant for deeper water experi-
ments (SSA_OT_q and SSA_OT_Q). This difference is probably
caused by roughness elements. According to Koziol (2013), a more
uniform distribution of normalized turbulence intensities (as ob-
served for OT flows) occurs because flow in this depth range in
the main channel adjoins roughness-affected flow on the floodplain
and features a considerable momentum exchange between the main
channel and the floodplain. For h=ym1>0.5, mildly increasing
310trends of u0=U,v0=U, and w0=Uare observed.
Fig. 4show the cross-sectional distributions of normalized
overall turbulence intensity k=Uat C.S.1 for SSA_OT_q
313and SSA_OT_Q, respectively. The dashed line represents the
F3:1 Fig. 3. Vertical distribution of normalized turbulence intensity at C.S.1 for (a) different transverse positions for SSA_OT_Q; and (b) all SSA ex-
F3:2 periments for Y¼110 mm. Specifically, Y¼0mm is the right channel wall, Y¼100 mm is the middle of the main channel, Y¼200 mm is the toe
F3:3 of the main channel bank, Y¼460 mm is the top of the main channel bank, and Y¼1,540 mm is the left channel wall.
© ASCE 5 J. Hydraul. Eng.
314 width-averaged water surface level. It is apparent that k=Ugradu-
315 ally decreases upward over the whole measurement range. A rel-
316 atively high magnitude of k=Uwas found on the floodplain and at
317 the top of the main channel bank, and a lower magnitude of k=U
318 occurs in the main channel. Similar results were obtained by Koziol
319 (2013). For the two flow rates, the general distribution pattern of
320 k=Uremains the same while the near-bottom (within 20 mm above
321 the bed) turbulence intensity changes significantly. Overall, the
322 k=Ulevel for the higher flow rate case (SSA_OT_Q) is only 5.5%
323 less than that for SSA_OT_q, but in the near-bottom region this
324 difference reaches 23.4%.
325 Flow Acceleration Toward Bridge Section
326 Cross-sectional flow distribution is expected to vary significantly
327 when reaching the bridge contraction from the upstream undis-
328 turbed region. It should be clarified that, at the bridge contraction,
329 the flow was subcritical in all cases of FS flows. For a few pressure
330 flow conditions, supercritical flows were observed where vertical
331 contraction occurred or above the bridge deck for overtopping
332 flows. However, those supercritical flows were minor and did
333 not influence the turbulence features and the corresponding scour
334 potential to be discussed later; the general flow regimes were sub-
335 critical both in the main channel and on the floodplain. Fig. 5shows
336 the transverse distribution of depth-averaged flow velocity (U) at
337 the approach section (C.S.1) and the downstream end of the bridge
338 deck (C.S.4) for LSA and SSA. The approach flow velocity distri-
339 butions in Figs. 5(a and b) show obviously higher velocities in the
340 main channel relative to the floodplain. It should also be clarified
341 that the relative magnitude of velocities for different flow types was
342 mainly controlled by the flow depth and total flow discharge prior
343 to commencing the experiments. For both abutment lengths, the
344 main channel velocities in the approach section were set at similar
345 magnitudes for different flow conditions. For either abutment
346 length, because the roughness elements on the floodplain were un-
347 changed, the results show that OT flows had the highest floodplain
velocities in the approach section, whereas FS flows had the lowest.
