## 3 Results  
For the precise characterization of some parameters of the rock mass rating systems, Equations (2)-(4) and (7) are suggested in this paper. The results of these Equations are compared with the lump/discrete and continuous rating in Figure 2, which shows that these fitted equations are suitable alternatives to achieve correct characterization. Figure 2: _Cont._  
Using the continuous rating approach, the 462 tunnel sections of Projects 1-2 [36] were characterized and classified based on \(RMR_{89}\). The details of characterization and classification are summarized in Table 4 and are shown in Figure 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{3}{c}{**Rating**} \\ \cline{2-4}  & \multicolumn{2}{c}{**Project 1**} & \multicolumn{2}{c}{**Project 2**} \\ \hline \multirow{4}{*}{Joint condition} & \(RQD\) (\%) & 6.44–20 & 3.33–20 \\  & UCS (MPa) & 4.042–6.95 & 4.245–8.73 \\ \cline{1-1}  & Joint Spacing (mm) & 7.88–16.89 & 7.88–14.69 \\ \hline \multirow{4}{*}{Joint condition} & Persistence (m) & 2 & 2 \\  & Aperture (mm) & 3 & 3 \\  & Roughness & 5 & 3 \\  & Infilling (mm) & 6 & 2, 4 and 6 \\  & Weathering & 5 & 3, 5 and 6 \\ \hline \multirow{4}{*}{Joint condition} & Ground Water & 0–15 & 0–15 \\  & \(RMR_{\text{basic}}\) & 56.53–79.84 & 32.98–73.84 \\  & \(F_{0}\) & \(-12\) to \(-2\) & \(-12\) to \(0\) \\  & \(RMR_{89}\) & 45.6–72.64 & 30.5–66.62 \\ \cline{1-1}  & Min. – Max (st. dev) & \(\frac{45.6-72.64}{64.0}\) (6.21) & \(\frac{30.5-66.62}{51.51}\) (7.966) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: \(RMR_{89}\) rating for Projects 1–2. Figure 2: Comparison of proposed equations results with suggested rating for different parameters. UCS: uniaxial compressive strength. Rock mass rating values were also obtained from different support categories and the supported span of the tunnel at all the sections of the two projects using back calculations and were defined as _RMR_*. The comparison of the calculated _RMR_89 and back calculated _RMR_ (_RMR_*) show that the actual supports installed are much heavier than those suggested by _RMR_89. Approximately 90% of the data show that _RMR_* is lower than _RMR_89. Their differences are shown in Figure 4 in terms of the percentage frequency. Figure 3: Percentage frequency of: (**a**) _RQD_ rating (\(R_{2}\)); (**b**) Joint/fracture spacing rating (\(R_{3}\)); (**c**) rating for groundwater (\(R_{5}\)); (**d**) adjustment rating for the joint orientation with respect to the tunnel axis and excavation direction (\(R_{6}\)); (**e**) _RMR_89 values for Projects 1–2. The mean ratio of \(RMR^{*}\) to \(RMR_{89}\), i.e., \(RMR^{*}/RMR_{89}\), is 0.855 (Table 5). The stress adjustment factor is applied to \(RMR_{89}\) as suggested based on strength-stress ratio. Details of the strength-stress ratio are shown in Figure 5. After this adjustment, the resultant \(RMR_{89}\) was defined as \(RMR_{89}\)*, and data were analyzed. After the application of the stress adjustment factor, the ratio of \(R  
Although \(RMR_{14}\) is discussed in this study, as it is the latest version of \(RMR\), Equations (9)-(13) indicate that without calculating \(RMR_{89}\), the determination of \(RMR_{14}\) is not possible. Rock mass ratings based on \(RMR_{14}\) for all selected sections of Projects 1-2 are summarized in Table 6, and details of the joint frequency and rock mass ratings (\(RMR_{14}\)) are shown in Figure 6.  
The comparison between \(RMR^{*}\) and \(RMR_{14}\) reveals that \(RMR^{*}<RMR_{14}\); details of this difference are shown in Figure 7.  
A correlation is established between \(RMR_{89}\) and \(RMR_{14}\), as shown in Figure 8, based on 462 tunnel sections of Projects 1-2. The correlation shows that \(RMR_{14}>RMR_{89}\). As the \(RMR_{89}\) system is extensively used for different purposes other than support, Figure 8 shows an excellent correlation between \(RMR_{89}\) and \(RMR_{14}\), as shown in Equation (24):  
\[RMR_{14}=1.0796 RMR_{89}+10.637,\ (R^{2}=0.96). \tag{24}\]