## 5 Analysis of Numerical-Simulation Results
### Prediction of the Effect of Particle Shape on the Pore Structure of the Filter Layer  
In Section 2.2.3, the pore structure of a filter layer with different particle shapes given a loose arrangement of single-size particles was examined. It was observed that under this arrangement, the porosity of the filter layer reached its minimum at \(\lambda=1.2\). Furthermore, for \(\lambda\) values less than 1.5, the porosity of the ellipsoidal-particle filter layer was lower than that of the spherical-particle filter layer. When \(\lambda\) exceeded 1.5, the porosity of the ellipsoidal-particle filter layer surpassed that of the spherical-particle filter layer, with an initial increase in growth rate that was followed by a decrease.  
In Section 5.4, the seepage performance of the mixed-tailings model with different particle sizes and filter layers with varying particle shapes was investigated. It was observed that the permeability coefficient of the filter layer model was minimized when \(\lambda\) was between 1.3 and 1.4. For \(\lambda\) values less than 1.6, the permeability coefficient of the ellipsoidal-particle filter layer model was lower than that of the spherical-particle filter layer. Conversely, for \(\lambda\) values greater than 1.6, the permeability coefficient of filter-layer models for all particle shapes exceeded that of the spherical-particle filter layer. When \(\lambda\) was between 1.7 and 1.8, the permeability coefficient of the filter layer model reached its maximum; this was followed by a deceleration in the rate of change in the permeability coefficient.  
The conclusions of these two sections are consistent; however, the \(\lambda\) values differ for two reasons. In Section 2.2.3, a filter layer with a single particle size was investigated,  
Figure 24: The permeability coefficient of [PERSON]’s formula for different particle shapes.  
Figure 25: The variation in soil porosity with particle-shape parameters.  
while in Section 5.4, a filter layer with a certain particle-size range was analyzed. Second, the ellipsoidal particles in Section 5.4 were approximated using spherical particles, while Section 2.2.3, by contrast, describes an approximation using ellipsoidal particles.  
In these two sections, the shape of ellipsoidal particles was examined and described by \(\lambda\); however, for various atypical particles (such as those in Figure 10), this representation is inadequate. Thus, these particles were characterized using the particle-shape parameter \(S\) introduced in Section 3.3.  
A comprehensive analysis of the contents of these two sections reveals that the particle shape does have an impact on the pore structure. It is reasonable to speculate that irregular natural particles of various shapes may also influence the pore structure of the filter layer. With the decrease in the value of the particle-shape parameter \(S\) (corresponding to the increase in the value of the ratio of the long axis to the short axis, \(\lambda\)), the porosity of the filter layer initially decreased and subsequently increased, although the rate of increase gradually diminished. There exists a critical particle-shape parameter, \(S_{a}\). Under the same particle arrangement, when \(S\) is less than \(S_{a}\), the pore size of the ellipsoidal filter layer is smaller than that of the corresponding spherical filter layer. Conversely, when \(S\) exceeds \(S_{a}\), the pore size of the ellipsoidal filter layer becomes larger than that of the corresponding spherical filter layer.