# Comparative Analysis for Slope Stability by Using Machine Learning Methods
## 1 Introduction
In earth slopes, in the absence of resistant surfaces or bedrock or layering with high strength, the sliding surface passes through locations with the lowest resistance, and F.S will be at its minimum. Thus, the slope will be stable if the F.S\({}_{\text{min}}\) is over the critical state (F.S = 1). On the other hand, if the F.S\({}_{\text{min}}\) value is less than the critical state, the slope is unstable. Accurate estimation of the F.S value can be used for stabilizations and provide reliable stability analysis for the slopes. Various stability analysis techniques have been developed over 300 years to calculate the F.S and identify the probable slip surface, the instability scale, and failure mechanism, which are categorized as routine evaluations, limit state criteria, planar failure, limit equilibrium, numeric, hybrid, high-order, and intelligent methods [10, 11, 12, 13]. Each of these approaches has its benefits and limitations; some of them, such as limit equilibrium methods (LEMs), have been of more interest due to their simplicity in implementation, fewer assumptions, and the capability of generalization and inoculation with other methods. Varied types of LEMs were used in stability analysis with a historical background, but [PERSON] [14] is one of the pioneers of stability analysis by engineering and computational methods. The Fellenius method is an established stability analysis based on the moment equilibrium around the failure circle center was applied on a circular slip surface, which is correct for rotational failures. [PERSON] [15] provides a vertical force equilibrium and moment equilibrium-based method to quantify rotational failures. [PERSON] [16] extended [PERSON]'s method for the more complicated condition of massive failures. [PERSON] et al. [17] introduce a simplified methodology based on slicing a main movable mass on an earth slope, which is used to calculate the F.S in rotational failures with circular slip surfaces. [PERSON] and his colleagues [18; 19] provide detailed LEMs-based methods for analyzing the stability conditions of earth slopes, which are capable of implementation in the general shape of slip surfaces. After these, researchers developing LEMs-based stability methods received considerable attention, which led to the introduction and application of various LEMs in stability analysis. Several of the well-known methods can be mentioned, such as the Swedish [20], USACE [21], Lowe-Karafiath [20], Sarma [22], Spencer [23], Morgenstern-Price [24], and Correia [25] methods. LEMs provide close results in calculating F.S, and the difference in the estimated values for F.S is generally about 6% [26]. [PERSON] et al. [27] stated that the LEM-based methods could be generalized for all types of methods, which can be applied to all kinds of slip surfaces for different failure mechanisms. The conventional LEMs methods perform the progressive instability analysis using iterative processes due to the limitations of the assumed surface for slip parameter evaluations. By advancing computer application in slope stability analysis, the LEM-based methods are significantly improved and capable of solving more complicated equations regarding F.S, which cover the traditional procedures in LEM analysis. Particularly, computational intelligent methods provide a highly accurate prediction about the slope condition, failure mechanism, and risk potential to slip [27; 28; 29; 30; 5]. Advanced technologies including artificial intelligence, especially machine learning, have provided significant help in the stability analysis of earth slopes regarding F.S estimation using predictive models. Predictive models attempt to forecast and evaluate the F.S according to the machine learning rate and specific accuracy. Machine learning algorithms attempt to build methods to understand the current circumstance of target data, learn, and operate to learn using training data.