## 3 Results and Discussion
### Parameter Screening with Plackett-Burman (PBD) and RSM Modeling
#### 3.1.1 Water Level Stability Factor Responses  
A higher stability factor means that the railway slope will perform better. The significance of the hydromechanical properties was evaluated for their principal effects on the overall static stability of the railway embankment slope during both rising and decreasingwater phases. The BBD-RSM analysis verified the Plackett-Burman sensitivity analysis results and ordered the primary effects of the parameters as follows: for dropping water levels, \(\phi>c>H>\rho_{s}\), and for rising water levels, \(\phi>\rho_{s}>c\).  
In this study, the models were chosen based on the highest-order polynomial, in which extra terms are significant and are not aliased. For this investigation, the dropping water level was studied using the same procedure (assuming an instantaneous pore water pressure change). High R-squared values, approaching unity, indicate that the quadratic and two-factor interaction (2 FI) equations for rising and falling water level models, respectively, have been appropriately calibrated to the actual data. The rising water level stability factor response demonstrated a significantly high F-value of 6173.65 and a \(p\)-value < 0.0001. The model's \(p\)-value was <0.05, indicating that an F-value of this magnitude has a 0.01% probability of occurring owing to noise.  
The results show that the model is competent for exploring the experimental space to determine the ideal conditions for railway slope design for rising water levels. The study shows that the SFRES was influenced in the following ascending order: internal friction angle (B) with an F-value of 3.52 \(\times\) 10\({}^{5}\), unit weight (C) with a 1.46 \(\times\) 10\({}^{5}\) F-value, cohesion (A) with a 9.6 \(\times\) 10\({}^{3}\) F-value, AC with an 84 \(\times\) 10\({}^{2}\) F-value, C2 with a 5.1 \(\times\) 10\({}^{2}\) F-value, and BC with an 8.1 \(\times\) 10\({}^{1}\) F-value, while AB, A2, and B2 are not significant to the stability factor of the railway embankment slope (Equation (8)).  
\[\begin{array}{ll}SRF_{1}=2.141+&0.0549A+0.1049B-0.0675C\\ &-0.0073 AC-0.00225 BC\\ &+0.0002A^{2}+0.0003B^{2}\\ &+0.0055C\end{array} \tag{8}\]  
The LF \(p\)-value was zero, indicating that the model LF is not significant, and the difference between the adjusted and predicted coefficient of determination (\(R^{2}\)) < 0.2 indicate reasonable agreement. This implies that the model is suitable for exploring the experimental parameters to find the best conditions for designing the railway slope for a falling water level. It is evident that the stability factor of the railway embankment slope was influenced in the following ascending order: internal friction angle (C) with an F-value of 2.1 \(\times\) 10\({}^{4}\), cohesion (B) with a 1.1 \(\times\) 10\({}^{3}\) F-value, water level (A) with a 4.3 \(\times\) 10\({}^{2}\) F-value, unit weight (D) with a 2.0 \(\times\) 10\({}^{2}\) F-value, BD with a 4.3 F-value, AB with a 3.5 F-value, and BC with 1.7 F-value, while AC, BC, AD, and CD are not significant to the stability factor of the railway embankment slope. The Equation (9) represents the regression model developed to predict the stability factor of the railway embankment slope during falling water levels.  
\[\begin{array}{ll}SRF_{fall}=1.9605&-0.0368A+0.0608B\\ &+0.0804C-0.0241D\\ &-0.0058 AB+0.0011 AC\\ &+0.0031 AD+0.0036 BC\\ &-0.0057 BD+0.0033 CD\end{array} \tag{9}\]