Three-Dimensional Analytical Model for Coupled Track-Tunnel-Soil System in a Multilayered Half-Space

An analytical model is presented in this paper to predict the three-dimensional dynamic response of a circular tunnel in an elastic multilayered half-space. By applying the transfer matrix method and wave transformation, the circular tunnel was coupled with the soil via the continuity condition of the tunnel–soil interface. The coupled tunnel-soil model could simulate the asymmetric dynamic responses induced by the load at an arbitrary angle. The track system was subsequently coupled to the tunnel-soil model by means of three-line support. After being validated via comparison with existing models in two special cases, the present model was applied to calculate the soil vibrations from a large-diameter double-line tunnel in a three-layered half-space. The results showed that the insertion gains for vertical and horizontal displacements between the single- and double-line loading cases are −15 to 20 dB and −15 to 11 dB, respectively, depending on the position of the observation point and frequency. The vibration levels generated by the double-line load were smaller than those generated by the single-line load at specific load frequencies.