## 5 Conclusions  
In this study, the finite element limit analysis was used to study the stability of embankment slopes subject to the slow water drawdown, considering the spatial variability of geomaterials. We assumed that the pore water pressure in the soil body has been dissipated during the slow drawdown. Hence, five different WLs were set to represent that the water level continues to drop.  
Figure 14: Typical realizations of the random field of cohesion (\(\mu_{c}=15\)kPa, \(\sigma_{c}=5\)kPa) for different \(l_{x}\) ((a) \(l_{x}=1\) m, (b) \(l_{x}=30\) m, (c) \(l_{x}=40\) m, (d) \(l_{x}=50\) m, (e) \(l_{x}=500\) m).  
Figure 15: FOS vs. \(l_{x}\) for different COVs (WL = 5 m) ((a) The Mean of FOS for five different COVs; (b) The Std. of FOS for five different COVs).  
The spatial variability of geomaterials is described by a random field model, which is determined by the mean, standard deviation and spatial correlation length of the shear strength cohesion and internal friction angle. Both the cohesion and internal friction angle are assumed to follow a log-normal distribution. The range of the COV is set from 0.1 to 0.5. The vertical correlation length is fixed at 1 m, and five different horizontal correlation lengths are set, namely 1 m, 30 m, 40 m, 50 m, and 500 m. All the mean values of FOS obtained from 1000 Monte Carlo simulations for different working conditions are lower than the corresponding deterministic analysis. The FOS increases with the decrease in the WL and decreases with the increase in COV. This is consistent with the actual situation that the shear failure surface is more likely to occur at the position where the soil strength is weaker. Although the mean value of FOS was greater than 1 for this test embankment, the probability of failure is still high, e.g., the probability of failure is 23.3% in Figure 11e.  
The study shows that the probability of potential risk is high because the FOS obtained from the deterministic analysis is higher than the random field analysis result. Hence, it is more reasonable to evaluate the stability of an embankment slope using the probability framework rather than the deterministic analysis. Further work will focus on the influence of rapid water drawdown on slope stability as well as the random field action.  
Conceptualization, Q.Z.; Data curation, X.X.; Formal analysis, X.W.; Funding acquisition, Q.Z.; Methodology, X.X. and X.Z.; Software, X.Z.; Writing--original draft, X.W.; Writing--review & editing, X.G. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (No. 12002118); the Fundamental Research Funds for the Central Universities (No. 2019B65814); the Research and Innovation Project for College Graduate of Jiangsu Province (No. SJKY19_0422); the National Key Research & Development Program of China (No. 2017 YFC1502603).  
This study does not require ethical approval.  
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.  
The data presented in this study are available on request from the first author.  
The author [PERSON] also gratefully acknowledges the support from China Scholarship Council (No. 202006710049) and UK-Jiangsu 20+20 World Class University Consortium.  
The authors declare no conflict of interest.