###### Abstract  
For water transmission tunnels constructed in high-risk seismic regions of western China, active faults pose threats of serious ruptures to the tunnels. To overcome this issue, a 3D discrete-continuum coupling approach is introduced into the study. By this approach, spherical discrete-element-method (DEM) particles are used to represent the surrounding rock mass, and the tunnel is considered to be the continuous finite-difference-method (FDM) zone. In this way, a 3D coupling model was established to study the longitudinal displacement profile and stress response of the tunnel lining under various fault dislocations. The failure pattern of the surrounding rock mass was investigated from a micro perspective. Meanwhile, the design strategy of flexible joint was investigated with the present numerical model. The results from a parametric study show that the smaller segment length, wider width and weaker strength of the flexible joints are beneficial to the anti-dislocation performance of the tunnel. Moreover, an orthogonal array test technique was utilized to investigate the influence level of the main design parameters of the flexible joint on the lining internal stress. With the obtained knowledge, the optimal combination for flexible joint design was presented. Findings may provide references for the anti-dislocation issue of tunnels across active faults. t 2019 9 2318 2019 2  
Due to the lack of actual observation data, numerical methods have been widely applied in the engineering field with the development of computational technology. In 1989, a 1D finite element model of a tunnel for soil-tunnel interaction effects was established by [PERSON] et al. [8]. The results showed that the mechanical response of an essentially infinite-length tunnel could be predicted. [PERSON] et al. [9] studied the stress response characteristics of tunnels across active faults based on finite element theory and the finite difference method. In addition, [PERSON] et al. [10] investigated the mechanical response of a 70 m-deep immersed tunnel crossing a normal fault in Greece, based on a nonlinear finite element model. The anti-dislocation measures of using elastic gaskets with appropriate thickness and reducing the segment length were put forward in the paper. Several studies have revealed that the continuum method is efficient and accurate, it is suitable for the study of a continuous medium and for small deformation problems. However, with these models, the failure pattern cannot be investigated from a micro perspective. More recently, researchers have been investigating the response of cross-active-fault tunnels with various discrete element models. A 3D discrete element model is used to study the dynamic response of the tunnel-fault system by [PERSON] et al. [11], and the failure process of the tunnel is inferred according to the stress and strain distribution characteristics of the tunnel. From the relevant research, it can be found that the discrete numerical simulation demonstrates advantages in simulating large deformation problems, but with low efficiency and accuracy [12]. The discrete-continuum coupling method, which combines the advantages of the methods mentioned, is proposed. With the 3D discrete-continuum coupling approach, mechanical behaviors, such as large deformation problems, are expected to be more complex than the discrete-continuum coupling approach.