The problem of scour downstream heading up structures is one of the most important problems that has received great attention from researchers. Because of its direct impact on the stability of the structures, where the scour downstream, the stilling basins empty the soil under its base which leads to failure. That leads to great damage or possibly sudden collapse, causing significant financial losses. Thus, the scour and energy dissipation have captured scholars' interest for many years. It is a highly complicated topic to study the downstream local scour process because it depends on a number of variables connected to the heterogeneity of the bed soil and the flow conditions that cause the erosive action [1]. The initial, development, and equilibrium stages of scouring are the three observable stages of scouring in a normal scouring process. A quick rate of scouring is characteristic of the early stage, a relatively slower rate of scouring is characteristic of the development or erosion stage, and an equilibrium stage, where variations in the scour depth following a lengthy scouring duration are undetectable [2]. A typical engineering approach is to build a strong apron downstream of the structures to reduce the impact of erosion from the structures, protecting them from failure due to the scouring action. Different methods have been used to decrease the local scour downstream sluice gates. Rajaratnam [3] studied the erosion caused by submerged plane-wall jets of air and water on beds of sand and polystyrene. Melville [4] studied scour at various hydraulic Structures: sluice gates, submerged bridges, low weirs. Mahmoud et al. [5] investigated the effect of different shapes of holes on energy dissipation through perpendicular screen. Sadeghfam et al. [6] studied the performances of screens in watercourses are investigated for dissipating energy of supercritical flows, capable of inducing scour or stabilising hydraulic jumps. Abbaspour et al. [7] studied experimentally screens with square holes and a porosity of 50%. In comparison to screens with an adverse slope of 0.015, those with an adverse slope of 0.025 dissipated more energy. Compared to screens with a single arrangement, those with a double layout displayed higher performance and used more energy. The effectiveness of screens in a sudden, expanding stilling basin for energy dissipations under the influence of the submerged hydraulic jump was investigated by Elaswad et al. [8]. According to their results, the best screen location was at 0.25 of the abutment lengths with a 0.285 relative screen area, which led to the highest energy loss with the lowest tailwater depth and submerged hydraulic jump length. Zhang et al. [9] conducted a clear-water scour experiment at a submerged weir. The submerged weir alters the mean flow significantly, forming a high-velocity zone above the weir and a vortex system near the scoured bed. As the scour develops, the high turbulence intensity zone and the high near-bed Reynolds shear stress zone both get closer to the upstream slope, and further away from the downstream slope of the scour hole. At the equilibrium stage, sediment travels in a recirculating fashion, preventing the scoured hole from expanding further. Xie and Lim [10] investigated the effects of jet flipping on local scour downstream of a sluice gate. Nik and Narayanan [11] carried out experiments for the effect of sand sizes, sluice openings, efflux velocities, and lengths of aprons on the local scour downstream of an apron. Ibrahim [12] studied the impacts of block shapes on the flow pattern downstream of a radial gate. Valinia [13] investigated the effect of floor blocks and block spacing from the drainage duct under different flow conditions on scouring downstream of the resting basin. Moghadam et al. [14] evaluated the effects of a perforated sill and its position on the length of a favourable B-type hydraulic jump in a stilling basin. Pagliara and Palermo [15] examined the scour downstream of a block ramp for non-uniform bed material, and the effect of sills was investigated. The sediment distribution of non-uniform bed mixtures is investigated at the scour equilibrium configuration. It was observed that the sediment is more uniformly distributed in the upstream portion of the scour hole close to the ramp exit and that the coarsest particles are displaced in the central region of the scour hole. Pagliara et al. [16] studied the effect of the ramp slope and the geometry of the expanding stilling basin on the local scour and the hydraulic jump. Oliveto et al. [17] investigated the temporal evolution of local scour downstream of a spillway followed by a positive-step stilling basin. Recently, numerous researchers used numerical models to forecast the scour features downstream sluice gate. Mirzaei et al. [18] vestigated the effect of the cylindrical deflectors over the end sill on minimizing or eliminating scour downstream of a stilling basin. Guan et al. [19] used artificial neural networks with a backpropagation learning algorithm to estimate the temporal variation of scour profiles downstream of submerged weirs under clear water conditions. Mostaani and Azimi [20] evaluated a new analytical method for predicting the scour profile downstream of a submerged sluice gate with an apron. Aamir et al. [21] investigated the effect of a rough, rigid apron on scour downstream of sluice gates. Samma et al. [22] investigated the complex fluid-sediment interactions that influence the development of the scour hole and ridge systems downstream of a near-bottom jet using a three-dimensional (3D) flow simulation. They pointed out that the numerical model accurately reproduces the geometric characteristics of the scour hole. The model, however, overestimates the extent of the scour hole. The model, however, overestimates the extent of the scour hole. Sharafati et al. [23] proposed several novel hybrid adaptive neuro-fuzzy inference system (ANFIS) methods as predictive models to estimate scour depth downstream of a sluice gate. Yousif et al. [24] examined the applicability of a modern data-intelligence technique known as extreme learning machines (ELM) to simulate scour characteristics. They mentioned that applying ELM with non-dimensional data can provide good accuracy when modeling complex hydrological problems. Najafzadeh et al. [25] studied the effects of influencing parameters on the scouring process in order to derive an accurate predictive equation of local scour depth downstream of a sluice gate. Najafzadeh [26] used a method of data handling to predict the maximum scour depth downstream of grade-control structures. Ibrahim et al. [27] used nanomaterials (Silica fume) to minimize the local scour downstream of the sluice gate. According to the percentage of silica fume, they explained that the wet mix successfully decreased local scour volumes by 34.65% and 83.05% and decreased silting volumes by 33.35% and 89.42%. From the previous study review, it was found that one of the most effective ways to reduce scour is to focus on the method of dispersing using perforated sills. The study's main aim is to study the effect of using a perforated sill (with different porosities and different hole shapes) on the maximum scour depth and the energy dissipation in the presence of a mobile bed using experimental data and the development of theoretical equations.

