A Slope Dynamic Stability Evaluation Method Based on Variable Weight Theory and Trapezoidal Cloud Model

Slope instability may cause severe casualties, property losses, and ecological damage. To accurately evaluate slope stability grades and mitigate geological hazards, a dynamic stability assessment method based on variable weight theory and trapezoidal cloud model is proposed. First, an evaluation index system for slope stability is established following the principles of uniqueness, purposefulness, and scientific validity. Then, to improve the accuracy of subjective constant weights, the intuitionistic fuzzy analytic hierarchy process (IFAHP) is employed to calculate subjective constant weights. Considering the contrast intensity and conflict among indicators, an improved CRITIC method is applied to determine objective constant weights. To balance subjective and objective factors and avoid constant weight imbalance, the optimal comprehensive constant weights are computed based on game theory, effectively reducing bias caused by single weighting methods. Furthermore, to fully account for the influence of indicator state values on their weights, variable weight theory is introduced to dynamically adjust the comprehensive constant weights. Finally, based on the variable weights of evaluation indicators, a trapezoidal cloud model is utilized to construct the slope stability evaluation model, which is validated through an engineering case study. The results indicate that the stability grade of Stage 1 is assessed as basically stable, while Stages 2 and 3 are evaluated as stable. Numerical simulations show the safety factors of the three stages are 1.36, 1.83, and 2.36, respectively, verifying the correctness of the proposed model. The proposed model demonstrates practical engineering value in slope stability assessment and can be referenced for slope reinforcement and hazard prevention in later stages.