## 2 Materials and Methods
### Drawdown Analysis  
Dam geometry, soil permeability, drawdown rate, and drawdown ratio are important factors in the occurrence of the rapid drawdown condition [37]. To investigate the effect of rapid drawdown on the earth dam's stability, each of these factors is taken into account. The drawdown ratio (L/H) is represented based on L as the final drop in the external water level (or drawdown water level, DWL) below the initial position of the normal water level (NWL) and H is the height of the NWL (see Figure 1) [14]. The concept of drawdown rate is the ratio of water level (groundwater head) changes over time and it is nominated as R [16] and is presented in Figure 1. The model is implemented based on \"transient\" time, so that the time is considered in all steps of the modeling. In modeling, regarding the dam's height, the discharge rate and the discharge volume are taken into account; time is implicitly observed. The discharge rate is considered as R, which is in meters per day. This discharge is calculated for different rates of R. Therefore, time is included in this variable. For example, for R = 1 the time is 56 days (by definition). So, for R = 0.4, the discharge time is 140 days. Therefore, it can be concluded that the minimum discharge time for the dam is 65 days (R = 1), which is also the longest time for the discharge rate (R = 0.01). In the drawdown analysis for the Alavian dam model, with five different drawdown rates, R = {0.01, 0.1, 0.2, 0.4, 1} metres per day, and various drawdown ratios L/H = {0.1, 0.2,..., 1}, with 3 distinct hydraulic permeabilities of core material k = \(10^{-10}\), \(10^{-9}\), \(10^{-8}\) m/s, being considered. Although it is possible to consider the anisotropy in hydraulic conductivity in this study for the seepage and consolidation analysis, the soil medium was assumed to be isotropic.  
Figure 3: A simple view of the comprehensive modeling for rapid drawdown conditions.  
Referring to [PERSON] et al. [38], soil compressibility and hydraulic conductivity control how quickly saturated soil can deform and respond to changes in pore pressure caused by changes in boundary conditions. Inaccurate modeling of compressibility will lead to an inaccurate prediction of the variations in pore pressure with time, and inaccurate evaluations of stability. In this paper, wherever hydraulic conductivity was discussed, it was associated with compressibility. The water content function or van Genuchten parameters for core materials are specified by the van Genuchten model. The van Genuchten model parameters (\(\alpha\), n, and m) were assumed based on values for a CL-CH with similar unit weight and Arterberg limits [38; 39], whereas the m\({}_{\rm v}\) coefficient is obtained from [PERSON] and Bentley [40]. As reported by [PERSON] et al. [38], it should be noted that both soil compressibility and hydraulic conductivity control how quickly saturated soil can deform and respond to changes in pore pressure caused by changes in boundary conditions. Inaccurate modeling of compressibility will lead to an inaccurate prediction of the variations in pore pressure with time and inaccurate evaluations of stability. The water content function for the core materials was specified by the van Genuchten model (\(\alpha\) = 28.57 kPa, n = 1.213, m = 0.176). The parameter m is set equal to 1 \(-\) n\({}^{-1}\). Moreover, the hydraulic conductivity function of the core materials was modified and shifted appropriately for the three values of k\({}_{\rm core}\) = 10\({}^{-8}\); 10\({}^{-9}\); 10\({}^{-10}\); m/s and k\({}_{\rm shell}\) = 2.75 \(\times\) 10\({}^{-4}\) m/s was used, where the main factor in hydraulic conductivity is focused on the dam's core. Also, the water content function for the shell materials is specified by the grain-sized analysis method according to d\({}_{10}\), d\({}_{60}\), and volumetric water content.