## 4 Conclusions  
This study investigated the effects of the different variables of rapid drawdown and various drawdown rates on stability status in earth-fill dams to provide comprehensive stability charts based on different seepage, drawdown rates, and permeability conditions. To this end, three permeabilities were used to estimate the safety terms regarding the various drawdown rates (R = 0.1, 0.2, 0.4, and 1 m/day). The calculation was performed based on the coupled stability analyses with FEM/LEM methods implemented in SEEP/W, SLOPE/W, and PLAXIS commercial software. The results were applied to draw the stability  
Figure 12: The comparative results of coupled FEM/LEM modeling with instrumentation: (**a**) upstream shell, (**b**) core.  
charts for both shallow and deep sliding surfaces. According to the results, the following can be stated:  
* Regarding the drawdown ratio estimated for both LEM and FEM methods, the results indicated that the FEM provided is more conservative than the LEM. Regarding this evaluation, the main variations in the F.S follows a close trend, but the LEM results indicated various harmonic safety factors, with different R and FEM models providing lower F.S.
* Referring to the LEM/FEM modeling results for various R-values, 0.2 to 0.6 is the most critical state for safety factors.
* By increasing the slip surface's depth and decreasing the hydraulic hydration, the reliability decreases, and sliding surfaces' sensitivity increases based on the drawdown rates.
* Looking at the stability charts, it can be mentioned the drawdown rate from 0.2 to 0.6 is the most critical state for safety factors that are showing significant declines.
* The LEM/FEM stability charts estimated for the drawdown ratio in shallow sliding indicated that the high rate of 0.4-0.6 for the drawdown ratio is shown with a reduction in F.S. This rate for deep sliding is 0.6-0.8.
* Referring to the comparison of the modeling results with instrumentation, it can be stated that the measured and estimated rates for water pressure follow a close trend for the dam which is from 1560 to 1550 m.
* The results were verified by conducting a comparative analysis and justification with ground information obtained using extensive instrumentation of the Alavian earth-fill dam, which is considered a case study. Based on justifications, the applied models provide reliable results to estimate the rapid drawdown simulations and critical state stability analysis.  
A.A. and A.E.I.: writing--original draft preparation, methodology, conceptualization, investigations, resources; M.A.: validation, visualization, formal analysis, methodology; M.H.B.: conceptualization, methodology, validation, visualization, supervision, writing--review and editing; F.B.S.: validation, visualization, supervision, writing--review and editing; R.D.: supervision, writing--review and editing. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The study did not report any data.  
The authors wish to thank the Department of Civil Engineering, University of Tabriz for providing permission to conduct the geotechnical investigations. Also, the authors would like to thank the anonymous reviewers for providing invaluable review comments and recommendations for improving the scientific level of the article.  
The authors declare no conflict of interest.