Research On Dynamic Response Of The Circular Tunnel To Moving Loadings

With the sustaining development of Chinese economy, the construction scale of the tunnel engineering is increasing continuously. The ground vibration and environmental impact caused by the rail transportation have become a more important issue. The expected research results will provide guidance for the design of the tunnel lines, structures and vibration isolations.In this study, based on the elastodynamics, Biot’s and acoustic theories, the frequency-wavenumber domain general solutions for tunnels embedded in the elastic soil, saturated soil and water are derived by performing the Fourier transform method. According to the solution, the dynamic response of the tunnel subjected to moving loadings is investigated. The following research work has been carried out:1. The dynamic response of the tunnel embedded in the elastic soil to moving loadings is investigated by using analytical methods. The lining and soil are described by elastic dynamic equations. One scalar potential and one vector potential are introduced to represent the displacement of the tunnel. Performing the Fourier transform method, the frequency-wavenumber domain general solutions for potentials in the cylindrical coordinate system are obtained. Using the boundary conditions and continuity conditions, the solution for the tunnel subjected to a single moving loading(SML) is determined. Superposition of the solutions for SMLs yields the representation for the response of the tunnel to a series of equidistant moving loadings(SEML), with which the resonance and cancellation conditions for the SEML are derived. Inversion of the double Fourier transform retrieves the time domain response of the tunnel. With the proposed model, the results of the lined tunnel are compared with those due to the unlined tunnel, and then, the critical velocity of the tunnel as well as the resonance and cancellation phenomena for the SEML are studied.2. The dynamic response of the tunnel embedded in the saturated soil to moving loadings is investigated by using analytical methods. The lining and soil are described by elastic dynamic equations and Biot’s theory, respectively. After treating the lining in the way we conducted before, two scalar potentials and one vector potential are introduced to represent the displacement of the solid skeleton and pore pressure when considering the saturated soil. Following the Fourier transform method, the frequency-wavenumber domain general solutions for potentials in the cylindrical coordinate system are derived. Using the boundary conditions and continuity conditions, the solution for the tunnel subjected to the SML is determined. Superposition of the solutions for SMLs yields the representation for the response of the tunnel to the SEML, with which the resonance and cancellation conditions for the SEML are derived. Inversion of the double Fourier transform retrieves the time domain response of the tunnel. With the proposed model, the results of the saturated soil are compared with those due to the elastic soil, and then, the critical velocity of the tunnel as well as the resonance and cancellation phenomena for the SEML are studied.3. The dynamic response of the submerged floating tunnel to moving loadings is investigated by using analytical methods. The tunnel and water are described by elastic dynamic and acoustic equations, respectively. Following the Fourier transform method, the frequency-wavenumber domain general solutions for the tunnel and water in the cylindrical coordinate system are derived. Using the boundary conditions along the tunnel surface and continuity conditions at the interface between the tunnel and water, the solution for the submerged floating tunnel subjected to a single moving loading is determined. Inversion of the double Fourier transform retrieves the time domain responses of the tunnel and water. With the proposed model, the results of the submerged floating tunnel are compared with those due to the tunnel embedded in the soil. Moreover, the critical velocity of the submerged floating tunnel is studied, and then, the effect of the dominant frequency on the time domain responses of the tunnel and water is investigated.