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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 81
PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 255
Impedance of Surface Footings on Layered Ground L. Andersen+ and J. Clausen*
+Department of Civil Engineering, Aalborg University, Denmark
Full Bibliographic Reference for this paper
L. Andersen, J. Clausen, "Impedance of Surface Footings on Layered Ground", in B.H.V. Topping, (Editor), "Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 255, 2005. doi:10.4203/ccp.81.255
Keywords: foundations, domain transformation method, boundary elements, wave propagation.
Summary
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,
![]() ![]() ![]() ![]() 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
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.
References
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