## 3 Results and Discussion  
### 3.1. Threate-Line Status under Rapid Drawdown  
The occurrence of a phreatic line within an earth-fill dam's core is mostly dependent on hydraulic permeability associated with material compressibility and drawdown rate. Low permeable soil has no chance for drainage under rapid drawdown conditions, which consequently affects the phreatic line within the low permeable core, which remains near its initial condition. As an example, the final phreatic line for cores with different hydraulic conductivities at the same drawdown rate (e.g., R = 1 cm/day) and L/H = 1 is conformable to the phreatic line within the shell material with high permeability (10\({}^{-8}\) m/s) at any moment of drawdown. Hence, it can be concluded that the pore-water pressure can rapidly dissipate because the shell materials are relatively permeable. On the other hand, even at a drawdown rate of R = 1 cm/day, it has led to a rapid drawdown. So, by increasing the permeability of the core's material, despite still preventing seepage, the instability risk of the upstream slope as a result of the rapid drawdown effect intensifies.  
For a better understanding of the problem, the phreatic-line variations under rapid drawdown are defined as h/H, where h is defined as a phreatic-line variation in the core materials compared to steady-state, and h is defined as a phreatic-line variation in the reservoir. Figures 4 and 5 present the h/H variations with respect to drawdown rate and permeability coefficient at the end of drawdown, respectively. Figure 4 presents the discharge rate (R) impact on the reliability by considering the various permeabilities for the critical failure conditions obtained using the Morgenstern-Price method (LEM). On the other hand, in Figure 5, the h/H is obtained based on various permeabilities with respect to the different R (0.1, 0.2, 0.4, and 1 m/day). From these figures, it can be concluded that the only case that is close to slow drawdown (h/H = 1) is based on drawdown with k\({}_{\rm core}\) = 10\({}^{-8}\) m/s and R = 1 cm/day. On the contrary, as shown in the figures, this rate, in the case of k\({}_{\rm core}\) = 10\({}^{-10}\) m/s, is considered a full rapid drawdown. Figure 4 indicates that a low permeable core (k\({}_{\rm core}\) = 10\({}^{-9}\); k\({}_{\rm core}\) = 10\({}^{-10}\) m/s) is more sensitive to an increase in drawdown rate than a relatively permeable core (k\({}_{\rm core}\) = 10\({}^{-8}\) m/s). Also, in the low permeable core, as the drawdown rate exceeds 20 cm/day, the curve becomes almost horizontal, which means that a low permeable core with a drawdown rate of R = 20 cm/day will not have the opportunity to drain; however, in a relatively permeable case (k\({}_{\rm core}\) = 10\({}^{-8}\) m/s), even at a drawdown rate of R = 1 m/day, the core materials are able to drain. According to Figure 5, at constant permeability, the phreatic-line drop rate within the core is reduced as the drawdown rate increases. Moreover, at a constant drawdown rate, the curve sharply declines when permeability decreases, and the most substantial part of this decline occurs between k\({}_{\text{core}}\) = 10\({}^{-8}\) and 10\({}^{-10}\), which shows that at a constant drawdown rate, the permeability coefficients between these coefficients are critical under rapid drawdown.  
Figure 4: Dependency of a drawdown on the discharge rate with different permeability coefficients.  
Figure 5: The Dependency of a drawdown on the permeability coefficient with different discharge rates.