# Effect of Scour on the Natural Frequency Responses of the Meteorological Mast in the Taiwan Strait

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{−3}, such that the foundation stiffness can be calculated using the initial slope of the load–deformation curve [5,6,7].

## 2. Met mast of TPC in the Chang-Bin offshore Wind Farm

## 3. Vibration Measurements and Analysis of the Met Mast

## 4. Numerical Model to Analyze the Dynamic Responses of Offshore Structures

#### 4.1. Load–Deformation Response of the Pile–Soil Interaction

^{3}); $D$ is the pile diameter (m); $\alpha ={\varphi}^{\prime}/2$; $\beta =45\xb0+{\varphi}^{\prime}/2$; ${K}_{0}$ is the coefficient of the lateral earth pressure at rest, ${K}_{0}=1-\mathrm{sin}{\varphi}^{\prime}$; ${K}_{a}$ is the coefficient of the active lateral earth pressure, ${K}_{a}={\mathrm{tan}}^{2}\left(45\xb0-{\varphi}^{\prime}/2\right)$; and ${n}_{h}$ is the initial modulus of subgrade reaction (kN/m

^{3}) determined by soil conditions, it is not related to the embedded pile depth or pile diameter. Figure 9 shows the relationship among the initial modulus of subgrade reaction, effective friction angle, and relative density as recommended by API [33].

#### 4.2. Effect of Scour on the Monopile Foundation Stiffness

## 5. Effect of Scour on the Vibration Responses of the Met Mast

#### 5.1. Verification of the Numerical Model

#### 5.2. Effect of Seabed Elevation Caused by Scour on the Natural Frequency

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Taiwan Power Company’s (TPC’s) met mast and borehole site at Chang-Bin offshore wind farm.

**Figure 8.**Simulation types of foundation of offshore structure. (

**a**) Coupled-springs foundation model; (

**b**) Distributed-springs foundation model.

**Figure 9.**Relationship of the initial modulus of subgrade reaction, the effective friction angle, and relative density.

**Figure 10.**Boundary conditions of different methods considering the effect of scour. (

**a**) Consider the soil below the bottom of scour hole; (

**b**) Consider the geometry of scour hole.

**Figure 11.**p–y curves for various scour depths at depth of 0.5D below the bottom of the scour hole. $\left({E}_{py,\text{}modified}/{E}_{py,\text{}unmodified}=2.8\right)$.

**Figure 12.**p–y curves for various scour depths at depth of 1.5D below the bottom of the scour hole. $\left({E}_{py,\text{}modified}/{E}_{py,\text{}unmodified}=1.8\right)$.

**Figure 13.**p–y curves for various scour depths at depth of 3D below the bottom of the scour hole. $\left({E}_{py,\text{}modified}/{E}_{py,\text{}unmodified}=1.4\right)$.

**Figure 15.**Numerical model of TPC’s met mast. (

**a**) Coupled-springs foundation model; (

**b**) Distributed-springs foundation model.

Soil Layer | Depth ($\mathbf{m}$) | Effective Unit Weight ${\mathit{\gamma}}^{\prime}$ ($\mathbf{k}\mathbf{N}/{\mathbf{m}}^{3}$) | Friction Angle ${\mathit{\varphi}}^{\prime}$ (^{o}) |
---|---|---|---|

Sand 1 | 0–10.8 | 8.5 | 29.5 |

Sand 2 | 10.8–26.1 | 9.5 | 32.0 |

Sand 3 | 26.1–47.2 | 9.6 | 32.3 |

Sand 4 | 47.2–71.5 | 9.5 | 33.0 |

Geometry of Met-Mast | Value | |
---|---|---|

Tower height above MWL | (m) | 92 |

Platform height above MWL | (m) | 19 |

Tower mass | (ton) | 216 |

Water depth | (m) | 15 |

Pile diameter | (m) | 3.8 |

Pile thickness | (m) | 0.05 |

Embedded pile length | (m) | 36.35 |

Mode Number | Mode Shape | Measured |
---|---|---|

1 | 1st bending mode (X or Y) | 0.6 |

2 | 2nd bending mode (X or Y) | 1.4 |

3 | 3rd bending mode (X or Y) | 2.7 |

4 | 1st torsional mode | 3.6 |

5 | 2nd torsional mode | 4.6 |

Condition | Type of Simulation for Monopile Foundation | Type of Simulation for Pile-Soil Interaction | |
---|---|---|---|

case 1 | coupled springs | Kallehave et al. [14] + Lin et al. [23] | (Figure 10b) |

case 2 | coupled springs | API [8] + the entire scoured layer is removed | (Figure 10a) |

case 3 | distributed springs | Kallehave et al. [14] + Lin et al. [23] | (Figure 10b) |

case 4 | distributed springs | API [8] + the entire scoured layer is removed | (Figure 10a) |

