# Estimation of Rock Load of Multi-Arch Tunnel with Cracks Using Stress Variable Method
## 3 Numerical Parametric Study of Three-Arch Tunnel Excavation for Rock Load Estimation
### Analysis of Rock Load Characteristics with Respect to Construction Steps  
Unlike a single tunnel, a multi-arch tunnel has a larger width than height and requires more construction steps. For a multi-arch tunnel, the concrete lining is constructed after the excavation of the central tunnel, and then, the construction of adjacent tunnels (left and right, as shown in Figure 15) begins. This results in complex construction sequences and stress superposition from the excavation of the adjacent tunnels. Therefore, in this study, the rock load is estimated in every case according to the construction steps involved in the excavation process.  
Figure 14: Relation between H/D and h/D for rock mass class V considering the factor of safety and stress variable.  
Based on a stress variable of 10%, the increasing trend in the estimated rock load (obtained using the contours) according to the construction steps is analyzed by considering the overburden value to be 40 m for different rock mass classifications. Figure 15 presents the rock load with respect to the construction steps for rock mass class III. As shown in Figure 15a, a small rock load developed after the excavation of the central tunnel was completed in step 6. However, a large amount of rock load developed after the completion of excavations of both the left and right tunnels, as shown in Figure 15b,c, respectively.  
The rock load values obtained for different rock classifications with respect to the construction steps are summarized in Table 4. The numerical simulation results show that the rock load had developed considerably when the final tunnel was excavated, especially in poor rock conditions. In this study, the rock load distribution was defined as the ratio of the developed rock load in the final step to the developed rock load in each construction step. In step 6, even though the values of rock load estimated for rock mass classes IV and V were greater than those for rock mass class III, the load distribution for rock mass class III (29.5%) was observed to be greater than that for rock mass classes IV (25.1%) and V (24.6%), as shown in Figure 16.  
Figure 15: Rock load estimation based on the stress variable of 10% according to the construction steps: (**a**) excavation of the central tunnel, completed in step 6; (**b**) excavation of the left tunnel, completed in step 13; (**c**) excavation of the right tunnel, completed in step 19.  
A similar pattern was observed in step 13. However, the difference between the load distribution for rock mass class III and that for rock mass classes IV and V was observed to be greater than the difference in step 6. In rock mass class III, the magnitude of rock load observed to be developed in each step was approximately equal. However, in rock mass classes IV and V, approximately 60% of the rock load was observed to develop between steps 13 and 19. The study results show that the load distribution is relatively greater when the central tunnel is excavated in good rock conditions as compared with the excavation in poorer rock conditions. This observed phenomenon is similar to the concept of the ground reaction curve, where the better the rock conditions for the excavation process, the lesser the displacement observed, and the earlier the occurrence of stress relaxation.  
The analyses results indicate that the rock load does not develop to a considerable level in rock mass class III. However, in rock mass classes IV and V, the rock load develops to a large extent with each construction step. Therefore, for all the rock conditions below rock mass class IV, the overall stability of the tunnel during the excavation of the left and right tunnels must be emphasized more than that during the excavation of the central tunnel, to perform the stability analysis.