# Stability Analysis of the Huasushu Slope Under the Coupling of Reservoir Level Decline and Rainfall
## 3 Numerical Analysis Model
### Numerical Model
#### 3.3.2 Three-Dimensional Numerical Model  
The simulation results of a two-dimensional model can provide the basis for a preliminary analysis. However, the actual damage mechanisms of a slope are more complex. Therefore, a three-dimensional model was established to more accurately reflect exact characteristics and damage mechanisms. Based on the geological conditions and topographic and geomorphological characteristics of the slope, the scope of the three-dimensional numerical simulation model was selected as follows: approximately 832 m along the direction of the Yangtze River flow and approximately 768 m perpendicular to the moving direction. The calculation domain included the landslide mass, sliding belt, and bedrock and was divided into 54,510 tetrahedral elements with 61,600 nodes (see Figure 5).  
Under the effects of water level changes and rainfall, the rock and soil body of a slope will undergo significant elastic-plastic deformation due to different degrees of unloading and loading processes, during which the rock body may be damaged by tension or compression shear. The yield criteria usually adopted in rock mechanics include the D-P criterion and the Mohr-Coulomb criterion [34; 35; 36], in which the yield surface of the D-P criterion is circular in the \(\pi\)-plane and conical in the principal stress space. There is no cusp problem, so it is better to deal with it; the yield surface of the Mohr-Coulomb criterion is an irregular, six-edge vertebral surface in the principal stress space, and it is an unequal angle hexagonal surface in the \(\pi\)-plane, so it is better to deal with it when considering the cusp. The hexagonal shape leads to some difficulties in dealing with the sharp corners. However, due to the continuous progress in numerical computation technology, the problem of sharp corners can be easily solved; thus, the composite criterion combining the Mohr-Coulomb criterion and the tensile damage criterion is used in the present calculation to determine the yield damage of the rock body under the loading effect of reservoir storage and rainfall conditions. The shape of the Mohr-Coulomb criterion in the principal stress space is shown in Figure 6, and the shape of the composite criterion in the (\(\sigma_{1}\), \(\sigma_{3}\)) plane is shown in  
Figure 4: Two-dimensional numerical slope model.  
Figure 5: Three-dimensional numerical slope model.  
\[f_{s}=\sigma_{1}-\sigma_{3}N_{\varphi}+2c\sqrt{N_{\varphi}} \tag{1}\]  
\(\varphi\)--angle of internal friction.  
\(c\)--cohesive force.  
\(N_{\varphi}=\frac{1+\sin(\varphi)}{1-\sin(\varphi)}\).  
In Figure 4, point B to point C is the pull-down criterion, \(f_{t}\) = 0, and \(f_{t}\) can be expressed by the following equation:  
\[f_{t}=\sigma_{3}-\sigma_{t} \tag{2}\]  
\(\sigma_{t}\)--tensile strength.  
The plastic potential function is represented by the shear plastic flow function, \(g_{s}\), and the tension plastic flow function, \(g_{t}\), where  
\[g_{s}=\sigma_{1}-\sigma_{3}N_{\psi} \tag{3}\]  
\(\psi\)--shear angle.  
\(N_{\psi}=\frac{1+\sin(\varphi)}{1-\sin(\varphi)}\)  
\[g_{t}=\sigma_{3} \tag{4}\]  
To more accurately simulate rainfall infiltration, the SEEP / W module in GeoStudio was utilized to simulate and analyze infiltration lines representing changes in groundwater levels. Using numerical simulation techniques, changes in pore water pressure within the slope were determined by analyzing infiltration lines [37]. Subsequently, the SLOPE/W module was used to integrate geotechnical parameters for limit equilibrium analysis.  
Figure 6: Mohr–Coulomb criterion in the principal stress space.  
Figure 7: Point A to point B is the Mohr–Coulomb yield criterion, \(f_{s}\) = 0, where \(f_{s}\) can be expressed as the equation below.