# Research on the Influence of Siltation Height of Check Dams the on Discharge Coefficient of Broad-Crested Weirs

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^{2}

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## Abstract

**:**

## 1. Introduction

^{2}. There are 5655 large check dams whose storage capacity is 500,000 to 5,000,000 m

^{3}, with a total storage capacity of 5.701 billion m

^{3}. Most of these large check dams are “two pieces”, lacking flood discharge facilities, so the main reinforcement work is to add a spillway. However, there is still a lack of relevant research on how to discharge floods using check dam under massive siltation. In this paper, the broad-crested weir of the spillway of a check dam is taken as the research subject, and the influence of the siltation height close to the bottom of the spillway on the hydraulic characteristics and discharge coefficient is studied, which can provide a theoretical reference for the risk elimination and reinforcement works in the Loess Plateau.

## 2. Experimental Design

#### 2.1. Experimental System

#### 2.2. Physical Model

_{L}= 14.8, the flow scale to λ

_{Q}= λ

_{L}

^{2.5}= 842.66, and the discharge scale to λ

_{V}= λ

_{L}

^{0.5}= 3.85.

#### 2.3. Measurement Scheme

#### 2.4. Experimental Case

^{3}/h, 35 m

^{3}/h, 50 m

^{3}/h, 65 m

^{3}/h, and 75 m

^{3}/h. In the experiment, according to the principle of single variable, only one of the many target variables is changed in each case.

#### 2.5. Test Principle

- (1)
- Average velocity of section$$v=\frac{Q}{A}$$
- (2)
- Total hydraulic head over the weir$${H}_{0}=H+\frac{{\alpha}_{0}{v}_{0}^{2}}{2g}$$
_{0}is the total head over the weir; H is the hydraulic head, that is, the height of the upstream water surface above the weir crest; V_{0}is the average velocity of the discharge section. - (3)
- Discharge calculation formula of the weir$$Q=\sigma \epsilon mb\sqrt{2g}{H}_{0}^{3/2}$$
_{0}is the total head over the weir.

## 3. Results

#### 3.1. Flow Pattern

^{3}/h and Q = 35 m

^{3}/h) the water level over the weir decreases more obviously as the siltation height increases. The water level decreases significantly when the siltation height increases to 13 cm, and the overall flow pattern is close to the open channel. In the high-discharge case, the change in siltation height has less influence on the flow pattern, and the overall flow pattern is still presented as a broad-created weir flow pattern.

#### 3.2. Variation in Water Surface Profile along the Weir

#### 3.2.1. Influence of Discharge on the Level of Flow at the Same Siltation Height

^{3}/h, 35 m

^{3}/h, 50 m

^{3}/h, 65 m

^{3}/h, and 75 m

^{3}/h, as shown in Figure 6.

#### 3.2.2. Influence of Siltation Height on the Level of Flow at the Same Discharge

^{3}/h, and the maximum change is Q = 65 m

^{3}/h. Taking the discharge Q = 20 m

^{3}/h as an example, at a siltation height of S = 0 cm, S = 5 cm, S = 7 cm, S = 10 cm, and S = 13 cm, the water surface profile reduction values of the adjacent siltation height in the first measurement section (30 cm before the weir) are 0.17 cm, 0.18 cm, 0.11 cm, and 0.22 cm, respectively, and the rates of change in the water surface line from the previous siltation height are 0.81%, 0.86%, 0.53%, and 1.06%, respectively. Compared with a discharge of Q = 20 m

^{3}/h, when the discharge was Q = 65 m

^{3}/h, the decrease in the water surface profile in the adjacent siltation height of the first measurement section (30 cm before the weir) is 0.55 cm, 0.80 cm, 0.72 cm, and 0.61 cm, respectively, and the rate of change in the water surface profile from the last siltation height is 1.99%, 2.95%, 2.73%, and 2.38%, respectively. The above analysis shows that the change in siltation height can affect the magnitude of the water surface profile of the weir flow, but the intensity of this effect is related to the discharge. The change in siltation height has the least effect on the surface line of weir flow at an incoming flow rate of Q = 20 m

^{3}/h, and the greatest effect is at a discharge of Q = 65 m

^{3}/h. The trend in the change in siltation height on the surface profile of the flow is as follows: with an increase in the siltation height, the surface profile of the flow under the same discharge condition gradually decreases.

#### 3.3. Distribution of the Velocity along the Weir

#### 3.3.1. Influence of Discharge on the Velocity of Flow at the Same Siltation Height

#### 3.3.2. Influence of Siltation Height on the Velocity of Flow at the Same Discharge

#### 3.4. Relationship between Hydraulic Head and Discharge or Siltation Height

_{0}of its overflow section is called the flow velocity in front of the weir. The measurement points should be selected at 15 to 75 cm upstream from the weir wall. To ensure consistent accuracy, the water level value of the C measurement point 30 cm upstream from the weir wall is used for calculation (see Figure 4). According to the test results, the relationship between the hydraulic head over the weir H and the discharge Q and the relationship between the hydraulic head over the weir H and the siltation height S are plotted, respectively, for each siltation height, in Figure 10 and Figure 11.

