###### Abstract
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **Time** & **Name** & **Magnitude** & **Damage of Tunnel** \\ \hline \multirow{4}{*}{1} & \multirow{4}{*}{1906} & \multirow{4}{*}{San Francisco earthquake, America} & \multirow{4}{*}{8.3} & The San Andreas dam catchment tunnel crossing the fault zone was seriously deformed by 2.4 m. Due to the influence of fault zone, the Wright No. 1 tunnel had a phenomenon of orbital uplift, and the horizontal displacement reached 1.37 m [3]. \\ \hline \multirow{4}{*}{2} & \multirow{4}{*}{1930} & \multirow{4}{*}{Izu earthquake, Japan} & \multirow{4}{*}{7.3} & The sidewall of the Danah Railway Tunnel cracked seriously. Great rupture of the tunnel occurred near the fault plane. The horizontal displacement was 2.39 m and the vertical displacement was 0.6 m [7]. \\ \hline \multirow{4}{*}{3} & \multirow{4}{*}{1971} & \multirow{4}{*}{San Fernand earthquake, America} & \multirow{4}{*}{6.4} & The lining of the San Fernando tunnel near the Sylmar fault was damaged and displaced on a large scale [7]. \\ \hline \multirow{4}{*}{4} & \multirow{4}{*}{1978} & \multirow{4}{*}{Ojima earthquake, Japan} & \multirow{4}{*}{7.0} & The Inatori tunnel was damaged under the fault dislocation. The inverted arch and sidewall were cracked, and the concrete of the vault roof was peeled off. The steel bar was pulled off, the rail was compressed and bent, and the track and sleeper were dislocated relatively [7]. \\ \hline \multirow{4}{*}{5} & \multirow{4}{*}{1995} & \multirow{4}{*}{Hanshin earthquake, Japan} & \multirow{4}{*}{7.2} & Five subway stations and approximately 3 km of subway tunnel were damaged during the earthquake. More than half of the mid-columns in the Nagata-Shinkaichi section were completely broken, resulting in roof collapse and serious land subsidence, with a maximum settlement of 2.5 m [4]. \\ \hline \multirow{4}{*}{6} & \multirow{4}{*}{1999} & \multirow{4}{*}{Chi-chi earthquake, Taiwan, China} & \multirow{4}{*}{7.3} & Under the dislocation of the Chelongpu fault, the Shigangba tunnel was damaged seriously near the fault plane. The vertical deformation of the tunnel reached 4.0 m and the horizontal deformation was up to 3.0 m [5]. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Examples of cross-fault tunnel seismic damages. deformations, can be simulated. In addition, the failure pattern can be investigated from a micro perspective, and at a greater speed [13; 14; 15; 16; 17]. In this paper, a 3D discrete-continuum coupling method was first introduced to study the failure mechanism of cross-active-fault tunnels. The micro parameters of the discrete particles were calibrated such that the macro mechanical behavior of the discrete particle assembly is consistent with the mechanical behavior of the in situ rock mass. On the basis of these works, the 3D coupling model was established. With the model, the longitudinal displacement profile and stress response of the tunnel lining under various fault dislocations were investigated. In addition, the failure pattern of the surrounding rock mass was studied from a micro perspective. Moreover, the design strategy for flexible joint was investigated, based on the present work. The tunnel lining structures were separated into several independent segments along the longitudinal direction, and the gaps between the lining segments were filled with materials of low strength. Then, a parametric study of the segment length, the width and the strength of the flexible joint were performed. The orthogonal array test technique was utilized to investigate the level of influence of the main design parameters of the flexible joint on the internal stress of the lining. With the obtained knowledge, the optimal combination for flexible joint design was presented.