# Comparative Analysis for Slope Stability by Using Machine Learning Methods
## 4 Results and Discussion
The studied earth slopes are composed of Quaternary alluvium, and no special layering or unique feature has been observed. Therefore, the main variables in geometric modeling are height and slope angle, which are illustrated in Table 2. Using this information helps to provide appropriate geometrical modeling for slopes. After preparing the slope geometry, the boundary conditions and behavioral model must be assigned to the model. The boundary conditions are easily defined in SLOPE/W. The Mohr-Coulomb (MC) failure criteria were selected as a behavioral model for stability analysis. The Mohr-Coulomb criteria, which represent the linear envelope obtained from a plot of the shear strength of a material versus the applied normal stress, are used to define the shear strength of soils at various effective stresses [44; 45; 46; 47; 48]. Table 3 is the index geo-materials properties used in modeling that are estimated based on ground survey and laboratory experiments assigned into the model as'material' specifications. When the models are prepared, they are solved based on [PERSON]'s method for slope stability analysis, and results are reported as F.S for slopes. Table 4 summarizes the ten studied slope stability calculations conducted by GeoStudio software as an illustration of the primary database used in predictive and LEM-based modeling. Figures 3 and 4 provide the results of the prediction process by the different classifiers plotted against measured data obtained from the LEM method via GeoStudio commercial software. The R\({}^{2}\) coefficients are estimated for both training and testing sets for all predictive algorithms with LEMs. According to these figures, MLP with R\({}^{2}\) = 0.951 in training and R\({}^{2}\) = 0.937 in testing stages reached the highest correlation with LEMs' results. This shows that the MLP classifier can effectively and accurately evaluate the F.S coefficient for earth slopes and provides more reliable results. A look at other class clauses, such as SVM, shows that this classifier is in second place after the MLP method in the prediction of F.S. The SVM provides R\({}^{2}\) = 0.930 in training and R\({}^{2}\) = 0.905 in the testing process, which can be considered as near approximations of F.S values to actual data. DT and RF provide less correlation with the LEMs-based results. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**No.** & **Slope Location** & **G\({}_{\text{s}}\)** & **\(\gamma\)4 (kN/m\({}^{3}\))** & **H (m)** & **\(\beta\) (\({}^{\circ}\))** & **c (kPa)** & **\(\varphi\) (\({}^{\circ}\))** & **F.S** \\ \hline
1 & Tehran & 2.62 & 18.22 & 12 & 45 & 124 & 35 & 1.65 \\
2 & Fars & 2.63 & 18.71 & 10 & 60 & 117 & 33 & 1.57 \\
3 & Fars & 2.60 & 18.20 & 7 & 63 & 93 & 33 & 0.98 \\
4 & Isfahan & 2.60 & 18.20 & 15 & 52 & 117 & 35 & 1.54 \\
5 & Tehran & 2.62 & 17.93 & 17 & 45 & 128 & 35 & 1.42 \\
6 & Fars & 2.62 & 18.00 & 20 & 63 & 155 & 32 & 1.57 \\
7 & Fars & 2.60 & 18.22 & 10 & 67 & 155 & 32 & 1.65 \\
8 & Tehran & 2.60 & 18.70 & 15 & 40 & 142 & 33 & 1.25 \\
9 & Tehran & 2.60 & 17.57 & 7 & 45 & 120 & 35 & 1.73 \\
10 & Isfahan & 2.63 & 18.00 & 17 & 52 & 117 & 35 & 1.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Studied slopes’ geometrical properties. and RF obtain 0.41, 0.62, and 0.45 losses, respectively. In Figure 5, the ROC curve analysis results of all models to evaluate the degree of the capability, which indicates that MLP provided the highest overall accuracy regarding the AUC (area under the curve) in the ROC curve, are illustrated. Based on the ROC curve results, MLP and SVM are reliable machine learning methods that can estimate F.S for earth slopes and provide suitable results. In the meantime, MLP can be recommended as an alternative technique that provides results that are appropriate and accurate. Referring to the ROC curve, MLP reaches an overall accuracy of up to AUC = 0.901 as the highest rank for the performance analysis of the machine learning classifier compared to the other classifiers. SVM and RF reach AUC = 0.873 and AUC = 0.835 as well.