Dynamic response of the periodic pile-reinforced composite foundation to harmonic seismic waves

The dynamic analysis of the pile-reinforced composite foundation (PCF) under seismic waves is important for the design of the PCF and corresponding upper structures. Owing to huge number of degrees of freedom (DOFs) in the modeling, it is still difficult to simulate the dynamic response of the PCF to seismic waves directly by means of traditional numerical methods. To overcome this difficulty, the PCF is simplified as the periodic pile-reinforced composite foundation (PPCF) in this study, and the harmonic wave finite element (HWFE) model for the PPCF under seismic waves is proposed. To establish the HWFE model, the response of the PPCF is decomposed into a series of horizontally propagating harmonic waves with amplitudes varying with the depth. Based on the principle of virtual work (PVW), the finite element method (FEM) equations for each harmonic wave are established. To impose the boundary conditions and input seismic waves at the bottom of the PPCF, the traction-displacement relation at the surface of the underlying half-space bedrock is derived. Solving the FEM equations for the PPCF and synthesizing the resulting solutions for the harmonic waves via the DFT method, dynamic responses of the PPCF to plane harmonic seismic waves are obtained. To verify the developed HWFE model, results obtained by the proposed HWFE model are compared with those by the propagator matrix method (PMM). The numerical results show that the resonance frequency of the PPCF increases with decreasing pile spacing; also, the presence of the stiffer soil layers will enhance the resonance frequency of the PPCF. •The periodic pile-reinforced composite foundation (PPCF) model is proposed.•A harmonic wave finite element (HWFE) model for the PPCF under seismic waves is developed in this study.•The Fourier space convolution form constitutive relation and expression for the inertial force are derived for the PPCF.•The traction-displacement relation at the bedrock surface is derived to input seismic waves at the PPCF bottom.