THREE-DIMENSIONAL ANALYTICAL METHOD FOR CALCULATING VIBRATIONS OF A COUPLED TUNNEL-SOIL-FLUID SYSTEM

Train-induced vibrations from underground railway tunnels transmit to the ground surface or water, which may disturb adjacent residents or rare fish. This study presents a three-dimensional analytical method for calculating the dynamic response of the coupled tunnel-soil-fluid system. The twin tunnels and soils are simulated as the elastic solid, while the air or water is simulated as the ideal fluid medium. The three-dimensional dynamic problem in the time-space domain is transformed into the frequency-wavenumber domain by using the double Fourier transforms of time and longitudinal coordinates. The boundary conditions on the fluid-soil interface and the tunnel-soil interface are satisfied by introducing the transformation between the cylindrical waves and the plane waves and the transform between different cylindrical waves. The solution for dynamic response of the coupled tunnel-soil-fluid system under point loads is therefore derived. The accuracy of the proposed method is verified by comparing with the Green’s function and FE-BE model for a coupled soil-fluid system. The dynamic responses of soil, water, and air induced by point loads in a single tunnel and twin tunnels are compared and analyzed via two numerical cases. The results demonstrate that the existence of the adjacent tunnel can change the energy distribution of train-induced waves in the soil, thus affecting the propagation characteristics of waves in the water or in the air. The influence of the adjacent tunnel is highly dependent of the loading frequency, the observation position and the relative position between twin tunnels. When the distance between the two adjacent tunnels is less than four times of the diameter of the tunnel, the dynamic interaction between the twin tunnels play a relevant role in the response of the water or the air. This study can provide benefit for the evaluation of vibrations and radiated noise in air or water from underground railway tunnels.