Analytical model for vibration prediction of two parallel tunnels in a full-space

This paper presents a three-dimensional analytical model for the prediction of ground vibrations from two parallel tunnels embedded in a full-space. The two tunnels are modelled as cylindrical shells of infinite length, and the surrounding soil is modelled as a full-space with two cylindrical cavities. A virtual interface is introduced to divide the soil into the right layer and the left layer. By transforming the cylindrical waves into the plane waves, the solution of wave propagation in the full-space with two cylindrical cavities is obtained. The transformations from the plane waves to cylindrical waves are then used to satisfy the boundary conditions on the tunnel-soil interfaces. The proposed model provides a highly efficient tool to predict the ground vibration induced by the underground railway, which accounts for the dynamic interaction between neighbouring tunnels. Analysis of the vibration fields produced over a range of frequencies and soil properties is conducted. When the distance between the two tunnels is smaller than three times the tunnel diameter, the interaction between neighbouring tunnels is highly significant, at times in the order of 20 dB. It is necessary to consider the interaction between neighbouring tunnels for the prediction of ground vibrations induced underground railways.