Figs. 5(c and d) show the accelerated flow both in the main channel
and on the floodplain. Apparently, more significant lateral contrac-
tion for SSA (Lα=Bf¼0.8) leads to higher velocities across the
contracted section than for LSA (Lα=Bf¼0.5). The maximum
velocity at the downstream end of the bridge deck (C.S.4) depends
on the magnitude of overtopping discharge, approach flow condi-
tion, abutment length, and the elevation of the bridge deck. For
both abutment lengths presented in Fig. 5, SO flows had the highest
flow velocities in the bridge section, whereas FS flows had the
Fig. 6shows the distribution of discharge per unit width at C.S.1
(q1) and C.S.4 (q2) for both abutment lengths (LSA and SSA). It
can be found that OT flows had the largest q1values across the
approach section, whereas in the bridge section SO flows had
the largest q2values. In the approach section, different flow types
had distinctly different q1values, whereas at the downstream end of
the bridge, the differences between q2values became insignificant
for different flow types. q2=q1>1can be observed for most of the
situations for FS and SO flows and both abutment lengths, whereas
q2=q1<1usually prevails for OT flows on the floodplain due to
flow relief. Therefore, with the increase of OT discharges, OT flows
are expected to have further reduced q2=q1values, particularly on
372Flow at Bridge Section (C.S.4 and C.S.5)
In the present study, detailed flow measurements were taken
at cross sections where the downstream end of the bridge deck
(C.S.4) and downstream toe of the embankment (C.S.5) were lo-
cated. These two cross sections were also investigated experimen-
tally by Hong et al. (2015), who found that the most turbulent flow
may occur at C.S.5. Specifically, in our study, only the near-bottom
layer (5 mm above the bed) was measured at C.S.5 for analysis, and
more comprehensive flow field measurements were taken at C.S.4
381to cover a larger part of the cross section.
F4:1 Fig. 4. Normalized overall turbulence distribution at C.S.1 for (a) SSA_OT_q; and (b) SSA_OT_Q.
© ASCE 6 J. Hydraul. Eng.
F5:1 Fig. 5. Flow velocity distribution at approach section (C.S.1) and bridge downstream end section (C.S.4) for (a and c) SSA; and (b and d)
F6:1 Fig. 6. Distribution of discharge per unit width at approach section (C.S.1) and bridge downstream end section (C.S.4) for (a and c) SSA; and (b and
F6:2 d) LSA.
© ASCE 7 J. Hydraul. Eng.
382 Fig. 7shows the distribution of the normalized flow velocity
383 components at C.S.5 for the SSAs and LSAs, where Ux,Uy,
384 and Uzare the streamwise, transverse, and vertical velocity com-
385 ponents, respectively. In this study, u%¼u%
m1for consistency in the
386 comparison of different embankment lengths for all three flow
387 types. u%
m1was determined by the fitting of logarithm velocity pro-
388 file using the data measured at Y¼100 mm (main channel center-
389 line) and every 1 mm down the vertical direction. Fig. 7shows that
390 the bridge deck increases the magnitude of the velocity components
391 across the bridge section but does not change their general distri-
392 butions. As shown in the subplots of streamwise velocity compo-
393 nents, vertical contraction causes Ux=u%for the SO and OT flows to
394 be larger than that for the FS flows. In addition, because the over-
395 topped discharge produces some flow relief, Ux=u%in the SO con-
396 dition is slightly larger than that in the OT condition. The positive
397 peaks of Uy=u%for SSA experiments indicate the existence of
398 clockwise vortices on the top of the main channel bank, and the
399 negative Uy=u%values for the rest of the main channel bank show
400 that downslope flow prevails on the slope.
401 Compared with the SSA, the LSA [Fig. 7(b)] has smaller
402 Ux=u%,Uy=u%, and Uz=u%, and smaller magnitude variations across
403 the section. For each flow condition, relatively constant Uy=u%
404 values occur on the floodplain, which weaken to zero at the top
405 of the main channel bank. For the rest of the main channel bank,
406 Uy=u%values remain small. This suggests that a discernable down-
407 slope flow demands a relatively strong transverse flow in the
409 To present the flow velocity distribution at the bridge section in
410 more detail, Fig. 8shows the cross-sectional velocity vectors,
411 which are perpendicular to the streamwise direction and determined
412 from the time-averaged values of Uyand Uz, superimposed on the
413 Uxdistribution at C.S.4 for SSA_OT_q, LSA_OT_q, LSA_OT_Q,
414 and MSA_OT_Q, respectively. The results show that for each abut-
415 ment length, Uxincreases from zero to fairly high magnitudes over
416 a similar transverse distance (approximately 120 mm) from the
417 abutment toe. The transverse flow shifting from the floodplain into
418 the main channel can entrain sediment upward into the OT flow.