^{3}/h, Q = 35 m

^{3}/h, Q = 50 m

^{3}/h, Q = 65 m

^{3}/h, and Q = 75 m

^{3}/h) are −0.07, −0.11, −0.18, −0.24, and −0.17, respectively. It can be seen that the overall change in the hydraulic head with the siltation height is most obvious at a discharge of Q = 65 m

^{3}/h.

#### 3.5. Formula for Discharge Coefficient of the Broad-Crested Weir

_{0}.

_{0}represents the discharge coefficient, H is the hydraulic head, and B is the weir width.

_{a0}. Therefore, the discharge equation can be derived as

_{a0}represents the discharge coefficient of the weir with siltation, H is the hydraulic head, and B is the weir width.

_{a0}is

_{a0}and relative weir height P/H. From the analysis in the figure, it can be seen that the discharge coefficient gradually decreases with an increase in relative weir height at the same siltation height. Similarly, the trend of discharge coefficient change at each siltation height is roughly similar. The curvature of the discharge coefficient m

_{a0}versus weir height P/H gradually decreases with the increase in relative weir height P/H, and the decreasing trend gradually becomes slower.

_{a0}calculated by Equation (7). Figure 14 shows the discharge coefficient comparison diagram.

_{a0}in the presence of siltation is a function of the relative weir height P/H and the siltation height S together, m

_{a}

_{0}= f(P/H,S). On the one hand, the new formula is considered to be compatible with the established empirical Formula (8). On the other hand, it can accurately reflect the current siltation state of the dam. Therefore, we make dimensionless the new derivation and introduce the concept of relative siltation height α = S/H. Then the overall equation functional relationship should be m

_{a0}= f(P/H,S/P). Finally, from the actual measured data, the formula for the discharge coefficient m

_{a0}of a broad-crested weir in the presence of siltation can be obtained using MATLAB 2021b software and statistical analysis.

## 4. Conclusions

- (1)
- With an increase in the siltation height, the backwater phenomenon of the flow in the upstream part of the broad-crested weir gradually decreases. The water level over the weir decreases, and the overall flow pattern gradually develops towards the open channel. This means that floods will pass more easily through spillways.
- (2)
- In the same siltation height condition, the water surface profile along the flow increases with an increase in discharge. However, in the same discharge condition, the water surface profile along the flow decreases with an increase in the siltation height, which reflects that the increase in siltation height improves the overflow capacity of the broad-crested weir.
- (3)
- The effects of discharge and siltation height change on the surface velocity of a broad-crested weir are concentrated in the front part of the weir, and the effects on the back part of the weir are smaller. In the same siltation condition, the surface velocity of the flow in front of the weir increases with an increase in the discharge. In the same discharge condition, the surface velocity of the water in front of the broad-crested weir gradually increases with an increase in the siltation height.
- (4)
- From the above analysis of hydraulic characteristics, we know that the influence of siltation on overflow should be considered in engineering design work. Therefore, we propose a new formula to calculate the discharge coefficient that meets the accuracy requirements. It can be applied to the estimation of discharge in practical reinforcement work on check dams.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 6.**Variation in water surface profile at different discharges: (

**a**) S = 0 cm; (

**b**) S = 5 cm; (

**c**) S = 7 cm; (

**d**) S = 10 cm; (

**e**) S = 13 cm.

**Figure 7.**Variation in water surface profile at different siltation heights: (

**a1**) Q = 20 m

^{3}/h; (

**a2**) Q = 20 m

^{3}/h part; (

**b1**) Q = 65 m

^{3}/h; (

**b2**) Q = 65 m

^{3}/h part.

**Figure 8.**Velocity distribution diagram of flow at different discharges: (

**a**) S = 0 cm; (

**b**) S = 5 cm; (

**c**) S = 7 cm; (

**d**) S = 10 cm; (

**e**) S = 13 cm.

**Figure 9.**Velocity distribution diagram of flow at different siltation heights: (

**a**) Q = 20 m

^{3}/h; (

**b**) Q = 65 m

^{3}/h.

**Figure 15.**Comparison of discharge coefficient between test value and new formula value (

**a**) Fitting curve; (

**b**) Relative error.

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**MDPI and ACS Style**

Wang, Z.; Gui, L.; Zhang, J.; Li, Y. Research on the Influence of Siltation Height of Check Dams the on Discharge Coefficient of Broad-Crested Weirs. *Water* **2023**, *15*, 510.
https://doi.org/10.3390/w15030510

**AMA Style**

Wang Z, Gui L, Zhang J, Li Y. Research on the Influence of Siltation Height of Check Dams the on Discharge Coefficient of Broad-Crested Weirs. *Water*. 2023; 15(3):510.
https://doi.org/10.3390/w15030510

**Chicago/Turabian Style**

Wang, Zhijian, Lili Gui, Jiaxuan Zhang, and Yongye Li. 2023. "Research on the Influence of Siltation Height of Check Dams the on Discharge Coefficient of Broad-Crested Weirs" *Water* 15, no. 3: 510.
https://doi.org/10.3390/w15030510