## 4 Simulation Verification
### Analysis of BBD Response Surface Method Results
The correlation between the compressive strength of the ore bonding model and the normal stiffness per unit area (\(x_{1}\)), the shear stiffness per unit area (\(x_{2}\)), the critical normal stress (\(x_{3}\)), and the critical shear stress (\(x_{4}\)) during uniaxial compression tests was also investigated. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Serial**} & \multicolumn{3}{c}{**Factor**} & \multicolumn{2}{c}{**Compressive**} \\ \cline{2-6}  & \(x_{1}\)/(N/m\({}^{3}\)) & \(x_{2}\)/(N/m\({}^{3}\)) & \(x_{3}\)/Pa & \(x_{4}\)/Pa & \(F_{n}\)/MPa \\ \hline
1 & \(5\times 10^{1  
Figure 4: Compare the actual value with the predicted value. Figure 5: The change tendency of predicted value and residual. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Source** & \
\begin{tabular}{c} **Sum of** \\ **Squares** \\ \end{tabular} & **df** &
\begin{tabular}{c} **Mean** \\ **Square** \\ \end{tabular} & **F-Value** & _p-Value_ & **Significance** \\ \hline Model & 14,575.81 & 14 & 1041.13 & 69.82 & \(<\)0.0001 & Significant \\ \(x_{1}\) & 13,044.25 & 1 & 13,044.25 & 874.72 & \(<\)0.0001 & Significant \\ \(x_{2}\) & 742.46 & 1 & 742.46 & 49.79 & \(<\)0.0001 & Significant \\ \(x_{3}\) & 107.94 & 1 & 107.94 & 7.24 & 0.0197 & Significant \\ \(x_{4}\) & 6.02 & 1 & 6.02 & 0.4037 & 0.5371 & \\ \hline \(x_{1}x_{2}\) & 214.77 & 1 & 214.77 & 14.40 & 0.0026 & Significant \\ \(x_{1}x_{3}\) & 2.22 & 1 & 2.22 & 0.1489 & 0.7064 & \\ \(x_{1}x_{4}\) & 0.8190 & 1 & 0.8190 & 0.0549 & 0.8187 & \\ \(x_{2}x_{3}\) & 13.00 & 1 & 13.00 & 0.8715 & 0.3689 & \\ \(x_{2}x_{4}\) & 279.06 & 1 & 279.06 & 18.71 & 0.0010 & Significant \\ \(x_{3}x_{4}\) & 61.00 & 1 & 61.00 & 4.09 & 0.0660 & \\ \(x_{1}^{2}\) & 24.01 & 1 & 24.01 & 1.61 & 0.2286 & \\ \(x_{2}^{2}\) & 24.64 & 1 & 24.64 & 1.65 & 0.2229 & \\ \(x_{3}^{2}\) & 2.67 & 1 & 2.67 & 0.1792 & 0.6795 & \\ \(x_{4}^{2}\) & 25.50 & 1 & 25.50 & 1.71 & 0.2155 & \\ \hline Residual & 178.95 & 12 & 14.91 & & & \\ Lack of Fit & 129.36 & 10 & 12.94 & 0.5217 & 0.8026 & Not Significant \\ Pure error & 49.59 & 2 & 24.80 & & & \\ Cor total & 14,754.76 & 26 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Analysis of variance of BBD response surface test. The results of the analysis of variance (ANOVA) indicate that the \(p\)-values associated with \(x_{1}\), \(x_{2}\), \(x_{3}\), \(x_{1}x_{2}\), and \(x_{2}x_{4}\) are less than 0.01, which suggests that the observed variation in these parameters has a notable impact on the model. A regression equation was employed to plot the response surface of the interaction of the factors on the compressive strength of the ore. The response surface diagram of the interaction of various factors on the compressive strength of ore is shown in Figure 6. Figure 6 illustrates the exploration of the degree of influence and trend of change of the bonding parameters, including normal stiffness per unit area, shear stiffness per unit area, critical normal stress, critical shear stress, and others, by modifying the values of the remaining two parameters while maintaining two fixed parameters to investigate their impact on compressive strength. The response surfaces of normal stiffness per unit area and shear stiffness per unit area for a fixed critical normal stress and critical shear stress are illustrated in Figure 6a. When the unit area shear stiffness is constant, with the increase in the unit area normal stiffness, the compressive strength shows a significant increase, and the increase is huge. The trend is very obvious; when the unit area's normal stiffness is maintained at a constant level, the compressive strength increases in proportion to the increase in the unit area shear stiffness. However, in the case of higher unit area normal stiffness, the increase in the unit area shear stiffness does not significantly affect the compressive strength. The response surfaces of unit-area normal stiffness and critical normal stress with fixed unit-area shear stiffness and critical shear stress are depicted in Figure 6b.