2Effects of Streamwise Abutment Length on Scour
3at Riprap Apron-Protected Setback Abutments
5Bruce W. Melville, M.ASCE1; Yifan Yang, A.M.ASCE2; Xiaozhou Xiong3;
6Robert Ettema, F.ASCE4; and Alireza Nowroozpour5
7Abstract: Scour at bridge abutments usually consists of local and contraction scour that correlate because of the flow field that develops both
8scours. Flume experiments were conducted using simulated compound channels to investigate the effect of a setback vertical-wall abutment’s
9streamwise contraction length on scour depth and pattern. The adequacy of the current design method for riprap aprons was also examined.
10 The prescour flow measurements showed that an abutment with small streamwise length may divert the highly turbulent zone2toward the main
11 channel and downstream that beyond the protection of the apron. By contrast, the turbulent zone of a long abutment tends to occur near the
12 abutment face and within the apron area. The erodible bed experiments showed that the abutment length may significantly affect scour depth,
13 morphology, and temporal development for apron-protected abutments but only has a minor influence on unprotected abutments. For apron-
14 protected abutments, an increased abutment length reduces the magnitude of the deepest scour and moves the scour hole closer to the con-
15 tracted section and the abutment face, which is consistent with the prescour flow field. Depending on the extent of setback, scour may also
16 extend into the main channel. It was found that the existing abutment scour predictors should consider streamwise abutment length in order to
17 reduce underestimation for short contractions and overestimation for long contractions. The design of riprap aprons should also be improved
18 accordingly and integrated with the predictors. DOI: 10.1061/(ASCE)HY.1943-7900.0001860.© 2020 American Society of Civil
4bridge abutments at rivers support a bridge’s deck at both
22 sides of the river crossing, the streamwise length of an abutment
23 (or a series of adjacent abutments) is likely an important variable
24 affecting scour depth at an abutment and in the region of flow con-
25 traction. This paper presents the findings of experiments that inves-
26 tigated this variable and its effect on the performance of riprap
27 aprons used as abutment-scour countermeasures. The experiments
28 give new insights into abutment scour at nonerodible vertical-wall
29 setback abutments of varying streamwise lengths.
30 Because the cross-sectional shapes of natural river channels are
31 usually compound (consisting of a main channel bordered by flood-
32 plains), a large number of bridge abutments are set back on the
floodplain, thereby minimizing flow contraction and enabling flood-
plain connectivity. During extreme floods, flow stages rise substan-
tially and submerge a river’s floodplain, leading to significant scour
around the abutment. 5
Fig. 1shows a typical layout of setback abut-
ments in a compound channel. Excessive abutment scour impairs
structural stability and safety redundancy of the bridge and may
39eventually lead to complete bridge failure.
Although abutment scour has been studied extensively, esti-
mates of scour depth at an abutment still vary substantially due to
the complexity of site conditions. As summarized by Melville and
Coleman (2000) and Sturm et al. (2011), the key factors influencing
scour depth and location include the length and shape of the abut-
ment, flow conditions (flow intensity, shallowness, unit discharge
ratio), channel conditions (geometry, roughness, sediment type), an
so forth. Knowledge regarding abutment scour has undergone sig-
nificant advancement in the last decade, with the help of several
large projects that focused on close-to-reality scour scenarios, in-
cluding Ettema et al. (2010), Hong et al. (2015), and Sturm et al.
(2018). Some other experimental studies, including Van Ballegooy
(2005), Fael et al. (2006), Ballio et al. (2010) and Hong and Abid
(2019), also provided useful information. Although Sturm et al.
(2011) delineated the dominant variables governing abutment
scour, the full influences of some variables are still unclear or
poorly defined. Hong et al. (2015) extended the theories of Sturm
(2006) and Ettema et al. (2010) to include both free-surface and
pressurized flow (flow congested by a bridge deck) conditions.
This adaptation integrated the long-contraction theory of Laursen
(1960,1963) into the new predictor and yielded good accuracy.
Further modifications were made by Sturm et al. (2018) by regres-
sion analysis based on a new large dataset. More information about
63those methods will be given in the following section.
The consensus is that any occurrence of local abutment scour
65is always accompanied by scour caused by channel contraction.
1Professor, Dept. of Civil and Environmental Engineering, Univ.
of Auckland, Private Bag 92019, Auckland 1142, New Zealand. Email:
2Honorary Research Fellow, Dept. of Civil and Environmental Engineer-
ing, Univ. of Auckland, Private Bag 92019, Auckland 1142, New Zealand
(corresponding author). ORCID: https://orcid.org/0000-0002-8205-9617.
3Formerly, Ph.D. Researcher, Dept. of Civil and Environmental Engineer-
ing, Univ. of Auckland, Private Bag 92019, Auckland 1142, New Zealand.
4Professor, Dept. of Civil and Environmental Engineering, Colorado
State Univ., Fort Collins, CO 80523. Email: email@example.com
5Ph.D. Candidate, Dept. of Civil and Environmental Engineering,
Colorado State Univ., Fort Collins, CO 80523. ORCID: https://orcid
.org/0000-0003-3906-3255. Email: firstname.lastname@example.org
Note. This manuscript was submitted on June 12, 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,ISSN0733-
© ASCE 1 J. Hydraul. Eng.
666 Those two scour types relate, though produce different magnitudes
67 of scour depth (Chang and Davis 1998,1999). Many numerical
68 studies (e.g., Paik and Sotiropoulos 2005;Koken 2018;Koken
69 and Constantinescu 2008a,b,2009,2014;Vui Chua et al. 2019)
70 have been done and have reported that the main hydrodynamic
71 forces causing local scour result from the turbulence structures gen-
72 erated as the flow separates from an abutment, while contraction
73 scour is mainly caused by flow acceleration into the contracted
74 area. The flow pattern may be further complicated in compound
75 channels with transverse momentum exchanges (Proust et al. 2017;
76 Proust and Nikora 2020). Some studies (Proust et al. 2006;Peltier
77 et al. 2013) have investigated the influence of lateral floodplain
78 contractions on the flow, but the existing knowledge is still far from
79 sufficient to draw general conclusions.
80 In general, this paper intends to investigate the effect of channel
81 contraction on scour at setback abutments in compound channels,
82 with the streamwise abutment length as the main variable. The
83 scope includes comparing the prescour flow fields for different
84 abutment lengths, understanding the postscour bed morphologies
85 and relating them to the flow, and exploring the necessity of inte-
86 grating streamwise abutment length in order to improve the accu-
87 racy of the existing scour prediction methods.
