## 1 Introduction  
In the field of geotechnical engineering and geohazard prevention, it is crucial to accurately assess the stability of slopes and calculate their factor of safety [1]. Among the many methods for solving the factor of safety of slopes, the limit equilibrium method and the strength reduction method are the most widely used [2, 3]. The limit equilibrium method assumes that the slope is in equilibrium in the limit state, and based on the equilibrium relationship between external and internal forces/moments, the stability equation is established to obtain the slope safety factor [4]. Although this method is simple and intuitive, its applicability is limited when dealing with complex slopes because it does not take into account the deformation and internal structural characteristics of the geotechnical body [5]. In contrast, the strength reduction method is usually combined with numerical calculation methods such as finite element and finite difference. These methods can consider more complex geological structures and analyze the force and deformation of geotechnical bodies, so that the calculation results are more in line with the engineering reality and have wider applicability [6, 7]. The core problem in slope stability analysis using the strength reduction method is to identify whether the slope has reached a state of ultimate equilibrium [8, 9]. Currently, the following three evaluation criteria are commonly used in numerical calculation methods:the convergence of unbalanced force [10], the sudden change of displacement in characteristic parts [11; 12] and plastic zone penetration [13]. Although reasonable results can be obtained in most cases, they may show limitations under specific conditions, e.g., the unbalanced force convergence criterion may lead to misjudgment when only local damage or small-scale large deformation occurs while the overall slope is still stable, and the latter two criteria depend on the selection of the feature site or the applicability of the plastic damage criterion. For this reason, some scholars have attempted to establish new judging indexes in order to more accurately and comprehensively identify the critical instability state of slopes. [PERSON] [14] constructed a fuzzy comprehensive evaluation model for slope stability analysis and a boundary value matrix of associated factors to comprehensively evaluate the stability of slopes. [PERSON] et al. [15] revealed the dynamic connection between microseismic activity, strength weakening and slope stability in the internal \"space\" damage deterioration of the slope rock mass, and realized the dynamic evaluation of slope stability by using the microseismic precursor information and strength reserve coefficient of the slope rock mass as the indexes. [PERSON] and [PERSON] [16] judged the slope damage based on the overall displacement vector of the slope. These research results have promoted the development of the strength discount method, but its feasibility and applicability on complex engineering slopes still need to be further studied. In recent years, with the rapid development of monitoring and early warning technology, deformation monitoring and early warning systems have been arranged on most of the important slopes in China, which provides a more direct means of judging the critical state of slopes. [PERSON] [17] used on the on-site deformation monitoring data to employ an improved genetic algorithm for predicting the critical slip destabilization of slopes in open-pit quarries. [PERSON] [18] established a joint multivariate prediction model of landslide displacement based on CEEMDAN-LSTM for slope displacement evolution and instability prediction. [PERSON] [19] revealed the correlation between slope stability and internal angle, and proposed to use angle change as a monitoring indicator to predict slope instability. Some scholars, such as [PERSON] et al. [20], also combine monitoring and warning with numerical calculation to analyze the stability of slopes.