京都大学防災研究所年報第５１号 B

平成２０年６月

ｐｐ633-652

Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No.51B, 2008 pp.633-652

Scour around Spur Dyke: Recent Advances and Future Researches

Hao ZHANG and Hajime NAKAGAWA
SynopsisScour is a common phenomenon in river engineering and a challenging problem
for hydraulic research. Scour may bring human either benefits or disasters depending onwhether the scour process is well understood and effectively managed. Investigation onscour around spur dyke has a long history and still receives much attention to date. This
paper provides background knowledge and research prospect on this topic. The paper isorganized mainly in three parts. The first part presents a state-of-the-art on related
researches such as the flow structure, estimation formulae for equilibrium scour depth,
temporal and spatial variation of scour and scour around grouped spur dykes. After that,recent advances in numerical modeling techniques are presented, including the principle
ideas, governing equations and solution methods. Finally, possible avenues for future
researches are suggested.
Keywords: spur dyke, scour, recent advances, future researches

1.

Introduction

Spur dykes are typical man-made hydraulicstructures and are widely constructed in alluvial
rivers all over the world. Spur dykes are generally
built perpendicular or at an angle to the channelbank or revetment, protruding into the watercourse.
Historically, spur dykes were constructed to prevent
channel banks or levees from erosion by divertingaway approaching flows, to improve rivernavigation conditions by deepening the main
channel bed or to secure water supply andagriculture irrigation by maintaining suitable flow
discharge and water level. Nevertheless, aesthetic
and environmental impacts of spur dykes haveattracted much attention since several decades
before. Nowadays, spur dykes are also considered
as a promising measure to enhance diversities ofchannel morphologies and riverine eco-systems.
Spur dykes may be classified into various types.
According to structure permeability, spur dykes are
generally categorized into two types: impermeable
and permeable (Fig.1a). Impermeable spur dykes－

are built of local soil, stones, gravels, rocks orgabions, while permeable ones usually consist of
one or several rows of timber, bamboo, steel orreinforced concrete piles. An impermeable spurdyke blocks and defects the river flow, while apermeable one allows water to pass through it at a
reduced velocity. Based on submergence conditions,submerged and non-submerged spur dykes are
distinguished (Fig.1b). In general, the submerged
condition is not desirable for impermeable spurdykes since the overtopping flow may cause severe
erosion and damage. Spur dykes may be classified
as attracting, deflecting or repelling spur dykes
according to their inclination as shown in Fig.1c.
An attracting spur dyke points downstream andattracts the flow towards its head and thus to thebank. In contrast, a repelling spur dyke inclines in
upstream direction and diverts the flow away from
itself. The spur dyke normal to the flow is a
deflecting one. It diverts the flow at its head andresults in a wake zone behind it. Classification of
spur dykes may also be made according to theirappearances (Fig.1d). Due to the importance of the633 －head as will be discussed later, spur dykes aredesigned with various appearances mainly in termsof the shape of the head. Apart from a straight spurdyke, alternatives may include a mole-head, L-head,T-head or hockey-shaped one.
Typical flow

Impermeable
Permeable(a) Permeability
Water surface

Submerged

Non-submerged(b) Submergence

Typical flow

Attracting

Deflecting(c) Inclination

Repelling

Flow direction

scour and local scour. General scour takes place ona channel bed as a result of sediment transport
irrespective of whether or not a spur dyke is there.
Constriction scour arises from the narrowing of thewatercourse by the presence of the spur dyke. Local
scour results directly from the impact of the spurdyke on the local flow pattern. It is noticed that
local scour is usually superimposed on constriction
scour. Based on the sediment transport mode by theapproaching flow, local scour is either a clear-water
scour or a live-bed scour. Clear-water scour refers
to conditions when the bed material upstream of thescour area is at rest, i.e. the near-bed shear stress u*
some distance away from the spur dyke is not
greater than the critical shear stress u*c for the
initiation of particle movement. Live-bed scour
takes place when the near-bed shear stress isgenerally greater than the critical one and the flow
induces general sediment transport. Clear-water
scour and live-bed scour are usually differentiatedin conventional analyses of local scour. The
temporal variation of the maximum scour depths
under clear-water scour and live-bed scour
conditions are schematically shown in Fig.2.

Protruding of a structure such as a spur dyke toa channel leads to changes on the flow patterns andbed configurations. These changes usually initiate ascour process, involving turbulent flow, sedimenttransport and erodible boundaries. This process is a
dynamic feedback process. A clear understanding
and a scientific interpretation of this process are aprior for successful design and sustainable
management of hydraulic structures. Consequently,
tremendous amount of researches have been
conducted over the years in laboratory experiments,
numerical simulations and field measurements. As
is known, scour is a localized lowering of channel
bed due to the imbalance of sediment transport. The
scour occurring at a spur dyke is generally divided
into three categories: general scour, constriction－

Live-bed scour
Equilibrium scour depth
Clear-water scourt(a) Temporal variation of local scour(after Chabert and Engeldinger, 1956)

Clear-water peak
Averaged scour depth

Straight Mole-head L-head T-head Hockey-shaped(d) Shape
Fig.1 Classification of spur dykes

Scour depth

Dynamic equilibrium scour depth

Live-bed peakLive-bed scour
Clear-water scour

0

1

2

3

4

u*/ u*c(b) Local scour against shear stress(after Chiew, 1984)
Fig.2 Sketch of clear-water and live-bed scour

634 －In general, clear-water scour may be divided
into several stages: initial stage, development stage,stabilization stage and equilibrium stage. The scour
develops quickly at initial and development stages
and shows insignificant changes at the stabilization
stage. An equilibrium stage is reached finally,
which usually takes a longer time compared with alive-bed scour. In case of live-bed scour, the scour
increases rapidly with time and then fluctuates
about a mean value in response to the passages ofbed forms (Fig.2a). Although the near-bed shear
stress under live-bed scour condition is larger thanthat under clear-water scour condition, themaximum scour depth in the former case is notnecessarily larger than that in the latter one. Scour
occurs when the near-bed shear stress is larger thana critical value (Fig.2b). With the increasing of thenear-bed shear stress, the scour depth at theequilibrium stage increases. A peak value occurs
when the near-bed shear stress equals to the critical
shear stress. This peak is called a clear-water peak.
The scour depth decreases from the clear-water
peak with the development of bed forms andreaches a minimum value when the deepest bed
forms take place. The scour depth increases to a
new peak with the further increasing of thenear-bed shear stress. This peak is named atransition flat bed peak (or live-bed peak), at which
stage bed forms disappear and more flow energy
contributes to the scour process. When the bed
forms appear again at still higher near-bed shear
stress and dissipate some of the flow energy, thescour depth decreases again.
Excessive scour is one of the major causes for
failures of spur dykes. On the other hand, thepool-riffle morphologies, as consequences of scour,
provide new river amenities and important habitats
for riverine species. Therefore, a balance should bewell maintained to achieve the maximum beneficial
effects and still afford an effective control of thescour. This necessitates a deep insight into theassociated problems and underlying processes,
together with advanced prediction methods andtools if available. This paper firstly presents a
review on up-to-date knowledge and conventional
approaches. After that, recent advances, especiallyin numerical modeling, are discussed. Avenues for
future researches are suggested at the final part.

－2.

Scour around a single spur dyke

2.1 Flow structure around a spur dyke
An insight into the nature of the flow is aprerequisite for the understanding of the scour
process. In general, the flow initiates and controls
the scour process. The flow past a spur dyke isgenerally complex and this complexity increases
with the development of the scour hole.
(1) Flow separation and vortex shedding
The flow past the spur dyke may be divided into
three zones: a main flow zone from the head of thespur dyke to the opposite side of the channel, awake zone behind the spur dyke and a mixing zone
in-between them (Fig. 3).
In the main flow zone, the velocity isaccelerated. Molinas et al. (1998) reported in theirexperimental research that the velocity at the spurdyke head might be increased up to 1.5 times theapproaching flow velocity, depending on the flow
conditions and spur dyke protrusion ratios. Ho et al.
(2007) presented similar results when they
investigated the flow around different impermeable
spur dykes with both experimental and numericalmethods.

