### Determination of Mechanical Parameters of Rock Mass  
The generalized H-B strength criterion accounts for three pivotal geological factors--lithology, rock mass quality, and in situ stress--providing a more rational representation of the damage progression in fractured rock tunnels following excavation [19]. This is demonstrated in Equation (1):  
\[\sigma_{1}=\sigma_{3}+\sigma_{\rm ci}\bigg{(}m_{\rm b}\frac{\sigma_{3}}{\sigma_{ \rm ci}}+s\bigg{)}^{a}, \tag{1}\]  
where \(\sigma_{1}\) and \(\sigma_{3}\) represent the maximum and minimum principal stresses when the rock mass yields, respectively; \(\sigma_{\rm ci}\) is the uniaxial compressive strength of rock; \(m_{\rm b}\), \(s\), and \(a\) are constants related to lithology and the structural plane of rock mass [20]. The calculation methods of rock mass parameters \(m_{\rm b}\), \(s\) and \(a\) are shown in Equations (2)-(4):  
\[m_{\rm b}=m_{\rm i}\exp\bigg{(}\frac{GSI-100}{28-14D}\bigg{)}, \tag{2}\]  
\[s=\exp\bigg{(}\frac{GSI-100}{9-3D}\bigg{)}, \tag{3}\]  
\[a=0.5+\frac{1}{6}\bigg{(}\exp\bigg{(}-\frac{GSI}{15}\bigg{)}-\exp\bigg{(}- \frac{20}{3}\bigg{)}\bigg{)}. \tag{4}\]  
_GSI_ is the geological strength index; \(D\) is the disturbance parameter of different grades of rock mass considering blasting damage and stress release [21], and its value range is 0-1; \(m_{\rm i}\) is the H-B constant of intact rock.  
The Basic Quality (BQ) value of rock mass is a critical parameter in rock engineering for assessing the quality of rock masses, taking into account a multitude of factors including the strength, integrity, structural characteristics, and degree of weathering of the rock mass. According to the Engineering rock mass classification standard [22] (GB/T50218-2014), the \(BQ\) value is calculated according to quantitative indexes such as the rock block integrity coefficient \(K_{\rm v}\) and rock uniaxial saturated compressive strength \(R_{\rm c}\), as shown in Equation (5):  
\[BQ=100+3R_{\rm c}+250K_{\rm v}. \tag{5}\]  
The BQ and the Rock Mass Rating (RMR) systems, as two methods for rock mass classification, inherently exhibit a certain degree of correlation. Based on the empirical formula of the correlation between the physical and mechanical parameters of rock mass and \(BQ\) in the specification [22] (GB/T50218-2014), the relationship equation between \(BQ\) and \(RMR\) can be derived:  
\[BQ=170\ln\frac{15+0.24 RMR}{5.7-0.06 RMR}. \tag{6}\]  
In 2005, [PERSON] and [PERSON] [23] proposed the relationship between \(GSI\) and \(RMR\):  
\[GSI=RMR_{1989}-5. \tag{7}\]  
Therefore, the empirical Equation (8) between \(GSI\) and \(BQ\) can be obtained:  
\[GSI=\frac{5.7\mathrm{e}^{BQ/170}-15}{0.24+0.06\mathrm{e}^{BQ/170}}-5. \tag{8}\]  
The deformation modulus and the elastic modulus share the same expression, which is the ratio of stress to strain. Although the deformation modulus can be obtained from laboratory physical experiments on rock blocks, these experiments are detached from the in situ environment of the rock mass and are insufficient to predict the deformation modulus of the rock mass at the tunnel face; in situ experiments are limited by time and the high cost of the experiments, making it difficult to widely conduct them at construction sites. [PERSON] and [PERSON] empirical formula [24] is used to estimate the deformation modulus. The expression is shown in Equation (9):  
\[E=E_{0}\bigg{(}0.02+\frac{1-D/2}{1+\mathrm{e}^{(60+15D-GSI)/11}}\bigg{)}, \tag{9}\]where \(E_{0}\) is the complete rock elastic modulus.