## 5 Conclusions  
The main conclusions of the paper are as follows:  
1. The data between the CT test results and the measured results are less than 10%, which give good applicability in the study of the permeability characteristics of tailings.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Relevance** & **Sort** \\ \hline Porosity & 0.7823 & 1 \\ Number of pores & 0.7073 & 2 \\ Hole–throat ratio & 0.5727 & 10 \\ Number of laryngeal tracts & 0.6851 & 3 \\ Maximum throat radius & 0.6188 & 5 \\ Mean laryngeal radius & 0.5849 & 7 \\ Minimum laryngeal radius & 0.5739 & 9 \\ Maximum pore radius & 0.5640 & 12 \\ Average pore radius & 0.5586 & 13 \\ Minimum pore radius & 0.5457 & 14 \\ Average pore volume & 0.5404 & 15 \\ Average number of coordinations & 0.6322 & 4 \\ Maximum laryngeal length & 0.5928 & 6 \\ Mean laryngeal length & 0.5844 & 8 \\ Minimum throat length & 0.5717 & 11 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Correlation between structural parameters and permeability \(K\).  
Figure 19: Fitting of porosity and permeability coefficients.  
2. The porosity of viscous tailings ranges from 25 to 35%, the surface porosity of the distribution along the height is similar, and the distribution becomes more uniform with the increase in particle size.
3. Based on the various microstructure characteristics of tailings, it can be seen that, compared with sand tailings and silty tailings, the viscous tailings have fewer edges and corners, a smoother surface, a geometric shape closer to a circle, a convexity greater than 0.85, a fractal dimension as low as 1.2, and a shape factor of 0.95.
4. According to the correlation analysis results of the microscopic parameters of tailings, the porosity, the number of pores and the number of throats are the three key factors affecting the permeability characteristics. The exponential relationship between the porosity \(n\) and the permeability coefficient \(K\) (\(\times 10^{-6}\) cm\(\cdot\)s\({}^{-1}\)) satisfies: \(K=2.64e^{0.07n}-13.60\), R\({}^{2}=0.9998\).
5. The effective porosity is the main factor that affects the permeability of tailings. This is in line with common sense.  
Conceptualization, Q.L., C.M. and C.Z.; data analysis, Q.L and C.M.; methodology, Q.L.; software, Q.L.; supervision, Y.G. and T.Z.; writing--original draft preparation, Q.L.; writing--review and editing, Q.L. and Y.G. All authors have read and agreed to the published version of the manuscript.  
This research is funded by the National Key Research and Development Program of China (NO.2021 YFC3001305; NO.2021 YFC3001303; NO.2023 YFC3012201); and funded by China Coal Technology Group Special key projects of scientific and technological innovation and entrepreneurship funds (NO.2022-ZD002).  
Not applicable.  
The original contributions presented in the study are included in the article; further inquiries can be directed to the author.  
The authors acknowledge all the participants and administrators in this study.  
Author [PERSON] was employed by the company Wushan Copper Mine, Jiangxi Copper Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.