Closed-Form Solution for the Lateral Dynamic Response of Pipe Piles Under Combined Loading in Unsaturated Soils

This study presents a closed-form analytical solution for the complex problem of the lateral steady-state vibration of pipe piles in unsaturated soils under combined loading. Based on the wave propagation theory for three-phase porous media, the proposed method decouples the governing wave equations using Helmholtz vector decomposition and separation of variables. By incorporating continuity conditions at the soil–pile interface, a closed-form analytical solution for the coupled pile–soil dynamic response is derived. The rationality and accuracy of the solution are rigorously validated. This study elucidates the dynamic behavior of pore water and pore gas pressures within the surrounding soil and their underlying mechanisms influencing soil strength. The effects of axial loading and saturation degree on the dynamic characteristics of the pile are revealed. Furthermore, the distribution characteristics of ground surface displacement are presented. Finally, the model is applied to the analysis of wind turbine monopile foundation. The results indicate that the differences in dynamic response between pore gas and pore water pressures are key factors contributing to changes in the strength of the soil surrounding the pile. An increase in axial load reduces the dynamic stiffness of the pipe pile. Both the dynamic stiffness, displacement, and internal forces of the pile are significantly influenced by the degree of soil saturation. Additionally, the lateral displacement response on the ground surface is a direct manifestation of the pile–soil dynamic interaction.