88 Contraction Scour and Local Scour for Setback
90 Contraction scour and local abutment scour at bridge waterways
91 have attracted wide research attention for many decades, and the
92 scour-depth effect of streamwise abutment length has been of in-
93 terest for quite a while. The following is a brief review of this
95 Straub (1934) proposed a theory regarding the formation of a
96 long contraction. His work was followed by a series of theoretical
97 and experimental studies, for example, Laursen (1960,1963),
98 Komura (1966), Webby (1984), Hager and Dupraz (1985), Lim and
99 Cheng (1998), Wu and Molinas (2001),7and Dey and Raikar (2005).
100 Briaud et al. (2005) tested fine-grained soils and showed that the
101maximum initial shear stress along the centerline of the channel
102is insensitive to the contraction length. Recent experiments by Now-
103roozpour (2020) indicated that contractions can be considered short
104when an abutment’s streamwise length is within about twice the
105width of the approach flow channel because of the influence of
106the abutment on turbulence generated in the flow field formed by the
108General formulations of abutment scour do not include an
109abutment’s streamwise length as a variable. Ettema et al. (2010)
110concluded that local scour at bridge abutments can be treated as an
111amplification of lateral contraction scour, and such amplification is
112due to abutment-induced local turbulence structures. Therefore, the
113classical equations of Laursen (1960,1963) for a long contracting
114stream tube were adapted to the following equations for relatively
115short contractions at bridge 8sites:
116where αAand αB= scour-amplification factor for Condition A
117(short setback or bankline abutments) and Condition B (long set-
118back abutments); yf1and ym1= approach flow depth on the flood-
119plain and in the main channel, respectively; qf1and qf2= unit
120discharge in the approach and contraction section on the floodplain,
121respectively; qm1and qm2= unit discharge in the approach and con-
122traction section in the main channel, respectively; τf1= shear stress
123in the upstream channel on the floodplain; τc= critical shear stress;
124Uf1and Uf1c= approach flow velocity and critical velocity on the
125floodplain, respectively; and yf2max and ym2max = maximum post-
126scour flow depth on the floodplain and in the main channel, respec-
127tively. Bed shear stress and turbulence kinetic energy (TKE) are
128closely correlated; therefore, TKE is usually used to predict the
129bed shear stress or show the locations that are scour-prone.
F1:1 Fig. 1. Typical layout of setback abutments for a bridge in a compound channel.
© ASCE 2 J. Hydraul. Eng.
130 Hong et al. (2015) extended the long contraction theory for pres-
131 surized flows (i.e., submerged orifice and overtopping flows). The
132 adapted equations are
133 where yf0and ym0= undisturbed tailwater depth on the floodplain
134 and in the main channel, respectively; and Um1and Um1c= ap-
135 proach flow velocity and critical velocity in the main channel, re-
136 spectively. Eq. (3) is suitable for long setback abutments, and
137 Eq. (4) is suitable for short setback or bankline abutments.
138 Sturm et al. (2018) proposed the most recent modification based
139 on a new large dataset and regression analysis. The equations can
140 be expressed as follows:
141 where Eq. (5) is for long setback abutments; and Eq. (6) is for short
142 setback or bankline abutments.
143 However, Eqs. (1)–(6) do not include an abutment’s streamwise
144 length as a variable. Moreover, the literature generally lacks infor-
145 mation about the effects of abutment length on the performance of
146 scour countermeasures, notably riprap aprons (e.g., Lagasse et al.
147 2009). This paper does not extensively review apron design and
148 performance, but a natural corollary of an investigation into the
149 scour-depth effects of abutment length is an investigation of the
150 same length effects on apron performance.
151 Flume Experiments
152 The experiments were conducted in a recirculating tilting flume in
153 the fluid mechanics laboratory at the University of Auckland and
154 were a simplification of the layout shown in Fig. 1. The experimen-
155 tal setup replicated half of a symmetrical channel, in which the
156 flume wall opposite the floodplain represented the centerline of
157 the compound channel. The flume was 1.54 m in width (B), 1.2 m
158 in depth, and 45 m in length. A 1.08-m-wide floodplain (Bf), a
159 0.26-m-wide main channel bank (2:1 slope), and a 0.2-m-wide
160 main channel were built along the flume, as shown in Fig. 2.
161 A 4.6-m-long test section was located 30 m downstream from
162 the inlet section. The test section comprised the floodplain and
163 the main channel and was filled with uniform quartz sand with a
164 median diameter d50 ¼0.84 mm and geometric standard deviation
165 σg¼1.3. Outside the test section, the floodplain was roughened
166 using uniform rocks, and the main channel was immobilized and
167 coated using the aforementioned sand.
168 Vertical-wall abutments of varying streamwise lengths (LC¼12,
169 45, 135, 810, 1,600, and 2,445 mm) and a constant transverse length
170 (Lα¼540 mm) were used in this study, with a representative geo-
171 metric scale of about 1:45 for actual bridges. The relative contraction
172 length (Lc=Bf) was, therefore, in the range of approximately 0.011–
173 2.26. The abutments extended down to the flume’s invert. The
174 lengths LCwere representative of bridges forming short contractions,
175 because LCwas less than the overall width of the approach channel
176 (Nowroozpour 2020); that is, LC<2×1.54 m¼3.08 m. The
177 acrylic box-shaped models were positioned on the floodplain near
the middle of the sand recess length. Experiments with and without
countermeasures (rock riprap apron) were carried out in this study in
180order to investigate the effect of countermeasures on scour. Apron
dimensions and apron-rock size were determined based on the rec-
ommendations in 9
HEC-23 (Lagasse et al. 2009). The extent of the
183apron was 170 mm from the abutment toe toward the bridge water-
184way and 170 mm from the abutment back along the embankment at
the downstream side. The median diameter of the riprap rocks was
about 20 mm. Fig. 2shows the experimental setup. Specifically,
187C.S.1 denotes the transverse section upstream of the abutment, and
188C.S.3 and C.S.4 denote the sections where the upstream and down-
stream abutment faces were located, respectively. No piers were
The parameters of the performed scour experiments are summa-
192rized in Table 1. The water depth on the floodplain was set at
193180 mm for all the experiments in this study. It was assumed that
the abutment had a negligible backwater effect on the approach
flow; that is, the flow depths in the upstream and downstream chan-
196nels were the same. Also checked were the effects of abutment
lengths on approach-flow conditions. In addition, the experiments
were limited to conditions that did not cause choking of the ap-
proach flow passing through the bridge waterway. Choking would
200produce supercritical flow through a major part of the waterway.
The mean Froude numbers in the approach flow channel were 0.23
in the main channel and 0.22 on the floodplain. Also, the design of
the experiments considered the scaling issues related to simulating
204turbulence intensities associated with flow fields involving flow
separation (Ettema et al. 2006). The discharge was designed to
ensure that a clear-water flow regime persisted in the approach
flow channel. Specifically, the flow intensity in the main channel
208(Um1=Um1c) was kept constant at 0.99 (Uf1=Uf1c¼0.78 on the
to the formal tests, the slope of the flume was adjusted to
ensure that uniform flow would occur. Multiple ultrasonic depth
sounders were positioned at C.S.3 and the expected scour hole lo-
213cations in order to record scour history during the experiments.
