Table 1
Changes in scouring based on flow intensity at 30°, 60°, 90°, 120°, 150°
angles of the curved channel.
The impact of abutment length on scour depth
As shown in Fig. 7 (a-j), the impact of the abutment length on scouring
along the curved channel is different at each bend angle. In a straight
channel, scour depth increases as the abutment length increases
(Kayaturk, 2005). However, in the present study, the scour depth in the
curved channel decreased as the abutment length on the outer bank
increased. In general, less scouring was observed for an abutment length
of 12 cm. This showed that the scour formed as a result of the velocity
distribution at the outer bank of a curved channel decreased in line
with a reduction in the effect of secondary flow as the abutment length
increased. When the bridge abutment is placed in the curved channels,
the scouring at the inner and outer banks differs. Local scour depth
occurs more often at the outer bank due to the effect of secondary flow
and maximum velocity path while deposition occurs at the inner bank.
Therefore, at the outer bank of the curved channels, a local scour takes
place due to the effect of both the secondary flow and downflow. As
shown in Fig. 7(a-j), the scouring at the outer bank is greater than the
scouring at the inner bank. Thus, it is important to know in advance the
properties of the flow in the curved channel when selecting a hydraulic
structure such as a water intake structure.
Fig. 7. Changes in t /tm andds /La based on differentLa values for α =30°, α =60°,α =90°, α =120° and α =150°
The impact of bend angle on scour depth
It was generally observed that, for scour depths at bend angles of theLa = 8 cm abutment located on the outside bank in
a 180° curved channel, the maximum scour increased in line with the
increasing bend angle. Thus, maximum scour usually occurs at a
150o bend angle. This is because the maximum velocity
in a linear channel occurs around the channel axis close to the water
surface. The local flow slows down when entering the curve and gains
momentum after passing the curve turning point. In a 180-degree curved
channel, the maximum velocity orbits diverge from the normal orbits,
first going towards the inner bank. When α = 45°, they start to
flow towards the outer bank and when α = 60°, they start to
settle at the outer bank. The maximum velocity orbit located at the
outer bank turns towards the channel axis after α = 120° and can
be observed near the channel axis at the curve exit. The scour depths at
the bend angles of a La = 8 cm abutment placed on
the inner bank of the curved channel demonstrated that the maximum scour
also increased in line with increasing bend angle. On the inner bank,
the maximum scour occurred at a 150° bend angle (Fig. 8). Based on all
bend angles, a variation of between 5% and 15% was observed for the
maximum scour depths formed.(Fig. 8).
In the second half of the curved channel, the scour depths formed on the
bridge abutments were greater than in the first half. At the entrance of
the channel, where the material transferred from the upstream
compensates the carried material, there was less scouring at 30°.
Therefore, if the bridge abutment is placed at the beginning of the
curve, there will be less scour depth.
Fig. 8. Variation on outer and inner bank scour depths forα =30°, α =60°, α =90°, α =120°, α =150°
bend angles.
The active length of the tailwater vortexes is longer than that of the
horseshoe vortexes. However, because the velocity of horseshoe vortexes
is greater than the velocity of the tailwater vortexes, the maximum
scour is observed in the abutment upstream. Another reason for this is
that the accumulation of particles unraveling from the upstream face in
a downstream direction due to the falling flow intensity. In the present
study, the maximum scour occurred around the upstream wall of the
abutment (see Fig. 9).
Fig. 9 Variations in scour depth on the inner bank at 8 cm
abutment.
Comparison of outer bank and inner bank scour depths
Figure 10 (a-o). A comparison of inner bank and outer bank maximum scour
depths in the curved channel at bend angles of 30°, 60°, 90°, 120°, and
150° demonstrated that the maximum scour depth in all bend angles of the
curved channel was higher on the outer bank than on the inner bank. This
was because the material moving as a result of the secondary flow causes
scouring on the outer bank and accumulation of the sediment on the inner
bank. Sanjou and Nezu (2009) stated that there is a strong relation
between the horizontal vortices and secondary flows. Furthermore, Minor
et al. (2007) reported that secondary flows are caused by turbulence
anisotropy at the wall in narrow channel bends.
