Equivalent-linear pile head impedance functions using a hybrid method

Majority of available solutions for determination of pile head dynamic stiffness and damping for use in substructure analysis of soil-pile interaction are based on linear elastic soil behavior and perfect contact at soil-pile interface. This paper presents a hybrid numerical-analytical methodology for equivalent-linear (EL) characterization of pile head impedance functions under inelastic soil-pile interaction. Inelastic continuum modeling, frequency-domain substructure formulation and closed-form derivation of impedance functions, based on Winkler assumption, are ingredients of the proposed approach. Results from three-dimensional (3D) nonlinear finite element (FE) analyses of single piles under dynamic pile head loading are used as input to the derivation algorithm. A new mathematical procedure for polynomial representation of the impedance functions is introduced, which allows for derivation of the EL impedances for “short-type” lateral behavior of an end-bearing pile, especially in the rock-socketed piles. The back-calculated impedances demonstrate variation of the pile head stiffness and damping in frequency domain as the inelasticity increases. They also reveal significant influence of inelastic interface (gap) and soil deformation on reduction of pile head stiffness, in particular radiation damping.