Impact of Flow Rate, Sediment Uniformity, and Outlet Size on Sediment Removal Upstream of a Cross-River Structure

Abstract

The sediment accumulation behind dams and cross-river structures reduces storage capacity, increases pool water level, reduces hydropower production, and causes damage to the blades of turbines. The operation of the impoundment hydropower and run-of-river plants is affected by the sediment accumulation in the vicinity of their water intake. In this study, the effectiveness of sediment removal through an outlet in a model of cross-river structure was experimentally investigated. The model was fixed tightly at the end of a 2 m working section in a laboratory flume with a length of 12 m, a width of 0.3 m, and a depth of 0.45 m. To study the impact of main variables on scour volume (V_s), a total of 27 experiments were conducted. The studied variables were flow rate (Q), area (A_o), location of outlet centerline outlet from the bed (h_s), and uniformity of the sedimentation used in the mobile bed of the working section. For the same outlet area (A_o = 47.5 cm²), results show that when the flow rate increased from 3.2 to 6.3 l/s, the scour volume in nonuniform sediment was increased by twofold. However, the above increment caused the scour volume in uniform sediment to increase by only 170%. In addition, the scour volume in the mobile bed of uniform sediment was found to be greater than that in nonuniform sediment by an average of 17%. For a flow of 3 l/s and when the outlet area was reduced by either 25% or 50%, the scour volume in both uniform and nonuniform sediment was reduced by 46%. The accuracy of the proposed dimensionless multiregression model was statistically tested by calculating the Nash efficiency coefficient (NEC) and found to be 0.91, which confirmed the accuracy of the model prediction. The outcomes of the present study are useful to engineers involved in dam design and management.

1. Introduction

The growing trend in using hydropower necessitates a deeper understanding of the associated problems. One of the main challenges is sediment accumulation near hydropower intakes. Accumulation of sediment in the vicinity of a turbine water intake results in reduced power production, damaged turbine blades, and environmental concerns [1]. Sedimentation in a reservoir impairs water storage and increases water levels [2]. Runoff that carries eroded materials from catchments is considered a source of sedimentation in rivers and storage reservoirs [3].

The geometry of selected river sections that were subjected to sedimentation was studied by using HEC-RAS (5.0.7) software. Before predicting the sedimentation volume in the selected rivers, calibration and validation processes of HEC-RAS were conducted by using hydrological and topographical data including the sediment loads [4,5,6]. Traditional removal of sediment accumulations by dredging is costly and disrupts the operation of turbines. However, sediment removal by hydrosuction through a gated outlet located near the water intakes of the turbines can be utilized as another effective method for sediment management.

The main focus of the published studies was on the mechanism of sediment transport, including the role of three-dimensional vortices in the formation of the scour hole upstream of cross-river structures. For this purpose, the studies employed either physical or numerical models.

The water depth and sediment size and uniformity have a significant effect on the depth, length, and width of the resulting scour hole [7,8]. Experimental investigations on mobile beds with different sediment coarseness and flow conditions (steady and unsteady) were used to estimate the maximum scour depth and geometry and size of the scour hole formed upstream and downstream of cross-river structures.

In addition, it was used to understand the mechanism of sediment transport and temporal evolution of the resulting scouring hole [9,10,11,12,13,14,15,16,17,18,19,20]. Ota and Sato [21] built a sophisticated computer model to simulate sediment transport through a slit weir. The model simulated both fluid flow and sediment movement based on the Reynolds-averaged Navier–Stokes equation, the interaction between water and sediment, and turbulence in the water (depending on the k-ω closure relation). The above model was adopted by Zhang et al. [22] to predict scour depth in the seabed below a pipeline. Ota et al. [23] then improved this model and used it to analyze 3D sediment transport problems (problems related to the transitions of rolling bed load into suspension in water columns). In addition, Ota and Sato [24] developed a model that was based on a nonlinear ordinary differential equation (ODE) and applied it to calculate the temporal variation of scour volume and maximum scour depth under steady and unsteady flow conditions upstream of a slit weir. Later, the model was subjected to further modifications by Ota et al. [25]. Moreover, Taha et al. [26] employed the commercial software, FLOW 3D (v11.1.0), to study sediment removal in a cleaning hole under a constant flow. By considering different flow conditions, Majeed et al. [27] applied computational fluid dynamics (CFD) including a turbulent model (k-ω) to investigate the sedimentation problems due to the operation of gates in a selected hydraulic structure. They concluded that the scouring depth and the amount of sediment removal were increased directly with the Froude number. Abed and Azzubaidi [28] studied the impact of varying velocity distribution on the sediment process and bed topography in the reservoir of Mandali Dam.

