# The Effect of Rough Rigid Apron on Scour Downstream of Sluice Gates

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## Abstract

**:**

## 1. Introduction

_{s}is the equilibrium scour depth; d

_{t}is the tailwater depth; and x

_{s}is the extent from the end of the stiff apron to the equilibrium scour depth.

_{d}= 12.78) and the lowest value of roughness (k

_{s}= 1 mm) [13]. For the highest value of roughness (k

_{s}= 5 mm), the least drop in the depth of scour was 93%, in comparison with a smooth apron. The average values of decrease in the length of the scour hole and the maximum scour depth for fine sand were 30.2% and 63.4%, respectively; whereas for coarse sand, these values were 44.2% and 20.6%, respectively [14]. Average decrease in the value of maximum scour depth under a launching apron was calculated to be 39%, having a minimum of 16.2% and a maximum of 57.3% [15]. Empirical equations were obtained for characteristic lengths of scour hole in non-uniform and uniform sediments, and guidelines were provided for designing a launching apron [16]. Aamir and Ahmad [17,18] investigated experimentally the characteristics of submerged jets causing scour downstream of an apron and developed an empirical equation for the prediction of equilibrium scour depth. Recently, researchers used soft-computing techniques to predict scour downstream of sluice gates and other hydraulic structures [19,20,21,22,23,24]. Aamir and Ahmad [25] put forth a review of scour under plane two-dimensional wall jets. Muller and Chanson [26] compared air entrapment in vertical plunging jets with that in the horizontal hydraulic jump. Aamir and Ahmad [27] investigated the flow characteristics of 2D horizontal jets and subsequent scour, and analyzed the effect of roughness of stiff apron on such characteristics. Studies have also been carried out to study the flow pattern and scour around other hydraulic structures [28,29,30,31,32,33]. It is quite evident that the primary emphasis of investigation has been the examination of flow characteristics and derivation of empirical equations for different parameters related to scour under 2D horizontal jets. However, the constriction of scour to avert damage to the foundation, and hence stability, of the hydraulic structure, especially in the case of wall jets, is a huge concern for engineers [34], which largely remains untouched.

## 2. Materials and Methods

_{s}= 1.00 mm, 1.79 mm, and 3.40 mm.

_{t}. The measurement of tailwater level and surface profile of water was carried out using a pointer gauge having an accuracy of ±1.0 mm.

^{3}to 1.3 × 10

^{4}.

^{2}and 1 × 1 mm

^{2}, respectively. The geometry of the scour hole that was traced along the transparent side wall of the flume was maintained at every longitudinal section of the flume, i.e., the flow, and hence, the scour profile was two-dimensional. To ensure this, some measurements of velocity profiles were made using a Nortek made Acoustic Doppler Velocimeter (ADV) at a number of x-y planes at distinct locations from the side wall (Figure 3), which revealed insignificant difference in the velocity distribution, signifying that the velocity profiles were constant at every transverse section of the flume, which validates the two-dimensional property of the flow. Measurement of the scour profiles at different vertical sections of the channel confirmed the two-dimensional property of the scour profile. The 2D property was also verified with the help of the in-built “bottom check” function of the ADV and matching this depth with that measured through the glass side walls. There was a negligible difference between the two, negating the existence of potential wall effects.

^{0.5}; g = gravitational acceleration. Clear-water scour condition was maintained during the experiments. Table 2 presents the range of experimental data collected in this study.

## 3. Dimensional Analysis

_{g}= geometric standard deviation of sediments; ρ = mass density of water; and ρ

_{s}= mass density of sediments. For a two-phase flow phenomenon involving sediment-water interaction, the terms g, ρ, and ρ

_{s}can appropriately be grouped as one independent parameter Δg in functional representation of d

_{s}; where Δ = s − 1; s = relative density of sediments; g = acceleration due to gravity. Also, since the flow is turbulent, the effect of kinematic viscosity ν on maximum scour depth is negligible (Rajaratnam, 1981). σ

_{g}also has a negligible effect upon maximum scour depth (Aamir and Ahmad, 2019). Using the Buckingham π theorem, the following is obtained:

_{s}/a; $\tilde{L}$ = L/a; ${\tilde{k}}_{s}$ = k

_{s}/a; ${\tilde{d}}_{t}$ = d

_{t}/a; and ${\tilde{d}}_{50}$ = d

_{50}/a, then the functional form can be written as

## 4. Results and Discussion

#### 4.1. Effect of Different Parameters on Maximum Scour Depth

_{s}/a on apron roughness/sluice opening ratio k

_{s}/a, for different values of sluice opening a and tailwater level d

_{t}. It is clearly evident from the figure that the equilibrium depth of scour decreases considerably with an increase in roughness height of the apron. Also, there is a sharp decrease in maximum scour depth for k

_{s}/a < 0.2. For values of k

_{s}/a > 0.2, the effect of apron roughness on equilibrium scour depth diminishes gradually. The maximum reduction in scour depth occurs for the run c17C (a = 15 mm, k

_{s}= 3.40 mm, and d

_{t}= 0.125 m), while the minimum value is observed for run a15C (a = 10 mm, k

_{s}= 1.00 mm, and d

_{t}= 0.15 m), with average reduction being in the range of 70–83%.

