Kinematic responses of pipe piles considering the effects of soil plugs and underlying strata subjected to P-waves

An innovative semi-analytical approach is devised to evaluate the dynamic characteristic of a friction-type pipe pile partially packed with soil plugs, subjected to time-harmonic seismic P-waves in a homogeneous soil medium. In this model, the shaft is conceptualized as a hollow structure with inner soil acting as continuum. The soil beneath the pile's vertical projection is viewed as a distinct soil pillar, while the surrounding soil and the column are collectively modeled as a uniform continuum. By examining the energy interactions between the inner soil and the pile-soil system and leveraging the Hamilton’s variational principle, the governing equations for both the shaft and the soil pillar, along with the interface contact requirements, are established. The attenuation characteristics of the surrounding soil are also derived. The solution employs variable separation techniques and an iteration methodology to resolve the coupled equations, satisfying the pile-soil system’s boundary and continuity constraints. This leads to a frequency-domain semi-analytical formulation for the seismic responses of the system. The accuracy of the developed solution is substantiated by comparing it with established results. Subsequently, numerical analyses are conducted to explore how varying material and geometric parameters impact the seismic interactions between the pile and soil.