# Analysis and Design of Monopile Foundations for Offshore Wind and Tidal Turbine Structures

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Hybrid Generation from Offshore Renewable Sources

#### 1.2. The Integration of Offshore Wind with Tidal Energy

- (a)
- Site investigation;
- (b)
- Criteria for design;
- (c)
- Evaluation of the stability of design under combined loads.

## 2. Environmental Parameters for Design

_{k}is 5.67z, and for z above 60 m, L

_{k}is 340.2 m [36]. As the height above sea level is 87m, the turbulence integral length scale is 340.2 m in this case.

## 3. Methods

## 4. Results

#### 4.1. Finite Element Analysis

#### 4.2. Macro-Element Model

- Steel monopile, diameter 6 m, ensures rigid behavior, as recommended by Jose and Mathai [52].

_{L}, K

_{R}, and K

_{LR}) can be determined based on the pile dimensions and soil type. Once K

_{L}, K

_{R}, and K

_{LR}are known, one can predict the system’s natural frequency [54]. The results for this design are:

_{L}= 3848.25 MN/m, K

_{LR}= −133,488 MN and K

_{R}= 7,252,848 MNm/rad.

#### 4.2.1. Wind Loads

#### 4.2.2. Wave Loads

_{x}and DAF

_{y}for wave scenarios are negligible, a higher value is applied to loads.

#### 4.2.3. Load Combinations for Ultimate Limit State (ULS)

_{P}) and monopile diameter (D

_{P}) as depicted below:

_{P}in Equation (A2) results in the required thickness:

_{P}and L

_{P}satisfy the above conditions. Therefore, the pile dimensions for the Terawhiti site to withstand total load are:

_{P}= 6 [m] t

_{P}= 0.083 [m] L

_{P}= 60 [m]

#### 4.2.4. Long-Term Deflection & Rotation of the Pile Mudline Moment

_{L}= 3848.25 MN/m, K

_{LR}= −133488 MN, and K

_{R}= 7252848 MNm/rad. Using these values in Equations (A8) and (A9) results in

## 5. Conclusions

- The proposed tower is a hollow steel tube wall with a thickness of 0.027 m, 68 m high above the platform, tapering from 5 m at the base to 3 m at the top, and weighing 255 tonnes.
- The proposed transition piece is a steel tube with an internal diameter $\left(\mathrm{of}\text{}6+\frac{2\times 83}{1000}=\right)\mathrm{of}\text{}6.16\text{}$m to fit the top of the monopile, wall thickness of 0.083 m and extending 29 m below the platform level, and sheathing on top of the monopile. Weight: 300 tonnes.
- The proposed foundation is a monopile inserted into the seabed. It would be solid steel, 6 m in diameter, and 60 m long, weighing 700 tonnes. It would project above the seabed for 30 m (the upper 20 m would be inserted into the transition piece), and the lower 20 m would be placed in the seabed. The pile would be driven with a hydraulic hammer into the seabed.
- The acting loads are transferred to the foundation; they can be static depending on the total weight of the structure, which is calculated and analyzed with OPTUM G3 software, or dynamic (cyclic), which is investigated by combining wind and wave loads.
- The wind and water produce aerodynamic and hydrodynamic loads (thrust and drag) on the structure, which depend on the operational speed of turbines. However, to know the acceptability of foundation design, it is necessary to combine wind and wave loads in ULS design and calculate maximum loads and find the driven scenarios. Then, find the required dimensions of the pile and, based on the maximum load of the driven scenario, calculate deflection and check in ULS if the deflection is allowable or not.
- The combination of wind and wave loads indicates that the maximum load occurs for the E-3 scenario. Applying loads of this scenario results in acceptable deflection, tilt, and natural frequency for Terawhiti.
- Several iterations were done to reach the required pile dimensions after finding the maximum combined load for the driving scenario.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

_{0}is the Eigen frequency, and ξ is the damping ratio and wave periods from Table 12 and ${\mathrm{f}}_{0}$ is 0.34 Hz.

