Formulation of Spectral Elements for Rock-Socketed Monopile Subjected to Horizontal Dynamic forces-Paper

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The study uses a spectral element method to examine the dynamic behavior of a rock-socketed monopile under horizontal loading. The pile is represented as interacting with viscoelastic soil springs, and its dynamic stiffness and damping are evaluated in layered soil–rock conditions. Five rock types, ranging from weathered rock to basalt, and socket depths of 1D–4D are considered. The analysis also examines horizontal translation and rocking of a foundation block supported by the pile.<br /><br />The results show that an underlying rock layer increases lateral stiffness compared with uniform soil. Stiffness rises with rock shear-wave velocity and density, and generally increases as socket depth grows. Basalt produces the stiffest response, while weathered rock produces the greatest damping. Damping changes relatively little with socket depth. These findings indicate that stronger rock better resists pile movement but dissipates less energy.<br /><br />Rock properties and socket depth also affect the system’s natural frequencies and vibration amplitudes. Stiffer rock shifts the first natural frequency to a lower value and increases modal participation near that frequency, while participation near the second natural frequency follows the opposite trend. Increasing socket depth shifts the second natural frequency upward. The reported response trends vary by motion and frequency: deeper socketing reduces lateral displacement, while rocking resonance can increase with socket depth. Overall, the work demonstrates how rock type and embedment depth jointly shape the dynamic performance of monopile foundations.

Keywords

spectral element method

rock-socketed monopile

dynamic stiffness

viscoelastic soil springs

layered soil-rock conditions

socket depth

rock shear-wave velocity

damping

natural frequencies

rocking response