osInternational Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 04, April 2019, pp. 2108-2128, Article ID: IJCIET_10_04_219
Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=10&IType=04
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
Scopus Indexed
NUMERICAL INVESTIGATION OF FLOW
PATTERN AND SCOUR CHARACTERISTICS
AROUND ELECTRICAL TOWER
FOUNDATIONS
Gamal M. Abdel-Aal, Maha R. Fahmy, Amany A. Habib and Mohamed Galal
Elbagoury
Water and Water Structures Engineering Department, Faculty of Engineering, Zagazig, Egypt
ABSTRACT
The presence of some high voltage towers in flood stream is one of the most
important problems that may lead to the collapse of these towers. The main reason for
collapse is the soil erosion around the tower foundation during flood. The shape of the
foundation is a vital factor in scouring process. This research is focused on studying
different shapes of a tower foundation and its effect on the maximum scour depth. A
sediment scour model has been investigated by using Flow 3D V 11.2 Program. The
numerical simulation results of the maximum scour depth surrounding a single square
pile model have been assured using prior experimental findings and showed good
agreement. After that, different four shapes of footing and five values of the inclination
angle for pyramid and cone footing have been investigated. The results of cuboid
footing have been used as a reference to compare with different shapes. Seventy-two
numerical runs have been carried out considering the wide range of Froude number
ranging from 0.26 to 0.50 under clear water condition. It is found that, for pyramid and
cone footing, the lager the inclination angle, the smaller the scour depth will be and
vice versa. The cone footing is better than the other footing shapes. An empirical
equation has been developed by using the nonlinear regression to predict the relative
maximum scour depth around the footing.
Keywords: Scour, Vortex, Footing, Flood, Flow-3D.
Cite this Article: Gamal M. Abdel-Aal, Maha R. Fahmy, Amany A. Habib and
Mohamed Galal Elbagoury, Numerical Investigation of Flow Pattern and Scour
Characteristics Around Electrical Tower Foundations. International Journal of Civil
Engineering and Technology, 10(04), 2019, pp. 2108-2128
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Gamal M. Abdel-Aal, Maha R. Fahmy, Amany A. Habib and Mohamed Galal Elbagoury
1. INTRODUCTION
Local scour around electric towers footing during flood may cause failure of these towers. Once
the scour depth around the footing is sufficiently deep, the foundation may become unsettled
or even broke down. Hence, for the safe and economic design of these towers, it has become
essential to foresee the scour depth around such towers with greater accuracy. The prognosis
of the scour depth around towers footing during a flood is important to determine the depth of
the foundation of such towers.
Several experimental studies have been carried out to investigate the local scour around
various shapes of piers. The studies showed that, the streamlined piers gave the minimum scour
depth. Ismael et al. (2015) examined the local scour around different shapes of piers like
downstream round-nosed, upstream round-nosed and circular bridge piers. The results
confirmed that, the downstream round-nosed pier was an efficient to decrease the depth of
scour. Khan et al. (2017) analyzed the scour around different shapes of the pier (circular and
square) and different sizes. In fixed experimental conditions of flow, sediment properties and
pier geometry the scour obtained from the square shaped model was greater than the scour
obtained from the circular model. By increasing the size of the pier the scour increased. Three
equations have been developed by using multi linear regression, genetic function and artificial
neural network. By comparing the experimental data with the previous equations, it was found
that the genetic function model worked better than the rest of the models. Al-Shukur and Obeid
(2016) investigated the effect of several shapes of bridge pier on local scour to obtain the
perfect shape that gave the least scour depth. The used shapes were rectangular, circular,
chamfered, octagonal, hexagonal, elliptical, joukowsky, oblong, sharp nose and streamline.
The experiments concluded that, the least scour depth was obtained from the streamline shape
while the largest scour depth was obtained from the rectangular shape. Vijayasree et al. (2017)
investigated the flow pattern and local scour around several shapes of pier like rectangular,
triangular-nosed, trapezoidal-nosed, oblong and lenticular. The results confirmed that, the
sharp nose with the curved body was perfect for the bridge pier since there was less scour depth
around the pier. Li and Tao (2017) investigated the effect of pier streamlining on local scour
under clear water scour conditions. It was noticed that, the streamlined piers gave minimum
scour depth from oblong piers. Fael et al. (2016) investigated the impact of pier shape on the
scour depth surrounding the single pier. Several pier shapes were examined such as circular,
rectangular (square and round nosed), oblong and pile groups. The results confirmed that, the
shape factor could be regarded as 1.0, for rectangular round nosed and oblong cross section
piers, and as 1.2, for rectangular square nosed and packed pile group cross section piers.
