Train-induced response of stiffness-degraded tunnel linings

Structural defects are common in railway tunnel linings, particularly in tunnels that have been in service for several years. Previous studies have investigated the impact of structural defects on the train-induced vibration of tunnel linings. However, modeling of these defects has always been restricted to the micro- or mesoscale, such as discrete cracks and material damage, which also limits relevance to engineering practices. To address this limitation, this study expands the analysis scale to the macro level by introducing the concept of stiffness degradation to investigate the impact of defects on the train-induced vibration of tunnel linings. A railway tunnel model is developed using the Gauss-Legendre-Lobatto (GLL)-based time-domain spectral finite element method (TD-SFEM), and eight types of stiffness degradation factors (SDFs) are incorporated into the governing equations of tunnel linings. By correlating each stiffness degradation with effective stress resultants, the vibration of stiffness-degraded tunnel linings induced by trains with different axle weights and running speeds is analyzed. The results show that the train type plays a primary role, while the structural defect plays a secondary role in determining the dynamic responses of the stiffness-degraded tunnel linings. The directivity of tunnel lining stiffness plays a crucial role in bearing train loads. Stiffness degradation mainly affects the average stress resultants in the circumferential direction, while the amplification of stress resultants is more pronounced in the longitudinal direction. These findings contribute to a better understanding of the impact of running trains on tunnel linings from a structural perspective, providing an intuitive and practical insight into the maintenance of railway tunnels.