_{P}, D

_{P}, and t

_{P}are the moment of inertia, diameter, and thickness of the monopile, respectively. The following criteria for maximum stress ${\sigma}_{m}$ (see Table 5) needs to be allowable [36]:

_{M}= 1.1 is the pile material safety factor and ${f}_{yk}$= 355 MPa is the pile yield stress (from Table 7). From Equation (A4), the required diameter is determined as:

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**Figure 2.**National Depth-averaged Tidal Current Speeds for Mean Spring Flows (in m/s) [37].

**Figure 3.**Wind Speed Histogram for Terawhiti [42].

**Figure 6.**The geometry after meshing (

**left**), displacement (

**middle**), and total dissipation energy (

**right**) for Loose Sand.

**Figure 7.**The geometry after meshing (

**left**), displacement (

**middle**), and total dissipation energy (

**right**) for Medium Sand.

**Figure 8.**The geometry after meshing (

**left**), displacement (

**middle**), and total dissipation energy (

**right**) for Dense Sand.

**Figure 9.**The geometry after meshing (

**left**), displacement (

**middle**), and total dissipation energy (

**right**) for Soft Clay.

**Figure 10.**The geometry after meshing (

**left**), displacement (

**middle**), and total dissipation energy (

**right**) for Firm Clay.

**Figure 11.**The geometry after meshing (

**left**), displacement (

**middle**), and total dissipation energy (

**right**) for Stiff Clay.

**Figure 12.**Mechanical Model of Foundation; K

_{V}(vertical stiffness), K

_{L}(lateral stiffness), K

_{R}(rocking stiffness), and K

_{LR}(cross-coupling) [54].

Location | Latitude (deg) | Longitude (deg) | Annual Average Water Velocity (m/s) | Depth of Water (m) | Average Yearly Wind Velocity (m/s) |
---|---|---|---|---|---|

Terawhiti | −41.279497° S | 174.524249° E | 1.09 | 30 | 7.10 |

Parameter | Symbol | Value | Unit |
---|---|---|---|

Significant wave height with a 50-year return period [39] | H_{s} | 15 | m |

Peak wave period | T_{s} | 13.73 | s |

Maximum wave height (50 years) | H_{m} | 27.62 | m |

Maximum wave peak period | T_{m} | 18.63 | s |

Maximum water depth (50-year high water level) | S | 30 | m |

Water density | ρ_{w} | 1030 | kg/m^{3} |

Site | Highest Astronomical Tide (HAT) | Lowest Astronomical Tide (LAT) | Average Current (m/s) | Peak Current (m/s) | Water Depth (m) |
---|---|---|---|---|---|

Terawhiti | 1.93 | 0.39 | 1.09 | 2.60 | 30 |

Parameter | Symbol | Value | Unit |
---|---|---|---|

Shape parameter-Weibull distribution [43] | s | 1.98 | [-] |

Scale parameter-Weibull distribution [43] | K | 7.99 | m/s |

Reference turbulence intensity [44] | I | 16 | % |

Turbulence integral length scale [36] | L_{K} | 340.2 | m |

Annual wind speed [42] | u_{ave} | 7.10 | m/s |

Air density [36] | ρa | 1.225 | kg/m^{3} |

**Table 5.**Main criteria for foundation design [36].

Parameter | Limit |
---|---|

The maximum stress (${\sigma}_{m}$)-yield strength (${f}_{yk}$) | ${\sigma}_{m}<{f}_{yk}$ |

Deflection of monopile (${\rho}_{0}$) | ${\rho}_{0}<0.2\mathrm{m}$ |

Tilt (${\theta}_{0}$) | ${\theta}_{0}<0.5\xb0$ |

Structural natural frequency(f_{0})-frequency of rotation of the rotor (f_{1P, max}) | f_{0} > 1.1f_{1P, max} = 0.24 Hz |