The horseshoe vortex was the main cause of the development of scouring around the pier
(Muzzammil and Gangadhariah 2003; Vijayasree et al. 2017). Muzzammil and Gangadhariah
(2003) investigated the features of horseshoe vortex around a cylindrical pier. By the evolution
of the scour hole, the horseshoe vortex gradually sank into the scour hole while its size
increased. At the initial stages the vortex strength and velocity increased while being decreased
at later stages. Unger and Hager (2007) explored the temporal development of the down flow
and horseshoe vortex at circular pier. The vertical jet and the horseshoe vortex were the main
reasons for the scouring process. Dey and Raikar (2007) noticed and analyzed the horseshoe
vortex during the development of a scour hole around cylindrical pier. With the evolution of
the scour hole, the horseshoe vortex shape became ellipse and its size became larger. Zhao et
al. (2012) studied the mechanism of local scour around cuboid-shape sub-sea caissons. The
height of the caisson models under study was less than or equal to their horizontal dimensions.
The results showed that the effect of horseshoe vortex was less than the velocity at the sharp
edge of the caisson.
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Khwairakpam et al. (2012) investigated the local scour surrounding a circular pier under
clear water conditions. An empirical equation had been developed to predict the parameters of
a scour hole (depth, length, width, area and volume) around a circular pier.
Few studies have been conducted to investigate the scour depth around conical pier. Givi
et al. (2011) used the FLUENT program to investigate the flow pattern and scour depth around
cylindrical pier and four conical piers with several slopes. It was found that, the scour depth
around conical pier was less than that of cylindrical pier. By increasing the slope of conical
pier the scour depth decreased. Aghaee-Shalmani and Hakimzadeh (2015) investigated the
scour around the conical pier with different lateral slopes under steady current. It was found
that, by increasing the conical pier angle the scour depth decreased compared with cylindrical
pier.
Zhao and Huhe (2006) investigated numerically the mechanism of scour and the turbulent
of flow surrounding a circular pier using Large Eddy Simulation. Zhao et al. (2010)
investigated experimentally and numerically the mechanism of local scour surrounding
submerged vertical pile under steady flow. It was found that, the scour depth that had been
estimated by numerical model was less than the experimentally measured scour by about 10 to
20%. Khosronejad et al. (2012) studied the scour around different shapes of pier such as
cylindrical, square and diamond under clear-water condition by using experimental and
numerical models. Baykal et al. (2015) studied the flow and scour around cylindrical pile due
to the steady flow by using three dimension numerical models. Nagata et al. (2005) created a
3D numerical model that had been used to simulate flow and scour geometry around hydraulic
structures. Experimental results of spur dike and cylindrical pier were compared to the findings
of the proposed numerical model. The comparison proved that, the numerical model
represented flow and scour surrounding these structures with great accuracy. Ghiassi and
Abbasnia (2013) developed 3D numerical model to simulate the flow pattern and the bed
deformation around a bridge pier and groyne used proposed equation. Elsaeed (2011) compared
the previous experimental data with numerical model results for the scour depth around a
square pile by using SSIIM program. Jia et al. (2017) simulated the local scour around
cylindrical pier using CCHE3D software. It was found that, the down flow and the turbulent
kinetic energy around the pier were the main factors in the scouring process. The strong down
flow transported the turbulent kinetic energy to the bed and leaded to an increase in shear stress,
so scour occurred. Salaheldin et al. (2004) used 3D numerical model FLUENT to simulate the
turbulent flow surrounding circular piers in clear water conditions. The numerical model results
had been compared with the previous experimental data and showed good agreement. Huang
et al. (2009) used the FLUENT program to investigate the effect of scale on turbulence flow
and sediment scour around the pier.
Several investigators have carried out a numerical study to simulate the local scour around
piers by using Flow 3D Program and comparing the numerical results with experimental
results. The studies showed that, the Flow 3D program could simulate the scouring process
around piers with high accuracy. Alemi and Maia (2016) investigated numerically the local
scour around the cylindrical pier under clear water scour conditions using SSIIM and FLOW
3D codes. The numerical results had been compared with the previous experimental data. The
results showed that, the two CFD codes could accurately predict the scour at the upstream side
and lateral sides of the pier but not the downstream side of the pier. The scour depth at downstream the pier was under-predicted by SSIIM code while it was over-predicted by FLOW 3D
code. Amini and Parto (2017) compared the previous experimental data with numerical results
for the characteristics of a scour hole around different arrangements of two piles by using Flow
3D program. The results concluded that the scour hole around groups of piles could be
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simulated by using Flow 3D Program. Wang et al. (2017) tested experimentally and
numerically (Flow 3-D) the influence of using sacrificial piles at upstream the pile to reduce
the scour depth. The result concluded that, the numerical model was an effective way to
investigate the phenomena of scouring around piles. Zhang et al. (2017) investigated
numerically by using a Flow 3-D program the scour hole characteristics around three piles with
different arrangements. During the comparison of the three models standard k-e model, RNG
model and LES model, it was found that the RNG model was more applicable than the others
in the indication of scour process phenomena. Omara et al. (2018) investigated numerically the
scouring process around vertical and inclined piers using the FLOW-3D program. The findings
of numerical model in terms of flow velocity, water depth, scour depth and shear stress
compared with various sets of previous experimental and numerical data. The results showed
that, the numerical model gave prediction of scour depth surrounding piers with great accuracy.
