# Investigation of Local Scouring around Hydrodynamic and Circular Pile Groups under the Influence of River Material Harvesting Pits

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## Abstract

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## 1. Introduction

_{e}/D (H

_{e}: scour depth at equilibrium time; D: pier diameter).

## 2. Dimensional Analysis

_{0}is the initial flow depth, g is the gravitational acceleration, ρ is the fluid density, ν is the kinematic viscosity, d

_{50}indicates the average particle diameter size, σ

_{g}is the deviation from average size, ρ

_{s}represents the sediment density, B is the flume width, D is the pier diameter, K

_{p}is the curvature of the upstream surface of the pier, K

_{r}is the pier surface roughness, m

_{p}is the length of the pier at the plan, L

_{sx}refers to the scour width, L

_{sy}is the scour length, d

_{s}indicates the scour depth, l

_{p}represents the length of the harvest pit, b

_{p}is the width of the harvest pit, and t is the time.

## 3. Numerical Model

#### 3.1. Flow Field Simulation

_{F}is the ratio of the volume of fluid passing through an element to the total volume of the element and ρ is the density of the fluid. The parameters u, v, and w are the velocities in the three coordinate directions. The symbols A

_{x}, A

_{y}, and A

_{z}indicate the fraction of area for flow in the x, y, and z directions, respectively. The terms R and x correspond to the selected coordinate system and take on values of 1 and 0, respectively [26].

_{DIF}represents a turbulent diffusion and R

_{SOR}is the mass source. It is related to the porous media and the entry of secondary flow into the computational domain. The equations of motion are as follows [27]:

_{x}, G

_{y}, and G

_{z}are the accelerations of gravity in the x, y, and z directions; and f

_{x}, f

_{y}, and f

_{z}are the viscous forces, respectively, in the three coordinate directions. The initial conditions for the momentum are as follows:

- A.
- The fluid is continuous and the stress is linearly related to the strain rate;
- B.
- The fluid is isotropic, i.e., the properties of the fluid are independent of direction. As a result, the law of deformation is independent of the chosen axis;
- C.
- When the strain rate is zero, the law of deformation is reduced to hydrostatic pressure.

#### 3.2. Turbulence Model

_{T}) performs as:

_{ij}is the strain rate tensor components in the i and j directions.

#### 3.3. Sediment Scour Model

_{s}is the fluid density, d is the particle diameter, and g is the acceleration of gravity. Equation (11) is applied to calculate the critical shear stress of sediment in a flat riverbed:

_{cr}is the critical shear stress of the sediment, s is the specific density, d

_{50}is the mean diameter of the sediment particles, and θ

_{cr}is the critical Shields number. The Soulsby–Whitehouse equation is used to calculate the dimensionless critical Shields parameter:

_{b}is bed load coefficient, and$\varphi $ is the dimensionless bed load transport rate, which is related to the volumetric bed load transport rate, q

_{b}, as follows:

_{p}is the main flow velocity at point p, k is von Kàrmàn’s constant (0.418), u* is the shear velocity related to the bottom shear stress (τ = ρu*

^{2}), E is Young’s modulus, ρ is the fluid density, c

_{μ}is the constant, kp is the turbulent kinetic energy at point p, z

_{p}is the distance from point p to the wall, and ∆B is the roughness function [42]. In this study, the parameters selected for sediment scour, obtained after calibration of many runs, were the critical Shields number (θ

_{cr}) of 0.03 and the bed load coefficient (C

_{b}) of 0.5

#### 3.4. Description of the Laboratory Experiment and Numerical Setup

_{50}exceeds 20–25, the size of the sediment particles does not affect the final scour depth. They also showed that the average particle diameter must be more than 0.7 mm to prevent the formation of ripples in the sedimentary bed. Therefore, the selected bed sediments were non-cohesive sands with a median size (d

_{50}) of 0.86 mm, a specific gravity (G

_{s}) of 2.65, and a geometric standard deviation (σ

_{g}) of 1.32. An oval pit was constructed with large and small dimensions of 1.01 and 0.8 m, respectively. The pit was located in the middle of the bed. Three groups of bridge piers were installed consecutively 1 m apart upstream and downstream of the material harvesting pit.

#### 3.5. Effect of the Computational Mesh on the Scour Depth Results

_{exp}is the experimental value and M

_{cal}is the calculated data. From this table, with a decreasing mesh size, the differences between the calculations and measurements decreased. For 2 cm meshes, there was a large difference between the calculations and the measurements (i.e., 84%). However, when the mesh sizes were reduced to 0.9 cm, the difference was reduced to 6.7% for the upstream pier. Similar improvements were observed at the downstream site as well. Table 2 provides a summary list of the results for the three different mesh sizes (0.02, 0.015, and 0.009 m).

#### 3.6. Validation of the Numerical Simulation

_{total}is the total time period of the simulation and d

_{s total}is the final scour depth in the equilibrium state.

^{2}), and the mean absolute error value (MAE). The definitions of these metrics are provided below:

_{exp}refers to the experimental values, and M

_{cal}refers to the calculated data. The fitting equations are acceptable when the RMSE values are close to zero and R

^{2}is ~1. From Table 3, it can be seen that based on the accuracy of the parameters applied (R

^{2}, MAE, RMSE, and E in Table 3), the numerical results are acceptable. For instance, with the first pier (relative error percentage of 6%) and the fourth pier (relative error percentage of 7%), the agreement is excellent. These two piers are the most upstream piers in the two pier groups.

