Lateral and vertical vibrations of a pile subjected to eccentric transient excitation

To investigate the lateral and vertical vibration responses of the pile under eccentric transient excitation, the theoretical calculation based on the Bernoulli-Euler (BE) beam theory and the three-dimensional (3D) numerical simulation are first carried out respectively, and the calculated results are compared with the test data of the model pile to verify their rationality. Then, the characteristics of the lateral velocity response on the pile-top are analyzed, and the differences between the lateral and vertical velocities are discussed. Finally, the influences of the cross-section size and shape, pulse width, pile length, soil stiffness and vertical narrow defects on the lateral vibration velocity of the pile-top are studied, and the applicability of the BE beam model and 3D numerical model is evaluated. The results show that when the eccentric excitation is applied, the flexural waves reflected from the pile-toe reach the pile-top in the form of group waves, and the propagation velocity of the first arrival reflected waves is close to that of the shear waves. In addition to that of the longitudinal waves, the propagation of the flexural waves can also trigger vertical vibration of the pile. With an increase in the stiffness of the surrounding soil, the strength of the reflected flexural waves caused by the pile-toe decreases, and the attenuation of the flexural waves is severer than that of the longitudinal waves. The flexural waves can be significantly reflected when they encounter the vertical narrow defect. It is also found that the vertical eccentric excitation method and the use of the lateral vibration velocity of the pile-top are beneficial to accurately detecting the pile integrity.