Several empirical equations are available to estimate the equilibrium depth of scour around
piers for non-cohesive soil. Mohamed et al. (2006) compared four empirical equations such as
HEC-18 (Richardson and Davis 2001), Melville and Sutherland (1988), Jain and Fischer
(1979), and Laursen and Toch (1956) with field data collected from bridges located in India,
Canada and Pakistan. The comparison showed that, the HEC-18 formula (Richardson and
Davis 2001) was the best from the other selected formula. Gaudio et al. (2010) compared six
empirical equations such as Breusers et al. (1977), Jain and Fischer (1979), Froehlich (1988),
Kothyari et al. (1992), Melville (1997) and HEC-18 formula (Richardson and Davis 2001) used
to predict the scour depth around the pier with synthetic and original field data. The comparison
results proved that the HEC-18 formula (Richardson and Davis 2001) was better than the other
selected formula in both clear-water and live-bed scour. Qi et al. (2016) compared three
empirical common equations such as Melville and Sutherland (1988) equations, Chinese
equations (Dongguang et al. 1993) and HEC-18 equations (Richardson and Davis 2001) with
laboratory and field data. The results showed that, the Chinese equations (Dongguang et al.
1993) gave satisfactory results with field data. The HEC-18 equations (Richardson and Davis
2001) gave good result with laboratory data. The Melville and Sutherland (1988) equations
gave over-estimated the scour depth for laboratory and field data. From the previous
comparisons, HEC-18 equations (Richardson and Davis 2001) and Chinese equations
(Dongguang et al. 1993) have been selected to be compared with current numerical results.
Kalaga and Yenumula (2016) discussed the different types of foundations used in
transmission line structures such as piers, spread, direct embedment, pile, micro-piles and
anchor foundations. To the authors’ knowledge, no efforts have been made to study the scour
around electrical tower foundations. The major objectives of this research are: (1) to confirm
the accuracy of numerical model in the prediction of scour around piers, (2) to investigate the
scour depth around new proposed shapes of towers footing under clear-water condition, (3) to
investigate the effect of new proposed shapes of towers footing on the down flow and horseshoe
vortex, (4) to develop an empirical equation to predict the maximum scour depth around
proposed footing.
2. DIMENSIONAL ANALYSIS
Dimensional analysis based on Buckingham theory is used to develop a functional relationship
between the maximum scour depth around the tower footing and the other relevant scour
variables. The different shapes of tower footing (cuboid, cylindrical, pyramid, and cone) are
shown in Figure. 1. The maximum scour depth ds can be expressed as follows:
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(
𝑑𝑠 = 𝑓(𝐵 𝑑1  ℎ 𝜃 𝐾𝑠  𝑦 𝑉 𝑄 𝜌 𝜌𝑠  g 𝑑50 )
1
)
where ds is the maximum scour depth around footing, B is the flume width, d1 is the lower
width or diameter of footing, h is the height of footing above channel bed, is the inclination
angle of cone or pyramid footing with vertical axis, Ks is the shape correction coefficient, y is
the upstream flow depth, V is the upstream mean velocity, Q is the flow rate,  is the density
of water,s is the density of sand particles, g is the gravitational acceleration, and d50 is the
mean diameter of sand layer.
Applying the Buckingham theorem with y, V,  as repeating variables, Eq. (1) can be
written in dimensionless form as:
(
𝑑𝑠
𝑑1 ℎ
= 𝑓 (𝐹 𝜃 𝐾𝑠 
 )
𝑦
𝑦 𝑦
2
)
There the ds/y is the relative maximum scour depth, F is the upstream Froude number, d1/y
is the relative lower width or diameter of footing and h/y is the relative height of footing.
(a)
(b)
Figure. 1 Different shapes of tower footing (a) cuboid and cylindrical footing, (b) pyramid and cone
footing
3. NUMERICAL WORK
3.1. Numerical Model Scale
The foundation of the tower consisted of a base mat and a square or circular pier (Kalaga and
Yenumula 2016) as shown in Figure. 2. The width or diameter of the pier depends on the
concrete bearing capacity and the value of the load, Therefore they are variable values. In this
study, fixed dimensions of the pier are selected with a width of 60 cm and a height of 50 cm.
These dimensions are the most common in the construction field. A scale of 1:5 is chosen to
estimate the numerical model dimensions.
Figure. 2 Concrete footing for lattice transmission towers (Kalaga and Yenumula 2016)
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3.2 Meshing and Geometry of Model
A sufficient distance is provided before and behind the pier to ensure that the flow returns to
the undisturbed pattern about 6 and 12 times the pier diameter respectively (Sarker 1998). In
this sense, the length of the numerical model is set as 30d1, with a fixed bed length of 7d1 at
the inlet to prevent the scour at the inlet. The footing is placed at distances 15.5d1 in x direction
and 0.5B in y direction from the origin point to the center of the footing.
