Rigorous Solution for the Kinematic Response of Single Disconnected Piles Subjected to Vertically Incident P-Waves

A rigorous solution for the kinematic response of the disconnected piles under vertically incident P-waves is presented. A new soil–pile column model is proposed with two fictitious soil columns as the extensions of the shaft along the pile top and tip. The discontinuity of the pile at the two ends is modeled using the Heaviside function to simulate the continuity of the soil–pile column. The total displacement of the soil is divided into the free-field and scattered components. The displacement of the soil–pile system is calculated in terms of the method of separation of variables and the soil–pile interaction. A parametric study indicates that for the disconnected pile, the displacement at the pile top increases significantly with the increase of the cushion thickness, and its effect on the scattered field is weak. The axial force of the disconnected pile decreases gradually with the increase of the cushion thickness. The displacement and axial force of the disconnected pile are significantly influenced by the slenderness ratio of the pile.