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Numerical Simulation of Skewed Slot Effect on
Local Scour Reduction
ARTICLE · JANUARY 2011

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Journal of Water Sciences Research,
ISSN: 2251-7405 eISSN: 2251-7413
Vol. 3, No. 1, Summer 2011, 69-80

Numerical Simulation of Skewed Slot Effect on Local
Scour Reduction
Taymaz Esmaeili1*, Amir Ahmad Dehghani 2, Mohammad Reza Pirestani 3, Tetsuya Sumi4
1. Department of Civil Engineering, Aq Qala Center, Islamic Azad University, Aq Qala, Iran
2 .Assistant Professor., Department of Water Engineering, Gorgan University of Agricultural Sciences & Natural Resources, Gorgan, Iran
3. Assistant Professor., Department of Civil Engineering, Islamic Azad University-South Tehran Branch, Tehran, Iran
4. Professor, Disaster Prevention Research Institute, Kyoto University, Uji- Kyoto 611-0011, Japan

Received: 11 Jun. 2011;

Accepted: 27 Aug. 2011

ABSTRACT
Local scouring around bridge piers is a natural phenomenon caused by the erosive process offlowing stream on alluvial beds. The 3D flow field around bridge piers interacting with the bed
materials increases complexity of local scour process. The local scour depth develops inaccelerated flows and if it is not predicted correctly, the bottom level of local scour hole will
exceed the original level of pier foundation. In this case the failure of bridge will occur. Using
different methods of local scour countermeasure for reducing the magnitude of local scouring
depth and retrofitting costs would be economically efficient. As a local scour countermeasuremethod, applying slots in the piers could reduce the local scour depth around circular piers. Since
in natural streams the piers are skewed to flow in most cases, it is more feasible to evaluate theskew slots effects on scour reduction. The present study focuses on numerical simulation of
maximum depth of scour due to the installing of slots in various angles of flow attacks byemploying a 3D numerical model (SSIIM program). The results show the ability of SSIIM formodeling the local scouring around bridge piers with slots.
Keywords
Local scouring; Numerical model; Bridge pier; 3D numerical model; SSIIM program
1. Introduction
Due to the diverse economic and social costs
that can be imposed by bridge failure theevaluation of the maximum local scour depth
around bridge piers is an important topic inriver engineering (Esmaeili 2009). Local
scouring around bridge piers can be a severe
problem, especially when a high flow occurs in
the river. When this undesirable event occurs, ascour hole appears around bridge piers The
local scour depth develops in high flows and if
it is not predicted correctly the bottom level*

Corresponding Author Email: (taymaz.esmaeili@gmail.com)

of local scour hole will exceed the originallevel of the pier foundation. In this case thesafety and stability of the bridge will be indanger. Bridge collapse during a flood raises
many direct and indirect economic and social
costs (Dehghani, et al. 2009). Streambed scour isthe leading cause of bridge failure in the UnitedStates (Murillo 1987). The costs associated withrestoring the damaged structures are substantial, but the indirect costs associated withthe disruption of traffic are even more thanfour times the direct costs (Roheds and Trent
1993). The three-dimensional flow field aroundNumerical simulation …, Esmaeili et al.