Main flow zone
Separation

Mixing zone
Return flow zone

Spur dyke

Reattachment point

Fig.3 Typical flow around spur dyke
The wake zone may be further subdivided into a
return flow zone and a reattachment zone. The
return flow zone is generally characterized by two
eddies of different rotating direction and size. A
small eddy is near to the spur dyke, the centre ofwhich locates at a distance almost equal to the spurdyke length L. A larger eddy is at the downstreamof the small one, whose centre locates a distance ofabout 6L away from the spur dyke. The
reattachment zone is an area where the separated
flow reattaches the channel bank downstream of thespur dyke. According to Chen and Ikeda (1997), thelength of the reattachment zone covers a distance of

635 －

－

flow velocity. The vortices shedding from the spurdyke merged with each other as they migrated
downstream. As a result, there were increases inboth length scale and time scale of the vortices.
(2) Flow structure in the scour area
The flow in local scour generally shows obvious
3D characteristics. This 3D flow may be divided
into several components. In front of the spur dyke,
there exists a bow wave near the water surface anda downflow towards the channel bed due to thestagnation of approaching flow. As the result of theflow separation, a horse-shoe vortex develops in thelocal scour hole and a wake vortex system forms
behind the spur dyke. A schematic diagram of theflow and local scour at the longitudinal section
passing the spur dyke head is shown as below.
Water surface

Spur dyke

Bow wave
Downflow
Horse-shoe vortex

Flow

Wake vortex
Channel bed

Fig.4 Typical flow in a scour hole
The authors have investigated the flow structure
in a scour hole with two sets of electro-magnetic
velocimetries in a laboratory flume. The hydrauliccondition is given in Zhang and Nakagawa (2008).
The local scour geometry is shown in Fig.5, which
is obtained with a laser displacement meter. The
mean velocity profiles at typical cross-sections areshown in Fig.6 and Fig.7. From these figures, one
may have a clear image on the complex vortex
systems in the proximity of the spur dyke.
Unit: cm
40
30

y (cm)

around 6L and locates over the range from 11L to
17L. The reattachment zone is usually simplified
into a point for the convenience of analyses. At thispoint, the time-averaged velocity is zero. But itshould be kept in mind that the instantaneous
reattachment point fluctuates back and forth. For
impermeable spur dykes, Ouillon and Dartus (1997)
reported that the location of the reattachment point
was 11.5L in experiments and 10.7L with anumerical model study. With a depth averaged
numerical model, Liu et al. (1994) found that theangle of inclination showed more remarkableeffects than the shape of the spur dyke on thereattachment point. Moreover, the location of thereattachment point is the farthest for a repellingspur dyke compared with a deflecting or an
attracting one with the same effective length. Ho etal. (2007) investigated the separation length(distance between the spur dyke and thereattachment point) behind a single spur dyke withdifferent permeability. They found that the
separation length decreases with the increasing of
spur dyke permeability. For 0% (impermeable),
20% and 80% permeability, the separation length is
12.5L, 5.7L and 1.8L, respectively. Furthermore, it
wa noticed that the wake zone shrank with thedevelopment of scour hole according to the authors’experimental studies. The flow structure on thewater surface entirely changed from a flat bed to ascoured bed. The change of the local bed
configuration and the development of the 3D vortex
systems were responsible for this phenomenon.
The vortex shedding in the mixing zone is an
important aspect of the flow field. By measuring thewater level fluctuations along the centerline of the
migrating vortices, Chen and Ikeda (1997) foundthat there were clear periodic water level
fluctuations. These fluctuations showed obvious
phase difference between two consecutive
measuring points, which suggested a strong
coherency between them. The correlation
coefficient was determined with FFT (Fast Fourier
Transformation) method for each pair of time seriesof water surface fluctuations. The lag time when thecorrelation coefficient took a peak was consideredas the migration time of a vortex. It was found thatthe migration velocity of the vortices was kept to beconstant, which was a little larger than the mean

20

-2
-4
-6
-8
-10

0

Flow
0

10

-12
-40

-20

0

-2
20

0

x (cm)
Fig.5 Scour around an impermeable spur dyke

636 －

40

30cm/s4reach. However, it should be noticed that the effectof these parameters might become important insome cases. For example, the change of theviscosity due to temperature variation may affectthe sediment threshold condition as well as thedevelopment of bed forms and thus the flow field.
According to a series of laboratory experiments
conducted in the authors’ group relating to scour
around spur dykes (e.g. Zhang, 2005), it is foundthat experiments in the winter season takes a longer
time than those in summer times in order to arriveat an equilibrium condition due to the differences inwater temperature.

z (cm)

0
-4
-8

-12

0

4

12

20

24

28

y (cm)

32

36

0
-4
-8
0

4

8

12

16

20

24

28

32

y (cm)(b) Transverse section x=0cm

36

4
0
-4
-8
-12

30cm/s

4
0
-4

8
4
0
-4
-8
-12

4

8

12

16

20

24

28

32

36

y (cm)(c) Transverse section x=4cm
Fig.6 Transverse flow velocity in a scour hole
2.2 Parameters related to scour at a spur dyke
The scour depth depends on a lot of parameterscharacterizing the fluid, the bed sediment, the flow
condition, the channel geometry and the spur dyke
structure. Researches have been conducted in theliterature to identify the roles of these parameterswith laboratory experiments, numerical simulations
or field measurements. However, there remain
many disputed points on which there is a lack ofgeneral agreement. Since a spur dyke is very similar
to an abutment in many aspects, results obtained forbridge abutments are considered to be applicablefor spur dykes as well. Based on existing researches,
the aforementioned parameters and their influenceson the scour process are detailed as follows.
(1) Parameters related to the fluid
Parameters include the fluid density ρ, thekinematic viscosity υ, the gravitational accelerationg and the temperature T. The change of theseparameters is generally assumed to be insignificant
in a specific hydraulic experiment or an actual river

－

4
0
-4
-8
-12

-20

-10

0

10

20

30

x (cm)(a) Longitudinal section y=6cm
30cm/s40(b) Longitudinal section y=10cm
-30

-20

-10

0

10

20

30

40

30

40

x (cm)(b) Longitudinal section y=10cm
30cm/sz (cm)

0(a) Longitudinal section y=6cm-30

z (cm)-8-12

30cm/sz (cm)-12z (cm)

16(a) Transverse section x=-4cm
30cm/s4z (cm)

8

-30

-20

-10

0

10

20

x (cm)(c) Longitudinal section y=14cm
Fig.7 Longitudinal flow velocity in a scour hole(2) Parameters related to bed sedimentParameters include the particle density ρs, theangle of repose φ, the mean diameter d, grain size
distribution, cohesiveness and bed consolidation.
Studies concerning the latter two parameters arestill in its infant and are not detailed here.
Laursen (1960) has stated that the maximum
scour depth was affected by sediment size underclear-water scour but not under live-bed scour. But
it was argued to be curious by many researchers.
Garde et al. (1961) did experiments with four sand637 －

sizes in range 0.29mm to 2.25mm under live-bed
scour condition and found that the sediment size
influenced both the rate of scour and the maximum
scour depth. He included the sediment size in a dragcoefficient and incorporated it into a semi-empiricalequation for the estimation of scour depth. Gill
(1972) reported that the rate of scour developmentof the fine sand was higher than that of the coarse
sand according to his experiments with two
sediment sizes (d=0.914mm and d=1.52mm). For
the same value of near-bed shear stress in theapproaching flow area, fine sediments resulted ingreater scour depth. The reduction in scour depth
for relatively large sediment might be due to large
particles impeding the erosion process at the base of
the scour hole and dissipating some of the flowenergy in the erosion zone. However, the coarse
sand was scoured deeper than the fine sand for thesame value of τ/τc, in which τ= near-bed shear stressin the approaching flow area and τc =critical shear
stress of bed material. Raudkivi and Ettema (1983)
believed that the relative grain size defined by L/d
had more meaning compared with the grain size ditself to analyze the effect of sediment size on scour
depth. The scour depth was independent of thesediment size if the relative grain size was large
enough. Melville (1997) agreed with them andincluded the relative grain size, rather than the grain
size itself, in his prediction formula.
The geometric standard deviation σg, generally
defined as  g  d84 / d16 is an important parameter forthe analysis of grain size distribution. It is
commonly accepted that the sediment may beconsidered uniform if σg <1.4 and nonuniform else.
Armor layer may form on the channel bed and in
the scour hole during the scour process innonuniform sediment bed. It has significant effecton the maximum scour depth. Melville andSutherland (1988) pointed out the existence of alimiting armor condition which represented thecoarsest or most stable armored bed for a given bed
material and could be characterized by a mean
velocity uca. Each sediment had a unique value ofuca, dependent on the sediment size and grading.
For nonuniform sediment bed, the clear-water peakwould be replaced by an armor peak. The criticalflow velocity at the armor peak ua was determinedusing ua=0.8uca. ua marked the transition from－clear-water scour to live-bed scour in nonuniform
sediment bed and was equivalent to uc for uniform
sediment. For velocities less than ua, armoring
occurred and the scour depth was limited
accordingly. Beyond ua, the armoring diminishedand the scour depth was reasonably constantirrespective of σg at the live-bed peak.
Raudkivi and Ettema (1983) found that the
maximum clear-water equilibrium scour depth, forsediment with a shape factor near one, depended on
σg. They proposed a practical relation to estimate
the equilibrium scour depth at a bridge pier innonuniform sediment bed in terms of the geometricstandard deviation as follows.