Classification of p–y Curves Used in This Study | S_{d}/D | 0 | 0.5 | 1 | 1.5 | |
---|---|---|---|---|---|---|

case 1 | ${K}_{uu}$ | ($\mathrm{kN}/\mathrm{m}$) | 6.29 × 10^{5} | 6.86 × 10^{5} | 7.21 × 10^{5} | 8.08 × 10^{5} |

${K}_{\theta u}$ | ($\mathrm{kNm}/\mathrm{m}$) | −4.24 × 10^{6} | −4.54 × 10^{6} | −4.71 × 10^{6} | −5.05 × 10^{6} | |

${K}_{u\theta}$ | ($\mathrm{kN}/\mathrm{rad}$) | −4.24 × 10^{6} | −4.54 × 10^{6} | −4.71 × 10^{6} | −5.05 × 10^{6} | |

${K}_{\theta \theta}$ | ($\mathrm{kNm}/\mathrm{rad}$) | 4.61 × 10^{7} | 4.77 × 10^{7} | 4.84 × 10^{7} | 4.98 × 10^{7} | |

case 2 | ${K}_{uu}$ | ($\mathrm{kN}/\mathrm{m}$) | 4.43 × 10^{5} | 4.70 × 10^{5} | 5.00 × 10^{5} | 5.36 × 10^{5} |

${K}_{\theta u}$ | ($\mathrm{kNm}/\mathrm{m}$) | −3.46 × 10^{6} | −3.61 × 10^{6} | −3.76 × 10^{6} | −3.92 × 10^{6} | |

${K}_{u\theta}$ | ($\mathrm{kN}/\mathrm{rad}$) | −3.46 × 10^{6} | −3.61 × 10^{6} | −3.76 × 10^{6} | −3.92 × 10^{6} | |

${K}_{\theta \theta}$ | ($\mathrm{kNm}/\mathrm{rad}$) | 4.20 × 10^{7} | 4.28 × 10^{7} | 4.36 × 10^{7} | 4.43 × 10^{7} |