Each experiment lasted 22–48 h, and the postscour bed bathymetry
was also measured using the depth sounders. Another two fixed-
bed experiments were performed in order to study the prescour flow
217field around a one-lane bridge abutment model (LC=Bf¼0.13)
and a six-lane bridge abutment model (LC=Bf¼0.78). The veloc-
ity measurements were made using a down-looking four-receiver
Vectrino+ acoustic Doppler velocimeter (ADV) with a sampling
221frequency of 200 Hz. Flow measurements were made at eight hori-
zontal planes (10, 25, 40, 55, 70, 85, 105, and 115 mm above the
bottom). In each horizontal plane, the grid size was 10 cm in both
the x- and y-directions. 13
The measurement locations are shown in
225Figs. 2(b and c) as small circles.
226Prescour Flow Characteristics
This section presents the prescour flow fields around two abut-
228ments. As an essential indicator, the near-bottom characteristics
of flow velocity around the structure are critical to the development
of scour depth. Therefore, in this section, the velocities measured at
23110 mm above the bed on the floodplain are discussed. Total turbu-
232lence kinetic energy [TKE ¼ðu02þv02þw02Þ=2] and an ensem-
ble of velocity vectors were used to characterize the flow field at the
model abutments. In particular, these variables indicate the contrac-
tion of flow and the wake vortices formed as the flow separated
236from the upstream and the downstream faces of the abutments.
237Fig. 3shows the distribution of the TKE amplification scale
238(i.e., normalized by the near-bed TKE in the upstream floodplain
© ASCE 3 J. Hydraul. Eng.
239 channel) and velocity vectors in the horizontal plane (x,y-plane)
240 at 10 mm above the bed of the floodplain. The dashed lines mark
241 the extent of the riprap aprons applied for the corresponding scour
242 experiments. The results showed that the distribution of TKE was
significantly affected by the streamwise contraction length in this
study. For the short contraction model [Fig. 3(a)], 14
values of TKE
scale peaked at about 20, and a relatively small area of high-
246intensity turbulence (TKE scale >18) was located about 260 mm
Table 1. Experimental parameters10
T1:1 Group No. Test yf1(mm) Lα(mm) LC(mm) Uf1=Ufc Um1=Umc LC=BfLc=Lat(h) Protection
T1:2 1 T1 180 540 12 0.78 0.99 0.011 0.02 22 N/A
T1:3 T2 180 540 12 0.78 0.99 0.011 0.02 48 Riprap apron
T1:4 2 T3 180 540 135 0.78 0.99 0.13 0.25 22 N/A
T1:5 T4 180 540 135 0.78 0.99 0.13 0.25 48 Riprap apron
T1:6 3 T5 180 540 810 0.78 0.99 0.75 1.50 22 N/A
T1:7 T6 180 540 810 0.78 0.99 0.75 1.50 48 Riprap apron
T1:8 4 T7 180 540 2,445 0.78 0.99 2.26 4.53 22 N/A
T1:9 T8 180 540 2,445 0.78 0.99 2.26 4.53 48 Riprap apron
T1:10 5 T9 180 540 45 0.78 0.99 0.042 0.08 48 Riprap apron
T1:11 T10 180 540 1,600 0.78 0.99 1.48 2.96 48 Riprap apron
Note: yf1= mean flow depth on the floodplain in approach section; Lα= transverse abutment length; LC= streamwise abutment length; Bf= floodplain width;
Uf1and Um1= mean flow velocity on the floodplain and in the main channel, respectively; Ufc and Umc = critical velocity on the floodplain and in the main
channel, respectively; and t= test duration.
F2:1 Fig. 2. Schematic drawing of the experimental set-up: (a) plan view; (b and c) flow measurement locations for fixed-bed experiments; and (d) cross
F2:2 section at the bridge contraction.
© ASCE 4 J. Hydraul. Eng.
247 downstream of C.S.3. The trajectory of the shedding turbulence
248 followed the centerline of the high-TKE area, along which the
249 scouring process was initiated for the experiment with an erodible
250 bed. From Fig. 3, note that the protection provided by the apron
251 was inadequate for the corresponding scour experiment; that is,
252 most of the high-turbulence-intensity area was not protected at
253 the initial stage of scour.
254 For the long contraction model [Fig. 3(b)], the peak TKE scale
255 values (approximately 23) were higher than for the short contrac-
256 tion model. A relatively large area of high-intensity turbulence
257 (TKE >18) was observed, and its center was located about 480 mm
258 downstream of C.S.3. It can be seen that the protection extent pro-
259 vided by the apron was generally adequate (i.e., covering most of the
260 high-TKE area) for the corresponding scour experiment. The trajec-
261 tory of the shedding turbulence, as well as the high-TKE area, for the
262 long abutment model moved slightly toward the abutment, compared
263 with the short abutment model. This phenomenon implies a probable
264 more rapid scour initiation and deeper scour hole for the short
abutment if countermeasures are applied for both abutments. In ad-
dition, Fig. 3also shows that, at the initiation stage of scour, the time-
averaged velocities in the horizontal plane were not significantly
268affected by the different abutment lengths.
To better show the differences between the two models, the
distribution of the differential TKE scale [calculated by ðlong
contraction −short contractionÞ=short contraction] is presented in
Fig. 4(a). The long 15
contraction model had over three times higher
TKE along the abutment’s side face, while the short contraction
model had higher TKE diagonally downstream of the abutment.
The red zone in Fig. 4(a) was protected by a long-extending apron
while the purple zone was not well protected by the corresponding
277apron. This difference is in accord with those observed in Fig. 3.
Similarly, the distribution of the differential scale of Reynolds
shear stress at 10 mm above the plane bed is shown in Fig. 4(b).
Here, the result of the principal Reynolds shear stress component
(τuv ¼−u0v0) is presented. The results in Fig. 4(b) align with those
in Fig. 4(a), showing that the long contraction abutment had
F3:1 Fig. 3. Distribution of TKE and horizontal velocity vectors at 10 mm above the plane bed for (a) short contraction (LC=Bf¼0.13); and (b) long
F3:2 contraction (LC=Bf¼0.75).
F4:1 Fig. 4. Distribution of the difference of (a) TKE; and (b) Reynolds shear stress between the short- and long-contraction experiments (the long-
F4:2 contraction data17 subtracted by the short-contraction data).
© ASCE 5 J. Hydraul. Eng.
283 relatively strong turbulence close to its side face, yet this area was
284 well protected by the apron in the corresponding scour experiment.
