## 4 Conclusions  
The main factors affecting the seepage field in the long-term operation of the dry-stack tailings pond were analyzed and then a calculation model of the seepage field of the dry-stack tailings pond was established. Numerical simulations were conducted to study the evolution process of the seepage field of the dry-stack tailings pond. Based on the method of water dynamic balance in the tailings pond, the final seepage field shape of the dry-stack tailings pond was determined and a new concept was proposed, named the relatively stable seepage field (RSSF). The seepage field can be used as the basis for the drainage system and dam slope design of dry-stack tailings ponds, and it also has a certain guiding role for the design of closed tailings ponds. Through the research on the RSSF under different working conditions, the following conclusions were obtained:  
1. In the early stage during the formation process of RSSF, the drainage flow of the initial dam was less than the average rainfall infiltration flow and the saturation line in the dam rose rapidly. As the drainage flow of the initial dam was gradually equal to the average rainfall infiltration flow, the seepage field of the dry-stack tailings pond gradually approached a relatively stable state and finally a RSSF was formed.
2. Since the fluctuation in the pore pressure curve is relatively small, it is easier to judge the RSSF formation standard of the dry-stack tailings pond by using the relationship between pore pressure and time at typical positions in the dam.
3. The final form of the RSSF is related to the total annual rainfall. With the increase in annual rainfall, the location of the saturation line corresponding to the RSSF will be higher. RSSF has little relation with rainfall patterns when the annual rainfall is constant. Therefore, in the calculation of RSSF, any reasonable rainfall time history curve can be selected, which brings great convenience to the calculation. In addition, under other constant conditions, the final form of RSSF is related to the topography (bottom slope) of the dry-stack tailings pond.
4. When evaporation is considered, the height of the phreatic line of the RSSF will decrease. In this calculation example, the minimum burial depth of the phreatic line (\(h_{b}\)) before and after evaporation is counted: when the annual rainfall is 400 mm/800 mm/1200 mm, the maximum change of \(h_{b}\) increased from 23.9 m/19.4 m/15.2 m to 28 m/24.9 m/19.1 m and increase ratio was 17.2%/28.4%/27.3%.
5. Because the formation of the RSSF in the dry-stack tailings pond takes a long time, it is easy for it to be ignored in the management and design of tailings ponds. Therefore, it is necessary to consider the influence of the RSSF on the design parameters in the design of dry-stack tailings ponds.  
Conceptualization, Q.L. and X.L.; methodology, Q.L. and B.-Z.W.; software, S.J.; validation, B.-Z.W., F.-H.Z. and S.G.; formal analysis, X.L.; investigation, X.L.; data curation, B.-Z.W.; writing--original draft preparation, Q.L.; writing--review and editing, X.L.; funding acquisition, Q.L. and X.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Natural Science Foundation of Hebei Province (E2019210304, E2021210092), the Youth Top Talent Project of Hebei Province, and S&T Program of Hebei (No. 22375412D).  
Not applicable.  
The authors declare no conflict of interest.