Longitudinal dynamic response of pile in layered soil based on virtual soil pile model

Taking the effect of finite soil layers below pile end into account, the longitudinal dynamic response of pile undergoing dynamic loading in layered soil was theoretically investigated. Firstly, finite soil layers below pile end are modeled as virtual soil pile whose cross-section area is the same as that of the pile and the soil layers surrounding the pile are described by the plane strain model. Then, by virtue of Laplace transform and impedance function transfer method, the analytical solution of longitudinal dynamic response at the pile head in frequency domain is yielded. Also, the semi-analytical solution in time domain undergoing half-cycle sine pulse at the pile head is obtained by means of inverse Laplace transform. Based on these solutions, a parametric study is conducted to analyze emphatically the effects of parameters of soil below pile end on velocity admittance and reflected wave signals at the pile head. Additionally, a comparison with other models with different supporting conditions from soil below pile end is performed to verify the model presented.