X-section cast-in-place concrete pile (X-section pile) is a kind of new special-shaped pile. Considering the distribution of dynamic friction resistance on concave arc section

convex arc section and soil-pile coupled vibration

treating the soil as axisymmetric homogeneous viscoelastic medium

the analytical solution in frequency domain is obtained by using Laplace transformation technique and coordinate transformation. The solution is compared with that of solid circular pile to verify the rationality. Moreover

by analyzing the effect of pile length

open arc spacing and open arc angle on complex dynamic stiffness and velocity admittance

the influence of dimension parameters on the vertical vibration characteristics of X-section pile is investigated. It shows that the complex dynamic stiffness at the top of pile increases

the oscillation amplitudes and resonant frequencies of the velocity admittance curves significantly decrease with the increase of pile length. The open arc spacing and open arc angle have little influence on the velocity admittance at low frequencies. At high frequencies

the velocity admittance decreases with the increase of open arc spacing and increases with the increase of open arc angle. However

oscillation amplitudes of the velocity admittance curves increase with the increase of open arc spacing and decrease with the increase of open arc angle.