## 6 Conclusions  
This paper primarily investigates the impact of particle shape on the pore structure and filtration characteristics of the filter layer. This paper primarily presents the following conclusions:  
(1) The effective pore radius of the ellipsoidal particles in various spatial arrangements was calculated, and the relationship between the porosity of the filter layer and the ratio of the major to minor axes of the ellipsoidal particles in a loosely arranged configuration was established.  
(2) A method for ellipsoidal arbitrarily shaped particles is presented, and the particle-shape parameter \(S\) was defined to characterize the shape of these particles.  
(3) The relationship between the particle-shape parameter \(S\) of ellipsoidal particles and the ratio of the major axis to the minor axis \(\lambda\) is summarized. Within a certain range, the particle-shape parameter \(S\) is approximately linear with respect to the ratio of the major axis to the minor axis \(\lambda\).  
(4) The basis and construction method for creating ellipsoidal particles in particle-flow software are presented. Considering actual tailings particles from Jinducheng Molybdenum Industry, the particle shape was analyzed. The foundational parameters for the construction of ellipsoidal particles are provided.  
(5) In the particle-flow software, the differences between spherical particles and ellipsoidal particles in the muddy-water seepage simulation tests were compared and analyzed. The analysis revealed that the particle shape influenced the permeability coefficient of the filter-layer model. As the ratio of the major axis to the minor axis \(\lambda\) increased, the permeability coefficient of the filter layer model first decreased and then increased, as verified by laboratory tests.  
(6) Through the analysis of the pore structure of spherical and ellipsoidal particles in this paper, the relationship between the pore structure and the particle-shape parameters of the irregular natural-particle filter layer with arbitrary shapes was predicted. It is proposed that there exists a boundary particle-shape parameter \(S_{a}\). Under the same particle arrangement, when \(S\) is less than \(S_{a}\), the pores of the filter layer are smaller than those of the corresponding spherical-particle filter layer. When \(S\) is greater than \(S_{a}\), the pore size of the filter layer is larger than that of the corresponding spherical-particle filter layer.  
**Author Contributions:** Conceptualization, W.-K.B.; Methodology, W.-K.B.; Software, W.-K.B.; Visualization. W.-K.B.; Writing--original draft, W.-K.B.; Funding acquisition, F.-N.D.; Project administration, F.-N.D.; Supervision, F.-N.D.; Validation, F.-N.D.; Writing--review and editing, F.-N.D.; Investigation, W.-W.Z.; Resources, Y.Y.; Data curation, H.-B.X.; Formal analysis, J.G. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported by Supported by the National Natural Science Foundation of China (Grant Nos: 51979225; 52009107; 52309172); Shaanxi Key R & D Program Key Industry Innovation Chain (Group) Project (Grant No: 2022 ZDLSF07-02); Shaanxi Natural Science Basic Research Program Youth Project (Grant No: 2020 JQ-627); China Postdoctoral Science Fund Project (Grant No: 2019M663943 XB). The financial support is gratefully acknowledged.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
**Conflicts of Interest:** The authors declare no conflict of interest.