# Application of the Improved Entry and Exit Method in Slope Reliability Analysis
## 1 Introduction  
With the exploration and exploitation of offshore oil and gas resources, underwater engineering has become increasingly diverse. Submarine landslides caused by earthquakes and other reasons have seriously threatened the safety of deep-sea oil and gas drilling platforms, submarine pipelines, and other underwater oil production facilities. Evaluating the stability of submarine slopes is one of the important topics in marine geotechnical engineering. When analyzing the stability of marine slopes, the soil is usually regarded as a homogeneous material, and the strength coefficients of the soil are taken as the average of the statistical data. The stability of the slope is evaluated through a safety factor. Due to the factors such as material composition, sedimentation history, and consolidation pressure, soil strength parameters exhibit spatial variability [1; 2; 3; 4], which significantly affects the slope stability [5; 6; 7; 8; 9; 10]. It is difficult to comprehensively reflect the reliability of submarine slopes by using safety factors to evaluate the stability of marine slopes. [PERSON] et al. [11] studied the role of spatial variability of the soil nature during rainfall infiltration on sandy slope steadiness; they discovered that the uncertainty in the effective friction angle parameter had a significant influence on the obtained safety factor and failure probability. [PERSON] et al. [12] proposed a reliability exploration method for assessing the earth dam slope failure possibility based on extreme gradient boosting (XGBoost), and by conducting parameter sensitivity analysis on case studies, they found that the parameter of variation and fluctuation scale of spatially variable soil properties significantly influenced the failure probability of earth dam slopes. Furthermore, strain rate or loading rate [13] is also one ofthe key coefficients that affect the shear strength and deformation response of soil particles. [PERSON] et al. [14] revealed the mechanism of toe loading through triaxial compression tests, verifying the important relationship between strain rate effect and slope sliding. However, in practice, it is unrealistic to conduct slope reliability analysis considering all influencing parameters. In such cases, the emerging methods based on model and field testing have been widely adopted for slope failure prediction in recent years. For example, [PERSON] et al. [15] proposed an improved Markov chain model that can accurately simulate soil boundary uncertainty and obtain more accurate reliability results based on limited site drilling information. [PERSON] et al. [16] conducted a set of model experiments and field tests to examine the tilting actions of landslides, and then they proposed a novel method that can effectively predict the remaining time before slope failure occurs. [PERSON] et al. [17] introduced a machine-learning-aided approach for the stochastic reliability analysis of spatially variable soil slopes; the model generated based on machine learning in this method not only accurately predicted the safety factor, but also greatly reduced the computational workload. The stability of slope is analyzed by extensively applying the limit equilibrium approach because of its simple principle and reliable results. Combining the limit equilibrium approach with the random field theory, [PERSON] [18] proposed the random limit equilibrium approach to analyze the reliability of slopes. The random limit equilibrium approach has been used by many scholars to analyze the reliability of slopes [19; 20; 21; 22; 23]. When combining the random limit equilibrium method with Monte Carlo simulation to calculate the failure probability of slopes, the number of Monte Carlo simulations and the time required for each Monte Carlo simulation are key factors that affect the efficiency of slope reliability calculation. The number of critical slip surfaces analyzed during each Monte Carlo simulation is a key factor that affects the efficiency of the calculation.