Under the condition of vertical load

the soil on the top of pile foundation after complete liquefaction is regarded as fluid

and the pile foundation is equivalent to the Euler-Bernoulli beam model. The vibration impedance of the pile top with embedded pile bottom is discussed. The expressions of relationships between displacement and internal force of pile’s top and pile’s bottom are obtained by means of the matrix transfer method after simulating liquefied soil using fluid dynamic equation and simulating lower non-liquefied soil layer with Winkler foundation

as well as considering the continuous conditions of displacement

rotation angle and internal force at the interface between the liquefied soil and the non-liquefied soil. Finally

according to the embedded conditions at the bottom of the end bearing pile

the expression of the impedance of the pile top is obtained. Compared with the existing literature

the correctness of the analysis process in this paper is verified. The parametric analysis of the conditions affecting the impedance shows that the liquefaction depth

the axial force exerted on the top of the pile and the fluid density have different effects on the impedance of the pile top.