## Materials and Methods
### Rock Mass Quality and Tunnel Support  
#### 2.6.1 Determination of Tunnel Support from Rock Mass Quality  
Both \(RMR\) and \(Q\) systems were designed--and have been specifically updated--for estimating tunnel support [2]. Because the support chart is based on empirical data, it is able to function as a guideline for the design of permanent supports in underground openings. Based on \(RMR_{89}\), recommended tunnel support guidelines were limited to a 10-m span conventional excavation tunnel and made available in table form, where the support requirement changes with rock mass quality [6]. Because the support technology improves with time, tunnel designers use different supports for various tunnel spans using the \(RMR_{89}\) tunnel support guidelines [37; 38; 39]. Design engineers predict supports for tunnel stability other than for those with a 10-m span, and the design process involves personal judgment. Personal judgment is also involved for different values of \(RMR_{89}\) in the same class, i.e., \(RMR_{89}=41\) and \(RMR_{89}=60\). After 24 years of experience, a major update in tunnel support through \(RMR_{89}\) was performed, in which the rock support is a function of the tunnel span and rock mass quality [15]. According to the modification, shotcrete thickness and rock bolt length (\(L_{b}\)) is function of rock mass quality and tunnel span. The length of the rock bolt can be calculated using Equation (17). \[span(m)=\frac{(L_{b}(m)+2.5)^{\frac{RMR_{89}+25}{32}}}{3.6} \tag{17}\]  
Rock bolt spacing (\(S_{b}\)) depends on rock mass quality and can be calculated using Equation (18). Spot bolting is needed for \(RMR_{89}>85\). The shotcrete design chart reveals that shotcrete thickness is highly influenced by the tunnel span (\(Span<10\) m) at low \(RMR_{89}\) values, whereas shotcrete thickness is highly influenced by \(RMR_{89}\) for larger tunnel spans (\(Span>10\) m). Because of this development in the support design for tunnels using \(RMR_{89}\), the calculation of rock mass quality as per suggestions through continuous rating is a more precise approach than the discrete one to achieve proper design, but with less personal judgment. The rock bolt spacing can be calculated as follows:  
\[S_{b}(m)=0.5+2.5\frac{RMR-20}{65},\ (20<RMR\leq 85); \tag{18a}\]  
\[S_{b}(m)=0.25+\frac{(RMR-10)^{1.5}}{140},\ (10<RMR\leq 20); \tag{18b}\]  
\[S_{b}(m)=0.25,\ (RMR\leq 10). \tag{18c}\]  
In the \(Q\) system support chart, the rock bolt spacing is a function of the rock mass quality, whereas shotcrete thickness is a function of the equivalent dimension (D\({}_{\rm e}\)) along with the rock mass quality. Differently to the \(RMR\) system, the characterization in the \(Q\) system has not been revised considerably. However, the support chart of the \(Q\) system has been continuously revised because of the development in the underground support philosophy and technology [9; 10; 11]. According to the support chart of the tunneling quality index system, the equivalent dimension (D\({}_{\rm e}\)) defines the bolt length. This D\({}_{\rm e}\) depends on the tunnel span and safety demanded excavation support ratio (ESR). The ESR value selection should be based on the safety of the working crew according to a country's safety standards, because each has its own criteria [40]. Secondly, ESR also depends on the rock mass quality [11]. The relationship between rock bolt length and D\({}_{\rm e}\) for hydropower projects reveals that ESR = 1 is also the appropriate value for hydropower tunnels [36]. The rock mass classification system suggests that the rock bolt (20-mm diameter and fully grouted) length and spacing for a tunnel cross section should be based on the rock mass quality. For the reinforcement and stability of the underground excavation, in the past few decades, several factors related to rock bolts have been studied through pull-out test results to investigate the performance of rock bolts.