Proceedings of the International Symposium on Water and Sediment Disasters in East Asia, March 23-25, 2010, Kyoto, Japan
H. Nakagawa, K. Toda, Y. Muto & H. Zhang (Eds.)

Non-uniform Sediment Transport around a Spur Dyke
Hao ZHANG*1, Hajime NAKAGAWA2 and Hideaki MIZUTANI3
1

Dr. of Eng., Assist. Prof., Disaster Prevention Research Institute, Kyoto University, Japan,
E-mail: zhang@uh31.dpri.kyoto-u.ac.jp
2
Dr. of Eng., Prof., Disaster Prevention Research Institute, Kyoto University, Japan
3
Hydro-soft Technology Institute, Co., Ltd, Osaka, Japan
Abstract
This paper describes a study on non-uniform sediment transport around a spurdyke with both experimental and numerical methods. A series of experiments wereconducted in a laboratory flume with/without a spur dyke protruding to a movable bed
consisting of uniform/non-uniform sediment. The bed variations in terms of both
elevation and bed-materials composition are measured with advanced experimental
facilities. A numerical model was developed based on an unstructured mesh to simulate
the complex local flow and bed variations around the spur dyke. The flow velocity issimulated with a 3D k-ε turbulence model. A non-equilibrium sediment transport model
was adopted considering both stochastic and deterministic nature of the movement of
sediment particles. The simulation results are consistent with those of the experiments.
Based on the research results, the effects of sediment mean size and size distribution onscour-deposition patterns and bed compositions around a spur dyke are discussed andcharacterized.

Keywords: non-uniform sediment, spur dyke, scour-deposition

1.

processes or parameters having implications of thequality and structure of riverine habitats, isreceiving more and more attention in the hydraulicengineering.
As one of the most typical human-introduced
measures in the hydraulic engineering, a spur dykehas been widely placed in natural rivers. In general,
spur dykes were designed to protect channel banks
and to improve navigation conditions. But thepositive impacts on river environment have been
confirmed in experiments and actual rivers. As aresult, investigation on the environmental
implications of spur dykes is of great interest
recently. It is well known that natural riverbeds are
generally characterized by non-uniform sediment,
consisting of a wide spectrum of particle sizes.

Introduction

Local bed deformation around a spur dyke is aconventional research topic in the hydraulicengineering. From simple empirical predictions of
the maximum scour depth to advanced numericalsimulations of the local scour process, a lot ofengineers and researchers have contributed to thisproblem. A review of those researches has been
made by Zhang and Nakagawa (2008a). However,the development of human society and the changing
of public awareness always pose new requirements
and challenges for scientific researches. Existingknowledge is likely to soon becoming insufficient
nowadays. With the significant increasing ofenvironmental concerns, investigation on the96

Investigation on the transport of the mixture of thoseparticles is of practical value to estimate and tocharacterize the responses of channel morphologies
as well as riverine habitats. Unfortunately,
researches taking into account non-uniform
sediment transport are still very few, in particular incase of the involvement of spur dykes. During the
bed evolution process, the main difference between
a non-uniform bed and a uniform bed is the selective
transport of sediment particles, known as sedimentsorting. The direct result of sediment sorting is thatthe bed surface is in shortage of fine particles and anarmor layer forms there. The fine particles may
deposit in some area or be transported to thedownstream of the river. The armor layer may
become a shelter for fine particles beneath it,
preventing the bed from degradation or be destroyedin some event. The non-uniformity of sedimentparticles exerts great impacts on the local scour
process and bed composition in the proximity of thespur dyke. However, the problem has never beenclarified up to date.
In this paper, the changes of the bed level andthe bed composition around an impermeable spurdyke are investigated with experimental andnumerical methods under non-uniform sedimenttransport conditions. Additional to conventionalparameters such as the maximum local scour depth
and scour hole area, special attention is paid to thespatial distribution of sediment sizes in theneighborhood of the spur dyke.
2.

Laboratory Experiments

2.1 Experiment setup
A series of experiments have been carried out ina straight tilting flume at the Ujigawa Open
Laboratory, Kyoto University. The flume is 8m-long,
40cm-wide and 40cm-deep, with a 1.5m-long inlettank upstream (Fig.1). A working area locates 4m
downstream from the inlet tank. It is 1.7m long andis covered with 20cm-thick sediment: silica sand.
The upstream and downstream parts of the working
area are fixed with 20cm-thick wooden boards. A
50cm-long sediment trap is set at the end of the
flume, followed by a tailgate. Experiments arecarried out under two scenarios: with no hydraulicstructure in the flume or with an impermeable spurdyke attached to the flume. In the latter scenario, thespur dyke is 1cm-thick and is perpendicular to theright side of the flume with a protruding length of
10cm.
The hydraulic conditions and specification of theexperimental cases are shown in Tab.1 and Tab.2.
Totally, 10 experiments have been conducted under
the same flow conditions. From Case1 to Case6,
relatively uniform sediment bed is prepared in theworking area. Case7 and Case8 deal with gap-gradedsediment bed consisting of particles with two
obviously distinguished size fractions. In Case9 andUnit: cm
150

120

50

400

180

50

Fixed bedyInstrument carriage

Spur dyke Working area(a) Plan viewz

Flow meter

x

x

Pump
(b) Section A-A
Fig.1 Experimental flume and setup

97

Fixed bed

Sediment trap

20

Inlet tank

40

A

A

Case10, the distribution curve of sediment sizes isrelatively smooth and the sediment bed is considered
as well graded.

