Experimental investigation of scour at a channel junctions of different diversion angles and bed width ratios

Catena 166 (2018) 10–20

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Experimental investigation of scour at a channel junctions of different diversion angles and bed width ratios

T

⁎

Nashwan K. Alomaria, Badronnisa Yusufb, , Thamer Ahmad Mohammadb, Abdul Halim Ghazalib a b

Department of Dams and Water Resources, College of Engineering, Mosul University, Mosul, Iraq Department of Civil Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

A R T I C LE I N FO

A B S T R A C T

Keywords: Diversion channel Scour Diversion angle Bed width ratio Channel junctions

Diversion flows from rivers or main channels affect bed morphology and cause erosion and sedimentation at the diversion channel junction. In a diversion channel flow system, the scour depth and scour length are considered important parameters and should be taken into account during the project construction stage because it affect the stability of main channel banks and crossing structures. In this study, the scour depth produced by diversion flow in a main channel was investigated using a physical sand bed model. The investigations considered five diversion angles (30°, 45°, 60°, 75°, and 90°), three bed width ratios (29%, 38%, and 48%), and five total discharges (7.25, 8.5, 9.75, 11, and 12.25 L/s). Results indicated that the scour depth in the main channel reduced as the diversion angle reduced. Empirical relationship to demonstrate relative scour depth (Kds) for different diversion angles and bed width ratios was proposed. Relative scour depth can be defined as a relative scour depth in case of a diversion angle of θ° to that with 90° for the same flow condition and bed width ratio. Empirical relationships to estimate the scour depth and scour length with the governing hydraulic parameters were also established with a good accuracy. Testing the proposed relationships gave reasonable mean errors of 3.46% and 10.3% in predicting scour depth and scour length, respectively.

1. Introduction The occurrence of scouring on the beds of rivers or unlined open channels is considered as the main factor causing the failure of hydraulic structures because it reduces the foundation cover of the structures and thereby threatens their stability. Diversion channels are widely used in irrigation networks, domestic use and hydropower projects (Meselhe et al., 2016). Moreover, diversion channel or river bifurcations are commonly found in natural rivers as a result of the rivers' dynamics processes (Kleinhans et al., 2013; Redolfi et al., 2016). Studying the flow behaviour in the diversion channel and flow diversion location is important for water management (Yousefi et al., 2011) and for sedimentation management downstream of the diversion (Baker et al., 2011). Flow in diversion channels with rigid boundaries has been investigated extensively for a long time (Grace and Priest, 1958; Taylor, 1944) and still receives attention (Mignot et al., 2014; Mignot et al., 2013; Seyedian et al., 2014). Hsu et al. (2002), Ramamurthy and Satish (1988), and Ramamurthy et al. (1990) studied the hydraulics of rightangle diversion channels and found diversion channel-to-main channel discharge ratio is a function of the Froude number upstream or

⁎

Corresponding author. E-mail address: [email protected] (B. Yusuf).

https://doi.org/10.1016/j.catena.2018.03.013 Received 21 June 2017; Received in revised form 8 February 2018; Accepted 12 March 2018 0341-8162/ © 2018 Elsevier B.V. All rights reserved.

downstream of the main channel and the water depths. This flow phenomenon is governed by many variables such as hydraulic, diversion geometry, and boundary material parameters. Although bed morphology is considered as an essential element of the design of a diversion channel (Xu et al., 2016), most of the studies related to diversion channel flow have been carried out with the rigid boundary condition (Mignot et al., 2014; Mignot et al., 2013; Momplot et al., 2017). Regarding sand bed condition, most of the diversion channel flow studies with a movable bed condition focused only on diversion channel flow with a diversion angle of 90° (Barkdoll et al., 1999; Herrero et al., 2015). While a few investigations have shown that the flow behaviour changes significantly at some diversion angles < 90°. For example, with fixing the diversion channel entrance width, the discharge in a diversion channel is maximum at an angle of 60° (Alomari et al., 2016). Keshavarzi and Habibi (2005) found from a laboratory study and by comparing separation zone sizes in different diversion angles (45°, 56°, 67°, 79° and 90°) that the optimum diversion angle is 55° according to separation zone size in the intake channel. Dehghani et al. (2009) recommended using an 115° rather than 150° diversion angle of the diversion channel from the bend flow because its recorded shorter length of the scour. Moghadam and Keshavarzi (2010)

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depth in the main flow due to diverting some of the flow over side weir. In addition, Melville and Chiew (1999) reported that development of the scour depth reaches to 80% of the equilibrium scour depth during a time of 5% to almost 40% of the equilibrium time. Therefore, 12 h running duration was chosen for the experiments of this study. The scour depth and scour length can be characterised as follows:

