## 4 Discussion  
The comparison of rock mass rating [5] and tunneling quality index [8] with other classification systems reveal that these two systems are internationally accepted empirical design tools in rock \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Site** & **Section** & \(RMR_{89}\) & **Calculated \(Q\)** & **Tunnel Span (m)** & **Back Calculated \(Q\)** \\ \hline \multirow{4}{*}{Himalaya half tunnel} & K1 & 78.01 & 18.38 & 12 & 43.88 \\  & K2 & 83.87 & 19.04 & 13 & 100 \\  & PI & 73.79 & 25.58 & 10 & 33.88 \\  & T7 & 74.6 & 19.04 & 12 & 51.64 \\ \hline \multirow{4}{*}{Sydney Tunnel} & I & 65.97 & 43 & 17 & 4.9 \\  & II & 57.9 & 19 & 17 & 2.07 \\  & III & 49.67 & 2 & 17 & 0.7 \\ \hline \multirow{4}{*}{Istanbul metro} & Sandstone & 68 & 10.8 & 6.16 & 7.33 \\  & Sandstone & 46.31 & 1.47 & 6.16 & 3.19 \\  & mudstone & 34.39 & 0.83 & 6.16 & 0.36 \\ \hline \multirow{2}{*}{Excavation in chalk rock} & Avedat & 60.56 & 1.6 & 8 & 11.15 \\  & Enzid & 58.22 & 2.4 & 10 & 2.67 \\ \hline \multirow{2}{*}{ Boztepe Dam} & Tuffle & 33.43 & 0.156 & 5 & 0.45 \\ \hline \multirow{4}{*}{Bilecik-Istanbul roadway in Turkey} & Section-1 & 37.0 & 0.016 & 12.9 & 0.47 \\  & Section-2 & 64.73 & 1.52 & 12.9 & 0.72 \\ \cline{1-1}  & Section-3 & 52.03 & 10.8 & 12.9 & 1 \\ \cline{1-1}  & Section-4 & 81.05 & 11.48 & 12.9 & 5.39 \\ \cline{1-1}  & Section-5 & 73.39 & 10.79 & 12.9 & 7.75 \\ \cline{1-1}  & Section-6 & 76.95 & 12.29 & 12.9 & 5.39 \\ \cline{1-1}  & Section-7 & 78.67 & 9.99 & 12.9 & 7.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of calculated and back calculated \(Q\). Figure 11: Correlation between \(RMR_{89}\) and predicted \(RMR_{89}\) based on the published data of Table 3.  
engineering, particularly for tunnel support design. The major reason, out of many, behind their international acceptance is that these two rock mass classification systems are updated continuously either in the form of characterization or support [6; 7; 9; 10; 15]. The ability of these systems to characterize and classify rock masses is highly dependent on the use of these systems according to predefined procedures, taking into consideration their limitations. Although charts are available for characterization for the \(RMR_{89}\)[6; 23], users prefer to use the discrete/lump table for that purpose, contrary to the very essence of these systems. To facilitate the calculations for the continuous rating of intact rock strength, \(RQD\), joint spacing, and joint frequency, equations are proposed. These proposed equations are the least difficult approaches for characterizing the intact rock strength, \(RQD\), discontinuity spacing, and fracture frequency in \(RMR_{89}\) and \(RMR_{14}\). Similarly, in the \(Q\) system, although the use of 5 as an interval of the \(RQD\) rating is suggested [8], that suggestion is not taken into account in literature. An evaluation of the application of \(RMR\) and \(Q\) systems for tunneling in a high stress environment indicates that the \(Q\)-system is preferred because of the stress reduction factor (\(SRF\)). Although the \(RMR\) system is modified [6; 7], it is evident that the application of \(RMR\) (\(RMR_{89}\), \(RMR_{14}\)) system for tunnel support design in high stress environments is still the limitation of the \(RMR\) system. The mean value of \(RMR^{*}\) and \(RMR_{89}\)* are lower than \(RMR_{89}\) because of the effect of stress. Although the ratio \(RMR^{*}/RMR_{89}\)* considerably approaches 1, the standard deviation in \(RMR_{89}\)* is 9.44, which reveals that this parameter in \(RMR_{89}\) requires some amount of special attention to extend its application for tunnel supports under high stress environments. The two versions of \(RMR\)[6; 7] (\(RMR_{89}\) after modification in 2013 and \(RMR_{14}\)) use the same four parameters and their corresponding ratings.