# Impact of Suspended Sediment Diffusion from the Implementation of Arresting Facilities on Cross-Sea Bridges

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

## 3. Numerical Hydrodynamic Model and Model Setup

#### 3.1. Hydrodynamic Governing Equations

_{bx}and τ

_{bx}are the bottom shear stress components in the x and y directions, respectively; S

_{xx}, S

_{xy}, S

_{yx}, and S

_{yy}are the components of the wave radiation stress tensor; and N

_{x}and N

_{y}are the coefficients of eddy viscosity, which are calculated based on the formulation of the Smagorinsky model [15] in the horizontal direction.

#### 3.2. Model Setup

^{1/3}/s−70 m

^{1/3}/s. The Courant–Friedrichs–Lewy (CFL) number was used to ensure stability in the numerical model. The critical CFL number was 0.8 in this paper.

#### 3.3. Pier Generalization Methods

_{d}is the drag coefficient; D is the diameter of the pier; U is the water flow; n is the roughness of the bed; n

_{p}is the equivalent roughness; and S is the area of the element where the pier is located.

_{rms}. The structure of Formula (6) is simple in form, comprehensive in its consideration of influencing factors, and easy to apply.

## 4. Validation of the Hydrodynamic Model

^{2}) between the calculated and measured data at the stations, shown in Table 2, indicated that the results of the model were in reasonable agreement with the measured datasets.

^{2}) between the modeled and measured data at the water level and flow stations. The results showed reasonable agreement between the model and the measured data.

## 5. Suspended Sediment Diffusion and Transport Model

#### 5.1. Governing Equations of the Sediment Model

_{x}and ε

_{y}are the diffusion coefficients in the x and y directions, respectively; and F

_{c}is the source–sink term for suspended sediment flux or sediment erosion or deposition, given by the following:

_{b}is the shear stress; τ

_{e}is the critical bed shear stress for erosion; and τ

_{d}is the critical bed shear stress for deposition.

#### 5.2. Validation of SSC

#### 5.3. Construction of Suspended Sediment Source Intensity and Source Point Distribution

^{3}of bottom sediment, construction material, and substrate; therefore, the instantaneous source strength was determined as 1.6 m

^{3}. According to the conditions of the mooring environment, construction process, and substrate composition, the sediment suspension rate was 20%, the dry density of the sediment was 700 kg/m

^{3}, and the instantaneous source strength was 112 kg/s when the mooring anchor was placed.

## 6. Results and Discussion

^{2}and concentrated within 500 m of the arresting facilities. When the arresting facilities near the western channel were implemented during rising tide, the area of the sea where the increase in SSC reached 10 mg/L was less than 2.5 km

^{2}and the farthest point was located 4.5 km to the north of the arresting facilities; when implementation occurred during falling tide, the corresponding sea area was less than 3.5 km

^{2}, and the farthest point was located 6.5 km south of the arresting facilities.

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Location of the Jintang bridge and the layout of the arresting facilities. (

**a**) Scheme of arresting facilities; (

**b**) arresting facilities site layout.

**Figure 3.**Study area used in the investigation: (

**a**) mesh generation and relief map of simulation area; (

**b**) layout of the observation stations.

**Figure 5.**Verification of the current speed and direction during spring tide at station S1, S2, and S3.

**Figure 9.**Distribution of the increase in suspended sediment concentration under all four conditions: (

**a**) condition 1; (

**b**) condition 2; (

**c**) condition 3; and (

**d**) condition 4.

Method | Generalization | Advantages | Disadvantages |
---|---|---|---|

Indirect | Roughness or water depth correction | Larger mesh size and shorter calculation time | Slightly lower precision |

Direct | Marking piers as solid boundaries | Accurately describes the boundaries of piers and has higher precision | As the mesh size decreases, the calculation time increases sharply |

**Table 2.**Correlation coefficients between calculated and measured values at the tidal and current stations.

Verification Station ID | R^{2} of Measured vs. Calculated | ||
---|---|---|---|

Tidal Level | Current Speed | Current Direction | |

Dinghai | 0.984 | / | / |

Zhenhai | 0.958 | / | |

S1 | / | 0.977 | 0.996 |

S2 | / | 0.961 | 0.990 |

S3 | / | 0.961 | 0.984 |

**Table 3.**Correlation coefficients between calculated and measured values at the tidal and current stations.

Verification Station ID | R^{2} of Measured vs. Calculated |
---|---|

SSC | |

S1 | 0.658 |

S2 | 0.709 |

S3 | 0.677 |

**Table 4.**Flow velocity at the representative position of each arresting unit during the flood and ebb of the spring tide.

Time | Western Channel (m/s) | Main Channel (m/s) | ||||||
---|---|---|---|---|---|---|---|---|

1# | 2# | 3# | 4# | 5# | 6# | 7# | 8# | |

Flood | 0.82 | 0.93 | 0.99 | 0.88 | 1.09 | 1.28 | 1.35 | 1.04 |

Ebb | 0.86 | 0.96 | 0.83 | 0.76 | 1.08 | 1.22 | 1.43 | 0.92 |

Conditions | Area km^{2} | ||||
---|---|---|---|---|---|

2 mg/L | 5 mg/L | 10 mg/L | 20 mg/L | 50 mg/L | |

Condition 1 | 6.127 | 0.166 | 0.081 | 0 | 0 |

Condition 2 | 3.716 | 0.204 | 0.019 | 0 | 0 |

Condition 3 | 17.198 | 4.381 | 2.199 | 0.484 | 0.031 |

Condition 4 | 14.047 | 5.315 | 3.108 | 1.140 | 0.115 |

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**MDPI and ACS Style**

Chen, P.; Li, Y.; Wu, J.; Li, R.; Song, Z.; Dai, L.
Impact of Suspended Sediment Diffusion from the Implementation of Arresting Facilities on Cross-Sea Bridges. *Sustainability* **2022**, *14*, 9559.
https://doi.org/10.3390/su14159559

**AMA Style**

Chen P, Li Y, Wu J, Li R, Song Z, Dai L.
Impact of Suspended Sediment Diffusion from the Implementation of Arresting Facilities on Cross-Sea Bridges. *Sustainability*. 2022; 14(15):9559.
https://doi.org/10.3390/su14159559

**Chicago/Turabian Style**

Chen, Peng, Yuting Li, Jiaxing Wu, Ruijie Li, Zhiyao Song, and Lu Dai.
2022. "Impact of Suspended Sediment Diffusion from the Implementation of Arresting Facilities on Cross-Sea Bridges" *Sustainability* 14, no. 15: 9559.
https://doi.org/10.3390/su14159559