a pier is extremely complex due to theseparation and generation of multiple vortices.
The complexity of the flow field is further
magnified due to the dynamic interaction
between the flow and move-able boundary
during the development of a scour hole
(Raudkivi and Ettema 1985). Accurate
prediction of scour pattern around bridge piers
strongly depends on resolving the flow structure
and the mechanism of sediment movement inand out of the scour hole (Mendoza-Cabrales
1993).
Many studies have been carried out todevelop the relationships for predicting the
maximum scour depth at bridge piers underclear-water scour condition and these
relations have been used extensively fordesigning purposes (Dehghani et al. 2009).
Implementation of bridges' pier foundation ina deeper depth than the maximum potential
local scour hole was accepted as a conservative
scour countermeasure in most of practical cases;
although that would require expensive and deeppiers in streambeds. Consequently, there is aninterest in finding reliable ways to reduce scour
depth and, thereby, requisite pier embedment
depth. Furthermore, prior studies by the
researchers regarding local scouring aroundbridge piers showed that geometricparameters of the pier is one of the mosteffective factors on the maximum local scour
depth.
Efforts have been made to reduce scour by
providing an array of piles in front of the pier(Chabert and Engeldinger 1956), a circularcollar around the pier, (Thomas 1967, Tanaka
and Yano 1967 and Ettema 1980), submerged
vanes (Odgaard and Wang 1987), a deltawing-like fin in front of the pier (Gupta andGangadharaiah 1992), combined methods(Garg, et al. 2008 and Moncada et al. 2009) a
slot through the pier (Chew 1992), (Grimaldi
et al. 2009) and (Tafarojnoruz et al. 2010).
Local scour around a solid pier resultsfrom the downflow at the upstream face ofthe pier and the horseshoe vortex at the baseof the pier. Hence, one way of reducing scour
is to weaken and possibly prevent theformation of the downflow and horseshoe
vortex. Depending on its location, a slot may
deflect the downflow away from the bed byaccelerating the bottom boundary layer flow
through itself as a horizontal jet, and by
breaking up the horseshoe vortex when theslot is placed near the bed. When placed near
the water surface, a slot effectively reduces
the downflow and horseshoe vortex. If ds s isthe depth of scour at a pier with a slot and ds
p is that for a pier without a slot, under thesame flow conditions, Vittal et al. (1994), in
their study of scour at a pier group, which isakin to a multislot, found that when ds s /ds p
is plotted versus Y L / Y 0 the value will be
unique (Kumar et al. 1999).
Nowadays,
numerical
modelsareextensively used in simulating different
problems in hydraulic science and one ofthese numerical models is SSIIM. This
program was developed for using in river,environmental, hydraulic and sedimentationengineering. SSIIM is an abbreviation for
sediment simulation in water intakes withmultiblock options. This 3D CFD model was
based on the finite volume method solving
the Navier-Stokes equations using the various
turbulence models (Olsen 1999).
In this study, the effect of slot on
reduction of local scour depth reduction
around a circular pier, by different lengths
has been numerically simulated. Then theslots by different orientation to the flow havebeen simulated by SSIIM model and theirpotential to reduction of the maximum local
scour depth around circular pier has beenassessed.
2. The Numerical Model
SSIIM model was developed based onanother Computational Fluid Dynamics model
called SSII that was first introduced by N.R.B.
70

Journal of Water Sciences Research, Vol. 3, No. 1, Summer 2011, 69-80

Olsen in 1990-91. SSII is an abbreviation for
sediment simulations in intakes and it had theability to apply 3D solution of convectiondiffusion equation for sediment calculations.
The main motivation for making SSII was thedifficulty to simulate fine sediments in physicalmodels. However, SSII model suffered fromusing a structured grid that made it possible justto have one block for an out blocked region
while, in practical cases a multi-block modelwith general out blocking possibilities will beneeded. Therefore, the capability of multi-blockmodelling was added to SSII and due toremarkable changes in the model, the new
established model called SSIIM.

model by Wilcox (2000). However, thedefault turbulence model is the standard kmodel.
The free surface is modeled as a fixed-lid,with zero gradients for all variables. The
locations of the fixed lid and its movement are
as a function of time, which can be computedby different algorithms. The 1D backwatercomputation is the default algorithm and it isinvokedautomatically.
Pressure
andBernoulli algorithm can be used for both
steady and unsteady computations. The
algorithm is based on the computed pressure
field. It uses the Bernoulli equation along thewater surface to compute the water surface
location based on one fixed point that does
not move. The algorithm is fairly stable, sothat it can also be used in connection withcomputation of sediment transport and bedchanges (Olsen 2007).
For the wall boundary treatment, it isassumed that the velocity profile follows acertain empirical function called a wall law. It
is a semi-analytical function to model the
turbulence near the wall in the boundary layer
and consequently the CFD model will notneed to resolve the turbulence of flow inboundary layer. As a result, it would not tohavenecessary too many grid points near thewall:

2.1. Tree-dimensional flow model
The SSIIM program solves the NavierStokes equations with the k- model on a three
dimensional
generalnon-orthogonal
coordinates. These equations are discretizedwith a control volume approach. The
SIMPLE or SIMPLEC methods can be used
for solving the pressure-Poisson equation. An
implicit solver is used, producing the velocity
field in the computational domain. The
velocities are used when solving theconvection-diffusion equations for different
sediment size (Olsen 2007).
The Navier-Stokes equations for noncompressible and constant density flow canbe modeled as:
∂u i
=0
∂xi

U
1
30 y
= ln
ux κ
ks

(1)

∂ui
∂u
1 ∂
+uj i =− Pδ ij − ρ ui′u′j∂t∂x j ρ ∂x j

(

)

(3)

where the shear velocity is denoted u x , κ is aconstant equal to 0.4, y is the distance to thewall and ks is the roughness equivalent to adiameter of particles on the bed.

(2)

The first term on the left side of the eq. [2]is the transient term. The next term is theconvective term. The first term on the righthand side is the pressure term and the second
term on the right side of the equation is the
Reynolds stress term. In order to evaluate thisterm, a turbulence model is required. SSIIM
program can use different turbulence models,such as the standard k- model or the k-

2.2. Morphological model
The sediment transport process in rivers is
described by the following equation, Exner’s
equation, which is the sediment continuity
equation integrated over the water depth:(1 − λ ) ∂zb + ∂qtx +
∂t

71

∂x

∂qty
∂y

=0

(4)

Numerical simulation …, Esmaeili et al.

where zb is the bed elevation, λ is theporosity of bed material, and qtx and qty are

sediment particles according to Shield’s
curve, w and S are the density of water andsediment, is the viscosity of the water and gis the acceleration of gravity.
Once eq. [5] is solved, the suspended load
can be calculated as follows:

components of total-load sediment transport
in x- and y-directions, respectively.
In this 3D CFD program, the suspended
load can be calculated with the convectiondiffusion equation for the sedimentconcentration, which is expressed as follows:
∂c
∂c
∂c
∂
∂c
( ΓT
)
+u j
+w
=
∂t
∂x j
∂z
∂x j
∂x j

q s ,i =νTτ − τc
τc

(6)

Sc

qb
D 501.5

where Sc is the Schmidt number representing
the ratio of diffusion coefficient to eddy
viscosity coefficient vt and set to 1.0 as default.
For calculating the suspended load in eq.
[4], eq. [5] is solved incorporated with theformula by van Rijn (1987) for computing
the equilibrium sediment concentration close
to the bed as the bed boundary. In order tosolve eq. [4] and eq. [5] conditions of z and C
should be given at inflow and outflow
boundaries. For the inlet boundary, due to theclear water scour conditions, z=C=0 can begiven and for the outlet boundary, far away

d 0.3
a

0.1

D 500.3( ρ S − ρw ) g

ρw ν 2(10)

where α b is the direction of bed-load
sediment transport.
3. Model properties and study caseExperimental results of Mia and Nago
(2003) were used for calibration andvalidation of model.
Their experimental studies carried out in a
flume 1600 cm long, 60 cm wide, and 40 cm
deep, located in the Hydraulics Laboratory of
Okayama University, Japan. Water wasconveyed to the flume from an elevated tankby a pipe through an approach channel inwhich the discharge was measured by meansof a sharp-crested weir.
The flow rate in the flume was adjusted
using a valve. The water depth was adjustedwith a tailgate. The head over the sharp
crested weir and the water surface were

1. 5

( ρs − ρw ) g

ρw

(9)
0 .1

qbx = qb cos(α b ); qby = qb sin (α b )the uniform flow.
The concentration formula has the following
expression:τ − τcτc( ρ s − ρw ) g= 0.053

