# Scale Model Experiment on Local Scour around Submarine Pipelines under Bidirectional Tidal Currents

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{c}, where u is flow velocity and u

_{c}is the critical velocity for sediment incipient motion). For the live bed conditions (u > u

_{c}) (Figure 1), the sandy bed outside the scour hole is also eroded due to high flow intensity and sediment is transported into the scour hole below the pipeline. This makes it more complex than clear-water scour. However, there are only a few studies in the literature [9,14,15] that reported experimental results.

_{wmax}T

_{w}/D, u

_{wmax}, T

_{w}which are the wave peak velocity and period, respectively, and D is the pipeline diameter) and found that the relative scour depth d

_{sm}/D (d

_{sm}is the maximum scour depth) is a function of KC

^{k}(k = 0.5). Several other relative empirical formulas about KC were also obtained to predict the scour depth caused by waves [19,20,21,22,23]. For wave plus current, scour development has also been investigated by Zhang et al. (2016), Zhang et al. (2017) [24] and Li et al. (2020) [25].

## 2. Experiment Setup

_{50}= 0.15 mm, density ρ

_{s}= 2650 kg/m

^{3}and angle of repose 32°. According to the critical Shields parameter of sediment and the logarithmic form of the velocity profile, the critical velocity for sediment incipient motion was calculated u

_{c}= 0.28 m/s. The diameter (D) of the modeled pipeline was 0.045 m, which was scaled down from the Cezhen pipeline (D = 0.9 m) in Hangzhou Bay, China, with a scaling factor of 1:20. In addition, another pipeline with D = 0.075 m was also used. A Cartesian coordinate system was established with the origin being the contact point of the pipeline and sand bed at the central line. An ADV (acoustic Doppler velocimetry) was used to measure the flow velocity upstream of pipeline. Additionally, there was a camera recording the pictures of the scour profile at regular intervals and the data of the scour profiles were acquired from the pictures using image recognition. This method was also compared with traditional depth probes and showed an accuracy of 1 mm.

_{c}) were studied in the experiment. Details of the experimental flow conditions are listed in Table 1. According to Froude’s law, the length scale between the model experiment and prototype was 1:20, and the time scale between the laboratory experiment and the prototype was 1:4.47. Therefore, the period of tidal current in the laboratory experiments was 2.68 h, corresponding to the period of 12 h in the prototype. The tidal current in the experiment was simplified as a regular sinusoid tide:

_{t}is tidal velocity at time t, u

_{max}is the maximum tidal velocity during the flood and ebb phases and T is tidal period. Considering the varying tidal velocity, root mean square velocity u

_{r}was also calculated as effective flow intensity, and for the sinusoidal form of the tidal velocity, u

_{r}could be estimated by u

_{r}= 2u

_{max}/π.

_{max}= 0.4 m/s. The time history of the experimentally generated tidal velocity was in good agreement with the theoretical value, indicating that the multi-pump frequency control system could generate an excellent bidirectional tidal current.

_{0}was equal to the maximum peak velocity u

_{max}in a tide period and the water depth was also equal to the value of the bidirectional tidal current (see Table 1 for details of the experimental runs).

## 3. Result and Discussion

#### 3.1. Scouring Process and Scour Profile

_{max}= 0.3 m/s, D = 0.045 m. As seen from the figure, in the first tidal half cycle (t < 0.5 T) (Figure 5a,b), the scour hole below the pipeline developed rapidly and there was a dune downstream of the pipeline, which gradually moved downstream with time. This phenomenon was similar to that under a unidirectional current. However, during the second half tidal cycle (0.5 T < t < 1.0 T) (Figure 5c,d) with negative flow direction, the sediment in the scour hole was transported out and formed another dune upstream of the pipeline induced by ebb flow, which made the scour profile at t = 1.0 T (Figure 5d) more symmetric around the pipeline. In the following tidal cycle, 1.0 T < t < 2.0 T (Figure 5e–h), it could be observed from the figures that the size of the dunes on both sides had a distinct fluctuation, whereas the scour hole below the pipeline and the maximum scour depth exhibited a creeping development. Moreover, by comparing the scour profiles at t = 3.0 T (Figure 5i) and t = 10.0 T (Figure 5j), there was no significant change in the scour hole (nearly 19 h). This implied that the scour profile at t = 3.0 T could be recognized as a dynamic equilibrium scour profile.

