## 3 Results  
### Saturated Seismic Analysis  
Figure 6 presents the slope model considered in this phase. The vertical seismic coefficient is neglected as it is very low or zero in most cases. The horizontal seismic load was applied using the seismic loading option in the Slide software. The seismic coefficients are dimensionless coefficients that represent the maximum earthquake acceleration as a fraction of the acceleration due to gravity. Typical values are in the range of 0.1 to 0.3. In this paper, the maximum value for the horizontal seismic coefficient is considered as 0.3.  
Figure 6: Slope model—saturated seismic case.  
The coordinates (m) of the slope are 0,0; 27,0; 27,5; 16,5, these vary with the slope angle, 16 and 16, 0. The model's coordinates are in meters. In the fifth coordinate, variations in the slope angle mean that this coordinate value changes from 70 to 88 degrees. For all of the 200 analyses, this coordinate has a unique value. This slope is analyzed dynamically by applying the maximum horizontal seismic coefficient of 0.3. The water table is applied at the upper surface of the slope. This analysis is performed in the total saturated condition. Normally slopes are subjected to rain and water, such as rivers, at the bottom. Therefore, the more accurate results will be considered as those which consider all of the environmental conditions. Studies regarding the rain effects on landsl are one of the most challenging fields in geotechnical engineering. It is observed that an increase in the water table will also increase water pore pressure, which pushes the soil particles away from each other, and hence reduces the stress between the particles resulting in soil slope failure. Two such papers [34; 35] may be used as a guide to finding the adequate literature on the most used or the most advanced approaches followed in every step of the procedure for defining reliable rainfall thresholds. Figure 7 presents the factor of safety values achieved in the case of Material 1 for slope angle ranges from 70 to 88 degrees, respectively.  
It is clear from Figure 7 that with increasing \(\beta\), FS will decrease at a constant rate. The FS values for Material 1 in the case of a saturated seismic condition are 0.624, 0.608, 0.598, 0.583, 0.573, 0.559, 0.552, 0.534, 0.519 and 0.510, respectively. A similar analysis was conducted for all material types, and the summary is provided in Tables 2 and 3 along with FS values.  
Figure 7: Factor of safety values in the case of Material 1—saturated seismic case.  
Figure 8a presents the shear strength and shear stress graphs achieved in the case of Material 1 having \(\beta\) equals 70 and 88 degrees in a saturated condition. Figure 8b presents shear strength and shear stress graphs in the case of Material 1 with \(\beta\) equals 78 and 88 degrees, respectively.  
Figure 8a,b presents a clear indication of shear strength dependency upon shear stress. The value increases till the failure point is reached and then declines. With the variation of \(\beta\), shear stress changes and hence shear strength also changes at a constant rate. All these parameters are closely related.  
In all these correlations, the applicability value R\({}^{2}\) is not less than 99% in any case. This presents the equation's reliability and applicability as very high. From Table 5, the final correlation is calculated by computing the average value, which is:  
\[\tau\ (\text{kPa})=30.482-0.385\beta\ (\text{deg.})+0.617\sigma\ (\text{kPa}) \tag{9}\]  
and the average R\({}^{2}\) comes out to be 99.5%.  
Figure 8: (a). Shear strength and shear stress graphs in the case of Material 1 and 10 in a saturated case. (b). Shear strength and shear stress graphs in the case of Material 5 and 1 in an unsaturated case.