419 The aforementioned features show how the compressed streamlines
420 behave close to the abutment toe, and that the flow behavior follows
a regular pattern irrespective of flow rate and geometric contraction
ratio. It is suggested that the design of scour countermeasures
should take the flow behavior into consideration when determining
the minimum protection width. For the rest of the floodplain, Uy
beneath the bridge deck appears to be uniform over the water depth.
In the main channel, Uyweakens significantly, and weak upward
As previously mentioned, significant transverse flow was ob-
served at the y-zplane at C.S.4 and was subject to the effect of
bridge deck submergence. Figs. 9–11 present the time-averaged
y-zplane flow patterns in the main channel area (including main
channel slope bank), where transverse flow features were especially
complex. The results show that both the abutment length and the
deck submergence condition significantly affect the y-zplane flow
pattern at the bridge section. Under the FS flow, enclosed circular
flows in the center of the main channel can be clearly seen for LSAs
and MSAs [Figs. 9(b–d)]. The circular secondary flow stems from
the diverted floodplain flow entering into the main channel along
the main channel bank, and the loop is completed by weak mass
transfer toward the abutment near the surface. This circular flow is
induced by a transverse flow shooting into the main channel, but it
can overwhelm the surface return transverse flow. The example is
shown in Fig. 9(a), in which case the SSA induces stronger trans-
verse flow, and hence the weak circular flow disappears. Under the
SO flow, both the Uyand Uzcomponents grow stronger due to the
vertical contraction, and the Uzcomponent becomes predominant
when close to the bridge deck. Open-ended circular flows can be
clearly seen for the LSAs and MSAs [Figs. 10(b–d)]. The circle is
discontinuous near the surface, where the Uycomponent (for SO
flow) has a magnitude similar to that of the FS flow, but the Uz
component increases appreciably due to the flow relief immediately
downstream of the bridge deck. OT flows have weak near-bottom
flow in the main channel, but feature the strongest upward flow
among the three flow conditions at C.S.4 in the upper flow layer
[Figs. 11(a–d)]. This is possibly because the OT flow generates a
wake vortex region featuring relatively lower pressure, which fur-
457ther draws up the flow beneath the deck.
For all the experiments conducted in this study, the near-bottom
459flow in the main channel bank area has an obvious downslope
F7:1 Fig. 7. Normalized flow velocity measured at C.S.5 (5 mm above the bed) for (a) SSA; and (b) LSA.
© ASCE 8 J. Hydraul. Eng.
460 component, generating an extra sweeping force on the sediment
461 particles. For all three flow conditions (FS, SO, and OT), the
462 SSA induces the strongest transverse downslope flow component
463 due to the strongest flow diversion and contraction at the bridge
464 section, which may consequently enhance bed mobility and exac-
465 erbate the erosion on the main channel bank. In addition, for the
466 same abutment length, the SO flow generates the strongest down-
467 slope flow due to the greatest flow pressurization under the bridge
468 deck. Therefore, it is suggested that the combination of SSA and
469 SO flow requires extra attention in terms of the stability problem of
470 the main channel bank.
471 In general, the y-zplane secondary flow pattern could be used to
472 better understand the transverse mass transfer/momentum ex-
473 change processes at the bridge section in a compound channel,
474 which are associated with the creation of near-bottom turbulence
475 and mixing that lead to sediment mobility. As stated by Proust et al.
476 (2017), in an unobstructed compound channel with a significant
477 transverse flow toward the main channel, shear layer turbulence
478 (and Reynolds shear stress) cannot develop over the floodplain.
479 However, it has been shown not to be the case in the present study
480 at the bridge section due to both lateral and vertical contraction.
481 Therefore, it is of obvious importance to further discover the
482 near-bottom turbulence quantities for understanding the potential
risk of excessive sediment erosion (and also other issues such
as transport of nutrients or pollutants), as also emphasized by
485Chrisohoides et al. (2003) and Hong et al. (2015).