Most of the published studies employed simplified 3D models to simulate sediment movement from upstream to downstream through an outlet in a cross-river structure. The models treat the sediment entrainment as no motion suspension and do not consider the transition from bed load motion to suspension. A few other studies conducted computations based on individual particle motion by using a discrete element method. Therefore, experimental investigations on sediment entrainment and the resulting scour holes in uniform and nonuniform mobile beds are still needed since reliable data on the volume and geometry of scour holes are essential in dam management and operation. In this study, extensive experimental work was conducted to investigate the impact of flow rate, sediment uniformity, and the size and location of the outlet of a cross-river structure on the volume of removed sediment upstream.

2. Materials and Methods

2.1. Description of the Physical Model

In the present study, a physical model was designed to test the effectiveness of using a gated outlet to reduce sediment accumulation near the water intakes of hydropower plants. The simulation model used for this purpose comprised a sediment recess, a laboratory flume, and a model of a cross-river structure with an outlet. The sediment recess represents the mobile bed with sediment accumulation while the flume represents the reservoir/river. However, the cross-river structure/dam with an outlet was represented by a thin Plexiglas model with an opening. It was recognized that the scale of the model should be carefully selected.

A series of experiments were conducted in a glass-sided tilting flume that was 0.30 m wide, 12 m long, and 0.45 m deep. The flume is located at the hydraulics laboratory of the Ministry of Water Resources, Baghdad, Iraq. To construct the physical model, modifications were made to the flume. The modifications included having a working section, a ramp, and a model of a cross-river structure with an outlet. The working section was 2 m long and 0.3 m wide and it was filled with sediment up to a depth of 10 cm. Two types of sediment (uniform and nonuniform) with the same median diameter (d₅₀ = 0.23 mm) were tested separately in the working section. The working section was located almost in the middle of the flume length. At the upstream end of the working section, a Plexiglass ramp with a slope of 1:10 was constructed. To prevent the flowing water in the flume from seeping underneath and around the ramp sides, a special type of glue was used to fix the ramp tightly to the flume bed and sides. At the downstream end of the working section, a 7 mm thick Plexiglass model of a cross-river structure with an outlet was tightly fixed to the flume bed and sides. The tested outlets were of different diameters (11 cm, 9 cm, and 7 cm), shapes (circle, semicircular, and three-quarters circle), and elevation from the mobile bed (3.5 cm and 5.0 cm). Figure 1 shows various components of the physical model (ramp, working section, and the model of a cross-river structure). The discharge was measured using a digital flow meter while the water depth was measured using a point gauge with an accuracy of ±1 mm. The flume discharge ranged from 3.0 l/s to 6.3 l/s.

2.2. The Experimental Design and Procedure

The experiments were mainly designed to demonstrate how a cross-river structure with a controlled outlet near the location of a hydropower intake reduces sediment accumulation and minimizes the risk of intake clogging. In the present study, the experimental design includes conducting 27 controlled experiments that considered the effect of the main independent variables on the volume of the scour hole formed upstream of the cross-river structure. The studied variables affecting the scour volume ($V_s$) upstream of the cross-river structure were flow rate (Q), outlet cross-sectional area (A_o), location of the outlet centerline from the bed of the working section (h_s), and uniformity of the sediment.

Table 1. Main studied variables and the number of experiments.

