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The dynamic response of a floating-slab track and underground railway tunnel embedded in saturated soils under moving loads are investigated by a hybrid analytical-numerical method. The tunnel is modelled as thin cylindrical shell surrounded by saturated soil of infinite radial extent. A two-layered beam structure is used to model the floating-slab track. In the continuous floating-slab track, the slab is an infinitely long Euler–Bernoulli beam while in the discontinuous one, the slabs are modelled as a periodic structure consisting of beams of finite length. The coupled equations of the tunnel-soil system are solved in the frequency-wavenumber domain with the aid of Fourier transform and Fourier decomposition. The track structure and tunnel-soil model are coupled by force and displacement continuity conditions at the tunnel invert. Numerical results for the track, tunnel and soil responses are presented for a moving point and train load. It is found the critical velocity of a track-tunnel-soil system approaches the shear wave speed of the soils. The natural frequencies of the track have significant influence on the soil displacement and pore pressure. Furthermore, an increase of the soil permeability leads to a decrease of the displacement as well as the pore pressure in the free field.

Hybrid analytical-numerical modelling of ground vibrations from moving loads in a tunnel embedded in the saturated soil