Vertical dynamic impedance of end‐bearing pile groups embedded in homogeneous unsaturated soils

Abstract Although soil is typically an unsaturated (three‐phase) medium, previous studies on the dynamic impedance of pile groups primarily considered the piles embedded in either the single‐phase or fully saturated (two‐phase) soils. In this work, the dynamic impedance of end‐bearing pile groups embedded in homogeneous unsaturated soil subject to a vertical time‐harmonic load is analytically obtained. The soil is modeled as a three‐dimensional axisymmetric continuum, and both the radial and vertical displacements as well as the influence of the saturation degree on the soil's dynamic shear modulus are considered. The governing equations of vibrating unsaturated soil are uncoupled by virtue of the potential function and operator decomposition methods. The attenuation function of soil displacement, surrounding soil resistance factor, and vertical dynamic impedance of a single pile are derived from the pile−soil compatibility conditions. Pile‐to‐pile dynamic interaction factors are then derived and used, along with the superposition principle, to find the vertical dynamic impedance of end‐bearing pile groups in the frequency domain. The proposed analytical solution is verified by comparison with two benchmark solutions. Finally, the influence of various parameters on the dynamic response of end‐bearing pile groups is determined.