An efficient semi-analytical method for dynamic responses of a tunnel in stratified soils with irregular interfaces

Dynamic tunnel-soil interaction is an important problem of long-standing interest in transportation and environmental engineering. Existing researches most focused on the dynamic problems in a homogeneous half-space with regular geometry. In this study, we develop an efficient semi-analytical method to calculate the dynamic responses caused by a time-harmonic line load acting on a circular tunnel embedded in stratified soils with irregular interfaces. This method uses the generalized reflection/transmission matrices (GRTM) to address wave propagation in a multi-layered half-plane with irregular interfaces. The multiple scattering theory and wave transformation are also applied to harmonize the functions describing various types of waves scattered by the irregular interfaces and the tunnel-soil interface. The present method has two attractive advantages: (1) It can handle arbitrarily shaped interfaces; (2) Only the irregular parts of the interfaces need to be discretized. The present method is verified by comparing to two existing results in the technical literature for simpler cases. A parametric study on a tunnel in a two-layered half-plane with a ladder-shaped interface is conducted to investigate the influence of irregular geometry on the dynamic responses. Additionally, a real case study of Nanjing metro line S6 is also conducted to show the applicability of the present method. Our results show that interface irregularities have a significant influence on the dynamic responses. The assumption of horizontal soil layer interface widely adopted in the previous studies and design analyses may cause considerable errors in predicting the dynamic responses.