285 The short contraction model caused a relative shearing effect at the
286 downstream side of the abutment, beyond the protection of the
287 apron. The negative zone was close to the center of the equilibrium
288 scour hole for the short contraction (marked by a cross), and scour
289 holes are discussed in the following section.
290 The skewness coefficient measures the asymmetry of the veloc-
291 ity distributions, and it reveals the presence of high-magnitude
292 events within the velocity signal (Buffin-Belanger and Roy 1998).
293 The events were produced by the convection of wake vortices
294 formed as flow separated from the upstream corner of the abutment.
295 A positive skewness suggests that relatively rare, large positive val-
296 ues are more frequent than large negative values and vice versa
297 (Lacey and Roy 2008;Lacey and Rennie 2012). The streamwise
298 and vertical components of skewness are defined as Skuuu ¼
uand Skwww ¼w0w0w0=σ3
w, respectively. To describe tur-
300 bulent events, the terms ejection (Skuuu <0and Skwww >0), sweep
301 (Skuuu >0and Skwww <0), inward interaction (Skuuu <0and
302 Skwww <0), and outward interaction (Skuuu >0and Skwww >0)
303 were used, following Nakagawa and Nezu (1977). Relatively rare
304 but strong turbulent events (sweeps and ejections) have been found
305 to account for most of the total Reynolds shear stress (Williams
306 et al. 1989;Lacey and Roy 2008) and are instrumental in the
transport of suspended and bedload sediments (Bennett and Best
1995;Williams et al. 1989). Fig. 5shows the spatial distributions
of Skuuu and Skwww at 10 mm above the plane bed for both models.
310The data in Fig. 5suggest the following points:
3111. Sweeping and ejection events mainly occurred in the vicinity of
3132. Inward interactions mainly occurred next to the abutment side
3153. Outward interactions dominated the rest of the measurement
316area, particularly where flow diverged toward the main channel.
The distributions of Skuuu resemble each other for both abut-
ment models. The short abutment produced more frequent sweep-
ing and ejection events around the toe of the abutment than did the
long model, whereas the long abutment produced more frequent
inward interaction events along the side face of the abutment than
322did the short abutment.
Furthermore, a holistic three-dimensional ( 18
3D) view of the dis-
tributions of TKE and flow velocities is given in Fig. 6to illustrate
the flow in the entire volume in which measurements were taken.
Specifically, in Figs. 6(a and c), TKE data are presented in five
vertical planes (x,z-planes) where Y¼960, 860, 760, 660, and
560 mm, respectively. The undisturbed upstream flow velocity dis-
tribution is also displayed. Figs. 6(b and d) show the velocity vec-
330tors and isosurfaces for TKE ¼60 and 120 cm2=s2(i.e., about 7.4
F5:1 Fig. 5. Distribution of skewness coefficients at 10 mm above the plane bed: (a) Skuuu for a short abutment; (b) Skuuu for a long abutment; (c) Skwww
F5:2 for a short abutment; and (d) Skwww for a long abutment.
© ASCE 6 J. Hydraul. Eng.
331 and 14.8 times the upstream near-bed TKE on the floodplain), re-
332 spectively. The results in Figs. 6(a and c) show that the long con-
333 traction model produced a more turbulent flow in the two nearest
334 transects (Y¼960 and 860 mm) but a less turbulent flow in the
335 farther transect (Y¼760 mm). Although the near-bottom turbu-
336 lence was slightly more energetic than other parts across the entire
337 depth, the decrease of TKE toward the water surface was not sig-
338 nificant for both models. For the other two outer transects (Y¼660
339 and 560 mm), no significant differences between TKE magnitudes
340 (and distributions) were observed. In Figs. 6(b and d), weak reverse
341 flows were observed near the abutment face, as shown in the close-
342 up subplots. The length of the reversal zone was proportional to the
343 streamwise contraction length and was presumably caused by the
344 flow separation at the upstream abutment corner. The TKE isosur-
345 faces suggest a more explicit contrast, that the long contraction
346 model featured a larger extent of the turbulent zone toward the abut-
347 ment face as well as a larger high-TKE core (TKE ≥120 cm2=s2)
348 across the flow depth.
349 Postscour Bed Morphology
19 LiDAR-scanned postscour bed elevation data for all scour ex-
351 periments are shown in Fig. 7to
20 illustrate the influence of abutment
352 length and riprap apron on the scoured bed morphology. The lo-
353 cations of the maximum scour depths both on the floodplain
354 and in the main channel are marked by crosses. The main findings
355 are as follows:
356 1. The effect of abutment length on the equilibrium bed morphol-
357 ogy is insignificant when the abutment is not protected by any
358 form of scour countermeasure; and
3592. The effect of abutment length on the equilibrium bed morphol-
ogy becomes significant when the abutment is protected by a
riprap apron; both the maximum scour depth and the scour hole
Specifically, two scour holes occurred for the unprotected abut-
ments; one hole formed on the floodplain, and the other hole formed
in the main channel. The deepest scour hole occurred at the upstream
corner of the abutment, as shown in Figs. 7(a, c, e, and g). These
scour holes resembled frustums of inverted circular cones and were
mainly caused by local turbulent structures (e.g., horseshoe vortex
and downflow). A relatively shallow scour hole occurred in the
main channel due to flow acceleration, separation, and a secondary
vortex formed between the floodplain and the main channel (Vui
Chua et al. 2019). The shape, dimensions, or location of the maxi-
mum scour hole were insensitive to the streamwise abutment length
and compound channel configuration. This observation is sup-
375ported by Xiong et al. (2013).
For apron-protected abutments, the equilibrium scour holes
were located downstream of C.S.3, as shown in Figs. 7(b, d, f,
h, i, and j). The shape, dimensions, and location of the scour holes
depended on the apron layout and especially on the abutment’s
streamwise length. Because the apron mitigated scour at the abut-
the observed scour holes formed consequent to flow contrac-
tion and turbulence structures related to flow contraction. The shorter
abutments caused larger and deeper scour holes. When LC=Bf¼
0.011–0.75, the deepest scour 22
hole formed around 800 mm down-
stream of C.S.3 and centered on the floodplain. By contrast, for rel-
atively long abutments (LC=Bf¼1.48–2.26), two relatively shallow
scour holes occurred: one hole about 470 mm downstream of C.S.3
and centered on the main channel bank, and the other hole about
389750 mm downstream of C.S.3 and centered in the main channel.
F6:1 Fig. 6. Integrated 3D view for the entire measurement volume: (a) TKE distribution at vertical planes (x,z-planes) for a short abutment; (b) velocity
F6:2 vectors and TKE isosurfaces for a short abutment; (c) TKE distribution at vertical planes (x,z-planes) for a long abutment; and (d) velocity vectors and
F6:3 TKE isosurfaces for a short abutment.
