Dynamic Response Of Lined Tunnel And Track System In Poroelastic Soil Under Subway Load

With the recent boom in constructions of urban rail-transportation infrastructures, environmental impacts caused by the rail transportation are becoming a more important issue. Basing on existing fundamental theories, it is of important significance to reveal mechanisms for vibrations of the rail, the liner and the surrounding saturated soil under the moving metro loads. The expected research findings will provide guidance for the design of railway lines, railway tracks and track-vibration isolations.In coastal areas in China, many metro lines are built in saturated soft ground. Hence it is more practice to deploy the saturated medium theory to simulate the soils surrounding the tunnel. Basing on Biot’s theory of saturated poroelastic medium, the metro loads, the track system, the liner system and the surrounding saturated soil are studied. The dynamic couplings among the metro track, the liner and the saturated soil due to the metro train are systematically studied for the first time by using analytical methods. The following research work has been carried out:1. Under the action of a moving point load, the three-dimensional dynamic responses of the unlined circular tunnel embedded in a saturated full space are derived by using analytical methods. After introducing two kinds of wave potentials, the displacement of the soil skeleton and the excess pore fluid pressure are solved for the saturated soil, which is modelled as a saturated poroelastic medium by using Biot’s theory. Using Fourier transformations, the wave potentials are solved by using modified Bessel equations. Once the boundary conditions are considered, the displacements and pore pressure responses can be readily solyed in frequency-wavenumber domain. Finally, the spatial-temporal domain responses are obtained by double Fourier inverse transformations. The variation of the soil-skeleton displacement and its spatial distribution are investigated for different load velocities. The effects of load velocity and soil permeability on the soil displacements are studied through numerical examples. 2. After modeling the lining as a cylindrical shell of infinite length and governing the soil by Biot’s equations, the three-dimensional dynamic responses of a circular lining tunnel in a saturated full space due to a stationary harmonic point load is investigated by using analytical method. By utilizing the characteristics of the external loading, the external load and the soil displacement can be directly expanded in a wave-motion form. After treating the saturated soil in the way we adopted before and introducing the boundary conditions, the soil displacements and pore pressures are obtained. The dynamic responses of a point in the surrounding soil, the tunnel invert and its underlying soil are computed. According to the computation results, the impacts of the load oscillating frequency and the soil permeability on the displacements of the soil and the invert as well as on the pore pressure responses are investigated.3. Under the action of a moving harmonic point load, the three-dimensional dynamic responses of a circular lining tunnel in a saturated full space are studied. Basing on the research work conducted above, the displacements and the pore pressures are solved by using Fourier transformations. The spectrums and the spatial distributions of the displacements of the tunnel lining and the surrounding soil are computed. The effects of load velocity, the load oscillating frequency, the soil permeability and the soil modulus on the displacement and pore pressure responses are investigated basing on the computation results.4. Basing on the foregoing research works, a three-dimensional model is established for the dynamic coupling among the rail track, the lining and the saturated full space by using the analytical method. The load is simplified into a moving harmonic point load first, and then modeled as a series of moving point loads with spatial distributions of the train. The displacements of the metro rail, the floating slab, the tunnel invert and the interaction forces between the slab and the lining are obtained in frequency-wavenumber domain by combining the dynamic equations of the track and the frequency response function of the invert. With recourse to the frequency response function of the observation point and the obtained interacting forces between the slab and the lining, the displacements of the tunnel and the soil as well as the pore pressure of the soil can also be computed in the transform domain. By applying double Fourier inverse transformations, the temporal responses of the rail, the floating slab, the tunnel structure and the saturated soil can be finally obtained. The impacts of the load velocity, the load oscillating frequency and the soil permeability on the dynamic responses of the metro track, the lining and the saturated soil are investigated.