Closed form solution for the first natural frequency of offshore wind turbine jackets supported on multiple foundations incorporating soil-structure interaction

Closed-form stiffnesses of multi-bucket foundations for OWT including group effect correction factors

“…Given the vast number of design requirements, see e.g. [3], simplified design procedures have been proposed [4,5], which allow obtaining reasonable designs at the initial stages. In such procedures, among…”

“…4. It is straightforward to obtain by inspection that the vertical, horizontal and sway-rocking stiffnesses of the foundation group (K grs u grs = f grs ) as: (5) where N ≥ 3 is the number of vertices. Moreover, considering that that the rocking stiffness K grs R of the foundation group depends on a rotation axis a contained in the x 1 − x 2 plane and defined by a = (cos ψ, sin ψ, 0), the following equation is obtained:…”

Dynamic design considerations for offshore wind turbine jackets supported on multiple foundations

“…However a detailed example on the methods of calculation for m2 (i.e. how to lump it to the tower tip) and kt using simple spreadsheet programs is provided in reference [17] and summarized in Appendix 2. Furthermore, guidance on the computation of the vertical stiffness of shallow caissons is provided in Appendix 3.…”

“…It may be noted that this method assumes the presence of translational restraints in the lateral direction at foundation level and only the vertical stiffness is considered due to the load transfer mechanism. Typically, the inherent lateral stiffness of the foundation will be sufficient, and the value of the vertical stiffness will govern the first natural frequency as shown in [17] by the authors. It was found in [17] that the idealization of the foundations (used in this paper) provides a close match with literature that utilized p-y and t-z springs for the foundations.…”

“…Typically, the inherent lateral stiffness of the foundation will be sufficient, and the value of the vertical stiffness will govern the first natural frequency as shown in [17] by the authors. It was found in [17] that the idealization of the foundations (used in this paper) provides a close match with literature that utilized p-y and t-z springs for the foundations. In practice, one requires to carry out a refined analysis and this can be modelled by adding lateral springs (KL) in addition to the vertical springs (k1 and k2).…”