To be able to study the effect of the perforated sill on the maximum scour depth downstream of a sluice gate, several preliminary experiments were performed. Based on the theoretic realization of the flow field between the sluice gate and the perforated sill, the majority of the flow parameters were characterized to perform the dimensional analysis as shown in Fig. (4).

(1)

B is the channel width, b is the contracted width of the channel, G is the gate opening, y_up is the upstream water depth, y1 is the initial water depth of jump, y3 is the water depth just downstream of the sluice gate, y4 is the depth of water at the end of submerged jump, Lj is the Jump length. g is the gravitational acceleration, E3 is the total energy just after the gate, E4 is the total energy at y4, and ΔE is the energy lost through jump.,ρ is the mass density of water, µ is the dynamic viscosity of water, A_sill is the total area of the perforated sill, A_hole is the Area for holes on the perforated sill, E_up is the total energy upstream the gate, d_sc is the max scour hole depth,V₁ is the velocity at venna contract, Osh is the hole shape factor, and F_G is the gate Froude number.

According to Buckingham's π-theorem and taking (G, g, and ρ) as repeated variables, the general form of relationship between these variables may be written as follows:

(2)

Where the relative energy loss through the hydraulic jump (E3- E4)/ E1=ΔE/E1 and the relative area of holes (sill porosity) Ar=A_hole/A_sill. The screen height, screen width, Median sediment diameter, and expansion ratio were constants throughout this study.

The effect of the relative sill porosity and the sill opening hole shape on the max scour depth downstream of the sluice gate was investigated.

Fig. (4). Definition sketch of the experimental model

Fig. (5). Relation between the relative maximum scour depth ds/G and Gate Froude number FG for different sill porosity.

4.2. Sill’s Porosity Effect on the Relative Energy Losses (∆E/E1).

Fig. (6) shows the relation between the Relative energy losses (∆E/E1) and the Gate Froude number (FG) for different gate opening (G =4, 5, and 6 cm) at a constant submerged ratio equal (). From the figure, it is observed that the Relative energy losses (∆E/E1) increase with increasing the Froude number for all experiments. The reason for this increase is the increase in turbulent flow downstream of the sills, which leads to an increase in the amount of energy loss as a result of their presence. In general, the dissipation of energy in the presence of sills shows a noticeable difference from the dissipation values in the absence of them. The sill with a porosity of 41.1% increases the dissipation of energy downstream of a sluice gate by 80%.

Fig. (6). Relation between the Relative energy losses ∆E/E1 and the Gate Froude number (FG) for different sill’s porosity.

4.3. Sill’s Porosity Effect on the Bed Morphology

The contour maps of bed morphology were drawn by using the Surfer program. Figs. (7) to 11) show the contour map of the bed for different cases of sill’s porosity at the same flow conditions (Q=12.6 L/s, G=4 cm) respectively. From these figures, it can be observed that the scour region is minimal in the case of Sill’s porosity of 41.1%. However, the deposition height and deposition length downstream of the gate are also smaller for the case of porosity (41.1%).

