Dynamic response of a saturated poroelastic medium due to a moving axial excitation in a lining tunnel

To investigate the propagation of subway vibration in the saturated poroelastic medium, a dynamic analysis model of the tunnel, lining and the saturated medium was established by using the moving axial excitation technology. The analytical solutions of dynamic responses in the frequency domain were derived by the wave function expansion method and the Fourier transform method. Moreover, an empirical formula for the critical velocity of the saturated poroelastic medium was given. The time-space domain solutions of dynamic responses were obtained by the discrete inverse fast Fourier transform. The results show that, for the tunnel without lining, the critical velocity of the saturated poroelastic medium is only related to the shear modulus and density of the medium, and its value is close to 1.1 times shear wave velocity of the medium. For the lining tunnel, the critical velocity of the medium increases with the increase of the shear modulus of the lining but decreases with the increase of the lining density. The lining has a certain weakening effect on the propagation of vibration. The weakening effect is more obvious when the difference of shear modulus between the lining and the medium is large. When the dynamic response frequency is close to the excitation frequency, the amplitude of the dynamic response becomes high but the corresponding critical velocity becomes low.