Case
Case1
Case2
Case3
Case4
Case5
Case6
Case7
Case8
Case9
Case10

Table1 Experiment casesσgSpur D (mm)

No
Yes
No
Yes
No
Yes
No
Yes
No
Yes

u* / u*c

1.03

1.229

0.832

1.70

1.183

0.622

0.31

1.356

1.177

1.00

2.323

0.846

0.86

2.080

0.909

2.2 Experiment procedure
Sediment is filled in the working area to makethe movable bed. Before each experimental run, thesediment bed surface is leveled with a scraper blade
mounted on a carriage riding on the rails over themodel channel banks. After that, the flume is slowly
filled with water. When the desired water depth isachieved, the pump is started with the designateddischarge and experiment starts. In cases with a spurdyke, the spur dyke is non-submerged. Moreover,
the approach flow velocity is less than the criticalflow velocity for the sediment entrainment except inCase5, 6. Channel beds in Case1 and Case3 areunchanged under the current flow condition. Hencethe bed variations are not measured. Basically, eachexperiment is carried out for 3hours. For
non-uniform bed cases without any hydraulicstructure (i.e. Case7, 9), the bed sorting process
seems very slow. Experiments are continued for
6.5hours. After the completion of each experiment,
the flume is drained out and the bed configuration ismeasured with a high-resolution laser displacement
meter (Model LK-500, Keyence, co., Ltd.). After
that, sediment samples are taken from the bed
surface (about 2.8mm thick) at several
representative locations. The size distributions of thesamples are analyzed with a nested column of sieves,together with a high-resolution balance scale(UW220H, Shimazu, co., Ltd.).

Table2 Hydraulic conditions
Flow discharge (l/s)
5.7
Channel slope
1/1000Channel width (cm)40
Flow depth (cm)5.0
Flow velocity (cm/s)
29.0
Friction velocity (cm/s)
1.98
Sediment density (g/cm3)
2.65
Spur length (cm)10.0
Spur thickness (cm)1.0
Reynolds number
14, 250
Froude number
0.41
100
Case1, 290

Percentage finer (%)

80

Case7, 870
Case5, 660

graded bed, sediment particles with much larger
diameters (i.e. Case3, 4) or much smaller diameters(i.e. Case5, 6) than those of Case1, 2 have been
adopted. Sediment size distribution at the initial bed
in each case is shown in Fig.2.

Case9, 10

50
40

3.

30
20

A 3D numerical model is developed to simulate
the complex flow, sediment transport and bed
variation in the neighborhood of the spur dyke. The
model consists of a hydrodynamic module, asediment transport module and a bed variation
module. The approach employed in this model may
be classified as an Euler-Lagrange coupling type, inwhich the flow and sediment are treated in quite
different ways. The details of the three modules arepresented hereafter.

10
Case3, 4

0
0.01

0.1

1

Numerical Model and Simulations

10

Diameter (mm)Fig. 2 Size distribution of sediment particles
The mean diameters of sediment particles either
in Case 7, 8 or in Case9, 10 are very close to thosein Case1, 2. Furthermore, in case of uniformly

983.1 Numerical model details
G = −ui′u ′j(1) Hydrodynamic module
In order to simulate complex turbulent flow
phenomena in complex geometries, Zhang (2005)
has developed a 3D numerical model based on theunsteady RANS (Reynolds-averaged Navier-Stokes
equations) with the widely-used k-ε equations forthe turbulence closure. The governing equations
written in the tensor form with the convention ofEinstein summation are as follows.
∂u j
∂x j

=0

(2)

∂k
∂k
∂ ⎡⎛
ν t ⎞⎤ ∂k
⎟⎥
+uj
=
+G −ε
⎢⎜⎜ν +∂t∂x j ∂x j ⎢⎣⎝σ k ⎟⎠⎥⎦ ∂x j

(3)

∂ε
∂ε
∂ ⎡⎛
ν t ⎞⎤ ∂ε
ε
⎟⎥
+uj
=
+ (C1ε G − C2ε ε )⎢⎜⎜ν +k∂t∂x j ∂x j ⎢⎣⎝σ ε ⎟⎠⎥⎦ ∂x j

(4)

