To investigate the propagation of subway vertical vibration in layered soil

an analysis model of layered foundation under a moving load is proposed. The Dirac function and the triplex Fourier transform are used to transform a moving harmonic load in time-space domain to a load in frequency-wavenumber domain based on the analysis model. The analytical solutions of the dynamic response of 3D layered foundation under a moving harmonic load and a moving line harmonic load are deduced by using the thin layer method and the moving coordinate system method. The range of the parameter n in the analytical solution of a moving line harmonic load is given. The influence of load speed on the dynamic response of 3D layered foundation

and the influence of the elastic modulus

Poisson’s ratio

damping ratio and load frequency on the critical speed of soil are analyzed. The results show that the influence scope of the load speed on the dynamic response of different frequency bands is different. The influence of moving speed on the low frequency response is greater than that of the high frequency response

and the elastic modulus has the greatest influence on critical speed of soil compared with Poisson’s ratio and damping ratio. The dynamic response amplitude will increase and the critical speed will decrease when the frequency of the dynamic response is close to the load frequency.