Mode Shape | Measured (Table 3) | Simulated | |||
---|---|---|---|---|---|

S_{d} = 0D | S_{d} = 0.5D | S_{d} = 1D | S_{d} = 1.5D | ||

1st bending mode (X or Y) | 0.6 | 0.575 | 0.568 | 0.561 | 0.555 |

0.588 | 0.580 | 0.572 | 0.566 | ||

2nd bending mode (X or Y) | 1.4 | 1.035 | 1.005 | 0.975 | 0.950 |

1.037 | 1.007 | 0.977 | 0.952 | ||

3rd bending mode (X or Y) | 2.7 | 2.196 | 2.140 | 2.088 | 2.049 |

2.207 | 2.151 | 2.099 | 2.059 | ||

1st torsional mode | 3.6 | 2.911 | 2.902 | 2.892 | 2.883 |

2nd torsional mode | 4.6 | 4.531 | 4.531 | 4.530 | 4.530 |

Mode Shape | Measured (Table 3) | Simulated | |||
---|---|---|---|---|---|

S_{d} = 0D | S_{d} = 0.5D | S_{d} = 1D | S_{d} = 1.5D | ||

1st bending mode (X or Y) | 0.6 | 0.566 | 0.559 | 0.552 | 0.545 |

0.578 | 0.570 | 0.563 | 0.556 | ||

2nd bending mode (X or Y) | 1.4 | 0.996 | 0.967 | 0.939 | 0.914 |

0.998 | 0.969 | 0.941 | 0.915 | ||

3rd bending mode (X or Y) | 2.7 | 2.126 | 2.077 | 2.034 | 1.996 |

2.137 | 2.088 | 2.044 | 2.006 | ||

1st torsional mode | 3.6 | 2.910 | 2.901 | 2.891 | 2.882 |

2nd torsional mode | 4.6 | 4.531 | 4.531 | 4.530 | 4.529 |

Mode Shape | Measured (Table 3) | Simulated | |||
---|---|---|---|---|---|

S_{d} = 0D | S_{d} = 0.5D | S_{d} = 1D | S_{d} = 1.5D | ||

1st bending mode (X or Y) | 0.6 | 0.623 | 0.617 | 0.611 | 0.604 |

0.640 | 0.633 | 0.626 | 0.619 | ||

2nd bending mode (X or Y) | 1.4 | 1.234 | 1.210 | 1.184 | 1.157 |

1.237 | 1.213 | 1.187 | 1.160 | ||

3rd bending mode (X or Y) | 2.7 | 2.755 | 2.670 | 2.580 | 2.493 |

2.785 | 2.688 | 2.595 | 2.506 | ||

1st torsional mode | 3.6 | 2.947 | 2.922 | 2.905 | 2.892 |

2nd torsional mode | 4.6 | 4.531 | 4.531 | 4.531 | 4.531 |

Mode Shape | Measured (Table 3) | Simulated | |||
---|---|---|---|---|---|

S_{d} = 0D | S_{d} = 0.5D | S_{d} = 1D | S_{d} = 1.5D | ||

1st bending mode (X or Y) | 0.6 | 0.623 | 0.617 | 0.611 | 0.604 |

0.640 | 0.633 | 0.626 | 0.619 | ||

2nd bending mode (X or Y) | 1.4 | 1.234 | 1.210 | 1.184 | 1.157 |

1.237 | 1.212 | 1.187 | 1.159 | ||

3rd bending mode (X or Y) | 2.7 | 2.754 | 2.668 | 2.579 | 2.492 |

2.783 | 2.686 | 2.593 | 2.505 | ||

1st torsional mode | 3.6 | 2.946 | 2.922 | 2.905 | 2.892 |

2nd torsional mode | 4.6 | 4.531 | 4.531 | 4.531 | 4.531 |

Mode Number | Mode Shape | Case 3 | Case 4 | ||||||
---|---|---|---|---|---|---|---|---|---|

S_{d} = 0D | S_{d} = 0.5D | S_{d} = 1D | S_{d} = 1.5D | S_{d} = 0D | S_{d} = 0.5D | S_{d} = 1D | S_{d} = 1.5D | ||

4 | fore-aft 1st bending mode | 1.234 | 1.21 | 1.184 | 1.157 | 1.234 | 1.21 | 1.184 | 1.157 |

5 | side-side 1st bending mode | 1.237 | 1.213 | 1.187 | 1.16 | 1.237 | 1.212 | 1.187 | 1.159 |

7 | fore-aft 2nd bending mode | 2.755 | 2.67 | 2.58 | 2.493 | 2.754 | 2.668 | 2.579 | 2.492 |

8 | side-side 2nd bending mode | 2.785 | 2.688 | 2.595 | 2.506 | 2.783 | 2.686 | 2.593 | 2.505 |

22 | 1st vertical mode | 12.368 | 11.87 | 11.329 | 10.872 | 12.272 | 11.77 | 11.24 | 10.803 |

24 | fore-aft 3rd bending mode | 12.926 | 12.215 | 11.53 | 11.006 | 12.754 | 12.074 | 11.431 | 10.923 |

36 | 2nd vertical mode | 21.803 | 21.266 | 20.739 | 20.221 | 21.804 | 21.268 | 20.739 | 20.221 |

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**MDPI and ACS Style**

Tseng, W.-C.; Kuo, Y.-S.; Lu, K.-C.; Chen, J.-W.; Chung, C.-F.; Chen, R.-C. Effect of Scour on the Natural Frequency Responses of the Meteorological Mast in the Taiwan Strait. *Energies* **2018**, *11*, 823.
https://doi.org/10.3390/en11040823

**AMA Style**

Tseng W-C, Kuo Y-S, Lu K-C, Chen J-W, Chung C-F, Chen R-C. Effect of Scour on the Natural Frequency Responses of the Meteorological Mast in the Taiwan Strait. *Energies*. 2018; 11(4):823.
https://doi.org/10.3390/en11040823

**Chicago/Turabian Style**

Tseng, Wei-Chen, Yu-Shu Kuo, Kung-Chun Lu, Jing-Wen Chen, Chiou-Fong Chung, and Ruey-Chyi Chen. 2018. "Effect of Scour on the Natural Frequency Responses of the Meteorological Mast in the Taiwan Strait" *Energies* 11, no. 4: 823.
https://doi.org/10.3390/en11040823