d  g 
D

 K

d
D

(1)

where D= bridge pier diameter and Kσ= coefficientwhich depended on σg, giving by a diagram.
According to experimental studies conducted by
Dey and Barbhuiya (2004), the scour depth at an
abutment with an armor-layer in clear-water scour
condition under limiting stability of surface
particles was always greater than that without anarmor-layer for the same bed sediments.
(3) Parameters related to flow condition
The approaching flow depth and mean velocity
are two important parameters. According toexperimental studies carried out by Gill (1972) andothers, it may be concluded that the maximum
scour depth increased at a decreasing rate with theincreasing in approaching flow depth. The scour
depth increased proportionately with the flow depth
for shallow flows and was independent of flow
depth in case of deep flows. An explanation wasthat the bow wave that formed in front of the spurdyke interfered with the down flow and horseshoe
vortex in shallow flows and the two had opposite
senses of rotation. With the increasing of flow
depth, the interference reduced and became
insignificant eventually. The flow velocity, being
incorporated in the shear stress in many researches,
deserves special attention. According to the ratio of
the flow velocity and the critical flow velocity for
sediment threshold, scour may be classified asclear-water scour and live-bed scour as has been
mentioned in the previous contexts. Since there are638 －significant differences between the two classes ofscour as discussed before, it is important toconsider them separately. In general, the effect offlow conditions is not discussed separately. They
usually come with, saying, the dimension of thespur dyke structure and the critical velocity or shear
stress for sediment threshold/armoring.
(4) Parameters related to geometry of channel
Rectangular channel has been assumed in mostof the researches and the channel width is the only
parameter which needs to be considered. But anactual river generally has various shapes. A
complex channel geometry poses great challenges
not only because there are many difficulties incharacterizing its dimensions but also because it
puts forward new problems on how to adequately
quantify other parameters such as the water depth,
the velocity and the effective length of spur dyke.
Sturm and Janjua (1994) studied the scour
around an abutment in a compound channel. The
abutment was situated in the floodplain setting wellback from the edge of the main channel. The main
channel was treated as fixed-bed channel, while thefloodplain was covered with sediment, clear-water
scour occurring at the abutment. A discharge
contraction ratio was introduced to account for thecompound channel effects. This ratio represented
the redistribution of flow between the main channel
and the floodplain as the flow passed through theabutment contraction. A more systematic study was
conducted by Melville (1995). The study was
limited to the case of an abutment spanning thefloodplain and extending into the main channel.

Type 1

Abutment Imaginary boundary

Type 2Main channel

Floodplain
Type 3aType 3b
Fig.8 Scour types in compound channel(after Melville, 1995)－

Melville (1995) suggested three types of scour
in idealized compound channels as shown in Fig. 8.
Type1 applied to an abutment spanning awell-defined channel without floodplain. In Type2,
the abutment spanned the floodplain and extended
into the main channel. In Type3, the abutment
spanned only part of the floodplain. Type3 wasfurther divided into two cases: the abutment in
Type3a extended only partly across the floodplain
while terminated at about the edge of the main
channel in Type3b. The effect of the channel
geometry on the scour depth was represented by amultiplying factor KG as will be discussed in thelatter contexts. The KG was defined as the ratio of
the scour depth at an abutment in a compoundchannel to a scour depth at an abutment in acorresponding rectangular channel. In general, KG
was a function of the size, shape, roughness of themain channel and the floodplain. Cardoso andBettess (1999) studied Type3 abutment scour with aset of laboratory experiments. Their results were inconformity with Melville’s suggestion that scour at
abutments on floodplains could be approximated byscour in rectangular channels if an imaginary
boundary (sketched in Type3a, Fig.5) was assumed
separating the flows in the main channel and thefloodplain. From this point, Type3 scour might betreated as special cases of Type1 scour. However,they observed that the time to equilibrium was
shorter, by up to a factor of 7, when the scour holeextended into the main channel than when the scour
hole was confined entirely to the floodplain.
(5) Parameters related to spur dyke structure
Parameters include the size, shape, alignment
and permeability of the spur dyke.
The effective length L is usually used in theanalysis of scour around spur dykes instead of theactual length. The effective length is defined as the
projected length of a spur dyke, i.e. the length
perpendicular to the flow. Therefore, spur dykes ofdifferent alignment extending the same lateral
distance into the flow have different actual lengths.
According to the ratio of L/h, Melville (1995)
classified bridge abutments as short, intermediate
length and long abutments. Melville (1995) statedthat for a long abutment, the scour depth was
independent of the abutment length.

639 －

－

50% permeability is given below (Zhang and
Nakagawa, 2008). The hydraulic condition for thisexperiment is the same as that in Fig.5, except thatthe impermeable spur dyke is replaced with apermeable one. Compared with the contour in Fig.5,
it is found that the maximum scour depth here isless than half of that in the impermeable case.
Unit: cm
40
030

y (cm)The shape of the spur dyke has a significant
effect on the local flow structure and hence thescour process. A streamlined body is usually
expected to reduce the drag exerted by the flow andto reduce the size of the wake and general flow
disturbances. A vertical wall abutment causes
greater scour depth in comparison with other types.
For a long abutment, Melville (1992) argued thatthe shape of the abutment became unimportant.
The inclination angle of the spur dyke to theapproaching flow significantly influences the scour
depth. Early researches carried out by Garde et al.
(1961) suggested that the maximum scour depth
was greatest for a spur dyke with an inclination
angle of 90o and smaller for all other inclinations
upstream and downstream. But this was disputed by
Tison (1962), who argued that the greatest
maximum scour depth was recorded for an
upstream spur dyke inclination, followed by the 90oand the downstream ones with evident experimental
data. Tison (1962) also gave explanations on theobserved variations of maximum scour depth with
the inclination angle using a simple theory, inwhich the importance of the vertical driving motion
on the scour development was emphasized. For
short abutment, Melville (1992) stated that theeffect of the inclination angle could be ignored.
The permeability of spur dyke also affects thescour depth significantly. The scour depth and area
at an impermeable spur dyke are remarkably larger
than those at a permeable one (Zhang, 2005). Yeo(2007) conducted a series of experiments toinvestigate the local scour at spur dykes withpermeability ranged from 0% to 80%. Normalizing
the maximum scour depth at a spur dyke with the
maximum scour depth at an impermeable spur dyke,
he found that the dimensionless scour depth
decreased with the increasing of the structure
permeability. The relation was nearly linear. The
locations of the maximum scour depth were almost
the same in both impermeable and permeable cases.
However, the scour area was concentrated at thehead of the impermeable spur dyke, whereas thechannel bed in the proximity of the spur dyke wassignificantly scoured in all permeable cases. Zhang(2005) observed that the scour hole had a V-shapealong the axis of the permeable spur dyke.
A typical scour at a permeable spur dyke with

-1

20

Flow
-4

10

-2

-3
1

-40

-20

0

x (cm)

-1

0

1 0

20

40

Fig.9 Scour around a permeable spur dyke
2.3 Equilibrium scour depth
In order to estimate the maximum scour depth,
a lot of relations and formulae have been developed.
Basically, these relations or formulae are grouped
into four categories: (1) regime approach relating
the scour depth to the increased discharge intensity;(2) dimensional analysis approach based on field or
experiment data; (3) analytical or semi-analytical
approach and (4) probabilistic approach.
(1) Regime approach
In the regime approach, scour depth is afunction of the flow discharge at the contracted
section. Based on Lacey’s regime formula, Inglis(1949) proposed a scour prediction equation.
d s  h  0.47ki (Q / f )1 / 3(2)

where ds= equilibrium scour depth; h= water depth
from initial bed; f=silt factor, is equal to 1.76 d ; d=mean diameter of sediment; Q= regime discharge
and ki= amplification factor for local scour depth,
depending on the type of obstructions. Anotherrepresentative relation is that presented by Ahmad(1953), having the form as

d s  h  ka q 2 / 3

640 －

(3)

where ka= constant depending on the flow intensity
and the inclination angle of the spur dyke and q=
discharge per unit width in the contracted section.
This kind of approach suffers from an inherent
drawback as the regime concept originates from theanalysis of general scour whereas the mechanism ofscour around a spur dyke is quite different from thatof general scour. As a consequence, some dominantfactors for maximum scour depth are not taken into
account such as the dimension of the spur dyke andthe mode of sediment transport.
(2) Dimensional analysis
Using dimensional analysis and experimental
and/or field data, a significant amount of formulae
are developed. As has been mentioned before, there
are a lot of parameters entering the problem. In
practice, those parameters are generally not directly
converted to dimensionless variables. Instead, they
are carefully selected and combined to work
together, resulting in variables such as the Froudenumber, the dimensionless shear stress and so on.
Garde et al. (1961) correlated the scour depthwith dimensionless parameters as

d s  h / h  f  , , Fr, CD 

(4)where   (B  L) / B , the opening ratio, in which B is
the width of the channel;  = angle of inclinationof spur dyke with the direction of approaching
flow; Fr  u / gh , the Froude number, in which u isthe approaching flow velocity and CD= dragcoefficient of sediment, defined as

C D  4( s  1) gd /(3 w s2 )(5)where s=ρs/ρ and ws= settling velocity of sediment.
Assuming constant relative density of sedimentand absence of viscous effect, Melville (1992)
proposed the following expression u2 L dds, , ,  g , Sh, Al , SG  f h gd h h(6)where Sh , Al = parameters describing the shapeand alignment of the abutment and SG= parameter
describing the effects of lateral distribution of flow
and cross-sectional shape of the approach channel.

