An analytical solution for vertical seismic response of an end-bearing pile in saturated soil considering pile-soil and free and scattered field water-soil interaction

A mathematical model is proposed to investigate the dynamic behavior of an end-bearing pile under vertical seismic loading in a water-pile-saturated soil system. The model is based on the Euler-Bernoulli beam theory and takes into account the stress balance between pile sections, representing the pile as a one-dimensional rod. The overall response of site is divided into two components: the free-field response and the scattered-field response. The pile and soil are considered as linearly viscoelastic materials with hysteresis-based damping, while water is modeled as a linear acoustic medium. By accounting for boundary conditions involving force equilibrium and displacement continuity at the pile-soil and water-soil interfaces, an analytical solution for the system response is derived. Analytical expressions of pore water pressure and displacements are obtained, on the basis of considering water-soil interaction in both fields. A parameterization study is then conducted to evaluate the impact of key parameters on the vibration characteristics of piles in a water-pile-saturated soil system.