Fig. 12 shows the distributions of the three normalized turbu-
lence intensity components at 5 mm above the bed of C.S.5, for
the experiments with a SSA and a LSA, respectively. The general
spatial distributions of these turbulence quantities are the same for
experiments of the same abutment length, regardless of the flow
rates and the flow conditions in this study. Transverse distributions
of turbulence intensities for SO and OT flows are nearly superim-
posed, suggesting that the OT discharge relief of OT flows has little
494effect on the near-bottom turbulence.
For the SSA [Fig. 12(a)], u0=u%,v0=u%, and w0=u%peak around
the same area (110–160 mm transversally away from the abutment
toe), where the streamlines are the most compressed [Fig. 8(a)].
On the floodplain, higher magnitudes of u0=u%,v0=u%, and
w0=u%were found for pressure flows than for FS flows, indicating
that the bridge deck intensifies turbulence in all three directions,
and therefore intensifies the overall turbulence. On the main chan-
nel bank and in the main channel, the magnitude differences among
the three flow conditions are small for v0=u%and w0=u%, but remain
distinguishable for u0=u%. For the LSA [Fig. 12(b)], each normal-
505ized turbulence intensity component falls within a narrow band
F8:1 Fig. 8. Flow velocity distribution at C.S.4 for (a) SSA_OT_q; (b) LSA_OT_q; (c) LSA_OT_Q; and (d) MSA_OT_Q.
© ASCE 9 J. Hydraul. Eng.
506 with mild peaks close to the abutment. For the same flow condition,
507 the spatial distributions of u0=u%,v0=u%, and w0=u%are nearly
508 superimposed, suggesting that the flow rate differences have a neg-
509 ligible effect. In contrast, for the SSA, normalized turbulence
intensity increases along with the flow rate in a more apparent
511way [Fig. 12(a)].
In terms of the cross-sectional distribution of turbulence inten-
513sities, the results in this study correspond well with those obtained
F9:1 Fig. 9. Spanwise and vertical velocity distribution at C.S.4 for free FS flow: (a) SSA_FS_Q; (b) LSA_FS_q; (c) LSA_FS_Q; and (d) MSA_FS_Q.
F10:1 Fig. 10. Spanwise and vertical velocity distribution at C.S.4 for SO flow: (a) SSA_SO_q; (b) LSA_SO_q; (c) LSA_SO_Q; and (d) MSA_SO_Q.
© ASCE 10 J. Hydraul. Eng.
514 by Hong (2012). The differences in the magnitudes of the normal-
515 ized turbulence intensities between this study and those of Hong
516 (2012) are probably because of different flow regimes, perhaps
517 with respect to the approach flow turbulence.
518 As shown in Fig. 13, the normalized Reynolds shear stress dis-
519 tributions (5 mm above the bed), τuv=u%2,τuw =u%2, and τvw=u%2,
also have similar spatial trends at C.S.5 for experiments with
the same abutment length. For SSA [Fig. 13(a)], the general dis-
tributions of τuv and τuw for each experiment feature troughs
around 160 mm away from the abutment toe, at which position
the normalized velocity and the normalized turbulence intensities
525feature peaks [Figs. 7(a) and 12(a)]. This correspondence is as
F11:1 Fig. 11. Spanwise and vertical velocity distribution at C.S.4 for OT flow: (a) SSA_OT_q; (b) LSA_OT_q; (c) LSA_OT_Q; and (d) MSA_OT_Q.
F12:1 Fig. 12. Normalized turbulence intensity measured at C.S.5 (5 mm above the bed) for (a) SSA; and (b) LSA.
© ASCE 11 J. Hydraul. Eng.
526 expected. τvw is uniformly distributed across the whole section
527 and maintains a near-zero magnitude. For the LSA [Fig. 13(b)],
528 the variations and the magnitudes of τuv ,τuw, and τvw are small,
529 in accordance with the spatial distributions of turbulence intensities
530 [Fig. 12(b)].
