Landslides are one of the most destructive and common geological disasters in the Tonglvshan mining area, which seriously threatens the safety of surrounding residents and the Tonglvshan ancient copper mine site. Therefore, to effectively reduce the landslide risk and protect the safety of the Tonglvshan ancient copper mine site, it is necessary to carry out a systematic assessment of the landslide susceptibility in the study area. Combining the unascertained measure (UM) theory, the dynamic comprehensive weighting (DCW) method based on the fuzzy analytic hierarchy process (AHP)-entropy weight method and the set pair analysis (SPA) theory, an improved UM-SPA coupling model for landslide susceptibility assessment is proposed in this study. First, a hierarchical evaluation index system including 10 landslide conditioning factors is constructed. Then, the dynamic comprehensive weighting method based on the fuzzy AHP-entropy weight method is used to assign independent comprehensive weights to each evaluation unit. Finally, we optimize the credible degree recognition criteria of UM theory by introducing SPA theory to quantitatively determine the landslide susceptibility level. The results show that the improved UM-SPA model can produce landslide susceptibility zoning maps with high reliability. The whole study area is divided into five susceptibility levels. 5.8% and 10.16% of the Tonglvshan mining area are divided into extremely high susceptibility areas and high susceptibility areas, respectively. The low and extremely low susceptibility areas account for 30.87% and 34.14% of the total area of the study area, respectively. Comparison with the AHP and Entropy-FAHP models indicates that the improved UM-SPA model (AUC = 0.777) shows a better performance than the Entropy-FAHP models (AUC = 0.764) and the conventional AHP (AUC = 0.698). Therefore, these results can provide reference for emergency planning, disaster reduction and prevention decision-making in the Tonglvshan mining area.

In this paper, combined with fuzzy analytic hierarchy process (FAHP), information entropy theory, and set pair analysis (SPA) theory, an improved set pair analysis model (EFAHP‐SPA) for open‐pit mine slope stability evaluation based on entropy method and FAHP is proposed. Taking the east‐side slope of Tonglvshan north open‐pit mine in Daye as an example, the proposed method is verified. First, an open‐pit mine slope stability evaluation index system with 14 indicators in 4 categories, namely the topography and geomorphology, geological structure, hydrogeology, and other factors, have been constructed. Second, the objective weight and subjective weight of each evaluation index are calculated by entropy and fuzzy analytic hierarchy process, and then the comprehensive weight of the evaluation index is estimated based on subjective weight and objective weight. Afterward, the single‐index connection degree between the evaluation index and the evaluation standard of the secondary subsystem is evaluated considering the improved set pair analysis theory, and the comprehensive connection degree of the system is obtained by combining it with the comprehensive weight of each evaluation index. Finally, the confidence criterion is established to discern the risk grade of slope stability in the east‐side slope of the north open pit in Daye Tonglvshan mine. Moreover, case studies and comparisons of the proposed model with fuzzy comprehensive evaluation method and Entropy‐SPA model were performed to confirm the validity and reliability. The results show that the evaluation results of the proposed EFAHP‐SPA model are consistent with the actual situation of open‐pit mines and the evaluation results of entropy‐SPA model and are somewhat different from those of fuzzy comprehensive evaluation method. It indicates that the proposed EFAHP‐SPA evaluation model can objectively evaluate the slope stability of the open‐pit mine.

The high-filling engineering of airports is common in mountainous cities, and as critical infrastructure for urban development, airports are prone to slope instability under extreme climate and mechanical coupling effects. Therefore, it is essential to investigate the geometric form of failure surfaces under limit stability conditions for airport slopes. The rational determination of the form of the rupture surface of a soil nailing support structure is a key factor in the structural safety of a project. In this study, we analyzed the rupture surface form and reinforcement mechanism of four common soil nailing support structures in engineering. First, we established theoretical model I and verified the consistency of the upper-limit theorem of plastic mechanics and energy conservation in this model. Next, a theoretical analytical model of the rupture surface form was established taking into consideration the existence of tension depth in a certain depth range at the top. The mathematical expressions of the rupture surface form with respect to h/H and L/H were derived by combining plasticity mechanics and energy conservation. Finally, the rupture surface forms of the structure were analyzed for different slope angles of soil nail-supported structures and different friction angles within the soil. The findings were compared with the rupture surface forms in the existing codes and literature. The results showed that L/H decreased continuously with the slope angle $\beta$ of the soil nailing support structure and decreased gradually with an increasing friction angle $\phi$ within the soil. Furthermore, h/H decreased with the slope angle of the soil nailing support structure, but it showed a trend with the increase in soil internal friction angle and the slope angle of the soil nailing support structure. The analysis revealed that only in some specific cases were $\beta$ and $\phi$ closely aligned with the values acquired using standard methods in specifications and the literature. The theoretical analysis provided important reference values for the design and improvement of soil nailing length in soil nailing support structures under certain conditions, thereby ensuring their enhanced stability and strength.