# Comparative Analysis for Slope Stability by Using Machine Learning Methods
## 4 Results and Discussion
\begin{table}
\begin{tabular}{l l l l l l} \hline
**Parameter** & **Unit** & **Max** & **Min** & **Mean** & **St.Dv.** \\ \hline Slope height (H) & m & 25 & 5.5 & 15.25 & 9.75 \\ Slope angle (\(\beta\)) & Degree & 73 & 30 & 51.5 & 21.25 \\ Slope topography * & - & Rough & Smooth & - & - \\ Water level in slope & m & 3 & 0 & 1.5 & 1.5 \\ Layers number & - & 1 & 1 & 0 \\ Tensile crack depth & m & 1.75 & 0.12 & 0.935 & 0.815 \\ Sliding surfaces depth ** & m & 27.4 & 1.3 & 14.35 & 13.05 \\ \hline \end{tabular}  
* Slope topography is estimated by intuitive mean ** Sliding surface is estimated by GeoStudio.  
\end{table} 
Table 2: Studied slopes’ geometrical properties. \begin{table}
\begin{tabular}{l l l l l l} \hline
**Parameter** & **Unit** & **Max** & **Min** & **Mean** & **St.Dv.** \\ \hline Water content & \% & 37.2 & 5.44 & 21.32 & 22.457 \\ Specific gravity (G\({}_{\text{s}}\)) & - & 2.63 & 2.60 & 2.61 & 0.0212 \\ \(\gamma_{\text{d}}\) & \(\text{kN}/\text{m}^{3}\) & 19 & 17 & 18 & 1.4142 \\ Slope height & m & 25 & 12 & 18.5 & 9.1923 \\ Slope angle & Degree & 72 & 40 & 56 & 22.627 \\ Cohesion (c) & kPa & 185 & 93 & 139 & 63.053 \\ Friction (\(\varphi\)) & Degree & 35 & 32 & 33.5 & 2.1213 \\ Poisson’s ratio (\(\
u\)) & - & 0.35 & 0.33 & 0.034 & 0.0141 \\ \hline \end{tabular}  
* \end{table} 
Table 3: Studied slopes’ geotechnical properties. The properties of the slope materials estimated by these tests used to investigate the general stability of the earth slope are based on computer-based calculations. The index geotechnical properties of the slope mass that are considered for calculation are presented in Table 3. These data were used for stability analysis in both machine learning-based and LEMs modeling as input data, which led to obtaining FS as output. The information about the geotechnical properties of earth slopes builds the primary dataset used in predictions. The training set is utilized for training the models, and the test set is applied to validate the predictions. Measured and predicted values obtained from LEM and predictive models were correlated by the R\({}^{2}\) index. R\({}^{2}\) is the link between the actual outcomes and the prediction values that generally range from 0 to 1, where if the value is closer to 1, a higher accuracy of the data overlap appears. Figure 2 provides the prediction results of FS by different machine learning classifiers on recorded samples in different earth slope training and testing sets. According to this figure, generally, predictive models have learned the process at an appropriate rate. In the meantime, the MLP classifier reaches more predictability for FS estimation. Figure 2: Measured and predicted results’ correlation on different classifiers based on (**a**) training and (**b**) testing sets. The results of the prediction process that led to evaluating the F.S were controlled by GeoStudio commercial software. GeoStudio is a two-dimensional, fully integrated software suite with LEM-based stability analysis and six finite element applications in various sub-models. Utilizing [PERSON]'s method, the SLOPE/W was used in this study to determine the F.S. Table 3 provides the geotechnical properties of the main slopes used in the stability analysis. The data from this table were entered into machine learning algorithms and the SLOPE/W program. SLOPE/W followed the several-stage modeling process, which can be categorized as geometric modeling, assignment of behavioral and materials characteristics, boundary conditions, and stability solutions. These steps are performed for the entire dataset (100 different slopes) and solved to calculate the minimum F.S of slopes. The calculated F.S was compared with the results of the machine learning predictive models. During geometric modeling, the geometry and topography of the slope, such as height, slope angle, layers, thickness of layers, slope surface conditions, and other (any) morphological complications, are designed and simulated.