_{s}/a with the ratio of sediment size and sluice opening d

_{50}/a for different values of sluice opening a and tailwater level d

_{t}. It is manifest from the figure that the maximum depth of scour decreases with increasing sediment size, which implies that the value of d

_{s}is lower for coarser sediment. This decrease in d

_{s}can be attributed to the reduction in the shear stress of the bed influencing the scour hole as the scour hole develops. Therefore, the equilibrium condition of scour is achieved at a lesser scour depth d

_{s}for sediments having coarser grain size, which require relatively larger critical shear stress to begin motion. On the other hand, an increase in sluice opening a reduces the issuing jet velocity V, as a consequence of which, the jet possesses lower scour potential (or lesser energy) at larger values of a. An interesting feature observed is that there is a sharp decrease in d

_{s}/a for d

_{50}/a < 0.15. Then, there is a considerable fall in the rate of reduction of d

_{s}/a, which becomes almost independent of d

_{50}/a for d

_{50}/a > 0.5.

_{s}/a on L/a for different sluice openings a and tailwater levels d

_{t}. It is evident that there is a decrease in d

_{s}/a with an increase in L/a. However, this reduction is rather small, having a maximum reduction of 12.2% and an average of 7.8%. Diffusion of the submerged jet over the stiff apron prior to encountering the sediment bed reduces its erosive capacity. The jet is diffused more as it travels a longer length over the apron, hence reducing its erosive capacity as it exerts a lesser amount of shear stress over the sediment bed, causing a decrease in d

_{s}. A comparison between different sluice openings indicates a reduction in d

_{s}for larger a.

_{d}[=V/(Δgd

_{50})

^{0.5}] on normalized maximum scour depth d

_{s}/a for different sediment sizes, tailwater levels, and apron lengths. It is apparent from the figures that the maximum depth of scour d

_{s}increases as densimetric Froude number F

_{d}increases. Densimetric Froude number is a property of inertial force as well as sediment size. When the inertial force is more (i.e., the value of V is increased in response to a decrease in the sluice opening), the value of F

_{d}also increases. Since F

_{d}is a function of d

_{50}, hence it is also evident in Figure 7a that F

_{d}is inversely proportional to the square root of d

_{50}. Therefore, d

_{s}increases with a decrease in d

_{50}, since a higher amount of energy is required by the incoming jet to move particles of larger size. The influence of length of stiff apron L on maximum scour depth d

_{s}is also apparent from this figure, which shows that there is an increase in d

_{s}with decreasing L.

_{s}/a on tailwater level/sluice opening ratio d

_{t}/a for different Froude numbers F and sediment sizes d

_{50}. A drooping nature is seen for the variation of d

_{s}/a with d

_{t}/a. It shows that a critical level of tailwater exists corresponding to the minimum d

_{s}/a [11,15]. A comparison between different Froude numbers F indicates that d

_{s}/a increases with an increase in Froude number F. This sagging nature can be partly ascribed to the change in the flow field and the scouring process with changing tailwater levels. At higher tailwater levels, reversal of flow is more prominent as compared to lower tailwater levels. Thus, this reversed flow, which develops into a roller, causes a further increase in the equilibrium depth of scour at higher tailwater levels. This effect, however, diminishes as the tailwater level is increased further and the maximum scour depth becomes independent of tailwater level at very high tailwater depths.

#### 4.2. Estimation of Maximum Scour Depth

_{d}≤ 12.04, 20 ≤ L/a ≤ 100, 6.67 ≤ d

_{t}/a ≤ 40, and k

_{s}/a ≤ 0.23. Data acquired from the present study was utilized to calculate the maximum depth of scour from Dey and Sarkar (2006) equation for comparison. Figure 9 shows the comparison of experimental d

_{s}/a with that computed using Dey and Sarkar [15] equation. The equation proposed by Dey and Sarkar [15] mostly under-predicts maximum scour depth for present data. Also, this equation cannot be used for equilibrium scour depth prediction in rough aprons.

_{s}/a with that computed using Equation (4). The coefficient of regression between the computed and observed maximum scour depths is 0.92. This indicates that the computed maximum scour depth is in conformity with the observed maximum scour depth. Other statistical parameters were found to be as follows: RMSE = 0.09, MAPE = 0.32, and Scatter Index = 0.24. The experimental data of Chatterjee et al. [7] and Dey and Sarkar [15] were also used to calculate the maximum depth of scour using Equation (4) and plotted in the same figure for comparison. The equation fairly predicts the maximum depth of scour for the experimental data of Dey and Sarkar [15], while over-predictions are observed for the data of Chatterjee et al. [7].

