# 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
### Estimation of Rock Load According to Overburden in Different Rock Mass Classes  
The simulation results of the rock load were obtained in the form of the factor of safety presented as contours for different overburdens in rock mass class III, as illustrated in Figure 8. The result contours presented herein for all the cases were obtained in step 19 for the estimation of the rock load. The contours were obtained for sequential excavation, considering the factor of safety to be greater than 1.0 with an increase in interval of 0.2. It was observed that the factor of safety increased as the distance from the tunnel periphery increased. The rock load was estimated by setting the criterion of the maximum factor of safety as 3.0 during the numerical simulations. The rock load around the tunnel periphery was less than 1 m until an overburden of 60 m, which is considerably less than the failure criterion. However, for an overburden of 70 m, the rock load increased significantly up to a value of 10.5 m, and the stresses acting on the rock mass, even at a considerable distance from the tunnel periphery, were observed to nearly satisfy the Mohr-Coulomb failure criterion. Based on the numerical simulation results, the relation between H/D and h/D was established according to the factor of safety for rock mass classes III, IV, and V, as illustrated in Figure 9. When the estimated rock load, h, is equal to overburden H, the values of H/D and h/D must be equal, as depicted in a linear line in Figure 9 that can be used as a reference line. It was observed that the relation between H/D and h/D for rock mass class III did not follow the reference line, in contrast to the other two rock mass classes. h/D was close to zero even though H/D increased. This indicates that the rock load (h) did not develop, despite the increase in overburden (H), because of the integrity of rock mass class III. However, for both rock mass classes IV and V, h/D followed the reference line up to an H/D of 1.0 and then started converging. This indicates that the rock load (h) developed proportionally with the increase in overburden (H). Therefore, the results demonstrate that the relation between the rock load (h) and the overburden (H) is strongly related to the rock mass class. Figure 10 presents the contours of the rock load in terms of the stress variable for different overburdens in rock mass class III. Starting from a stress variable of 0%, the contours were obtained for simultaneous excavation with an increase in intervals of 2%. The stress variable was observed to decrease with the decrease in the distance from the tunnel periphery. The rock load was estimated by setting the criterion of the minimum stress variable to be 10% during the simulations. When the overburden was less than 40 m, the rock load was equal to the overburden. When the overburden was greater than 40 m, a smaller rock load was computed, compared to the overburden. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Shatcrete** & **Unit Weight** & **Compressive** & **Deformation** & **Poisson’s** \\  & **(kN/m\({}^{3}\))** & **Strength (MPa)** & **Modulus (MPa)** & **Ratio** \\ \hline Soft shotcrete & 24 & 1.1 & 5000 & 0.20 \\ Hard shotcrete & 24 & 10 & 15,000 & 0.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material properties of shotcrete used in the simulation. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Construction Steps** & **Construction Condition** & **Load Distribution Ratio (\%)** \\ \hline
14 & Excavation of top-heading in right tunnel & 45 \\
15 & Soft shotcrete at top-heading in right tunnel & 35 \\
16 & Hard shotcrete at top-heading in right tunnel & 20 \\
17 & Bench excavation in right tunnel & 45 \\
18 & Soft shotcrete at bench in right tunnel & 35 \\
19 & Hard shotcrete at bench in right tunnel & 20 \\ \hline \hline \end{tabular}
\end{table}