Keywords: foundations, domain transformation method, boundary elements, wave propagation.

Traditionally only the static bearing capacity and stiffness of the ground is considered in the design of wind turbine foundations. However, over the last decades wind turbine towers and blades have increased significantly in height and length, respectively, with only a small increase in weight. Thus modern wind turbines are flexible structures showing a dynamic response, even at low frequencies. The terminology "eigenmodes" does not apply, since mechanical energy dissipates from the base of the turbine tower into the surrounding soil. Further, the rotation of the rotor leads to parametric excitation. However, strong resonance of the structure is identified at a number of frequencies in the range 0.2 to 3 Hz. The first circular resonance frequency of the wind turbine, , and the circular frequency of blades passing the tower, , are of special interest. Typically and are close to each other. Hence, even a slight change in one of these frequencies may change the dynamical properties of the system significantly, possibly leading to large amplitudes of vibration.

The aim of this paper is to investigate whether soil stratification may lead to dynamic soil-structure interaction which is significantly different from the situation for a homogeneous half-space. For this purpose the impedance of surface footings is studied, employing a semi-analytical model based on the domain transformation method and the Green's function for a stratified ground [1,2]. A model is proposed which may be applied for the analysis of foundations with arbitrary shapes. The contact stress between the footing and the subsoil is modelled by a number of distributed loads, each applied with radial symmetry around a point on the soil-structure interface. This allows a fast transformation from wavenumber domain to space domain, because the inverse fourier transformation only involves numerical evaluation of a line integral.

A comparison with a boundary element solution [3] for a homogenous viscoelastic half-space shows that the present method provides results of satisfactory accuracy; but computation time is small--also for a layered half-space. This is important, both when parameter studies are to be carried out, and when the impedance of a footing has to be included in the aero-elastic codes utilized in the wind turbine industry.

Finally, the influence of soil stratification is studied, adopting a hysteretic material model for the ground. Figure 255.1 shows example results for a circular footing with radius R₀=10m on a 20 m deep layer with the Young's modulus 2 MPa, the Poisson ratio 0.3, the mass density 1000 kg/m³ and the loss factor 0.05. The top layer is underlaid by a homogeneous half-space with the Young's modulus 200 MPa. The remaining material properties are the same as those of the layer. In Figure 255.1 C₂₂ and C₃₃ are the horizontal and vertical impedances, respectively, while C₄₄ and C₆₆ are the rocking and torsion impedances, respectively. These have been normalized with respect to the static vertical stiffness, C₀=C₃₃ . There is a pronounced dip in C₂₂ and C₃₃ for frequencies around 0.25 Hz, and C₄₄ is reduced by about 40% for frequencies near 0.5 Hz compared with the static stiffness. In the case of a homogeneous half-space with no layer on top, no or only a small reduction of the impedances is observed.

It is concluded from the analysis that both rocking and translation impedances may be influenced significantly at low frequencies close to the first resonance frequency of a wind turbine. Thus, soil stratification should be taken into consideration in models for the prediction of dynamic soil-structure interaction of wind turbine foundations.

1

L. Auersch. "Wave propagation in layered soils: Theoretical solution in wavenumber domain and experimental results of hammer and railway traffic excitation", Journal of Sound and Vibration, 173(2), 233-264, 1994. doi:10.1006/jsvi.1994.1228

2

X. Sheng, C.J.C. Jones and M. Petyt. "Ground vibration generated by a harmonic load acting on a railway track", Journal of Sound and Vibration, 225(1), 3-28, 1999. doi:10.1006/jsvi.1999.2232

3

J. Domínguez, "Boundary elements in dynamics", Computational Mechanics Publications, Southampton, 1993.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £135 +P&P)