## 5 Conclusions  
This paper reports a systematic investigation into the spatial variability characteristics of jointed rock masses in the southern slope of the Bayan Obo open-pit mine and their impact on slope stability. The principal findings are summarized as follows:  
1. By constructing three-dimensional DFNs at varying scales, this research elucidates the scale-dependent behavior of jointed rock masses. The analysis identifies an REV of 14 m \(\times\) 14 m \(\times\) 14 m for the study area. This optimal dimension accurately represents the in situ geological structures while balancing computational efficiency with analytical precision.
2. A spatially variable block model of the rock mass mechanical parameters was developed to support the slope stability assessments. The RQD data were extracted from 40 borehole cores using digital image processing techniques. The three-dimensional spatial interpolation for the unsampled regions employed a spherical semivariogram model (nugget effect = 60; sill = 420; range = 230 m), establishing an RQD block model. The geological parameters were subsequently transformed into mechanical parameters via the generalized Hoek-Brown criterion, enabling the spatial visualization of the rock mass's mechanical properties.
3. The model's credibility is supported by the leave-one-out cross-validation, which indicates minimal interpolation bias and spatially unstructured errors. The lithology-grouped regressions reveal an exponential E-GSI relation and a near-linear depth dependence of the equivalent cohesion, which together rationalize the observed increase in stiffness and cohesion with depth.
4. Comparative stability analyses of the homogeneous and heterogeneous slope models were conducted using the PSF method. When contrasted against three homogeneous baselines (5 th/25 th/50 th percentiles), the heterogeneous parameterization not only aligns with the mapped 2020 sliding surface but also avoids the underestimation (Fs \(<\) 1.0) seen in the 5 th percentile case and the overestimation (Fs \(\gg\) 1.0) in the 50 th percentile case; the commonly used 25 th percentile baseline still overpredicts the stability (Fs \(\approx\) 1.17-1.34). These results indicate that spatial heterogeneity governs both the magnitude and geometry of instability, and that homogeneous benchmarks--regardless of the percentile chosen--are insufficient to reproduce the observed failure. Notably, the stability assessments reveal that the limestone formation within the southern slope represents a critical instability hazard, necessitating prioritized geotechnical monitoring and reinforcement measures.  
Conceptualization, X.D. and T.Y.; methodology, X.D., Y.G., F.L. and Y.Z.; software, X.D., Z.Z. and P.N.; validation, T.Y., Y.G. and F.L.; formal analysis, F.L. and Y.Z.; investigation, Y.G. and Y.L.; resources, Y.G.; data curation, Y.L. and P.N.; writing--original draft preparation, X.D.; writing--review and editing, X.D. and T.Y.; visualization, X.D. and Z.Z.; supervision, T.Y.; project administration, T.Y. and Y.Z.; funding acquisition, T.Y., F.L. and Y.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Research and Development Program of China (Nos. 2022 YFC2903902 and 2022 YFC2903903), the National Natural Science Foundation of China (Nos. 52374157 and 52204080), the Young Elite Scientists Sponsorship Program of CAST (Nos. 2023 QNRC001), the Key Science and Technology Project of the Ministry of Emergency Management of the People's Republic of China (Nos. 2024 EMST080802), and the Fundamental Research Funds for the Central Universities (Nos. N2401005).  
The data presented in this study is available on request from the corresponding author.  
The funders had no role in the design of the study; in the collection, analysis, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.