Research on Slope Stability Based on Bayesian Gaussian Mixture Model and Random Reduction Method

Slope stability analysis is conventionally performed using the strength reduction method with the proportional reduction in shear strength parameters. However, during actual slope failure processes, the attenuation characteristics of rock mass cohesion (c) and internal friction angle (φ) are often inconsistent, and their reduction paths exhibit clear nonlinearity. Relying solely on proportional reduction paths to calculate safety factors may therefore lack scientific rigor and fail to reflect true slope behavior. To address this limitation, this study proposes a novel approach that considers the non-proportional reduction of c and φ, without dependence on predefined reduction paths. The method begins with an analysis of slope stability states based on energy dissipation theory. A Bayesian Gaussian Mixture Model (BGMM) is employed for intelligent interpretation of the dissipated energy data, and, combined with energy mutation theory, is used to identify instability states under various reduction parameter combinations. To compute the safety factor, the concept of a “reference slope” is introduced. This reference slope represents the state at which the slope reaches limit equilibrium under strength reduction. The safety factor is then defined as the ratio of the shear strength of the target analyzed slope to that of the reference slope, providing a physically meaningful and interpretable safety index. Compared with traditional proportional reduction methods, the proposed approach offers more accurate estimation of safety factors, demonstrates superior sensitivity in identifying critical slopes, and significantly improves the reliability and precision of slope stability assessments. These advantages contribute to enhanced safety management and risk control in slope engineering practice.