Sway-Rocking Spring System Applicable to Short-Rigid Monopile Foundations

Abstract

Sway-Rocking (SR) spring system is a foundation modelling method in which a 2 × 2 spring stiffness matrix represents the foundation stiffness at seabed level. Since each individual element of the spring stiffness matrix is a function of a few physical properties of the soil and pile, it is the simplest and computationally cheapest method to estimate the deformation at the seabed level and the natural frequency of an offshore wind turbine structure. Formulae currently available are only applicable to conventional long-flexible piles or perfectly rigid foundations such as footings or caissons. This study aims to extend the application of the SR spring system to a so-called short-rigid pile range, which lays between the two ranges: long-flexible and perfectly rigid. Monopiles, the most commonly selected type of offshore wind foundations, are categorized in the short-rigid pile range. By conducting three-dimensional finite element analyses, the short-rigid pile behaviour is investigated. Based on the results, a new set of formulae of the SR spring stiffness, which is applicable to a wide range (long-flexible, short-rigid and perfectly rigid) of piles, is proposed. The new formulae also improve the accuracy of frequency estimation for practical use cases.

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source: Wind-Europe 2017, 4C Offshore 2018 and IRENA 2019)

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Abbreviations

H :

Lateral force at the seabed (N)

M :

Moment at the seabed (Nm)

u :

Lateral displacement (m)

\(\theta\) :

Rotational displacement (rad)

\(K_{L}\) :

Lateral spring stiffness (N/m)

\(K_{LR}\) :

Coupling spring 1 stiffness (N/rad)

\(K_{RL}\) :

Coupling spring 2 stiffness (Nm/m)

\(K_{R}\) :

Rotational spring stiffness (Nm/rad)

\(\eta_{L}\) :

\(K_{L}\) Normalized by \(E_{s}\) and \(D_{p}\) (–)

\(\eta_{LR}\) :

\(K_{LR}\) Normalized by \(E_{s}\) and \(D_{p}\) (–)

\(\eta_{RL}\) :

\(K_{RL}\) Normalized by \(E_{s}\) and \(D_{p}\) (–)

\(\eta_{R}\) :

\(K_{R}\) Normalized by \(E_{s}\) and \(D_{p}\) (–)

\(E_{s}\) :

Young’s modulus of soil (Pa)

\(E_{p}\) :

Effective pile stiffness (Pa)

\(\nu\) :

Poisson’s ratio (–)

\(L_{p}\) :

Embedded length of pile (m)

\(D_{p}\) :

Diameter of pile (m)

\(t_{p}\) :

Wall thickness of pile (m)

\(EI_{p}\) :

Bending stiffness of pile (Nm2)

\(L_{t}\) :

Tower height (m)

\(D_{t}\) :

Diameter of tower (m)

\(t_{t}\) :

Wall thickness of tower (m)

\(EI_{t}\) :

Bending stiffness of tower (Nm2)

\(K_{t}\) :

Tower stiffness in lateral way (N/m)

\(M_{eff}\) :

Effevtive mass at the top of tower (kg)

\(m_{t}\) :

Total mass of tower (kg)

\(m_{RNA}\) :

Mass of RNA (kg)

\(\upomega _{1}\) :

Angular velocity (1st mode) (rad/s)

\(\upomega _{FB}\) :

Fixed-base angular velocity (rad/s)

\(f_{1}\) :

Natural frequency (1st mode) (Hz)

\(f_{FB}\) :

Fixed-base natural frequency (Hz)

\(\zeta_{L}\) :

\(K_{L}\) normalized by \(K_{t}\) and \(L_{t}\) (–)

\(\zeta_{LR}\) :

\(K_{LR}\) normalized by \(K_{t}\) and \(L_{t}\) (–)

\(\zeta_{R}\) :

\(K_{R}\) normalized by \(K_{t}\) and \(L_{t}\) (–)

\(\chi\) :

Soil-pile-tower interaction factor (–)

\(\upomega _{D}\) :

Angular velocity with damping (rad/s)

\(\xi\) :

Damping ratio (–)

\(E_{p_{dynamic}}\) :

Dynamic pile effective stiffness (Pa)

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Acknowledgements

The first author studied at ENPC to obtain the engineering degree besides the master degree of Tokyo Tech, financially supported by BGF and Tobitate. This research topic has been selected by the author who was inspired by her ENPC supervisors Jean-Michel Pereirra and Aphrodite Michael as well as her colleagues during an internship at Mott MacDonald.

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Correspondence to Akihiro Takahashi.

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Yukiho Kamata: Formerly Department of Civil and Environmental Engineering, Tokyo Institute of Technology, Tokyo, Japan.

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Kamata, Y., Takahashi, A. Sway-Rocking Spring System Applicable to Short-Rigid Monopile Foundations. Geotech Geol Eng (2021). https://doi.org/10.1007/s10706-021-01678-2

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Keywords

  • Offshore wind turbine structure
  • Monopile
  • Short-rigid pile
  • Sway-rocking spring system
  • Natural frequency