－

Sturm and Janjua (1994), on the other hand,
introduced the following expression when they
investigate abutment scour in a compound channel.

d s / h  f Fr , Frc , M (7)where Fr= approaching Froude number in thefloodplain, defined by the velocity and depth
upstream of the end of the abutment; Frc= criticalvalue of the approaching Froude number for
initiation of motion and M= discharge contraction
ratio, defined as the ratio of the discharge
approaching section through the opening width tothe total discharge.
The equations derived from dimensional
analysis are evaluated with laboratory experimental
data and/or field data. A lot of empirical formulae
are then developed. Some formulae are developed
for clear-water scour, some are for live-bed scour,and some are intended to include both. The
estimation formula proposed by Melville (1997)
includes extensive data from bridge piers andabutments. It has been frequently cited in theliterature. This formula is written as

d s  K hL K I K d K s K K G(8)where K= empirical expressions accounting forvarious influences on scour depth, termed K-factors
hereafter. K hL = factor for flow depth and abutment
length; K I = factor for flow intensity; K d = factor for
sediment size; K s = factor for abutment shape; K =factor for abutment alignment and K G = factor forchannel geometry. The K-factors are considered
individually and are evaluated by fitting envelope
curves to existing data for bridge foundations.
Melville (1997) suggested following estimation
methods for the factors of K hL and K I .

 2L

K hL   2 hL
 10 h


if
if
if


1
if


KI  
 u  (ua  uc )
if

uc


641 －

L
1
h
L
1   25
h
L
 25
h

u  (ua  uc )1
ucu  (ua  uc )
1
uc

(9)

(10)

in which, the critical velocity may be related to thecritical frictional velocity via the logarithmic formof the velocity profile, i.e.

uch
 5.75 log 5.53 
u*c
d



(11)


uca
h 
 5.75 log 5.53 
u*ca
d
a 


(12)

Table 1 Shape factors (after Melville, 1992)

The critical shear velocities u*c, u*ca are determinedfrom the sediment size d and the median armor sizeda, using the Shields diagram or other relations. The
median armor size of the sediment is found with anempirical expression given by Chin et al. (1994)
d a  d max / 1.8(13)where dmax= the maximum particle size of thenonuniform sediment material.
The expression in Eq. (10) indicates that thescour depth is approximately proportional to theflow intensity under clear-water scour but is
independent of flow velocity under live-bed scour.
The factor related to sediment size K d has thefollowing form. In case of nonuniform sediment,
the d is replaced with da.

if
1.0


Kd  
L
0.57 log 2.24  if
d




L
 25
d

(14)

L
 25
d

Selecting the vertical wall abutment as theprimary shape, the shape factor K s for typicalshape of abutment is given in Table 1.
Because the shape effects become unimportant
at longer abutments, Melville (1997) recommended
using the adjusted shape factor K s* in the prediction
formula as follows.

L

10
Ks
if

h

L
L
(15)
Ks*  Ks  0.667(1 Ks )( 1) if 10  25
10h
h

L

1.0
 25
if

h
Selecting the right angle as reference, thealignment factor K is given in Table 2.

－

Shape

Ks

Vertical wall

1.00

Semicircular ended

0.75

Wing-wall

0.75

Spill-through with slope
horizontal:vertical 0.5:1
horizontal:vertical 1:1
horizontal:vertical 1.5:1

0.60
0.50
0.45

Model

Table 2 Alignment factors (after Melville, 1992)



30

60

90

120

150

Kθ

0.90

0.97

1.00

1.06

1.08

Melville (1992) recommended that thealignment factor be applied to longer abutments
only and gave the adjusted alignment factor K* as

L

K
if
3

h

L
L
K*  K  (1 K )(1.5  ) if 1   3
h
2h

L

if
1.0
1

h

(16)

Finally, the effect of the channel geometry for acompound channel is given by

KG  1B *   h* 
1   B   h 


5/3

n* 

n


(17)

where B, B*= width of the main channel and thefloodplain, respectively; h*= water depth in thefloodplain; n, n*= Manning’s roughness coefficientfor the main channel and floodplain, respectively.
With the all the K-factors known, the maximum
scour depth is readily estimated.
(3) Analytical and semi-analytical approach
The dimensional analysis approach has beensuccessful to predict local scour in many laboratory
flumes. However, this kind of approach does not

642 －include any treatment to model the physical process
unique to the scour phenomenon. Hence, theapplicability and generality of this kind of method
are quite questionable, especially in prototype
scales. In early investigations, Laursen (1960,
1963) developed formulae, based on scour at longcontraction, for clear-water and live-bed scour
depths at vertical-wall abutments as follows.
For live-bed scour (Laursen, 1960)
7/6
L d   1 d
 2.75 s   s  1  1h
 h   r h



(18)

For clear-water scour (Laursen, 1963) u* p   1
 u*c  

7/6L
 d  1 d  
 2.75 s  s   1h
 h  r h  (19)where u*p= shear stress associated with sedimentparticles; r= ratio of scour depth at abutment toscour depth in equivalent long contraction. It is
assumed that r=11.5 for live-bed scour and r=12 forclear-water scour.
Based on the premise that the flow obstruction
and the subsequent increases in bed shear stress dueto the projection of abutment are responsible for thescour, Lim (1997) developed a semi-empiricalformula for clear-water scourd s / h  K s 0.9 X a  2(20)

where Ks= shape factor as given in Table1,
and X a   *ca0.375 Fda0.75 (d / h) 0.25[0.9( L / h) 0.5  1] , where Fda=
sediment densimetric Froude number based on daFda  u / ( s  1) gd a

(21)

After introducing a generalized bed-loadtransport relation, Lim and Cheng (1998) extended
Lim’s work to live-bed scour conditions as ds 
1 
 2h 

11.2

4/ 3



L
h

u  u   L tan  1  
1u  u   ds

2
*c
2
*

2
*c
2
*

(22)
2/ 3

(4) Probabilistic approach
There are many uncertainties during the－estimation of the scour depth. Johnson and Dock
(1998) classified the uncertainties into three groups:
1) model; 2) hydraulics and 3) parameters. The
model uncertainty comes from the using of a modelthat may not be completely representative of thephysical process. Hydraulic uncertainty is the result,for example, of attempting to estimate flow depth
and velocity for a specific discharge at a particularlocation. Parameter uncertainty results from an
inability to accurately access parameters and model
coefficients required in the model.
Probabilistic approach for scour is still very few.
In order to obtain a probabilistic scour depth, forexample, Johnson and Dock (1998) suggested aworking procedure using the Monte Carlo method.
The procedure is as follows: 1) generate values foreach of the random variables in a deterministic
model; 2) estimate the scour depth from thedeterministic model based on the generated randomvariables; 3) repeat Procedure2 for N simulation
cycles; 4) Calculate the mean and deviation for the
N values of scour depth; 5) Obtain the distributionof the N values of scour depth.
2.4 Temporal variation of scour depth
The time required by a given discharge to scour
to its full potential is generally much larger than thetime for which it runs (Kothyari and Ranga Raju,
2001). Therefore, temporal variation of scour is ofgreat significance, in particular to predict the scour
in an actual river where the flow is unsteady anddischarge changes rapidly.
Kothyari and Ranga Raju (2001) noticed thatscour process around a spur dyke was similar to thataround a pier except that the boundary layer effectinduced by the channel wall might cause less scourin the spur dyke case. They introduced the conceptof an analogous pier, the size of which was
determined through an analysis of the drag force
experienced by the pier and the spur dyke.
Estimation formula for scour process around piers(Kothyari et al. 1992) was then used to predict thescour around a spur dyke. The model was verified
under both clear-water and live-bed scour
conditions. Coleman et al. (2003) presented an
expression to predict the temporal variation ofscour depth by determining a function relating thetime-dependent scour depth to the equilibrium

