## 2 Methodology
### Calculation of Refined Rock Mass Strength Parameters
This revision not only refined the narrow-scope Hoek-Brown criterion but also expanded the applicability of the empirical strength criterion, making it more comprehensive and specific. The corresponding expression is as follows:  
\[\left\{ \begin{array}{l}m_{b}=m_{i}\exp\Bigl{(}\frac{GSI-100}{9-3\Omega} \Bigr{)}\\ s=\exp\Bigl{(}\frac{GSI-100}{9-3\Omega}\Bigr{)}\\ a=\frac{1}{2}+\frac{1}{6}\Bigl{(}e^{-\frac{GSI}{15}}-e^{-\frac{30}{3}}\Bigr{)} \end{array} \right. \tag{7}\]  
In the equation, \(m_{i}\) is the Hoek-Brown constant for the intact rock blocks. By substituting the GSI, \(m_{i}\), and disturbance factor \(D\) values, the parameters \(m_{b}\), \(s\), and \(a\) can be calculated. With these values, the rock mass strength parameters can be determined using rock mechanics principles. The friction angle and cohesion of the rock mass can be determined using Equations (8) and (9), respectively. The specific results of the rock mass strength parameter calculations are shown in Table 2.  
\[\phi=\sin^{-1}\Biggl{[}\frac{6 am_{b}\bigl{(}s+m_{b}\sigma_{3\text{n}}\bigr{)} ^{a-1}}{2(1+a)\bigl{(}2+a\bigr{)}+6 am_{b}\bigl{(}s+m_{b}\sigma_{3\text{n}} \bigr{)}^{a-1}}\Biggr{]} \tag{8}\]  
\[c=\frac{\sigma_{c}\bigl{[}(1+2a)s+(1-a)m_{b}\sigma_{3\text{n}}\bigr{]}\bigl{(} s+m_{b}\sigma_{3\text{n}}\bigr{)}^{a-1}}{(1+a)\bigl{(}2+a\bigr{)}\sqrt{1+\frac{6 am_{b} \bigl{(}s+m_{b}\sigma_{3\text{n}}\bigr{)}^{a-1}}{(1+a)(2+a)}}} \tag{9}\]  
\[\left\{ \begin{array}{l}\sigma_{3\text{n}}=\frac{\sigma_{3\text{max}}}{\sigma _{c}}\\ \sigma_{3\text{max}}=0.72\frac{\sigma_{3\text{max}}}{\rho_{3\text{PM}}}-0.91 \end{array} \right. \tag{10}\]  
where \(\sigma_{3\text{max}}\) is the upper limit of the stress constrained by the relationship between the Hoek-Brown criterion and the Mohr-Coulomb criterion, \(\rho\) represents the density of the rock mass, \(g\) is the gravitational acceleration, \(H\) is the burial depth, and \(\sigma_{\text{cm}}\) denotes the overall strength of the rock mass. The specific results of the rock mass strength parameter calculations are shown in Table 2. The rock mass quality grades in Table 2 are determined using the RMR method [32]. In this study, to meet the requirements for the refined calculations, the refined mechanical parameters must also be computed. Using the aforementioned basic database and the demonstrated calculation method, rock mass strength calculations are performed on samples from different spatial locations and lithologies. This results in the establishment of a rock mass strength database. A drilling database is then constructed in 3 Dmine, and the rock mass strength parameters are applied to the model using the inverse distance weighted (IDW) method [33]. The IDW method is a deterministic mathematical approach used to estimate values at unsampled locations. This method employs a linearly weighted combination of known sample points to estimate the values at unsampled locations, where the weights are determined by the inverse distance between the sample points and the estimated point. It assumes that the similarity of values for a spatially distributed variable \(z\) decreases as the distance \(d\) and the power \(p\) of the distance increase. The equation for IDW interpolation is as follows:  
\[\hat{z}(x_{0})=\frac{\sum_{i=1}^{n}\frac{z(x_{i})}{d_{i}^{p}}}{\sum_{i=1}^{n} \frac{1}{d_{i}^{p}}} \tag{11}\]  
where \(\hat{z}(x_{0})\) is the estimated value at unsampled location \(x_{0}\), \(x_{i}\) is the known locations, \(i=1\) to \(n\), \(d\) is the distance, and \(p\) is the power parameter. The default power value is 2. Through this process, the refined mechanical parameters of the model are obtained. As an example, in Figure 7, the refined cohesion distribution contour map for the 115 m sublevel cross-section of the model is presented and analyzed.