#### 3.7. Simulation of Local Scouring around the Hydrodynamic Pile Group

## 4. Results

#### 4.1. Results of Laboratory Study

#### 4.2. Comparison of Scour for the Hydrodynamic and Circular Pile Groups

#### 4.3. Flow Patterns around the Hydrodynamic and Circular Pile Groups

#### 4.4. Investigation of the Material Harvest Pit Changes

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Sediment bed, material harvesting pit, and arrangement of the bridge pile groups in the laboratory model.

**Figure 4.**Comparison of scouring around the piers between the laboratory and numerical studies. (

**a**) Laboratory scouring around the upstream and downstream pile groups. (

**b**) Numerical scouring around the upstream and downstream pile groups. (

**c**) Time changes of the local scouring depth in the laboratory model. (

**d**) Comparison of the time changes of the local scouring depth between the laboratory model and the numerical simulation.

**Figure 5.**3D view of the hydrodynamic pile groups and the sediment bed (all dimensions are in meters).

**Figure 9.**Flow patterns for the pier group and the material harvest pit: (

**a**) Circular model; (

**b**) hydrodynamic model.

**Figure 10.**Bed elevation changes from around the group piles and the material harvest pit: (

**a**) Circular model; (

**b**) hydrodynamic model.

**Figure 11.**Changes in the harvest pit in the plane (plane x–y): (

**a**) circular model, (

**b**) hydrodynamic model.

**Figure 12.**Material harvest pit changes in the x–z plane: (

**a**) Circular model; (

**b**) hydrodynamic model.

Test No. | Q (L/s) | y_{0} (m) | u (m/s) | Fr | Re | u/u_{cr} | d_{50} (m) | G_{s} | σ_{g} |
---|---|---|---|---|---|---|---|---|---|

T1 | 45 | 0.132 | 0.284 | 0.25 | 25,600 | 0.72 | 0.00086 | 2.65 | 1.32 |

**Table 2.**Comparison of the numerical results for different mesh cell sizes with the laboratory results.

Model | Number of Cells | d_{s} of the 1st Pier Upstream (m) | $\mathbf{E}(\%)=\frac{{\mathbf{M}}_{\mathbf{exp}}-{\mathbf{M}}_{\mathbf{cal}}}{{\mathbf{M}}_{\mathbf{exp}}}\times 100$ | d_{s} of the 1st Pier Downstream (m) | $\mathbf{E}(\%)=\frac{{\mathbf{M}}_{\mathbf{exp}}-{\mathbf{M}}_{\mathbf{cal}}}{{\mathbf{M}}_{\mathbf{exp}}}\times 100$ |
---|---|---|---|---|---|

Physical model | - | 0.1 | - | 0.124 | - |

Mesh size 0.02 m | 307,360 | 0.016 | 84 | 0.024 | 80 |

Mesh size 0.015 m | 707,762 | 0.047 | 53 | 0.056 | 54 |

Mesh size 0.009 m | 3,332,516 | 0.107 | 6.7 | 0.135 | 8.8 |

Pier Number | The Dimensionless Scour Depth at the End of the Laboratory Model | The Dimensionless Scour Depth at the End of the Numerical Model | ${\mathbf{R}}^{2}$ | $\mathbf{M}\mathbf{A}\mathbf{E}$ | $\mathbf{R}\mathbf{M}\mathbf{S}\mathbf{E}$ | E |
---|---|---|---|---|---|---|

1st | 1.1226 | 1.1876 | 0.99 | 0.05 | 0.06 | 0.06 |

2nd | 1.0989 | 0.9404 | 0.99 | 0.10 | 0.13 | 0.15 |

3rd | 0.7647 | 0.9826 | 0.93 | 0.10 | 0.14 | 0.21 |

4th | 1.405 | 1.5009 | 0.92 | 0.14 | 0.21 | 0.07 |

5th | 0.9940 | 1.020 | 0.95 | 0.08 | 0.15 | 0.03 |

6th | 0.6710 | 1.0792 | 0.98 | 0.14 | 0.21 | 0.36 |

Pier Model | 1st Pier | 2nd Pier | 3rd Pier | 4th Pier | 5th Pier | 6th Pier |
---|---|---|---|---|---|---|

Scour depth around the hydrodynamic piers (m) | 0.0868 | 0.0821 | 0.0734 | 0.1083 | 0.0643 | 0.0880 |

Scour depth around the circular piers (m) | 0.1067 | 0.0838 | 0.0883 | 0.1349 | 0.0915 | 0.0968 |

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## Share and Cite

**MDPI and ACS Style**

Daneshfaraz, R.; Ghaderi, A.; Sattariyan, M.; Alinejad, B.; Asl, M.M.; Di Francesco, S.
Investigation of Local Scouring around Hydrodynamic and Circular Pile Groups under the Influence of River Material Harvesting Pits. *Water* **2021**, *13*, 2192.
https://doi.org/10.3390/w13162192

**AMA Style**

Daneshfaraz R, Ghaderi A, Sattariyan M, Alinejad B, Asl MM, Di Francesco S.
Investigation of Local Scouring around Hydrodynamic and Circular Pile Groups under the Influence of River Material Harvesting Pits. *Water*. 2021; 13(16):2192.
https://doi.org/10.3390/w13162192

**Chicago/Turabian Style**

Daneshfaraz, Rasoul, Amir Ghaderi, Maryam Sattariyan, Babak Alinejad, Mahdi Majedi Asl, and Silvia Di Francesco.
2021. "Investigation of Local Scouring around Hydrodynamic and Circular Pile Groups under the Influence of River Material Harvesting Pits" *Water* 13, no. 16: 2192.
https://doi.org/10.3390/w13162192