Research on 3D stability algorithm of spatial concave slope.

The stope end wall in open - pit mining, which acts as a pivotal structure connecting the mining face, presents a concave spatial configuration. Ensuring the stability of such slopes is of paramount importance in mining engineering endeavors. Utilizing the concave slope at the southern extremity of the Nanfen Open - Pit Iron Mine in China as a case study, this research conducts an initial investigation into the instability mechanisms of such heterogeneous slopes through numerical simulation. It formulates a spatial equation for potential sliding surfaces and introduces a novel analytical method. The sliding surface is segmented into micro - strip regions, and by resolving their stress state via constitutive relationships and static equilibrium equations, the forces along the primary sliding direction are aggregated to obtain two - dimensional equivalent shear strength parameters for each row of microbars, incorporating three - dimensional effects. Subsequently, employing the rigid body limit equilibrium technique, a theoretical calculation formula for ascertaining the stability coefficient of three - dimensional concave slopes is deduced. The findings suggest that the potential landslide surface on concave slopes resembles an ellipsoidal form. Furthermore, there is an exponential correlation between the three - dimensional stability coefficient and the radius of curvature; specifically, as the radius increases, the coefficient decreases gradually, with its rate of reduction becoming milder over time. This study successfully addresses the issue of three - dimensional stability on concave slopes and offers more dependable theoretical approaches for mining engineering.