_{0}= u

_{max}= 0.3 m/s, 0.4 m/s and 0.5 m/s are plotted in Figure 6, respectively. As detailed in Figure 6, there were two significant differences of scour profiles between the unidirectional and bidirectional currents. The first one is that there was only one dune downstream of the pipeline for the unidirectional steady current, whereas there were two dunes for the bidirectional tidal current and the scour profile was more symmetric. Moreover, the scour depth and width under the unidirectional current were both larger than those of the bidirectional tidal current. Additionally, with increasing velocity the size of the scour hole, including scour depth and width, also both increased.

#### 3.2. Temporal Development of Scour Depth

_{t}/u

_{max}is also shown. The figure demonstrated that scour depth increased rapidly during the first half of the tidal cycle. After that, the scour depth only increased slightly when the flow was near maximum flood or ebb tidal velocity and there was no scour development when the flow was close to zero velocity. It could also be seen that the decrease in scour depth induced by sediment backfilling did not obviously occur, which may be ascribed to the fact that the flow was turbulent enough to keep the sediment in suspension longer, allowing it to be transported out of the scour hole.

_{0}or u

_{max}= 0.3 and 0.4 m/s). It was evident that the scour depth development was much slower for the bidirectional tidal current compared to that under unidirectional steady current, whose velocity equaled the maximum velocity of the tide. This implied that the effective flow intensity, u

_{r}, under bidirectional tidal currentd with varied flow velocity was smaller than that of the unidirectional steady current based on u

_{max}.

#### 3.3. Maximum Scour Depth under Bidirectional Tidal Currents

_{sm}increased with flow velocity, and also increased with pipeline diameter in the same flow conditions. In order to evaluate the difference of maximum scour depth between unidirectional and bidirectional tidal currents, the equilibrium scour depths were transformed to dimensionless values d

_{sm}/D (Figure 10). As seen from Figure 10, the maximum scour depths d

_{sm}/D at the same flow conditions were nearly the same with different pipeline diameters. Moreover, it was also seen that the maximum scour depth under the bidirectional tidal current d

_{sm}/D was smaller than those of the unidirectional current for u

_{0}= u

_{max}, and was on average 0.8 times of that of the unidirectional current.

#### 3.4. Prediction of Maximum Scour Depth

_{sm}/D was a constant value, 1.73. However, the scour depth of each tidal current case from the present experiment was far less than 1.73, which implied that the scour under the bidirectional tidal current could not be regarded as that under wave.

_{0}/u

_{c}was proposed by nonlinear multiple regression (see Equation (5)). Figure 13 shows the comparisons of predicted values using Equation (5) with measured values. It could be seen that the predicted values using Equation (5) were in good agreement with the measured values and the relative error was within 20%. Compared to Equations (2)–(5), it was more suitable for predicting the maximum scour depth of a steady current in live-bed conditions.

#### 3.5. Comparison with Field Data

_{max}), water depth (h) and sediment properties (u

_{c}). However, in practical engineering, the hydrodynamic conditions are larger than in laboratory flow conditions. To accurately predict the scour depth in the field, it is necessary to make sure which equation is more applicable in practical engineering. Consequently, in this study, field data from 2014 from the Cezhen pipeline in tide-dominated Hangzhou Bay were used to validate the predicted equations. According to the field data, there were 15 free span segments mainly located in three regions KP3, KP12 and KP16, and the maximum scour depths of each span segment are listed as follows:

- KP3: three span segments and maximum scour depths of 0.3 m, 0.4 m and 0.6 m.
- KP12: four span segments and maximum scour depths of 0.2 m, 0.3 m, 0.4 m and 0.8 m.
- KP16: eight span segments and maximum scour depths of 0.3 m, 0.2 m, 0.1 m, 0.5 m, 0.2 m, 0.1 m, 0.1 m and 0.2 m.

