# Influence of Multi-Cross Structures on the Flood Discharge Capacity of Mountain Rivers in the Yellow River Basin

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Mathematical Model

#### 2.2. Model Solution

## 3. Case Analysis and Results

#### 3.1. Overview of the Research Area

^{2}. There are many high mountains, valleys, pits and streams upstream of the Huang Stream, with torrents and surging waves during the rainy season. During the dry season, the river dries up, and the flow rate greatly changes. After inflow into Yiyuan County, the flow velocity declines, which facilitates sediment deposition, and the riverbed is relatively flat. The vegetation upstream of the Huang Stream is abundant. The terrain on both banks of the middle and lower reaches is low. In cases of high floods, the main river channel overflows into the low-lying areas on both banks, driving sediment into the river. Bridges and weirs have been built in the Huang Stream for flood and sand control purposes. The study area is located downstream from the Huang Strean reach where it joins the Dawen River and is depicted in yellow in Figure 3.

#### 3.2. River Simplification

#### 3.3. Hydraulic Calculation Boundary Conditions

^{3}/s and the Meijiayuan Stream having a peak flow of 35.8 m

^{3}/s. The water level at the confluence of the Huang Stream and Dawen River was set as the outlet boundary at 128.20 m.

#### 3.4. Flood Discharge Capacity under Current Conditions

#### 3.5. Analysis of the Influence of Weirs on the Flood Discharge Capacity

#### 3.6. Analysis of the Influence of Bridges on the Flood Discharge Capacity

_{0}, while the water level upstream of the bridge was recorded as H

_{1}. $\Delta \mathrm{H}$ represents the change in water level before and after removing the bridge, and $\Delta \mathrm{Z}$ represents the distance between the upstream water level and beam elevation. The findings are summarized in Table 2. A total of seventeen bridges were analyzed to assess their impact on flood discharge capacity. This analysis included flat-slab and arch bridges under different conditions, considering the presence or absence of bridges, as well as the number of bridge openings (one, two or three holes). The calculation results for each working condition are presented in Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18, Figure 19, Figure 20, Figure 21, Figure 22, Figure 23, Figure 24, Figure 25, Figure 26, Figure 27 and Figure 28.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Shih, D.S.; Yeh, G.T. Studying Inertia Effects in Open Channel Flow Using Saint-Venant Equations. Water
**2018**, 10, 1652. [Google Scholar] [CrossRef] [Green Version] - Wu, G.; Yang, F.; Huang, M. Study on seasonal channel flood routing model coupled with leakage term. S-to-N Water Trfs. Water Sci. Technol.
**2018**, 16, 33–37. [Google Scholar] - Reggiani, P.; Todini, E.; Meißner, D. On mass and momentum conservation in the variable-parameter Muskingum method. J. Hydrol.
**2016**, 543, 562–576. [Google Scholar] [CrossRef] - Kalinin, G.P.; Milyukov, P.I. On the computation of unsteady flow in open channels. Met. Gidrol.
**1957**, 10, 10–18. [Google Scholar] - Montes, N.; Aranda, J.Á.; García-Bartual, R. Real Time Flow Forecasting in a Mountain River Catchment Using Conceptual Models with Simple Error Correction Scheme. Water
**2020**, 12, 1484. [Google Scholar] [CrossRef] - Lee, E.H. Development of a New 8-Parameter Muskingum Flood Routing Model with Modified Inflows. Water
**2021**, 13, 3170. [Google Scholar] [CrossRef] - Li, Z.; He, M.; Yan, F.; Hu, Y.; Liu, Z.; Tong, B. Applications of channel flood routing methods in middle part of Huaihe River and Hutuo River. J. Hohai. Univ. Nat. Sci.
**2020**, 48, 95–101. [Google Scholar] - Fenton, J.D. Flood routing methods. J. Hydrol.
**2019**, 570, 251–264. [Google Scholar] [CrossRef] - Saeed, M.; Li, H.; Ullah, S.; Rahman, A.U.; Ali, A.; Khan, R.; Hassan, W.; Munir, I.; Alam, S. Flood Hazard Zonation Using an Artificial Neural Network Model: A Case Study of Kabul River Basin, Pakistan. Sustainability
**2021**, 13, 13953. [Google Scholar] [CrossRef] - Tamiru, H.; Dinka, M.O. Application of ANN and HEC-RAS model for flood inundation mapping in lower Baro Akobo River Basin, Ethiopia. J. Hydrol. Reg. Stud.
