To analyze the vertical vibration characteristics of a solid pile with vibration isolation layer

a vertical dynamic impedance analytical model of the vibration propagation medium and the solid pile was established. The model was based on the Rayleigh-love rod model and Novak plane strain theory

considering the radial and longitudinal non-uniformity of the vibration propagation medium around the pile and the lateral inertia effect of the pile. Utilizing the Laplace transfer method

complex stiffness transfer method

and impedance function transfer method

the analytical solution of dynamic impedance at the solid pile head under arbitrary vertical load in a viscous damping medium was derived. The rationality of this solution was verified by comparing with the existing analytical solution. It is found that the amplitude of the pile head dynamic stiffness has an obvious influence on the dynamic response at the pile head

indicating a high correlation. Further

the effects of different thicknesses and longitudinal depths of the rubber layer and different types of vibration isolation material on the pile head dynamic stiffness are investigated. The results show that in the frequency range of 1-80 Hz: (1) The dynamic stiffness curve shifts to a lower (higher) frequency as the rubber layer thickness increases (decreases)

with the thickness variation having an insignificant effect on the feature frequency and the dynamic stiffness; (2) The amplitude and oscillation frequency of the dynamic stiffness curve increase (decrease) significantly as the rubber layer longitudinal depth increases (decreases); (3) When the vibration isolation material is softer than the surrounding soil

the amplitude and oscillation frequency of the dynamic stiffness curve increase as the shear modulus of the vibration isolation material decreases; (4) When the vibration isolation material is harder than the surrounding soil

the amplitude of the dynamic stiffness curve slightly increases as the shear modulus of the vibration isolation material increases

and the oscillatory property disappears.