# 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

## References

- Ti, Z.; Zhang, M.; Li, Y.; Wei, K. Numerical study on the stochastic response of a long-span sea-crossing bridge subjected to extreme nonlinear wave loads. Eng. Struct.
**2019**, 196, 109287. [Google Scholar] [CrossRef] - Zhang, M.; Yu, J.; Zhang, J.; Wu, L.; Li, Y. Study on the wind-field characteristics over a bridge site due to the shielding effects of mountains in a deep gorge via numerical simulation. Adv. Struct. Eng.
**2019**, 22, 3055–3065. [Google Scholar] - Wei, K.; Liu, Q.; Qin, S. Nonlinear assessment of offshore steel trestle subjected to wave and current loads. Ships Offshore Struct.
**2019**, 1–13. [Google Scholar] [CrossRef] - Liang, F.; Wang, C.; Yu, X. Performance of Existing Methods for Estimation and Mitigation of Local Scour around Bridges: Case Studies. J. Perform. Constr. Facil.
**2019**, 33, 04019060. [Google Scholar] [CrossRef] - Melville, B.W. Local Scour at Bridge Sites; The University of Auckland: Auckland, New Zealand, 1975. [Google Scholar]
- Blanco, G.; Ye, A.; Wang, X.; Goicolea, J.M. Parametric Pushover Analysis on Elevated RC Pile-Cap Foundations for Bridges in Cohesionless Soils. J. Bridge Eng.
**2019**, 24, 04018104. [Google Scholar] [CrossRef] - Wang, X.; Ye, A.; Shang, Y.; Zhou, L. Shake-table investigation of scoured RC pile-group-supported bridges in liquefiable and nonliquefiable soils. Earthq. Eng. Struct. Dyn.
**2019**, 48, 1217–1237. [Google Scholar] [CrossRef] - Zhang, J.; Wei, K.; Qin, S. An efficient numerical model for hydrodynamic added mass of immersed column with arbitrary cross—Section. Ocean Eng.
**2019**, 187, 106192. [Google Scholar] [CrossRef] - Sumer, B.M.; Fredsøe, J. The Mechanics of Scour in the Marine Environment; World Scientific: Singapore, 2002. [Google Scholar]
- Melville, B.W.; Coleman, S.E. Bridge Scour; Water Resources Publications: Highlands Ranch, CO, USA, 2000. [Google Scholar]
- Arneson, L.A.; Zevenbergen, L.W.; Lagasse, P.F.; Clopper, P.E. Evaluating Scour at Bridges, 5th ed.; Hydraulic Engineering Circular No. 18 (HEC-18); Federal Highway Administration: Washington, DC, USA, 2012. [Google Scholar]
- Ataie-Ashtiani, B.; Beheshti, A.A. Experimental Investigation of Clear-Water Local Scour at Pile Groups. J. Hydraul. Eng.
**2006**, 132, 1100–1104. [Google Scholar] [CrossRef] [Green Version] - Oliveto, G.; Hager, W.H. Temporal Evolution of Clear-Water Pier and Abutment Scour. J. Hydraul. Eng.
**2002**, 128, 811–820. [Google Scholar] [CrossRef] - Penna, N.; Coscarella, F.; Gaudio, R. Turbulent Flow Field around Horizontal Cylinders with Scour Hole. Water
**2020**, 12, 143. [Google Scholar] [CrossRef] [Green Version] - Oliveto, G.; Comuniello, V.; Bulbule, T. Time-dependent local scour downstream of positive-step stilling basins. J. Hydraul. Res.
**2011**, 49, 105–112. [Google Scholar] [CrossRef] - Breusers, H.N.C.; Nicollet, G.; Shen, H.W. Local scour around cylindrical piers. J. Hydraul. Res.
**1977**, 15, 211–252. [Google Scholar] [CrossRef] - Wang, S.; Wei, K.; Shen, Z.; Xiang, Q. Experimental Investigation of Local Scour Protection for Cylindrical Bridge Piers Using Anti-Scour Collars. Water
**2019**, 11, 1515. [Google Scholar] [CrossRef] [Green Version] - Schendel, A.; Welzel, M.; Hildebrandt, A.; Schlurmann, T.; Hsu, T.-W. Role and Impact of Hydrograph Shape on Tidal Current-Induced Scour in Physical-Modelling Environments. Water
**2019**, 11, 2636. [Google Scholar] [CrossRef] [Green Version] - McGovern, D.J.; Ilic, S.; Folkard, A.M.; McLelland, S.J.; Murphy, B.J. Time Development of Scour around a Cylinder in Simulated Tidal Currents. J. Hydraul. Eng.
**2014**, 140, 04014014. [Google Scholar] [CrossRef] - Wang, J. Research on Local Scour at Bridge Pier under Tidal Action. Matec Web Conf.
**2015**, 25, 01013. [Google Scholar] [CrossRef] - Zhang, J.-S.; Gao, P.; Zheng, J.-H.; Wu, X.-G.; Peng, Y.-X.; Zhang, T.-T. Current-Induced Seabed Scour Around a Pile-Supported Horizontal-Axis Tidal Stream Turbine. J. Mar. Sci. Technol.