531 Figs. 14(a and b) show the cross-sectional distributions of
532 normalized turbulence intensity k=u%at C.S.4 for SSA_OT_q
533 and LSA_OT_q, respectively. For LSA_OT_q, the most turbulent
534 zones are centralized beneath the bridge deck. This zone migrates
535 laterally into the main channel for SSA_OT_q, due to a stronger
536 transverse flow from the floodplain. The flow pattern near the
537 abutment toe presents zones of alternate high and low turbulence,
538 corresponding with the behavior of compressed streamlines
539 [Figs. 8(a and b)]. It is also found that the cross-sectional distribu-
540 tion of u0=u%is very similar to that of k=u%. On the floodplain,
541 although the flow is significantly disturbed laterally by the abut-
542 ment and vertically by the bridge deck, the streamwise turbulence
543 component was found to contribute the most to the overall TKE.
544 The data show that, on average, u0=u%¼0.70 for SSA_OT_q, and
545 u0=u%¼0.73 for LSA_OT_q. Figs. 14(c and d) show the distribu-
546 tions of subtractions of k=u%and Ux=u%at C.S.4 (i.e., the values of
547 SSA_OT_q–LSA_OT_q) for the overlapping area, respectively.
548 The results show that the cross-sectional distributions of k=u%
549 are highly negatively correlated with those of Ux=u%, i.e., the high
550 k=u%zone is accompanied by a low Ux=u%zone, and vice versa. An
551 explanation is that a stronger Uxin the main channel smoothens
552 pressure flow and weakens the effect of wake vortices immediately
553 downstream of the bridge deck. A comparison of the turbulence
554 distribution with the velocity distribution in Figs. 8(a and b) sug-
555 gests that, at the bridge section, the main source of the overall TKE
556 comes from the streamwise TKE component.
558 As shown in the previous sections, the flow at the bridge section is
559 subject to significant redistribution and magnified turbulence en-
560 ergy, which leads to a major risk of sediment entrainment and scour.
561 The judgement of scour initiation and erosion rate is usually made
562 according to the value of bed shear stress (τ), i.e., major scour is
initiated where the maximum τoccurs and the threshold value (τcr )
is exceeded. Figs. 15(a and b) compare the estimated bed shear
565stress and the threshold bed shear stress at C.S.4.
566The measurements for the estimated bed shear stress were all
conducted at 10 mm above the bed, following Guan et al. (2014).
The threshold shear stress τcr on the plane boundary is obtained
from the 8
modified Shields formula proposed by Brownlie (1981),
and the estimation of τcr on the main channel bank is based on the
571Lane (1955) relation.
Fig. 15(a) shows that a live-bed flow regime (τ=τcr >1) pre-
vails over the whole cross section of SSA_OT_Q. The shear stress
on the floodplain considerably exceeds the threshold values, espe-
cially at around Y¼510 mm (on the floodplain and close to the
main channel bank slope), where τ=τcr reaches 11. Therefore, it is
reasonable to infer that sediment erosion in this region develops
578most rapidly during the initial stage if the bed is erodible. Based
on HEC-23 (Lagasse et al. 2009), the launching apron set for
SSA_OT_Q in this study extends 170 mm from the abutment toe
to Y¼505 mm, where the sediment is the most vulnerable to ero-
582sion by the flow.
Fig. 15(b) shows the results for the LSA. The results show that,
around the abutment toe, the launching apron designed based on
HEC-23 affords sufficient protection for the FS flows, but insuffi-
cient protection for the pressure flows. It can be seen that, for the
pressure flows, the most vulnerable region is near the abutment
toe, where 2.16 ≤τ=τcr ≤6.30. On the main channel bank and
in the main channel, τexceeds τcfor most of the measurements
590(0.80 ≤τ=τcr ≤3.84). For the FS flows, in contrast, the most vul-
nerable region is in the main channel and on the main channel bank,
where on average τ=τcr ¼1.49 for LSA_FS_q and τ=τcr ¼2.63
for LSA_FS_Q. Near the abutment toe, the maximum value of
τ=τcr is 0.93 for LSA_FS_q and 1.98 for LSA_FS_Q. These re-
sults imply that, for the LSA, vertical contraction significantly af-
fects the location and strength of the erodible regions, and thereby
the vulnerability of the embankment toe to erosion. These results
highlight the necessity of further investigating the required dimen-
sions of the launching apron for pressure flows, for both LSAs
601Figs. 16(a and b) show the variations of turbulence intensity
602terms, i.e., kmax=u%and kf=u%, with different Lα=Bfvalues for
F13:1 Fig. 13. Normalized Reynolds shear stress measured at C.S.5 (5 mm above the bed) for (a) SSA; and (b) LSA.
