# Experimental Study on the Local Scour of Submerged Spur Dike Heads under the Protection of Soft Mattress in Plain Sand-Bed Rivers

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Methods

#### 2.1. Conditions for Experimental Simulation

#### 2.2. Model Design

_{p}= θ

_{m,}

^{2}(350 g/m

^{2}of woven fabric + 150 g/m

^{2}of non-woven fabric). Stress carrier on the mattress were concrete blocks with a density of 2400 kg/m

^{3}. In the model, the mattress for river bottom protection was simulated by cotton cloth, the concrete blocks were simulated by epoxy resins adhered with a 0.41 g aluminum sheet, and functions of bottom protection structures such as soil protection, adhesion and stability were also simulated. See Figure 3 for a sketch of the model soft mattress.

#### 2.3. Model Setup and Validation

#### 2.4. Experimental Tests

## 3. Local Scour Features of Submerged Spur Dike

#### 3.1. Relationship between Scale of Local Scour and Relative Height of Dam

#### 3.2. Relationship between Scale of Local Scour and Width of Remaining Soft Mattress of Bottom Protection

#### 3.3. Relationship between Scale of Local Scour and Flow Force as Well as Longitudinal Slope of the Dam Head

## 4. Calculating Research on the Scale of Local Scour under the Condition of Bottom Protection

#### 4.1. Dimensional Analysis

_{c}. The volume weight of sediment γ

_{s}and that of water γ both have constant values that can be ignored. Therefore, Equations (7) and (8) can be simplified as the dimensionless forms in Equations (9) and (10):

_{1}and k

_{2}are constant coefficients.

#### 4.2. Calculating Research of the Largest Depth of Local Scour

#### 4.3. Calculating Research of the Distance from the Deepest Local Scoring Point to the Dam Axis

#### 4.4. Analysis of Test

## 5. Conclusions

- (1)
- Currently, the number of research findings on local scouring characteristics of renovating buildings in submerged spur dikes is relatively low. Effective methods of calculating methods to reach the biggest local scouring depth near the submerged spur dike and distance under conditions of bottom protection have not been established.
- (2)
- This paper adopts the undistorted model experimental research method and studies the corresponding relationships among the maximum depth of local scouring and the form of the submerged spur dike head, relative dam height, width of bottom protection, force condition of the incoming flow and longitudinal slope of the dam head. Our findings suggest that the relationships between relative dam height, the force of the incoming flow and scouring depth and distance can be expressed by a power relation, whereas the relationships between the width of the bottom protection, longitudinal slope of the dam head and scouring depth and distance can be expressed by an exponential relation. The formula for the maximum local scouring depth of the submerged spur dike on the plain sand bed and distance to the dam axis under conditions of bottom protection was established based on the principles of dimensional analysis, which can be used as a reference for protective measures.
- (3)
- The water depth and velocity in the formula can be provided by numerical model calculations or a physical model test of the whole river reach. The starting velocity of sediment can be calculated by theoretical formula, and the structural parameters of the dam can be obtained from engineering design data. This formula can be used as a reference for the application of submerged dams in plain river regulation projects.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${\alpha}_{L}$ | Horizontal scale | v | Velocity of flow (m/s) |

${\alpha}_{H}$ | Vertical scale | B | Width of bottom-protection soft mattress (m) |

${\alpha}_{V}$ | Flow velocity scale | v_{c} | Incipient velocity of sediment (m/s) |

${\alpha}_{{V}_{c}}$ | Scale of silt incipient motion | γs | Volume weight of sediment (N/m^{3}) |

${\alpha}_{{t}_{1}}$ | Time scale of water flow movement | γ | Volume weight of water (N/m^{3}) |

${\alpha}_{{t}_{2}}$ | Time scale of riverbed erosion and deposition | θ | Jet angle (rad) |

θ_{p} | Underwater rest angle of prototype sand | m | Longitudinal grade of the dam head |

θ_{m} | Underwater rest angle of model sand | g | Gravitational acceleration (m/s^{2}) |

${\alpha}_{{\gamma}_{0}}$ | Scale of the dry density of silt | d | Grain size d of the bed material (mm) |