reported that the secondary currents consider as an important factor affect the erosion and sedimentation at the entrance of the diversion channel. These secondary currents depend upon many factors, such as the diversion angle and bed width ratio. Many investigators to determine the safe foundation depth for the structures have studied the scour depth in the beds of rivers and movable bed channels around hydraulic structures. These studies have investigated different types of hydraulic structures such as pile group (Amini et al., 2012), complex bridge piers (Amini and Mohammad, 2017) and complex pier component (Amini et al., 2011), rock structures (Khosronejad et al., 2013; Pagliara et al., 2016), groynes (Dehghani et al., 2013), submerged obstacles (Euler and Herget, 2012), spur dykes (Duan et al., 2009), cross-vane structures (Pagliara and Kurdistani, 2013) and downstream hydraulic structures (Termini, 2011). At the open channel junctions in right-angle diversion channels, Barkdoll et al. (1999) and Herrero et al. (2015) observed a scour hole in the main channel bed at the downstream diversion channel conjunction edge. This scour hole is caused by secondary vortexes generated in the junction region. These vortexes play a major role in changing the bed morphology in the main channel downstream of the diversion channel. The main objective of the current study, which is drawn from the above literature review, is to investigate the effect of the diversion channel flow with different diversion angles and bed widths on both the scour depth and scour length and to describe the flow field at diversion. Other objectives of the study are to study the influence of a range of water discharge, water depth and velocity in the main channel at upstream of the diversion section on the scour hole, and find empirical relationships to determine the scour depth and scour length under laboratory-controlled conditions.

d s or L s = f (Bm , Bb , θ, Vu, Qu , Qb , yu, g, Vc)

Carrying out dimensional analysis (Pi theory) yields these dimensionless parameters: ds Bb

or

π2 =

Vu Vc yu

π1 =

π3 =

Ls Bb

Bb

π4 = Br π5 = θ π6 = Q r π7 = Fu The scour depth and scour length can be described as shown in Eqs. (2) and (3):

ds V y = f ⎡ u , u , Br , θ, Q r , Fu⎤ ⎢ ⎥ Bb ⎣ Vc Bb ⎦

(2)

Ls V y = f ⎡ u , u , Br , θ, Q r , Fu⎤ ⎢ ⎥ Bb ⎣ Vc Bb ⎦

(3)

where Ls is the scour length, Fu is the Froude number for the main channel at the upstream, Vu/Vc is the flow intensity, Br is the bed width ratio, and Qr is the discharge ratio. The bed width ratio and discharge ratio can be expressed as follows:

2. Methodology 2.1. Dimensional analysis Many parameters affect the scour hole size. In case of the local scour due to bridge piers, (Melville and Chiew, 1999) classified these parameters as follows: 1. 2. 3. 4. 5.

(1)

Geometrical parameters Flow property parameters Fluid property parameters Bed material parameters Experiments running duration (t)

Br =

Bb Bm

(4)

Qr =

Qb Qu

(5)

2.2. Experimental work In this study, experiments were performed at the hydraulic laboratory of the Department of Civil Engineering, Universiti Putra Malaysia. For the experiments, a rectangular diversion channel system was used, which consisted of a main channel (12.5-m long, 0.6-m deep, and 0.313-m wide) and a diversion channel (2.75-m long and 0.6-m deep). The diversion channel was connected firmly to the left side wall of the main channel, and its bed width could be adjusted to 0.15, 0.12, and 0.09 m. Both the main and diversion channels had glass side walls. The diversion channel was designed to be flexible so that its connection angle with the main channel could be adjusted to obtain the required diversion angle. A sufficient amount of bed material was prepared by sieving sandy soil and re-distributing it again to obtain sand particles with medium diameter of 0.4 mm (standard deviation of 1.46) and specific gravity of 2.53. Part of the prepared sand was used to fill the flume bed with a 0.18-m-thick sand layer and addition amount was stored in a storage tank. Before starting each experiment, sand bed was flattened and if there any deficiency in the bed material, the sand in the storage tank can be used. Chiew (1984) considered a bed material with σg < 1.5 as being uniform. The diversion channel is fitted at the middle of the working section. Water and sediment are re-circulated through the diversion channel system by collecting them at the ends of the system and pumping them into the system again. A control valve and flow meter were installed at the pump outlet to control and measure the total discharge in the main channel, respectively. A volumetric method was used to measure the discharge in the diversion channel. A

In diversion channel flow, the geometric parameters represented by the bed widths of the main and diversion channels Bm and Bb, respectively; and the diversion angle θ. Flow property parameters represented by the water discharge in the main channel at the upstream Qu (Note that Qu reflects the total discharge); the water discharge in the diversion channel Qb; the main channel velocity and water depth at the upstream Vu and yu, respectively; and the acceleration due to gravity g. Fluid property parameters represented by the water density and viscosity ρ and υ, respectively. Bed material parameters represented by the medium particles diameter d50; the standard deviation for the bed material σg; the density of the bed material ρs; and the critical shear velocity and critical velocity of the particles inception motion U⁎c and Vc, respectively. Because only one type of bed material was used and the temperature of the water was kept constant during the experiments, the fluid property parameters for the bed material are not included in the analyses. With respect to experiments running duration, Aǵaçcioǵlu and Önen (2005) and Yanmaz and Altinbilek (1991) reported that the 6 h can be considered as a sufficient experiment running duration of scour modelling because the prototype duration corresponding to the modelling duration is quite long. The experimental work for Yanmaz and Altinbilek (1991) was included investigation of scour depth around the piers. While, Aǵaçcioǵlu and Önen (2005) investigated the scour 11

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Qb Diversion channel Water tanks

