## 2 Materials and Methods  
### Rock-Mass Classification System and Rock-Bolt Design  
In each empirical rock-mass classification system, the classification criterion is unique, owing to the rock-mass characterization, followed by the classification, and the rock-mass quality is obtained in the numerical, as well as descriptive, form. The value obtained from each empirical system is used, along with the tunnel span, for support-design decisions, and, further, these systems relate each rock-mass class to a specific engineering problem in tunneling. The range of the RMR system is from 0 to 100, dividing the rock mass into five quality classes (very good, good, fair, poor, and very poor), with 20 points each. In the RMR system, rock-bolt design (20 mm diameter, fully grouted) is based on the tabulated guidelines for 10 m wide horseshoe-shaped tunnels, where the bolt length and spacing are the functions of rock-mass quality [2]. After the successful utilization of RMR for decades, the rock-bolt design rules were modified for any size of tunnel, taking the rock-bolt pattern (length and spacing) as a function of the tunnel size and rock-mass quality. According to the modification, rock-bolt length (\(L_{b}\)) is a function of the rock-mass quality and tunnel span, and it can be calculated by using Equation (1). The rock-bolt spacing (\(S_{b}\)) depends upon the rock-mass quality and can be calculated with Equation (2) [10]. For RMR values higher than 85 points, the system suggests spot bolting. \[span\;(m)=\frac{(L_{b}(m)+2.5)^{\frac{RMR_{89}+25}{52}}}{3.6} \tag{1}\]  
\[S_{b}\;(m)=0.5+2.5\frac{RMR_{89}-20}{65}\;(20<\text{RMR}_{89}\leq 85)\]  
\[S_{b}\;(m)=0.25+\frac{(RMR_{89}-10)^{1.5}}{140}\;(10<\text{RMR}_{89}\leq 20)\]  
\[S_{b}\;(m)=0.25\;(\text{RMR}_{89}\leq 10) \tag{2}\]  
In Q-system classifications, the rock mass is divided into nine classes (exceptionally good, extremely good, very good, good, fair, poor, very poor, extremely poor, and exceptionally poor), based on the rock-mass quality values obtained from Equation (3) or (4) [3,5]. \[Q=\left(\frac{RQD}{J_{n}}\right)\times\left(\frac{J_{r}}{J_{a}}\right)\times \left(\frac{J_{w}}{SRF}\right) \tag{3}\]  
\[Q_{c}=\left(\frac{RQD}{J_{n}}\right)\times\left(\frac{J_{r}}{J_{a}}\right) \times\left(\frac{J_{w}}{SRF}\right)\times\left(\frac{\sigma_{c}}{100}\right) \tag{4}\]  
where \(RQD\) (rock quality designation) has a minimum score of \(10,J_{n}\) symbolizes the score of the joint set number, \(J_{r}\) is the score for the roughness of the joint surface, \(J_{a}\) symbolizes the score for the clay filling or degree of alteration, \(J_{w}\) symbolizes the groundwater pressure effect scores, and the stress reduction factor (\(SRF\)) is the score for faulting, strength, and stress ratios in hard rocks, and squeezing or swelling. In Equation (4), \(\sigma_{c}\) is the uniaxial compressive strength of intact rock. The rock-mass quality value is combined with the equivalent dimension (\(D_{c}\)), to obtain the necessary support for the tunnel. \(D_{c}\) is based on the safety requirement and tunnel span and can be calculated with Equation (5). The safety requirements depend upon the use of the tunnel. For safety requirements, the excavation support ratio (ESR) was introduced. \[D_{e}=\frac{Span\;(m)}{ESR} \tag{5}\]  
\(ESR\) values are suggested for different tunnel categories based on their use; however, this can be used in each country, as per their safety standards for the tunnel [15,16]. The length of the rock bolt depends upon the tunnel span (B), as calculated with Equation (6) [3]:  
\[L_{b}(m)=2+\frac{0.15B}{ESR} \tag{6}\]  
The rock-bolt spacing can be found from the Q-system support chart that is a function of the rock-mass quality and presence of fiber-reinforced shotcrete (either sprayed or otherwise) for a 20 mm diameter fully grouted rock bolt [5,11]. The RMi system was proposed by [PERSON], based on the reduced rock strength caused by jointing, and it divides rock masses into five classes (very high, high, medium, low, and very low) [6,7].