## 3 Numerical Model Test
### Coupling Model  
In the present paper, a particular model is first presented to simulate the Xianglushan tunnel under the dislocation of the Longpan-Qiaohou fault. With it, the longitudinal displacement profile and stress response of the lining under the fault dislocations are studied. The failure pattern of the surrounding rock mass is investigated from a micro perspective. In the coupling model, the continuum method is used to simulate the tunnel and is fixed, while the discrete particle assembly is used to represent the surrounding rock mass. The intersection angle between the tunnel and the fault is approximately \(50^{o}\). Meanwhile, the surrounding rock mass consists of two parts (see Figure 3): the left portion is fixed and the right portion possesses an upward velocity. Thus, the dislocation of the surrounding rock mass is simulated by the motion of the right portion.  
Modeling of Tunnel: the FLAC Model. In the numerical model, the tunnel is simulated as the continuous zone. The tunnel section is circular. The inner and outer diameters of the section are 7 and 8 m, respectively, and are approximately equal to the diameter of the Xianglushan tunnel (see Figure 4). The lining thickness is 0.5 m. In addition, the trial calculations show that the tunnel length of 90 m is sufficient to reasonably determine the stress response of the lining. Meanwhile, the lining is assumed to be elastic, and C30 concrete is used as the material in the model, which has a 'Young's modulus of 30 GPa and Poisson's ratio of 0.2.  
Modeling of Surrounding Rock Mass: the PFC Model. Owing to the limited calculation capacity, only approximately 150,000 discrete particles could be used to simulate the surrounding rock mass. It is generally believed that when the surrounding rock range exceeds the tunnel radius by 6 to 10 times, the boundary conditions would have little effect on the numerical calculation results. In this paper, the surrounding rock range is selected as six times the tunnel radius. Thus, the volume with the dimensions of 150 m x 64 m x 64 m outside the tunnel is filled with discrete particles. By considering  
Figure 3: Vertical section diagram of the fault model.  
Figure 2: (**a**) Location of Xianglushan tunnel; (**b**) geological longitudinal profile of the Xianglushan tunnel with the Longpan-Qiaohou fault.  
the volume outside the tunnel and the number of discrete particles, the diameter of the discrete particles is determined to be between 0.5 and 1.0 m.  
Then, the specific micro parameters of the particles are assigned. In the discrete particle assembly, a specified set of micro parameters corresponds to only one macro feature mode [25; 26]. The macro mechanical behaviors of the in situ rock mass are obtained according to the engineering data and results from previous studies. In this model, the macro mechanical behaviors of the discrete particle assembly are guaranteed to be consistent with the mechanical behavior of the in situ rock mass by parameter calibration [27; 28]. With a specified set of micro parameters of the particles, the triaxial compression tests are carried out on the model to obtain the test values under various confining pressures. From the final micro parameters of the discrete particle assembly shown in Table 2, in the triaxial compression test, the Young's modulus of the model is measured as E = 6.7 GPa, and the Poisson's ratio is measured as \(\mu\) = 0.25, which are similar to the macro mechanical parameters of the surrounding rock mass, listed in Table 3. It is observed that the macro mechanical behaviors of the discrete particle assembly are the same as those of the surrounding rock mass in the Xianglushan tunnel. The model thus accurately reflects the strength and deformation behaviors of the in situ rock mass.