Time-domain analysis of velocity waves in a pipe pile due to a transient point load

The propagation of stress waves in a pipe pile subjected to a transient point load cannot be expressed using traditional one-dimensional (1D) wave theory. This paper presents an analytical solution used to investigate the wave propagation in a pipe pile under an axial point load. The soil resistance is simulated using the Winkler model, and the excitation force is simulated with a semi-sinusoidal impulse. A time-domain analytical solution for the three-dimensional wave equation is derived using the separation of variables and variation of constants methods. The solution is verified with a frequency domain analytical solution in which the time-domain response is calculated by numerical Fourier inverse transformation. Furthermore, the solution proposed in this paper is compared with the results of model testing and 3D FEM analysis. The comparisons show that the analytical solution proposed in this study agrees well with the results of previous studies. The proposed solution is subsequently applied in case studies. The vertical velocity responses in the circumferential and axial directions are analyzed to reveal the propagation characteristics of transient waves in the pipe pile. Moreover, the effects of the location and period of the excitation force, the side and tip resistances and high-order modes are studied in detail.