α_{q} | Scale of bed material transport rate of unit width | D | Largest scouring depth near the spur dike head (m) |

P | Height of spur dike (m) | S | Distance from the dam axis near the spur dike head (m) |

e | Euler number | h | Pre-scouring water depth at the spur dike (m) |

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**Figure 2.**Sketch of submerged spur dike structure: (

**a**) Top-down view of the spur dike; (

**b**) Cross section of the spur dike body.

**Figure 5.**Relationship between the form of local scouring hole and height of dam: (

**a**) when the h/p is equal to 5. (

**b**) when the h/p is equal to 2; (

**c**) when the h/p is equal to 1.33.

**Figure 6.**Relationship between the form of the local scouring hole and width of the remaining soft mattress of bottom protection: (

**a**) when the B is equal to 0; (

**b**) when the B is equal to 90 m; (

**c**) when the B is equal to 180 m.

**Figure 9.**Comparison between experimentally measured values and formula-based computed values of local scouring depth of submerged spur dike head.

**Figure 10.**Comparison between calculated values and measured values of the maximum scouring depth of submerged spur dike head.

Name | Signal | Numerical Value |
---|---|---|

Horizontal scale | ${\alpha}_{L}$ | 60 |

Vertical scale | ${\alpha}_{H}$ | 60 |

Flow velocity scale | ${\alpha}_{V}$ | 7.7 |

Time scale of water flow movement | ${\alpha}_{{t}_{1}}$ | 7.7 |

Time scale of riverbed erosion and deposition | ${\alpha}_{{t}_{2}}$ | 112 |

Group No. | Prototype | Model | ||||||
---|---|---|---|---|---|---|---|---|

Dimension of Dam Body | Flow Condition | B(m) | Flow Condition | |||||

P (m) | Cross Slope of Dam Body | Longitudinal Slope of Dam Head | h (m) | v (m/s) | h (m) | v (m/s) | ||

BT-1 | 6 | 1/2 | 1/3 | 12 | 2.5 | 0 | 0.20 | 0.32 |

BT-2 | 6 | 9 | 0.15 | |||||

BT-3 | 6 | 15 | 0.25 | |||||

BT-4 | 3 | 1/2 | 1/5 | 15 | 0.25 | |||

BT-5 | 9 | 12 | 0.20 | |||||

BT-6 | 6 | 1/2 | 1/3 | 12 | 1.1 | 0 | 0.20 | 0.14 |

BT-7 | 1.5 | 0.19 | ||||||

BT-8 | 6 | 1/2 | 1/3 | 12 | 2.0 | 0 | 0.20 | 0.26 |

BT-9 | 45 | |||||||

BT-10 | 90 | |||||||

BT-11 | 150 | |||||||

BT-12 | 6 | 1/2 | 1/5 | 12 | 3.0 | 0 | 0.20 | 0.39 |

BT-13 | 90 | |||||||

BT-14 | 180 | |||||||

BT-15 | 6 | 1/2 | 1/5 | 12 | 2.0 | 0 | 0.20 | 0.26 |

BT-16 | 1/2 | 1/5 | 12 | 2.5 | 0 | 0.20 | 0.32 |

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**MDPI and ACS Style**

Xu, H.; Li, Y.; Zhao, Z.; Wang, X.; Zhang, F.
Experimental Study on the Local Scour of Submerged Spur Dike Heads under the Protection of Soft Mattress in Plain Sand-Bed Rivers. *Water* **2023**, *15*, 413.
https://doi.org/10.3390/w15030413

**AMA Style**

Xu H, Li Y, Zhao Z, Wang X, Zhang F.
Experimental Study on the Local Scour of Submerged Spur Dike Heads under the Protection of Soft Mattress in Plain Sand-Bed Rivers. *Water*. 2023; 15(3):413.
https://doi.org/10.3390/w15030413

**Chicago/Turabian Style**

Xu, Hua, Yangfan Li, Zeya Zhao, Xiaojun Wang, and Fanyi Zhang.
2023. "Experimental Study on the Local Scour of Submerged Spur Dike Heads under the Protection of Soft Mattress in Plain Sand-Bed Rivers" *Water* 15, no. 3: 413.
https://doi.org/10.3390/w15030413