# 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

Table 2: _Cont._Figure 8: Estimation of rock load based on the factor of safety = 3.0 in rock mass class III, (**a**) overburden = 40 m (1.3 D); (**b**) overburden = 50 m (1.7 D); (**c**) overburden = 60 m (2.0 D); (**d**) overburden = 70 m (2.3 D). Figure 9: Relation between H/D and h/D from the factor of safety method. Similarly, the relation between H/D and h/D was investigated with regard to the stress variable for the different rock mass classes (i.e., classes III, IV, and V), as shown in Figure 11. Unlike the previous analysis, the rock load was equal to the overburden for all the rock mass classes, which followed the reference line up to an H/D of 1.0, even though their relation followed the reference line up to 1.5 for both rock mass classes IV and V. After reaching the reference values of 1.0 and 1.5, h/D dropped slightly and converged as H/D increased. Figure 11: Relation between H/D and h/D from the stress variable method. Figure 10: Estimation of rock load in terms of the stress variable of 10% in rock mass class III, (**a**) overburden = 40 m (1.3 D); (**b**) overburden = 50 m (1.7 D); (**c**) overburden = 60 m (2.0 D); (**d**) overburden = 70 m (2.3 D). Figure 12 presents the comparison of rock loads estimated from different methods such as the factor of safety, stress variable, empirical method [13; 14], RMR89, and Terzaghi's rock load classification in terms of the relations between H/D and h/D for rock mass class III. As the overburden cannot be considered for RMR89 and Terzaghi's classification, the constant values of h/D for rock mass class III considering RMR89 and Terzaghi's classification were 0.4 and 0.2, respectively. For the factor of safety, the maximum value of h/D was obtained as 0.3, even when the value of H/D was as high as 2.3. However, for the stress variable, the rock load was computed to be equal to the overburden until H/D was equal to 1.0. When H/D was greater than 1.0, the h/D value slightly decreased and converged at approximately 0.4. In addition, when H/D was greater than 1.0, the h/D value for the empirical method was computed to be the greatest among all the methods. Figure 13 represents the relations between H/D and h/D for rock mass class IV. The constant values of h/D for rock mass class IV, considering RMR89 and [PERSON]'s classification, were 0.6 and 0.3, respectively. For the factor of safety, the rock load was estimated to be equal to the overburden until the value of H/D was up to 1.0. When H/D was greater than 1.0, the h/D value slightly increased and converged at approximately 1.0, which is close to the result of the empirical method. For the stress variable, the rock load was estimated to be equal until the overburden was up to 1.3. Beyond the H/D value of 1.3, the value of h/D fell to 0.6 and converged to the RMR89 line. Figure 12: Relation between H/D and h/D for rock mass class III considering the factor of safety and stress variable. Figure 13: Relation between H/D and h/D for rock mass class IV considering the factor of safety and stress variable. Figure 14 represents the relations between H/D and h/D for rock mass class V. The constant values of h/D for rock mass class V, considering both RMR\({}_{89}\) and Terzaghi's classification, were 0.8. As shown in the figure, for both the factor of safety and stress variable methods, the displayed results were similar to those of rock mass class IV. The factor of safety method converged at the value of the empirical method and the stress variable method converged at the value of both RMR\({}_{89}\) and [PERSON]'s classification. The results demonstrate that the empirical and factor of safety methods had a certain drawback in computing the rock load induced by the overburden. In the empirical method, the rock load was constant, regardless of the overburden. The rock load did not develop for rock mass class III, even though the overburden increased in the factor of safety method, resulting in an underestimated design.