3.1.3. Box–Behnken Test

Based on the parameter selection from the PB test and the level selection from the steepest climbing test, a Box–Behnken test design (BBD) was carried out, and the results are shown in Table 5. The regression model describing the relationship between the stacking angle and selected parameters can be described as:

Stacking angle = 53.57 + 2.18B − 1.71D − 0.4179E + 6.81J + 1.25BD + 0.5006BE − 2.76BJ + 1.15DE− 1.01DJ <sup>+</sup> 1.53EJ <sup>+</sup> 0.0268B<sup>2</sup> <sup>−</sup> 0.6149D2 <sup>+</sup> 2.86E2 <sup>−</sup> 3.41J2 (1)




**Table 5.** *Cont.*

The ANOVA results of the quadratic model for BBD are listed in Table 6. The regression model's *p*-value = 0.0001 demonstrated a significant relationship between the responses and parameters. Consistent with the results of the PB test, B, D and J significantly affected the stacking angle. Moreover, the quadratic terms E2 and J<sup>2</sup> had significant influence on stacking angle. The lack of fit was insignificant, and the correlation coefficient (*R*<sup>2</sup> = 0.8962) of the model was high, which demonstrated that the regression model fit well.

**Table 6.** ANOVA of the quadratic model for BBD.


Note: \* and \*\* represent the significance at the 0.05 and 0.01 probability level, respectively.

By considering the measured stacking angle (51.15◦) as the target value and solving the regression model by using the optimization function of the software Design Expert, the optimal values of the four parameters were obtained as B = 2.43 MPa, D = 0.77, E = 0.41, and J = 0.34 J·m<sup>−</sup>2. The obtained optimal parameters were employed to perform the DEM validation test. The simulated stacking angle was 50.89◦, and its relative error with the measured stacking angle was 0.51% (Figure 4), indicating that the DEM models calibrated in this work were found to have good accuracy.

**Figure 4.** Comparison of the shape of peat pile between the (**a**) simulation test and (**b**) physical test.
