Based on rule of stress diffusion

diffused fictitious soil pile model was constructed and the response of soil-pile under axial dynamic loading in inhomogeneous soil was investigated. Firstly

complex stiffness of different soil layers beside pile was gotten by using complex stiffness transfer model of radial multi-zone plane strain. And then combined with boundary condition

initial condition and continuity condition

the dynamical equations of diffused fictitious soil pile and real-body pile were solved from the bottom up. After that the analytical solutions of dynamic response at pile top in frequency domain and the relevant semi-analytical solution of dynamic response in time domain were gained. Finally

the influence analysis of angles of diffused fictitious soil pile

thickness of diffused soil layer

inhomogeneity of lateral soil of pile and length of pile were carried out. Based on diffused fictitious soil pile model

characteristics of the pile-soil coupling interaction in vertical vibration were gotten. The results can provide theoretical basis for dynamic pile design and testing.