## 3 Results and Analysis
### Response Surface Experimental Design and Result Analysis  
To determine the optimal parameter combination of discrete element simulation for FTB, a Box-Behnken experiment was employed with the maximum shear force serving as the response variable. The detailed experimental design and corresponding results are shown in Table 7. Based on the results of the steepest ascent method, a regression equation was established with the maximum shear force (\(Y\)) as the response, as well as the significant influencing factors \(x_{2}\), \(x_{3}\), and \(x_{6}\) as the independent variables. \[ \begin{split} Y=-583.67-62.65\times 10^{8}x_{2}+9.08\times 10^{8}x_{3}+ 835.5x_{6}+14.45\times 10^{16}x_{2}x_{3}+54.14\times 10^{8}x_{2}x_{6}-13.28 \times 10^{8}x_{3}x_{6}-3.37\\ \times 10^{16}x_{2}{}^{2}+4.42\times 10^{16}x_{3}{}^{2}-289.26 \alpha_{6}{}^{2}\end{split}  \tag{8}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Serial** & & & & \\
**Numbers** & \(x_{2}\)**/(\(\times\)10\({}^{8}\) N\(\cdot\)m\({}^{-3}\))** & \(x_{3}\)**/(\(\times\)10\({}^{8}\) N\(\cdot\)m\({}^{-3}\))** & \(x_{6}\)**/mm** & **Shear Force/N** \\ \hline
1 & 0.3 & 0.3 & 1.3 & 14.3 \\
2 & 1.1 & 1.1 & 1.38 & 37 \\
3 & 1.9 & 1.9 & 1.46 & 75 \\
4 & 2.7 & 2.7 & 1.54 & 106.8 \\
5 & 3.5 & 3.5 & 1.62 & 132.5 \\
6 & 4.3 & 4.3 & 1.7 & 141.2 \\ \hline \hline \end{tabular} Note: \(x_{2}\) is the normal stiffness per unit area, \(x_{3}\) is the tangential stiffness per unit area, and \(x_{6}\) is the bonding radius.  
\end{table} 
Table 6: Schemes and results of the steepest ascent method. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Serial Numbers** & \(x_{2}\)**/**(\(\times\)10\({}^{8}\) N\(\cdot\)m\({}^{-3}\))** & \(x_{3}\)**/(\(\times\)10\({}^{8}\) N\(\cdot\)m\({}^{-3}\))** & \(x_{6}\)**/mm** & **Shear Force/N** \\ \hline
1 & 0.3 & 0.3 & 1.3 & 14.3 \\
2 & 1.1 & 1.1 & 1.38 & 37 \\
3 & 1.9 & 1.9 & 1.46 & 75 \\
4 & 2.7 & 2.7 & 1.54 & 106.8 \\
5 & 3.5 & 3.5 & 1.62 & 132.5 \\
6 & 4.3 & 4.3 & 1.7 & 141.2 \\ \hline \hline \end{tabular} Note: \(x_{2}\) is the normal stiffness per unit area, \(x_{3}\) is the tangential stiffness per unit area, and \(x_{6}\) is the bonding radius.  
\end{table} 
Table 7: Shear test, Box-Behnken experimental design, and results. Significance analysis of the Box-Behnken experimental data was conducted in the Design-Expert software, with the outcomes presented in Table 8. The model was found to be significant, while the non-significant lack-of-fit term indicates that no other unaccounted factors influenced the response variable. The coefficient of determination (R\({}^{2}\)) was 0.9750, and the adjusted coefficient of determination (R\({}_{\text{adj}}\)\({}^{2}\)) was 0.9428, with both values approaching 1. The difference between the adjusted (R\({}_{\text{pre}}\)\({}^{2}\)) and R\({}_{\text{adj}}\)\({}^{2}\) coefficients was less than 0.2, indicating that the model fits well and reliably reflects the relationship between the maximum shear force and factors \(x_{2}\), \(x_{3}\), and \(x_{6}\). The \(p\)-values for \(x_{2}\) and \(x_{3}\) were both less than 0.001, indicating their statistically significant effect on the maximum shear force. The \(p\)-values for \(x_{6}\) and the interaction term \(x_{2}x_{3}\) were both less than 0.01, suggesting a substantial influence. The remaining terms exhibited \(p\)-values above 0.05, indicating no statistically significant effect on the maximum shear force. The response surfaces of normal stiffness (\(x_{2}\)) per unit area, tangential stiffness (\(x_{3}\)) per unit area, and bonding radius (\(x_{6}\)) with respect to the maximum shear force are obtained based on the regression equation, as, respectively, presented in Figure 11a-c.