## 3 Engineering Case Study
### Slope Stability Assessment  
Given the inadequacy of the block model for accurately characterizing the slope topography, a three-dimensional numerical grid model was established utilizing surface triangular meshes. Acknowledging that the influence of deep rock masses on the slope stability attenuates with depth, the grid density was progressively decreased from the slope surface toward the interior during model construction. Thus, one-to-one mapping between the original blocks and numerical grid was avoided. Consequently, the mechanical parameters were transferred from the block model to the numerical grid by means of a Python-implemented linear interpolation using SciPy's griddata function, after which the point safety factors for the southern slope were calculated in FLAC3D version 7.0. The numerical modeling results are presented in Figure 14. The three-dimensional model (1700 m \(\times\) 800 m \(\times\) 450 m), constructed through parameter interpolation, has dimensions comparable to the original block model. Discretization yields 1,920,566 computational units. The boundary conditions were implemented as follows: full fixation at the base; normal displacement constraints on all lateral boundaries; and unrestricted deformation on the slope surface to accurately simulate gravitational loading effects. For the material  
Figure 14: Numerical computation of 3D models: (**a**) heterogeneous model; (**b**) 5 th percentile homogeneous model; (**c**) 25 th percentile homogeneous model; (**d**) 50 th percentile homogeneous model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Lithologies**} & \multirow{2}{*}{**Number of Blocks**} & \multicolumn{2}{c}{\(\boldsymbol{E_{m}-GSI}\) (Log-Linear Fits)**} & \multicolumn{2}{c}{\(\boldsymbol{c^{\prime}-H}\) (Linear Fits)} \\ \cline{3-7}  & & \(\boldsymbol{\alpha_{0}}\) & \(\boldsymbol{\alpha_{1}}\) & \(\boldsymbol{R_{\text{log}}^{2}}\) & \(\boldsymbol{\beta_{0}}\) & \(\boldsymbol{\beta_{1}}\) & \(\boldsymbol{R^{2}}\) \\ \hline Slate & 130,311 & \(-\)1.429 & 0.0576 & 1.000000 & 196.936 & 0.564 & 0.210 \\ Weathered slate & 9539 & \(-\)1.862 & 0.0576 & 0.999988 & 6.087 & 0.535 & 0.909 \\ Dolomite & 10,665 & \(-\)1.157 & 0.0576 & 1.000000 & 221.260 & 1.406 & 0.540 \\ Mica schist & 6308 & \(-\)1.710 & 0.0576 & 1.000000 & 99.195 & 0.204 & 0.214 \\ Limestone & 2848 & \(-\)1.391 & 0.0576 & 1.000000 & 139.222 & 0.489 & 0.577 \\ Fault & 9905 & \(-\)2.398 & 0.0576 & 0.999998 & 21.364 & 0.122 & 0.342 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical regression analysis results. parameter assignment, the heterogeneous model (Figure 14a) incorporated the block mechanical parameters calibrated using the generalized Hoek-Brown criterion. In parallel, three corresponding homogeneous control models (Figure 14b-d) were established, with the lithology parameters set to the 5 th, 25 th, and 50 th percentile values of their heterogeneous counterparts. Since the block model does not include [PERSON]'s ratio, its value was taken from Table 2. Only self-weight (gravitational) loading was considered in the simulations; the influences of water pressure, seismic shaking, and cyclic loading were deliberately excluded. The PSF distributions were evaluated along six representative cross-sections (Profiles 1-6). In the heterogeneous model (Figure 15a), a continuous potential sliding surface develops, most prominently on Profile 3 (1650-1514 m benches) and Profile 5 (1650-1542 m benches); the strength reduction analysis yields safety factors (Fs) of 1.08 and 1.03 for these two profiles, respectively. By contrast, the homogeneous models exhibit percentile-dependent failure patterns: for the 5 th percentile case (Figure 15b), low Fs zones on Profiles 4-6 coalesce into a sliding  
Figure 15: PSF calculation results: (**a**) heterogeneous model; (**b**) 5 th percentile homogeneous model; (**c**) 25 th percentile homogeneous model; (**d**) 50 th percentile homogeneous model; (**e**) lithological profile and location of the sliding surface.