The construction of pipe pile will cause the inhomogeneity of the surrounding soil. By considering the influence of the radial inhomogeneity effect and the vertically layer characteristic on the vertical vibration dynamic impedance of pipe pile

a multi-circle plane strain model based on soil viscous damping was proposed

and a simplified model for vertical vibration analysis of pipe pile in radially and vertically layered soil was established. Based on the Laplace transformation and the transitivity of impedance function

the analytical solution of the dynamic impedance of the pile head was derived. Computational results show that the vertical soft and hard interlayer had a significant effect on the amplitude of the dynamic impedance curve in a certain low frequency range

where the softer (harder) the interlayer was

the higher (lower) the amplitude of the dynamic impedance curve at the resonance frequency became. The radial inhomogeneity caused by construction disturbance had a significant influence on the complex stiffness curve of the pile head. In the analysis of vertical vibration characteristics of pipe piles

the analytical solution derived by the proposed soil-pile interaction model was more reasonable.