Estimation of Wind Turbine Foundation Rotational Stiffness Based on Fully Non-Linear Dynamic Analysis-Paper

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The study examines whether conventional pseudo-static rotational stiffness estimates adequately predict the dynamic behavior of wind turbine foundations. Standard design methods represent the foundation and soil as linear springs, although real soil response is nonlinear and may change under repeated loading. These simplifications can lead to overly conservative designs, particularly for pier foundations supporting larger turbines.<br /><br />The authors modeled the full soil–foundation–tower–turbine system in Plaxis 3D, using a nonlinear hardening-soil model with small-strain behavior and dynamic acceleration time histories. A 2 MW turbine was represented with a tower and lumped nacelle mass. Pier lengths of 20, 24, 28, and 32 ft were compared. The system was subjected to 60 seconds of acceleration followed by 60 seconds of free vibration; static and dynamic rotational stiffnesses were then assessed.<br /><br />Results showed that longer piers generally reduced vibration amplitudes, but increasing pier length from 28 to 32 ft made little difference to the system’s frequency response. Shorter piers had lower fundamental frequencies. Soil stiffness increased after loading, consistent with densification of the initially loose, cohesionless soil. However, dynamic rotational stiffness varied with moment demand and did not consistently match pseudo-static results. The 28-ft pier’s unexpectedly poor dynamic stiffness, despite strong pseudo-static performance, may relate to partial fixity and warrants further investigation.<br /><br />The study concludes that a single linear rotational spring cannot fully represent foundation behavior, including soil nonlinearity, cyclic effects, and changes between rigid-body and flexible deformation. Nonlinear dynamic analysis can provide a more realistic basis for design and may help reduce unnecessary foundation costs without compromising turbine performance. The authors identify simplified design guidance based on such analyses as an area for future work.

Keywords

wind turbine foundations

pseudo-static stiffness

dynamic rotational stiffness

soil nonlinearity

Plaxis 3D

hardening soil model

foundation vibration

pier foundations

frequency response

nonlinear dynamic analysis