Variations in the scour depth between the inner and outer banks of the
main channel at bend angles α = 30°, 60°, 90°, 120° and 150° of
the curved channel (based on the dimensionless parameters denominated
with ds/La on the y-axis andt/tm on the x-axis) are displayed in Figure 11
(a-o). Examination of the scour depths along the curved channel shows
that the scour depth at each bend angle was greater on the outer bank
than the inner bank. This was due to the formation of secondary and
helicoidal flow in the curved channel. The secondary flow also occurs
due to the porousness of the wall and pressure oscillations. In meander
oscillations, the secondary flow effect is strengthened due to the
centrifugal force. The outer bank is scoured while the sediment is
accumulated on the inner bank. As described by Onen and Agaccioglu
(2013), this is because the secondary movement starts before the curve
entrance in a curved channel, accelerates in the curvature, and
decreases toward the curvature exit. One of the most important
characteristics of the curved flow is the helicoidal flow; another is
the maximum velocity path motion. The helicoidal flow is caused by
friction, and by centrifugal and inertia forces. The helicoidal flow is
defined as the ratio of the mean kinetic energy of the secondary action
in a given cross-section to the total kinetic energy of the flow. Onen
and Agaccioglu (2013) stated that the velocity of fluid particles near
the channel bed is significantly delayed by the boundary resistance.
Fluid that moves with a lower velocity near the bed is forced to follow
a sharper curved orbit to establish an equilibrium between centrifugal
and pressure forces; conversely, the orbits of fluid particles closer to
the surface move towards the channel bed due to the higher inertia
caused by higher speed. To maintain the fluid mass, the water moves
towards the bed at the outer bank and towards the surface from the bed
at the inner bank. Thus, in addition to the longitudinal velocity
component, a radial velocity component perpendicular to the channel axis
is formed. This forms the secondary flow in the cross section plan.
Fig. 10 Variation on outer and inner bank scour depths
The variation in dimensionless maximum scour depth with dimensionless
time was investigated for different median sediment grain sizes
(d 50) and constant abutment length, and for
constant flow intensity for values of bend curvature angles, as shown in
Fig. 11. This clearly shows that as the grain diameter decreases, the
depth of scour increases.
Fig. 11 ds /Laversus t /t m ford 50=1.16, d 50=1.34,d 50=3.72 mm: (a) α=60°, (b) α=120°
Empirical correlations predicting the equilibrium scour depth were
developed for the oblong bridge abutment at the inner banks of the
curved channel with bend curvature α = 30°, 60°, 90°, 120°, and
150°. The resulting correlation is given in Eq. (13) and the values of
the constants and the correlation coefficients (R) are presented in
Table 2. Eq. (14) gives the relation between the inner and outer bank
based on the experimental data in the current study. For Eq. (14), the
correlation coefficient is 0.98.
\(\left(\frac{d_{\text{se}}}{L_{a}}\right)_{\text{inner\ bank}}=a\left(\frac{L_{a}}{y}\right)^{b}\ \left(\frac{V}{V_{c}}\right)^{c}\left(F_{d}\right)^{d},\left(\frac{L_{a}}{B}\right)^{e}\left(\frac{L_{a}}{B_{a}}\right)^{f}\)(13)
where dse is the equilibrium depth (m),La is the length of abutment (m), y is the
flow depth (m), V is the mean flow velocity (m/s),Vc is the critical velocity (m/s),
Fd is the densimetric Froude number (-), Bis the width of channel (m), and Ba is the width
of abutment (m).
\(\left(\frac{d_{\text{se}}}{L_{a}}\right)_{\text{outer\ bank}}=1.45\left(\frac{d_{\text{se}}}{L_{a}}\right)_{\text{inner\ bank}}\)(14)
The predicted equilibrium scour depth
(dse )p is compared with the
observed equilibrium scour depth
(dse )o to yield the average
percent error ε as
\(\varepsilon=\frac{100}{N}\sum_{i=1}^{N}\left\lfloor\frac{\left(d_{\text{se}}\right)_{o}-\left(d_{\text{se}}\right)_{p}}{\left(d_{\text{se}}\right)_{o}}\right\rfloor\)(15)
in which N is the number of data points. The average percent
error ε is a function of the constant in the equilibrium scour
depth equation. The average percent error values for Eq. (15) are given
in Table 2. Good agreement is obtained between the observed equilibrium
scour depth and the values computed from the predictive Eq. (13).