1.5

where D 50 is the mean size of sediment. Then,the components of bed-load sedimenttransport in x- and y-directions can becalculated as follows:∂C ∂z== 0 can be given due tofrom the pier,∂x ∂x

C bed = 0.015(8)

u i c dz

where q s ,i (i=1,2)
arecomponentsofsuspended-load sediment transport in x- andy-directions, respectively.
For calculating the bed load in eq. [4], thefollowing relation proposed by van Rijn’s
formula (1987) is used:(5)

where w is the fall velocity of sedimentparticles and ΓT is the diffusion coefficientand can be expressed in the following way:
ΓT =

zf
a

(7)

ρw ν 2where, C bed is the sediment concentration, dis the sediment particle diameter, a is areference level set equal to the roughness
height, is the bed shear stress, c is thecritical bed shear stress for movement of72

Journal of Water Sciences Research, Vol. 3, No. 1, Summer 2011, 69-80

measured using a point gauge, sensitive to avariation of 0.1 mm. A mobile bed zone 100
cm long, 60 cm wide, and 57 cm deep was
prepared at a distance 800 cm downstream of
the flume beginning, and was filled withsediment of a median particle size d 50 =1.28

vertical grid distribution, the total number ofcells in the computational domain is1128000.
For the inflow boundary condition, thevelocity distribution was specified while thegradient of pressure is given zero. At theoutflow boundary, the vertical gradient ofvelocity is zero and the hydrostatic pressure
distribution is specified according to thewater depth. For the solid boundary, walllaws introduced by Schlichting (1979) wereused for the side walls and the bed.
Moreover, the bed roughness can be given asa user input and it is a function of theexperimental sediment size.
Moreover, in order to model verification
another numerical run was conducted by theboundary condition of discharge equal to 0.04
m 3 /s and water level of 20 cm. In this case,computed equilibrium scour depth was 77.5mm after 140 minutes, while experimental
results showed the scour depth 78 mm. Fig. 3
illustrates the scour hole shape at the end ofsteady flow condition for calibration andverification stages.
The first step in running the numericalcode is model calibration. In this study, by
employing the experimental data of Mia andNago (2003) in which, boundary condition ofdischarge and water level was 0.05 m 3 /s and23.5 cm respectively, model was calibrated.
When the model calibrated, the equilibrium
local scour depth obtained 87.5 mm after 270
minutes whereas, the experimental datashows 89 mm at the end of correspondingtime.

mm and geometric standard deviation σ g=1.29. A vertical circular pier of diameter D=6 cm was placed in the center of the mobile
zone. The mobile bed was leveled before
starting a test. The experiments were stopped
at a stage when there was less than 1 mm
scour by 1 h or no scour at all (Mia andNago 2003). In their experimental study,
temporal variation of scour depth understeady flows was measured and a method for
calculating time variation of scour depth was
proposed. Cross section and plan view of the
flume has been illustrated in Fig. 1.
4. Numerical Simulations
4.1. Domain description and model calibration
Making an appropriate grid is a very
important process in the preparation of input
data for SSIIM program. The size andalignment of the cells will strongly influence
the accuracy, the convergence and thecomputational time (Olsen 2007). For getting
more precise results, it is better to refine themesh around bridge piers (Dehghani, et al.
2009).
A preprocessing code was used for
dividing flow field area into regions ofdifferent sizes. In this study, the length ofchannel is divided by eight sections and ineach section the various cell sizes were used.
The distribution of mesh in upstream half ofthe channel has been presented in Fig. 2. In
the first region, in x- and y-directions, thesize of cells is 2.5 cm × 0.5 cm, in the second
region cells are 2 cm × 0.5 cm and in thethird region size is 1 cm × 0.5 cm. The
central part of the flume is 1 m long and thesize of cells is 0.5 cm × 0.5 cm. Due to the