No.	Shape of Outlet	Diameter (cm)	hs (cm)	Discharge (l/s)	No. of Experiments
					Bed with Uniform Sediment	Bed with Nonuniform Sediment
1	circle	11	5.5	6.3	1	1
2	three-quarter circle	11	5.5	6.3	1	1
3	semicircle	11	5.5	6.3, 5.8, 5, 4.2, 3.2	5	5
4	circle	9	4.5	6.3	1	1
5	circle	7	3.5	3.5	2	2
	circle	7	5	3	1	1
6	circle	5	5	3	1	1
7	three circles	3	1.5	3, 2.8	2	2

Note(s): h_s is the distance in cm between the center of the outlet and the bed of the working section before conducting the experiments.

gives more details on the variables considered in the experimental work. After the commencement of each experiment, the measurements taken include scouring depth at intervals of 5 mm along and across the scoured hole formed in the working section. The other measurements were water depth, velocity at a selected point across the flume at the selected section upstream, and the discharge. The water and scour depths were measured using a point gauge with an accuracy of ±1 mm, while the velocity of flowing water at selected points in the flume was measured by a current meter. The flume discharge was recorded using a calibrated digital flowmeter. Depending on the type of sediment in the mobile bed (uniform or nonuniform), the time domain for scour volume was found to be between 5 and 7 h.

2.3. The Dimensional Analysis

By following the Buckingham π-Theorem, the variables (quantities) governing the scour volume that occurred upstream of a cross-river structure with an outlet are described in dimensional form by Equation (1). The variables given below represent inertia, gravity, fluid, flow, geometry of outlet, and mobile bed.

$$\mathrm{f}(h_s, \mathit{\mu }, g, U, U_c, A_o, V_s, y, d_{50})=0$$

(1)

The definition of each variable (quantity) with its unit is shown in

Table 2. The variables governing the scour volume upstream of the cross-river structure.

Parameter	Definition	Dimension
${\mathit{V}}_{\mathit{s}}$	Scour volume	L3
${\mathit{A}}_{\mathit{o}}$	Area of outlet	L2
μ	Water dynamic viscosity	M L−1T−1
g	Acceleration due to gravity	LT−2
$\mathit{U}$	Approach velocity	LT−1
${\mathit{U}}_{\mathit{c}}$	Critical velocity	LT−1
${\mathit{h}}_{\mathit{s}}$	Distance between outlet centerline and mobile bed	L
y	Water depth	L
${\mathit{d}}_{\mathbf{50}}$	Median diameter of sediment	L

. The scour volume ($V_{\mathrm{s}}$) is the independent variable while the others are considered dependent variables. In this study, the median size ($d_{50}$) of the sediment used in the working section was not changed ($d_{50}$ = 0.23 mm) and, therefore, can be discarded from Equation (1) as shown below

$$V_s=\mathrm{f}(h_s, \mathit{\mu }, g, U, U_c, A_o, y)$$

(2)

The temperature of the water used in the experiments was measured and found constant and equal to 20 °C. Therefore, the dynamic viscosity of the water (μ) can also be discarded, and Equation (2) can be written as

$$V_s=\mathrm{f}(h_s, g, U, U_c,{ A}_o, y)$$

(3)

After identification of the repeating variables together with other dependent variables, the procedure required by the π-theorem was followed and the resulting dimensionless groups are shown in Equation (4).

$$V_s/y^3=\mathrm{f}(U_c/U, \mathit{Fr}, A_o/y^2, h_s/y)$$

(4)

2.4. The Case Study

The sedimentation at a run-of-river hydropower station that was built as part of the new Hindiya barrage was selected as a case study. The new Hindiya barrage is located on the Euphrates River south of Musayyib City, Babylon Governorate, Iraq. The barrage and power plant were constructed between 1984 and 1989 after abandoning the old Hindiya Barrage, which became a UNESCO World Heritage site. The total length of the new Hindiya barrage is 215 m and it consists of 6 gates with a width of 16 m and a run-of-river hydropower station with a maximum power production capacity of 15 MW when operated under a discharge of 420 m³/s and a head of 4.3 m. During normal conditions, the estimated average annual volume of sediment accumulation upstream of the Hindiya barrage is 7 × 10⁵ m³ while it reaches 1 × 10⁶ m³ during flood years. Usually, the sedimentation upstream of the barrage extends up to a distance of 1200 m. Figure 2 shows an aerial photo of the site of the Hindiya barrage. The methodology of the present study is summarized in the flow chart shown in Figure 3.

