Numerical analysis of foundation damping for monopiles

For offshore wind energy structures, fatigue loads, which depend on the natural frequency and the damping of the structure, are of crucial importance and often design-driving. One source of damping, besides aerodynamic, hydrodynamic and structural damping, is foundation damping. The knowledge about the magnitude of foundation damping and in particular its dependency on loading conditions is scarce. Often, the global damping ratio is just increased by a certain roughly estimated amount or foundation damping is even fully neglected. In recent studies, resultant foundation damping values were derived from 1g model tests on monopiles in sand (Sanders et al., 2025) and the distribution of damping along the embedded monopile length was investigated (Jindal et al., 2024). In this paper, the foundation damping of a monopile is investigated by means of a numerical model. The Hardening Soil Small (HSS) material law available in the used Plaxis3D programme is applied to account for the complex elastoplastic material behavior of soil. By applying un- and reloading with varying mean loads and cyclic load amplitudes, both resultant foundation damping and the distribution of local foundation damping along the embedded monopile length was determined. The mentioned 1g model tests from literature served as validation data for the numerical model. With the validated model, a parametric study on magnitude and distribution of damping dependent on loading conditions and soil conditions was conducted. The results confirm that foundation damping is highly dependent on loading conditions. Finally, recommendations on the consideration of foundation damping in practical design are given.