## 2 Materials and Methods
### Tunnel Support and Back-Calculation of Rock-Mass Quality
For this purpose, the difference between two values (calculated _RMR_89 through characterization and back-calculated _RMR_ (_RMR_*), i.e., (_RMR_89-_RMR_*)) was used for the extension of _RMR_89 in a high-stress environment using Equation (14), where _Fstress_-89 rating, depending on the strength-stress ratio and selection criterion, is shown in Table 4[16]. \[RMR_{89}^{*}=RMR_{89}+F_{stress-89} \tag{14}\]  
where _RMR_89* is the stressed adjusted _RMR_89. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Range of Ratio \(\sigma_{d}\)/\(\sigma_{1}\)**} & \multicolumn{3}{c}{**Rating**} \\ \cline{2-4} \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} \\ \cline{2-4} \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} \\ \hline
5–4 & \(-\)5 & \(-\)22.326 \\
4–3 & \(-\)10 & \(-\)27.169 \\
3–2 & \(-\)15 & \(-\)32.012 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Stress adjustment factor selection for _RMR_89 and _RMR_14 based on the strength–stress ratio. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Classification System**} & \multicolumn{1}{c}{**LT**} & \multicolumn{1}{c}{**NJHP**} & \multicolumn{1}{c}{**KT**} & \multicolumn{1}{c}{**GGHP**} \\ \hline \multirow{4}{*}{\(RMR_{89}\)} & Minimum & 45.6 & 30.5 & 40.8 & 48.6 \\ \cline{2-6}  & Maximum & 72.64 & 66.62 & 72.22 & 63.19 \\ \cline{2-6}  & Mean & 64.0 & 51.51 & 62.85 & 59.48 \\ \cline{2-6}  & Standard Deviation & 6.21 & 7.97 & 7.53 & 3.97 \\ \hline \multirow{4}{*}{\(RMR_{14}\)} & Minimum & 56.33 & 42.74 & 58.02 & 59.53 \\ \cline{2-6}  & Maximum & 88.5 & 84.63 & 85.29 & 72.08 \\ \cline{2-6}  & Mean & 79.19 & 67.09 & 77.03 & 67.85 \\ \cline{2-6}  & Standard Deviation & 7.52 & 9.39 & 6.02 & 3.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of rock-mass rating values of _RMR_89 and _RMR_14 for the 542 tunnel sections obtained through rock-mass characterization approach. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Hypothesis**} & \multicolumn{3}{c}{**Values of \(\sigma_{d}\)/\(\sigma_{1}\)**} \\ \cline{2-5}  & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} \\ \cline{2-5}  & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} \\ \hline
1 & & \(-\)5 & \(-\)10 & \(-\)15 \\ \hline
2 & \(\text{F}_{\text{stress}{-89}}\) & \(-\)5 & \(-\)10 & \(-\)10 \\ \hline
3 & & \(-\)10 & \(-\)10 & \(-\)10 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Hypothesis used for the stress adjustment factor for _RMR_89. The \(RMR_{14}\) system is in the development stage, and the support design chart is not revised thus far for this version of \(RMR\)[19]. However, as can be observed from the data in Table 2, the \(RMR_{14}\) values are higher than \(RMR_{89}\), and a strong correlation exists between them [16; 19]. The correlation between the two versions of \(RMR\) based on the data of the four projects is expressed in Equation (15). Taking into consideration this correlation equation, a stress adjustment factor is also suggested for \(RMR_{14}\), as shown in Equation (16). The selection criterion for \(F_{stress-14}\) in Equation (16) is shown in Table 4 based on the strength-stress ratio. \[RMR_{14}=0.9686\times RMR_{89}+17.483,\ (R^{2}=0.92) \tag{15}\]  
\[RMR_{14}^{*}=RMR_{14}+F_{stress-14} \tag{16}\]  
where \(RMR_{14}\)* is the stressed adjusted \(RMR_{14}\). Although a modified \(Q\) value (\(Q_{c}\)) is obtained owing to the additional normalized factor in Equation (13), the support chart remained unchanged. The resultant rock quality obtained from the back analysis can be defined as \(Q\) or \(Q_{c}\). Equation (12) is rearranged to obtain Equation (17), and this equation was used for the \(SRF\) (\(SRF_{Q}\)) calculation for all the sections of the four projects while taking the back-calculated value as \(Q\).