#### 4.3. Scour Profiles

_{0−3}and n

_{0−3}= coefficients. A small amount of sediment was washed out at the edge of the apron due to flow-reversal, resulting in exposure of a small vertical portion of the apron, having a depth ɛd

_{st}, where ɛ is a parameter with a value less than 1. Scour profile characteristics and boundary conditions can be used to determine the coefficients m

_{0}, m

_{1}, m

_{2}, and m

_{3}, and n

_{0}, n

_{1}, n

_{2}, and n

_{3}.

_{0}= −0.15, m

_{1}= −0.58, m

_{2}= 0.114, m

_{3}= −0.005, n

_{0}= 0.934, n

_{1}= −0.561, n

_{2}= 0.077, and n

_{3}= −0.003. Figure 12 shows that the normalized scour profiles are in good agreement with those computed from Equations (5) and (6).

_{s}and deposition of sediment as ridge ξ

_{d}can be obtained as:

#### 4.4. Temporal Variation of Scour Depth

_{st}at any time t as:

_{50}= median particle size of sediment. In functional form, the normalized time scale can be written as:

_{c}/(Δρgd

_{50})]; τ

_{c}= threshold value of shear stress on horizontal bed; and ρ = mass density of water. Figure 13 shows the variation of ${T}_{\ast}$ with F

_{d}for different d

_{50}and ${\tau}_{c}^{\ast}$. It is evident that the non-dimensional time scale ${T}_{\ast}$ increases linearly with F

_{d}. For coarser sediments, the variation of ${T}_{\ast}$ with F

_{d}is relatively steeper. From the present study, it was revealed that equilibrium scour condition was reached at 6 h time for fine sediments, however, for coarser sediments, this time was even further reduced. However, some experiments were carried out for 10 h, but the equilibrium scour depths obtained after this time were similar to those obtained after 6 h. Therefore, equilibrium scour time was taken as 8 h in this study.

## 5. Conclusions

- The maximum scour depth reduces significantly with a rise in the roughness of stiff apron. Further, equilibrium scour depth decreases with increasing sediment size. It is more for a shorter length of the stiff apron than for longer aprons. Also, the maximum depth of scour is higher for smaller slit size of sluice gate a. An increase in the maximum scour depth is observed with increasing densimetric Froude number.
- The influence of depth of tailwater level on maximum scour depth is such that there exists a critical tailwater level conforming with the minimum value of maximum scour depth. Thereafter, an increase in the maximum scour depth is seen with an increase in tailwater level.
- A new empirical equation for the prediction of maximum scour depth under smooth and rough apron is proposed. The proposed equation takes into account the influence of apron roughness on maximum scour depth, while the existing equations do not account for this parameter. Polynomial equations are also proposed for scour profiles under smooth and rough aprons.
- The maximum scour depth predicted using the proposed equation, which is applicable to both smooth and rough aprons, is in conformity with that obtained experimentally.
- The temporal scour profiles at distinct intervals of time obey a particular resemblance in geometry, both in the case of rough and smooth aprons. The scour profiles can be obtained from the proposed polynomial equations, which are satisfactory. The time variation of depth of scour was scaled by an exponential law. There is a linear increase in the time scale with densimetric Froude number.
- There is a significant reduction observed in the maximum scour depth due to roughness, which is in the range of 70–83%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Run | d_{50}(mm) | a (mm) | k_{s}(mm) | d_{t}(m) | V (m/s) | L (m) | d_{s}(cm) |
---|---|---|---|---|---|---|---|