The mesh block has non-uniform cells that become finer close to the footing where the area
of scour is existed as shown in Figure. 3. For accurate and efficient results, the size ratio
between adjacent cells and cell aspect ratios should not exceed 1.25 and 3.0 respectively. For
all geometric configurations the number of cells is about 1856512 cells.
In x direction, the total model length in this direction is 3.60 m. Four mesh planes are
installed at distances 0.00, 1.68, 2.04 and 3.60 m respectively from the origin point. From first
to second mesh plane, the cell size decreasing gradually from 0.0095 m to 0.005 m. Constant
cell size 0.005 m from second to third mesh plane where the area of scour is existed. From third
to fourth mesh plane, the cell size increasing gradually from 0.005 m to 0.0095 m.
In y direction, the total model length in this direction is 0.66 m. Four mesh planes are
installed at distances 0.00, 0.15, 0.51 and 0.66 m respectively from the origin point. From first
to second mesh plane, the cell size decreasing gradually from 0.0095 m to 0.005 m. Constant
cell size 0.005 m from second to third mesh plane where the area of scour is existed. From third
to fourth mesh plane, the cell size increasing gradually from 0.005 m to 0.0095 m.
In z direction, the total model length in this direction is 0.25 m. Three mesh planes are
installed at distances -0.15, 0.00 and 0.10 m respectively from the origin point. From first to
second mesh plane, the cell size decreasing gradually from 0.014 m to 0.0032 m. From second
to third mesh plane, the cell size increasing gradually from 0.0032 m to 0.01 m.
Figure. 3 Meshing of footing model in FLOW-3D
3.3. Boundary Condition
The boundary conditions for the mesh block of the numerical model have been defined
carefully to simulate the experimental flow conditions accurately as shown in Figure. 4. The
upstream boundary is defined as volume flow rate with different discharge (Q = 12, 13, 15, 16,
18, 21, 24 and 26 l/sec). The downstream boundary is defined as outflow. The right side, the
left side, and the bottom boundary are defined as a wall. The top boundary is defined as
specified pressure with standard atmospheric pressure value. The fluid is defined as a fluid
region with initial depth (y = 8 cm) and initial velocity in x direction.
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Figure. 4 Numerical model and boundary conditions
The critical velocity could be estimated from the logarithmic Eq. (3) of the velocity profile
as used by Melville (1997):
𝑉𝑐
𝑦
= 5.75 log (5.53
)
𝑈∗ 𝑐
𝑑50
(3)
Where Vc is the critical velocity, U*c is the critical shear velocity, y is the flow depth and
d50 is the mean diameter of soil.
The shear velocities were determined from Eq. (4), which was illustrated by Melville
(1997) as a useful approximation to the Shields diagram for quartz sediments in water at 20C:
𝑈∗ 𝑐 = 0.0305𝑑50 0.5 − 0.0065𝑑50 −1
(4)
In which U*c is in m/sec and d50 is in mm, and valid for the range of 1 mm < d50 < 100 mm.
3.4. Numerical Model Validation
A comparison between the numerical model and previous experimental results (Moussa 2018)
has been investigated to achieve the accuracy of the numerical model. The experiments had
been carried out in a straight open flume with a vertical square pile (6 cm x 6 cm). The flume
was consisted of a rectangular cross section with a width 0.66 m, a depth of 0.65 m and a length
of 16.2 m, which contained a 20 cm deep layer of fine sand with a mean particle diameter of
1.4 mm. The time for each experiment was one hour, at which, 85% of the equilibrium scour
depth was achieved based on preliminary experiments.
The numerical model has been set-up in Flow 3D program with a diameter of sand = 1.4
mm and mass density = 2650 kg/cm3. The device needs ten days to complete the calculation of
numerical model using core i7 processor. Ten numerical runs are carried out with different
discharge and flow depth to achieve the accuracy of numerical model as shown in
Table 1. By comparison the previous experiments (Moussa 2018) and present numerical
results, it is noticed that the numerical model gives a good agreement with an error by about ±
8.0% as shown in
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Table 1 and Figure. 5.
Table 1 Comparison between experimental and numerical results
Run Q (l/s) y (m)
1
2
3
4
5
6
7
8
9
10
15.00
20.16
20.16
20.16
24.85
24.85
24.85
30.38
30.38
30.38
0.08
0.12
0.10
0.08
0.14
0.10
0.08
0.14
0.10
0.08
V
(m/s)
F
0.28
0.25
0.31
0.38
0.27
0.38
0.47
0.33
0.46
0.58
0.32
0.23
0.31
0.43
0.23
0.38
0.53
0.28
0.46
0.65
Exp.
ds
(cm)
4.60
4.00
5.80
7.00
4.00
7.20
9.20
7.10
10.60
12.00
Num.
ds
(cm)
4.55
3.91
5.72
7.14
4.32
7.48
9.35
6.79
9.82
11.40
Error
1.09
2.25
1.38
-2.00
-8.00
-3.89
-1.63
4.37
7.36
5.00
± 8.0
1.6
Numerical ds/y
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Measured ds/y
Figure. 5 Relative maximum scour depth between experimental and numerical results
4 ANALYSIS AND DISCUSSIONS
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4.1. Local Scour Mechanism
To illustrate the mechanism of local scour around electric tower foundation during flood,
cuboid footing (12 cm x 12 cm) has been investigated. The details of the numerical runs for
cuboid footing are listed in Table 2. Figure. 6 shows the flow streamlines around the cuboid
footing
at
the
initial
stage
of
scour
at
time
80
sec.