**2015**, 23, 929–936. [Google Scholar] - Schendel, A.; Hildebrandt, A.; Goseberg, N.; Schlurmann, T. Processes and evolution of scour around a monopile induced by tidal currents. Coast. Eng.
**2018**, 139, 65–84. [Google Scholar] [CrossRef] - Ma, L.; Wang, L.; Guo, Z.; Jiang, H.; Gao, Y. Time development of scour around pile groups in tidal currents. Ocean Eng.
**2018**, 163, 400–418. [Google Scholar] [CrossRef] - Xiang, Q.; Li, Y.; Wei, K.; Wang, S.; Yao, C. Review of Bridge Foundation Scour. J. Southwest Jiaotong Univ.
**2019**, 54, 235–248. [Google Scholar] - Veerappadevaru, G.; Gangadharaiah, T.; Jagadeesh, T.R. Vortex scouring process around bridge pier with a caisson. J. Hydraul. Res.
**2011**, 49, 378–383. [Google Scholar] [CrossRef] - Veerappadevaru, G.; Gangadharaiah, T.; Jagadeesh, T.R. Temporal variation of vortex scour process around caisson piers. J. Hydraul. Res.
**2012**, 50, 200–207. [Google Scholar] [CrossRef] - Zhao, M.; Zhu, X.; Cheng, L.; Teng, B. Experimental study of local scour around subsea caissons in steady currents. Coast. Eng.
**2012**, 60, 30–40. [Google Scholar] [CrossRef] - Liang, F.; Wang, C.; Huang, M.; Li, J. Scale Effect on Local Scour Configurations around Caisson Foundation and Dynamic Evolution. China J. Highw. Transp.
**2016**, 29, 59–67. [Google Scholar] - Oliveto, G.; Marino, M.C. Temporal scour evolution at non-uniform bridge piers. Proc. Inst. Civ. Eng.-Water Manag.
**2017**, 170, 254–261. [Google Scholar] [CrossRef] - Burkow, M.; Griebel, M. A full three dimensional numerical simulation of the sediment transport and the scouring at a rectangular obstacle. Comput. Fluids
**2016**, 125, 1–10. [Google Scholar] [CrossRef] - Gao, Z.R.; Huang, J.W.; Zhao, X.D. Research on Local Scour during Settling of Steel Caissons for Large-scale Bridges. Ocean Eng.
**2006**, 24, 31–35. [Google Scholar] - Sun, M.X. Study on Local Scour Characteristics of Caisson under the Action of Wave and Flow; Southewest Jiaotong University: Chengdu, China, 2018. [Google Scholar]
- Soulsby, R.L.; Whitehouse, R.J.S. Threshold of sediment motion in coastal environments. In Pacific Coasts and Ports ’97: Proceedings of the 13th Australasian Coastal and Ocean Engineering Conference and the 6th Australasian Port and Harbour Conference, Christchurch, New Zealand, 7–11 September 1997; University of Canterbury: Christchurch, New Zealand; pp. 145–150.
- Soulsby, R.L. Dynamics of Marine Sands; Tomas Telford Ltd.: New York, NY, USA, 1998. [Google Scholar]
- Babaeyan-Koopaei, K.; Ervine, D.A.; Carling, P.A.; Cao, Z. Velocity and Turbulence Measurements for Two Overbank Flow Events in River Severn. J. Hydraul. Eng.
**2002**, 128, 891–900. [Google Scholar] [CrossRef] - Marta, K.; Zbigniew, P. Bed Shear Stress Influence on Local Scour Geometry Properties in Various Flume Development Conditions. Water
**2019**, 11, 2346. [Google Scholar] - Biron, P.M.; Robson, C.; Lapointe, M.F.; Gaskin, S.J. Comparing different methods of bed shear stress estimates in simple and complex flow fields. Earth Surf. Process. Landf.
**2004**, 29, 1403–1415. [Google Scholar] [CrossRef] - Sumer, B.M.; Christiansen, N.; Fredsøe, J. Time scale of scour around a vertical pile. In Proceedings of the 2nd International Offshore and Polar Engineering Conference, San Francisco, CA, USA, 14–19 June 1992; Volume 3, pp. 308–315. [Google Scholar]
- Vasquez, J.A.; Walsh, B.W. CFD Simulation of Local Scour in Complex Piers under Tidal Flow. In Proceedings of the 33th IAHR Congress: Water Engineering for a Sustainable Environment, Vancouver, BC, Canada, 9–14 August 2009; Volume 604, pp. 913–920. [Google Scholar]
- Wang, C.; Yu, X.; Liang, F. A review of bridge scour: Mechanism, estimation, monitoring and countermeasures. Nat. Hazards
**2017**, 87, 1881–1906. [Google Scholar] [CrossRef]

**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 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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