Keywords: soil-structure interaction, finite elements, boundary elements, dynamics.

Modern wind turbines have natural frequencies close to 0.2 Hz. This may be critical regarding the excitation by wave and wind-induced loads. In particular, the rotor blades pass the tower at a frequency which is near the first natural frequency. Hence, to predict the dynamic response and the fatigue lifespan of a wind turbine, the dynamic stiffness of the structure must be modelled with sufficiently high accuracy. This includes an adequate model of the soil-structure interaction.

Offshore wind turbines are typically placed on monopiles or gravitational footings. Recently, the bucket foundation has been developed as a hybrid between these two foundation concepts. Whereas traditional suction anchors only carry vertical loads, the bucket foundation is designed to withstand loads and moments in all directions.

In this paper, the dynamic stiffness of bucket foundations is studied with focus on torsional vibrations and coupled horizontal sliding and rocking. A three-dimensional coupled boundary-element/finite-element (BE/FE) analysis is performed in the frequency domain, employing quadratic spatial interpolation. The bucket foundation is modelled by continuum finite elements, and the subsoil is modelled by boundary elements employing a hysteretic material dissipation model.

To check the validity of the BE/FE model, a comparison is made with the analytical solution provided by Veletsos and Wei [1] for the coupled horizontal sliding and rocking of a surface footing and the static stiffness computed by the commercial finite-element code ABAQUS [2]. In both cases, the BE/FE model produces results of high accuracy, even with few degrees of freedom. Furthermore, it provides great flexibility regarding the geometry of the structure.

The dynamic stiffness of the bucket foundation is studied for different geometries and material properties. In particular, the influence of changing the skirt length or Poisson's ratio of the soil is examined. The shear stiffness of the soil and the diameter of the lid are included implicitly by a normalisation of the foundation impedance and the frequency.

In conclusion, the impedance of the bucket foundation is highly dependent on the frequency. At some frequencies, resonance of pressure or shear waves occurs inside the bucket, whereas anti-resonance occurs at other frequencies. Consequently, the foundation becomes more flexible or stiff, respectively, than an embedded rigid foundation taking up the same space within the soil. A change in Poisson's ratio causes a shift in the resonance and anti-resonance frequencies, whereas an extension of the skirts further into the ground leads to amplification of both resonance and anti-resonance in addition to a general increase of the dynamic stiffness.

1

A.S. Veletsos, Y.T. Wei, "Lateral and Rocking Vibration of Footings", Journal of the Soil Mechanics and Foundation Engineering Division, ASCE, 97, 1227-1248, 1971.

2

ABAQUS--Version 6.4 2003, ABAQUS, Inc, 1080 Main Street, Pawtucket, RI 02860-4847, 2003.

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