# Research on Slope Stability Based on Bayesian Gaussian Mixture Model and Random Reduction Method
## 5 Conclusions  
Integrating energy dissipation theory and the Bayesian Gaussian Mixture Model (BGMM), this study innovatively proposes a slope stability analysis method that incorporates random reduction paths. By numerically simulating dissipated energy under varying reduction coefficients and using energy evolution characteristics as criteria, a comprehensive safety factor with clear physical significance is defined. The main conclusions are as follows:  
(1) The limitations of conventional non-proportional reduction methods (e.g., fixed reduction paths and ambiguous physical meaning of safety factors) are addressed through the proposed random-path strength reduction method. This approach resolves the subjectivity in path selection and clarifies the physical interpretation of safety factors. (2) A BGMM-dissipated energy joint criterion is established to achieve precise classification of slope states. Compared to traditional displacement mutation criteria, this model demonstrates higher accuracy in distinguishing stable/unstable boundaries for slopes under complex geological conditions (e.g., pointed or multilayered soils). In practice, the method incurs higher computational costs. However, unlike the iterative calculations of \begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **FOS** \\ \hline Proposed method & 1.338 \\ Traditional SRM & 1.371 \\ Mean value method & 1.369 \\ Arithmetic square root & 1.369 \\ Mathematical fitting & 1.369 \\ Shortest path SRM & 1.587 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of safety factors using different methods. traditional methods, it enables parallel computing. When multiple devices are employed for simultaneous calculations, the required time may be further reduced. (3) A novel definition of the comprehensive safety factor based on the shear strength ratio is proposed, explicitly reflecting the dynamic equilibrium between material strength reserves and stress states on potential slip surfaces. This provides an intuitive quantitative metric for engineering decision-making. (4) Comparative validation with existing methods demonstrates the superiority of the proposed approach. For slopes under complex geological/engineering conditions, this method achieves more accurate classification of stable and unstable states, enhancing robustness while maintaining independence from specific reduction paths. Future Prospects:  
This study has preliminarily validated the effectiveness of the proposed method under relatively idealized geological conditions. It should be noted that the characteristics of the BGMM render it not amenable to conventional cross-validation methods. Meanwhile, the model has not been validated with actual data (e.g., field monitoring measurements). Therefore, the results are only applicable to conditions similar to the rock types and configurations considered in this study. To showcase its reliability and generalizability in real-world, complex geological scenarios, future research will focus on applying the method to a wider range of geologically more complex environments (e.g., those exhibiting strong heterogeneities, fault zones, or abrupt lithological changes). By conducting extensive case studies in these diverse and challenging geological settings, we will further elucidate the method's robustness and potential for adaptation in addressing practical geological exploration challenges. Furthermore, regarding the model analysis, while adopting the non-proportional reduction in dual parameters represents an improvement over the traditional proportional reduction method by better approximating the progressive failure mechanism of actual slopes (e.g., the inconsistency in the decay paths of cohesion and internal friction angle), it still assumes a uniform reduction in parameters across the entire slope mass. Real slope failures often involve the strain-softening behavior of the material and the development of localized failure zones, exhibiting strong spatial heterogeneity.