All dimensions are in cm

Sieve 31.3 Main channel Sand bed θ 50

Qu

Qd

Control valve

Flow meter

Water pump

750 1250 Fig. 1. Plan view of the diversion channel system.

with a 75 μm mesh size (99% of the sand particle diameters were > 75 μm) was used to collect the sand particles. Blue dye was used to detect the dividing streamlines pattern and vortexes generated at the junction region. This dye was injected smoothly into the water flow using a smooth nozzle in order not to distort the dye line pattern. The discharge between the main and diversion channels was regulated by installing teeth-shaped Perspex pieces with 70% flow contraction at the end of both the channels, as shown in Fig. 2. These teethshaped pieces were used to set the discharge ratio, and they help the sediment particles to pass without any blockage at the end of the channels. Increasing or decreasing the flow contraction while using the same percentage at the ends of both the channels does not significantly affect the discharge ratio (Herrero et al., 2015). However, increasing the flow contraction usually decreases the flow velocity and increases the water depth and vice versa. As a result of using Perspex pieces with 70% flow contraction, flow intensity was ranged for different cases between 1.1 and 1.5. Therefore, the experiments were performed under live bed condition.

continuity equation was used to determine the discharge in the main channel at the downstream, Qd. During the experiments, the laboratory temperature was measured and maintained at approximately (27 ± 1.5) °C, and the running duration for each experiment was 12 h. Five diversion angles (30°, 45°, 60°, 75°, and 90°) were used in this study. For each diversion angle, diversion channel-to-main channel bed width ratios of 29%, 38%, and 48% were used. For each diversion angle and diversion channel bed width, five total discharges (7.25, 8.5, 9.75, 11, and 12.25 L/s) were circulated through the model. In total, 75 experiments were performed in this study. Fig. 1 shows a plan of the diversion channel system. A vertical mesh was installed at the main channel inlet to eliminate flow turbulence. The inlet and outlet working sections of the diversion channel system were protected against the local scour using a special arrangement, as shown in Fig. 2, in order to protect the working section from failure. In addition, presenting the erosion in the beginning of the section work leads to increasing the bed load and introduce sediment particles in scour hole. Before starting the experiment, the sand bed was flattened by special smooth plastic pieces. Then, the channel outlets were closed and water was allowed to flow slowly into the channels up to a suitable depth. Following this, the channel outlets were opened, and the flow was set to the required discharge for 12 h. The water depth and scour depth were measured using a vertical point gauge with precision up to parts of the mm at selected locations, and the discharge in the diversion channel was measured many times throughout the experiment (at the beginning, after 6 h and after 12 h) in order to check the discharge and to be sure that is no change in flow condition. Before starting the experiments, the point gauge was calibrated based on flat bed level. With starting the experiments, the uniform sand waves on the bed start to form (ripple to dune). The average bed level with these uniform sand waves should be equal the original flat bed. Therefore, the bed depth was considered as a distance between the water level and original flat bed level. Scour depth for different cases was measured at the bottom of the scour hole, which presents the maximum depth of the scour, each 30 min at the first 2 h and each hour after that. At the end of the experiment, the water in the channels was slowly drained, and the bed topography in the junction region was measured using a vertical point gauge. Average diversion channel total sediment transport load was measured by collecting sand particles at the end of the diversion channel. This sediment transport load including suspended and bed load. Most of it transported near the bed. A sieve

2.3. Critical velocity of the sand inception motion Shield's diagram was used to determine the critical shear velocity, which give the value of U⁎c = 0.014 m/s (Simons and Şentürk, 1992). For estimating the critical mean velocity of the inception motion, many methods are available, such as Melville and Sutherland's equation (Eq. (6)) (Melville and Sutherland, 1988), Neill's 1967 Eq. (7) and 1968 equations (Simons and Şentürk, 1992), and Hjulstrom's diagram (Hickin, 1995). Each method gives different values of the critical velocity. These differences in critical velocity values between the different equations come from the different factors, such as different dimensions of the flume, sand properties and flow condition. Therefore, before starting the experiments, many tests were performed for this study flume dimension and sand properties to estimate the critical velocity. When using one type of soil, the d50 and ρs are constant. In addition, shear velocities is a function of sand, flow and channel properties (Simons and Şentürk, 1992). Therefore, the critical velocity becomes a function of the water depth. Fig. 3 shows the critical velocity estimated using Melville and Sutherland's equation, Neill's 1967 equation, and Eq. (8) for the sand specifications mentioned above. Eq. (8) was adopted in this study to estimate the critical velocity. 12

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(a)

(b) Teeth-shaped pieces

Sand covered by Perspex pieces Fig. 2. Use of Perspex pieces to protect (a) upstream and (b) downstream channels against scour.