1A | 0.27 | 5 | 0 | 0.1 | 1.67 | 0.5 | 10.1 |

2A | 0.27 | 5 | 0 | 0.125 | 1.67 | 0.5 | 9.5 |

3A | 0.27 | 5 | 0 | 0.15 | 1.67 | 0.5 | 10.1 |

4A | 0.27 | 10 | 0 | 0.1 | 0.83 | 0.5 | 5.5 |

5A | 0.27 | 10 | 0 | 0.125 | 0.83 | 0.5 | 4.8 |

6A | 0.27 | 10 | 0 | 0.15 | 0.83 | 0.5 | 4.9 |

7A | 0.27 | 15 | 0 | 0.1 | 0.56 | 0.5 | 4.0 |

8A | 0.27 | 15 | 0 | 0.125 | 0.56 | 0.5 | 3.8 |

9A | 0.27 | 15 | 0 | 0.15 | 0.56 | 0.5 | 3.9 |

10B | 6.70 | 5 | 0 | 0.1 | 2.67 | 0.5 | 4.5 |

10B1 | 6.70 | 5 | 0 | 0.11 | 2.67 | 0.5 | 4.2 |

11B | 6.70 | 5 | 0 | 0.125 | 2.67 | 0.5 | 4.6 |

11B1 | 6.70 | 5 | 0 | 0.14 | 2.67 | 0.5 | 4.7 |

12B | 6.70 | 5 | 0 | 0.15 | 2.67 | 0.5 | 4.9 |

12B1 | 6.70 | 5 | 0 | 0.16 | 2.67 | 0.5 | 5.1 |

12B2 | 6.70 | 5 | 0 | 0.18 | 2.67 | 0.5 | 5.2 |

12B3 | 6.70 | 5 | 0 | 0.20 | 2.67 | 0.5 | 5.4 |

13B | 6.70 | 10 | 0 | 0.1 | 1.33 | 0.5 | 3.8 |

13B1 | 6.70 | 10 | 0 | 0.11 | 1.33 | 0.5 | 3.6 |

14B | 6.70 | 10 | 0 | 0.125 | 1.33 | 0.5 | 3.9 |

14B1 | 6.70 | 10 | 0 | 0.14 | 1.33 | 0.5 | 4.0 |

15B | 6.70 | 10 | 0 | 0.15 | 1.33 | 0.5 | 4.2 |

15B1 | 6.70 | 10 | 0 | 0.16 | 1.33 | 0.5 | 4.3 |

15B2 | 6.70 | 10 | 0 | 0.18 | 1.33 | 0.5 | 4.5 |

15B3 | 6.70 | 10 | 0 | 0.20 | 1.33 | 0.5 | 4.6 |

16B | 6.70 | 15 | 0 | 0.1 | 0.89 | 0.5 | 1.1 |

16B1 | 6.70 | 15 | 0 | 0.11 | 0.89 | 0.5 | 1.0 |

17B | 6.70 | 15 | 0 | 0.125 | 0.89 | 0.5 | 1.3 |

17B1 | 6.70 | 15 | 0 | 0.14 | 0.89 | 0.5 | 1.5 |

18B | 6.70 | 15 | 0 | 0.15 | 0.89 | 0.5 | 1.6 |

18B1 | 6.70 | 15 | 0 | 0.16 | 0.89 | 0.5 | 1.7 |

18B2 | 6.70 | 15 | 0 | 0.18 | 0.89 | 0.5 | 1.9 |

18B3 | 6.70 | 15 | 0 | 0.20 | 0.89 | 0.5 | 2.0 |

10C | 2.67 | 5 | 0 | 0.1 | 2.67 | 0.5 | 5.3 |

10C1 | 2.67 | 5 | 0 | 0.11 | 2.67 | 0.5 | 5.2 |

11C | 2.67 | 5 | 0 | 0.125 | 2.67 | 0.5 | 5.5 |

11C1 | 2.67 | 5 | 0 | 0.14 | 2.67 | 0.5 | 5.8 |

12C | 2.67 | 5 | 0 | 0.15 | 2.67 | 0.5 | 6.0 |

12C1 | 2.67 | 5 | 0 | 0.16 | 2.67 | 0.5 | 6.1 |

12C2 | 2.67 | 5 | 0 | 0.18 | 2.67 | 0.5 | 6.3 |

12C3 | 2.67 | 5 | 0 | 0.20 | 2.67 | 0.5 | 6.4 |

13C | 2.67 | 10 | 0 | 0.1 | 1.33 | 0.5 | 4.2 |

13C1 | 2.67 | 10 | 0 | 0.11 | 1.33 | 0.5 | 4.1 |

14C | 2.67 | 10 | 0 | 0.125 | 1.33 | 0.5 | 4.7 |

14C1 | 2.67 | 10 | 0 | 0.14 | 1.33 | 0.5 | 4.5 |

15C | 2.67 | 10 | 0 | 0.15 | 1.33 | 0.5 | 4.5 |

15C1 | 2.67 | 10 | 0 | 0.16 | 1.33 | 0.5 | 4.6 |

15C2 | 2.67 | 10 | 0 | 0.18 | 1.33 | 0.5 | 4.8 |

15C3 | 2.67 | 10 | 0 | 0.20 | 1.33 | 0.5 | 4.9 |

16C | 2.67 | 15 | 0 | 0.1 | 0.89 | 0.5 | 2.5 |

16C1 | 2.67 | 15 | 0 | 0.11 | 0.89 | 0.5 | 2.4 |

17C | 2.67 | 15 | 0 | 0.125 | 0.89 | 0.5 | 2.9 |

17C1 | 2.67 | 15 | 0 | 0.14 | 0.89 | 0.5 | 2.8 |

18C | 2.67 | 15 | 0 | 0.15 | 0.89 | 0.5 | 2.9 |

18C1 | 2.67 | 15 | 0 | 0.16 | 0.89 | 0.5 | 3.0 |

18C2 | 2.67 | 15 | 0 | 0.18 | 0.89 | 0.5 | 3.2 |

18C3 | 2.67 | 15 | 0 | 0.20 | 0.89 | 0.5 | 3.3 |

10D | 1.79 | 5 | 0 | 0.1 | 2.67 | 0.5 | 5.7 |

10D1 | 1.79 | 5 | 0 | 0.11 | 2.67 | 0.5 | 5.5 |

11D | 1.79 | 5 | 0 | 0.125 | 2.67 | 0.5 | 5.4 |

11D1 | 1.79 | 5 | 0 | 0.14 | 2.67 | 0.5 | 5.6 |

12D | 1.79 | 5 | 0 | 0.15 | 2.67 | 0.5 | 5.7 |

12D1 | 1.79 | 5 | 0 | 0.16 | 2.67 | 0.5 | 5.8 |

12D2 | 1.79 | 5 | 0 | 0.18 | 2.67 | 0.5 | 6.1 |

12D3 | 1.79 | 5 | 0 | 0.20 | 2.67 | 0.5 | 6.3 |

13D | 1.79 | 10 | 0 | 0.1 | 1.33 | 0.5 | 4.4 |

13D1 | 1.79 | 10 | 0 | 0.11 | 1.33 | 0.5 | 4.2 |

14D | 1.79 | 10 | 0 | 0.125 | 1.33 | 0.5 | 4.0 |

14D1 | 1.79 | 10 | 0 | 0.14 | 1.33 | 0.5 | 4.3 |

15D | 1.79 | 10 | 0 | 0.15 | 1.33 | 0.5 | 5.0 |

