Stochastic seismic response analysis and seismic reliability assessment of the mountain tunnel considering spatial variability of the fault fracture zone

In numerous earthquake disasters, it has been observed that cross-fault tunnels suffer more significant damage. Consequently, the seismic response mechanism of the cross-fault tunnel has become a prominent focus. However, the properties of the fault fracture zone (FFZ) are often treated as fixed values in existing research, neglecting the impact of spatial variability. A seismic response analysis framework for cross-fault tunnels is proposed in this study to address this gap. It utilizes the probability density evolution method (PDEM) and the Karhunen-Loève expansion method (KLEM) to investigate the influence of the FFZ spatial variability on tunnel seismic responses. Initially, a multi-dimensional non-uniform representative sample point set is developed using the Generalized F-discrepancy method. Subsequently, non-stationary random fields of the FFZ are generated based on the representative point set and the KLEM. Following this, a three-dimensional numerical model that incorporates the spatial variability of the FFZ is constructed using ABAQUS. Finally, the PDEM and equivalent extreme value events are employed to perform probability analysis and seismic reliability of the seismic response of cross-fault tunnels. The results show that the lateral relative deformation of the spandrel-springline exhibits greater dispersion. Furthermore, as the structure's plastic deformation increases, the variability of its longitudinal relative deformation also rises, with an increase range of 10 %–100 %. Moreover, the plastic strain extreme value progresses through three stages: the elastic stage, the rapid growth stage, and the slow growth stage. The framework proposed can reflect the impact of the spatial variability of the FFZ on the tunnel.