σk =1.0 σε =1.3kε1 ⎛ ∂u ∂u j ⎞Sij = ⎜ i +⎟2 ⎜⎝ ∂x j ∂xi ⎟⎠C1ε =1.44

C2ε =1.92(7)

The governing PDEs (Partial differential
equations) are integrated over a series of control
volumes covering the study domain with an FVM(Finite volume method). The conserved equations
are discretized on a collocated unstructured mesh.
The power law scheme has been adopted during the
spatial discretization. The surface fluxes arecalculated from the Rhie-Chow momentum
interpolation method in order to avoid the so-called
checkerboard phenomenon. For the temporal
integral, the second order implicit Crank-Nicolson
scheme is employed. The widely used SIMPLE(Semi-implicit
methodforpressure-linked
equations) procedure is included in the model forthe coupling of the pressure and the velocity. The
final algebraic equations resulted from thediscretization process are solved with apreconditioned GMRES (Generalized minimal
residual method) incorporated with an ILUTP(Incomplete LU factorization with threshold andpivoting) preconditioner. The detailed discretizationand solution methods are referred to Zhang (2005).

where ui, uj = velocity components; xi, xj = Cartesian
coordinate components; ρ = the density of the fluid;
fi = body force components; p = the pressure field; v= the molecular kinematic viscosity of the fluid; τij =Reynolds stresses. Due to the existence of the
Reynolds stress terms, equation system Eq. (1) andEq. (2) is not closed. In a k-ε model, the Reynolds
stresses are evaluated from the information of themean flow after introducing a concept of eddy
viscosity vt and constructing two transport equations,i.e. Eq. (3) and Eq. (4), for the turbulence kinetic
energy k and its dissipation rate ε. Then the
Reynolds stress terms are estimated from thefollowing expression.
2
τ ij = − ρ ui′u ′j = 2 ρν t Sij − ρ kδ ij
(5)
3
where
ν t = Cμ(6)

The model parameters in Eq. (3) and Eq. (4)generally take the following values for practical
use.

(1)

∂ui
∂u
∂ 2 ui
1 ∂p
1 τ ij+ u j i = fi −
+ν
+
ρ ∂xi
∂t
∂x j
∂x j ∂x j ρ ∂x j

∂ui
∂x j

(2) Sediment transport module
Modeling of the sediment transport process andits morphological consequences is a bottleneck of
the application of numerical methods in thehydraulic engineering nowadays. It is mostly due tothe shortage of a clear understanding anddescription, preferably in a mathematic form, of theassociated physical process. This process is quite
sophisticated. If only bedload is considered, themovement of a sediment particle may be divided
into a three-stage process: be picked up from thebed, transport near the bed and deposit onto the bed.
If these three stages could be quantified, thesediment movement and bed deformation were able
to be simulated. It is known that for an individual
particle, its movement must follow the basic
mechanical laws. On the other hand, when a group⎧1 if i = j⎩0 if i ≠ j

δij = ⎨

in which ui’, uj’ = the fluctuating velocity
component in i, j direction, respectively; νt = theeddy viscosity; Sij = the strain-rate tensor, δij = theKronecker delta and Cμ = coefficient, being
usually set as a constant 0.09. In the transport
equations for k and ε, G = the rate of turbulence
production and is defined as99

of sediment particles are concerned, the problem
may turn into a stochastic problem in which the
turbulence flows, the bed conditions and theinterparticle collisions are all uncertain. In thispaper, the problems related to the sediment pick-up
and deposition are considered as stochastic
problems and those related to the transport stage aretreated in a deterministic way. In order to estimate
the bed variation process, the following modelingprocedure is proposed. Firstly, the amount of
sediment of different sizes being picked up at any
specified location is estimated. After that the
trajectory of each sediment size fraction is sought.
Then, the deposition amount of sediment particles
along each trajectory is estimated. The deposition
amount is interpolated to any specified computation
point if necessary. By introducing an algorithm forbed sorting, the temporal bed variation in terms ofboth configuration and composition is obtained
finally.
a) Sediment pick-up
Considering the effect of local bed slope,
Nakagawa et al. (1986) has proposed the following
expression to estimate the pick-up rate of sedimentparticles from a bed.
p s (k )⎛ k p Φτ ∗ck ⎞⎟= F G τ ⎜1 −(σ ρ − 1)g 0 ∗ ∗k ⎜⎝τ ∗k ⎟⎠d (k )

mp(8)

in whichG∗ =cosψ + k L μ s
1 + kL μsτ ∗k =u*2(σ / ρ − 1) gd ( k )Φ=μ s cos θ b − sin θ b cosα 1 + k L μ scosψ + k L μ s
μs

