6.4.1. Influences of Fault Thickness on Seismic Response of the Lining

The maximum displacements and maximum tensile stresses of the lining monitoring points under different fault thicknesses are plotted in Figure 17, and the damage coefficients of the haunch monitoring point under different fault thicknesses are plotted in Figure 18.

**Figure 17.** Maximum response values of the monitoring points under different fault thicknesses: (**a**) displacement; (**b**) tensile stress.

**Figure 18.** Damage coefficients of the haunch monitoring point under different fault thicknesses.

We can see from Figure 17 that as the fault thickness increased, the maximum displacements of the three typical parts decreased gradually, tending to be stable when the thickness exceeded 30 m. Similarly, the changing of the maximum tensile stresses with fault thickness showed the same laws. This is mainly because the larger the fault thickness, the farther the lining monitoring section from the contact interface between the rock mass and the fault, so that the influence of the fault dislocation on the monitoring points is smaller. When the fault thickness exceeds a certain size, the influence of the fault dislocation on the monitoring points can be ignored. It should be noted that the maximum tensile stress of the haunch reached the tensile strength of concrete when the fault thickness did not exceed 20 m, and this part may then suffer damage. Furthermore, we can see from Figure 18 that as the fault thickness increased, the damage coefficient of the lining haunch decreased gradually, remaining at zero when the thickness exceeded 30 m.

6.4.2. Influences of Fault Dip Angle on Seismic Response of the Lining

The maximum displacements and maximum tensile stresses of the lining monitoring points under different fault dip angles are plotted in Figure 19, and the damage coefficients of the haunch monitoring point under different fault dip angles are plotted in Figure 20.

**Figure 19.** Maximum response values of the monitoring points under different fault dip angles: (**a**) displacement; (**b**) tensile stress.

**Figure 20.** Damage coefficients of the haunch monitoring point under different fault dip angles.

We can see from Figure 19 that as the fault dip angle increased, both the maximum displacements and maximum tensile stresses of the three typical parts first increased and then decreased, reaching a maximum at 45◦. This indicates that the fault dip angle had a great influence on the seismic response of the lining monitoring section. It should be noted that the maximum tensile stress of the haunch reached the tensile strength of concrete when the fault dip angle did not exceed 60◦, and this part may then suffer damage. Furthermore, we can see from Figure 20 that as the fault dip angle increased, the damage coefficient of the lining haunch first increased and then decreased, reaching a maximum at 45◦. When the fault dip angle exceeded 75◦, the damage coefficient of the lining haunch remained zero.

#### **7. Conclusions**

(1) Considering the dynamic deterioration characteristics of a rock structural plane under seismic action, a mathematical model reflecting the seismic deterioration effect of the contact interface between the rock mass and the fault was established. Based on the point-to-point contact type in the traditional dynamic contact force method, the point-tosurface contact type was also considered, and an improved dynamic contact force method considering the large sliding characteristics of the contact interface was established. Then, a nonlinear dynamic simulation method for the rock–fault contact system was developed. The calculation flow of the improved dynamic contact force method was designed, and the accuracy of the method was verified using the example of a sliding elastic block.

(2) Based on the improved dynamic contact force method, the nonlinear seismic damage characteristics of a deep tunnel through a normal fault were studied. The relative movement and seismic deterioration effect of the contact interface between the rock mass and the fault, and the characteristics of displacement, stress, and damage to the lining, were analyzed. The results indicated that the movements of the rock mass and the fault were not synchronous under large seismic action, and the seismic deterioration effect of the contact interface accumulated gradually over time. The proposed method can effectively simulate the vibration deterioration degree of the contact interface and the nonlinear large sliding problem of the rock–fault contact system.

(3) When the dynamic interaction between the rock mass and the fault was considered, the displacement and stress responses of the lining were greatly affected by the transverse dislocation displacement between the two, shown by a clear increase in the values. Compared with the lining at the footwall, the displacement of the lining at the hanging wall was more easily affected by the fault. Tensile damage appeared on the lining in the seismic loading process, and the damage area of the lining was mainly distributed in a certain range near both sides of the fault and at the parts where the fault passes through, especially at the haunch. Compared with the contact interface between the footwall and the fault, the damage to the lining at the contact interface between the hanging wall and the fault was more serious. This indicates that considering the dynamic interaction between rock mass and fault can more objectively reflect the seismic response characteristics of the tunnel structure.

(4) The influences of different fault thicknesses and different fault dip angles on the seismic response of the tunnel structure were discussed. As the fault thickness increased, both the maximum displacements and the maximum tensile stresses of the lining monitoring points decreased gradually, tending to be stable when the thickness exceeded 30 m. The damage coefficient of the lining haunch decreased gradually, and remained zero when the fault thickness exceeded 30 m. As the fault dip angle increased, both the maximum displacements and maximum tensile stresses of the lining monitoring points first increased and then decreased, reaching a maximum at 45◦. The damage coefficient of the lining haunch first increased and then decreased, reaching a maximum when the fault dip angle was 45◦ and remaining zero when the fault dip angle exceeded 75◦.

**Author Contributions:** Conceptualization, G.L.; methodology, Y.Z.; software, M.X.; validation, Y.Z.; formal analysis, G.L.; investigation, J.R.; resources, M.X.; data curation, J.R.; writing—original draft preparation, G.L.; writing—review and editing, G.L.; visualization, J.R.; supervision, Y.Z. and M.X.; project administration, G.L.; funding acquisition, Y.Z. and M.X. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the National Key Research and Development Program of China (grant number 2017YFC0404901), and the National Natural Science Foundation of China (grant number 52079097).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
