Keywords: wind turbines, foundations, layered soil, stochastic analysis, dynamics, Monte Carlo.

Today, foundations for offshore wind turbines are designed according to standards based on partial factors of safety and, or the total safety while assuming quasi-static loading. The aim is to avoid collapse of the foundation and structure in the ultimate limit state and unacceptably large displacements in the serviceability limit state. A special concern is the fatigue life which may be significantly reduced as a result of cyclic loading from wind and waves. In this context, a reliable estimate of the natural frequency of the combined foundation and turbine structure is of major importance.

Typically, the natural frequency will be close to the frequency of the blades passing the turbine tower and only slightly higher than the excitation frequency from waves. To avoid dynamic amplification of the response, the natural frequency of the wind turbine has to lie within a narrow range. Unfortunately, the uncertainty of the natural frequency of the structure cannot be quantified by a deterministic method based on partial factors of safety or a total safety factor. Instead, this paper suggests the use of reliability based design.

The dynamic properties of the turbine structure are subject to relatively small uncertainties compared to the properties of the subsoil. The seabed is not a homogeneous half-space but contains layers of sand, clay, etc. with depths that vary from one position to another. Further, the properties of the materials within a single layer are subject to uncertainties, leading to uncertainties of the dynamic stiffness of the foundation.

A semi-analytical solution is employed, based on the Green's function for a layered half-space and a discretized traction distribution at the soil-foundation interface [1]. The material within each layer is assumed to be homogeneous with a lognormal distribution of the respective material properties. The layer depths are introduced as stochastic variables with a lognormal distribution. A simple structural model of a wind turbine is utilized and Monte Carlo simulation is carried for a numerical determination of the probability density function for the foundation stiffness and the natural frequency of the wind turbine. The influence of the uncertainty on each property of the soil is discussed and a cost-effective method for reducing the uncertainties is proposed. The main purpose of the analyses carried out in this paper has been to quantify the uncertainties related to the first natural frequency of a wind turbine on a gravity footing.

1

L. Andersen, J. Clausen, "Impedance of surface footings on layered ground", Computers and Structures, 86(1-2), 72-87, 2008. doi:10.1016/j.compstruc.2007.05.030

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