*Article* **Vertical Stiffness Functions of Rigid Skirted Caissons Supporting Offshore Wind Turbines**

**AbdelRahman Salem 1,2, Saleh Jalbi 3,\* and Subhamoy Bhattacharya <sup>2</sup>**


**Abstract:** Suction Bucket Jackets (SBJs) need to be fundamentally designed to avoid rocking modes of vibration about the principal axes of the set of foundations and engineered towards sway-bending modes of tower vibration. Whether or not such type of jackets exhibit rocking modes depends on the vertical stiffness of the caissons supporting them. This paper therefore derives closed form solutions for vertical stiffness in three types of ground profiles: linear, homogenous, and parabolic. The expressions are applicable to suction caissons having an aspect ratio (depth: diameter) between 0.2 and 2 (i.e., 0.2 < L/D < 2). The work is based on finite element analysis followed by non-linear regression. The derived expressions are then validated and verified using studies available in literature. Finally, an example problem is taken to demonstrate the application of the methodology whereby fundamental natural frequency of SBJ can be obtained. These formulae can be used for preliminary design and can also be used to verify rigorous finite element analysis during detailed design.

**Keywords:** suction caissons; vertical stiffness functions; natural frequency; jackets; offshore wind turbines