where ps (k ) = pick-up rate for size fraction k; d (k ) =the diameter of size fraction k; σ = the density of
sediment; F0, kp and mp are constants (=0.03, 0.7
and 3, respectively) as suggested by Nakagawa et al.
(1986); G* =coefficient accounting for the direction
deviation between near bed velocity and sediment
movement direction; Ψ = the angle between thenear bed velocity and the sediment movement
direction; τ *k = the dimensionless shear stress forsize fraction k; u* = the near-bed friction velocity;
τ *ck = the dimensionless critical shear stress for size
fraction k; Φ =coefficient accounting for local bed

slope; μ s = the static friction factor (=0.7); k L = theratio of lift force to drag force (=0.85); θ b = thelocal bed slope; α = the angle between the
maximum local bed slope and sediment movement
direction. In the computational domain, the volumeof sediment being picked up from a mesh is thenestimated from the following expression.
V p (k ) =A3 d (k )A2p s ( k ) S p pb ( k )(9)where V p (k ) = sediment pick-up volume of size
fraction k from a mesh; S p = projected area of thecomputational mesh onto the horizontal plane;pb (k ) = percentage of sediment of size fraction k in
the bed surface; A2 , A3 = shape coefficients of
sediment particles for 2D and 3D geometricalproperties (= π / 4 and π / 6 , respectively). Nagata et al.
(2005) and Onda et al. (2007) employed this method
for uniform sediment beds and verified its
applicability. In this study, it is extended to
non-uniform beds. It is noted that he availability of
sediment particles of any size fraction in the bed
surface layer has been considered in Eq. (9).
b) Trajectory of sediment movement
After being picked up, sediment particles will
move near the bed and some of them may deposit
onto the bed somewhere. The sediment movement
velocity and information on the trajectory of the
movement of sediment particles are of importance.
Omitting the inter-particle collisions, the movement
velocity used of a sediment particle is estimated fromits moment equation. Defining two unit vectors
paralleling to the local bed surface: pb1 on xz-planeand pb2 on yz-plane, the moment equation in pbj
direction is written as below for a particle belonging
to size fraction k.
⎞
3 d u sedj
+ C m ⎟⎟ A3 d (k )= Dkj + Wkj − Fkj
dt
⎝ρ
⎠
⎛σ

ρ ⎜⎜

( j = 1,2)

(10)

in which usedj= component of sediment movement
velocity in j direction; Cm= coefficient of added
mass; Dkj = component of drag force on a particle inj direction; Wkj= component of submerged weight of
sediment particle in j direction; Fkj = component offriction force between sediment particle and the bed
in j direction. The magnitude of the drag force,
particle submerged weight and friction force are
obtained as below

100

D(k ) =CD ρ
2
2
u bj − u sedj ce A2 d (k )2(

W(k ) = (σ − ρ )gA3 d (k )

)

3

⎛
⎞
cosθ bx cosθ byF(k ) = μ k ⎜W(k )− k L D(k ) ⎟⎜⎟sin θ p
⎝
⎠

(11)
(12)

f s (s(k ,n ) ) =(13)

where D(k)= the drag force on sediment particle ofsize fraction k; W(k)= the submerged weight of
sediment particle of size fraction k; F(k)= the friction
force between the bed and sediment particle of size
fraction k; ubj= component of near bed flow velocity
in j direction; CD= the drag coefficient; ce= thecoefficient accounting for the effective application
area of the drag force; θ bx , θ by = the angle of thelocal bed inclination in x and y direction,
respectively; θ p = angle between pb1 and pb2. When
Eq. (10) is solved, the velocity components of asediment particle are obtained. Hence, the positionof a particle at any time after being picked up is
known. After nth step of movement, the position of
the particle belonging to size fraction k is as below.

p sed (k ,n ) = p sed (k ,n−1) + Δt ⋅ u sed (k ,n )(14)where psed(k,n), psed(k,n-1)= the position of sedimentparticle after nth and (n-1)th time step,
respectively; Δt =time step; used(k,n)= the sediment
movement velocity. At this position, the total distantof movement of the particle from its original
location is written ass(k ,n ) = ∑ Δt u sed (k ,n )(15)

where s(k,n) = the movement distance of a sedimentparticle of size fraction k after nth time step.
c) Sediment deposition
During the transport stage, some of the sedimentparticles may keep moving following the trajectory
as described above, while some of them may settle
down and deposit onto the bed at certain place. The
amount of sediment deposition onto the bed along
the sediment transport trajectory is estimated withthe aid of the probability density function for the
step length, i.e.
Vd (k ,n ) = V p (k ) f s (s(k ,n ) )Δt u sed ( k ,n )k after nth step of movement; f s ( s( k ,n ) ) = theprobability density function of step length and isestimated from the following expression.