Fig. (7). Contour map of bed morphology for the case of no sill at (Q=12.6 L/s, G=4 cm).

Fig. (8). Contour map of bed morphology for the sill porosity of 10.3% at (Q=12.6 L/s, G=4 cm).

Fig. (9). Contour map of bed morphology for the sill porosity of 18.3% at (Q=12.6 L/s, G=4 cm).

Fig. (10). Contour map of bed morphology for the sill porosity of 28.5% at (Q=12.6 L/s, G=4 cm).

Fig. (11). Contour map of bed morphology for the sill porosity of 41.1% at (Q=12.6 L/s, G=4 cm).

Fig. (12). Relation between the relative scour depth ds/G and the Gate Froude Number (FG) for different opening shapes.

4.6. The Hole’s Shape Effect on the Bed Morphology

Figs. (14 to 18) shows the contour map of the bed for different cases of sill’s porosity at the same flow conditions (Q=14.6 L/s, G=4 cm) respectively. From these figures, it can be observed that the scour region is minimal in the case of a square hole shape. However, the deposition height and deposition length downstream of the gate are also smaller in the case of a square hole opening.

 

Fig. (13). Relation between the Relative energy losses ∆E/E1 and the Gate Froude Number (FG) for different hole shapes.

Fig. (14). Contour map of bed morphology for the case of no sill at (Q=14.6 L/s, G=4 cm).

Fig. (15). Contour map of bed morphology for the sill porosity of 41.1% at (Q=14.6 L/s, G=4 cm).

Fig. (16). Contour map of bed morphology for the square sill at (Q=14.6 L/s, G=4 cm).

Fig. (17). Contour map of bed morphology for the horizontal rectangular sill (Q=14.6 L/s, G=4 cm).

Fig. (18). Contour map of bed morphology for the vertical rectangular sill at (Q=14.6 L/s, G=4 cm).

Table 1. Equation conditions.

Variables	Range
Gate opening	4, 5, and 6 cm
Gate Froude number(FG)	1.10 to 2.70
perforated sill	Opening shape	Shape factor (Osh)	Porosity
	Square opening	1	41.10%
	Horizontal rectangular	1.09	41.10%
	vertical rectangular	1.31	41.10%
	Circular open 6mm diameter.	2.09	10.30%
	Circular open 8mm diameter.	1.97	18.30%
	Circular open 10mm diameter.	1.34	28.50%
	Circular open 12mm diameter.	1.06	41.10%
	No sill	1.66	100%

Table 2. Regression Statistics.

Multiple R	0.975634017
R Square	0.951861736
Adjusted R Square	0.947979617
Standard Error	0.076064132
Observations	90

The regression analysis was applied for all simulated cases to have prediction models correlating the relative maximum scour depth with other independent parameters. Many trials were carried out to have a general equation representing the whole independent parameters. The determination coefficient for this equation was very small and cannot express the relative scour depth. Therefore, predicted equations for different simulated models were created as follow:

(3)

The proposed equation is valid for the following characteristics of different parameters as shown in Table 1. Therefore, this equation is not suggested to be used beyond the range of the parameters mentioned above. The associated errors for computing the maximum depths by Equation (3) were consistent and did not exceed ±7.60% as shown in Table 2. Fig. (19) shows the relation between Residuals and measured (ds/G). It was found that the predicted equations express well the measured data.

Fig. (19). Comparison between predicted and experimental (ds /G).

Experimental studies related to the sudden expansion of a stilling basin supported by a perforated sill were done to show the effect of the presence of the perforated sill on the maximum scour depth and the energy dissipation downstream of a sluice gate. The present study introduces the following results;

• The maximum scour depth increases with increasing the Froude number for all experiments.
• The sill with a porosity of 41.1% gave the minimum value of the maximum scour depth downstream of a sluice gate, and the sill with a porosity of 10.3% gave the maximum value of the maximum scour depth.
• The sill with a porosity of 41.1% reduces the maximum scour depth downstream of a sluice gate by 50%.
• The circular hole’s shape gave the maximum energy dissipation.
• The sill with a porosity of 41.1% increases the dissipation of energy downstream of a sluice gate by 80%.
• The perforated sill with a square porosity of 41.1% reduces the maximum scour depth downstream of a sluice gate by 60%.
• The scour region is minimal in the case of a square hole shape. However, the deposition height and deposition length downstream of the gate are also smaller in the case of a square hole opening.