Based on the Biot’s theory of wave propagation

a saturated virtual soil pile model is proposed. Considering the three-dimensional wave effect and saturation characteristics of surrounding soil and beneath the pile toe

a three-dimensional system including saturated viscoelastic soil

virtual soil pile and solid pile is established. The analytical solution for displacement of saturated soil is also derived by potential function method. The vertical dynamic impedance at the pile head is obtained using the pile-soil compatibility conditions. Finally

the obtained solution is reduced to verify its validity with existing solutions. Furthermore

extensive parametric analysis is performed to investigate the effects of saturated soil parameters on the vibration characteristics at the pile head. The computational results show that the amplitude and resonance frequency of dynamic impedance at the pile head in saturated soil decrease with increase of saturated soil thickness beneath the pile toe. When the thickness of saturated soil beneath the pile toe increases to a certain extent

the pattern of staggering peak become evident. The porosity of saturated soil beneath the pile toe has significant effects on both the resonance amplitude and resonance frequency of the dynamic impedance at the pile head

while the porosity of saturated surrounding soil only influence the resonance amplitude. With increasing shear modulus of surrounding soil and soil beneath the pile toe

the amplitude of the dynamic impedance at the pile head is significantly reduced

and it is more affected by the shear modulus of surrounding soil.