15D1 | 1.79 | 10 | 0 | 0.16 | 1.33 | 0.5 | 5.5 |

15D2 | 1.79 | 10 | 0 | 0.18 | 1.33 | 0.5 | 5.8 |

15D3 | 1.79 | 10 | 0 | 0.20 | 1.33 | 0.5 | 6.0 |

16D | 1.79 | 15 | 0 | 0.1 | 0.89 | 0.5 | 3.5 |

16D1 | 1.79 | 15 | 0 | 0.11 | 0.89 | 0.5 | 3.3 |

17D | 1.79 | 15 | 0 | 0.125 | 0.89 | 0.5 | 3.2 |

17D1 | 1.79 | 15 | 0 | 0.14 | 0.89 | 0.5 | 3.3 |

18D | 1.79 | 15 | 0 | 0.15 | 0.89 | 0.5 | 3.4 |

18D1 | 1.79 | 15 | 0 | 0.16 | 0.89 | 0.5 | 3.5 |

18D2 | 1.79 | 15 | 0 | 0.18 | 0.89 | 0.5 | 4.8 |

18D3 | 1.79 | 15 | 0 | 0.20 | 0.89 | 0.5 | 5.2 |

19D | 1.79 | 5 | 0 | 0.1 | 2.67 | 0.4 | 5.6 |

20D | 1.79 | 5 | 0 | 0.125 | 2.67 | 0.4 | 5.5 |

21D | 1.79 | 5 | 0 | 0.15 | 2.67 | 0.4 | 5.9 |

22D | 1.79 | 10 | 0 | 0.1 | 1.33 | 0.4 | 4.8 |

23D | 1.79 | 10 | 0 | 0.125 | 1.33 | 0.4 | 4.7 |

24D | 1.79 | 10 | 0 | 0.15 | 1.33 | 0.4 | 4.9 |

25D | 1.79 | 15 | 0 | 0.1 | 0.89 | 0.4 | 4.2 |

26D | 1.79 | 15 | 0 | 0.125 | 0.89 | 0.4 | 4.2 |

27D | 1.79 | 15 | 0 | 0.15 | 0.89 | 0.4 | 4.3 |

28D | 1.79 | 5 | 0 | 0.1 | 2.67 | 0.3 | 5.9 |

29D | 1.79 | 5 | 0 | 0.125 | 2.67 | 0.3 | 5.7 |

30D | 1.79 | 5 | 0 | 0.15 | 2.67 | 0.3 | 6.1 |

31D | 1.79 | 10 | 0 | 0.1 | 1.33 | 0.3 | 5.2 |

32D | 1.79 | 10 | 0 | 0.125 | 1.33 | 0.3 | 5.0 |

33D | 1.79 | 10 | 0 | 0.15 | 1.33 | 0.3 | 5.5 |

34D | 1.79 | 15 | 0 | 0.1 | 0.89 | 0.3 | 4.8 |

35D | 1.79 | 15 | 0 | 0.125 | 0.89 | 0.3 | 4.6 |

36D | 1.79 | 15 | 0 | 0.15 | 0.89 | 0.3 | 4.9 |

a10C | 2.67 | 5 | 1.00 | 0.1 | 2.67 | 0.5 | 3.4 |

a11C | 2.67 | 5 | 1.00 | 0.125 | 2.67 | 0.5 | 2.8 |

a12C | 2.67 | 5 | 1.00 | 0.15 | 2.67 | 0.5 | 3.6 |

a13C | 2.67 | 10 | 1.00 | 0.1 | 1.33 | 0.5 | 2.8 |

a14C | 2.67 | 10 | 1.00 | 0.125 | 1.33 | 0.5 | 2.3 |

a15C | 2.67 | 10 | 1.00 | 0.15 | 1.33 | 0.5 | 3.1 |

a16C | 2.67 | 15 | 1.00 | 0.1 | 0.89 | 0.5 | 1.5 |

a17C | 2.67 | 15 | 1.00 | 0.125 | 0.89 | 0.5 | 1.1 |

a18C | 2.67 | 15 | 1.00 | 0.15 | 0.89 | 0.5 | 1.8 |

b10C | 2.67 | 5 | 1.79 | 0.1 | 2.67 | 0.5 | 2.1 |

b11C | 2.67 | 5 | 1.79 | 0.125 | 2.67 | 0.5 | 1.9 |

b12C | 2.67 | 5 | 1.79 | 0.15 | 2.67 | 0.5 | 2.4 |

b13C | 2.67 | 10 | 1.79 | 0.1 | 1.33 | 0.5 | 1.6 |

b14C | 2.67 | 10 | 1.79 | 0.125 | 1.33 | 0.5 | 1.5 |

b15C | 2.67 | 10 | 1.79 | 0.15 | 1.33 | 0.5 | 1.8 |

b16C | 2.67 | 15 | 1.79 | 0.1 | 0.89 | 0.5 | 1.4 |

b17C | 2.67 | 15 | 1.79 | 0.125 | 0.89 | 0.5 | 1.3 |

b18C | 2.67 | 15 | 1.79 | 0.15 | 0.89 | 0.5 | 1.5 |

c10C | 2.67 | 5 | 3.40 | 0.1 | 2.67 | 0.5 | 1.6 |

c11C | 2.67 | 5 | 3.40 | 0.125 | 2.67 | 0.5 | 1.3 |

c12C | 2.67 | 5 | 3.40 | 0.15 | 2.67 | 0.5 | 1.6 |

c13C | 2.67 | 10 | 3.40 | 0.1 | 1.33 | 0.5 | 1.1 |

c14C | 2.67 | 10 | 3.40 | 0.125 | 1.33 | 0.5 | 0.9 |

c15C | 2.67 | 10 | 3.40 | 0.15 | 1.33 | 0.5 | 1.3 |

c16C | 2.67 | 15 | 3.40 | 0.1 | 0.89 | 0.5 | 0.7 |

c17C | 2.67 | 15 | 3.40 | 0.125 | 0.89 | 0.5 | 0.5 |

c18C | 2.67 | 15 | 3.40 | 0.15 | 0.89 | 0.5 | 0.8 |

## References

- Rouse, H. Criteria for similarity in transportation of sediment. In Proceedings of the 1st Hydraulic Conference, Iowa City, IA, USA, 12–15 June 1939; pp. 33–49. [Google Scholar]
- Laursen, E.M. Observations of the Nature of Scour. In Proceedings of the 5th Hydraulic Conference, University of Iowa, Iowa City, IA, USA, 9–12 June 1952; pp. 179–197. [Google Scholar]
- Tarapore, Z.S. Scour below a submerged sluice gate. Master’s Thesis, University of Minnesota, Minneapolis, MN, USA, 1956. [Google Scholar]
- Hogg, A.J.; Huppert, H.E.; Dade, W.B. Erosion by planar turbulent wall jets. J. Fluid Mech.