(16)

where Vd (k ,n ) = the deposition volume of size fraction⎛ s(k ,n ) ⎞⎟exp⎜ −⎜ λ( k ) ⎟
λ(k )
⎝
⎠
1

(17)

where λ (k ) = the average step length of sedimentparticle belonging to size fraction k, which isestimated following Einstein’s suggestion as below(Einstein, 1950).
λ( k ) = λ0 d (k )∗∗⎛ r2 ⎞
exp⎜⎜ − ⎟⎟dr
2π
⎝ 2 ⎠
1

B∗ / τ ∗ −1 η 0∫− B /τ −1 η

0

(18)

where η 0 = coefficient of variation of lift force;
λ 0 = 100 and B*=0.156, are two constants.
(3) Bed variation module
With the methods introduced above, the behaviorof sediment particles is traced in an explicit way.
Detailed information of sediment particles
movement is obtained along their moving
trajectories. In general, these trajectories do notcoincide with the computational mesh. In order tosimulate the bed deformation process, theinformation at the center of any computational meshmust be obtained based on that along the sedimentmoving trajectories. The change of the bed level ishence calculated in the following procedure: The
pick-up volume of size fraction k from mesh i is
calculated with Eq. (9). Then the position of
sediment particles belonging to each size fraction
after nth time step is estimated with Eq. (14). The
corresponding deposition volume there is estimatedfrom Eq. (16) and the mesh where the sedimentparticles locate is specified. The calculated
deposition volume is then distributed to this meshand its neighbors. For each mesh, the deposition
amount is a summation of distributed deposition
volume of sediment particles deposit within themesh itself or its neighbors. As a result, theestimation of the change of the bed level becomes
possible, i.e.
V
− V p (k )∂z b
A A ∑ d (k ) ∑k= 1 2 k
A3
Sd
∂t

(19)

where z d = bed level; A1= shape coefficient of
sediment particle for 1D geometrical properties(=1.0); Vd ( k ) = the deposition volume of size fraction

101

k at mesh center; Sd= the projected area of the meshonto the horizontal plane.
It has to be mentioned that after a group of
sediment particles are picked up from a mesh, themovement of them is traced until all the particles
deposit. Sometimes, it takes a long time for all theparticles to settle down. In other words, newsediment particles are picked up from a mesh while
the sediment particles picked up in the previous
pickup event is still in motion. Since all theinformation should be memorized, it consumes
exhaustive computer resources. For the time being,different time steps are used in this research for thecomputation of the pickup event and the deposition
event. The time step for the pickup event is a little
larger than that for the deposition event.
Besides the bed level, the bed composition also
plays an important role in sediment transportmodeling. In this study the bed sorting processsuggested by Liu (1991) is adopted. The bed isvertically divided into an active layer, a transition
layer and a series of deposition layers. The active
layer changes its elevation and sediment size
distribution with the transport of bedload but keeps
a constant thickness. The change of the bed level isexpressed by the changing of the thickness of thetransition layer and the number of the deposition
layers. Detailed information is referred to Liu(1991) and Zhang (2005).
(4) Solution procedure
The solution procedure of the numerical model issummarized as below.
(a) Solve momentum equations for each velocity
component.
(b) The resulted velocity is used to calculatemass fluxes through CV surfaces. Improve
velocity field in the SIMPLE method.
(c) Solve transport equations for turbulencekinetic energy and its dissipation rate andupdate the eddy viscosity.
(d) Repeat the above procedures until theresidual level becomes sufficiently small.
(e) Estimate the near bed flow velocity and shear
stress.
(f) Estimate sediment pickup volume at eachtime step. The volume is adapted to that for
the time step used in the deposition
calculation.

(g) Compute sediment moving trajectory anddeposition along the trajectory.
(h) Estimate sediment deposition volume at eachmesh.
(i) Calculate bed level change at each meshbased on the pickup volume and deposition
volume.
(j) Calculate the change of bed composition.
(k) Adjust local bed slope if it is larger thansome critical angle (angle of repose
underwater is used in this research forsimplicity). Corresponding adjustment in the
bed composition is made as well.
(l) Generate new mesh for next computation.

3.2 Computational conditions
The numerical model is used to simulate the flow
field and bed variation process in the experimental
flume. Two of the experimental cases are selected in
the numerical simulations: Case2 and Case8. The
movable bed consists of uniform sediment in Case2
and it is non-uniform in Case8. However, it may be
noted that the mean size of the sediment used inthese two cases is very close.
Unstructured mesh is used in the simulations inorder to test the performance of the model. The planview of the computational mesh in theneighborhood of the spur dyke is shown in Fig.3.
The mesh is hybrid consisting of both hexahedra
and prisms. The total mesh number is 6344 and thetotal node number is 4030.
Unit: cm
40
30
20
10
0

-60

-40

-20

0

20

40

60

Fig.3 Plan view of the computational mesh
The computational domain is not the same as theexperimental domain. It covers a 2.4m-long reach of
the experimental flume longitudinally with the spurdyke at the middle of the reach in order to savecomputational time. Simulations are finished after a
2-hour bed deformation process since the movable
bed shows insignificant changes and aquasi-equilibrium stage is reached.

