Analytical solution for simplifying the pile-soil interaction to a spring-damping system under horizontal vibration

An analytical solution is developed to investigate the model of simplifying the pile-soil interaction to a spring-damping system when the horizontal earthquake input or the top of the model is subjected to horizontal dynamic load. Based on Euler-Bernoulli theory, the dynamic equilibrium equations of pile in soil and air are established, respectively. Then, utilizing the corresponding boundary conditions, potential function decomposition, and transfer matrix method, the analytical expression of impedance at the pile head whether the horizontal earthquake input or the top of the system is subjected to horizontal dynamic load can be presented. Furthermore, the model of the pile-soil complex interaction can be simplified as a spring-damping system according to the stress equilibrium at the pile bottom in the air. Moreover, the rationality of the present solution (without simplification) is verified by comparison with existing methods, and then the difference between the present solution (without simplification) and the spring-damping system (simplification) is also compared. Finally, the influence of the parameter variation in the pile buried in the soil and soil free-field on the simplified model are discussed. The research results will be instructive for the simplification of numerical model for pile-soil interaction.