Figure. 7 shows the flow streamlines behind the cuboid footing at the initial stage of scour at
time 80 sec and the equilibrium state of scour. Figure. 8 shows the scour contour map around
the cuboid footing at the equilibrium state. Figure. 9 illustrates the relationship between the
relative maximum scour depth and Froude number for cuboid footing.
The scour occurs due to presence of footing in front of the flow, which acts as obstruction
to change the direction of flow to down which is called the down flow as shown in Figure. 6.
The down flow is the main cause to create the scour hole, which acts as a vertical jet to remove
the grains from the bed. Due to the separation of the flow at the edges of the footing with the
effect of down flow, the flow changes its direction in the scour hole creating the helical flow
which is called the horseshoe vortex as shown in Figure. 6. Both of the down flow and the
horseshoe vortex lead to an increase in the bed shear stress on the soil. Once the shear stress is
more than the critical shear stress, the grains on the bed surface can be removed.
The dead zone behind the footing gains velocity in the opposite direction of the flow as a
result of accelerating the flow at the rear edges of the footing, creating a vortex in this area
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which
is
called
wake
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Numerical Investigation of Flow Pattern and Scour Characteristics Around Electrical Tower
Foundations
Figure. 7a. The wake vortex acts as a little storm lifting the grains from the bed and form a
scour hole downstream of the footing. The effect of down flow, horseshoe vortex and wake
vortex (
Figure. 7) becomes weaker gradually in time, thus lower bed shear stress occurs. Once the
value of the shear stress is lower than the critical shear stress, the grains on the bed surface
cannot be removed. As a result, the scour depth reaches to a state of equilibrium as shown in
Figure. 8.
Table 2 Numerical data for cuboid footing
Run
1
2
3
4
5
6
d1
Q (l/s) y (cm)
(cm)
12.0 12.0 7.85
12.0 13.0 7.76
12.0 15.0 7.65
12.0 16.0 7.62
12.0 18.0 7.58
12.0 24.0 8.43
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V
(m/s)
0.23
0.25
0.30
0.32
0.36
0.43
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V/Vc
F
0.51
0.56
0.66
0.71
0.80
0.95
0.26
0.29
0.34
0.37
0.42
0.47
ds
(cm)
4.97
6.26
8.70
9.50
11.00
13.90
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Figure. 6 Flow streamlines show the down flow and the horseshoe vortex in front of the cuboid
footing at time 80 sec
Figure. 7 Flow streamlines show the wake vortex behind the cuboid footing at (a) time 80 sec and (b)
equilibrium state
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Figure. 8 Contour map shows the change in bed elevation around cuboid footing at the equilibrium
state
Figure. 9 Relationship between ds/y and F for different shapes of footing
4.2. Effect of Different Shapes of Footing
The pyramid footing is the most common in the tower construction field, so the effect of
different inclination angles ( = 5º, 10º, 15º, 20º and 25º) for pyramid footing on the maximum
scour depth has been investigated. The details of the numerical runs for different pyramid
footing are listed in Table 3. Figure. 9 illustrates the relationship between the relative maximum
scour depth and Froude number for pyramid and cuboid footing. Figure. 10 shows the flow
streamlines around the pyramid footing with angle  = 25º at the initial stage of scour at time
80 sec. Figure. 11 shows the scour contour map around the pyramid footing with angle  = 25º
at the equilibrium state.
By comparing the behavior of flow and the scour contour maps around the different
pyramid footing with cuboid footing, it is found that, the inclination angle in pyramid footing
directs part of the flow upwards. By increasing the value of this angle, the flow upwards
increases and the down flow decreases. Once the down flow decreases the horseshoe vortex
decreases (see Figure. 6 and Figure. 10). As a result, the shear stress on soil surface decreases
and then the scour decreases around the pyramid footing (see Figure. 11). The pyramid footing
with different inclination angles in all operating conditions records a reduction in the relative
maximum scour depth as shown in Table 3.