3. Results and discussion

24 Vc/U*c

21

= 3.22.ln (y/d50) - 1.96 R² = 0.8331

3.1. Flow field at diversion The effects of different diversion angles, bed width ratios, and total discharges were investigated. Fig. 4 shows the bed topography for different diversion angles, a total discharge of 9.75 L/s, and a bed width ratio of 38%. The discharge ratio in these cases was (25 ± 1.5)%. Fig. 4 shows that the maximum scour depth occurred in the bed of the main channel downstream of and immediately after the channel junction. Changing the flow direction leads to increasing the shear stress (Ahmad et al., 2017). That leads to presenting the scour when this shear stress exceeds the scour threshold value. The scour formation downstream of the channel junction is attributed to this increasing of the shear stress due to changing some of the flow direction toward the diversion channel and occurrence of turbulence in the region. In the diversion junction, many sets of vortexes are produced (Herrero et al., 2015). These vortexes are produced due to the turbulence, which is affected by the junction angle between the main and diversion channels. Using dye material, three main sets of vortexes at the junction region were visualized (V1, V2, and V3 in Fig. 4). The scour depth is mainly affected by vortex V1. As shown in Fig. 4, vortex V1 almost acts perpendicular to the main flow, is generated just downstream of the channel junction, and moves slightly toward the downstream main channel when the diversion angle decreases. In the initial stage of forming a scour hole, the capacity of the transporting sediment from the scour hole location too much higher than the supplying sediment to it. With time, the scour hole starts to grow and leads to reduction the ability of V1 to transport the sediment particles out of the hole. Therefore, the scour hole was rapidly grow in size at the fist minutes, as shown in Fig. 5. The average scour depth for different cases at the beaning of 30 min and 60 min reached about 50% and 65%, respectively, from that after 12 h. After that, because of the experiments performed under live bed conditions (Vu/Vc between 1.1

Vc/U*c

18 15 Melville and Sutherland, 1988 Neill, 1967 present study

12 9 0

100

200

300 400 y/d50

500

600

700

Fig. 3. Estimation of the critical velocity of the sand inception motion.

y Vc = 5.75 log ⎛5.53 u ⎞ d U∗c 50 ⎠ ⎝ ⎜

⎟

(6) −0.2

Vc =

ρ d 2.5 ⎛⎜ s − 1⎞⎟ gd50 ⎜⎛ 50 ⎟⎞ ⎠ ⎝ρ ⎝ yu ⎠

y Vc = 3.22 ln ⎛ u ⎞ − 1.96 U∗c ⎝ d50 ⎠ ⎜

(7)

⎟

(8)

where yu is the water depth in the main channel at the upstream.

13

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Fig. 4. Bed topography in the junction region at different diversion angles (Qu = 9.75 L/s and Br = 38%).

16

and 1.5), bed form at the upstream main channel was presented (ripple or dune at the higher values of the stream power). In live bed conditions, the scour hole is continuously received sediment and refilled (Hosseini and Amini, 2015). This happened due to moving the sand waves along the bed toward the flow direction. This leading to fluctuate the scour depth with time. In case of the diversion channel flow, the diversion channel receives more water from the main channel's lower layers where the sediment particles are concentrated (Barkdoll, 2004). The main channel's upper layers have higher momentum and tend to continue downstream past the diversion channel while the lower momentum in lower layers are easily diverted to the diversion channel (Herrero et al., 2015). Therefore, a large part of the migration sand waves from the main channel at the upstream diverted toward the diversion channel. Therefore, the suppling sediment to the scour hole is reduced (as it is located downstream the diversion channel) and the sand waves are less impact on the fluctuating the scour depth values as shown in Fig. 5. Scour hole continues increasing in its size until the effect of the V1 reduce sufficiently due to increasing

ds (cm)

12

8 30° 45° 60° 75° 90°

4

0 0

100

200

300

400

500

600

700

800

Time (min) Fig. 5. Timeline of the scour depth at different diversion angles (Qu = 7.25 L/s and Br = 38%).

Table 1 Scour depth and relative scour depth values. (Br)

48%

38%

29%

a

Qu (L/s)

7.25 8.5 9.75 11 12.25 7.25 8.5 9.75 11 12.25 7.25 8.5 9.75 11 12.25

ds (cm)

Kds

(30°)

(45°)

(60°)

(75°)

(90°)

(30°)

(45°)

(60°)

(75°)

(90°)

6.5 7.1 8 9.9 10 7.6 8.3a 9.8a 10.95a 10.65 7.4 9.6a 11.3 10.15 11.1a

9.5 10.6 11.2 12.6 14a 9.3a 11.75a 11.4 12.35 13.4a 10.6 11.1a 11.6 11.8 11.4

10a 11.65 13.95 15.1a 15.9 10.6 11.6a 12.65 13.5 15.7 10.75 11.3 12.5a 12.7 13.2a

10.8 12.25 13.1a 14.75a 16.2 10.8 13 13.25 14.6 15 10.5a 11 12.5 13.3a 14a

12.2a 13.3a 14.1 15.8 17.5 11.8 12.4a 14a 14.5 16.1 10.6 11.7a 13.2 13.4 14.4

0.53 0.53 0.57 0.63 0.57 0.64 0.67 0.70 0.76 0.66 0.70 0.82 0.86 0.76 0.77

0.78 0.80 0.79 0.80 0.80 0.79 0.95 0.81 0.85 0.83 1.00 0.95 0.88 0.88 0.79

0.82 0.88 0.99 0.96 0.91 0.90 0.94 0.90 0.93 0.98 1.01 0.97 0.95 0.95 0.92

0.89 0.92 0.93 0.93 0.93 0.92 1.05 0.95 1.01 0.93 0.99 0.94 0.95 0.99 0.97

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

These data sets were used to validate the Eqs. (10) and (11). While, data without

a

were used to derive the Eqs. (10) and (11).

