## 4 Simulation Verification
### Analysis of BBD Response Surface Method Results  
Once the compression test simulation model had been constructed, the uniaxial compression simulation test was initiated. The velocity of the indenter was set to 0.005 m/s in the downward direction, resulting in an overall time step of \(1.26\times 10^{-7}\) s for the simulation model. Based on the determined parameter values of the basic contact model and the Box-Behnken Design, uniaxial compression simulation tests of ore particles were conducted for four adhesion parameters: normal stiffness per unit area (\(x_{1}\)), shear stiffness per unit area (\(x_{2}\)), critical normal stress (\(x_{3}\)), and critical shear stress (\(x_{4}\)). Three sets of identical tests are \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Encoding**} & \multicolumn{4}{c}{**Factor**} \\ \cline{2-5}  & \(x_{1}\)**/(N/m3)** & \(x_{2}\)**/(N/m3)** & \(x_{3}\)**/Pa** & \(x_{4}\)**/Pa** \\ \hline \(-1\) & \(2.5\times 10^{11}\) & \(1\times 10^{10}\) & \(1.5\times 10^{9}\) & \(1.5\times 10^{8}\) \\ \(0\) & \(5\times 10^{11}\) & \(3\times 10^{10}\) & \(4.5\times 10^{9}\) & \(4.5\times 10^{8}\) \\ \(1\) & \(7.5\times 10^{11}\) & \(5\times 10^{10}\) & \(7.5\times 10^{9}\) & \(7.5\times 10^{8}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experiment factors codes. Figure 3: The process by which the pressure on the bond changes during compression. \begin{table}
\begin{tabular}{l c} \hline \hline
**Argument** & **Numerical Value** \\ \hline Poisson’s ratio of ore & 0.3 \\ Density of Ore (kg/m3) & 6071 \\ Shear modulus of ore (Pa) & \(2.46\times 10^{10}\) \\ Poisson’s ratio of steel & 0.3 \\ Density of steel & 7850 \\ Shear modulus of steel (Pa) & \(7.92\times 10^{10}\) \\ Particle-steel collision recovery coefficient & 0.0025 \\ Particle-steel static friction coefficient & 0.007 \\ Particle-steel rolling friction coefficient & 0.001 \\ Particle-to-particle collision recovery coefficient & 0.2 \\ Coefficient of static friction between particles & 0.5 \\ Coefficient of rolling friction between particles & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Discrete element simulation parameters. set up in the horizontal direction at the center of the response surface, resulting in a total of 27 sets of simulation tests. In order to simulate the accuracy and reliability of the test results, each group of tests must be repeated more than three times, with the average of the results of multiple simulation tests taken as the final test results. The response surface test design and simulation test results are shown in Table 5.  
The fitting analysis, based on the results of the response surface test, demonstrated that the coefficient of determination of the model reached 0.9879 when the quadratic full model was employed for fitting. The results of the ANOVA are presented in Table 6. Furthermore, Figure 4 illustrates a high degree of agreement between the experimental values and the model predictions. Figure 5 displays a random distribution of values with no evident pattern, indicating that there is no correlation between the standardized residuals and the predicted values. This validates the quadratic response-regression equation. A review of the data in Table 6 indicates that the \(p\)-value observed during the secondary full simulation is below the significance level of 0.01, which provides compelling evidence that the experimental variables exert a significant influence on the model. Furthermore, the \(p\)-value of the misfit term exceeded 0.05, indicating that the misfit term was not significant. This confirmed that the constructed quadratic regression equation was in good agreement with the actual and adequately and accurately described the correlation between the variables.