## 2 Materials and Methods
During the deformation calculations, the left and right boundaries are constrained in the horizontal direction, and the bottom boundary is fixed in all directions. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Property** & **FLAC Sample** & **This Study** \\ \hline Dry density (kg/m\({}^{3}\)) & 2000 & 1720 \\ Drained cohesion (Pa) & 0 & 10,500 \\ Drained friction angle (degrees) & 30 & 18 \\ Saturated hydraulic conductivity (m/s) & \(10^{-5}\) & \(6\times 10^{-7}\) \\ Porosity & 0.10 & 0.30 \\ van Genuchten parameter, a & 0.336 & 0.335 \\ van Genuchten parameter, \(P_{0}\) (MPa) & 0.015 & 0.035 \\ \hline \end{tabular}
\end{table} 
Table 1: Some geotechnical and hydromechanical properties of the soils. Figure 2: The SWRC of the soil. FLAC runs tp-flow of water and air as wetting (\(w\)) and non-wetting (\(g\)) fluids, respectively. The capillary pressure (\(P_{c}\)), namely, the matric suction, is defined as the difference between the pressures of non-wetting (\(P_{g}\)) and wetting (\(P_{w}\)) fluids, as follows in Equation (1):  
\[P_{c}=P_{g}-P_{w} \tag{1}\]  
The capillary pressure, \(Pc\), can be related to the effective saturation (\(S_{e}\)) where both can also be related to the residual saturation (\(S_{w}^{r}\)) and actual saturation (\(S_{w}\)). Equation (2) presents the relation between the capillary pressure and the saturation characteristics. \[S_{e}=\left[\left(\frac{P_{c}}{P_{0}}\right)^{\frac{1}{1-a}}+1\right]^{-a}= \frac{S_{w}-S_{w}^{r}}{1-S_{w}^{r}}=\frac{\theta-\theta_{r}}{\theta_{s}-\theta _{r}} \tag{2}\]  
where:  
\(P_{0}\) is used in FLAC as being related to the air entry value;  
\(a\) is used in Flac as the m constant in van Genuchten parameters;  
\(\theta\) is the actual volumetric water content;  
\(\theta_{r}\) is the residual volumetric water content;  
\(\theta_{s}\) is the saturated volumetric water content. Then, matric suction (as capillary pressure, \(P_{c}\)) can be derived as follows in Equation (3). \[P_{c}=P_{0}\left[S_{e}(^{-\frac{1}{2}})-1\right]^{(1-a)} \tag{3}\]  
Equation (3) can be used to determine the matric suction values for any saturation degree in relation with the effective saturation, air entry value, and van Genuchten parameter, a. The mobility coefficient (\(k\)) in FLAC is related with saturated hydraulic conductivity (\(k_{s}\)), gravitational acceleration (\(g\)), and density of water (\(r_{w}\)), and given in Equation (4). \[k=\frac{k_{s}}{g\cdot\rho_{w}} \tag{4}\]  
For all classical equations used during the seepage calculations and deformation analysis, comprehensive explanation can be found in the manual of FLAC [26] and related core studies [33; 34; 35; 10; 36]. During the analyses, the rainfall intensities were chosen as 2.5 mm/h, 5 mm/h, and 10 mm/h, representing the light, moderate, and heavy rainfall conditions, respectively. The initial saturation degrees were selected to vary between 40% and 60%. In order to conduct an analysis, it is first necessary to arrange the initial saturation degree. This should be carried out using the proper initial pore pressure and infiltration characteristics related to the soil's unsaturated properties. Otherwise, it is not possible to arrange the desired saturation degree unless the appropriate pairs of characteristics are input. Thus, initially, each parameter was calculated and applied to the model to enhance the desired initial saturation degree value. The mentioned saturation degrees were valid for the soil part close to the surface where the shallow slope failure is expected due to the rainfall. For the rest of the soil profile, the saturation degrees were set to increase gradually. An example for the unsaturated zone of the soil profile for 55% saturation for FLAC sample is given in Figure 3.  
The effects of antecedent saturation and rainfall conditions were investigated with different approaches combined. As a start, the factor of safety (FoS) values for each soil at its initial saturation degrees between 40% and 60% were determined for comparison.