## 3 Results and Discussion
### Simulations vs. Experiments for Single Shovels
#### 3.1.1 Simulations of the Interactions between Soil and a Single DZ  
The ANOVA (analysis of variance) of the simulated draught force of DZ is listed in Table 5, and the corresponding response surfaces are shown in Figure 9. The regression equation related to the response surfaces is obtained and expressed as Equation (8),  
\[ \begin{array}{l}F_{D}=3.85-2.13v-12.27D-120.09\gamma+8.40 vD+\\ 0.05v\gamma+0.42D\gamma-0.07v^{2}+23D^{2}-6.12\gamma^{2}\times 10^{-4}\end{array}  \tag{8}\]  
Figure 8: Testing system used in field draught force tests (**a**): (1) laptop, (2) signal receiver, (3) signal acquisition and transmission device, (4) upper pull rod sensor and (5) lower suspension pin sensor. Sampling area partition for field draught force experiments (**b**): L\({}_{1}\), L\({}_{2}\) and L\({}_{3}\) represent the experimental travelling distance, S\({}_{1}\) represents the preparation area, S\({}_{2}\) represents the sampling area and S\({}_{3}\) represents the finishing area. This regression equation is highly significant at \(p<0.0001\), and the value of its R\({}^{2}\) is 0.9942. The statistical analysis for DZ demonstrates the keen sensitivity of \(F_{D}\) to all factors (i.e., cutting speed \(v\), digging depth \(D\) and mounting angle \(\gamma\) (see Figure 3a)), which can also be supported by Figure 9a-c in which the increases in these three factors all result in the increase in the draught force. The need to accelerate more soil mass and overcome increased friction is the major reason for increasing the draught force caused by the increase in cutting speed and digging depth [41]. The higher the \(\gamma\), the larger the projected area facing soil mass, and thus, the draught force increases, which was reported by [PERSON] [36], [PERSON] et al. [42] and [PERSON] et al. [43]. Moreover, Figure 9 shows that the response surfaces evolve sharply along the change both in \(D\) and \(v\), but it turns tame along the change in \(\gamma\), which can also be concluded based on their F values in Table 5, and thus the contributions of the factors to the draught force follow the order \(D>v>\gamma\). Additionally, \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Factors**} & \multicolumn{6}{c}{**Simulated Values**} \\ \cline{2-9}
**Run No.** & \(v\) & \(D\) & \(\gamma\) & \multicolumn{2}{c}{\(F_{D}\) **(kN)**} & \multicolumn{2}{c}{**DR**} & \multicolumn{2}{c}{\(f\)} \\ \cline{4-9}  & \(v\) & \(D\) & \(\gamma\) & \multicolumn{2}{c}{**DZ**} & **YS** & **(\%)** & **YS** & **DZ** \\ \hline  
\hline \hline \end{tabular} Notes: The \(F_{D}\) refers to the draught force, and the \(f\) refers to the soil rupture distance ratio. The DR refers to the reduction rate of the draught force of YS compared with that of DZ and it is calculated as DR (%) = (the draught force of DZ- the draught force of YS)/(the draught force of DZ) \(\times\) 100%.  
\end{table} 
Table 4: Experimental scheme and the simulated results for single shovels. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Sum of** & **DF** & **Mean** & **F Value** & \(p\)**Value** & **Significance** \\ \hline Model & 5.72 & 9 & 0.64 & 133.12 & \textless{}0.0001 & **\\ \(v\) & 0.83 & 1 & 0.83 & 172.90 & \textless{}0.0001 & **\\ \(D\) & 4.25 & 1 & 4.25 & 889.76 & \textless{}0.0001 & **\\ \(\gamma\) & 0.22 & 1 & 0.22 & 47.01 & 0.0002 & **\\ \(vD\) & 0.18 & 1 & 0.18 & 36.94 & 0.0005 & **\\ \(v\gamma\) & 0.14 & 1 & 0.14 & 29.45 & 0.0010 & **\\ \(D_{\gamma}\) & 0.087 & 1 & 0.087 & 18.23 & 0.0037 & **\\ \(\gamma^{2}\) & 0.0013 & 1 & 0.0013 & 0.27 & 0.6193 & \\ \(D^{2}\) & 0.014 & 1 & 0.014 & 2.92 & 0.1315 & \\ \(\gamma^{2}\) & 0.0038 & 1 & 0.0038 & 0.79 & 0.4026 & \\ \hline Residual & 0.033 & 7 & 0.0048 & & & \\ Lack of fit & 0.033 & 3 & 0.011 & & & \\ Pure error & 0 & 4 & 0 & & \\ \hline Cor total & 5.7542 & 16 & & & & \\ \hline \hline \end{tabular} Notes: ** means highly significant (\(p<0.01\)).**  
\end{table} 
Table 5: ANOVA of the simulated draught force of DZ.