**1997**, 338, 317–340. [Google Scholar] [CrossRef] [Green Version] - Carstens, M.R. Similarity laws for localized scour. J. Hydraul. Div.
**1966**, 92, 13–36. [Google Scholar] [CrossRef] - Chatterjee, S.S.; Ghosh, S.N. Submerged horizontal jet over erodible bed. J. Hydraul. Div.
**1980**, 106, 1765–1782. [Google Scholar] [CrossRef] - Chatterjee, S.S.; Ghosh, S.N.; Chatterjee, M. Local scour due to submerged horizontal jet. J. Hydraul. Eng.
**1994**, 120, 973–992. [Google Scholar] [CrossRef] - Rajaratnam, N. Erosion by plane turbulent jets. J. Hydraul. Res.
**1981**, 19, 339–358. [Google Scholar] [CrossRef] - Rajaratnam, N.; Macdougall, R.K. Erosion by plane wall jets with minimum tail water. J. Hydraul. Eng.
**1983**, 109, 1061–1064. [Google Scholar] [CrossRef] - Hassan, N.M.K.N.; Narayanan, R. Local scour downstream of an apron. J. Hydraul. Eng.
**1985**, 111, 1371–1385. [Google Scholar] [CrossRef] - Ali, K.H.M.; Lim, S.Y. Local scour caused by submerged wall jets. Proc. Inst. Civ. Eng.
**1986**, 81, 607–645. [Google Scholar] - Aderibigbe, O.; Rajaratnam, N. Effect of sediment gradation on erosion by plane turbulent wall jets. J. Hydraul. Eng.
**1998**, 124, 1034–1042. [Google Scholar] [CrossRef] - Hamidifar, H.; Omid, M.H.; Nasrabadi, M. Scour downstream of a rough rigid apron. World Appl. Sci. J.
**2011**, 14, 1169–1178. [Google Scholar] - Ali, H.M.; El Gendy, M.M.; Mirdan, A.M.H.; Ali, A.A.M.; Abdelhaleem, F.S.F. Minimizing downstream scour due to submerged hydraulic jump using corrugated aprons. Ain Shams Eng. J.
**2014**, 5, 1059–1069. [Google Scholar] [CrossRef] [Green Version] - Dey, S.; Sarkar, A. Scour downstream of an apron due to submerged horizontal jets. J. Hydraul. Eng.
**2006**, 132, 246–257. [Google Scholar] [CrossRef] - Sarkar, A.; Dey, S. Scour downstream of aprons caused by sluices. Proc. Inst. Civ. Eng. Water Manag.
**2005**, 158, 55–64. [Google Scholar] [CrossRef] - Aamir, M.; Ahmad, Z. Estimation of scour depth downstream of an apron under 2D horizontal jets. In Proceedings of the HYDRO 2015 International—20th International Conference on Hydraulics, Water Resources and River Engineering, Indian Institute of Technology, Roorkee, India, 17–19 December 2015. [Google Scholar]
- Aamir, M.; Ahmad, Z. Prediction of local scour depth downstream of an apron under wall jets. In Development of Water Resources in India; Garg, V., Singh, V., Raj, V., Eds.; Water Science and Technology Library; Springer: Cham, Switzerland, 2017; Volume 75, pp. 375–385. [Google Scholar]
- Azamathulla, H.M.; Ahmad, Z. Gene-expression programming for transverse mixing coefficient. J. Hydrol.
**2012**, 434–435, 142–148. [Google Scholar] [CrossRef] - Azamathulla, H.M.; Deo, M.C.; Deolalikar, P.B. Neural networks for estimation of scour downstream of a ski-jump bucket. J. Hydraul. Eng.
**2005**, 131, 898–908. [Google Scholar] [CrossRef] - Azamathulla, H.M.; Deo, M.C.; Deolalikar, P.B. Estimation of scour below spillways using neural networks. J. Hydraul. Res.
**2006**, 44, 61–69. [Google Scholar] [CrossRef] - Azamathulla, H.M.; Ghani, A.A.; Zakaria, N.A.; Guven, A. Genetic programming to predict bridge pier scour. J. Hydraul. Eng.
**2010**, 136, 165–169. [Google Scholar] [CrossRef] [Green Version] - Bashiri, H.; Sharifi, E.; Singh, V.P. Prediction of local scour depth downstream of sluice gates using harmony search algorithm and artificial neural networks. J. Irrig. Drain. Eng.