643 －scour depth. In case of uniform sediment andclear-water scour condition, an equation was
proposed to evaluate the time to equilibrium scour,which was defined as the time required for the rateof scouring to reduce to 5% of the smaller of thespur dyke length L or the flow depth h in the
succeeding 24h period.
Dey and Barbhuiya (2005) developed a modelfor the temporal variation of scour depth based on
the concept of mass conservation of sedimentparticles, considering the horse-shoe vortex as themain agent for scouring and assuming a layer bylayer scour process. Apart from other models, theyobtained the temporal variation of scour depth bysolving a differential equation instead of relating itto the equilibrium scour depth. The model was
successfully applied to predict the scour process
around short abutments of different shapes in
uniform and non-uniform sediments underclear-water scour conditions.
2.5 Geometry of scour at a spur dyke
The volume and geometry of a scour hole isvaluable for assessing the potential benefit to theaquatic habitat. Shields et al. (1995) documented
significant increases in fish numbers, sizes, species
and the area of aquatic habitat after the enlargementof local scour in a river restoration project. In theproximity of the historically built spur dykes along
the Yodo River in Osaka, Japan, favorable
environment for the growth and habitant of avariety of living things have also been observed.
(Kinki Regional Development Bureau, MLIT, Japan
2002). Unfortunately, very few studies have been
carried out on this subject to date.
Kuhnle et al. (1999, 2002) investigated theshape and volume of local scour around different
types of spur dykes under different flow conditions
with experimental methods. They plotted the
topographic maps showing the geometries of thescour around spur dyke and suggested a simple
prediction scheme for the area and volume of scour
holes. In the prediction method, the maximum scour
depth was predicted firstly based on Melville’s
relation as described before, and then the scour
depth was converted to a volume using relations
derived from experimental data. According to theirreports, the overtopping ratio (approach flow depth－

divided by spur dyke height) and the protrusion
angle were two important parameters which
affected the geometry of local scour. Larger
overtopping ratios caused the region of maximum
scour to shift toward channel bank and caused asecondary scour zone to form downstream of thespur dyke. Compared with deflecting and attracting
spur dykes, repelling spur dykes generally resulted
in maximum scour volume and minimum near-bankerosion.
Ishigaki and Baba (2004) reported anexperimental study on the scour around deflecting
and attracting spur dykes under submerged andnon-submerged conditions. They pointed out thatthe deflecting spur dyke was more effective than
the attracting one in protecting channel bankerosion, coinciding with the observations in Kuhnle
et al (2002). Ishigaki and Baba (2004) also argued
that scour holes occurred at the head of thedeflecting spur dyke and located near the root of theattracting one in submerged conditions.
Typical scour holes around an impermeable anda permeable spur dyke under clear-water scour
condition have been shown in Fig.5 and Fig.9,
respectively.
3.

Scour around grouped spur dykes

In order to improve the efficiency, spur dykes
are generally organized in a group. A single spurdyke is not commonly observed in actual rivers.
For a group of spur dykes, there are some newparameters that should be paid much attention, forexample, the spacing between two consecutive spurdykes, termed embayment in this paper.
3.1 Main channel-embayment exchanges
The embayment between two consecutive spurdykes attracts a lot of attention nowadays mainly
due to its environmental function, i.e. maintaining awide variety of fauna and flora in the river system.
The exchange process between the main channel
and the embayment plays an important role indetermining the effectiveness of spur dykes.
Nakagawa et al. (1995), Muto et al. (2000) andZhang (2005) investigated the flow structure inrectangular embayments of different aspect ratios.
The aspect ratio was defined as W/L, in which W

644 －was the length of the embayment and L was theeffective length of the spur dyke. They concluded
that the aspect ratio determined the shape andstability of circulating flow induced in theembayment. An aspect ratio close to unity gave rise
to a single circulation, whose center almost
coincided with the geometrical center of theembayment. Larger aspect ratios resulted in two
circulating flows. One was large and located in thedownstream part of the embayment. Another one
was small and emerged just behind the upstream
spur dyke. The two circulations were in opposite
direction. With extreme large aspect ratio of six,
penetration of the main channel flow into theembayment would be observed as shown in
Uijttewaal (1999). However, the two circulatingflows remained in a relatively stable position.
The flow near an embayment is characterized
by the generation of coherent vortex in-between themain channel and the embayment and free-surface
oscillation inside it. Kimura and Hosoda (1997)
investigated the two processes and theirinteractions with both experimental and numericalmethods. According to their results, a large
coherent vortex with subsequent small vortices took
place periodically, consistent with that of the freesurface oscillation. The temporal velocity variation
might be decomposed into two components thatwere caused by the free surface oscillation and theshear instability in the mixing area. Due to thenon-linear interaction between the shear instability
and free surface oscillation, the vortex caused by
the shear instability was amplified selectively.
Once the vortex was amplified, the following
vortices merged into the main circulation until next
period started.
Uijttewaal et al. (2001) conducted physicalscale model experiments in a 20m-long and3m-wide channel with a series of embayments.
According to their result, reducing the main
channel velocity had no effect on the flow patternin the embayment, whereas lowering the waterlevel did. In the latter case, the effects of thebottom slope became more pronounced, shifting thecentre of the circulation flow towards the main
channel. Uijttewaal et al. (2001) also argued thatthe shape of the spur dyke was of minor importancefor the exchange process.

－Researches of Muto et al. (2000) and Uijttewaal
et al. (2001) indicated that horizontal circulation
was dominant in embayments under non-submerged
conditions. Small-scale 3D turbulence played aminor role in the mass and momentum exchange
process between the main channel and theembayment. Under submerged condition, however,
Nakagawa et al. (1995) pointed out that verticalcirculation was important according to theirexperimental study. Kimura et al. (2002) reported
obvious vertical circulating flow in an embayment
with numerical simulations, consistent with theoriginal experimental data.
3.2 Scour caused by grouped spur dykes(1) Main channel degradation
The degradation of the main channel caused bya group of spur dykes is generally treated as a long
constriction scour. The reduction of the channel
width due to the construction of spur dykes results
in increases in near-bed shear stress and hence
considerable scour within the constricted reach.
Nevertheless, the main channel degradation causedby grouped spur dykes is slightly different fromthat of a solid long constriction due to the flow
separation around the heads of spur dykes.

W
L
B1

B

Fig. 10 Definition of factor λMichiue et al. (1984) and Suzuki (1989)
suggested an equivalent constriction width byintroducing a factor λ which modifies theconstriction width caused by the construction ofgrouped spur dykes as B1 , where B1 is theconstriction width as sketched in Fig.10. Fromknown values for the bed degradation in flume
experiments and numerical computation, the factor
λ is determined with a diagram. λ takes a value of
1.0 when aspect ratio approaches 0 or is between 4
and 8 and the spur dykes work almost the same as along constriction. λ is larger than unity when the

645 －From the perspective of waterfront recreation
and river environment, investigation on the main
channel degradation or the local scour alone is far
from enough. There is a great public demand on
researches concerning diversity of river flow andchannel morphology after the construction of spurdykes. It is expected that people might take full use
of rivers’ aesthetic and ecological values if spurdykes are effectively arranged.
4 / 76 / 72 z  B1 u  B1 Zhang (2005) and Zhang et al. (2005) studied(23) 1  1h  B 2gh  B 
the morphological consequences of a series of
impermeable and permeable spur dykes in(2) Local scour around each spur dykelaboratory experiments. The permeable spur dykes
Local scour varies with the location of the spur
have a permeability of 50%. The experiments were
dyke in the group. In general, the scour depth at thecarried out under clear-water scour regime and lasthead of the most upstream spur dyke (denoted asaround 2 months in order to achieve the equilibrium
first spur dyke hereafter) is similar to that of acondition. The bed deformation is shown in Fig. 11.
single one, whereas which far from the first spur
According to the experimental result, main
dyke is different from a single one due to thechannel degradation caused by the impermeableinfluence of the neighboring spur dykes.
spur dykes was quite similar to that of thepermeable ones. However, severe local scour took
From experimental result, Suzuki (1989) andplace at the most upstream pair of impermeable
Zhang (2005) found that local scour holes showed
spur dykes, which had a potential to undermine theinsignificant changes from the 4th spur dyke. Suzuki
foundation of spur dykes. Local scour around other(1989) suggested to estimate the maximum scour
impermeable spur dykes was relatively smaller anddepth at the first spur dyke d s1 with any prediction
was expected to provide suitable pool habitat forformula for a single spur dyke as discussed before
and proposed the following expression for the scour
aquatic species. Considering the effect on thethdepth after the 4 spur dyke d sc in a group.
formation of pool-riffle morphology, Zhang et al.
(2005) suggested to combine the impermeable and
d sc
W
(24)
 0.07  0.14
permeable spur dykes in a group. In order tod s1
Lprevent the channel bank from erosion by the returnx (cm)(3) Morphological consequences of spur dykes
currents, an aspect ratio less than three wasy (cm)y (cm)

aspect ratio is larger than 8 and takes a value of
B/B1 when the aspect ratio approaches infinity. Thatis, spur dykes work independently when the aspectratio is very large. Furthermore, the main channel
degradation is larger than that of a long constriction
when the aspect ratio is between 0 and 4 (i.e. λ isless than unity). The suggested estimation formulafor the main channel degradation z is as below.

z (cm)x (cm)
Fig. 11 Morphological consequences of grouped spur dykes (Impermeable, Top; Permeable, Bottom)

－

646 －

recommended by Zhang (2005) based on bothexperimental and numerical results.
Besides the permeability and the aspect ratio,
orientation angle also plays an important role in thearrangement of spur dykes. Tominaga andMatsumoto (2006) investigated the pool-riffle
morphology caused by grouped spur dykes with anangle to the channel bank under submerged flow
conditions. For spur dyke groups inclined towards
upstream, severe scour holes were observed aroundthe heads of spur dykes and deposition regions
occurred beside the channel bank. For spur dyke
groups orienting downstream, front regions of spurdykes and area near the channel bank weresignificantly scoured. An alternate arrangement of
spur dykes inclined towards upstream wassatisfactory to create pool-riffle morphology.
4.