102y (cm)y50(cm)50-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

40

0

1

2

3

40

30

30

20

20

10

10

0

-40

-20

0

20

40

60

80

0

100

-40

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

0

-20

60

0

20

40

1

2

3

80

x (cm)x (cm)(b) Case 4(a) Case 2y (cm)50

y50(cm)-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

40

0

1

2

3

40

30

30

20

20

10

10

0

-40

-20

0

20

40

60

80

0

100

-40

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

0

-20

60

0

20

40

1

2

3

80

x (cm)(d) Case 6y (cm)50

y50(cm)-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

0

1

2

3

40

30

30

20

20

10

10

0

-40

-20

0

20

40

60

80

0

100

-40

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0

-20

60

0

20

40

1

2

3

80

x (cm)(f) Case 8y (cm)

50

50-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

0

1

2

3

40

30

30

20

20

10

10

0

-40

100

x (cm)(e) Case 7y (cm)
40

100

x (cm)(c) Case 5

40

100

-20

0

20

40

60

80

0

100

-40

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

0

-20

60

0

20

40

1

2

3

80

x (cm)

100x (cm)(g) Case 9(h) Case 10

Fig.4 Final bed configuration (Experiment results)
60

y (cm)

y50(cm)50
40-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

0

1

2

3

40

30

30

20

20

10

10

00

00

10 20 -20
30 40 50-40
0 60 70
20 80 90
40 100 110
60 120 130
80 140 150
100-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

0

1

2

3

10
30 40 50
70 80 40
90 100 110
150-40 20 -20
0 60 2060 120 130
80 140 100

x (cm)
Fig.6 Simulated bed configuration (Case8)x (cm)
Fig.5 Simulated bed configuration (Case2)

103

4

Results and Discussions

4.1 Bed configuration
The bed contours at the final stage in theexperiments are shown in Fig.4. The contours ofcases without any spur dyke are firstly discussed,
which provide reference information for theinvestigation on the impacts of the spur dyke later.
For uniform sediment bed in Case5, bed forms
develop as the critical shear stress is smaller than theactual bed shear stress. For non-uniform sedimentbeds in Case7 and Case9, bed shear stresses are
smaller than the critical ones calculated based on
sediment mean diameters. But bed change is stillobserved although the magnitude is very small. Thisis a typical phenomenon taking place in alluvial
rivers and the reason has been well documented.
Due to the selective transport of fine particles, bed
will be degraded. On the other hand, the remaining
particles in the surface layer become shelters for theparticles beneath them and prevent the bed fromfurther degradation. It has to be mentioned that a
few amount of coarse particles are captured by the
sediment trap at the downstream of the flume in theexperiment. The change of inter-particle contact
conditions after the erosion of fine particles is
considered to be mainly responsible for thisphenomenon.
The contours in Fig.4 demonstrate that thepresence of the spur dyke has significant impacts
on the bed configuration. In the approach flow area,
one may find that the bed level shows insignificant
change, indicating a reduction of shear stress there.
The main features of the deformed bed are a local
scour hole, followed by a long distance of
deposition area. These features can be evidently
observed in the contours shown in Fig.4. In order toclarify the change of the bed configuration aroundthe spur dyke, in particular the local scour
dimensions, a summary is presented in Fig.7
including the main features of the surface extent of
the scour hole. The values of the key parameters
resulting from the current experiments are shown in
Tab.3.
For relatively uniform sediment bed (i.e. Case2,
Case4 and Case6), the maximum scour depth andthe area of the scour extent increase with thedecreasing of the sediment mean diameter, which iseasily observed from the contours in Fig.4. The
quantitative evidence is shown in Tab.3 with thevalues of a/L, b/L, c/L and dmax. It may be
explained that the entrainment of coarse particles
necessitates more flow energy and hence they are
not easily eroded. The representative slopes of thescour hole also show some relation with the mean
sediment diameter. Take a look at θ1, θ2 and θ3 in
Tab.3, one may conclude that the slope of the scour
hole is relatively steeper in case of coarser sediment.
Moreover, compared with the slope upstream and in
front of the spur dyke, the slope is very gentle at thedownstream part of the scour. It is the result of theadjustment with the local flow field, especially thevortex system. Case6 deserves special attention
since it is conducted under live-bed scour condition
and without sediment supply from the upstream
boundary. Besides the local scour area, erosion also
appears in the downstream of the spur dyke due tothe development of bed forms. Compared with
Case5, the bed forms in Case6 are superimposed
upon the bed configuration caused by the spur dyke,
having sophisticated features and dimensions.
θ1, θ2, θ3: Slope at designated section
dmax: Maximum scour depth (cm)

