The offshore wind industry is a quickly growing market because the increasing demand for clean energy sources. Large wind speeds and the abundance of potential wind farm locations make Offshore Wind Turbines an interesting solution. Because of high continuous dynamic loading and extreme environmental conditions, the structural design requires a detailed assessment, especially in the Fatigue Limit State. In this thesis, the focus lies on improving the modeling of monopile foundations for Offshore Wind Turbines, which could pave the way towards more efficient foundation design.

The conventional method of modeling the monopile foundation of an Offshore Wind Turbine is with a nonlinear elastic distributed spring stiffness along the monopile (using p-y curves). Damping related to the soil is considered through either global damping (like Rayleigh damping) or local viscous damping. However, the response of the soil around the monopile under wind and wave loading is better described through a nonlinear hysteretic (rate-independent) model, which is computationally demanding to model in the time domain. Next to that, a conventional frequency domain method can not be combined with any nonlinearity. Therefore, linear elastic models are used to model the soil response in frequency-domain simulations.

The goal of this thesis is to combine a nonlinear hysteretic soil model with a frequency-domain analysis. A response amplitude-dependent linearization of the nonlinear hysteretic element is made. The combination of the response amplitude-dependent element with an iterative solution strategy, the Equivalent Linear method, is shown to approximate a nonlinear time-integration under both harmonic and multiharmonic loading, as long as the nonlinearity is limited.

A nonlinear hysteretic model is fit to available soil reaction data and a response amplitude-dependent linearization is generated. A Finite Element model that can be combined with the Equivalent Linear method is set up and verified with a case study structural model of an Offshore Wind Turbine. The model is subjected to (high) Fatigue Limit State wave loading. The results are compared to both a conventional frequency-domain method (with a linear elastic small-strain soil model) and a nonlinear time-domain method (with a nonlinear elastic soil model). The deflections and deflection spectra in the foundation found through the Equivalent Linear method correspond to results from the nonlinear time-domain method, provided the influence of higher harmonics is limited and the response has a similar amplitude throughout the analyzed time window.

Results from the Equivalent Linear method show that the main frequency of the first resonance peak is around 2% smaller than the first natural frequency of the system, which is consistent with the results found through the nonlinear time-domain method. The identified soil damping in the first mode is 0.64-0.8% critical (4-5% log. dec.), which is similar to other literature. By combining observed system properties with literature about fatigue damage estimation, a hypothesis is stated: the fatigue damage in the foundation calculated through an Equivalent Linear method with a nonlinear hysteretic soil model will be lower than the fatigue damage calculated through a nonlinear time-domain method with a nonlinear elastic soil model.

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With increasing evidence of human-induced accelerated climate change, the need of sustainable, non-polluting, energy sources becomes evident. Offshore wind generated electricity is currently one of the most promising sources of energy to create a sustainable global energy mix. The offshore wind industry has developed rapidly over the last years. The cumulative installed capacity shows an exponential growth. Monopiles remain the most popular substructure type of all installed substructures in Europe. This thesis focuses on calculation methods to evaluate the response of that foundation type.

The interaction between a monopile and soil is called soil-structure interaction (SSI). In the offshore wind industry, SSI is commonly modelled as a 1D local Winkler foundation with local nonlinear elastic springs to represent the lateral soil stiffness. The stiffness is often based on semi-empirical relations between the lateral displacement of the pile and the soil pressure (p-y method). This approach neglects the interaction effects between different soil layers and there are uncertainties regarding the validity of applying this method to large diameter, rigidly behaving, monopiles.

In this thesis, a 3D linear-elastic (LE) finite element (FE) model is used to compute 1D global (non-local) complex-valued dynamic soil stiffness, which captures the coupled 3D reactions of soil to the pile. The frequency dependence of local and non-local linear-elastic lateral, rotational and coupling dynamic soil stiffness is analysed for heterogeneous soil stratigraphy. The effect of different boundary conditions in the 3D model formulation to the frequency dependence of dynamic soil stiffness is analysed.

The complex-valued-frequency dependent dynamic soil stiffness kernels are approximated by frequency independent coefficient matrices for added mass, damping and stiffness. The performance of the coefficient matrices in terms of representing the complex-valued dynamic soil stiffness is analysed with cost functions. It was found that the dynamic soil stiffness can be approximated by frequency independent added mass, stiffness and damping coefficient matrices in the frequency range of interest for offshore wind.

A 1D Timoshenko beam model is developed in the frequency-domain and is discretised in space by Euler’s central finite difference method. The added mass, stiffness and damping matrices, which represent the non-local Winkler foundation, are incorporated in the model. The SSI response of the 1D model to the dynamic loading is compared with the response of the 3D LE FE model in the frequency domain.

As a last step, a superstructure and turbine are integrated with the monopile SSI model and the total integrated model is transferred to the time domain. Time domain computations are performed for free vibrations, harmonic loading and realistic aero-/hydrodynamic loading scenarios. The transformation into the time domain is important since it allows the user to incorporated nonlinear wave and wind loading and air-turbine interaction effects that are considered to have a major impact on the resulting dynamic system response. The developed time-domain model is computationally very efficient in predicting the time-domain SSI response of an offshore wind turbine for varying loading scenarios.
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