4.2. Simulation results and discussion
In order to numerically investigate theeffect of slot without orientation on local
scour reduction, different lengths of slots
were employed. Kummar et al. (1999)
concluded that the ratio of ds s /ds p is only afunction of the dimensionless geometricparameters related to the slot, so the results of73

Numerical simulation …, Esmaeili et al.

their study employed on experimental runs of
Mia and Nago (2003). In the selected
experimental run, pier diameter was 6 cm andthe boundary condition of discharge and waterlevel were 0.04 m 3 /s and 20 cm respectively.
The applied width of slot in the numericalsimulation was half of the pier diameter thatwas equal to 3 cm. In order to compare theresults of numerical model to experimental
data, a dimensionless graph which wasdemonstrated in the study of Kummar et al.
(1999), was employed. The mentioned graphhad been obtained based on study of Chiew(1992) and the modification of Vittal et al.
(1994). Fig.4 illustrates the geometry ofslotted pier that was modelled in numericalsimulations and effect of different length ofslot respect to water surface in the reductionof local scouring depth.
As can be clearly observed, when the lengthof slot increases and places near the bed, local
scour depth starts to decrease. This is due to thisfact that when slot length increases through thepier, vortices that have the major role in local
scouring become weak. Fig. 4 also reveals
that, numerical results have a good agreementwith those gained through experimental runs.
Although slot without orientation could
reduce the magnitude of local scour depth as
a local scour countermeasure, it is morefeasible to evaluate the skewed slots’ effects
on the reduction of scour hole in natural
streams where the position of piers are
skewed to flow in most cases.

Upstream flow
depth

Circular pierSand bed
Outlet valve

Flow direction

XZ
800 cm100 cm700 cm

(a)
X

60 cm

Y
800 cm700 cm100 cm(b)
Fig. 1. Geometric properties of the flume in which experiments were done by
Mia & Nago (2003); (a) longitudinal section, (b) plan view (not scaled).

74

Journal of Water Sciences Research, Vol. 3, No. 1, Summer 2011, 69-80

y
x

7m

1m

0.5 m

(a)
Water level

z
y

(b)
Fig. 2.(a) Plan view of computational domain used for numerical modeling (not scaled)and (b) Vertical grid distribution.

Fig. 3. (a) Bed changes in the vicinity of circular pier at the end of
calibration and (b) verification stage75

Numerical simulation …, Esmaeili et al.
b

w

Y

Y

L

Channelbed
Rectangular
slot

0

(b)

(a)

Fig. 4. (a) Geometric properties of slotted pier which was used in the study and (b) Variation of local scouring depth
versus non-oriented slot length when the slot width is half of the pier diametert= 140 min

Fig. 5. Bed changes around pier with 45 degrees skewed slot at the end of recalibration stage

In regard to sensitivity of flow field andvortices pattern around skewed slots, model
was recalibrated for the experiment of Mia &Nago (2003) in which the boundary conditionof discharge and water level was 0.04 m 3 /s
and 20 cm respectively. For the recalibration
stage, a slot by orientation of 45 degrees toflow direction and width equal to 0.25 of pierdiameter was implemented through the whole
length of the pier which was extender to thesand bed. In this case, time step androughness obtained 3s and 9.6 mm. In therecalibration stage, local scour depth was 84
mm where the experimental results ofKummar et al. (1999) showed 83 mm. Fig. 5
illustrates the bed topography at the end of
the recalibration stage for evaluating theskewed slot effect in local scouring depth.
Effect of four other slot orientations (i.e.,= 0º, 10º, 20º and 30º) on local scour depth
was numerically simulated by SSIIM model
whereas the boundary conditions were similar
for all other runs and they just differ ingeometric parameter of slot orientation. Fig.
76

Journal of Water Sciences Research, Vol. 3, No. 1, Summer 2011, 69-80

6 shows horizontal flow velocity vectors andtheir deflection when they confront withskewed slot.
Fig. 7 illustrates the bed topography at theend of simulation procedure for each slot
orientation. As it can be clearly seen from theoutputs of SSIIM model in Fig. 7, due to theflow deflection after facing the oriented slot,
down flow vortices and consequent horseshoe

vortex will lose its symmetric nature. Moreover,tendency of horseshoe vortex is to extend along
the slot direction and gain an asymmetricpattern and so scour hole shape will beasymmetric in the same way. Furthermore, it
seems that by increasing the slot skew to flow
direction, horseshoe vortex and the resulting
bed changes in the vicinity of bridge pier tend
to further extend along the slot direction.

