Up to now horizontal vibration response of a single pile in unsaturated soil is analyzed theoretically. The unsaturated soil surrounding pile is described by three-phase poro-elastic theory

which takes into account the viscous and inertial coupling between solid skeleton and pore fluids as well as the matrix suction

while the pile embedded in unsaturated soil is end bearing and treated as a Timoshenko beam model to describe the shear deformation and rotational inertia effects. The Helmholtz decomposition and variable separation method are firstly adopted to decouple the governing equations of the unsaturated soil. And then a rigorous mathematical formulation of the pile-head frequency–response function is deduced by virtue of the three-dimensional continuum model proposed by Novak and the compatibility between the pile and soil. The influences of degree of saturation on the impedances of pile and soil together with the distribution of displacement and internal force along the pile are discussed in detail. Results indicate that both the complex impedance of soil and the dynamic impedance of pile top increase with the increasing degree of saturation of soil

while the deformation and the internal force of pile are reduced. The contribution of pore water to dynamic behavior is made only when the soil is close to the saturated condition. At low frequencies

short pile has a large stiffness factor. A longer pile will lead to a higher damping factor

but a low resonance frequency. The impedance at the top of pile would be approximately invariant as the pile’s slenderness ratio exceeds 10.