A three-dimensional viscous fluid-pile-soil interaction analysis model is established to analyze the vibration response of pile foundation in liquefied soil under simple harmonic excitation horizontal dynamic load. The liquefied soil around the pile is regarded as viscous incompressible fluid

and the fluid motion equation is established. The analytical expressions of viscous fluid dynamic pressure and fluid velocity potential are obtained by using Helmholtz decomposition and variable separation method

combining fluid boundary conditions

pile-fluid displacement

velocity continuity conditions and pile boundary conditions

so as to obtain the expression of pile resistance. The saturated unliquefied soil layer is simulated using the saturated porous medium model. Based on the existing analytical solution of vibration response of saturated unliquefied soil layer

the analytical solution of pile top impedance of horizontal vibrating pile foundation in saturated unliquefied soil is derived. The correctness of the solution of the proposed model is verified by comparing with the free vibration solution of the existing cantilever beam in water. Finally

the effects of fluid viscosity coefficient

pile length and pile-soil modulus ratio on pile top impedance are analyzed. The results show that neglecting the viscosity characteristics of liquefied soil will overestimate the stiffness and impedance of pile foundation and underestimate the damping impedance.