A three-dimensional semi-analytical method for calculating vibrations from a moving load on a periodic jointed tunnel

Most underground railway lines are constructed by the shield method, resulting in the periodic jointed characteristic of tunnel structure in the longitudinal direction. This paper presents a new semi-analytical method to predict the three-dimensional dynamic response of a periodic jointed tunnel in the soil. The tunnel rings are conceptualized as cylindrical shells, and the tunnel ring joints are modelled as a series of springs with continuous supports around the circumference. The soil surrounding the tunnel is simulated using the elastic continuum theory. By applying the periodic-infinite structure theory, the solution for a harmonic moving load applied to the periodic jointed tunnel is obtained. The tunnel is subsequently coupled with the surrounding soil via the boundary conditions on the tunnel-soil interface. The accuracy of the proposed method is verified via comparisons with the existing methods and model test results. The numerical results show that the existence of the tunnel ring joint has a significant effect on the soil vibrations, resulting in an increase in soil vibration levels of 5–10 dB.