Vertical vibration of pile based on fictitious soil-pile model in inhomogeneous soil

The dynamic response of pile in inhomogeneous soil was analyzed under vertical dynamic loads by considering the influence of finite soil layers under pile.The dynamic interaction model was conducted based on the finite soil layers of which the cross-section area is equal to the pile were modelled as fictitious soil-pile.The dynamic equations of fictitious soil-pile,pile and soil were built by complex stiffness transfer model of radial multi-zone plane strain and solved by using the continuity condition of fictitious soil-pile,pile and soil.Then the analytical dynamic response solution in frequency domain and the semi-analytical dynamic response solution in time domain at the top of pile were obtained.Parametric studies of fictitious soil-pile were performed to examine the effect on the dynamic responses of pile.The curves of the velocity admittance,reflected wave and complex stiffness at the top of pile were obtained.