## 3 Case Study
### Stability Evaluation Based on Genetic Algorithm and Discrete Element Analysis  
(1) Rock Mass Constitutive Model and Parameter Range  
By conducting field-based plate-loading compression creep tests, the constitutive model and parameters of the left bank Shuiwan Rock mass slope were determined. The test applied a constant load to the surface of the rock mass using a flexible hydraulic cushion, measured the creep of the rock mass, and derived the creep equation based on the viscoelastic creep model. This creep equation was used to fit the experimental creep curve, invert the creep model, and optimize the model parameters. The field compression creep test curve indicates that the creep curve of this rock mass material is very similar to the typical creep curve of the generalized Kelvin model. As shown in Figure 3a, the original model of the generalized Kelvin creep model is presented, and Figure 3b illustrates the typical creep curve. The field test data were subjected to nonlinear fitting, and based on the fitting results, the parameters of the generalized Kelvin model were determined, as shown in Table 2 below. The parameter values for the generalized Kelvin model, derived from the fitting results, are presented in Table 3. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Test Point** & **Pressure** & \multicolumn{4}{c}{**Generalized Kelvin Model Parameters**} \\ \cline{3-5}
**No** & **(MPa)** & **E\({}_{\textbf{1}}\) (GPa)** & **E\({}_{\textbf{2}}\) (GPa)** & **H (GPa-h)** & **r\({}^{2}\)** \\ \hline C36-101 & 11.23 & 13 & 98 & 1380 & 95\% \\ C36-102 & 12.06 & 18 & 173 & 8951 & 96\% \\ C36-103 & 11.38 & 7 & 56 & 550 & 94.2\% \\ C36-201 & 11.38 & 15 & 79 & 5000 & 96.2\% \\ C36-202 & 12.06 & 10 & 94 & 3840 & 90\% \\ C36-203 & 12.14 & 8 & 49 & 6900 & 97.4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of fitted parameters for the generalized Kelvin model. Figure 3: Generalized Kelvin element model and typical creep curve. (**a**) Generalized Kelvin element model; (**b**) typical relationship between deformation and time for the generalized Kelvin constitutive model. 2 Development of the Numerical Model Using the Discrete Element Method  
The numerical computation model is illustrated in Figures 4-7. Based on the project background introduced in the case study, the Hydraulic Prestressed Anchoring Technical Standards (SL/T 212-2020) [44], issued by the Ministry of Water Resources of the People's Republic of China, are applicable to the design and construction of prestressed anchorage in hydraulic structures. These standards specify the  
Figure 4: Numerical computation model. Figure 5: Stratigraphic distribution in the numerical model. Figure 6: Distribution of unloading zones in the numerical model. 3. Optimization Using Genetic Algorithm  
The genetic algorithm (GA) was implemented to optimize the parameters of the numerical model. The key steps involved in the algorithm are described as follows:  
Encoding of Variables  
The model parameters to be optimized were encoded into chromosomes using real-number representation, which facilitates precision in continuous parameter optimization. Each chromosome corresponds to a potential solution in the parameter space. Initialization of Population  
An initial population comprising N chromosomes was randomly generated within the defined parameter bounds. This ensured a broad exploration of the search space at the beginning of the evolution process. Fitness Evaluation  
A fitness function was defined based on the discrepancy between the numerical simulation results and field monitoring data (e.g., displacement, stress distribution, or anchor force). The fitness of each individual was evaluated using the objective function. Its mathematical expression is given in Equation (1) below:  
\[f(x)=\sum_{i=1}^{n}\omega_{i}\Big{|}T_{i}^{measured}-T_{i}^{simulated}(x)\Big{|} \tag{1}\]