## 3 Material and Methods
### Data Preparation
Slopes with heights of 15, 20, 25, and 30 metres and inclinations of 20\({}^{\circ}\), 25\({}^{\circ}\), 30\({}^{\circ}\), and 35\({}^{\circ}\) were produced. In terms of rigid behaviour, all of the models were placed on top of bedrock. Figure 1: Limit equilibrium model for the stability analysis, (W: weight, \(\tau\): shear strength, \(k_{h}\): seismic coefficient, g: acceleration due to gravity, \(\beta\): is slope inclination, H: slope height). The failure criterion used in this method was the Mohr-Coulomb failure criterion  
\[\tau=c+\sigma tan\varphi \tag{3}\]  
where \(c\): cohesion, \(\varphi\): friction angle, \(\sigma\): normal stress for slopes with soils with cohesion and internal friction, for a slope subjected to circular failure. The parametric values used were cohesion of 20, 30, 40, and 50 kPa and internal friction angle of 20\({}^{\circ}\), 25\({}^{\circ}\), 30\({}^{\circ}\), 35\({}^{\circ}\), and 40\({}^{\circ}\). The effect of earthquake motion on slope behaviour was considered in the current analysis. For the purposes of this analysis, the soil unit weight was assumed to be 18 (kN/m\({}^{3}\)). The amplitudes were defined as 0.1, 0.2, 0.3, and 0.4 g. On all of the slope models, thirty slices were used as slip surfaces. To achieve FOS values in this analysis, a grid and radius slip surface were used. The calculated FOS should be almost in the centre of the grid by using the grid and radius method. The FOS from the dataset was then separated manually into groups of safe slope or SS and unsafe slope or US in order to meet the objective of analysing and classifying all the slope stability cases in the dataset. Table 2 shows the input and output parameters used in the database development. In this study, 700 homogeneous slopes were simulated using GeoStudio which utilizes the LEM method shown in Figure 1, along with the most critical FOS parameters. In these 700 slopes, different values of the mentioned parameters in Table 2 were used and their FOS values were recorded. Based on a literature review conducted, the parameters presented in Figure 1 are considered to be the most important. The best relationships between these input parameters and the output (i.e., FOS) were calculated. In this way, simple regression analysis (one to one relationship) was employed. The highest R\({}^{2}\) value was achieved by the PGA parameter through a polynomial trend-line (as the best trend-line among applied linear, exponential, logarithmic, and power) as follows:  
\[\text{FOS}=0.0612(\text{PGA})^{2}-0.3512(\text{PGA})+1.4545 \tag{4}\]  
A value of R\({}^{2}\) equal to 0.305 was reported for the above equation. Besides PGA, the parameter \(\phi\) showed the best relationship with FOS values with R\({}^{2}\) = 0.122 through an exponential trend-line. To determine the relative effect of each input parameter on the output parameter, a sensitivity analysis was performed. The following equation was used to perform the same analysis:  
\[r_{ij}=\frac{\sum_{k=1}^{m}x_{ik}x_{jk}}{\sum_{k=1}^{m}x_{ik}^{2}\sum_{k=1}^{m }x_{jk}^{2}} \tag{5}\]  
where, \(r_{ij}\) is the strength of relation between each input and output, \(x_{ik}\) is the _ith_ sample of input \(k\), \(j\) is the number of each sample in the output set, and \(m\) is the total number of data samples. Table 3 shows the strengths of the relations (\(r_{ij}\) values) between the inputs