© ASCE 12 J. Hydraul. Eng.
603 all the experiments. kmax is the maximum turbulence intensity at
604 5 mm above the bed across C.S.5, and kfis the width-averaged
605 turbulence intensity across the floodplain section of C.S.5. At this
606 stage, experiments without embankments, i.e., no lateral contrac-
607 tion (Lα=Bf¼0), were also performed to provide comparisons and
608 extend the data range of this study. Results that include Lα=Bf¼0
609 show that kmax=u%and kf=u%exhibit approximately linear relation-
610 ships with Lα=Bffor all three flow conditions for the specific com-
611 pound channel geometry in these experiments. The trends for SO
612 flows and OT flows nearly coincide, which can also be seen in
613 Fig. 12. The pressure flows produce higher turbulence intensity
614 than the FS flow, but both trends have similar gradients. For each
615 flow condition in this study, the scour prediction formula proposed
616 by Melville (1995) in a compound channel is adapted to
in which ds= maximum scour depth; KI,Kd,K%
s, and K%
eters accounting for flow intensity, sediment gradation factor, ad-
justed abutment shape factor, and adjusted bridge orientation factor,
respectively; and αk= constant for each flow condition. Because
the same channel geometry is used, for the investigated abutment
lengths, the channel geometry factor KGis assumed to be a con-
stant; the values of ym2,KI,Kd,K%
s, and K%
θare constant for each
624flow condition, with Lαthe only variable.
Eq. (7) suggests that, for each flow condition in this study, ds
has an approximately linear relationship with ﬃﬃﬃﬃﬃﬃ
p. As shown in
Fig. 16,kmax=u%and kf=u%are also linearly related to Lα(Bfis
constant). Therefore, the linear relationships mentioned previously
suggest that the relationship between kmax =u%(or kf=u%) and scour
depth dsmay be expressed as a function of Lα, i.e., kmax=u%(or
kf=u%)¼ds×fðLαÞ. This indicates that the scour depth around
the abutment (i.e., the final topography) is closely related to the
prescour turbulence intensity at the bridge section, which is also
634in accord with the conclusions of Hong et al. (2015).
F14:1 Fig. 14. Turbulence intensity distribution at C.S.4: (a) k=u%for SSA_OT_q; (b) k=u%for LSA_OT_q; (c) subtraction of k=u%(SSA_OT_q -
F14:2 LSA_OT_q); and (d) subtraction of Ux=u%(SSA_OT_q - LSA_OT_q).
© ASCE 13 J. Hydraul. Eng.
635 Fig. 17(a) shows the relationship between kmax=u%and qf2=qf1,
636 and Fig. 17(b) shows the relationship between kf=u%and qf2=qf1.