Pile wall thickness (t_{P}) | t_{P} ≥ $6.35+\frac{{D}_{P}}{100}$ |

Parameter | Symbol | Value | Unit |
---|---|---|---|

Turbine Power | P | 3.6 | MW |

Turbine rotational Speed (Cut in/out) | u_{in}/u_{out} | 5-13 | rpm |

Operational wind speed range | V | 4-25 | m/s |

Rated wind speed | u_{R} | 16.5 | m/s |

Mass of the nacelle (NA) | m_{NA} | 125 | tonnes |

Hub height from mean sea level | H | 87 | m |

Density of tower, monopile and TP-S355 Steel | ρ | 7860 | kg/m^{3} |

Tower data | |||

Top diameter | D_{t} | 3 | m |

Bottom diameter | D_{b} | 5 | m |

Weight | m_{t} | 255 | tonnes |

Tower height | L_{T} | 68 | m |

Wall thickness | t_{T} | 0.027 | m |

Monopile data | |||

Monopile Young’s module-S355 Steel | E_{P} | 200 | GPa |

Soil’s unit weight | γ | 16 | kN/m^{3} |

Soil’s internal friction | ϕ | 30 | ° |

Monopile length | L_{P} | 60 | m |

Monopile diameter | D_{P} | 6 | m |

Monopile thickness | t_{P} | 0.083 | m |

Monopile yield stress | ${f}_{yk}$ | 355 | MPa |

Monopile weight | W_{P} | 700 | t |

Transition piece (TP) data | |||

TP Young’s module-S355 Steel | E_{TP} | 200 | GPa |

TP weight | W_{TP} | 300 | t |

Transition piece internal diameter | D_{TP} | 6.16 | m |

Transition piece thickness | t_{TP} | 0.083 | m |

Transition piece length | L_{TP} | 29 | m |

Grout and TP combined thickness | t_{G}+t_{TP} | 0.15 | m |

Rotor and blade data | |||

Turbine rotor diameter | D | 107 | m |

Swept area | TSA | 8992 | m^{2} |

Mass of rotor + hub | m_{R} | 100 | tonnes |

Rotor overhang | b | 4 | m |

Blade root diameter | B_{root} | 4 | m |

Blade tip chord length | B_{tip} | 1 | m |

Blade length | L | 52 | m |

Parameter | Symbol | Value | Unit |
---|---|---|---|

Turbine Power | P | 2 | MW |

Turbine rotational Speed (Cut in/out) | Ω | 1–3.05 | rpm |

Operational tidal speed range | V | 1–4.5 | m/s |

Turbine rotor diameter | D | 20 | m |

Height from the seabed | ZS | 25 | m |

Rotor Swept area | TSA | 314 | m^{2} |

Mass of two turbines | m | 300 | tonnes |

**Table 8.**Load Case Scenarios [36].

Scenario | Name and Description | Wind Model | Wave Model | Alignment |
---|---|---|---|---|

E-1 | Normal operational conditions. Wind and wave action in the same direction (no misalignment). | NTM at u_{R} (U-1) | 1-yr ESS (W-1) | Collinear |

E-2 | Extreme wave load scenario. Wind and wave action in the same direction (no misalignment). | ETM at u_{R} (U-2) | 50-yr EWH (W-4) | Collinear |

E-3 | Extreme wind load scenario. Wind and wave action in the same direction (no misalignment). | EOG at u_{R} (U-3) | 1-yr EWH (W-2) | Collinear |

E-4 | Cut-out wind speed and extreme operating gust scenario. Wind and wave action in the same direction (no misalignment). | EOG at u_{out} (U-4) | 50-yr EWH (W-4) | Collinear |

E-5 | Wind and wave misalignment scenario. Same as E-2, except the wind and wave are misaligned at an angle of $\varphi $ = 90°. Due to low aerodynamic damping, the dynamic amplification is higher in the cross-wind direction. | ETM at u_{R} (U-2) | 50-yr EWH (W-4) | Misaligned at $\varphi $= 90° |

Item | Loose Sand-MC | Medium Sand-MC | Dense Sand-MC | Soft Clay-MC | Firm Clay-MC | Stiff Clay-MC |
---|---|---|---|---|---|---|

Cohesion c (kPa) | 0 | 0 | 0 | 5 | 10 | 20 |

Friction angle ϕ (°) | 30 | 35 | 40 | 18 | 20 | 22 |

Soil Unit Weight γ (kN/m^{3}) | 16 | 18 | 20 | 19 | 20 | 21 |

Item | Loose Sand-MC | Medium Sand-MC | Dense Sand-MC | Soft Clay-MC | Firm Clay-MC | Stiff Clay-MC |
---|---|---|---|---|---|---|