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Figure. 10 Flow streamlines show the down flow and the horseshoe vortex in front of the pyramid
footing ( = 25º) at time 80 sec
Figure. 11 Contour map shows the change in bed elevation around pyramid footing ( = 25º) at the
equilibrium state
Table 3 Numerical data for pyramid footing
Run º
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
5
5
5
5
5
5
10
10
10
10
10
10
15
15
15
15
15
15
20
20
20
20
20
20
25
25
25
25
Q
(l/s)
12.0
13.0
15.0
21.0
24.0
26.0
12.0
13.0
14.0
15.0
24.0
25.0
12.0
15.0
18.0
21.0
24.0
26.0
12.0
13.0
18.0
21.0
24.0
26.0
12.0
15.0
18.0
21.0
y (cm)
7.81
7.55
7.42
8.45
8.66
8.62
7.75
7.70
7.36
7.09
8.97
8.61
7.77
8.12
8.39
8.75
9.11
8.97
7.82
7.84
8.68
8.86
8.98
8.95
7.73
8.01
8.52
8.66
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V
(m/s)
0.23
0.26
0.31
0.38
0.42
0.46
0.23
0.26
0.29
0.32
0.41
0.44
0.23
0.28
0.33
0.36
0.40
0.44
0.23
0.25
0.31
0.36
0.40
0.44
0.24
0.28
0.32
0.37
V/Vc
F
0.52
0.58
0.69
0.82
0.92
0.99
0.52
0.57
0.65
0.72
0.88
0.96
0.52
0.62
0.71
0.79
0.86
0.95
0.52
0.56
0.69
0.78
0.88
0.96
0.52
0.63
0.70
0.80
0.27
0.30
0.36
0.41
0.46
0.50
0.27
0.29
0.34
0.38
0.43
0.48
0.27
0.31
0.36
0.39
0.42
0.47
0.27
0.29
0.34
0.39
0.43
0.47
0.27
0.32
0.35
0.40
2121
ds
(cm)
4.55
6.44
8.16
11.20
13.00
13.70
4.48
5.78
7.08
8.30
12.10
12.40
3.85
6.42
7.86
10.10
11.70
12.40
3.21
4.08
7.00
9.40
11.00
11.80
2.60
4.97
6.27
8.60
ds/y
(%)
11.88
4.22
7.33
7.48
6.28
9.37
15.43
10.66
11.52
10.25
10.65
14.71
26.63
16.76
20.81
13.93
12.60
16.21
37.69
34.37
26.30
18.92
18.68
20.35
51.26
37.05
35.55
27.46
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35 25 24.0 8.97 0.41 0.88 0.43 9.30 31.34
36 25 26.0 8.93 0.44 0.96 0.47 11.10 25.20
To illustrate the effect of sharp edges in the cuboid and pyramid footing on the scour depth,
cylindrical footing has been investigated. The details of the numerical runs for cylindrical
footing are listed in Table 4. Figure. 12 shows the flow streamlines around the cylindrical
footing
at
the
initial
stage
of
scour
at
time
80
sec.
Figure. 13 shows the scour contour map around the cylindrical footing at the equilibrium
state. Figure. 14 illustrates the relationship between the relative maximum scour depth and
Froude number for cylindrical and cuboid footing.
By comparing the behavior of flow and the scour contour maps around the cylindrical
footing with cuboid footing, it is found that, the smooth body of the cylindrical footing reduces
the obstruction of the flow during separation, which leads to a decrease in the effect of down
flow. As a result, the relative maximum scour depth decreases (see
Figure. 13). The cylindrical footing in all operating conditions records a reduction in the
relative maximum scour depth as shown in Table 4.
Figure. 12 Flow streamlines show the down flow and the horseshoe vortex in front of the cylindrical
footing at time 80 sec
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Figure. 13 Contour map shows the change in bed elevation around cylindrical footing at the
equilibrium state
1.8
1.6
1.4
ds/y
1.2
1.0
0.8
cuboid
cylindrical
cone 5 degree
cone 10 degree
cone 15 degree
cone 20 degree
cone 25 degree
0.6
0.4
0.2
0.0
0.25
0.30
0.35
F
0.40
0.45
0.50
Figure. 14 Relationship between ds/y and F for different shapes of footing
Table 4 Numerical data for cylindrical footing
Run Q (l/s) y (cm)
37
38
39
40
41
42
12.0
15.0
18.0
21.0
24.0
26.0
7.78
8.08
8.35
8.60
8.77
8.71
V
(m/s)
0.23
0.28
0.33
0.37
0.41
0.45
V/Vc
F
0.52
0.62
0.72
0.81
0.90
0.99
0.27
0.32
0.36
0.40
0.45
0.49
ds
(cm)
3.91
6.11
8.01
9.20
10.60
11.70
ds/y
(%)
25.20
21.49
19.77
22.91
22.97
22.22
Cone footing has been suggested for studying, as it combines the characteristics of both the
pyramid footing and the cylindrical footing. The effect of different inclination angles ( = 5º,
10º, 15º, 20º and 25º) for cone footing on the maximum scour depth has been investigated. The
details of the numerical runs for cone footing are listed in Table 5. Figure. 14 illustrates the
relationship between the relative maximum scour depth and Froude number for different cone
footing. Figure. 15 shows the flow streamlines around the cone footing with angle  = 25º at
the initial stage of scour at time 80 sec. Figure. 16 shows the scour contour map around the
cone footing with angle  = 25º at the equilibrium state.