_{50}, of the seabed near the pipeline was approximately 0.01 mm and the critical velocity for sediment incipient motion ranged from 0.8 to 1.2 m/s [30] (Table 2), based on a famous fine sediment incipient formula of Zhang et al. [31]. According to the flow and sediment parameters in the field, the maximum scour depths were predicted, respectively, by Equations (3)–(6). Figure 15 shows the predicted values using different equations with field data and Table 3 lists the absolute error (predicted value field data) of each equation. It was shown that the predicted maximum scour depth by Equation (6) was much closer to the field data, with absolute error within 0.1 D, whereas absolute errors using Equations (3) and (4) were 0.04–0.29 D and 0.13–0.38 D, respectively. In addition, it was also found that Equation (4) overestimated the scour values in the field data, while it underestimated the scour values in the experimental data (Figure 12). This may be because Equation (4) was highly sensitive to sediment size d

_{50}, especially smaller values. By evaluating the application of Equation (6) in the field and laboratory experiments, it was validated that Equation (6) was more accurate than the present equations, both in practical engineering and on the laboratory scale.

## 4. Conclusions

- Under a bidirectional tidal current, the scour profile, with two dunes on both sides of submarine pipeline, was more symmetric than that subject to a unidirectional current. In addition, the scour width and depth under a bidirectional tidal current were both smaller than those under a unidirectional tidal current.
- For bidirectional tidal currents, the scour depth increased rapidly during the first half of the tidal cycle. After that, the scour depth only increased slightly when the flow was near maximum flood or ebb tidal velocity, and there was no scour development when flow was close to zero velocity. Additionally, the equilibrium scour depth under a bidirectional current was averagely 0.8 times of that under a unidirectional current whose flow velocity was equal to the maximum tidal velocity.
- An equation to predict live-bed scour depth around submarine pipelines under bidirectional tidal currents was developed. In this equation, the scour depth under a bidirectional current was predicted based on a new fitted equation for live-bed scour depth in unidirectional current coupling with a reduction coefficient of 0.8. This equation was used to predict scour depth in practical engineering and showed good agreement with field data, indicating that the present new equation could accurately predict live-bed scour depth around submarine pipelines under bidirectional currents in the field.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Notations