637 qf1and qf2are the width-averaged unit discharge on the floodplain
638 at C.S.1 and C.S.4, respectively. For pressure flows, only the flow
639discharging under the bridge deck was considered. The experi-
ments without embankments are denoted by NA. Prior to s 9
641flow parameters on the floodplain are more representative of tur-
642bulence conditions than those in the main channel, and hence
qf2=qf1is discussed here. The parameter qf2=qf1is a combined
644expression of channel configuration, lateral contraction, and verti-
cal contraction. The parameters kf=u%and kmax=u%are related to
646the magnitude of normalized TKE. Fig. 17 shows that, besides
NA data, the smallest values of qf2=qf1are obtained for the experi-
648ments with pressure flows, in which situations the submergence
649of the bridge deck impedes the discharge underneath while increas-
ing turbulence magnitudes. The peak values of kf=u%and kmax=u%
occur for SSAs with pressure flows when qf2=qf1≈1.3−1.4. FS
flows prevail for the higher values of qf2=qf1(1.5–2.0), and the
largest values of qf2=qf1are observed for LSAs, as less flow is
shifted to the main channel. Eventually, kf=u%and kmax=u%reduce
655asymptotically toward a constant level. It should be noted that
656trends in Fig. 17 are very similar to the variation of ymax =yC
with qf2=qf1, which was obtained for spill-through abutments
658by Ettema et al. (2010). Specifically, ymax is the maximum flow
659depth at the location of maximum scour, and yCis the estimated
660hypothetical long contraction scour depth. ymax =yCis regarded
661as a depth-amplification factor, which mainly accounts for the
662additional scour attributable to macroturbulence generated by flow
663passing the abutment. This similarity with the results of Ettema
664et al. (2010) indicates that pressure flows could be treated the
665same way as FS flow. In addition, this agreement suggests that
kf=u%and kmax=u%could be alternative depth-amplification factors
667for evaluation of the contribution of macroturbulence to final
668scour, as verified by Hong et al. (2015) for clear-water flow
F15:1 Fig. 15. Estimated bed shear stress at C.S.4 (10 mm above the bed) for (a) SSA; and (b) LSA.
F16:1 Fig. 16. Variation of normalized maximum turbulence intensity
F16:2 (kmax=u%) and normalized width-averaged turbulence intensity (kf=u%)
F16:3 with relative abutment length (Lα=Bf) at C.S.5.
© ASCE 14 J. Hydraul. Eng.
670 Future Research and Applications
671 Further research is recommended to improve the robustness of the
672 results in this study. The recommendations for future research are
673 as follows:
674 •More flow measurements can be performed to further examine
675 the influence of bridge deck submergence with the same flow
676 rate and momentum. Currently, the setup of the bridge model in
677 this study is fixed and does not allow vertical adjustment, which,
678 for example, entails a significant increase of flow rate for a tran-
679 sition from SO to OT flow.
680 •Scour tests can be carried out with erodible beds, wider ranges
681 of flow intensity, or cohesion of bank/floodplain materials that
682 are more representative of prototype conditions.
683 •Varying levels of submergence of the bridge deck should be ex-
684 tensively investigated under close-to-reality experimental condi-
685 tions. It would be helpful to study the scour patterns for a wide
686 range of the ratio of OT discharge to total discharge.
687 •The effectiveness of scour countermeasures can be further ex-
688 amined by performing scour tests with different extents and
689 thicknesses of rock riprap apron for pressure flow conditions.
690 The findings and data given in this paper can either be used di-
691 rectly to evaluate the risk of sediment scour or be compared to other
692 studies to validate numerical models. A more comprehensive
693 framework of scour risk evaluation can be built when more exper-
694 imental data become available.
695 Summary and Conclusions
696 Flow field and turbulence features at bridge sites in a compound
697 channel are studied experimentally using setback abutments and
698 different pressure flow conditions. The results show that the up-
699 stream flow pattern is not significantly affected by the downstream
700 obstruction. Moving from the floodplain to the main channel, the
701 distributions of u0=U,v0=U, and w0=Uin the approach channel
702 tend to merge, presenting near-isotropic turbulence. Flow rate
703 differences do not result in significant changes in the general tur-
704 bulence pattern but do result in magnitude differences both in the
705 main channel and on the floodplain, particularly for the near-
706 bottom region. Greater lateral and vertical contraction leads to
707 higher flow velocity at the bridge site. For the same abutment
708 length, SO flow has the highest flow velocity magnitudes at C.S.4,
709 whereas FS flows had the lowest. The unit discharge ratio q2=q1is
710 greater than 1 for most FS and SO flows, but q2=q1<1becomes
711 predominant for OT flows on the floodplain due to flow relief.