© ASCE 7 J. Hydraul. Eng.
390 The data in this study were insufficient to obtain a clear relation be-
391 tween LC, apron extent, and the location of the deepest scour hole.
392 However, Fig. 7indicates that the scour hole moved upstream and
393 toward the main channel as abutment length increased. In effect, in-
394 creasing LC=Bfincreased the distance between the upstream and
395 downstream regions offlow separation. This trend was evident when
396 comparing TKE values in Figs. 6(b and d). It is presumed that a near-
397 uniform flow may occur in a long contraction. As reported by Proust
398 et al. (2013), the region of high Reynolds shear stress in a compound
399 channel is located on the interface ofthe main channel and floodplain
400 when the flow is uniform. This region is shifted over the floodplain
401 with mass transfers toward the floodplain or displaced in the main
channel with mass transfers toward the main channel. The measured
403postscour bed morphology supported this theory.
shows the transverse bed profiles for both unprotected
and apron-protected abutments measured at the locations of maxi-
mum scour depths. For unprotected abutments [Fig. 8(a)], the side
slopes of the scour holes were consistent (i.e., β1≈β2≈27°),
which was similar to the slope of the original main channel bank
and the angle of repose of the sediment. In contrast, in Fig. 8(b),
the transverse profiles for apron-protected abutments depended
heavily on the streamwise abutment length. For longer abutments
(LC=Bf¼0.75–2.26), the deepest scour occurred in the con-
413tracted area with a residue apron width Ws, indicating that a
F7:1 Fig. 7. Bed morphology at equilibrium stage for all the experiments in this study: (a) LC=Bf¼0.011, unprotected; (b) LC=Bf¼0.011, apron-
F7:2 protected; (c) LC=Bf¼0.13, unprotected; (d) LC=Bf¼0.13, apron-protected; (e) LC=Bf¼0.75, unprotected; (f) LC=Bf¼0.075, apron-protected;
F7:3 (g) LC=Bf¼2.26, unprotected; (h) LC=Bf¼2.26, apron-protected; (i) LC=Bf¼0.042, apron-protected; and (j) LC=Bf¼1.48, apron-protected.
© ASCE 8 J. Hydraul. Eng.
414 certain level of protection remains. The deepest scour depths oc-
415 curred at the boundary of the main channel bank and the flood-
416 plain with a side slope of approximately β3¼27°. Th is w as in
417 accord with the flow measurements of Proust et al. (2013). For
418 shorter abutments (LC=Bf¼0.011–0.13), the scour holes were
419 located downstream of the contracted areas (outside the apron-
420 protected area) and diverted transversely toward the floodplain
421 direction, but the side slopes (β4≈27°) were still similar. The
422 effect of apron length may be separated from the effect of
423 LC=Bfand needs further study to define.
424 Although the aforementioned differences of scour patterns were
425 evident, the definition of a long contraction is still vague. Komura
426 (1966) and Webby (1984) defined a long contraction (in rectangular
427 channels) as LC=B>1. Nowroozpour (2020), however, indicated
428 that when LC=B<1to 2, a contraction should be considered as a
429 short-length contraction, because the upstream and downstream re-
430 gions of flow separation from the contraction connect and interact.
431 Therefore, the threshold value depends on several parameters, in-
432 cluding transverse abutment length, abutment shape, and extent of
433 riprap apron, and further investigation is still needed.
434 Temporal Scour Evolution
435 To better understand the temporal scour evolution for apron-
436 protected abutments with different streamwise lengths, real-time
437 bed elevations were measured at various transverse transects:
438 •For Tests CC2 (LC=Bf¼0.011) and CC8 (LC=Bf¼2.26), five
439 ultrasonic depth sounders were positioned on C.S.3. The results
440 showed that for any transverse position on C.S.3, the scour de-
441 velopments at the upstream corner were very similar regardless
442 of the difference of streamwise abutment length. This finding
443 was in accord with the similar final bed morphologies around
444 C.S.3 in Fig. 7; and
445•For Tests CC9 (LC=Bf¼0.042) and CC10 (LC=Bf¼1.48),
446six ultrasonic depth sounders were positioned at transects at
447which the maximum scour depths occurred (835 mm down-
448stream of C.S.3 for CC9 and 350 mm downstream of C.S.3
449for CC10). The results are shown in Fig. 9.
450In Fig. 9, the scour histories within the scour holes varied sig-
451nificantly if riprap aprons were employed, and the short abutment
452produced a much deeper final scour hole but a slower scour rate at
453the initiation stage [Figs. 9(c–e)]. For the short abutment (LC=Bf¼
4540.042), the equilibrium scour hole was centered at Y¼600 mm,
455which was situated on the floodplain. For the long abutment
456(LC=Bf¼1.48), the equilibrium scour hole was centered at Y¼
457400 mm, which was situated on the main channel bank. This differ-
458ence supports the findings of bed morphologies in the previous
459sections (Fig. 7) from another perspective. 24The differences can
460be attributed to the different near-bottom turbulence distributions
461around the short and long abutments (Figs. 3and 6) and the coverage
462of the riprap apron, which may not be sufficient for short abutments.
25 463The apron extent along can be an important factor influencing both
464the postscour bed morphology and the scour history, and more study
465is needed in the future.
467Considering the nonuniform transverse bed geometry and flow dis-
468tribution in a compound channel, the scour depths in the main chan-
469nel and on the floodplain should be presented separately (Fig. 10).
470Fig. 10(a) shows the relation between the normalized scour depth
471(dsFP=yf1) on the floodplain and the normalized contraction
472length (LC=Bf). Here, dsFP is the scour depth calculated from
473the initial floodplain level (i.e., Z¼0mm). For unprotected abut-
474ments, the values of dsFP =yf1stayed more or less constant with
475varying abutment length due to an insignificant variation of the
F8:1 Fig. 8. Cross-sectional postscour bed profiles at the deepest scour holes: (a) unprotected abutments; and (b) apron-protected abutments.
© ASCE 9 J. Hydraul. Eng.
F9:1 Fig. 9. Temporal evolution of scour measured at the scour holes for two apron-protected abutments with LC=Bf¼0.042 and 1.48: (a) Y¼100 mm;
F9:2 (b) Y¼330 mm; (c) Y¼400 mm; (d) Y¼460 mm; (e) Y¼600 mm; and (f) Y¼860 mm.
F10:1 Fig. 10. Relationship between the normalized scour depth and the normalized length of abutment for (a) normalized scour depth dsFP=yf1measured
F10:2 on the floodplain; and (b) normalized scour depth dsMC=ym1measured in the main channel.
© ASCE 10 J. Hydraul. Eng.