d_{50} | sediment median diameter |

D | pipeline diameter |

Fr | Froude number |

g | gravitational acceleration |

h | water depth |

d_{s} | scour depth at x = 0.0 D |

d_{sm} | final maximum scour depth |

KC | Keulegan–Carpenter number |

t | time |

T | tidal period |

T_{w} | wave period |

u_{t} | velocity of tidal current at time t |

u_{max} | maximum peak velocity of tidal current |

u_{c} | critical velocity for sediment incipient motion |

u_{0} | velocity of unidirectional current |

u_{wmax} | peak velocity of wave |

x | horizontal direction |

z | vertical direction |

ρ_{s} | sediment density |

ρ | water density |

## References

- Chiew, Y.M. Prediction of maximum scour depth at submarine pipelines. J. Hydraul. Eng.
**1991**, 117, 452–466. [Google Scholar] [CrossRef] - Sumer, B.M.; Fredsøe, J. The Mechanics of Scour in the Marine Environment; World Scientific Publishing Company: Singapore, 2002. [Google Scholar]
- Fredsøe, J. Pipeline–seabed interaction. J. Waterw. Port Coast. Ocean Eng.
**2016**, 142, 03116002. [Google Scholar] [CrossRef] [Green Version] - Zhang, Q.; Draper, S.; Cheng, L.; An, H. Scour below a subsea pipeline in time varying flow conditions. Appl. Ocean Res.
**2016**, 55, 151–162. [Google Scholar] [CrossRef] [Green Version] - Zhang, Q.; Draper, S.; Cheng, L.; Zhao, M.; An, H. Experimental study of local scour beneath two tandem pipelines in steady current. Coast Eng. J.
**2017**, 59, 1750002. [Google Scholar] [CrossRef] - Zhang, Z.Y.; Shi, B.; Guo, Y.K.; Chen, D.Y. Improving the prediction of scour around submarine pipelines. Proc. Inst. Civ. Eng. -Marit. Eng.
**2016**, 169, 163–173. [Google Scholar] [CrossRef] [Green Version] - Yang, L.P.; Guo, Y.K.; Shi, B.; Kuang, C.P.; Xu, W.L.; Cao, S.Y. Study of scour around submarine pipeline with a rubber plate or rigid spoiler in wave conditions. ASCE J. Waterw. Port Ocean Coast Eng.
**2012**, 138, 484–490. [Google Scholar] [CrossRef] - Yang, L.P.; Shi, B.; Guo, Y.K.; Zhang, L.X.; Zhang, J.S.; Han, Y. Scour protection of submarine pipelines using rubber plates underneath the pipes. Ocean Eng.
**2014**, 84, 176–182. [Google Scholar] [CrossRef] [Green Version] - Mao, Y. The Interaction between A Pipeline and An Erodible Bed; The Technology University of Denmark: Kongens Lyngby, Denmark, 1986. [Google Scholar]
- Chiew, Y.M. Mechanics of local scour around submarine pipelines. J. Hydraul. Eng.
**1990**, 116, 515–529. [Google Scholar] [CrossRef] - Kjeldsen, S.P.; Gjorsvik, C.; Bringaker, K.G.; Jacobsen, J. Local scour near offshore pipelines. In Proceedings of the 2nd International Port and Ocean Engineering under Arctic Conditions, Reykjavik, Iceland, 27–30 August 1973; pp. 309–331. [Google Scholar]
- Bijker, E.W.; Leeuwestein, W. Interaction between pipelines and the seabed under the influence of waves and currents. In Seabed Mechanics; Denness, B., Ed.; Springer: Dordrecht, The Netherlands, 1984; pp. 235–242. [Google Scholar]
- Yang, L.P.; Shi, B.; Guo, Y.K.; Wen, X.Y. Calculation and experiment on scour depth for submarine pipeline with a spoiler. Ocean Eng.
