## 4 Numerical Evaluation and Engineering Application  
### Numerical Evaluation of the Combined Use of PRPS and CGPR  
To better investigate the combined effect of PRPS and CGPR, two cases, namely, without (Case 1) and with (Case 2) the combined implementation of PRPS and CGPR, were numerically compared. The ground settlements of the two cases are shown in Figure 14. The plastic zone contours before and after the uses of PRPS and CGPR are provided in Figure 15.  
Figure 14: Ground settlement of triple tunnels: (**a**) without PRPS or CGPR (Case 1); (**b**) with PRPS and CGPR (Case 2).  
Figure 13: Effect of grouting thickness of curtain grouting pre-reinforcement (CGPR) on MCS and PPR.  
We noted the following mechanical characteristics:  
1. In Case 1, three small rock arches were formed above each tunnel. Besides, a large combined rock arch was also formed across the triple tunnels (Figure 14a). This large combined rock arch was generally entered plastic state (Figure 15a). Similar trends have also been analytically studied by [PERSON] [29]. This finding implied that the loosen rock mass above each tunnel might be connected due to the multiple excavation interactions.
2. During the left and right tunnel excavations of Case 1, the rock pillar was severely disturbed and lost the ability to bear loosen rock. The stress concentration phenomenon of the rock pillar was prominent, and the plastic zone completely penetrated the rock pillar (Figure 15a). It inevitably worsened the middle tunnel excavation and caused a larger plastic zone around the middle tunnel. The range of the final plastic zone was considerably large, with more than 15 m extended to the deep surrounding rock.
3. With the combined use of PRPS and CGPR (Case 2), the development of the three separated rock arches to the large combined rock arch was effectively restricted (Figure 14 b), the stress state of the rock pillar was greatly improved (Figure 15b). The safety of the tunnel roof was ensured, with a 56.3% reduction of the MCS. The plastic zone development was also significantly constrained. The plastic zone was primarily confined inside the grouting ring, and the PPR sharply decreased to 30.4%.
4. Moreover, the combined application of PRPS and CGPR (Case 2) showed better performance than that of the independent use of them. The MCS decreased to 24.6 mm, considerably smaller than that of the independent application of PRPS (34.1 mm, Figure 12) or CGPR (42.0 mm, Figure 13). The PPR reduced to 30.4%, more effective than that of the independent application of PRPS (96.8%, Figure 12) or CGPR (35.4%, Figure 13). It could be attributed to the synergistic effect between PRPS and CGPR. PRPS had longer advanced length, larger rigidity, faster construction speed, and smaller reinforcement zone, while CGPR had shorter advanced length, smaller rigidity, slower construction speed, and larger reinforcement zone. Owing to the longer advanced  
Figure 15: Development of plastic zone (red elements) around triple tunnels: (**a**) without PRPS or CGPR (Case 1); (**b**) with PRPS and CGPR (Case 2).  
length, larger rigidity, and shorter construction period of PRPS, a strong arch structure could be timely formed far ahead of the tunnel face. Therefore, PRPS could effectively bear vertical rock pressure and protect the tunnel crown. Owing to the broader grouting range of CGPR, the CGPR could greatly improve mechanical properties and the self-stability of the surrounding rock. Thus, the development of plastic zone could be effectively restricted by CGPR. Overall, PRPS and CGPR have complementary advantages in time, space, and mechanical properties, they mutually and actively formed a strong permanent ring in front of the tunnel face.