Max Displacement (m) | 1.0483 | 1.012 | 1.0203 | 1.0294 | 1.1341 | 1.2819 |

Total Dissipation Energy (kJ) | 0.00049 | 0.0012 | 0.0678 | 0.016 | 0.0456 | 0.133 |

Parameters | Wind Scenario (U-1) | Wind Scenario (U-2) | Wind Scenario (U-3) | Wind Scenario (U-4) |
---|---|---|---|---|

Standard deviation of wind speed${\sigma}_{U}\left[\mathrm{m}/\mathrm{s}\right]$ | 2.69 | 3.1 | 2.7 | 2.7 |

Standard deviation in f > f_{1P} | 0.89 | 1.01 | - | - |

Turbulent wind speed component$u\left[\mathrm{m}/\mathrm{s}\right]$ | 1.13 | 2.02 | 7.1 | 7.1 |

Total wind load F_{wind} [MN] | 1.68 | 1.86 | 3 | 0.69 |

Total wind moment M_{wind} [MNm] | 196.5 | 217.62 | 351 | 80.7 |

Parameters | Wave Scenario (W-1) | Wave Scenario (W-2) | Wave Scenario (W-3) | Wave Scenario (W-4) |
---|---|---|---|---|

Wave period T [s] | 12.2 | 16.66 | 13.73 | 18.63 |

Wave height H [m] | 12 | 22.10 | 15 | 27.62 |

Wave frequency f [Hz] | 0.081 | 0.060 | 0.072 | 0.053 |

Dynamic amplification-along-wind DAF_{x} [-] | 1.060049 | 1.032081 | 1.046857 | 1.024857 |

Dynamic amplification-cross-wind DAF_{y} [-] | 1.1060158 | 1.032136 | 1.046939 | 1.024899 |

Total wave load F_{w}[MN] | 3.1 | 7.4 | 4.6 | 8.04 |

Total wave moment M_{w} [MNm] | 55.6 | 164.3 | 119 | 210.93 |

Total wave load with DAF F_{w,DAF} [MNm] | 3.42 | 7.63 | 4.81 | 8.24 |

Total wave moment with DAF M_{w,DAF} [MNm] | 61.5 | 169.5 | 124.5 | 216.1 |

Parameter | Normal Operation E-1 | Extreme Wave Scenario E-2 | Extreme Wind Scenario E-3 | Cut-out Wind+ Extreme Wave Scenario E-4 | Wind-Wave Misalignment E-5 |
---|---|---|---|---|---|

Maximum wind load [MN] | 1.68 | 1.86 | 3 | 0.69 | 1.86 |

Maximum wave load [MN] | 3.1 | 8.04 | 7.4 | 8.04 | 8.04 |

Combined maximum load [MN] | 4.78 | 9.9 | 10.4 | 8.73 | 9.9 |

Maximum wind moment [MNm] | 196.5 | 217.62 | 351 | 80.7 | 217.62 |

Maximum wave moment [MNm] | 55.6 | 210.93 | 164.3 | 210.93 | 210.93 |

Combined maximum moment [MN] | 252.1 | 428.55 | 515.3 | 291.63 | 428.55 |

Cycle time period [s] | 12.2 | 18.63 | 16.66 | 18.63 | 18.63 |

frequency [Hz] | 0.081 | 0.053 | 0.060 | 0.053 | 0.053 |

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**MDPI and ACS Style**

Nasab, N.M.; Kilby, J.; Bakhtiaryfard, L. Analysis and Design of Monopile Foundations for Offshore Wind and Tidal Turbine Structures. *Water* **2022**, *14*, 3555.
https://doi.org/10.3390/w14213555

**AMA Style**

Nasab NM, Kilby J, Bakhtiaryfard L. Analysis and Design of Monopile Foundations for Offshore Wind and Tidal Turbine Structures. *Water*. 2022; 14(21):3555.
https://doi.org/10.3390/w14213555

**Chicago/Turabian Style**

Nasab, Navid Majdi, Jeff Kilby, and Leila Bakhtiaryfard. 2022. "Analysis and Design of Monopile Foundations for Offshore Wind and Tidal Turbine Structures" *Water* 14, no. 21: 3555.
https://doi.org/10.3390/w14213555