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1.2

Kds = sinθ (1.44Br) R2 = 0.872

1.0 0.8

Br = 29%

Kds

Br = 38%

0.6

Br = 48%

0.4

=50% BrBr = 48% = 40% BrBr = 38% = 30% = 29% BrBr Eq. (9)

θ Be

Qu

Qd

0.2 0.4

0.5

0.6

0.7

0.8

0.9

1.0

sinθ = Bb/Be Fig. 6. Experimental values of relative scour depth (Kds) against (Bb/Be) for different cases of bed width ratio.

Fig. 7. Longitudinal cross-sectional view of the bed in the main channel at the junction region (cross-section was taken parallel to the main channel 3 cm from the diversion side-wall) (different diversion angles, Qu = 9.75 L/s and Br = 38%).

Table 2 Diversion channel water discharge and discharge ratio values. (Br)

48%

38%

29%

Qu (L/s)

7.25 8.5 9.75 11 12.25 7.25 8.5 9.75 11 12.25 7.25 8.5 9.75 11 12.25

Qb (L/s)

Qr (%)

(30°)

(45°)

(60°)

(75°)

(90°)

(30°)

(45°)

(60°)

(75°)

(90°)

2.25 2.65 3 3.33 3.72 1.91 2.17 2.49 2.78 3.12 1.48 1.79 2.03 2.29 2.6

2.22 2.59 3.02 3.43 3.77 1.85 2.25 2.55 2.9 3.18 1.525 1.78 2.08 2.3 2.55

2.125 2.39 2.87 3.23 3.6 1.83 2.17 2.45 2.81 3.16 1.46 1.75 2.02 2.26 2.45

2.03 2.37 2.7 3.15 3.48 1.77 2.1 2.31 2.71 2.98 1.32 1.62 1.875 2.15 2.3

2.12 2.51 2.85 3.25 3.59 1.66 1.99 2.34 2.74 2.9 1.34 1.63 1.85 2.14 2.37

31.03 31.18 30.77 30.27 30.37 26.34 25.53 25.54 25.27 25.47 20.41 21.06 20.82 20.82 21.22

30.62 30.47 30.97 31.18 30.78 25.52 26.47 26.15 26.36 25.96 21.03 20.94 21.33 20.91 20.82

29.31 28.12 29.44 29.36 29.39 25.24 25.53 25.13 25.55 25.8 20.14 20.59 20.72 20.55 20

28 27.88 27.69 28.64 28.41 24.41 24.71 23.69 24.64 24.33 18.21 19.06 19.23 19.55 18.78

29.24 29.53 29.23 29.55 29.31 22.9 23.41 24 24.91 23.67 18.48 19.18 18.97 19.45 19.35

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maximum value at a diversion angle of 90°. However, when the diversion angle reduces, the effect of vortexes V1 and V3 reduces because of the separation of V1 and V3, and the recorded scour depth also reduces. The secondary currents at the junction are affected by many factors, such as the diversion angle (Moghadam and Keshavarzi, 2010). Therefore, the turbulence is affected due to changing the diversion angle. In addition, the entrance width decreases as the diversion angle increasing. The velocity of the flow at the entrance decreases with decreasing the width of the diversion channel (Barkdoll et al., 1999) leading to decreasing the strength of the vortexes as it affected by the flow velocity. Therefore, the strength of the vortexes mainly depends on the value of the diversion angle. Thus, the strength of the vortexes mainly depends on the value of the diversion angle. The second vortex, V2, occurs in the main channel and at the tail of V1, and the direction of the rotation axis of V2 is parallel to the main flow direction. It is generated because of the change in bed topography and the formation of a scour hole. It is limited to the extent of the scour hole length. Barkdoll et al. (1999) and Herrero et al. (2015) observed the main flow vortexes, V1 and V2, during the investigation of 90° diversion angle. 3.2. Effect of the diversion angle and bed width ratio on the scour depth Fig. 5 shows the effect of the diversion angle on the scour depth with time for selected discharge (7.25 L/s) and a bed width ratio of 38%. Other study cases considered following a similar trend. Generally, scour depth decreases as the diversion angle decreases. A relative scour depth (Kds) is used in this study to investigate the effect of the diversion angle and bed width ratio on the scour depth. The (Kds) can be defined as a scour depth in case of a diversion angle of θ° to that with 90° for the same flow condition and bed width ratio. Experiments datasets of the scour depth for different cases of the diversion angles, bed width ratios and total discharges are listed in Table 1. Table 1 also includes the values of the relative scour depth. Non-linear regression analysis can be used to correlate the effect of geometrical variables on the relative scour depth (Ahmad et al., 2017). Therefore, non-linear regression analysis was done to correlate the relative scour depth (Kds) with (Bb/ Be) and (Br) as expressed in Eq. (9) and Fig. 6.

