## 3 Soil Parameter Discrete Element Calibration
### Soil Particle Simulation Parameters and Discrete Element Modeling  
The soil-soil contact parameters include static friction, rolling friction, and recovery coefficients. It is known from the literature that the Poisson's ratio of sandy soil physical parameters is 0.15-0.25 [27], taken as 0.2, and the modulus of elasticity is 7-20 \(\mathrm{MN}/\mathrm{m}^{2}\)[19], taken as 13.5 \(\mathrm{MN}/\mathrm{m}^{2}\). The parts of the rest angle tester that are in direct contact with the soil are made of steel with a density of 7865 kg/m\({}^{3}\), Poisson's ratio of 0.3, and shear modulus of 79,000 MPa. Soil particle density, also known as soil specific gravity, depends on the type and relative content of solid-phase constituent substances. A forestry industry standard, Determination of soil particle density in forest soils [28], defines soil particle density as the ratio of the mass of the solid part of the soil (without water) to the mass of the same volume of water (40 \({}^{\circ}\)C). Therefore, soil particle density is not related to soil water content, soil porosity, etc. The density of sieved sandy soil particles was measured using the density bottle method, and the result was 1.38 g/cm\({}^{3}\). Reviewing the relevant literature [22; 27], some simulation parameters were obtained, as shown in Table 4. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{2}{c}{**Materials**} \\ \cline{2-3}  & \multicolumn{2}{c}{**Soil Particles**} & **Steel** \\ \hline Poisson’s ratio & 0.2 & 0.3 \\ Shear modulus (MPa) & & 79,000 \\ Modulus of elasticity (MPa) & 13.5 & \\ Density (kg/m\({}^{3}\)) & 1380 & 7865 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of discrete element simulation. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Water Content** **(\%)**} & \multirow{2}{*}{**Solidity** **(MPa)**} & \multirow{2}{*}{**Load**} & \multirow{2}{*}{**Section Correction** **Radius** **(mm)**} & \multirow{2}{*}{**Corrected** **(mm\({}^{2}\))**} & \multirow{2}{*}{**Axial** **(mm)**} & \multirow{2}{*}{**Compressive** **Strength without** **Lateral Limit**} & \multirow{2}{*}{**Normal** **Stiffness per**} \\  & & & & & & & **(MPa)** \\ \hline \multirow{4}{*}{6} & 0.34 & 298.6 & 31.83 & 3182.9011 & 2.87 & 0.0943 & 3.2688 \(\times\) 10\({}^{7}\) \\  & 0.945 & 856 & 33.56 & 3358.2929 & 1.99 & 0.2431 & 1.2157 \(\times\) 10\({}^{8}\) \\  & 1.55 & 895.6 & 33.25 & 3473.2270 & 2.41 & 0.2591 & 1.0700 \(\times\) 10\({}^{8}\) \\  & 2.155 & 916.2 & 31.21 & 3060.1126 & 2.96 & 0.3006 & 1.0115 \(\times\) 10\({}^{8}\) \\  & 2.76 & 1060 & 33.75 & 3578.4704 & 2.32 & 0.2962 & 1.2773 \(\times\) 10\({}^{8}\) \\ \hline \hline
3 & & 34.4 & 28.92 & 2627.5225 & 1.14 & 0.0114 & 1.1484 \(\times\) 10\({}^{7}\) \\
9 & 1.55 & 994 & 33.79 & 3586.9577 & 1.02 & 0.2771 & 2.7168 \(\times\) 10\({}^{8}\) \\
12 & & 1043 & 32.14 & 3245.2011 & 2.73 & 0.3205 & 1.1775 \(\times\) 10\({}^{8}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of unconfined compressive tests on soil with different moisture content and firmness. According to the soil particle size distribution, the ratio of sand, powder, and nuclage is about 0.91:0.08:0.01, so the nuclage component was ignored in the modeling, the proportion of sand particles with 2 mm diameter was set to 90%, and the proportion of powder particles with 0.02 mm diameter was set to 10%. Since the particles were very small, the roundness of their shape was ignored, and they were set to a spherical shape uniformly and modeled as shown in Figure 6.  
The 3D model of the rest angle meter was built by using SOLIDWORKS 2017 software, and the model size was kept consistent with the actual size and imported into the EDEM 2020 software. The contact model was set to choose the Hertz-Mindlin model with the JKR contact model and the particle generation mode was dynamic generation at 20,000 particles per second. The simulation process is shown in Figure 7.  
Figure 6: Soil particle model. Figure 7: The simulation process of the rest angle.