# A Simulation Method for Layered Filling of Grain Piles Based on the Discrete Element Method
## 3 Results and Discussion
### Porosity Distribution and Tortuosity  
The distribution of porosity is of significant importance for studying the ventilation system of grain piles. Typically, in the design of ventilation schemes, the porosity follows a specific curve. However, in actual grain piles, the porosity may exhibit local variations due to different stacking methods. Therefore, it is necessary to simulate grain piles using the DEM to obtain an approximate distribution of porosity. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{5}{c}{**CASE**} \\ \cline{2-5}  & **C1** & **C2** & **C3** & **C4** & **D1** \\ \hline Kinetic energy & 3.39 \(\times\) 10\({}^{-9}\) & 1.356 \(\times\) 10\({}^{-10}\) & 3.39 \(\times\) 10\({}^{-11}\) & 1.356 \(\times\) 10\({}^{-12}\) & Reference condition \\ Search range & 0.075 & 0.075 & 0.075 & 0.075 & Reference condition \\ \(H_{\mathrm{s}}\) & 0.1 & 0.1 & 0.1 & 0.1 & Reference condition \\ C\({}_{\mathrm{b}}\) & 5 & 5 & 5 & Reference condition \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters for LFM cases. Figure 7: Actual stacking process with LFM. (**a**) Sub-pile 1; (**b**) Sub-pile 2; (**c**) Sub-pile 3; (**d**) main pile; and (**e**) pile. Figure 8 illustrates the porosity distribution and error distribution of grain piles under different conditions. Due to the relatively large aspect ratio of the silo, the frictional forces on the silo walls result in minimal variation in porosity along the height direction. Simultaneously, the presence of dead corners at the bottom of the silo leads to an increased porosity in the lower part. In comparison to the PFM, the grain pile simulated using the LFM model exhibits slightly higher porosity. As the stability conditions of the particles decrease, the porosity gradually approaches that of the direct method, maintaining a consistent overall trend. Based on Figure 8b, it is apparent that C2 exhibits the highest error at a height of 800 mm, reaching a maximum value of 1.14%. The average relative errors for the four cases are 3.05%, 4.56%, 2.93%, and 3.12%, respectively, all of which fall below 5.00%. Hence, it can be concluded that the influence of the LFM on porosity can be deemed negligible. Tortuosity is an extensively employed key parameter to predict the transport characteristics of porous media and represents the airflow resistance within grain piles. To compare the variations in tortuosity under different conditions, three points were randomly selected at the bottom of the grain pile ((0, 0, 0), (0.015 m, 0, 0), and (0, \(-\)0.028 m, 0)) as the air entry points (AEPs). It is important to note that the AEP should be sufficiently distant from the vertical wall to minimize the impact of wall effects on the results. As depicted in Figure 8, the most significant variation in porosity primarily occurs below the 800 mm mark. Hence, Table 4 provides the length and tortuosity of the widest airflow path below this level. It is apparent that different AEPs yield distinct airflow paths. Among the three airflow paths observed under various operational conditions, the majority exhibit widths ranging from 2 mm to 3 mm, consistent with the findings of [PERSON] [35]. The longest path measures 1462.18 mm, while the shortest path measures 1357.13 mm. Based on the relative error variations of tortuosity, as shown in Table 5, it is evident that tortuosity is influenced not only by the stability parameters but also by the position of the air inlet. The closer the air inlet is to the central position of the grain pile, the greater