## 2 Materials and Methods
### Characterization of Rock Mass Based on the \(Q\) System  
The tunneling data-based \(Q\) system categorizes rock mass into nine classes on a logarithmic scale, ranging in value from 0.001 to 1000 (exceptionally poor to exceptionally good, respectively). It is calculated through Equation (1) [16]:  
\[Q=\left(\frac{RQD}{J_{n}}\right)\times\left(\frac{J_{r}}{J_{a}}\right)\times \left(\frac{J_{w}}{SRF}\right), \tag{1}\]  
where \(RQD\) is the rock quality designation, \(J_{n}\) denotes the rating of the number of joint sets, \(J_{r}\) is the rating for the joint surface roughness, \(J_{a}\) denotes the rating for the degree of alteration or clay-filling joint set, \(J_{w}\) denotes the ratings for groundwater inflow and pressure effects, and \(SRF\) is the stress reduction factor. The ratio \(RQD/J_{n}\) is the relative block size in a selected domain, \(J_{r}/J_{a}\) is a measure of the inter-block frictional strength in that domain, and \(J_{w}/SRF\) is the effect of water, the strength-stress ratio, faulting, swelling or squeezing, and defined active stress. The role of \(\sigma_{c}\) is substantial in the properties of rock mass. Therefore, a normalization factor was applied to Equation (1) and modified to \(Q_{c}\) (Equation (2)) [18]:  
\[Q_{c}=\left(\frac{RQD}{J_{n}}\right)\times\left(\frac{J_{r}}{J_{a}}\right) \times\left(\frac{J_{w}}{SRF}\right)\times\left(\frac{\sigma_{c}}{100}\right). \tag{2}\]  
The New Austrian Tunneling Method (NATM) approach, which considers the ground behavior, was used for the excavation and support of the tunnels in the first four projects. This approach also included the geological documentation in the construction of conventional tunneling [41]. Therefore, the available data from the excavation face mapping is appropriate for the characterization of the \(RQD\), \(J_{n}\), \(J_{r}\), \(J_{a}\), \(J_{w}\), and \(\sigma_{c}\). Rockburst is a dynamic phenomenon that is linked with highly stressed environments in underground excavations. It is dominant in massive rock, and excavation in jointed rock mass has a positive impact under the same stress state as compared to massive rock. The increase in \(SRF\) that is shown in Table 2 is for massive rock based on \(RQD/J_{n}\)[17]. In jointed rock mass, the extreme value of the old \(SRF\) (1974 version) is proposed [42]. Equation (3) [43] and Equation (4) [42] are based on mining cases in South Africa and Australia, respectively, for the characterization of \(SRF\) (1974 version) for competent rock having rock stress problems. \[SRF=0.244\times K^{0.346}\times\left(\frac{H}{\sigma_{c}}\right)^{1.322}+0.176 \times\left(\frac{\sigma_{c}}{H}\right)^{1.413} \tag{3}\]  
\[SRF=31\times\left(\frac{\sigma_{1}}{\sigma_{3}}\right)^{0.3}\times\left(\frac {\sigma_{c}}{\sigma_{1}}\right)^{-1.2} \tag{4}\]  
The average unit weight of the intact rock for maximum sections of the first four projects in this study is about 0.027 MN/m\({}^{3}\). Equation (3) can be rewritten as Equation (5):\[SRF=28.29\times\left(\frac{\sigma_{1}}{\sigma_{3}}\right)^{0.346}\times\left(\frac{ \sigma_{c}}{\sigma_{1}}\right)^{-1.322}+0.00107\times\left(\frac{\sigma_{c}}{ \sigma_{1}}\right)^{1.413} \tag{5}\]  
Equation (6) was developed for the calculation of \(SRF\) in the \(Q\) system using the data of the Nathpa Jhakri project in India [44]:  
\[SRF=5.84\times\left(\frac{\sigma_{c}}{H}\right)^{0.001}\times\left(\frac{I_{r} ^{3}}{J_{n}}\right)+2.58. \tag{6}\]  
Equation (6) can be rewritten, with 0.027 MN/m\({}^{3}\) as the unit weight of the rock, as Equation (7):  
\[SRF=5.82\times\left(\frac{\sigma_{c}}{\sigma_{1}}\right)^{0.001}\times\left( \frac{I_{r}^{3}}{J_{n}}\right)+2.58. \tag{7}\]  
[PERSON] [18] divided the rock mass into massive and jointed, based on its \(RQD/J_{n}\) ratio, and revealed that a massive rock can have a ratio from 25 to 200, while a jointed rock mass has a typical ratio of 10. According to the rock mass fabric index approach, the maximum limit of the \(RQD/J_{n}\) ratio for a jointed rock mass is 16.5 [45].