Flow

c

θ2

b

θ3
L

θ1

a
Fig. 7d

Sketch of scour dimensions

Table 3 Scour dimensions
Case2

Case4

Case6

Case8

Case10

a/L

2.1

1.4

2.4

1.9

2.1

b/L

2.9

2.3

4.0

2.9

3.0

c/L

4.0

2.1

3.9

2.3

3.7

d/L

1.4

0.0

1.4

0.4

0.9

θ1

26

o

o

o

o

22 o

θ2

31 o

33 o

29 o

26 o

25 o

θ3

16

o

18

o

o

19

o

12 o

dmax(cm)

11.4

9.1

12.1

9.2

9.4

d(mm)

1.03

1.70

0.31

1.00

0.86

34

26

14

27

Should one take a look at the cases of non-uniform
sediment only (i.e. Case8 and Case10), similar

104

conclusion would be drawn that the increasing of themean sediment diameter will result in decreasing of
the local scour depth and the scour extent area aswell as increasing of local bed slopes of the scourhole. It has been mentioned that the movable bed in
Case8 is gap-graded and that in Case10 is wellgraded. But this difference seems not affect so muchon the scour geometry under the current experimental
conditions. However, the non-uniform sediment beds
do show different features from those of the uniform
ones if one compares all the listed cases. It is veryclear that the maximum scour depth in either Case8
or Case10 is much smaller than that in Case4,
although the mean sediment diameter in the formercase is slightly smaller than the latter one. It seems tobe summarized that the local scour will be smaller ina non-uniform sediment bed compared with auniform one with the same mean diameter. The
formation of an armor layer at the bottom of thescour hole is a probable reason. The local slopes ofthe scour hole seem to be milder in a non-uniform
sediment bed if only θ1 and θ2 are taken into account.
Further experiments are needed to validate it.
The numerical results for Case2 and Case8 areplotted in Fig.5 and Fig.6. The maximum local scour
depths are 10.4cm and 8.6cm after 2hours,
respectively. Compared with those of theexperimental results (11.4cm and 9.2cm after 3hours,
respectively), the predicted results are quite well.
The geometries of the scour holes are also similar to
those of the experiments but exhibit slightdifferences. The reason is not evidently clarified.
However, similar phenomena have been observed byZhang and Nakagawa (2008b) in similar simulations
with sediment transport models of equilibrium type.
It might imply that the problem is caused by theinherent deficient of the turbulence model or
improper interpretation of the information from theturbulent flow domain to the near bed flow domain.

4.2 Bed composition
The non-uniformity of sediment particles affects
not only the bed configuration but also the bed
composition, in particular in the bed surface. Thechanges of the bed composition in Case8 are plottedin Fig.8 and Fig.9. Fig.8 is a sampling result fromthe experiment while Fig.9 shows the prediction
with the numerical model. In both figures, the bed

surface is coarsened in most of the area and there are
two belts consisting of relatively fine sediment. One
belt is near the side of the flume and starts from thespur dyke wake, while the other one is near thelongitudinal centerline of the flume and starts fromthe head of the spur dyke. The two belts are notreadily distinguished from the bed contours shownin Fig.4 and Fig.6.
y50(cm)
0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7

40

C
D
E
F

30

A

20
10
0

-40

B

-20

(mm)

0

20

40

60

80

x (cm)
Fig.8 Mean size distribution (Case8, Experiment)y50(cm)0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7

40

C
D

30
20

A

10

00
10
-40

(mm)

E

B

F
20 -20
30

40

50
0

60

70
20

80

90
40 100 110
60 120 130
80

x (cm)
Fig.9 Mean size distribution (Case8, Simulation)
For clarity, the area around the spur dyke isdivided into 6 zones as shown in Fig.8 and Fig.9.
Zone A stands for the approach flow area and Zone
B is the local scour hole. Zone C and Zone E
represent the places where sediment is obviouslycoarsened. Zone D and Zone F are the belts withrelatively fine sediment. It is very obvious that thenumerical result is quite encouraging if one
compares the results in all those zones. In particular,
the capability to predict the alternate distribution offine and coarse sediment particles demonstrates thatthe numerical model is powerful. On the other hand,attention should also be paid to the differences
between the experimental and computational results.
In Zone B, one may find that the lower part of thescour hole is relatively coarse while the upper partof which is rather fine. It is due to the existence of avortex system in the scour hole. There are somedifferences between the experimental and numerical105

