Ground motions induced by vibration of a large-diameter end-bearing pile subjected to vertically distributed uniform loads

Abstract

This study develops a comprehensive analytical solution for predicting three-dimensional ground motions induced by the vibration of large-diameter end-bearing piles subjected to vertically distributed uniform loads. Both the pile and the surrounding soil are treated as elastic continuum media to capture the coupled effects of P-SV and Rayleigh waves accurately. General solutions for wave potentials, displacements, and stresses are derived using small-strain theory and continuum elasticity. Modal wave numbers are determined through a root-searching approach employing the argument principle and subdivision method. Bi-orthogonality relationships are reorganized using Betti’s theorem. Soil–pile interactions are rigorously modeled through continuity conditions at the soil–pile interface. Mode-matching method is used to solve the unknown coefficients. The boundary-value problem is reduced to a system of linear algebraic equations with series truncation to ensure convergence and computational efficiency. Parametric studies reveal that excitation frequencies significantly influence the distribution of soil and pile responses. Shear waves corresponding to pile frictions dominate near-field responses and Rayleigh waves resulting from surface load propagate at larger distances. Transient displacement responses show the significant influence of complex Rayleigh wave propagation and the secondary subsurface scattering on the ground motions. The particle motions reveal the Rayleigh waves are generating and propagating through the ground surface induced by pile vibrating. This study contributes to the accurate prediction of ground motions and supports the design of vibrating grounds which ensures the safety of pile-supported structures in urban and displacement-sensitive environments.