Numerical modeling of scour at spur dyke

Conventional methods for scour prediction
involve lots of empiricism, simplifications anduncertainties. It is quite risky to implement thesemethods in engineering practice if a deep insight is
not assured into the problem to be solved. With therapid development of CFD (Computational fluid
dynamics) and computer sciences, more generaland reliable approaches become attainable. Since
scour is a localized degradation of channel bed due
to imbalance of sediment transport, numericalmodels developed for sediment transport and bed
deformation in alluvial channels could be applied
to predict scour process. But generally it is not thefact in practice. Scour around spur dyke is arelatively local problem and necessitates theresolution of many local quantities. Unfortunately,
local phenomena are commonly ignored or not
well-resolved in general alluvial river models.
Therefore, although alluvial river modeling has
been presented in many literatures such as Cao andCarling (2001), it is still necessary to have a section
to discuss the numerical modeling of scour aroundspur dyke, emphasizing on some unique aspects.
In general, three kinds of numerical modelingresearches have been conducted in the past several
decades: (1) numerical modeling of flow field withplanar or unscoured bed (e.g. Mayerle et al., 1995;
Ouillon and Dartus, 1997; Peng and Kawahara,－

1998; Kimura et al., 2002; Nakagawa et al., 2004
and Ho et al., 2007); (2) numerical modeling offlow field with scoured bed (e.g. Marson et al.,
2003; Tominaga and Matsumoto, 2006 andTeraguchi et al., 2008) and (3) numerical modelingof flow field and bed deformation with movablebed (e.g. Michiue and Hinokidani, 1992; Yoseef
and Klaassen, 2002; Bhuiyan et al, 2004; Nagata etal., 2005; Zhang et al., 2006; Onda et al., 2007 andZhang et al., 2008). The performances of existing
numerical models are mostly evaluated according
to researchers’ preferences as well as verification
data at hand. Some of these models are reported towell resolve the typical horseshoe vortex in thescour hole area (e.g. Marson et al., 2003 andNagata et al., 2005) and some are concentrated on
the reasonable reproduction of the reattachment
length behind the spur dyke (e.g. Mayerle et al.,
1995, Ouillon and Dartus, 1997 and Ho et al. 2007).
Some are focused on the elaborateness of the
turbulence model (e.g. Yossef and Klaassen, 2002)
and some pay more attention on the sedimenttransport routines (e.g. Onda et al., 2007). It isnoticed that reliable and detailed experimental datais still insufficient both in amount and in quality
concerning the 3D flow and scour around spurdykes. Therefore, there is still a long way for theverification of numerical models. Moreover, inorder to have a practicable model for actual use inriver engineering, much space remains to improvethe model elaborateness and cost-effectiveness.
4.1 General approach on scour modeling
Modeling the scour process, in essence, is themodeling of a strongly coupled system involving
flow, sediment and morphology. Direct resolving
this system is almost impossible to date and seems
hardly attainable in near future. As an alternative, it
is usually decoupled in the numerical modeling.
Bed configuration & composition
Flow field
Sediment transport
Bed configuration & composition
Fig. 12 Typical flow-chat of scour modeling647 －A typical flow chart for the simulation of scour
at spur dyke is shown in Fig. 12. It is evident from
Fig. 12 that a numerical model generally consists ofthree modules: a hydrodynamic module for thesimulation of the flow field, a sediment module forthe modeling of sediment transport and a bed
variation module to account for the change of the
bed topography and sediment composition.

involves much empiricism. Sediment is generally
divided into bedload and suspended load. Since theadjustment of bedload transport process to the flow
condition proceeds rapidly, the transport of bedload
is usually modeled with empirical formulae. For
example, the relation proposed by Ashida andMichiue (1971) is written asu   / 2
1  *cm 1  *cm  17 pbm *3em
u*   *m 
sgd

qbm

4.2 Turbulent flow modeling
The LES (Large eddy simulation) based on thespace-filtered Navier-Stokes equations experienced
significant development in the past several decades.
But its application is still confined in experimental
fumes and is very limited in scour modeling. Full
3D modeling of flow of engineering interest is built
on the RANS (Reynolds-averaged Navier-Stokes)
equations. Particularly, the k-ε model is widelyused, whose governing equations are written as
u i
0
xi

(25)

ui
u
2ui 1  ij
1 p u j i  fi 
v

t
x j
 xi x j x j  x j

(26)

vt  k 
 
k
k


uj
 v  G  k  x j x j x j 
t

(27)

vt   


 
 (28)
uj v     C1 G  C2  ktx j x j     x j 

where ui= averaged velocity field; xi= Cartesian
coordinate component; fi= body force; p= pressure;' ij    u i' u 'j , Reynolds stress, where ui is thefluctuating velocity field; k= turbulence kinetic
energy; ε= dissipation rate of k; G= turbulence
production rate; the eddy viscosity vt=Cμk2/ε andcoefficients C 0.09, k 1.0,  1.3, C1 1.44, C2 1.92.
Despite its success in solving many engineering
problems in practice, the k-ε model suffers fromsome inherent drawbacks such as the assumption of
local isotropic turbulence. Nagata et al. (2005)
found that the original model could be improved
after introducing a quadratic relation between the
Reynolds stress and the rate of strain.
4.3 Sediment transport and bed variation
Compared with researches on flow modeling,simulation of sediment transport is far lagged and

－

3
m

(29)

where subscript m= sediment size fraction (bedload fraction here); qbm= bed load discharge; dm=
diameter of fraction m; pbm= percentage of
sediment size fraction m in the bed composition;
τ *m,τ *cm,τ *em= dimensionless shear stress,
critical shear stress and effective shear stress,
respectively; u*cm= critical friction velocity.
The local bed slope affects the sedimenttransport significantly. Van Rijn (1993) pointed outthat the critical shear stress for the sedimententrainment and the transport rate should becorrected. He separated the local bed slope as alongitudinal slope and a transverse slope andintroduced correction methods correspondingly.
Zhang et al. (2006) believed that the separation of
the local bed slope into two slopes was physicallyunreasonable and derived a correction method in
3D directly. Moreover, unrealistic bed slope over
the angle of sediment repose should be avoided in
the simulation. Zhang et al. (2006) introduced amethod to correct bed slope at the end of each time
step. The method guaranteed that the bed slope was
not greater than the angle of sediment repose as
well as ensured that sediment conservativeness wasmaintained. Sekine (2004) and Nagata et al. (2005),
however, assumed an ad hoc sediment transport
rate due to a sliding process. They included thesediment transport rate in the bed deformation
model instead of correcting the local bed slope after
the bed deformation model was solved.
Suspended sediment is usually solved from theadvection-diffusion equation as follow.
CmC  vt  Cm 
 u j  wsm j3 m 
 

t
x j x j  c  x j 





(30)

where Cm= volumetric sediment concentration;

648 －wsm= sediment settling velocity for each fraction;
σ c= turbulent Schmidt number and δ ij=
Kronecker delta. The suspended load layer
exchanges with the bedload layer via upward anddownward fluxes and hence influences the bed
topography and composition.
As is known, it takes time and space forsediment transport to adapt to its possible capacity
under the specific local flow conditions. The
non-equilibrium transport of sediment load aroundspur dykes has been reported by some researchers(e.g. Michiue and Hinokidani, 1992 and Nagata etal., 2005). Since most bedload transport formulae
give transport rate under equilibrium condition, theresults are questionable. There are two alternatives
in the literature: introducing a non-equilibrium
adaptation coefficient to account for the difference
between the actual sediment transport and theprevailed transport under equilibrium condition (e.g.
Minh Duc, et al., 2004), or employing stochastic
models for sediment pickup and deposition (e.g.
Onda et al., 2007).
When the sediment transport rate is known, thebed deformation is generally solved from thesediment continuity equation in the bedload layer.
In a stochastic model, however, Nagata et al.
(2005) obtained the temporal change of the bed
level from the volumes of pickup and deposition.
4.4 Solution methods
To date, the FVM (Finite volume method) isthe commonplace in CFD simulations. In an FVM,
the governing equations are integrated over a seriesof CVs (Control volumes) covering the study
domain instead of being solved directly. The meshdata for CVs may be organized in a structured way
or an unstructured way. Structured mesh is very
efficient for domains with relatively simple
geometries (Bhuiyan et al., 2004). With theincreasing of the geometry complexity, moresuitable mesh system such as the boundary-fitted
mesh may be employed (e.g. Onda et al., 2007).
With a boundary-fitted mesh, some additionalterms are introduced and governing equations may
become very complex. However, boundary-fitted
mesh still belongs to structured mesh and it may
take full use of computational techniquesdeveloped for structured mesh. For most problems－of engineering interest, an unstructured meshsystem is promising, which provides an accurate
resolution of complex geometries and boundaries aswell as allows mesh adaptation (e.g. Zhang, 2005
and Zhang et al., 2006).
5.