By comparing the behavior of flow and the scour contour maps around the different cone
footing with cuboid footing and pyramid footing, it is found that, the inclination angle in cone
footing directs part of the flow upwards. By increasing the value of this angle, the flow upwards
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Numerical Investigation of Flow Pattern and Scour Characteristics Around Electrical Tower
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increases and the down flow decreases as in the pyramid footing. The smooth body for the cone
footing reduces the obstruction of the flow during separation, which leads to a decrease in the
down flow when it is compared with the pyramid footing at the same angle (see Figure. 10 and
Figure. 15). Once the down flow decreases the horseshoe vortex decreases (see Figure. 6,
Figure. 10 and Figure. 15). As a result, the shear stress on soil surface decreases and then the
scour decreases around the cone footing (see Figure. 16). The cone footing with different
inclination angles in all operating conditions records a reduction in the relative maximum scour
depth as shown in Table 5.
Figure. 15 Flow streamlines show the down flow and the horseshoe vortex in front of the cone
footing ( = 25º) at time 80 sec
Figure. 16 Contour map shows the change in bed elevation around cone footing ( = 25º) at the
equilibrium state
Table 5 Numerical data for cone footing
Run º
43
44
45
46
47
48
49
50
51
52
5
5
5
5
5
5
10
10
10
10
Q
(l/s)
12.0
15.0
18.0
21.0
24.0
26.0
12.0
15.0
18.0
21.0
y (cm)
7.67
7.89
8.51
8.60
8.59
8.63
7.72
7.85
8.37
8.65
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V
(m/s)
0.24
0.29
0.32
0.37
0.42
0.46
0.24
0.29
0.33
0.37
V/Vc
F
0.53
0.64
0.70
0.81
0.92
0.99
0.52
0.64
0.72
0.80
0.27
0.33
0.35
0.40
0.46
0.50
0.27
0.33
0.36
0.40
2124
ds
(cm)
3.49
5.69
7.21
8.80
10.50
10.70
3.00
5.10
7.06
8.09
ds/y
(%)
35.89
29.59
25.98
26.23
24.68
29.19
43.84
37.47
29.02
31.83
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53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
10
10
15
15
15
15
15
15
20
20
20
20
20
20
25
25
25
25
25
25
24.0
26.0
12.0
15.0
18.0
21.0
24.0
26.0
12.0
15.0
18.0
21.0
24.0
26.0
12.0
15.0
18.0
21.0
24.0
26.0
8.78
8.96
7.75
8.13
8.41
8.68
9.05
8.87
7.74
8.25
8.37
8.66
9.00
9.17
7.74
8.08
8.31
8.55
9.03
9.15
0.41
0.44
0.23
0.28
0.32
0.37
0.40
0.44
0.23
0.28
0.33
0.37
0.40
0.43
0.24
0.28
0.33
0.37
0.40
0.43
0.90
0.95
0.52
0.62
0.71
0.80
0.87
0.97
0.52
0.61
0.71
0.80
0.88
0.93
0.52
0.62
0.72
0.81
0.87
0.93
0.45
0.47
0.27
0.31
0.36
0.40
0.43
0.48
0.27
0.31
0.36
0.40
0.43
0.45
0.27
0.32
0.36
0.41
0.43
0.45
9.90
10.10
2.49
4.50
6.21
7.73
9.60
10.10
2.16
3.65
5.69
7.05
8.80
8.88
2.02
3.39
5.25
6.56
8.05
9.10
27.98
31.81
52.83
41.49
37.18
34.67
28.66
32.20
59.33
51.33
42.79
40.50
34.88
39.18
62.01
56.46
47.69
45.26
40.25
37.76
5 VERIFICATION
The results of numerical models for cuboid (d1= 6.0 cm and 12.0 cm) and cylindrical (d1 = 12.0
cm) footing have been compared with other equations such as HEC-18 equation (Richardson
and Davis 2001) and Chinese Equation (Dongguang et al. 1993).
Table 6 illustrates the selected equations to predict the local scour depth around the footing.
The scour depths for present and previous data are divided by 0.85 to reach an equilibrium
scour depth. A comparison of the relative scour depth that has been measured by numerical
models and other predicted equations shown in Figure. 17. It is found that, Chinese Equation
(Dongguang et al. 1993) gives strong agreement with the present numerical results.
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2.3
+20%
2.0
Predicted ds/y
1.7
1.4
-20%
1.1
0.8
HEC-18 Eq.
0.5
65-2 Chinese Eq.
