Theoretical modelling of the dynamic interaction between twin tunnels in a multi-layered half-space

The vast majority of existing underground railway lines consist of twin tunnels. However, most previous studies on the prediction of vibrations induced by underground railways only considered a single tunnel. This paper presents a semi-analytical model for the dynamic interaction between twin tunnels in a multi-layered half-space. Multiple scattered waves are generated by the two cylindrical cavities, layer interfaces, and ground surface in such a complex model that cannot be solved theoretically by the method used for a single–tunnel model. In this regard, the translation between two different cylindrical waves is first introduced. Combining the transfer matrix method and the transformation between plane and cylindrical waves, the solution for the dynamic interaction between twin tunnels in a multi-layered half-space is obtained by means of the boundary conditions at the tunnel–soil interfaces. The accuracy of the proposed model is evaluated by comparing with the existing numerical models. The train-induced vibrations from twin tunnels embedded in a multi-layered half-space are subsequently investigated by coupling the proposed model with a vehicle–track model. The numerical results demonstrate that the existence of a neighbouring tunnel has a significant effect on the ground vibrations.