476 main scour agents. For apron-protected abutments, the values of
477 dsFP=yf1decreased from 1.72 to 1.13 when LC=Bfincreased from
478 0.01 to 2.46. This decrease occurred because the impact of the main
479 scour agents (e.g., shedding turbulence, secondary vortices) were
480 affected by the extent of the riprap apron and the flow pattern
481 downstream of C.S.3. For the data obtained, a near power func-
482 tional relationship exists between dsFP =yf1and LC=Bffor apron-
483 protected abutments, with dsFP=yf1approaching a lower limit
484 asymptotically for LC=Bf>2.
485 Fig. 10(b) shows the relation between the parameters dsMC=yf1
486 and LC=Bf. Here, dsMC is the scour depth calculated from the ini-
487 tial main channel level (i.e., Z¼−130 mm). For unprotected abut-
488 ments, dsMC=yf1increased significantly with larger LC=Bf.
489 reason for this was that the flow was laterally restricted for a long
490 distance by a long abutment, while a short abutment partly relieved
491 the contracted flow, which then returned to the floodplain. For
492 apron-protected abutments, the decreasing trend was similar to that
493 on the floodplain, as shown in Fig. 11(a). The long-extending rip-
494 rap apron effectively mitigated the scouring process.
495 Ettema et al. (2010) defined the scour depth at a long setback
496 abutment as an amplification of the purely contraction-induced
497 scour, as expressed by Eq. (2). This amplification is widely accepted
498 as the consequence of local turbulence structures due to the presence
499 of the abutment. Following the long contraction theory of Laursen
500 (1963), the theoretical contraction-induced flow depth on the flood-
501 plain in this study is equal to yf1½ðUf1=Uf1cÞðqf2=qf1Þ&7=6¼
502 192 mm. Thus, the amplification factor αBcan be calculated by
503 αB¼yf2max=192. The results are shown in Fig. 11. It can be seen
504 that the amplification factor αBranges from 2.0 to 2.6 for the apron-
505 protected long setback vertical-wall abutments in this study, and a
506 decreasing trend can be observed with increasing LC=Bfvalues.
507 This decrease is attributable to the following reasons:
508 1. A longer extent of the riprap apron can better mitigate the scour-
509 ing impact of the turbulence structures generated by flow sep-
510 aration at the abutments; and
511 2. The near-bottom turbulence structures vary with abutment
512 lengths; therefore, the values of αBvary with contraction lengths.
513 Combining the results in this study with those calculated by
514 Hong et al. (2015) shows that αBis approximately 2.6 for long
515 setback short-contraction abutments in free-surface flows. The re-
516 sults in Hong et al. (2015) were obtained for apron-protected spill-
517 through and wing-wall abutments, and the proposed amplification
518 factor was 2.51, as shown in Eq. (3).
This study’s findings showed that the parameter LC=Bfinflu-
enced the maximum scour depth. However, the most recent abut-
ment scour predictors, for example, Hong et al. (2015) and Sturm
et al. (2018), did not consider the influence of streamwise contrac-
tion length. The developed equations [e.g., Eqs. (3) and (5)] are
based on a large dataset with a constant LC=Bfvalue (0.248). The
performance of the current predictors is shown in Fig. 12. The scour
depth on the floodplain calculated using Eq. (3) is significantly
larger than that calculated using Eq. (5), the latter underestimation
being nonnegligible for very short abutments (LC=Bf<0.1). Eq. (3)
generally provides an adequate safety redundancy for small LC=Bf
values, but the overestimation for long abutments may be too large to
produce an economical design. The design of LC=Bf¼0.248 was
based on a standard two-lane prototype bridge. Thus, it is reasonable
to conclude that the equations proposed Sturm et al. (2018) can be
534used for deep-founded abutment forms (two-lane or wider).
A major limitation of this study is that the design of the riprap
apron is associated with the streamwise abutment length with a
fixed width from the abutment walls. Although using this design
makes the data consistent and comparable with previous studies
(Hong et al. 2015;Sturm et al. 2018), the apron length alone may
also significantly affect the scour pattern. For example, extending
the apron further downstream of a short contraction and toward the
main channel may better protect the high-TKE zone and minimize
scour [Fig. 3(a)]. Further study should be performed in the future to
better address this issue and improve the existing criteria for apron
design. In addition, the effect of transverse abutment length was not
tested in this study but is a key variable in determining the flow
distribution as well as the type of scour damage at bridge sites. This
study is the start of a large test series that attempts to understand
scouring processes at bridge sites under an integrated framework.
Furthermore, caution should be exercised when applying the results
of this study to real cases, in which spill-through and wing-wall
abutment forms are usually adopted and geotechnical conditions
tend to be more complicated. 27
A rived channel comprised of cohe-
sive soils may have a different mechanism of bank failure or col-
lapse and way in which bed materials are eroded. Currently, only
limited information is available regarding this issue (e.g., Briaud
557et al. 2005).
F11:1 Fig. 11. Variation of the amplification factor [αBin Eq. (1)] with the
F11:2 normalized contraction length.
F12:1Fig. 12. Evaluation of the abutment scour-depth predictors by Hong
F12:2et al. (2015) and Sturm et al. (2018).
© ASCE 11 J. Hydraul. Eng.
559 The streamwise length of an apron-protected abutment significantly
560 influences scour depth and pattern at the abutment. The main con-
561 clusions from the present study are as follows:
562 1. Prescour flow fields were correlated with the corresponding
563 postscour bed morphology. For a short contraction (LC=Bf¼
564 0.13), the most turbulent zone was located along the abutment’s
565 streamwise face. For a long contraction (LC=Bf¼0.75), this
566 zone was located diagonally downstream of the abutment;
567 2. Regarding the postscour bed morphology, the deepest scour for
568 unprotected abutments centered at the upstream corner and was
569 insensitive to LC=Bf. For apron-protected abutments, however,
570 the equilibrium scour depth increased with decreasing LC=Bf,
571 and the scour pattern also varied significantly. Specifically, with
572 a shorter abutment (LC=Bf¼0.011–0.13), the equilibrium
573 scour hole shifted downstream of the contracted section and fur-
574 ther toward the floodplain from the main channel bank. The
575 temporal scour evolution data also supported these findings;
576 3. Although the extent of the riprap apron was associated with abut-
577 ment size in this study, it may also affect the scour pattern as the
578 sole variable. The current design method (28 Lagasse et al. 2006) is
579 inadequate for short contractions (LC=Bf¼0.011–0.13). How
580 to extend the apron further downstream and toward the main
581 channel for scour-prone cases is obviously of significance for fu-
582 ture research;
583 4. Regarding the equilibrium scour depth, for apron-protected
584 abutments, both the scour depths on the floodplain (dsFP)
585 and in the main channel (dsMC) decreased with increasing
586 LC=Bfand approached a lower bound asymptotically. In con-
587 trast, for unprotected abutments, dsFP was insensitive to, and
588 dsMC was proportional to, LC=Bf. For short contractions
589 (LC=Bf¼0.011–0.13), the presence of aprons may have
590 shifted the scour hole location but did not change the scour
591 depth; and
592 5. The scour predictor by Sturm et al. (2018) showed reasonable
593 agreement with the data in this study involving deep-founded
594 abutments of common widths (LC=Bf¼0.13 or wider). Further
595 modification can be made to consider the influence of LC=Bf
596 and reduce over- and underestimation.