**2012**, 55, 191–198. [Google Scholar] [CrossRef] - Ibrahim, A.; Nalluri, C. Scour prediction around marine pipelines. In Proceedings of the 5th International Offshore Mechanics and Arctic Engineering, Tokyo, Japan, 13–18 April 1986; pp. 679–684. [Google Scholar]
- Moncada-M., A.T.; Aguirre-Pe, J. Scour below Pipeline in River Crossings. J. Hydraul. Eng.
**1999**, 125, 953–958. [Google Scholar] [CrossRef] - Cevik, E.; Yuksel, Y. Scour under submarine pipelines in waves in shoaling conditions. J. Waterw. Port Coast. Ocean Eng.
**1999**, 125, 9–19. [Google Scholar] [CrossRef] - Lin, Z.B.; Guo, Y.K.; Jeng, D.-S.; Liao, C.C.; Rey, N. An integrated numerical model for wave–soil–pipeline interactions. Coast. Eng.
**2016**, 108, 25–35. [Google Scholar] [CrossRef] [Green Version] - Sumer, B.M.; Fredsøe, J. Scour below pipelines in waves. J. Waterw. Port Coast. Ocean Eng.
**1990**, 116, 307–323. [Google Scholar] [CrossRef] - Pu, Q.; Li, K.; Gao, F.P. Scour of the seabed under a pipeline in oscillatory flow. China Ocean Eng.
**2001**, 16, 129–137. [Google Scholar] - Etemad-Shahidi, A.; Yasa, R.; Kazeminezhad, M.H. Prediction of wave-induced scour depth under submarine pipelines using machine learning approach. Appl. Ocean Res.
**2011**, 33, 54–59. [Google Scholar] [CrossRef] [Green Version] - Yasa, R. Prediction of the Scour Depth under Submarine Pipelines—In Wave Condition. J. Coast. Res.
**2011**, 64, 627–630. [Google Scholar] - Zhang, J.; Shi, B.; Guo, Y.K.; Xu, W.L.; Yang, K.J.; Zhao, E.J. Scour Development Around Submarine Pipelines due to Current Based on the Maximum Entropy Theory. J. Ocean Univ. China
**2016**, 15, 841–846. [Google Scholar] [CrossRef] - Liu, M.M. Numerical investigation of local scour around submerged pipeline in shoaling conditions. Ocean Eng.
**2021**, 234, 109258. [Google Scholar] [CrossRef] - Zhang, Q.; Draper, S.; Cheng, L.; An, H. Time Scale of Local Scour around Pipelines in Current, Waves, and Combined Waves and Current. J. Hydraul. Eng.
**2017**, 143, 04016093. [Google Scholar] [CrossRef] - Li, Y.; Ong, M.; Fuhrman, D.R.; Larsen, B.E. Numerical investigation of wave plus-current induced scour beneath two submarine pipelines in tandem. Coast. Eng.
**2020**, 156, 103619. [Google Scholar] [CrossRef] - Zeng, J.; Chen, G.; Pan, C.; Zhang, Z. Effect of dike line adjustment on the tidal bore in the Qiantang Estuary, China. J. Hydrodyn.
**2017**, 29, 452–459. [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] - 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] - 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] - Zhu, L.; Liu, K.; Fan, H.; Cao, S.; Chen, H.; Wang, J.; Wang, Z. Scour beneath and adjacent to submarine pipelines with spoilers on a cohesive seabed: Case study of Hangzhou Bay, China. J. Waterw. Port Coast Ocean Eng.
**2019**, 145, 05018009. [Google Scholar] [CrossRef] - Zhang, R.J.; Xie, J.H.; Wang, M.F. River Sediment Dynamics; China Water and Power Press: Beijing, China, 1998. [Google Scholar]

