衬砌隧道中移动轴向激励作用下两相多孔介质动力响应

为了研究衬砌隧道中地铁振动在饱和地层中的传播情况，采用移动轴向激励模拟技术，建立了隧道-衬砌-两相介质的动力分析模型；利用波函数展开法、傅里叶变换法等，推导了频域内衬砌隧道移动轴向激励作用下两相多孔介质动力响应的解析解，并给出了两相多孔介质临界速度的经验公式；通过离散快速傅里叶逆变换得到了时-空域内两相介质的动力响应。结果表明：无衬砌隧道中移动的轴向常激励作用下，两相介质临界速度只与介质的剪切模量和密度有关，且数值接近其剪切波速的1.1倍；对于衬砌隧道，介质的临界速度随着衬砌剪切模量的增大而增大，随着衬砌密度的增大而减小，衬砌对振动向介质中的传播有一定的削弱作用，衬砌剪切模量与介质剪切模量相差越大，削弱越明显；动力响应频率越接近激振频率，其幅值越大，所对应的临界速度越小。

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.