Three-dimensional slope stability analysis based on irregular ellipsoid sliding surface

The determination of the critical sliding surface is a crucial aspect of slope stability analysis. In reality, the environment in which slopes are located is often very complex, and the sliding surfaces have different shapes. Therefore, a three-dimensional stability study is proposed, using irregular ellipsoidal shapes as the sliding surface. By constructing the equation of the irregular ellipsoid and applying spatial geometric transformations, an irregular ellipsoid controlled by six parameters, (semi-axis length (a), width (b), height (c), rotation angle (θ), and spatial displacements (tx and tz)), is obtained. The interpolation method is employed to apply the irregular ellipsoid to 3D slopes, thereby generating irregular ellipsoidal sliding surfaces. The slope stability coefficient is calculated by using the residual thrust method and genetic algorithm to determine the critical sliding surface. A comparative stability analysis is conducted between the standard ellipsoidal sliding surface and the irregular ellipsoidal sliding surface through a classic case study. The results show that the Type II irregular ellipsoidal sliding surface aligns well with the mining area. Finally, the research findings are applied to the 3D slope stability analysis of the Shengli West No.2 Open-Pit Coal Mine in China, validating the feasibility of the proposed method.