## 2 Discrete Element Parameter Model and Parameter Calibration of Soil-Soil Interaction
### Simulation Test  
#### 2.5.1 Plackett-Burman Design Test  
Not all parameters in the contact and contact model parameters have a significant impact on the heap angle. Parameters without a significant impact cannot be calibrated based on the heap angle, otherwise the calibrated parameters would be inaccurate. There \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Materials** & **Poisson’s Ratio** & **Shear Modulus/Pa** & **Density/(g\(\cdot\)cm\({}^{-3}\))** \\ \hline Soil & 0.35 & \(1.00\times 10^{6}\) & 1.57 \\ Steel plate & 0.30 & \(7.94\times 10^{10}\) & 7.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Basic parameters of soil and steel plate. fore, based on existing literature research and comprehensive analysis, the range of parameter values to be calibrated was determined. The Plackett-Burman Design module in Design Expert was utilized to select parameters with a significant impact from multiple parameters. Considering the parameters required for EDEM simulation and excluding those directly measurable, such as density, Poisson's ratio, and elastic modulus of soil particles, seven parameters were selected for calibration, as shown in Table 3: soil-particle-soil-particle restitution coefficient (A), soil-particle-soil-particle static friction coefficient (B), soil-particle-soil-particle rolling friction coefficient (C), soil-particle-steel restitution coefficient (D), soil-particle-steel static friction coefficient (E), soil-particle-steel rolling friction coefficient (F), and JKR surface energy (G). According to reference [9], the range of soil particle restitution coefficient is 0.35-0.8, the static friction coefficient is 0.36-0.6, the rolling friction coefficient is 0.2-0.7, the range of restitution coefficient between soil particles and steel is 0.2-0.5, the static friction coefficient is 0.5-0.8, the rolling friction coefficient is 0.05-0.4, and the range of soil JKR surface energy is 3.5-10.5 J\(\cdot\)m\({}^{-2}\). In this study, a Plackett-Burman design table with N = 12 was used, with the soil particle heap angle Y as the response value. Each parameter in Table 3 took one high level and one low level, and a total of 12 tests were conducted. The experimental items and results are shown in Table 4.  
The Design-Expert 13.0 software was used to conduct a significance analysis of the results, leading to the determination of the significance of each simulation parameter, as shown in Table 5. The JKR surface energy coefficient (G) of the soil had a \(p\)-value of less than 0.01, signifying an extremely significant impact on the simulated pile angle. The restitution coefficient among soil particles (A) and the static friction coefficient between soil and steel (E) had \(p\)-values lower than 0.05, indicating a significant influence on the simulated pile angle. For the remaining simulation parameters, with \(p\)-values greater than 0.05, their impact on the simulated pile angle was minimal. As indicated by the Pareto \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{5}{c}{**Test Parameter**} & \multicolumn{5}{c}{**Repose Angle**} \\  & **A** & **B** & **C** & **D** & **E** & **F** & **G** & \\ \hline
1 & 0.80 & 0.80 & 0.20 & 0.20 & 0.50 & 0.40 & 3.50 & 32.24 \\
2 & 0.35 & 0.36 & 0.20 & 0.50 & 0.50 & 0.40 & 10.50 & 41.82 \\
3 & 0.80 & 0.36 & 0.70 & 0.50 & 0.80 & 0.05 & 3.50 & 30.09 \\
4 & 0.35 & 0.36 & 0.70 & 0.20 & 0.80 & 0.40 & 3.50 & 32.66 \\
5 & 0.35 & 0.80 & 0.70 & 0.20 & 0.80 & 0.40 & 10.50 & 40.11 \\
6 & 0.35 & 0.36 & 0.20 & 0.20 & 0.50 & 0.05 & 3.50 & 34.38 \\
7 & 0.35 & 0.80 & 0.70 & 0.50 & 0.50 & 0.05 & 3.50 & 35.37 \\
8 & 0.35 & 0.80 & 0.20 & 0.50 & 0.80 & 0.05 & 10.50 & 40.68 \\
9 & 0.80 & 0.36 & 0.20 & 0.20 & 0.80 & 0.05 & 10.50 & 39.67 \\
10 & 0.80 & 0.80 & 0.20 & 0.50 & 0.80 & 0.40 & 3.50 & 29.79 \\
11 & 0.80 & 0.80 & 0.70 & 0.20 & 0.50 & 0.05 & 10.50 & 37.25 \\
12 & 0.80 & 0.36 & 0.70 & 0.50 & 0.50 & 0.40 & 10.50 & 44.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Scheme and results of Plackett–Burman Design.