基于三相多孔介质波动方程，考虑孔隙中水和空气两种不相混溶流体间的耦合效应，通过算子分解和分离变量法，在求得轴对称条件下非饱和自由场波动域解答的基础上，结合上下区域的连续性条件以及桩端 Winkler 弹性支承假定，通过求解桩的振动微分方程，对部分埋入弹性支承桩在竖向稳态谐振作用下的频域响应进行了理论推导，获得了桩顶阻抗函数的封闭解． 通过对比饱和条件下完全埋入桩的桩顶复阻抗曲线，发现该退化解与已有的边界元法和虚拟桩法的结果基本吻合，验证了解答的正确性． 参数分析结果表明:桩顶复刚度随自由段桩长的增加而大幅降低，孔隙水的参与作用仅在接近完全饱和时才得以发挥，而饱和度和土底反力系数的影响较为有限．

In this paper，first，the motion response of unsaturated free field under symmetrical condition is obtained via operator splitting and variable separation，in which the wave equation of three-phase porous media and the cou-pling of two immiscible fluids (namely water and air) filled in pores are taken into consideration． Then，on the ba-sis of the continuity condition of upper and lower regions as well as the assumption of Winkler's elastic support at the pile tip，the differential equation of pile vibration is deduced，the frequency domain response of the partially-embedded elastic support pile under steady harmonic vibration is theoretically analyzed，and the closed forms of the impedance function of pile top are obtained． Finally，the complex impedance curves of pile top in unsaturated soil are compared with those in saturated soil，and good agreement is found between the theoretical results and the re-sults obtained from the existing boundary element method and the virtual pile method，which means that the theoret-ical derivation is correct． Parameter analysis results indicate that the complex stiffness of pile top significantly de-creases with the increase of extended segment length; and that the pore water contributes to the dynamic behavior only in approximately saturated condition，while the influences of the saturation and the reaction coefficient at soil layer bottom are rather limited．