results. The omission of the suspended load in the
numerical model might be responsible for thesedifferences. Due to strong vortices in the scour area,some of the sediment particles transport assuspended load in the scour hole. These particles
move to the downstream as bedload in thecomputation as they are not coarse enough.
Consequently, the bottom of the scour hole becomesvery coarse. However, they are suspended in thescour area in the experiments and settle down when
the pump is stopped. In Zone C and Zone E, themean sizes of sediment particles are also
overestimated in the simulation. This discrepancy
might be resulted from the discrepancy in theprediction of the local bed configuration and hence,
the local flow field. Moreover, Zone D in theexperiment is slightly closer to the longitudinal
centerline of the flume than that in the simulation.
The discrepancy in the prediction of the bed
configuration as well as the corresponding local
flow field is also believed to be the cause.
Nevertheless, further investigations with morecomputational cases are needed.
The alternate distribution of fine and coarse
sediment is also observed in another experimentcase, i.e. Case10, which demonstrates the generalityof this phenomenon for non-uniform sediment beds.
It is known that the change of the size distribution of
sediment particles in the bed surface is closely
related to the complex flow structure in theproximity of the spur dyke. Under the complex flow
condition, sediment particles of different sizes taketheir moves following different trajectories. The
detailed flow structure around a spur dyke is notshown here, which may be found in many referencessuch as Zhang et al. (2009). Instead, a sketch of the
movement of sediment particles near the bed in
Case8 is shown in Fig.10 according to experimental
observations.
y 50
(cm)
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

40
30

0

1

2

3

z (cm)

80

100

Zone D20

Due to the difference in sizes, the entrainment
conditions, movement trajectories and the travelling
time vary a lot for different sediment particles evenunder the same flow conditions. As a result, the size
distribution patterns shown in Fig.8 and Fig.9 areformed.

5

Conclusions

In this paper, a recent study was presented on the
non-uniform sediment transport around a spur dyke
with both experimental and numerical methods.
Experimental data indicates that a spur dyke hassignificant impacts on the bed configuration and bed
composition. For relatively uniform sediment bed,
the maximum scour depth and the scour area
increase with the decreasing of the particle diameter.
While the local slope of the scour hole increases
with the increasing of the particle size. The local
scour in a non-uniform sediment bed is generally
smaller compared with that in a uniform bed of thesame sediment mean diameter. In the local scour
hole, the bottom part is rather coarser than the upper
part. Due to the sediment sorting process, the bed
materials generally become coarser in theneighborhood of the spur dyke and armor layers
form there. However there exist two longitudinalbelts consisting of relatively fine sediment.
The numerical model is based on unstructured
mesh, being able to solve problems in complex
geometries and/or with irregular boundaries. The
model takes into account the stochastic anddeterministic nature of sediment transport, capableof simulating sediment transport in non-equilibrium
conditions. The simulated local scour and size
distribution around the spur dyke are in reasonableagreement with those of the experiments. However,
the model still needs refinement to improve theaccuracy of flow velocity prediction and to shorten
the computation time. Moreover, fundamental
experiments are also needed to investigate theunderlying processes associated with the pickup anddeposition events of non-uniform sediment particles.

100

Acknowledgements

Zone E
-40

-20

0

20

40

60

x (cm)
Fig.10 Sketch of sediment movement

This research is supported in part by a research
grant from the Kinki Construction Association,

106

Japan (PI: H. Zhang, No.25-1) and the GCOE-HSE
Program (Kyoto University Global Center for
Education and Research on Human Security
Engineering in Asian Megacities, PI: Y. Matsuoka).

References
Einstein, H. A. (1950): The bed-load function for
sediment transportation in open channel flows,
Technical Bulletin, No. 1026, U.S. Department ofAgriculture,
Soil
Conservation
Service,
Washington D.C.
Liu, B.Y. (1991): Study on Sediment Transport andBed Evolution in Compound Channels, Ph.D
Thesis, Kyoto University.
Nagata, N., Hosoda, T., Nakato, T. and Muramoto,Y. (2005): Three-dimensional numerical model forflow and bed deformation around river hydraulicstructures, Journal of Hydraulic Engineering,
ASCE, Vol.131, No.12, pp. 1074-1087.
Nakagawa, H., Tsujimoto, T. and Murakami, S.
(1986): Non-equilibrium bed load transport alongside slope of an alluvial stream, Proceedings of theInternational
Symposium
on
River
3rd
Sedimentation, University of Mississippi, pp.
885-893.
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 Journal of Hydraulic Engineering, JSCE,
vol.51, pp.943-948 (in Japanese).
Zhang, H. (2005): Study on Flow and Bed Evolution
in Channels with Spur Dykes, Doctoral
Dissertation, Kyoto University.
Zhang, H. and Nakagawa, H. (2008a): Scour aroundspur dyke: recent advances and future researches,
Annuals of the Disaster Prevention ResearchInstitute, Kyoto University, No. 51B, pp. 633-652.
Zhang, H. and Nakagawa, H. (2008b): Investigation
on morphological consequences of spur dyke withexperimental and numerical methods, Advances inHydro-science and Engineering (Wang, Kawahara,
Holtz, Tsujimoto & Toda eds), Vol.8, Nagoya,Japan, CD-ROM.
Zhang, H., Nakagawa, H., Kawaike, K. and Baba, Y.
(2009): Experiment and simulation of turbulent
flow in local scour around spur dyke, International
Journal of Sediment Research, Vol.24, No.1, pp.
33-45.

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