3. Results and Discussion

In most previous studies, prediction of bed deformation and scour near hydropower intake was conducted using three-dimensional (3D) numerical models that consider the motion of sediment media either as a continuum (as described by sediment transport functions) or as individual sediment particles [29,30,31,32]. To simplify the modeling process, the 3D numerical models treated the sediment entrainment with no motion in suspension (i.e., did not consider the transition from bed motion to suspension). Conversely, the utilization of a physical model for the simulation of sediment movement from upstream to downstream through an outlet in a cross-river structure accurately reflects the actual sediment motion (transition process from bed load motion to suspension). This process occurs because the formed turbulence and vortices are strong enough to entrain the sediment particles and carry them in suspension. Compared with numerical modeling, experimental data on scour volume upstream of a cross-river structure is considered more representative. A study of the influence of sediment nonuniformity on the scour volume upstream of a slit weir was recommended by Ota et al. [24]. In the present study, the influence of sediment uniformity was considered by comparing the scour volume resulting from the use of uniform sediment with that resulting from the use of nonuniform sediment. For a reasonable comparison, in the experiments, both sediment types had the same median size ($d_{50}$ = 0.23 mm).

3.1. Impact of Uniform and Nonuniform Sediment on Scour Volume

In this study, uniform and nonuniform sediment were tested separately in a 10 cm deep working section.

For uniform and nonuniform sediment, the values of geometric standard deviation (${\sigma }_g$) were found to be 1.29 and 1.55, respectively, while the median diameter ($d_{50}$) for each tested sediment was 0.23 mm. The same value of $d_{50}$ for the uniform and nonuniform sediment was obtained after many trials of mixing sediment of different sizes. The grading curves for the uniform and nonuniform sediment are shown in Figure 4 and Figure 5. The values of ${\sigma }_g$ for both uniform and nonuniform sediment were calculated using the following equation [33].

$${\sigma }_g=\sqrt{{\displaystyle \frac{d_{84}}{d_{16}}}}$$

(5)

For uniform and nonuniform sediment, the values of $d_{84}$, $d_{50}$, and $d_{16}$ were obtained from the grading curves shown in Figure 4 and Figure 5 while Equation (5) was used to determine ${ \sigma }_g$.

If the calculated value of ${\sigma }_g$ ≤ 1.3, then the sediment is uniform, otherwise the sediment is nonuniform. For nonuniform sediment, the values of $d_{max}$ and $d_{min}$ can be obtained from the grading curve shown in Figure 5. According to Melville and Coleman [33], the value of $d_{max}$, which is the largest sediment size for nonuniform sediment, can be taken as $d_{90}$, and Equation (6) was used to calculate the value of the median particle size of the armor layer ($d_{50a}$).

$$d_{50a}={\displaystyle \frac{d_{max}}{1.8}}$$

(6)

In this study and after the values of $d_{max}$, $d_{50a}$, and $d_{min}$ were obtained from both Figure 5 and Equation (6), the grading curve for the armor layer in the mobile bed of the working section was fitted following the procedure outlined by Melville and Coleman [33]. For all experiments, the uniform and nonuniform sediment in the mobile bed of the working section were tested under clear water conditions.

Clear water conditions occur when the value of the flow intensity for uniform sediment ($U$/$U_c$) or that for nonuniform sediment [$U$ − ($U_a$ − $U_c$)]/$U_c$ is less than one. From Shields’ diagram and for sediment with a median size (d₅₀) ranging between 0.1 mm to 1 mm and a flowing water temperature of 20 °C, the critical shear velocity of sediment particle entrainment ($U_{*c}$) can be calculated by applying the following formula [33],

$$U_{*C }=0.0115+0.0125d_{50}^{1.4}$$

(7)

The critical velocity for sediment particle entrainment ($U_c$) can be determined from the following logarithmic relationship

$${\displaystyle \frac{U_c}{U_{*c}}}=5.57log\left(5.53{\displaystyle \frac{y}{d_{50}}}\right)$$

(8)

where $U_c$ is the critical shear velocity for particle entrainment.

