## 2 Materials and Methods
### RMi System and Tunnel Support Design
#### 2.4.2 Tunnel Support Design by RMi System in Discontinuous Ground  
By definition, RMi is the uniaxial compressive strength (UCS) of rock mass, which only includes the inherent features affecting its strength. RMi has various applications in rock engineering, including tunnel support design. After the effective use of RMi in the tunneling field, some significant changes and adjustments for estimating preliminary rock supports by using the block volume and tunnel diameter were made [23]. The stability in blocky (jointed) ground is mainly influenced by the block size and shape, the shear strength of the joints delineating the blocks, and the orientation of the same joints relative to the tunnel axis. For the support application, RMi and tunnel span were adjusted based on the ground condition factor (\(G_{c}\)) and the size ratio factor (\(S_{r}\)), respectively, using Equations (13) and (14), as shown in Figure 4. The support parameters, which include all of these features, are used in the support chart. \[G_{c}=RMi\times SL\times C=\sigma_{c}\times 0.2\sqrt{jC}\times Vb^{D}\times SL \times C \tag{13}\]  
\[S_{r}=CF\times\frac{C_{0}}{N_{j}}=\left(\frac{D_{t}}{D_{b}}\right)\times\left( \frac{C_{0}}{N_{j}}\right) \tag{14}\]  
Here:  
\(SL=\) Adjustment parameter for stress level  
\(C=\) Gravity adjustment parameter for support in the roof or wall  
\(CF=\) Continuity factor, which is the ratio of the tunnel diameter (\(D_{t}\)) and the block diameter (\(D_{b}\)), differentiating between continuous and discontinuous ground and discontinuous ground having  
\(CF\) in the range from five to 100  
\(C_{0}=\) Adjustment for joint orientation  
\(N_{j}=\) Adjustment for number of joint setsThe _RMi_ system uses more parameters than the \(Q\) system, and it is relatively more complicated to use than the \(Q\) system. According to [PERSON] and [PERSON] [15], the groundwater factor is not properly included in the _RMi_ system. In this study, the rating for \(jL\) is equal to one, because the persistence of joints is from three to 10 m. According to the \(Q\) system [19], support at the wall and roof is independent of its location in a high-stress environment; therefore, the rating for the gravity adjustment factor (C) is also one. The ratings for joint roughness and joint alteration show that there are four different cases based on the \(J_{r}/J_{a}\) and \(jR/jA\) values, as shown in Table 4.  
The _RMi_ system uses block volume, which is formed by joints in a three-dimensional network in an underground environment. This parameter is usually determined on a two-dimensional surface or by a one-dimensional borehole or scan line. Only a limited part of a joint can be correctly measured in a given location, and the direct characterization of each block size is not practical at the excavation face. Since it can be difficult to recognize the actual size and shape of individual blocks, the block size and shape must sometimes be determined from reasonable simplifications. Indirect approaches are used for the determination of block size. The generalized correlation between the block volume (\(V_{b}\)) and the volumetric joint count (\(J_{v}\)) is given in Equation (15), where block shape influences the correlation [47]:  
\[V_{b}=\beta\times J_{v}^{-3}, \tag{15}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case No.** & \(J_{r}/J_{a}\) & \(jR/jA\) & **Project** \\ \hline
1 & 3 & 5 & LT, KT, GGHPP \\
2 & 1.5 & 1.5 & NJHEP \\
3 & 0.75 & 0.5 & NJHEP \\
4 & 0.5 & 0.375 & NJHEP \\ \hline \hline \end{tabular}
\begin{tabular}{c} LT = Lowari Tunnel; KT = Kohat Tunnel; GGHPP = Golen Gol Hydropower Project; NJHEP = Neelum–Jhelum Hydroelectric Project. \\ \end{tabular}
\end{table} 
Table 4: Ratio of joint roughness and joint alteration rating based on \(Q\) and _RMi_ systems for the four projects. Figure 4: Flowchart for the tunnel support estimation using the _RMi_ system in discontinuous ground.