The wave function method for calculation of vibrations from a twin tunnel in a multi-layered half-space

The ground vibrations due to underground moving trains cause disturbances to nearby buildings and their residents, which has been viewed as an important environmental issue. Various numerical or semi-analytical models are used to calculate the vibrations from underground railways, however, most of the prediction models adopt a single tunnel-soil system for modelling vibrations from underground trains and neglect the influence of a neighboring tunnel. In this paper, a semi-analytical wave function method is proposed for modelling vibrations from twin tunnels in a multi-layered viscoelastic and poroelastic half-space. The two tunnels are modelled as two hollow cylinders while the surrounding soil is modelled as a multi-layered half-space containing two circular cavities. The vibrations of the tunnel walls are taken as a superposition of outgoing and regular cylindrical waves. The wave field in the soil layer containing two cavities consists of down-going and up-going plane waves and cylindrical waves propagating outwards from each tunnel. In the wave function method, the transformation and translation of the plane and cylindrical waves make it possible to apply the boundary conditions at the scattering surfaces. Numerical results show that the half-space model predicts higher surface vibrations than a full-space model at equivalent surface locations. When the second tunnel is added near a deeper existing tunnel, a wider range of the free-field response above the two tunnels is significantly changed, however, the response below twin tunnels is less affected. If the separation distance between the two tunnels is smaller than five times the tunnel diameter, a twin tunnel model in a half-space is more suitable for an accurate vibration prediction at the ground surface. The cutoff effect of the rigid base is more visible for shallow bedrock at lower frequencies while the influence of the bedrock is quite limited at higher frequencies.