0.2
0.2
0.5
0.8
1.1
1.4
1.7
2.0
2.3
Measured ds/y
Figure. 17 Comparison of relative scour depth measured by flow 3D and other predicted equations
Table 6 Pier scour equations
Name
Equation
𝑑𝑠
𝑑1 0.65 0.43
= 2.0𝐾1 𝐾2 𝐾3 𝐾4 ( )
𝐹
HEC-18 𝑦
𝑦
Notes
Reference
K1 is the shape factor,
K2 is the flow skew angle factor,
K3 is the dune factor and
K4 is the correction factor for armoring by
bed material size.
Richardson
and Davis
(2001)
𝑉𝑐 = 0.28 (𝑑50 + 0.7)0.5
65-2
𝑑𝑠
=
/
/ 𝑛
𝑉 − 𝑉𝑐
0.60 0.15 −0.07
0.46𝐾𝑠 𝑑1 𝑦 𝑑50 (
)
/
𝑉𝑐 − 𝑉𝑐
𝑉𝑐 = 0.12 (𝑑50 + 0.5)0.55
𝑉 ≤ 𝑉𝑐  𝑛 = 1.0
𝑉𝑐 9.35+2.23 log 𝑑50
𝑉 > 𝑉𝑐  𝑛 = ( )
 𝑛 < 1.0
𝑉
Dongguang
et al.
(1993)
6. STATISTICAL REGRESSION
The scour depth value increases in both of the cuboid footing and the pyramid footing by
comparing it with cylindrical footing and cone footing respectively. The reasons for the
increase of the scour depth are the sharp edges. The sharp edges are expressed by shape
correction coefficient Ks as shown in Eq. (5). The shape correction coefficient for cuboid and
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Gamal M. Abdel-Aal, Maha R. Fahmy, Amany A. Habib and Mohamed Galal Elbagoury
pyramid footing is calculated from Eq. (5) as shown in Table 7. Different values of shape
correction coefficient are shown in Table 8.
An empirical equation (6) has been developed by using a technique of nonlinear regression
analysis to predict the relative maximum scour depth around different shapes of footing. For
cuboid and cylindrical footing, the inclination angle equals zero = 0):
(
𝑑𝑠
𝑑𝑠
( )
= 𝐾𝑠 ( )
𝑦 Shape 1
𝑦 Shape 2
5
)
(
𝑑𝑠
𝑑1 0.25
= 4.73 𝐾𝑠 (cos 𝜃)2.95 𝐹1.65 ( )
𝑦
𝑦
6
)
Figure. 18 illustrates a comparison between the predicted values for maximum depth of a
scour hole by Eq. (6) and numerical results for all numerical model tests. It is found that, the
results indicate a good agreement between the numerical and predicted values of ds/y where,
R2 = 0.95.
Table 7 Shape coefficient for cuboid and pyramid footing
Shape 1
Cuboid
Pyramid ( = 5º)
Pyramid ( = 10º)
Pyramid ( = 15º)
Pyramid ( = 20º)
Pyramid ( = 25º)
Shape 2
Cylindrical
Cone ( = 5º)
Cone ( = 10º)
Cone ( = 15º)
Cone ( = 20º)
Cone ( = 25º)
Ks
1.29
1.29
1.32
1.31
1.35
1.27
1.30
Table 8 Correction coefficient based on the shape of the footing
Footing
Cylindrical and Cone
Cuboid and Pyramid
Shape coefficient Ks
1.00
1.30
1.8
1.6
Predicted ds/y
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Measured ds/y
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Figure. 18 Comparison between the measured and predicted data for all numerical data
7 CONCLUSIONS
The following results have been created from this research:
1. The numerical model results give a good agreement with an error by about ± 8.0%.
2. The cylindrical, pyramid and cone footing record a reduction in the relative
3.
4.
5.
6.
maximum scour depth.
In both of pyramid footing and cone footing, the larger the inclination angle, the
smaller the scour depth will be.
At the same inclination angle in both of pyramid footing and cone footing, the cone
footing is better than the others.
Chinese Equation (65-2) gives well acceptance with the present numerical model
results.
An empirical equation is developed by regression analysis to predict the relative
maximum scour depth around different footing.
8 LIST OF SYMBOLS
B
Flume width
ds
Maximum scour depth around footing
d1
Lower width or diameter of footing
d2
Upper width or diameter of footing
h
Ks
Height of footing above channel bed
Inclination angle of cone or pyramid footing
with vertical axis
Shape coefficient
t
Sand layer thickness
y
Upstream flow depth
F
Upstream Froude number
V
Upstream mean velocity
Vc
Critical velocity of bed material
U*c
Critical shear velocity
Q
Flow rate

Density of water
s
Density of sand particles
g
Gravitational acceleration
d50
Mean diameter of the sand layer
ds/y
Relative maximum scour depth

 ds/y Reduction in relative maximum scour depth
d1/y
Relative lower width or diameter of footing
h/y
Relative height of footing
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Gamal M. Abdel-Aal, Maha R. Fahmy, Amany A. Habib and Mohamed Galal Elbagoury
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