# Experimental Study of Local Scour around Caissons under Unidirectional and Tidal Currents

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Testing Facilities

#### 2.2. Calculation of Test Parameters

_{50}of 0.316 mm and a sediment specific gravity $\mathrm{s}$ of 2.69 was used as the bed sediment in this study. The water depth h was set to 0.4 m. The non-dimensional particle size is defined as ${\mathit{d}}_{*}={\left[\mathbf{g}\left(\mathit{s}-\mathbf{1}\right)/{\mathit{\nu}}^{\mathbf{2}}\right]}^{\mathbf{1}/\mathbf{3}}{\mathit{d}}_{\mathbf{50}}$, in which the kinematic viscosity $\mathit{\nu}={\mathbf{10}}^{-\mathbf{6}}{\mathbf{m}}^{\mathbf{2}}/\mathbf{s}$. The critical Shields parameter ${\mathit{\theta}}_{\mathit{c}\mathit{r}}$ of the sediment can be calculated according to the method proposed by Soulsby and Whitehouse [33] as follows, and is equal to 0.0363:

**g**is the acceleration due to gravity, and ${\mathit{\tau}}_{\mathit{s}}$ is the shear stress due to bottom friction, which is fundamental to check whether the prepared experiments are in clear water or live bed conditions. Two methods are used to estimate the value of ${\mathit{\tau}}_{\mathit{s}}$, respectively.

^{−3}by calculation; $\mathit{\kappa}=\mathbf{0.4}$ is the Karman constant, ${\mathit{z}}_{\mathbf{0}\mathit{s}}={\mathit{d}}_{\mathbf{50}}/\mathbf{12}$ is the roughness height and $\overline{\mathit{U}}$ is the depth-average flow velocity. In the following tests, the constant flow velocity close to the water surface is set to 0.35 m/s with a depth-averaged value of 0.322 m/s. The shear stress ${\mathit{\tau}}_{\mathit{s}}$ according to Equation (3) equals to 0.2228 N/m

^{2}. The value of ${\mathit{\theta}}_{\mathit{s}}$ for the sediment is 0.0434.

^{−4}[37]. This method assumes that the average flow velocities are equal to the depth-averaged velocity across the entire cross-section $\overline{\mathit{U}}$:

^{2}. the value of ${\mathit{\theta}}_{\mathit{s}}$ for the sediment is hence equal to 0.065.

#### 2.3. Testing Currents and Cases

_{p}) of tidal current was 10 min, which was also adopted by Vasquez and Walsh [39]. The velocity and direction versus time for unidirectional current and tidal current in the experiments are shown in Figure 4. The quantities t

_{0}and T

_{p}represent the duration of unidirectional current and period of tidal current, respectively.

## 3. Results

#### 3.1. Local Scour around Caissons Settled into the Sediment

#### 3.1.1. Circular Caisson

#### 3.1.2. Square Caisson

#### 3.1.3. Diamond Caisson

#### 3.1.4. Analysis and Comparison of the Maximum Scour Depths

**D**(dimension perpendicular to flow for a caisson), the non-dimensional time ${\mathit{t}}^{*}$ of diamond caisson was smaller than that of the circular and square caissons at the same time. However, it can still be seen from Figure 11a that diamond has the slowest temporal developing speed of scour and can reach quasi-equilibrium state easier, while square has the fastest speed. At t = 180 min t* = 10.97 for circular and square, t* = 5.49 for diamond, the maximum scour depths of the diamond caisson and the square caisson were 22% larger and 21.5% smaller, respectively, than that of the circular caisson. Compared with the square caisson, the circular caisson was more similar to an active scour countermeasure because a circular water-facing surface can divert the current, change its direction, and decrease the strength of the current; thus, the scouring ability is weakened [40]. The diamond caisson also had two 45° sides on the water-facing surface, which could play a certain energy-dissipating role. The two side corners could result in the acceleration of velocity, but generation of the horseshoe vortex was not easy here, which can result in a smaller scour depth than the circular caisson. However, the square caisson did not show diversion on the water-facing surface, which led to a vortex with a strong scouring ability; thus, the maximum scour depth was the largest of the three caissons.