**2018**, 144, 06018002. [Google Scholar] [CrossRef] - Najafzadeh, M.; Oliveto, G. More reliable predictions of clear-water scour depth at pile groups by robust artificial intelligence techniques while preserving physical consistency. Soft Comput.
**2021**, 25, 5723–5746. [Google Scholar] [CrossRef] - Aamir, M.; Ahmad, Z. Review of literature on local scour under plane turbulent wall jets. Phys. Fluids
**2016**, 28, 105102. [Google Scholar] [CrossRef] - Muller, L.; Chanson, H. Singular air entrapment at vertical and horizontal supported jets: Plunging jets versus hydraulic jumps. Environ. Fluid Mech.
**2020**, 20, 1075–1100. [Google Scholar] [CrossRef] - Aamir, M.; Ahmad, Z. Effect of apron roughness on flow characteristics and scour depth under submerged wall jets. Acta Geophys. 2021; in press. [Google Scholar] [CrossRef]
- Asadollahi, M.; Vaghefi, M.; Akbari, M. Effect of the position of perpendicular pier groups in a sharp bend on flow and scour patterns: Numerical simulation. J. Braz. Soc. Mech. Sci. Eng.
**2020**, 42, 422. [Google Scholar] [CrossRef] - Bhave, S.; Kumar, S.; Singh, U.K.; Pandey, M.; Ahmad, Z. Experimental investigation of a trench weir with T-shaped bars. J. Braz. Soc. Mech. Sci. Eng.
**2020**, 42, 535. [Google Scholar] [CrossRef] - Dehghan, D.; Vaghefi, M.; Ghodsian, M. Experimental study of the effect of the length-to-width ratio and skewness angles of the pier installed at the bend on scour pattern. J. Braz. Soc. Mech. Sci. Eng.
**2021**, 43, 150. [Google Scholar] [CrossRef] - Pandey, M.; Oliveto, G.; Pu, J.H.; Sharma, P.K.; Ojha, C.S.P. Pier scour prediction in non-uniform gravel beds. Water
**2020**, 12, 1696. [Google Scholar] [CrossRef] - Vaghefi, M.; Faraji, B.; Akbari, M.; Eghbalzadeh, A. Numerical investigation of flow pattern around a T-shaped spur dike in the vicinity of attractive and repelling protective structures. J. Braz. Soc. Mech. Sci. Eng.
**2018**, 40, 93. [Google Scholar] - Vaghefi, M.; Solati, S.; Chooplou, C.H. The effect of upstream T-shaped spur dike on reducing the amount of scouring around downstream bridge pier located at a 180° sharp bend. Int. J. River Basin Manag.
**2021**, 19, 307–318. [Google Scholar] [CrossRef] - Bestawy, A.; Eltahawy, T.; Alsaluli, A.; Almaliki, A.; Alqurashi, M. Reduction of local scour around a bridge pier by using different shapes of pier slots and collars. Water Supply
**2020**, 20, 1006–1015. [Google Scholar] [CrossRef] - Chavan, R.; Kumar, B. Prediction of scour depth and dune morphology around circular bridge piers in seepage affected alluvial channels. Environ. Fluid Mech.
**2018**, 18, 923–945. [Google Scholar] [CrossRef] - Keshavarzi, A.; Shrestha, C.K.; Melville, B.; Khabbaz, H.; Ranjbar-Zahedani, M.; Ball, J. Estimation of maximum scour depths at upstream of front and rear piers for two in-line circular columns. Environ. Fluid Mech.
**2018**, 18, 537–550. [Google Scholar] [CrossRef] - Pandey, M.; Sharma, P.K.; Ahmad, Z.; Singh, U.K. Experimental investigation of clear-water temporal scour variation around bridge pier in gravel. Environ. Fluid Mech.
**2018**, 18, 871–890. [Google Scholar] [CrossRef] - Aamir, M.; Ahmad, Z. Estimation of maximum scour depth downstream of an apron under submerged wall jets. J. Hydroinformatics
**2019**, 21, 523–540. [Google Scholar] [CrossRef] - Sumer, B.M.; Christiansen, N.; Fredsoe, J. Influence of cross section on wave scour around piles. J. Waterw. Port Coast. Ocean. Eng.
**1993**, 119, 477–495. [Google Scholar] [CrossRef]

