## 3 Results and Discussion
### Influence of Self-Compaction on the Airflow Resistance
A reduction in pore volume \(\varepsilon\) of 0.413, 0.404, 0.397 and 0.391 was found from fitting analysis for \(H_{b}\) of 1.0, 2.0, 3.0 and 3.4 m. The variation of the pressure drop \(\Delta P\) using the variable pore volumes \(\varepsilon\) is displayed in Figure 3c, where the fitted curves have accurately described the course of the experimental data. When using adjusted pore volume \(\varepsilon\), the distribution of data was closely dispersed around the line \(\Delta P_{pred}\) = 0.97\(\Delta P_{obs}\) + 38.72 in close proximity with line \(\Delta P_{pred}\) = \(\Delta P_{obs}\), hence revealing a high accuracy prediction with \(R^{2}\) = 0.995 by the employed model (Figure 3d). These results were accredited to the vertical decrease of pore volume \(\varepsilon\) by 5.30%, which was in line with the findings of [PERSON] et al. [61] for compressive pressure levels ranging from 0 to 50 kPa. This behavior can be explained by the pressure of the overlying grain mass, which increases the in-situ intergranular stresses between kernels due to the dead weight of the overlying bulk [33]. Consequently, the pressure drop \(\Delta P\) increased non-uniformly with the increase of the bulk depth \(H_{b}\). Figure 3: Experimental and predicted pressure drop \(\Delta P\) vs. airflow velocity \(v_{a}\) at bulk depth \(H_{b}\) of 1.0, 2.0, 3.0 and 3.4 m and storage time \(t\) of 1 h storage time fitted with (**a**) default pore volume \(\varepsilon_{0}\) of 0.421 and (**c**) adjusted pore volume \(\varepsilon\) between 0.391 and 0.413. Markers represent the experimental data points (\(\pm\)SD), dashed-dotted lines indicate fitting with the Matthies and Petersen model; Predicted pressure drop \(\Delta P_{pred}\) vs. observed pressure drop \(\Delta P_{obs}\) for (**b**) default and (**d**) variable pore volume. Since self-compaction is a dynamic process, the \(\Delta P\) vs. \(v_{a}\) were fitted for different storage times \(t\) and the pore volume \(\varepsilon\) was also adjusted. Results of \(\varepsilon\) for bulk depths \(H_{b}\) of 1.0, 2.0, 3.0 and 3.4 m and storage time \(t\) of 1, 65, 164 and 236 h are shown in Figure 4. The default pore volume \(\epsilon_{0}\) was indicated by the grey plane in the chart. For the different bulk depths \(H_{b}\) of 1.0 to 3.4 m, a temporal decrease of \(\varepsilon\) from 0.413 to 0.391, from 0.406 to 0.385, from 0.400 to 0.379 and from 0.390 to 0.370 was observed when storage time \(t\) increased from 1 to 65, 164 and 236 h. The resultant stresses are believed to initially influence the reorientation of the kernels and then cause the irreversible plastic deformation once the rupture force is attained, which eventually decreases the pore volume \(\varepsilon\)[33]. The compaction of the grain mass can be attributed to the visco-elastoplastic properties of kernels. However, Figure 4 shows that the grain mass did not settle completely and a longer time can be required to achieve the permanent equilibrium. Figure 5 presents the pressure drop \(\Delta P\) vs. airflow velocity \(v_{a}\) for storage time \(t\) predicted with the Matthies and Petersen model. It can be seen that the pressure drop manifested a temporal increase throughout 236 h of storage time \(t\), which can be ascribed to the gradual and irreversible dynamic compaction of the bulk [62; 63]. Hence, a variation of pressure drop \(\Delta P\) from 1231.92 to 1536.97 Pa was estimated for 3.40 m bulk depth \(H_{b}\) at \(v_{a}=0.10\) m\(\cdot\)s\({}^{-1}\) once the storage time \(t\) increased from 1 to 236 h, which accounted for an increase of 24.76%. The higher pressure drops are mainly attributed to the dense fill created by the kernel packing due to the reduction of pore volume \(\varepsilon\), which leads to increased kinetic energy dissipation due to friction and turbulence and higher intergranular resistances of the airflow. Similar outcomes were reported by [PERSON] and [PERSON] [32], [PERSON] et al. [37] and [PERSON] et al.