**2021**, 36, 100855. [Google Scholar] [CrossRef] - Liu, Z.; Feng, S.; Lan, F.; Chen, S.; Liang, H.; Fei, K. Regulation scheme of Shegong River based on watershed flood hazard analysis. Water Res. Prot.
**2018**, 34, 38–43+64. [Google Scholar] - Bulti, A.T. The Influence of Dam Construction on the Catchment Hydrologic Behavior and its Effects on a Discharge Forecast in Hydrological Models. Water Resour. Manag.
**2021**, 35, 2023–2037. [Google Scholar] [CrossRef] - Wang, Q.; Peng, W.; Dong, F.; Liu, X.; Ou, N. Simulating Flow of An Urban River Course with Complex Cross Sections Based on the MIKE21 FM Model. Water
**2020**, 12, 761. [Google Scholar] [CrossRef] [Green Version] - Karymbalis, E.; Andreou, M.; Batzakis, D.V.; Tsanakas, K.; Karalis, S. Integration of GIS-Based Multicriteria Decision Analysis and Analytic Hierarchy Process for Flood-Hazard Assessment in the Megalo Rema River Catchment (East Attica, Greece). Sustainability
**2021**, 13, 10232. [Google Scholar] [CrossRef] - Liu, Q.; Qin, Y.; Zhang, Y.; Li, Z. A coupled 1D–2D hydrodynamic model for flood simulation in flood detention basin. Nat. Hazard.
**2015**, 75, 1303–1325. [Google Scholar] [CrossRef] - Liu, J.; Wang, J.; Xiong, J.; Cheng, W.; Cui, X.; He, W.; He, Y.; Duan, Y.; Yang, G.; Wang, N. Dynamic Assessment of the Flood Risk at Basin Scale under Simulation of Land-Use Scenarios and Spatialization Technology of Factor. Water
**2021**, 13, 3239. [Google Scholar] [CrossRef] - He, C.; Wei, J.; Song, Y.; Luo, J.-J. Seasonal Prediction of Summer Precipitation in the Middle and Lower Reaches of the Yangtze River Valley: Comparison of Machine Learning and Climate Model Predictions. Water
**2021**, 13, 3294. [Google Scholar] [CrossRef] - Liu, L.; Wu, Z.; Li, Q. Overtopping Risk Analysis of Earth Dams Considering Effects of Failure Duration of Release Structures. Complexity
**2020**, 2020, 3528350. [Google Scholar] [CrossRef] - Malik, R.; Setia, B. Interference between pier models and its effects on scour depth. SN Appl. Sci.
**2019**, 2, 68. [Google Scholar] [CrossRef] [Green Version] - Subedi, A.; Sharma, S.; Islam, A.; Lamichhane, N. Quantification of the Effect of Bridge Pier Encasement on Headwater Elevation Using HEC-RAS. Hydrology
**2019**, 6, 25. [Google Scholar] [CrossRef] [Green Version] - Ren, M.; Xu, Z.; Su, G. Comparative analysis on bridge backwater depths estimated using 2-D hydrodynamic model and empirical formulas. J. Hydroelectr. Eng.
**2017**, 36, 78–87. [Google Scholar] - Vaheddoost, B.; Safari, M.J.S.; Ilkhanipour, Z.R. Discharge coefficient for vertical sluice gate under submerged condition using contraction and energy loss coefficients. Flow Meas. Instrum.
**2021**, 80, 102007. [Google Scholar] [CrossRef] - Mohamed, I.M.; Abdelhaleem, F.S. Flow Downstream Sluice Gate with Orifice. KSCE J. Civ. Eng.
**2020**, 24, 3692–3702. [Google Scholar] [CrossRef] - Zhang, M.; Wang, L.; Zhang, F.; Zhang, C.; Wu, M.; Tang, H.; Zhu, H. Launch condition and flood diversion effect of flood diversion area named Garden Lake. J. Hohai. Univ. Nat. Sci.
**2020**, 48, 209–214. [Google Scholar] - Baird, D.C.; Abban, B.; Scurlock, S.M.; Abt, S.B.; Thornton, C.I. Two-Dimensional Numerical Modeling of Flow in Physical Models of Rock Vane and Bendway Weir Configurations. Water
**2021**, 13, 458. [Google Scholar] [CrossRef] - Seyedjavad, M.; Naeeni, S.O.; Saneie, M. Flow velocity pattern around trapezoidal piano key side weirs. Flow Meas. Instrum.
**2020**, 76, 101847. [Google Scholar] [CrossRef] - Li, G.; Li, S.; Hu, Y. The effect of the inlet/outlet width ratio on the discharge of piano key weirs. J. Hydraul. Res.
**2020**, 58, 594–604. [Google Scholar] [CrossRef] - Atashi, V.; Bejestan, M.S.; Lim, Y.H. Flow Pattern and Erosion in a 90-Degrees Sharp Bend around a W−Weir. Water
**2023**, 15, 11. [Google Scholar] [CrossRef] - Skilodimou, H.D.; Bathrellos, G.D.; Alexakis, D.E. Flood Hazard Assessment Mapping in Burned and Urban Areas. Sustainability
**2021**, 13, 4455. [Google Scholar] [CrossRef] - Salehi, S.; Azimi, A.H. Discharge Characteristics of Weir-Orifice and Weir-Gate Structures. J. Irrig. Drain. Eng.
**2019**, 145, 04019025. [Google Scholar] [CrossRef]