For an armor layer of nonuniform sediment with a size of median particle ($d_{50}$) between 0.1 mm and 1 mm, the mean velocity ($U_a$) at the armor peak can be determined by applying Equations (9)–(11).

$$U_{*ca}=0.0115+0.0125d_{50a}^{1.4}$$

(9)

$${\displaystyle \frac{U_{ca}}{U_{*ca}}}=5.57log\left(5.53{\displaystyle \frac{y}{d_{50a}}}\right)$$

(10)

After determining $U_{ca}$, $U_a$ can be determined by applying the following equation

$$U_a=0.8U_{ca}$$

(11)

where, $U_{ca}$ is the limit of the mean velocity of flow for bed sediment armoring, y is the flow depth, and $U_{*ca}$ is the critical shear velocity for particle entrainment of the armor layer.

The value of $d_{50a}$ was calculated using Equation (6) and found to be 0.7 mm. Other flow parameters were calculated and are shown in

Table 3. The ranges of average velocity, critical velocity, and flow intensity for all conducted runs using uniform sediment in the working section.

Range of Average Velocity, $\mathit{U}$ (cm/s)	Range of Critical Velocity for Sediment Entrainment, ${\mathit{U}}_{\mathit{c}}$(cm/s)	Range of Flow Intensity, $\mathit{U}$/${\mathit{U}}_{\mathit{c}}$	Flow Condition
2.60–9.50	29.14–32.43	0.080–0.32	Clearwater

. In the present study, the values of flow intensity for all runs of the uniform and nonuniform sediment were found to be less than one, which confirmed that the flow falls under clear water conditions (Table 3 and

Table 4. The ranges of average velocity, critical velocity, and flow intensity for all conducted runs using nonuniform sediment in the working section.

Range of Average Velocity, $\mathit{U}$ (cm/s)	Range of Critical Velocity for Sediment Entrainment, ${\mathit{U}}_{\mathit{a}}$ (cm/s)	Range of Flow Intensity, $(\mathit{U}-({\mathit{U}}_{\mathit{a}}$$-{\mathit{U}}_{\mathit{c}}$$\left)\right)/{\mathit{U}}_{\mathit{c}}$	Flow Condition
2.60–9.50	17.07–18.54	0.31–0.39	Clearwater

).

For each run, the scour depths were measured at the corners of 5 m × 5 mm grids and the measurements covered the upstream scoured area. The data on scour depth were used as input data to the Surfer visualization software program.

In addition, the Surfer program was used to draw the scour contours and to calculate the scour volumes and scour areas. For various runs, the scour contours upstream of the cross-river structure model with an outlet area of 47.5 cm² were plotted for both uniform and nonuniform sediment and are shown in Figure 6.

In this study, the scour is considered to reach equilibrium after an average time of almost 6 h after the commencement of the experiment. Data on bed topography were collected and then entered into the Surfer program to calculate the volume of the scour. Almost 80 to 90% of the scour hole is formed between 6 and 8 h after the commencement of the experiments [34,35]. In addition, the location of the maximum scour depth was identified. For different flow rates and outlet sizes, the scour volumes were determined for uniform and nonuniform sediment used in the working section. For the same flow rate and outlet area, collected data revealed that the scour volume in the working section with uniform sediment was greater than that in the working section with nonuniform sediment. For an outlet with an area of 47.5 cm², the average difference in scour volume between the uniform and nonuniform sediment was 17.20%. In nonuniform sediment and when the flow was capable of removing all sizes of widely graded bed sediment, the coarser sediment particles formed an armor layer at the surface of the mobile bed. Consequently, the critical velocity required to entrain the coarse sediment particles in the armor layer formed in the working section was greater than that required for the finer particles of uniform sediment. The armor layer protects finer sediment particles situated below the layer. Therefore, the armor layer inhibits erosion. Melville and Coleman [33] confirmed that when armoring occurred, the degradation of a riverbed may be significantly reduced. In addition, they reported that the size of the particles forming the armor layer is frequently found to be the size of the maximum particle or d₉₀. For the nonuniform sediment used in the working section, the size of particles forming the armor layer was found to be 1.25 mm.