712 At the bridge section, flow types and discharge may influence
713 the magnitudes of normalized flow velocities, turbulence inten-
714 sities, and Reynolds shear stresses in all three coordinate directions,
715but the general turbulence pattern and the compressed streamlines
716stay the same. The transverse-vertical flow pattern (either enclosed
717or open-ended) in the main channel of the bridge section depends
718on the pressure flow type and abutment length. The combination of
719SO flow with a SSA may produce the strongest downslope flow on
720the main channel bank.
721The near-bottom turbulence intensity is linearly correlated with
722the abutment length for the given compound channel geometry. For
723each abutment length, the near-bottom turbulence intensity exhibits
724alternate high and low zones, answering to the behaviors of com-
725pressed streamlines. A strong interdependence exists between tur-
726bulence intensity and convective velocity at the rest of the bridge
727section. The estimated shear stress results show that, around the
728abutment toe, the launching apron design based on HEC-23 pro-
729vides adequate protection for FS flows but inadequate protection
730for the pressure flows, especially with a SSA.
731The clear relationships between the normalized turbulence
732intensities (kf=u%and kmax=u%) and the unit discharge ratio
733(qf2=qf1) suggest that pressure flows could be treated the same
734way as FS flow using the long contraction theory. The normalized
735turbulence intensity parameters (kf=u%and kmax=u%) could be used
736to evaluate the contribution of macroturbulence to final scour.
737More insights for future research and application are also given
738in this paper.
739Data Availability Statement
740All data obtained in this study are available from the corresponding
741author upon reasonable request.
743A portion of this work was sponsored by AASHTO, in cooperation
744with the Federal Highway Administration, and was conducted in
745the National Cooperative Highway Research Program (NCHRP),
746which is administered by the Transportation Research Board
747(TRB) of the National Academies of Sciences, Engineering, and
750The following symbols are used in this paper:
751Bf= floodplain width;
752ds= scour depth;
753d50 = median diameter of sediment particles;
754Ff= dimensionless frequency of ADV;
F17:1 Fig. 17. Variation of normalized maximum turbulence intensity (kmax =u%) and normalized width-averaged turbulence intensity (kf=u%) with qf2=qf1.
© ASCE 15 J. Hydraul. Eng.
755 fR= recording frequency of ADV;
756 h= distance from measurement point to bed level;
757 k= total TKE;
758 kmax = maximum TKE at C.S.5;
759 kf= width-averaged turbulence kinetic energy on floodplain at
761 L= energy-containing eddy length scale;
762 Q= total discharge;
763 QOT = overtopping discharge;
764 qf1= width-averaged unit discharge on the floodplain at
765 approach section (C.S.1);
766 qf2= width-averaged unit discharge on the floodplain at bridge
767 section (C.S.4);
768 U= mean flow velocity;
769 Um= mean flow velocity at approach section (C.S.1) in main
771 Um c = critical velocity in main channel;
772 Ufl = mean flow velocity at approach section (C.S.1) on
774 Uflc= critical velocity on floodplain;
775 Ux= streamwise flow velocity component;
776 Uy= transverse flow velocity component;
777 Uz= vertical flow velocity component;
778 u0= streamwise fluctuating velocity components;
779 u%= shear velocity;
m1= calculated shear velocity in main channel at approach
781 section (C.S.1);
782 V= convective flow velocity;
783 v0= transverse fluctuating velocity components;
784 w0= vertical fluctuating velocity components;
785 Y= distance from the measurement point to right flume wall;
786 yf0= mean flow depth on floodplain at far downstream;
787 yf1= mean flow depth on floodplain at approach section (C.S.1);
788 yf2= mean flow depth on floodplain at bridge section (C.S.4);
789 ym1= mean flow depth in main channel at approach section
791 ym2= mean flow depth in main channel at bridge section (C.S.4);
792 Z= vertical elevation coordinate (Z¼0at floodplain surface);
793 ρ= density of water;
794 σg= geometric standard deviation of sediment particles;
795 τ= bed shear stress;
796 τcr = critical bed shear stress;
797 τuv = Reynolds shear stress component 1;
798 τuw = Reynolds shear stress component 2; and
799 τvw = Reynolds shear stress10 component 3.
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