Suggestions for future researches

Although there have been great achievements onscour around spur dykes over the past years, a lot ofchallenges remain for future researches.
The deposition and erosion of nonuniform
sediment have significant influence on the scour
process and are closely related to riverine habitat.
But the progress is very slow in developing reliablepredictive tools mainly due to the shortage ofscientific knowledge in bed sorting mechanisms andhigh-quality experiment or field data. Since
sediment particles in actual rivers generally cover awide spectrum of sizes, this is a research field to be
explored urgently.
The effect of the groundwater pore pressure on
the scour process deserves special attention as well.
The gradient of the pore pressure during thedrawdown of a flood or tsunami may causesignificant reduction in the effective shear stress inthe substrate and therefore enhanced scour (Sumer,2008). Transient scour may develop rapidly behinda spur dyke when there is a sudden change in the
ground water level. This phenomenon may result in
the undermining of the spur dyke and a degradationof the pool habitat around the spur dyke. Therefore,
incorporating ground water in the morphologicalmodel is a new challenge and of great value.
Up to now, sediment transport has beencorrelated with the mean flow and near-bed shear
stress. However, this concept is found to be notsufficient for quantitatively accurate prediction ofscour (Chrisoholdes, et al., 2003). The importanceof the turbulent coherent structure on sedimentthreshold and transport has been pointed out bysome researchers such as Gyr and Hoyer (2006). An
entire image of the scour process necessitates a
breakthrough in linking the understanding at small
scales such as the micromechanics of flow andsediment transport to large scales such as vortex
systems and bed deformation in laboratory flumes
and actual rivers.

649 －Acknowledgements
This research is financially supported by the
Toujiro ISHIHARA Research Fellowship from the
Association of Disaster Prevention Research, Japan.
References
Ahmad, M. (1953): Experiments on design andbehavior of spur dikes, Proc. IAHR Convention,
Minnesota, pp. 145-159.
Ashida, K. and Michiue, M. (1972): Studies on bed
load transportation for nonuniform sediment andriver bed variation, Annuals of DPRI, Kyoto Univ.,
No. 14B, pp. 259-273. (in Japanese)
Bhuiyan, ABM F., Huque, F. and Saifuddin, AKM(2004): Numerical modeling of flow pattern & bed
evolution around spur-type structures, Proc. 9th Int.
Symp. on Riv. Sed., Yichang, pp. 1497-1502.
Cao, Z. and Carling, P. (2001): Mathematicalmodeling of alluvial rivers: reality and myth. Part
1: general review, Water & Maritime Eng., ICE,
Vol. 154, No. 3, pp. 207-219.
Cardoso, A.H. and Bettess, R. (1999): Effects oftime & channel geometry on scour at bridge
abutments, J. Hydraul. Eng., ASCE, Vol. 125, No.
4, pp. 388-399.
Chabert, J. and Engeldinger, P. (1956): Etude desafouillements autour des piles des ponts,
Laboratoire National d’Hydraulique, Chatou,
France. (in French)
Chen, F.Y. and Ikeda, S. (1997): Horizontal
separation flows in shallow open channels withspur dikes, J. Hydrosci. & Hydraul. Eng., JSCE,
Vol. 15, No. 2, pp. 15-30.
Chiew, Y.M. (1984): Local scour at bridge piers,
Report No. 355, Univ. of Auckland, School ofEng., New Zealand.
Chin, C.O., Melville, B.W. and Raudkivi, A.J.
(1994): Streambed armoring, J. Hydraul. Eng.,
ASCE, Vol. 120, No. 8, pp. 899-918.
Chrisoholdes, A, Sotiropoulos, F. and Strum, T.W.
(2003): Coherent structures in flat-bed abutment
flow: computational fluid dynamics simulations
and experiments, J. Hydraul. Eng., ASCE, Vol.
129, No. 3, pp.177-186.
Coleman, S.E., Lauchlan, C.S. and Melville, B.W.
(2003): Clear-water scour development at bridge－

abutments, J. Hydraul. Res., IAHR, Vol. 41, No. 5,
pp. 521-531.
Dey, S. and Barbhuiya, A.K. (2004): Clear-water
scour at abutments in thinly armored beds, J.
Hydraul. Eng., ASCE, Vol.130, No.7, pp.622-634.
Dey, S. and Barbhuiya, A.K. (2005): Time variationof scour at abutments, J. Hydraul. Eng., ASCE,
Vol. 131, No. 1, pp.11-23.
Garde, R.J., Subramanya, K. and Nambudripad,
K.D. (1961): Study of scour around spur-dikes, J.
Hydraul. Div., Proc. ASCE, Vol. 87, No. HY6, pp.
23-37.
Gill, M.A. (1972): Erosion of sand beds aroundspur dikes, J. Hydraul. Div., Proc. ASCE, Vol. 98,
No. HY9, pp. 1587-1602.
Gyr, A. and Hoyer, K. (2006): Sediment Transport:a Geophysical Phenomenon, Springer.
Ho, J., Yeo, H.K., Coonrod, J. and Ahn, W.S.
(2007): Numerical modeling study for flow
pattern changes induced by single groyne, 32nd
Congress of IAHR, Venice, Italy, CD-ROM.
Inglis, C.C. (1949): The behaviour and control ofrivers and canals, C.W.I.N.R.S. Poona, Res. Pub.
No. 13.
Ishigaki, T. and Baba, Y. (2004): Local scour
induced by 3D flow around attracting & deflecting
groins, Proc. 2nd Int. Conf. on Scour and Erosion,
Meritus Mandarin, Singapore, pp. 301-308.
Johnson, P.A. and Dock, D.A. (1998): Probabilistic
bridge scour estimates, J. Hydraul. Eng., ASCE,
Vol. 124, No. 7, pp. 750-754.
Kimura, I. and Hosoda, T. (1997): Fundamental
properties of flows in open channels with deadzone, J. Hydraul. Eng., ASCE, Vol. 123, No. 2, pp.
98-107.
Kimura, I., Hosoda, T. and Onda, S. (2002):
Prediction of 3D flow structures around skewed
spur dikes by means of a non-linear k-ε model,RiverFlow 2002, Bousmar & Zech (eds), Balkema,
Vol. 1, pp. 65-73.
Kinki Regional Development Bureau, MLIT, Japan(2002): Lake Biwa & the Yodo River.
Kothyari, U.C. and Ranga Raju, K.G. (2001): Scouraround spur dikes and bridge abutments, J.
Hydraul. Res., IAHR, Vol. 39, No. 4, pp. 367-374
Kothyari, U.C., Garde, R.J. and Ranga Raju, K.G.
(1992): Temporal variation of scour aroundcircular bridge piers, J. Hydraul. Eng., ASCE, Vol.

