## 4 Discussion  
The already supported tunnel sections data is used in this article. The same data is used for the extension of the RMR [18; 19], tunneling quality index [12; 26], and RMR index [29] in highly stressed jointed rock-mass environments [16; 17]. For the extension process, the back-calculation approach is used for the calculation of the rock-mass quality. In the back-calculation approach, the rock bolt spacing and shotcrete thickness are used along with the tunnel span for determining the rock-mass quality. As can be observed from Figure 1, the final rock-mass quality depends on the rock-mass quality obtained from the rock bolt spacing and shotcrete thickness in combination with the tunnel size. Although the average weightage is used for the calculation of the final rock-mass quality, owing to the unavailability of any criterion, the different weightage effect was not studied. Therefore, five different weightages were selected for the final rock-mass quality determination as shown in Table 6, and the obtained results are presented. For illustration, an example is used, the results of which are summarized in Table 7.  
Approximately 86% of the data shows that the back-calculated _RMR_ (_RMR*_) is lower than the calculate _RMR_ (_RMR_89) obtained using Equation (1), which indicates that the _RMR_89 suggested supports are lighter than the actual support. This difference is shown in Figure 2 in terms of the difference between _RMR_89 and _RMR*_ and reveals that for all cases of weightage, this difference is highest in the rage of 10 to 15 points of _RMR_. In each range of difference (\(<\)5, 5-10, 10-15, 15-20, and \(>\)20) the average vales for the five cases are 14.87, 27.22, 34.10, 18.46, and 5.34 with a standard deviation of 1.83, 2.21, 2.68, 5.59, and 2.43, respectively. This shows that for all the five ranges of differences, the deviation from the average of the five cases is very low except in the case of the range of 15-20, wherein the deviation is 5.59. This high deviation is due to the higher frequency of Case 3 with respect to other cases in the range 15-20. The percentage frequency of the difference between _RMR_89 and _RMR_* (_RMR_89-_RMR*_) in the range of 5 to 20 decreases with the case number, and these values are 84, 82, 81, 77, and 75 for Case 1--5, respectively. As the weightage of the rock-bolts-based back-calculated _RMR_ (_RMR_1*) decreased along with the increase in the shotcrete-based _RMR_ (_RMR_2*), the percentage frequency decreased. This decrease is due to the higher value of _RMR_1* than _RMR_2* in the maximum tunnel sections. After the application of the stress adjustment factor based on the strength-stress ratio as per the guidelines of Table 3, the percentage frequency of the difference between the stress-adjusted _RMR_ (_RMR_89*) and _RMR_* is the greatest in the range of \(-\)5 to 5 for all the five cases of the weightage except Case 3 and Hypothesis 2, as shown in Figure 3. For this case, the percentage frequency is 48 for (_RMR_89*-_RMR*_) in the range of \(-\)5 to 5. Hypothesis 1 of Table 3 was selected as the stress adjustment factor based on strength-stress ratio obtained for _RMR_89[16]. The leading case in terms of percentage frequency, where (_RMR_89*-_RMR*_) is in the range of \(-\)5 to 5 for Hypothesis 1, is Case 1 followed by Cases 2-5. Their values are 63, 62, 61, 60, and 57, respectively. _RMR_14 is the latest version of the _RMR_ system, and therefore, the result of this version and _RMR*_ are compared for each section and expressed in Figure 4 in terms of their difference. In each range of difference, in Figure 4, the percentage frequency of each case is very close with a very low value of standard deviation. The maximum standard deviation is obtained for the difference range 30-35 with a value of 2.09 from the average value of 18.19.