Condition | #1 Weir Height | #2 Weir Height | Backwater Range | Maximum Backwater Height | Impact |
---|---|---|---|---|---|

1 | 2.00 | 0.75 | [928.09, 1283.00] | 1.33 | No |

2 | 0.00 | 0.75 | [1255.14, 1283.00] | 0.19 | No |

3 | 2.00 | 0.00 | [891.53, 962.43] | 0.24 | No |

4 | 0.00 | 0.00 | 0.00 | 0.00 | No |

Bridge Number | Location | Type | N | H_{0} | H1 | $\mathbf{\Delta}\mathbf{Z}$ | ||
---|---|---|---|---|---|---|---|---|

Without Bridge | With Bridge | $\mathbf{\Delta}\mathbf{H}$ | ||||||

1# | 25.37 | Flat slab | 1 | 138.80 | 138.14 | 138.14 | 0.00 | −0.66 |

2# | 195.82 | Flat slab | 2 | 137.42 | 137.53 | 137.64 | 0.11 | 0.22 |

3# | 261.84 | Flat slab | 2 | 136.41 | 137.2 | 137.50 | 0.30 | 1.09 |

4# | 392.89 | Flat slab | 3 | 135.63 | 136.7 | 137.21 | 0.51 | 1.58 |

5# | 471.74 | Flat slab | 2 | 135.42 | 136.02 | 136.39 | 0.37 | 0.97 |

6# | 550.25 | Flat slab | 1 | 134.62 | 135.65 | 135.79 | 0.14 | 1.17 |

7# | 652.04 | Flat slab | 1 | 134.83 | 134.95 | 135.12 | 0.17 | 0.29 |

8# | 790.29 | Flat slab | 1 | 133.38 | 133.88 | 134.09 | 0.21 | 0.71 |

9# | 912.53 | Flat slab | 2 | 132.98 | 133.11 | 133.3 | 0.19 | 0.32 |

10# | 955.64 | Flat slab | 3 | 132.90 | 132.7 | 132.92 | 0.22 | 0.02 |

11# | 979.22 | Flat slab | 2 | 133.06 | 132.56 | 132.75 | 0.19 | −0.31 |

12# | 1032.00 | Arch | 1 | 132.19 | 132.5 | 132.67 | 0.17 | 0.48 |

13# | 1076.39 | Arch | 1 | 133.16 | 132.38 | 132.51 | 0.13 | −0.65 |

14# | 1155.53 | Flat slab | 2 | 131.85 | 132.05 | 132.15 | 0.10 | 0.30 |

15# | 1401.87 | Flat slab | 1 | 131.31 | 129.94 | 129.94 | 0.00 | −1.37 |

16# | 1572.66 | Flat slab | 1 | 131.03 | 128.86 | 128.86 | 0.00 | −2.17 |

17# | 1719.09 | Flat slab | 1 | 130.50 | 128.28 | 128.28 | 0.00 | −2.22 |

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**MDPI and ACS Style**

Hu, J.; Shen, H.; Zhang, J.; Meng, Z.; Zhang, Y.; Han, W.
Influence of Multi-Cross Structures on the Flood Discharge Capacity of Mountain Rivers in the Yellow River Basin. *Water* **2023**, *15*, 2719.
https://doi.org/10.3390/w15152719

**AMA Style**

Hu J, Shen H, Zhang J, Meng Z, Zhang Y, Han W.
Influence of Multi-Cross Structures on the Flood Discharge Capacity of Mountain Rivers in the Yellow River Basin. *Water*. 2023; 15(15):2719.
https://doi.org/10.3390/w15152719

**Chicago/Turabian Style**

Hu, Jianyong, Hui Shen, Jinxin Zhang, Zhenzhu Meng, Yuzhou Zhang, and Wei Han.
2023. "Influence of Multi-Cross Structures on the Flood Discharge Capacity of Mountain Rivers in the Yellow River Basin" *Water* 15, no. 15: 2719.
https://doi.org/10.3390/w15152719