K ds = sinθ(1.44Br)

(9)

From Table 1, the scour depth of 30° diversion angle shows average values of the relative scour depth of 0.78, 0.69 and 0.57 for bed width ratios of 29%, 38% and 48%, respectively. While, the average values of the relative scour depth in case of 45° diversion angle equal to 0.9, 0.85 and 0.79 for bed width ratios of 29%, 38% and 48%, respectively. As mentioned earlier, one reason for this trend is the decrease in the strengths of V1 and V3 as the diversion angle decreases. The flow is more streamlined at smaller diversion angles than at larger ones, leading to a decrease in the vortex strength. This is why the recorded scour depth is small at small diversion angles and large at larger angles. The shape of the downstream diversion channel conjunction edge also affects the scour depth. As the diversion angle decreases, this edge becomes more pointed and sharp and its effect on the scour depth decreases. In addition, the scouring area trapped near-bed sediment particles and V1 transported them toward the diversion channel entrance. Next, V3 collected these sediment particles and transported them into the diversion channel. Lowering the bed level of the diversion channel entrance assisted V3 in transporting sediment particles into the diversion channel. As the diversion angle increased, the centre of the scour hole moved toward and lowered the bed level of the diversion channel entrance, as shown in Fig. 7. Lowering the bed of diversion channel entrance eased the transport of sediment particles into the diversion channel, increased the diversion channel sediment-transport rate and subsequently decreased the downstream main channel sediment-transport rate. Sediment-transport rate at the diversion channel for the some

Fig. 8. Normalised scour depth as a function of the normalised water depth at the upstream: (a) Br = 48%; (b) Br = 38%; (c) Br = 29%.

the depth of the scour and increasing the hardness of transport the sediment out of the scour hole. Finally, the amount of the sediment trapped by the scour hole almost equal that amount transported out by V1. As can be seen in Fig. 4, the beginning of V1 is close to that of V3, which is the diversion channel vortex, and interference and combining occur between these two vortexes. Because of the combined effect of vortexes V1 and V3, the recorded scour depth is large, and reaches its 16

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Table 3 Water depth and flow velocity values at the upstream main channel. (Br)

48%

38%

29%

Qu (L/s)

7.25 8.5 9.75 11 12.25 7.25 8.5 9.75 11 12.25 7.25 8.5 9.75 11 12.25

yu (cm)

Vu (m/s)

(30°)

(45°)

(60°)

(75°)

(90°)

(30°)

(45°)

(60°)

(75°)

(90°)

8.55 9.35 10.15 11.1 11.7 8.8 9.75 10.7 11.45 12.3 9.2 10.1 11.05 12 12.9

8.4 9.35 10.2 11 11.8 8.75 9.8 10.5 11.45 12.4 9.2 10.1 11 11.9 12.9

8.2 9.25 10.1 10.8 11.75 8.7 9.7 10.5 11.4 12.45 9.05 10.05 10.9 11.95 12.85

8.4 9.25 10.1 10.85 12 8.65 9.7 10.4 11.35 12.2 8.95 10 10.85 11.85 12.7

8.35 9.15 9.9 11 11.75 8.6 9.6 10.35 11.4 11.95 8.95 10 10.8 11.85 12.8

0.27 0.29 0.31 0.32 0.33 0.26 0.28 0.29 0.31 0.32 0.25 0.27 0.28 0.29 0.30

0.28 0.29 0.31 0.32 0.33 0.26 0.28 0.30 0.31 0.32 0.25 0.27 0.28 0.30 0.30

0.28 0.29 0.31 0.33 0.33 0.27 0.28 0.30 0.31 0.31 0.26 0.27 0.29 0.29 0.30

0.28 0.29 0.31 0.32 0.33 0.27 0.28 0.30 0.31 0.32 0.26 0.27 0.29 0.30 0.31

0.28 0.30 0.31 0.32 0.33 0.27 0.28 0.30 0.31 0.33 0.26 0.27 0.29 0.30 0.31

diversion flow with 90° diversion angle and 100% bed width ratio, Casas (2013) observed formation of an erosion pit in the main channel just downstream diversion junction. This pit with a maximum difference in bed level in relation to the main channel at upstream bed bathymetry equivalent to 2 to 3 times the water depth. The effect of the water depth of the main channel at the upstream on the scour depth for various diversion angles is shown in Fig. 8. The datasets of normalised scour depth, (ds/Bb), and the normalised water depth at the upstream, (yu/Bb) were fitted as power relationships in these figures for different cases. Fig. 8 illustrates that the normalised scour depth increases with an increase in the normalised water depth at the upstream side. This can be attributed to the increase in the strength of vortex V1, which is affected by the pressure gradient existing at the diversion channel site. Ramamurthy et al. (2007) observed a stagnation point at the downstream conjunction edge of the diversion channel entrance (at the scouring area). The stagnation pressure in the diversion channel flow leads to developing a roller at the water surface due to water impact with downstream diversion channel conjunction edge. While, the V1 is generated near the bed. This roller with a different rotation direction with the V1 and causes a reduction in V1 strength. Because of the roller developed near the surface and the V1 developed near the bed, the interference between the water surface roller and V1 is reduced as the water depth increases leads to the V1 strength increases. Based on experimental datasets emerged from this study (Tables 1 and 3), the water depth directly affects the scour depth. However, it does not affect the relative scour depth under the same diversion angle and bed width ratio condition. For an instant, the values of the (Kds) for diversion angle of 30° and Br of 48% equal (0.58 ± 0.05). While, the (yu) increased from 8.55 to 11.7 cm.

