## 2 Numerical Simulation of CSG Dam upon Overburden
### Grey Relational Grade Analysis  
To more clearly demonstrate the influence of the geometric parameters of the dam body and the characteristics of the overburden material on the maximum settlement and maximum compressive stress of the CSG dam, and to consider the amount of data required for neural network training in the following text, a numerical simulation experiment with six factors and three levels (a total of \(3^{6}\) = 729 groups) was conducted. In order to maximize the calculation efficiency, a nonrepetitive permutation combination method is adopted for the combination of parameters, using MATLAB software to call ANSYS for multistep loading, and implementing secondary development of finite element post-processing and batch data processing in MATLAB. Based on the previous analysis, it can be seen that the  
Figure 8: Factors affecting maximum settlement. (**a**) Factors of geometric dimensions; (**b**) factors of performance of overburden. Figure 9: Factors affecting maximum compressive stress. (**a**) Factors of geometric dimensions; (**b**) factors of performance of overburden. maximum settlement and maximum compressive stress of the dam are affected by the upstream and downstream slope coefficients of the first and second stages of the dam body, as well as the elastic modulus and Poisson's ratio of the overburden. Grey relational grade is introduced to analyze and obtain the correlation level of each influencing factor. This method uses correlation to show the relationship between various factors. If the changing trends between the two factors are similar, it indicates that the correlation between the two is relatively high, otherwise the correlation is small [26]. The formula for grey correlation analysis using MATLAB software for maximum settlement of the dam is as follows:  
\[\Delta=\left|X_{i}-Y_{i}(j)\right| \tag{5}\]  
\[B_{ij}=\frac{\Delta_{\min}+\rho\Delta_{\max}}{\Delta_{ij}+\rho\Delta_{\max}} \tag{6}\]  
\[R_{j}=\frac{1}{k}\sum_{i=1}^{k}B_{ij} \tag{7}\]  
where \(\Delta\) is the difference coefficient matrix; \(X_{i}\) is column matrix, representing the sequence of maximum settlements here; \(Y_{i}(j)\) is \(i\)-th element of the \(j\)-th influencing factor; \(B_{ij}\) is the correlation coefficient matrix; \(\Delta_{\min}\) is the minimum value in the \(\Delta\); \(\Delta_{\max}\) is the maximum value in the \(\Delta\), \(\Delta_{ij}\) is the element in the \(i\)-th row and \(j\)-th column of the \(\Delta\); \(\rho\) is the resolution coefficient, with a value range of 0-1, 0.5 is taken [27]. \[X_{i}= \begin{bmatrix}0.2717\\ 0.3209\\ 0.3702\\ 0.2916\\ \ldots\\ 0.0083\end{bmatrix} \]  
\[Y_{i}(j)= \begin{bmatrix}0.2717&\cdots&0.2283\\ 0.1791&\cdots&0.1791\\ 0.6298&\cdots&0.1298\\ 0.2084&\cdots&0.2084\\ \vdots&\ddots&\vdots\\ 0.4917&\cdots&0.9917\end{bmatrix} \]  
\[B_{ij}= \begin{bmatrix}0.7158&\cdots&0.7584\\ 0.8134&\cdots&0.8134\\ 0.4889&\cdots&0.8771\\ 0.7798&\cdots&0.7798\\ \vdots&\ddots&\vdots\\ 0.5570&\cdots&0.3703\end{bmatrix} \]  
\[R_{j}= \begin{bmatrix}0.7367&0.7345&0.7329&0.7332&0.7415&0.7189\end{bmatrix} \]  
\(Y_{i}(j)\) is obtained by normalizing all input variables, resulting in a matrix with 729 rows and 6 columns. Each element normalized in \(X_{i}\) corresponds to the maximum settlement of the dam body of each input variables (i.e., variables normalized for each row in \(Y_{i}(j)\)) in sequence. In \(Y_{i}(j)\), each column from left to right corresponds to \(m_{1}\), \(m_{2}\), \(m_{3}\), \(m_{4}\), \(E_{ob}\), and \(\mu_{ob}\), respectively. After conducting a grey relation analysis between the influencing factors and the maximum settlement of the dam according to Equation (6), correlation coefficient matrix \(B_{ij}\) is calculated. By summing up the elements in each column and taking the average value, the relation degree between the corresponding influencing factors and the maximum settlement values of the dam body is obtained. Finally, it is obtained that the grey correlation matrix is R = [0.7367 0.7345 0.7329 0.7332 0.7415 0.7189].