## 2 Materials and Methods
### Tunnel Support and Back-Calculation of Rock-Mass Quality  
The tunnel span along with the already fixed support (in terms of rock bolt spacing and shotcrete thickness) can be used for the calculation of the rock-mass quality by using the support charts of the two classification systems (\(RMR\) and \(Q\)) and Equation (11) [13]. Equation (11) and the support chart of the \(Q\) system show that the spacing of the rock bolts is based on the rock-mass quality only, and this spacing of rock bolts can be directly used for obtaining the rock-mass quality during (\(RMR\) and \(Q\) value) the back-calculation. These back-calculated \(RMR\) and \(Q\) values are defined as \(RMR_{1}\)* and \(Q_{1}\)*, respectively, as shown in Figure 1. The spraying of the fiber-reinforced shotcrete is compulsory during tunnel construction, and the thickness of this sprayed fiber-reinforced shotcrete depends on the quality of the rock mass (\(Q\) or \(RMR\)) in addition to the tunnel span or \(D_{e}\). The thickness of this shotcrete along with the tunnel size can also be used to identify the rock-mass quality through the back analysis of an already supported tunnel section based on the support charts of \(RMR_{89}\) and \(Q\) system. These back-calculated \(RMR\) and \(Q\) values are as defined \(RMR_{2}\)* and \(Q_{2}\)*, respectively, in Figure 1. During the back-calculation of \(RMR_{1}\)* and \(Q_{1}\)*, only the rock bolt spacing is required. In the case of the back-calculation of \(RMR_{2}\)* and \(Q_{2}\)*, the shotcrete thickness in addition to the supported tunnel span are required. During the \(RMR_{2}\)* and \(Q_{2}\)* calculation, the contribution of the rock-mass quality to the shotcrete thickness is important for the final calculation of the rock-mass quality (\(RMR\)* and \(Q\)*). These values depend on the inclination of a tangent in the shotcrete support line as found in the support charts of \(RMR\) and \(Q\) systems, respectively. The final rock-mass quality for both the systems can be evaluated using two different rock-mass quality values (rock-mass quality obtained using rock bolt spacing (\(RMR_{1}\)* and \(Q_{1}\)*) and that obtained using shotcrete thickness (\(RMR_{2}\)* and \(Q_{2}\)*)) through their weightage. In this study, the data of the four projects named Lowari tunnel (LT), Neelum Jhelum Hydropower (NJHP), Kohat tunnel (KT), and Golengol Hydropower (GGHP) are used. These detailed data that were used for the extension of the \(RMR\) and \(Q\) system in a highly stress-jointed rock-mass environment are  
Figure 1: Back-calculation of rock-mass quality (\(RMR\)* and \(Q\)*) based on five different cases, while considering the weightage of the rock-mass quality obtained from the rock bolts spacing and shotcrete thickness along with the tunnel span. available [16]. For the purposes of the extension of the _RMR_ system, the _RMR_ values were calculated using two different approaches: (1) as per normal procedure of characterization (_RMR_89 and _RMR_14), and (2) using the back-calculation approach (_RMR_*). Following Approach 1, the summary of the _RMR_89 and _RMR_14 values obtained for 542 sections of the four tunneling projects are expressed in Table 2.  
Along with intact rock properties, the joints and in situ stresses are the other parameters affecting the rock-mass behavior during the tunnel construction and the stress parameter is not taken into consideration in the _RMR_89 or _RMR_14 versions of the _RMR_. A different classification, known as SRC (surface rock classification), which has a relevant parameter for stresses based on tunnels experience in weak rocks [28], was used to capture the rock-mass behavior in the case of tunneling in a stressed environment. On considering the rating for stresses in SRC classification as a reference, a stress adjustment factor was suggested based on three hypotheses to extend the application of _RMR_89 systems in a highly stressed jointed rock-mass environment, as shown in Table 3[16].