**D**of the circular and diamond caissons are the same under the action of tidal current, the maximum scour depth of both will be close to each other.

_{tid,t}/S

_{uni,t}for different cross-sections of caissons as a function of non-dimensional time t*. S

_{tid,t}represents the maximum scour depth under the action of tidal current at time t* and S

_{uni,t}represents the maximum scour depth under the action of unidirectional current at time t*. The scour depth ratio S

_{tid,t}/S

_{uni,t}can reflect the degree to which the scour depth of caissons with different cross-sections is affected by tidal current. The larger the S

_{tid,t}/S

_{uni,t}ratio is, the less sensitive the caisson with this cross-section is to tidal current. Compared with the scour under unidirectional current, the square caisson was more sensitive, while the diamond caisson was less sensitive to the tidal current.

#### 3.2. Local Scour under Caissons Suspended in Water

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Description of the caisson model: (

**a**) top view; (

**b**) side view of the caisson suspended in the water; (

**c**) installation of the caisson model.

**Figure 4.**Velocity and direction versus time in the tests: (

**a**) unidirectional current; (

**b**) tidal current.

**Figure 5.**Photographs of the scour pit (left) and development of scour depth (right) around the circular caisson: (

**a**) unidirectional current; (

**b**) tidal current.

**Figure 6.**Comparison of the development of scour depth around the circular caisson at different measuring points (left: unidirectional current; right: tidal current): (

**a**) front points; (

**b**) lateral points; (

**c**) rear points.

**Figure 7.**Photographs of the scour pit (left) and development of scour depth (right) around the square caisson: (

**a**) unidirectional current; (

**b**) tidal current.

**Figure 8.**Comparison of the development of scour depth around the square caisson at different measuring points (left: unidirectional current; right: tidal current): (

**a**) front points; (

**b**) lateral points; (

**c**) rear points.

**Figure 9.**Photographs of the scour pit (left) and the development of scour depth (right) around the square caisson: (

**a**) unidirectional current; (

**b**) tidal current.

**Figure 10.**Comparison of the development of scour depth around the diamond caisson at different measuring points (left: unidirectional current; right: tidal current): (

**a**) front points; (

**b**) rear points.

**Figure 11.**Comparison of the maximum scour depth for caissons with different cross-sections: (

**a**) unidirectional current; (

**b**) tidal current.

**Figure 13.**Development of the maximum scour depth over time when the caisson is suspended in water or settled into the sand: (

**a**) unidirectional current; (

**b**) tidal current.

Case | Shape of Caissons | Horizontal Dimension in the Cross-Flow Direction D (m) | Type of Current | Clearance c (cm) | Velocity (m/s) | Water Depth (m) |

1 | Circular | 0.15 | Unidirectional | −20 | 0.35 | 0.4 |

2 | Square | 0.15 | ||||

3 | Diamond | 0.212 | ||||

4 | Circular | 0.15 | Tidal | |||

5 | Square | 0.15 | ||||

6 | Diamond | 0.212 | ||||

7 | Circular | 0.15 | Unidirectional | 5 | ||

8 | 0 | |||||

9 | Tidal | 5 | ||||

10 | 0 | |||||

11 | Square | Unidirectional | 5 | |||

12 | 0 | |||||

13 | Tidal | 5 | ||||

14 | 0 |

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**MDPI and ACS Style**

Xiang, Q.; Wei, K.; Qiu, F.; Yao, C.; Li, Y. Experimental Study of Local Scour around Caissons under Unidirectional and Tidal Currents. *Water* **2020**, *12*, 640.
https://doi.org/10.3390/w12030640

**AMA Style**

Xiang Q, Wei K, Qiu F, Yao C, Li Y. Experimental Study of Local Scour around Caissons under Unidirectional and Tidal Currents. *Water*. 2020; 12(3):640.
https://doi.org/10.3390/w12030640

**Chicago/Turabian Style**

Xiang, Qiqi, Kai Wei, Fang Qiu, Changrong Yao, and Yadong Li. 2020. "Experimental Study of Local Scour around Caissons under Unidirectional and Tidal Currents" *Water* 12, no. 3: 640.
https://doi.org/10.3390/w12030640