Rigorous solution for kinematic response of end-bearing pile under vertically incident P-waves

Abstract

Considering the pile–soil interaction, this study investigates a displacement model for the steady-state kinematic response of a single pile to vertically incident P-waves based on a continuum model. A rigorous solution for the vertical kinematic response of an end-bearing pile is presented herein. The scattered waves were uncoupled from the total wavefield using a reasonable displacement assumption. According to the governing equations and boundary conditions, scattered waves can be easily expressed in an infinite series form, representing the superposition of each vibration order. The generalized expression of the pile–soil dynamic resistance is obtained using Hamilton’s principle. The pile–soil resistance is divided into the Winkler-spring part (produced by elastic shear force) and the dynamic-membrane-spring part (produced by normal elastic stress and inertial force) along the pile–soil interface. Similar to scattered waves, the displacement of the pile and free-field can be expressed in an infinite series form. According to the assumption of the displacement field, all undetermined constants are determined, and the final series solution is provided. The presented has a more concise and definite physical meaning and has excellent application prospects in pile seismic design. Based on the given rigorous analysed solution, a parametric study was conducted to investigate the effects of the pile and soil parameters on the dynamic response of the pile–soil system. Comparing the responses of piles with different stiffnesses, the characteristic stiffness represented a rigid pile (ℜ≤2) and a flexible pile (ℜ≥3).