## 3 Results  
The rock-mass quality was calculated using Equation (1) for the 542 tunnel sections of the four tunnel projects following the two approaches of calculating rock-mass quality through characterization (\(RMR_{89}\)) and back-calculation (\(RMR^{*}\)). All the five cases of Table 6 were considered in the \(RMR^{*}\) calculation. Of the 542 tunnel sections, 468 sections show that \(RMR_{89}>RMR^{*}\) for all the five cases \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case No.** & **Weightage of \(RMR_{1}\)\({}^{*}\) and Q\({}_{1}\)\({}^{*}\)** & **Weightage of \(RMR_{2}\)\({}^{*}\) and Q\({}_{2}\)\({}^{*}\)** \\ \hline
1 & 100 & Actual \({}^{*}\) \\ \hline
2 & 75 & 50 \\ \hline
3 & 50 & 50 \\ \hline
4 & 50 & 75 \\ \hline
5 & 50 & 100 \\ \hline \hline \end{tabular} \({}^{*}\) Explained in Example 1.  
\end{table} 
Table 6: Five different cases for calculating \(RMR^{*}\) and Q\({}^{*}\) (Figure 1) while considering the weightage of the rock-mass quality obtained from rock bolts spacing and shotcrete thickness along with tunnel span. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Case No.**} & \multicolumn{2}{c}{**Scenario 1**} & \multicolumn{2}{c}{**Scenario 2**} \\ \cline{2-5}  & \(RMR^{*}\) & \(Q^{*}\) & \(RMR^{*}\) & \(Q^{*}\) \\ \hline
1 & 55.55 & 2.77 & 47.55 & 0.60 \\ \hline
2 & 54.16 & 2.52 & 48.0 & 0.64 \\ \hline
3 & 52.30 & 2.15 & 48.50 & 0.70 \\ \hline
4 & 50.44 & 1.78 & 49.0 & 0.76 \\ \hline
5 & 49.2 & 1.53 & 49.33 & 0.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Back-calculated rock-mass quality values for two different scenarios of Example 1 based on the weightage cases of Table 6.  
of weightage. The cases that show the difference (_RMR_89-_RMR_*) as a positive value are plotted in Figure 2.  
To evaluate the effect of the weightage for all the five cases in the stress adjustment factor for _RMR_89, three hypotheses were adopted for the _Fstress_-89. These hypothesis were also used for the extension of the _RMR_89 application for the rock-mass quality determination in highly stressed jointed rock-mass environments [16]. The details of the hypothesis tested for the rating selection based on intact rock strength to major principal stress (\(\sigma_{1}\)) ratio (\(\sigma_{c}\)/\(\sigma_{1}\)) are shown in Table 3.  
Using Equation (14), after applying the stress adjustment factor _Fstress_-89, based on the selection criterion expressed in Table 3 for all the 468 tunnel sections, _RMR_89 was adjusted for the stress parameter (_RMR_89*). The _RMR_* was calculated using five different weightages of Table 6. For each case, the _RMR_89* and _RMR_* are compared in terms of their difference (_RMR_89*-_RMR_*) for all the five cases of weightage and for three hypotheses and the obtained results are expressed in Figure 3.  
In case of _RMR_14, the rock-mass quality was calculated using Equation (5) for the 542 tunnel sections of the four tunnel projects through characterization and was compared with the back-calculated _RMR_ while considering all the five cases of Table 6. The comparison between the calculated _RMR_ (_RMR_14) and back-calculated _RMR_ (_RMR_*) for all the sections reveal that _RMR_14 > _RMR_* for all the five cases, and the details in terms of their difference (_RMR_14-_RMR_*) are shown in Figure 4.  
To evaluate the effect of the weightage for all the five cases in the stress adjustment factor for _RMR_14, the three hypotheses were considered for the stress adjustment factor (_Fstress_-14). The details of the hypothesis tested for the rating selection based on (\(\sigma_{c}\)/\(\sigma_{1}\)) for _RMR_14 are summarized in Table 8.  
Using Equation (16), after applying the stress adjustment factor based on the selection criterion expressed in Table 7 for all the tunnel sections, _RMR_14 was adjusted for a stress parameter as _RMR_14* using Equation (16).