**Figure 5.**Time process of scour profile for Tide 01: u

_{max}= 0.3 m/s, D = 0.045 m. (

**a**) t = 0.25 T; (

**b**) t = 0.50 T; (

**c**) t = 0.75 T; (

**d**) t = 1.0 T; (

**e**) t = 1.25 T; (

**f**) t = 1.50 T; (

**g**) t = 1.75 T; (

**h**) t = 2.0 T; (

**i**) t = 3.0 T; (

**j**) t = 10.0 T.

**Figure 6.**Comparisons of scour profiles under unidirectional and bidirectional tidal currents. (

**a**) u

_{0}= u

_{max}= 0.3 m/s; (

**b**) u

_{0}= u

_{max}= 0.4 m/s; (

**c**) u

_{0}= u

_{max}= 0.5 m/s.

Test | Pipe Diameter D (m) | Water Depth h (m) | u_{0}(m/s) | u_{max}(m/s) | u_{0}/u_{c}or u _{max}/u_{c} | Root Mean Velocity u _{r} (m/s) | Maximum Scour Depth d _{sm} (m) |
---|---|---|---|---|---|---|---|

Uni01 | 0.045 | 0.30 | 0.30 | 1.07 | 0.30 | 0.034 | |

Uni02 | 0.045 | 0.30 | 0.35 | - | 1.25 | 0.35 | 0.038 |

Uni03 | 0.045 | 0.30 | 0.40 | - | 1.43 | 0.40 | 0.046 |

Uni04 | 0.045 | 0.30 | 0.45 | 1.61 | 0.45 | 0.050 | |

Uni05 | 0.045 | 0.30 | 0.50 | - | 1.79 | 0.50 | 0.054 |

Uni06 | 0.075 | 0.30 | 0.30 | 1.07 | 0.30 | 0.051 | |

Uni07 | 0.075 | 0.30 | 0.40 | - | 1.43 | 0.40 | 0.068 |

Uni08 | 0.075 | 0.30 | 0.50 | - | 1.79 | 0.50 | 0.078 |

Tide01 | 0.045 | 0.30 | - | 0.30 | 1.07 | 0.19 | 0.024 |

Tide02 | 0.045 | 0.30 | - | 0.35 | 1.25 | 0.22 | 0.034 |

Tide03 | 0.045 | 0.30 | - | 0.40 | 1.43 | 0.25 | 0.038 |

Tide04 | 0.045 | 0.30 | - | 0.45 | 1.61 | 0.29 | 0.041 |

Tide05 | 0.045 | 0.30 | - | 0.50 | 1.79 | 0.32 | 0.043 |

Tide06 | 0.075 | 0.30 | - | 0.30 | 1.07 | 0.19 | 0.045 |

Tide07 | 0.075 | 0.30 | - | 0.40 | 1.43 | 0.25 | 0.058 |

Tide08 | 0.075 | 0.30 | - | 0.50 | 1.79 | 0.32 | 0.066 |

Hung Segment Location | Pipeline Diameter D (m) | Water Depth H (m) | Maximum Tidal Velocity u _{max} (m/s) | Sediment Incipient Velocity u _{c} (m/s) | u_{max}/u_{c} | Froude Number Fr | Measured Scour Depth d _{sm}/D |
---|---|---|---|---|---|---|---|

KP3 | 0.9 | 5.0 | 1.6 | 0.8 | 2.0 | 0.23 | 0.67 |

KP12 | 0.9 | 8.0 | 2.1 | 1.0 | 2.1 | 0.24 | 0.89 |

KP16 | 0.9 | 10.0 | 1.8 | 1.1 | 1.6 | 0.18 | 0.56 |

Field Data d_{sm}/D | Equation (6) | Equation (3) | Equation (4) | |||
---|---|---|---|---|---|---|

Predicted Value d_{sm}/D | Absolute Error | Predicted Value d _{sm}/D | Absolute Error | Predicted Value d _{sm}/D | Absolute Error | |

0.67 | 0.74 | 0.07 | 0.60 | −0.07 | 0.89 | 0.22 |

0.89 | 0.83 | −0.06 | 0.60 | −0.29 | 1.02 | 0.13 |

0.56 | 0.65 | 0.09 | 0.60 | 0.04 | 0.94 | 0.38 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, Z.; Guo, Y.; Yang, Y.; Shi, B.; Wu, X.
Scale Model Experiment on Local Scour around Submarine Pipelines under Bidirectional Tidal Currents. *J. Mar. Sci. Eng.* **2021**, *9*, 1421.
https://doi.org/10.3390/jmse9121421

**AMA Style**

Zhang Z, Guo Y, Yang Y, Shi B, Wu X.
Scale Model Experiment on Local Scour around Submarine Pipelines under Bidirectional Tidal Currents. *Journal of Marine Science and Engineering*. 2021; 9(12):1421.
https://doi.org/10.3390/jmse9121421

**Chicago/Turabian Style**

Zhang, Zhiyong, Yakun Guo, Yuanping Yang, Bing Shi, and Xiuguang Wu.
2021. "Scale Model Experiment on Local Scour around Submarine Pipelines under Bidirectional Tidal Currents" *Journal of Marine Science and Engineering* 9, no. 12: 1421.
https://doi.org/10.3390/jmse9121421