Median Size d _{50}(mm) | Geometric Standard Deviation σ _{g} | Relative Density s | Angle of Repose ϕ (Degree) | Shields Parameter ${\tau}_{c}^{*}$ |
---|---|---|---|---|

0.27 | 1.45 | 2.65 | 29 | 0.039 |

1.79 | 1.14 | 2.65 | 31.5 | 0.04 |

2.67 | 1.11 | 2.65 | 33 | 0.043 |

6.70 | 1.26 | 2.65 | 37.5 | 0.055 |

No. of Experimental Runs | d_{50}(mm) | a (mm) | k_{s}(mm) | d_{t}(m) | V (m/s) | L (m) | d_{s}(cm) |
---|---|---|---|---|---|---|---|

126 | 0.27–6.70 | 5–15 | 0–3.40 | 0.1–0.2 | 0.56–2.67 | 0.3–0.5 | 0.5–10.1 |

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**MDPI and ACS Style**

Aamir, M.; Ahmad, Z.; Pandey, M.; Khan, M.A.; Aldrees, A.; Mohamed, A.
The Effect of Rough Rigid Apron on Scour Downstream of Sluice Gates. *Water* **2022**, *14*, 2223.
https://doi.org/10.3390/w14142223

**AMA Style**

Aamir M, Ahmad Z, Pandey M, Khan MA, Aldrees A, Mohamed A.
The Effect of Rough Rigid Apron on Scour Downstream of Sluice Gates. *Water*. 2022; 14(14):2223.
https://doi.org/10.3390/w14142223

**Chicago/Turabian Style**

Aamir, Mohammad, Zulfequar Ahmad, Manish Pandey, Mohammad Amir Khan, Ali Aldrees, and Abdullah Mohamed.
2022. "The Effect of Rough Rigid Apron on Scour Downstream of Sluice Gates" *Water* 14, no. 14: 2223.
https://doi.org/10.3390/w14142223