## 2 Materials and Methods
### Coupled Model Preparation  
It is apparent and intuitively understood that the stability of a slope should be influenced by the stress-versus-strain characteristics of the soil. In conjunction with the stress-strain analysis approach, there are two other procedures. One is the consideration of stress level on the potential failure surface, and the other is the strength-reduction technique [9; 33]. In the first procedure, a finite element stress analysis combined with a limit equilibrium analysis is called the enhanced limit method (ELM) or coupled LEM/FEM method. The ELM provides greater certainty and flexibility regarding the internal distribution of stresses within the soil mass. The normal force along any selected slip surface can be calculated from the stress distribution that has been calculated using a linear or nonlinear stress analysis (Figure 2). The overall safety factor is defined in accordance with the finite element slope stability method described by [PERSON] [33] and expressed as the ratio of the sum of the increment resisting shear strength (S\({}_{\rm r}\)) to the sum of the mobilized shear forces (S\({}_{\rm n}\)) along the slip surface, as presented in Equation (1).  
\[\rm{F.S_{LEM/FEM}}=\frac{\sum S_{r}}{\sum S_{n}} \tag{1}\]  
One of the essential ingredients for a successful finite element analysis of a geotechnical problem is an appropriate soil constitutive model. There is not a single constitutive model currently available that can reproduce all aspects of real soil behavior. It is, therefore, important to recognize in the analysis what aspects of the problem are of major interest and to choose a model accordingly. It is apparent that the FEM analysis of stresses, deformations, and hydraulics in embankments is an exceedingly complex problem. So, it must consider both saturated and unsaturated conditions and perform a coupled analysis [36].  
Regarding the LEM/FEM modeling by using the GeoStudio package and PLAXIS software, it can be stated that the modeling is implemented in four steps that include geometrical modeling, boundary conditions, material specifications, and mechanical mod  
Figure 2: The stability analysis based on LEM/FEM [33].  
eling that leads to solving the stability analysis. The geometric model is based on the actual conditions of the dam. In the study dam, three main areas of the core, shell, and foundation are considered. The geometric dimensions of the model are determined based on the dimensions designed for the dam, and the closed and open boundary conditions are assigned to the dam, the same as in Table 1. The fine mesh is selected in a numerical model for a detailed analysis. Also, both triangular and rectangular grids are selected for the FEM model. The combination of the two in networking results in a regular, continuous, and coordinated network between borders. Material specifications are assigned based on field survey, sampling, and geotechnical characteristics (Table 2) to provide an accurate view of the dam in simulations. For the samples taken from the Alavian earth-fill dam site, various geotechnical tests based on ASTM instructions such as triaxial, permeability, geodemetry, direct-shear, etc. were conducted. These specifications are used in the model as the material characteristics for the core, shell, and foundation. After these preparations, the model was solved. The results of simulations were used in stability assessments of the dam. The rapid drawdown condition is implemented in each R and k value individually that is used for preparing the stability charts. Figure 3 provides an example of the modeling view of the rapid drawdown conditions.