= 0º

= 10º

= 20º

= 30º

Fig. 6. Deflection of flow velocity vectors after facing skewed slots.

= 0º

= 10º

0

0

= 20º

= 30º

0

0

Fig. 7. Bed changes pattern in the vicinity of pier with different degrees of skewed slot
77

Numerical simulation …, Esmaeili et al.

1.2

ds s / ds p

1
0.8
0.6
0.4
Numerical
Experimental

0.2
0
0

10

20

30

40

50

Angle of attack

Fig. 8. Variation of local scouring depth around slotted piers with different degrees of skew

Fig. 8, demonstrates the variation of
maximum local scour depth in the vicinity ofcircular pier versus slot skew degree that was
obtained from numerical simulations by
SSIIM program. The numerical results werecompared to experimental data which were
gained by Kummar et al. (1999) and a good
agreement has been illustrated between
numerical and experimental results. It must
be noted that the experimental data provided
by Kummar et al. (1999) were summarized in
the form of a non-dimensional graph.
There is a general trend that, indicated byboth in numerical and experimental results,
when angle of attack to a slotted pier goes up,
scour depth increases and the reduction ofscour depth due to slot extension starts tooffset. More specifically, when the angle ofattack is about 40 degrees, the scour depth in
this occasion will as the same as one of pierwithout slot. It seems that when angle ofattack with slot starts to increase, turbulence
further magnifies. In addition, downflow andhorseshoe vortices will empower as a result
and subsequently the reduction effect of slot
on local scouring becomes neutral by thereinforced vortices.

around circular pier has been conducted by
employing a SSIIM model. The following
results are obtained from the present study:- When the angle of flow approach with slot
is equal to zero, rectangular slot has apotential to reduce the local scouring,particularly when the slot length increases
respect to the water surface. The local
scour depth can be reduced up to 30% in
the vicinity of a pier with a slot which
was implemented through the whole
length of pier and extender to the bed,
compare to a pier without slot. It is due tothis fact when the length of rectangularslot increases, down flow vortex as well
as horseshoe vortex becomes weaker thanthe case in which there is not any
apparatus implemented through the pier.
However, additional studies on slots withdifferent widths should be done in orderto develop an applicable designing
relationship.
- Although slots could reduce the local
scour depth, in most of the practicalcases, piers are skewed to flow and it was
depicted that slots are likely to beineffective especially when the angle offlow approach with slot increases. It isnoticeable that when the slot skew to theapproach flow is about 30 to 45 degrees,
the local scour depth will be similar to thecondition without slot and from this stage

5. Conclusion
The numerical simulation of geometricparameters effects of rectangular slot withand without orientation on local scouring
78

Journal of Water Sciences Research, Vol. 3, No. 1, Summer 2011, 69-80

on, by increasing the slot skew, the scour
depth will exceed the original local scour
depth around the pier without slot. In thiscondition, the turbulence is predominant
and the reduction factor of slot on local
scouring starts to be offset.

κ

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a
C bed
d
D 50
g
ks
q s ,1
q s,2
q tx
q ty
Sc
ui
ux
w
y
zb

reference level set equal to theroughness height (m)sediment concentration close to bed(kg/kg)the sediment particle diameter (m)mean size of sediment (m)ρsdensity of sediment (kg/m³)

λνT

the porosity of bed material
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ΓTdiffusion coefficientcEsmaeili T., (2009). Hydraulic and Geometric
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bed-load sediment transport in x
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flow velocity in i direction (m/s)
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