3.2. Impact of Flow Rate on the Scour Volume

The collected data from the experimental work showed that the scour volume upstream of the model of a cross-river structure was affected by the flow rate passing through the outlet. In this study, the effect of five different flow rates on scour volume upstream of the above model was investigated. The values of the tested flow rates were 3.2, 4.2, 5, 5.8, and 6.3 L/s. However, any increment beyond 6.3 L/s caused the water to overflow the top of the model. To demonstrate the impact of flow rate on the scour volume when uniform and nonuniform sediment were used in the working section, the area of the outlet in the model of the cross structure was kept unchanged and equal to 47.5 cm². The experimental data showed that when the flow rate was changed from 3.2 to 6.3 L/s, the scour volume doubled (200%) for nonuniform sediment while it increased by 170% for uniform sediment (Figure 7). A comparison between the scour volumes in uniform and nonuniform sediment showed an average increment of 17% when uniform sediment was used in the working section. The difference in scour volumes is attributed to the formation of an armor layer in the scour hole of the nonuniform sediment. According to Melville and Coleman [33], the armor layer is usually formed from coarser sediment particles after the finer surface particles are removed. When the flow rate increased from 3.2 L/s to 6.3 L/s, the average velocity was increased from 5.77 cm/s to 9.54 cm/s. The velocity increment strengthened the vortices formed at the vicinity of the outlet, which ultimately increased the pickup of sediment particles from the mobile bed.

3.3. Impact of Outlet Size on the Scour Volume

In this study, the effect of outlet area on scour volume for both uniform and nonuniform sediment was experimentally investigated. This was conducted by fixing the flow rate and changing the area of the outlet in the model of a cross-river structure. For each type of sediment used in the working section, a flow rate of 6.3 L/s was used to estimate the scour volume upstream of outlets with areas of 95 cm², 71.30 cm², and 47.50 cm². The scour volume in both uniform and nonuniform sediment was reduced by 46% when the outlet area was reduced either by 25% or by 50%. For the same flow rate, a reduction in the outlet area resulted in a lowering of approach velocity, increasing the flow depth and reducing the scour volume. Figure 8 shows the variation in scour volume for different outlet sizes, while Figure 9 shows the measured velocity resulting from using different outlet areas at a selected location upstream of the cross-river structure model.

3.4. Impact of Outlet Centerline from the Mobile Bed ($h_s$) on Scour Volume

The impact of outlet centerline from the mobile bed ($h_s$) on scour volume was studied by conducting two experiments. The first experiment was conducted on a circular outlet with a diameter of 7 cm, $h_s$ = 3.5 cm, and a flow rate of 3.0 L/s, while in the second experiment, the only change was taking $h_s=5 \mathrm{c}\mathrm{m}.$ Figure 10 shows sectional elevations for the studied cases.

3.5. The Proposed Model

After the main variables governing the scouring upstream of the cross-river structure were identified, dimensional analysis following the π-Theorem was conducted and the dimensionless groups were identified (Equations (1)–(4)). The related laboratory data were used to prepare a new data set for the dimensionless groups. The new data set was divided into two groups. The first group included 70% of the new data set and it was used to obtain the multiregression model using PSS (Version 20) software. The model is described by Equation (12). The second group, which formed 30% of the laboratory data, was used for model validation as described in the next subsection.

$${\displaystyle \frac{V_s}{{\mathrm{y}}^3}}=47.0 (\mathit{Fr}{)}^{1.33} ({\displaystyle \frac{h_s}{y}}{)}^{-0.26} ({\displaystyle \frac{U}{U_c}}{)}^{0.333} ({\displaystyle \frac{A_o}{y^2}{)}^{1.18}}$$

(12)

where $V_s$, y, $h_s$, and A_o are as defined before.

From the experimental results, the estimated scour volume for uniform sediment resulting from using $h_s$ = 3.5 cm was found to be 240.6 cm³ while it was 13 cm³ when the value of $h_s$ was taken as 5 cm. The percentage difference between the two was found to be 94%. Almost the same percentage difference was obtained for nonuniform sediment. Figure 11 shows the estimated scour volume for the studied cases. When $h_s$ = 3.5 cm, the opening of the outlet was tangential to the mobile bed and this makes the transport of sediment through the outlet easier. As a result, the scour volume was greater than that obtained when using $h_s=5 \mathrm{c}\mathrm{m}.$ For uniform and nonuniform sediment, the scour contours of the studied cases are shown in Figure 12.

3.6. Validating the Proposed Model

The second group in the data set included 30% of the new data set and it was used to validate the model as shown in Figure 13.

