Analytical Solution for Dynamic Responses of Distinct Tubular Piles Under Vertical Seismic Excitation Considering Water–Pile–Soil Interaction

Offshore tubular pile systems in earthquake-active marine regions face risks from vertical seismic excitation, water dynamics, and pile–soil interactions. Thus, an analytical solution for offshore tubular piles considering multi-physical field coupling (the mutual interactions between seawater, tubular pile, and surrounding soil) is developed to investigate their dynamic responses under vertical seismic loading. Firstly, the dynamic response of the tubular pile system is decomposed into free-field and scattered-field components. The governing equations for water, soil, and tubular piles (one-dimensional and three-dimensional tubular pile models) are established, with the strict enforcement of boundary conditions such as displacement continuity and stress equilibrium. Then, analytical solutions for both one-dimensional and three-dimensional tubular pile models are derived. The proposed framework is validated by comparison with existing literature solutions, confirming its rationality. Subsequently, parametric analyses are conducted to explore the influences of key factors. The results indicate that it is essential to consider the coupled effects of vertical earthquakes and water–pile–soil interaction in the design of offshore tubular piles, as neglecting multi-field coupling or adopting oversimplified models can lead to inaccurate predictions of dynamic responses.