cases with the same flow condition, such as same total discharge and main channel flow depth at upstream were measured to show the influence of the amount of the diversion sediment on the scour depth. These measurements show that the amount of the diversion sediment is affected by the diversion angle, and this effect directly affects the scour depth. For instance, sediment-transport rates in the diversion channel for a total discharge of 7.25 L/s, a bed width ratio of 38%, and diversion angles of 30°, 45°, 60°, 75°, and 90° and were found to be 0.01, 0.03, 0.15, 0.11, and 0.14 g/s, respectively. A decrease in the sedimenttransport rate in the diversion channel leads to an increase in the sediment-transport rate in the main channel and eventually contributes to the replenishment of sediment in the scour hole. Another factor that influences the scour depth is the flow velocity at the entrance of the diversion channel. A smaller diversion angle provides a larger entrance width. Therefore, when the diversion angle decreases, the velocity at the entrance of the diversion channel also decreases. For example, the entrance width at a diversion angle of 30° is twice that at a diversion angle of 90°. Decreasing the velocity at the diversion channel entrance leads to a decrease in the strength of vortexes V1 and V3. Fig. 6 shows also the effect of the bed width ratio on the relative scour depth. The values of Kds show decreasing with its values as the bed width ratio increases. In addition, the exponents of the Eq. (9) show increasing in its values as the bed width ratio increases. This means that the curve depicting the relationship between (Kds) and (Bb/Be) in the case of Br = 48% is steeper than that in the other cases and that the slope of the curve decreases as the bed width ratio decreases. This trend indicates that the effect of the diversion angle on the (Kds) increasing as the bed width ratio increases. In other words, a change in the diversion angle has a stronger effect on the (Kds) at a larger bed width ratio. If the flow condition is fixed, an increased bed width ratio will increase the diversion channel water discharge due to increasing diversion channel capacity and that will increase discharge ratio. The diversion channel water discharge (Qb) and discharge ratio (Qr) values are listed in Table 2. From Table 2, the average values of the discharge ratios for different case of diversion angle and total discharges are (19.8 ± 1.6%), (24.7 ± 1.8%) and (29.5 ± 1.7%) for bed width ratios of 29%, 38% and 48%, respectively. Basing on the Eq. (2), discharge ratio is considered an effective parameter and it is believed to be responsible for recording stronger effect on the (Kds) with increasing its value.

3.4. Effect of the velocity on the scour depth The flow velocity can be considered as an important factor affecting the scour depth (Melville and Chiew, 1999; Solaimani et al., 2017). Fig. 9 shows the relationships between the normalised scour depth and flow intensity in the main channel at the upstream side, (Vu/Vc), fitted as power relationships. Fig. 9 shows that the normalised scour depth increases with an increase in the flow intensity. An increase in the velocity plays a significant role in increasing the strength of vortexes V1 and V3 and thus increasing the scour depth. Experimental datasets in Tables 1 and 3 show that the velocity of the flow in the main channel at the upstream directly affects the scour depth. Nevertheless, it does not affect the relative scour depth under the same diversion angle and bed width ratio condition. For an instant, the values of the (Kds) for diversion angle of 30° and Br of 48% equal

3.3. Effect of the water depth on the scour depth Generally, the water depth is one of the parameters that influence the scour depth (Aǵaçcioǵlu and Önen, 2005). In some cases of 17

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Fig. 10. Comparison of estimated and measured data for: (a) scour depths; (b) scour lengths.

Regression analysis was used to determine the relationship between the dependent parameters (ds/Bb) and (Ls/Bb) in terms of other effective parameters, as expressed in Eqs. (10) and (11). The relationships were found with coefficient of determination R2 values of 0.931 and 0.834 for the scour depth and scour length, respectively.

ds = Bb

Vu · Vc

yu/Bb · sin θ ·Q r 0.75 Br

Ls V 0.7 y 1.5 = 245 ⎡ u · u ·Br 0.65 ·sin θ0.4 ·Q r 2.35⎤ ⎢ ⎥ Bb Bb ⎣ Vc ⎦

Fig. 9. Normalised scour depth as a function of the flow intensity: (a) Br = 48%; (b) Br = 38%; (c) Br = 29%.

(10)

(11)

In this study, the variation in the Froude number for the main channel at the upstream, Fu, for all the experiments was approximately 0.29 ± 0.3. Therefore, its effect on the scour depth and scour length was neglected. Eqs. (10) and (11) were validated by using the datasets not used in the regression analysis, as shown in Fig. 10. A comparison between the measured and estimated scour depths and scour lengths shows that most of the data points are located within the ± 10% error lines. The Mean Absolute Percentage Error (MAPE), which is expressed in Eq. (12) (Kim and Kim, 2016) and Root Mean Square Error (RMSE), which is expressed in Eq. (13) (Willmott et al., 2012), were used to assess the performance of Eqs. (10) and (11).

(0.58 ± 0.05). While, the (Vu) increased from 0.27 to 0.33 m/s.