650 －118, No. 8, pp. 1091-1106.
Kuhnle, R.A., Alonso, C.V. and Shields Jr., F.D.
(1999): Geometry of scour holes associated with
90o spur dyke, J. Hydraul. Eng., ASCE, Vol. 125,
No. 9, pp.972-978.
Kuhnle, R.A., Alonso, C.V. and Shields Jr., F.D.
(2002): Local scour associated with angled spurdyke, J. Hydraul. Eng., ASCE, Vol. 128, No. 12,
pp.1087-1093.
Lausen, E.M. (1960): Scour at bridge crossing, J.
Hydraul. Div., Proc. ASCE, Vol. 86, No. HY2, pp.
39-54.
Lausen, E.M. (1963): Analysis of relief bridge
scour, J. Hydraul. Div., Proc. ASCE, Vol. 89, No.
HY3, pp. 93-118.
Lim, S.Y. (1997): Equilibrium clear-water scour
around an abutment, J. Hydraul. Eng., ASCE, Vol.
123, No. 3, pp. 237-243.
Lim, S.Y. and Cheng, N.S. (1998): Prediction of
live-bed scour at bridge abutment, J. Hydraul.
Eng., ASCE, Vol. 124, No. 6, pp. 635-638.
Liu, J., Tominaga, A and Nagao, M. (1994):
Numerical simulation of the flow around the spurdikes with certain configuration and angles withbank, J. Hydrosci. & Hydraul. Eng., JSCE, Vol.
12, No. 2, pp. 85-100.
Marson, C., Caroni, E., Fiorotto, V. and Da Deppo,
L. (2003): Flow field analysis around a groyne,
31st IAHR Congress, Thessaloniki, Greece, Vol. 2,
pp. 377-384.
Mayerle, R., Toro, F.M. and Wang, S.S.Y. (1995):
Verification of a three-dimensional numericalmodel simulation of the flow in the vicinity ofspur dikes, J. Hydraul. Res., IAHR, Vol. 33, No. 2,
pp. 125-136.
Melville, B.W. (1992): Local scour at bridge
abutments, J. Hydraul. Eng., ASCE, Vol. 118,
No.4, pp. 615-631.
Melville, B.W. (1995): Bridge abutment scour incompound channel, J. Hydraul. Eng., ASCE, Vol.
121, No. 12, pp.863-868.
Melville, B.W. (1997): Pier and abutment scour:integrated approach, J. Hydraul. Eng., ASCE, Vol.
123, No. 2, pp.125-136.
Melville, B.W. and Sutherland, A.J. (1988): Design
method for local scour at bridge piers, J. Hydraul.
Eng., ASCE, Vol. 114, No. 10, pp. 1210-1226.
Michiue, M. and Hinokidani, O. (1992): Calculation－of 2-dimensional bed evolution around spur-dike,
Annual J. Hydraul. Eng., JSCE, Vol. 36, pp. 61-66.
(in Japanese)
Michiue, M., Suzuki, K. and Hinokidani, O. (1984):
Formation of low-water bed by spur-dikes inalluvial channels, Proc. 4th APD-IAHR Congress.
Minh Duc, B., Wenka, T. and Rodi, W. (2004):
Numerical modeling of bed deformation inlaboratory channels, J. Hydraul. Eng., ASCE, Vol.
130, No. 9, pp. 894-904.
Molinas, A., Kheireldin, K. and Wu, B. (1998):
Shear stress around vertical wall abutments, J.
Hydraul. Eng., ASCE, Vol. 128, No., pp. 811-820.
Muto, Y., Imamoto, H. and Ishigaki, T. (2000):
Turbulence Characteristics of a shear flow in an
embayment attached to a straight open channel,
Proc. 4th Int. Conf. on Hydrosci.& Eng., Seoul,
Korea, pp.232-240.
Nagata, N., Hosoda, T. Nakato, T. and Muramoto,Y. (2005): Three-dimensional numerical model
for flow and bed deformation around river
hydraulic structures, J. Hydraul. Eng., ASCE, Vol.
131. No. 12, pp. 1074-1087.
Nakagawa, H., Zhang, H., Ishigaki, T. and Muto, Y.
(2004): Prediction of 3D flow field with
non-linear k-ε model based on unstructured mesh,
J. Appl. Mech., JSCE, Vol. 7, pp. 1077-1088.
Nakagawa, K. Kawahara, Y. and Tamai, N. (1995):
Experimental study on hydraulic characteristics offlows in embayments, Annual J. Hydraul. Eng.,
JSCE, Vol. 39, pp. 595-600. (in Japanese)
Onda, S., Hosoda, T. Kimura, I. and Iwata, M.
(2007): Numerical simulation on local scouring
around a spur dyke using equilibrium andnon-equilibrium sediment transport models,
Annual J. Hydraul. Eng., JSCE, Vol. 51, pp.
943-948. (in Japanese)
Ouillon,S.
andDartus,D.
(1997):
Three-dimensional computation of flow aroundgroyne, J. Hydraul. Eng., ASCE, Vol. 123, No. 11,
pp. 962-970.
Peng, J. and Kawahara, Y. (1998): Application of
linear and non-linear k-ε models to flows aroundspur dykes, Annual J. of Hydraul. Eng., JSCE, Vol.
42, pp. 643-648.
Raudkivi, A.J. and Ettema, R. (1983): Clear-water
scour at cylindrical piers, J. Hydraul. Eng., ASCE,
Vol. 109, No. 3, pp. 338-350.

651 －Sekine, M. (2004): Numerical simulation of braided
stream formation on the basis of slope-collapse
model, J. Hydrosci. & Hydraul. Eng., JSCE, Vol.
22, No. 2, pp. 1-10.
Shields, F.D.Jr. Cooper, C.M. and Knight, S.S.
(1995): Experiment in stream restoration, J.
Hydraul. Eng., ASCE, Vol. 121, No. 6, pp.
494-502.
Sturm, T.W. and Janjua, N.S. (1993): Clear-water
scour around abutments in floodplains, J. Hydraul.
Eng., ASCE, Vol. 120, No. 8, pp. 956-972
Sumer, B.M. (2007): Mathematical modeling ofscour: a review, J. Hydraul. Res., IAHR, Vol. 45,
No. 6, pp. 723-735.
Suzuki, K. (1989): Hydraulic functions & problemsof river training structures, JSCE Summer Course
in Hydraul. Eng., pp. A-4-4-A-4-22. (in Japanese)
Tison, Jr. G. (1962): Discussion on Study of scour
around spur-dikes, J. Hydraul. Div., Proc. ASCE,
Vol. 88, No. HY4, pp. 301-306.
Tominaga, A. and Matsumoto, D. (2006): Diverse
riverbed figuration by using skew spur-dikegroups, RiverFlow 2006, Lisbon, pp. 683-691.
Uijttewaal, W.S.J. (1999): Groyne field velocity
patterns determined with particle tracking
velocimetry, 28th IAHR Congress, Graz, Austria.
Uijttewaal, W.S.J., Lehmann, D. and van Mazijk, A.
(2001): Exchange processes between a river andits groyne fields: model experiments, J. Hydraul.
Eng., ASCE, Vol. 127, No. 11, pp. 928-936.
Van Rijn, L.C. (1993): Principles of SedimentTransport in Rivers, Estuaries and Coastal Seas,
AQUA Publications.
Yeo, H.K. (2007): Nature-friendly river-training
structure using groynes, the 4th Joint Seminar
between IWHR-KICT, July 9, Beijing.
Yossef, M.F.M. and Klaassen, G.J. (2002):
Reproduction of groyne-induced river bed
morphology using LES in a 2-D morphologicalmodel, RiverFlow 2002, Bousmar & Zech (eds),
Balkema, pp. 1099-1108.
Zhang, H. (2005): Study on flow and bed
deformation in channels with spur dykes, Doctoral
Dissertation, Kyoto Univ.
Zhang, H. and Nakagawa, H. (2008): Investigation
on morphological consequences of spur dyke withexperimental and numerical methods, Proc. 8th Int.
Conf. on Hydrosci. & Eng., Nagoya. (to appear)
Zhang, H., Nakagawa, H., Ishigaki, T. and Muto, Y.
(2004): Prediction of 3D flow field and local
scouring around spur dykes, Annual J. Hydraul.
Eng., JSCE, Vol. 49, pp. 1003-1008.
Zhang, H., Nakagawa, H., Ishigaki, T., Muto, Y.
and Khaleduzzaman, A.T.M. (2005): Flow & bed
deformation around a series of impermeable &permeable spur dykes, Proc. Int. Conf. on
Monitoring, Prediction and Mitigation of
Water-related Disasters, Kyoto, pp. 197-202.
Zhang, H., Nakagawa, H., Muto, Y., Baba, Y. and
Ishigaki, T. (2006): Numerical simulation of flow
and local scour around hydraulic structures, River
Flow 2006, Lisbon, pp. 1683-1693.

水制周辺の局所洗掘に関する研究：進展と展望

張 浩・中川 一

要 旨
水制周辺の局所洗掘は一般的な水理現象であるものの，課題の多い研究テーマである。局所洗掘が人間にとって利益となるか災害となるかは，洗掘の過程が十分に解明され効果的に管理されているかどうかに依存するため，長年にわたって研究され，多くの関心を集めてきた。本論文では関連する研究の背景および展望について報告する。論文は三つの部分から構成される。まず，水制周辺流れの特性，最大洗掘深の予測，洗掘の時・空間的変化特性，水制群による洗掘に関する研究の現状を概観する。次に，モデル構築の基本原則，支配方程式，数値計算方法を含めた数値シミュレーシ
ョン技術の進展について述べる。最後に，将来の研究方向をいくつか提示する。

キーワード:水制，局所洗掘，進展，展望－652 －