## 3 Engineering Case Study  
### Engineering Overview  
The Bayan Obo open-pit mine is located in Baotou City, Inner Mongolia Autonomous Region, China (Figure 3a). The primary mining area spans approximately 1620 m in length and 1140 m in width, exhibiting a predominantly east-west orientation. Engineering geological investigations have indicated that the southern slope of the main mining area comprises four distinct lithological units: slate, dolomite, limestone, and mica schist (Figure 3b).  
On 29 August 2020, a landslide occurred on the southern slope of the main mining area at the Bayan Obo open-pit mine (Figure 4a). Field investigations and measurements revealed that the landslide's trailing edge was exposed at the 1650 m platform, extending approximately 500 m in length. The leading edge shear outlet was positioned at the 1542 m level, with the displaced material ultimately accumulating on the 1458 m platform. A geometric analysis of the landslide mass indicated a maximum north-south horizontal width of 55 m, a projected area of 1.23 \(\times\) 10\({}^{4}\) m\({}^{2}\), and an estimated total volume of approximately 9.2 \(\times\) 10\({}^{5}\) m\({}^{3}\). This failure was driven by the combined effects of a poorly confined convex slope face, multiple intersecting faults that weakened the rock mass, and long-term bench excavation that progressively reduced stability.  
Figure 2: Verification of the PSF method: (**a**) calculation results using the PSF method (\(c^{\prime}=50\) kPa, \(\phi^{\prime}=24^{\circ}\)); (**b**) calculation results using the PSF method (\(c^{\prime}=40\) kPa, \(\phi^{\prime}=22^{\circ}\)); (**c**) maximum shear strain (\(c^{\prime}=40\) kPa, \(\phi^{\prime}=22^{\circ}\)); (**d**) distribution of the plastic zone (\(c^{\prime}=40\) kPa, \(\phi^{\prime}=22^{\circ}\)). In subfigure (**d**), the red area indicates the plastic zone, while the light blue area represents the elastic region.  
A regional tectonic analysis (Figure 4b) revealed well-developed fault structures within the landslide area, characterized by predominantly east-west striking faults with dip angles exceeding 60\({}^{\circ}\) and individual fault thicknesses ranging from 5 to 30 m. These reverse-dipping fault structures, particularly their intersecting patterns, significantly compromised slope stability through their synergistic effects.  
A high-density resistivity survey was performed on the 1650 m platform, with the results illustrated in Figure 5. The southern slope displays exceptionally thick weathered material, extending to a maximum depth of 50 m, and exhibits localized fracture zones. An engineering geological analysis indicated that the rock mass exhibits \"double-weakness\" characteristics--manifesting highly developed structural planes and comparatively low mechanical parameters. These conditions represent significant intrinsic factors contributing to slope instability.  
Figure 4: Overview of the south slope of the Bayan Obo open-pit mine: **(a)** landslide on the south slope (29 August 2020); **(b)** stereographic projection diagram (lower hemisphere projection).  
Figure 5: Interpretation of high-density electrical method for survey line on the south slope.  
Figure 3: General overview of the Bayan Obo mining area: **(a)** the location of the Bayan Obo open-pit mine. The red star and red dot indicate the locations of Beijing and the Bayan Obo iron mine, respectively; **(b)** the lithological distribution of the Bayan Obo open-pit mine. The dashed black box marks the boundary of the open-pit area.