3.5. Estimation of the scour depth and scour length in the diversion channel The scour depth and scour length in the diversion channel system can be described by Eqs. (2) and (3). In this study, two-thirds of the datasets were randomly selected to derive empirical equations and the remaining one-third was used to validate the equations. 18

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MAPE% =

1⎡ M −E ∑ i M i ⎤⎥ × 100 n ⎢ i=1 i ⎦ ⎣

⎡1 RMSE = ⎢ n ⎣

n

M

∑ ⎛Bi ⎜

i=1

⎝

b

Acknowledgments (12)

This work was supported by a Putra grant (GP-IPS/2015/9453100) provided by Universiti Putra Malaysia. The authors express their special thanks to the technicians of the hydraulic laboratory and all the civil engineering department laboratories of Universiti Putra Malaysia, who greatly assisted the authors during the experimental work.

2 0.5

−

Ei ⎞ ⎤ Bb ⎠ ⎥ ⎦ ⎟

(13)

where Mi and Ei are the measured and estimated values of the scour depth or scour length, respectively. n is the total number of datasets. The MAPE and RMSE values are found to be 3.46% and 0.043 for testing Eq. (10) and 10.3% and 0.595 for testing Eq. (11). The importance of Eqs. (10) and (11) is that they give a general impression about the weight of each parameter and the strength of its effect on the scour depth.

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Clear-water local scour around pile groups in shallow-water flow. J. Hydraul. Eng. 138, 177–185. http://dx.doi.org/ 10.1061/(ASCE)HY.1943-7900.0000488. Baker, D.W., Bledsoe, B.P., Albano, C.M., Poff, N.L., 2011. Downstream effects of diversion dams on sediment and hydraulic conditions of Rocky Mountain streams. River Res. Appl. 27, 388–401. http://dx.doi.org/10.1002/rra.1376. Barkdoll, B.D., 2004. Discussion of “subcritical 90° equal width open channel dividing flow” by Chung-Chieh Hsu, Chii-Jau Tang, Wen-Jung Lee, and Mon-Yi Shieh. J. Hydraul. Eng. 130, 171–172. Barkdoll, B.D., Ettema, R., Odgaard, A.J., 1999. Sediment control at lateral diversions: limits and enhancements to vane use. J. Hydraul. Eng. 125, 862–870. http://dx.doi. org/10.1061/(ASCE)0733-9429(1999)125:8(862). Casas, A.H., 2013. Experimental and theoretical analysis of flow and sediment transport in 90-degree fluvial diversions. In: Doctoral Dissertation Thesis. Universitat Politècnica of Catalunya, Barcelona. 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4. Conclusions In the present study, the effect of the diversion channel on the scour in the main channel at the downstream was investigated experimentally. Investigations were conducted for different diversion angles (30°, 45°, 60°, 75°, and 90°) and bed width ratios (29%, 38%, and 48%). In the investigations, the total discharges in the main channel were varied between 7.25 and 12.25 L/s for different flow intensities between 1.1 and 1.5. Therefore, the experiments were performed under live bed conditions. Observing scour depth with time showed that about 50% of the scour depth formed during the first 30 min of the running duration and about 65% during the first 60 min. The results obtained from this study showed that the diversion angle has a direct effect on the scour depth in the main channel. This effect is attributed to increasing shear stress at the junction region due to diverting some of the flow and the formation of vortexes V1 and V3 in the junction region. The scour depth at a diversion angle of 30° significantly reduces compared to that at a diversion angle of 90°. Equation to demonstrate the effect of different diversion angles and bed width ratios on the relative scour depth (Kds) was proposed (Eq. (9)). Effect of changing the diversion angle has a stronger effect on the (Kds) at a larger bed width ratio (Br) because increasing (Br) leads to increasing discharge ratio (Qr). The water depth and velocity at the upstream main channel (yu and Vu) directly affect the scour depth. Nevertheless, no significant changing was observed in (Kds) with changing the (yu and Vu). Therefore, Eq. (9) is applicable for a wide range of total discharge, water depth and velocity flow in the main channel at upstream. Equations were proposed with a good accuracy to estimate the scour depth and scour length (Eqs. (10) and (11)) and were tested using experimental data. The coefficient of determination, R2, was found to be 0.931 and 0.834 for the scour depth and scour length, respectively. The equations are valid for the one type of soil used in the experiments (d50 = 0.4), Fu = 0.29 ± 0.3, Qr = 20%–30%, Br = 29%–48% and under live bed conditions for Vu/Vc = 1.1–1.5. The results of this study indicate that the diversion angle should be decreased as much as possible to decrease the scour depth, which directly affects the stability of channel banks. Scour depth and other effect parameters, such as flow intensity, are significantly affected by the soil properties. Therefore, it will be important to consider different soil types in the future studies. In addition, the water depth and discharge in the diversion channel are the result of boundary condition at the end of both main and diversion channels (with 70% flow contraction). Therefore, investigating different water depths and discharges in the diversion channel for the same flow condition in the main channel at the upstream are believed affecting the scour depth and need to be considered in the future work. Finally, validation the proposed equations at full scale using field data and different conditions experiment date is required.

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