597 Data Availability Statement
598 All data obtained in this study are available from the corresponding
599 author upon reasonable request.
601 This study was undertaken in parallel with29 NCHRP Project 24-37,
602 for which the third author was a key researcher. The authors wish to
603 acknowledge Professor Terry Sturm,30 PI for Project 24-37, for pro-
604 viding leadership and for giving generous help in understanding
605 scour processes at bridge foundations, which indirectly improved
606 the research reported herein.
608 The following symbols are used in this paper:
609 B= approach flow channel width;
610 Bf= floodplain width;
611 dsFP = scour depth on the floodplain;
612 dsMC = scour depth in the main channel;
613d50 = median diameter of sediment particles;
614LC= streamwise abutment length;
615Lα= transverse abutment length;
616qf1= unit discharge on the floodplain at approach section;
617qf2= unit discharge on the floodplain at contracted section;
618qm1= unit discharge in the main channel at approach section;
619qm2= unit discharge in the main channel at contracted
621Skuuu = skewness coefficient in streamwise direction;
622Skwww = skewness coefficient in the vertical direction;
623t= test duration;
624Uf1= mean flow velocity on the floodplain at approach
626Uf1c= critical velocity on the floodplain at approach section;
627Um1= mean flow velocity in the main channel at approach
629Um1c= critical velocity in the main channel at approach
631u0= streamwise turbulent velocity component;
632v0= transverse turbulent velocity component;
633Ws= residue apron width;
634w0= vertical turbulent velocity component;
635ym0= flow depth in the main channel far downstream of the
637ym1= flow depth in the main channel in approach channel;
638ym2= flow depth in the main channel at contraction;
639ym2max = flow depth in the main channel caused by combined
641yf0= flow depth on the floodplain far downstream of the
643yf1= flow depth on the floodplain in approach section;
644yf2= flow depth on the floodplain at contraction;
645yf2max = flow depth on the floodplain caused by combined
647αA= scour amplification factor for short setback or bankline
649αB= scour amplification factor for long setback abutments;
650β1,β2,β3, and β4= side slope angles of scour holes;
651σg= geometric standard deviation of sediment particles;
652σu= standard deviation of streamwise flow velocity;
653σw= standard deviation of vertical flow velocity;
654τc= critical bed shear stress;
655τf1= bed shear stress on the floodplain at approach section;
657τuv = principal Reynolds shear stress component.
659Ballio, F., A. Radice, and S. Dey. 2010. “Temporal scales for live-bed scour
660at abutments.”J. Hydraul. Eng. 136 (7): 395–402. https://doi.org/10
662Bennett, S. J., and J. L. Best. 1995. “Mean flow and turbulence structure
663over fixed, 2-dimensional dunes—Implications for sediment transport
664and bedform stability.”Sedimentology 42 (3): 491–513. https://doi.org
666Briaud, J. L., H. C. Chen, Y. Li, Nur, P. Tjahyo, and J. Wang. 2005. “SRI-
667COS-EFA method for contraction scour in fine-grained soils.”J. Geo-
668tech. Geoenviron. Eng. 131 (10): 1283–1294. https://doi.org/10.1061
670Buffin-Belanger, T., and A. G. Roy. 1998. “Effects of a pebble cluster on
671the turbulent structure of a depth-limited flow in a gravel-bed river.”
672Geomorphology 25 (3–4): 249–267. 31
© ASCE 12 J. Hydraul. Eng.
673 Chang, F., and S. Davis. 1998. “Maryland SHA procedure for estimating
674 scour at bridge waterways, part 1–live bed scour.”In Stream stability
675 and scour at highway bridges, edited by E. Richardson, and P. Lagasse,
676 401–411. Reston, VA: ASCE.
677 Chang, F., and S. Davis. 1999. “Maryland SHA procedure for estimating
678 scour at bridge waterways, part 2–clear water scour.”In Stream stability
679 and scour at highway bridges, edited by E. Richardson and P. Lagasse,
680 412–416. Reston, VA: ASCE.
681 Dey, S., and V. Raikar. 2005. “Scour in long contractions.”J. Hydraul. Eng.
682 131 (12): 1036–1049. https://doi.org/10.1061/(ASCE)0733-9429
684 Ettema, R., G. Kirkil, and M. Muste. 2006. “Similitude of large-scale tur-
685 bulence in scour around cylinders.”J. Hydraul. Eng. 132 (1): 33–40.
687 Ettema, R., T. Nakato, and M. Muste. 2010. Estimation of scour depth at
688 bridge abutments. Final Rep. No. NCHRP 24-20. Washington, DC:
689 Transportation Research Board.
690 Fael, C. M. S., S.-G. Gonzalo, J.-P. Martin-Vide, and A. H. Cardoso.
691 2006. “Local scour at vertical-wall abutments under clear-water flow
692 conditions.”Water Resour. Res. 42: W10408. https://doi.org/10.1029
694 Hager, W. H., and P. A. Dupraz. 1985. “Discharge characteristics of local,
695 discontinuous contractions.”J. Hydraul. Res. 23 (5): 421–433. https://
697 Hong, S. H., and I. Abid. 2019. “Scour around an erodible abutment with
698 riprap apron over time.”J. Hydraul. Eng. 145 (6): 06019007. https://doi
700 Hong, S. H., T. W. Sturm, and T. Stoesser. 2015. “Clear water abutment
701 scour in a compound channel for extreme hydrologic events.”J. Hy-
702 draul. Eng. 141 (6): 04015005. https://doi.org/10.1061/(ASCE)HY
704 Kohli, A., and W. H. Hager. 2001. “Building scour in floodplains.”Proc.
705 Inst. Civ. Eng. Water Marit. Eng. 148 (2): 61–80. https://doi.org/10
707 Koken, M. 2018. “Coherent structures at different contraction ratios caused
708 by two spill-through abutments”J. Hydraul. Res. 56 (3): 324–332.
