## 3 Results
The stress-adjusted _RMR_14 (_RMR_14*) and _RMR_* are compared in terms of their difference (_RMR_14*-_RMR_*) for all the five cases of weightage and for the three hypotheses, and the obtained results are expressed in Figure 5.  
Table 6.0 Percentage frequency of the calculated _RMR_89 and back-calculated _RMR_ difference considering the five cases of Table 6.1  
Table 6.2 Percentage frequency of the calculated _RMR_14 and back-calculated _RMR_ (_RMR_*) difference considering the five cases of Table 6.3  
Table 6.4 Effect of weightage (Table 6) during back-calculation of rock-mass quality (_RMR_*) (Figure 1) in terms of difference between stress-adjusted _RMR_89 (_RMR_89*) and _RMR_* using hypothesis of Table 6.5  
The data of the 542 tunnel sections (as summarized in Table 5) were used in Equation (17). For Equation (17), the back-calculation rock-mass quality (\(Q^{\star}\)) was determined using the five different weightages of \(Q_{1}\)\({}^{\star}\) and \(Q_{2}\)\({}^{\star}\) as per the details in Table 6.6 On separating the number of cases based on \(\sigma_{c}\)/\(\sigma_{1}\) from the 542 sections, 156 tunnel sections were found to have this ratio in the range of 4 to 5. In the range of 3 to 4, 232 cases exist, and the remaining 154 sections have a strength-stress ratio in the range of 2 to 3. Cases 1 and 3 of Table 6 are already respectively used for the extension of the application of the \(Q\) system of [PERSON] and the rock-mass index (_RMI_) system of Palmstorm for a highly stress-jointed rock-mass environment [16; 17]. The back-calculated rock-mass quality in Figure 1 for all the five cases of weightage was taken as the \(Q\) value in Equation (17) for the calculation of the _SRF_ (\(SRF_{Q}\)). This \(SRF_{Q}\) was plotted against the relative block size (\(RQD\)/\(J_{n}\)) for different ranges of  
Table 6.7 Effect of weightage (Table 6) during back-calculation of rock-mass quality (\(RMR^{\star}\)) (Figure 1) in terms of difference between stress-adjusted \(RMR_{14}\) (\(RMR_{14}\)*) and \(RMR^{\star}\) using hypothesis of Table 6.8 \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Hypothesis**} & \multicolumn{4}{c}{**Values of \(\sigma_{c}\)/\(\sigma_{1}\)**} \\ \cline{3-5} \multicolumn{2}{c}{} & **4-5** & **3-4** & **2-3** \\ \hline
1 & & \(-\)22.326 & \(-\)27.169 & \(-\)32.012 \\ \hline
2 & Fstress-14 & & \(-\)22.326 & \(-\)27.169 & \(-\)27.169 \\ \hline
3 & & \(-\)27.169 & \(-\)27.169 & \(-\)27.169 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Hypothesis used for the \(F_{stress-14}\) in tunnel support design. strength-stress ratio for all the five cases of \(Q^{*}\) based on their weightage (Table 6). The results are shown in Figure 6. The best fit equation for Case 1 is Equation (19), and for the remaining four cases is Equation (20). Equations (19) and (20) are already suggested for Case 1 and 3, respectively [16; 17]. For Case 2, the best fit Equation (20) has the same values for the constant \(\alpha\). However, in Cases 4 and 5, the constant \(\alpha\) values are different, as shown in Figure 6.  
\[SRF_{Q}=2.054\exp\left(0.205\frac{RQD}{J_{n}}\right)+14.865\exp\left(-0.41 \frac{\sigma_{c}}{\sigma_{1}}\right) \tag{19}\]  
\[SRF_{Q}=2.0\times\exp\left(0.21\times\frac{RQD}{J_{n}}\right)+12.0\times\exp \left(-\alpha\times\frac{\sigma_{c}}{\sigma_{1}}\right) \tag{20}\]  
Figure 6: _Cont._  
Figure 6: Effect of weightage (Table 6) during back-calculation of rock-mass quality index value (Q*) (Figure 1) in \(SRF_{\text{Q}}\) versus RQD/Jn plots for different ranges of strength–stress ratio. (**a**) \(\sigma_{c}\)/\(\sigma_{1}\) = 4–5, (**b**) \(\sigma_{c}\)/\(\sigma_{1}\) = 3–4, (**c**) \(\sigma_{c}\)/\(\sigma_{1}\) = 2–3.