Figure 13 shows that the predicted scour volumes were scattered around the line of perfect agreement. However, the majority of the predictions were found to be very close to the line. In addition, the Nash efficiency coefficient (NEC) described by Equation (13) was used to test the model prediction [36].

$$\mathrm{NEC}=1-{\displaystyle \frac{\sum (V_{s,m}-V_{s,p}{)}^2}{\sum (V_{s,m}-V_{s,a}{)}^2}}$$

(13)

where, $V_{s,m}$ is the measured volume, $V_{s,p}$ is the predicted volume and $V_{s,a}$ is the average of measured volumes.

The model prediction is not reliable when the value of NEC is 0, and it is perfect when the value of NC is 1. In the present study, the value of NEC was calculated and found to be 0.91, which confirmed the accuracy of the proposed model.

3.7. Sedimentation at the Hydropower Station of the Hindiya Barrage

In order to demonstrate the importance of the studied problem and the applicability of the proposed solution, data on sedimentation upstream of Hindiya barrage and the intake of run of the river powerhouse from 2019 to 2023 was acquired from the office in charge of operation and maintenance of the barrage.

The acquired data include the cross sections of the Euphrates River that showed that the effect of sedimentation extended to a distance of 1200 m upstream of the barrage. The sedimentation upstream of the Hindiya barrage is affecting the operation of the powerhouse. To overcome the problem, dredging was conducted by the respective authority near the hydropower intake upstream. Figure 14 shows a selected cross-section of the Euphrates River upstream of the Hindiya barrage on which the sedimentation and dredging areas were marked.

The estimated annual volume of sedimentation for the period 2019–2023 ranged from 361,595 m³ to 566,337 m³, while the volume of dredging for the same period ranged from 82,400 to 285,000 m³ as shown in Figure 15. To study the sediment characteristics in the Euphrates River upstream of the Hindiya Barrage, a sample from the sedimentation in the river was collected and taken to a laboratory. Grain size analysis was conducted and the grading curve was plotted as shown in Figure 16. Previously, many studies were conducted on the types of sedimentation in the Tigris River, Iraq [37].

From Figure 17 and Equation (6), the value of the geometric standard deviation (${\sigma }_g$) for the sediment of the Euphrates River at the location of the Hindiya barrage was found to be 1.13. This confirmed that the sediment type at that location is uniform with a median diameter ($d_{50}$) of 0.22 mm. Based on this result, a similar size of uniform sediment ($d_{50}$ = 0.23 mm) was used in the mobile bed of the present study. In this study, a comparison was made between the volume of sedimentation removed by dredging upstream of the powerhouse of Hindiya barrage and that removed through the outlet in the cross-river structure by considering the horizontal and vertical scales between them. Figure 17 shows a comparison between the volume of dredged sediment near the intake of the Hindiya hydropower plant and that estimated based on experimental data after taking into consideration the scale effect. The calculation showed that the estimated equivalent sediment volume removed by the method proposed in the present study was 66% of that removed by dredging upstream of the Hindiya hydropower plant (Appendix A).

4. Conclusions

In this study, the impact of sediment uniformity, flow rate, and outlet area on the scour hole formed upstream of a cross-river structure was experimentally investigated. For the same outlet area ($A_o$ = 47.5 cm²), results show that when the flow rate was increased from 3.2 to 6.3 l/s, the scour volume in nonuniform sediment increased twofold. However, the increment in the scour volume for uniform sediment was only 170%. In addition, the scour volume in the mobile bed of uniform sediment was found to be greater than that in nonuniform sediment by an average of 17%. For a flow of 6.3 l/s and when the outlet area was reduced by either 25% or 50%, the scour volume in both uniform and nonuniform sediment was reduced by 46%. The accuracy of the proposed dimensionless multiregression model for predicting the scour volume upstream of a cross-river structure was statistically tested by calculating the Nash efficiency coefficient (NEC). The calculated value of NEC was found to be 0.91, which confirmed the accuracy of the model prediction.

After considering the vertical and horizontal scales, the average scour volume obtained from the physical model was converted from cm³/cm run to m³/m run. The resulting scour volume was 66% of that removed by dredging from the Euphrates River at the water intake of the Hindiya run-of-river hydropower station. This shows the effectiveness of sediment removal by the method used in the present study.