SEMI-ANALYTICAL METHOD FOR THREE-DIMENSIONAL DYNAMIC RESPONSE OF IRREGULAR SOIL-TUNNEL COUPLED SYSTEM

Due to the influence of geology and environment during the formation process, natural foundations have obvious irregular characteristics, which directly affect the vibration propagation in soil generated by rail transit load driving in the tunnel. In response, this article proposes a semi-analytical method for the three-dimensional dynamic responses of an irregular half-space-tunnel system. Both the soil and the tunnel are assumed to be elastic and homogeneous media that remain constant along the longitudinal direction. By using a dual Fourier transform of time and longitudinal coordinates, the three-dimensional dynamic problem in the time-space domain is transformed into the frequency-wavenumber domain to be solved. The wavenumber discretization method and the plane wave expansion method are combined with boundary integral equations to establish a set of simultaneous equations for solving the complex scattered wavefield within the irregular half-space. Furthermore, utilizing the wave transformation method, the boundary conditions of the tunnel-soil interface are satisfied to couple the irregular half-space and tunnel together, and then the semi-analytical solution for the dynamic response from a tunnel in an irregular half-space excited by a harmonic load is obtained. This method can handle arbitrarily shaped surfaces, which breaks the limitations of existing methods that assume the ground surface to be a horizontal boundary. Only the irregular parts of the surface need to be discretized. This method has high computational efficiency. Through conducting a real case study of Shenzhen Metro Line 5, the results indicate that irregular ground surfaces have a significant impact on displacement responses, and it is related to the load frequency. Neglecting the irregular characteristics of the ground surface can lead to a prediction error of approximately 5 to 20 dB. The research findings provide theoretical support for the vibration assessment and reduction design of the rail transit system.