710 Koken, M., and G. Constantinescu. 2008a. “An investigation of the flow
711 and scour mechanisms around isolated spur dikes in a shallow open
712 channel: 1. Conditions corresponding to the initiation of the erosion
713 and deposition process.”Water Resour. Res. 44 (8).3435
714 Koken, M., and G. Constantinescu. 2008b. “An investigation of the flow
715 and scour mechanisms around isolated spur dikes in a shallow open
716 channel: 2. Conditions corresponding to the final stages of the erosion
717 and deposition process”Water Resour. Res. 44 (8).3637
718 Koken, M., and S. G. Constantinescu. 2009. “An investigation of the dy-
719 namics of coherent structures in a turbulent channel flow with a vertical
720 sidewall obstruction.”Phys. Fluids 21 (8): 085104. https://doi.org/10
722 Koken, M., and G. Constantinescu. 2014. “Flow and turbulence structure
723 around abutments with sloped sidewalls.”J. Hydraul. Eng. 140 (7):
724 04014031. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000876.
725 Komura, S. 1966. “Equilibrium depth of scour in long constrictions.”
726 J. Hydraul. Div. 92 (5): 17–37.38
727 Lacey, R. W. J., and C. D. Rennie. 2012. “Laboratory investigation of tur-
728 bulent flow structure around a bed-mounted cube at multiple flow
729 stages.”J. Hydraul. Eng. 138 (1): 71–84. https://doi.org/10.1061
731 Lacey, R. W. J., and A. G. Roy. 2008. “Fine-scale characterization of the
732 turbulent shear layer of an instream pebble cluster.”J. Hydraul. Eng.
733 134 (7): 925–936. https://doi.org/10.1061/(ASCE)0733-9429(2008)
735 Lagasse, P. F., L. W. Zevenbergen, L. A. Arneson, P. E. Clopper, J. E.
736 Pagán-Ortiz, J. D. Schall, and L. G. Girard. 2009. Bridge scour and
737 stream instability countermeasures–experience, selection, and design
738 guidelines. Rep. No. FHWA NHI 09-111. Washington, DC: USDOT.
739 Laursen, E. M. 1960. “Scour at bridge crossings.”J. Hydraul. Div.
740 86 (HY2): 39–54.39
741Laursen, E. M. 1963. “An analysis of relief bridge scour.”J. Hydraul. Div.
74289 (HY3): 93–117. 40
Lim, S. Y., and N. S. Cheng. 1998. “Scouring in long contractions.”J. Irrig.
744Drain. Eng. 124 (5): 258–261. https://doi.org/10.1061/(ASCE)0733
746Melville, B. W., and S. E. Coleman. 2000. Bridge scour. Water Resources
748Nakagawa, H., and I. Nezu. 1977. “Predication of the contributions to the
749Reynolds stress from bursting events in open-channel flows.”J. Fluid
750Mech. 80 (01): 99–128. https://doi.org/10.1017/S0022112077001554.
751Nowroozpour, A. 2020. “Observations from a series of flume experiments
752on contraction scour along a wide channel.”Ph.D. dissertation,
753Colorado State Univ. 42
754Paik, J., and F. Sotiropoulos. 2005. “Coherent structure dynamics up-
755stream of a long rectangular block at the side of a large aspect ratio
756channel.”Phys. Fluids 17 (11): 115104. https://doi.org/10.1063/1
758Peltier, Y., S. Proust, N. Riviere, A. Paquier, and K. Shiono. 2013. “Tur-
759bulent flows in straight compound open-channel with a transverse em-
760bankment on the floodplain.”J. Hydraul. Res. 51 (4): 446–458. https://
762Proust, S., J. N. Fernandes, J. B. Leal, N. Rivière, and Y. Peltier. 2017.
763“Mixing layer and coherent structures in compound channel flows:
764Effects of transverse flow, velocity ratio, and vertical confinement.”
765Water Resour. Res. 53 (4): 3387–3406. https://doi.org/10.1002
767Proust, S., J. N. Fernandes, Y. Peltier, J. B. Leal, N. Riviere, and A. H.
768Cardoso. 2013. “Turbulent non-uniform flows in straight compound
769open-channels.”J. Hydraul. Res. 51 (6): 656–667. https://doi.org/10
771Proust, S., and V. I. Nikora. 2020. “Compound open-channel flows: Effects
772of transverse currents on the flow structure.”J. Fluid Mech. 885 (Feb). 43 44
773Proust, S., N. Rivière, D. Bousmar, A. Paquier, Y. Zech, and R. Morel.
7742006. “Flow in compound channel with abrupt floodplain contraction.”
775J. Hydraul. Eng. 132 (9): 958–970. https://doi.org/10.1061/(ASCE)
777Straub, L. G. 1934. “Effect of channel contraction works upon regimen of
778movable bed streams.”Trans. Am. Geophys. Union 15 (2): 454–463. 45
779Sturm, T., I. Abid, B. Melville, X. Xiong, T. Stoesser, B. F. Bugallo, K. V.
780Chua, S. Abt, and S. Hong. 2018. Combining individual scour compo-
781nents to determine total scour. Final Rep. No. NCHRP project 24-37.
782Washington, DC: Transportation Research Board.
783Sturm, T. W. 2006. “Scour around bankline and setback abutments in com-
784pound channels.”J. Hydraul. Eng. 132 (1): 21–32. https://doi.org/10
786Sturm, T. W., R. Ettema, and B. W. Melville. 2011. Evaluation of bridge-
787scour research: Abutment and contraction scour progresses and pre-
788diction. Final Rep. No. NCHRP project 24-27(02). Washington, DC:
789Transportation Research Board.
790Van Ballegooy, S. 2005. “Bridge abutment scour countermeasures.”Ph.D.
791thesis, Univ. of Auckland. 46
Vui Chua, K., B. Fraga, T. Stoesser, S. Ho Hong, and T. Sturm. 2019. “Ef-
793fect of bridge abutment length on turbulence structure and flow through
794the opening”J. Hydraul. Eng. 145 (6): 04019024. https://doi.org/10
796Webby, M. G. 1984. The effect of entrance shape on the depth of
797clear water scour at a contraction. Rep. No. 3-86/2. Lower Hutt,
798New Zealand: Ministry of Works and Development.
799Williams, J. J., P. D. Thorne, and A. D. Heathershaw. 1989. “Measurements
800of turbulence in the benthic boundary-layer over a gravel bed.”Sedi-
801mentology 36 (6): 959–971. https://doi.org/10.1111/j.1365-3091.1989
803Wu, B., and A. Molinas. 2001. “Choked flows through short contractions.”
804J. Hydraul. Eng. 127 (8): 657–662. https://doi.org/10.1061/(ASCE)
806Xiong, X., B. W. Melville, and H. Friedrich. 2013. “Effects of contraction
807length on abutment scour.”In Proc., 35th IAHR World Congress, edited
808by Z. Wang, 1898–1907. Chengdu, China. 47
© ASCE 13 J. Hydraul. Eng.