# Machine-Learning-Based Classification Approaches toward Recognizing Slope Stability Failure
## 2 Data Collection and Methodology  
To acquire a reliable dataset, the use of a single-layer slope was proposed. It was supposed that a purely cohesive soil, which only had undrained cohesive strength (C\({}_{\mathrm{u}}\)), comprises the body of this slope (see Figure 1). The main factors that affect the strength of the slope against the failure (i.e., FOS) were considered to be the slope angle (\(\beta\)), setback distance ratio (b/B), and applied surcharge on the footing installed over the slope (w). These parameters are illustrated in Figure 1. To calculate the FOS, Optum G2 software, which is a comprehensive finite element program for geotechnical stability and deformation analysis, was used [32]. Regarding the possible values for the strength of the soil (C\({}_{\mathrm{u}}\)) and applied surcharge (w), different geometries of the slope (\(\beta\)), and displacements of the rigid foundation (b/B), 630 possible stages were modelled and analyzed in Optum G2 to calculate the FOS of each stage as the output. In the modeling process, the mechanical parameters of Poisson's ratio, soil unit weight, and internal friction angle were assigned to be 0.35, 18 kN/m\({}^{3}\), and 0\({}^{\circ}\), respectively. Also, [PERSON]'s modulus (E) was varied for every value of C\({}_{\mathrm{u}}\). In this sense, E was set to 1000, 2000, 3500, 5000, 9000, 15,000, and 30,000 kPa for the following respective values of C\({}_{\mathrm{u}}\): 25, 50, 75, 100, 200, 300, and 400 kPa. The graphical relationship between the FOS and its influential factors is depicted in Figure 2a-d. In these charts, C\({}_{\mathrm{u}}\), \(\beta\), b/B, and \(w\) are each placed on a horizontal (x) axis versus the obtained FOS (i.e., from Optum G2 analyses) on the vertical (y) axis. The FOS ranges within [0.8, 28.55] for all graphs. Not surprisingly, as a general view, the slope experienced more stability when a higher value of C\({}_{\mathrm{u}}\) was assigned to the soil (see Figure 2a). As Figure 2b,d illustrate, the parameters \(\beta\) (5\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), and 75\({}^{\circ}\)) and w (50, 100, and 150 KN/m\({}^{2}\)) were inversely proportional to the FOS. This means the slope was more likely to fail when the model was performed with higher values of \(\beta\) and w. According to Figure 2c, the FOS did not show any significant sensitivity to the b/B ratio changes (0, 1, 2, 3, 4, and 5). Figure 1: A view of the geometry of the slope. Table 1 provides an example of the dataset used in this paper. The dataset was randomly divided into training and testing sub-groups, with the respective ratios of 0.8 (504 samples) and 0.2 (126 samples), based on previous studies [33]. Note that the training samples were used to train the MLR, MLP, RBF, SMO-SVM, IBK, RF, and RT models, and their performance was validated by means of the testing dataset. The 10-fold cross-validation process was used to select the training and test datasets (Figure 3). The results achieved were based on the best average accuracy for each classifier using 10-fold cross-validation (TFCV) based on the 20%/80% training/test split. In short, TFCV (which is a specific operation of k-fold cross-validation) divided our dataset into 10-partitions. In the first fold, a specific set of eight partitions of the data was used to train each model, whereas two partitions were used for testing. The accuracy for this fold was then indicated. This complied with using a various 20%/80% combinations of the data for training/testing, whose accuracy is also indicated. In the end, after all 10 folds were finished, the overall average accuracy was calculated [34; 35]. Figure 2: The relationship between the input parameters (**a**) strength of the soil (C\({}_{\text{u}}\)), (**b**) slope angle (\(\beta\)), (**c**) setback distance ratio (b/B), and (**d**) applied surcharge on the footing installed over the slope (w) versus the obtained factor of safety (FOS). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**No.