## 2 Materials and Methods  
### Problem of Seepage Field in Dry-Stack Tailings Ponds  
#### 2.1.1 Analysis of Influencing Factors of Water in Dry-Stack Tailings Ponds  
When analyzing the seepage field of dry-stack tailings ponds, both water entering and drainage out of the seepage field should be firstly considered, as shown in the Figure 1. The main sources of water entering the seepage field include: residual water of tailings, rainfall, and infiltration of flood water after ponding in the dry beach. The drainage out of the seepage water mainly includes: the drainage through the initial dam, the drainage through drainage pipe buried in the dam, evaporation, and leakage through the pond bottom. From Figure 1, taking the dry-stack tailings pond as the hydrogeological unit, the volume of water entering the seepage field is calculated by Equation (1):  
\[\mathrm{d}V_{in}=\mathrm{d}V_{r}+Q_{m}\mathrm{d}t+Q_{f}\mathrm{d}t \tag{1}\]  
where, \(V_{in}\) is volume of water entering the tailings pond, \(V_{0}\) is initial volume of water in the tailings, \(Q_{m}\) is the flow caused by rainfall infiltration, and \(Q_{f}\) is the infiltration flow of flood after ponding in the dry beach under extreme rainfall. The residual water content of tailings is related to the tailings concentration process, and it can be considered through the initial water content in the calculation. \(V_{0}\) has nothing to do with time, so Equation (2) is satisfied:  
\[\mathrm{d}V_{0}=0 \tag{2}\]  
The confluence of the flood on the dry beach generally occurs only after extreme rainfall. Current specifications in China require that the flood is drained through the flood drainage system within 3 days. In ordinary times, there is no water in the dry beach of the tailings pond. This part has little impact on the long-term seepage field of the tailings pond and can be ignored in the calculation, which satisfies Equation (3):  
\[Q_{f}=0 \tag{3}\]  
Rainfall infiltration is the main source of the seepage field evolution of dry-stack tailings ponds. From the literature review in the introduction, it can be seen that short-term rainfall infiltration has little impact on the seepage field of tailings ponds. So, it is essential to consider the cumulative effect of multi-year rainfall on the seepage field of dry-stack tailings ponds. Therefore, in the design of a tailings pond or the management of a closed tailings pond, it is necessary to consider the effect of accumulated rainfall infiltration on the seepage field during the life cycle of the tailings pond. Figure 1: Diagram of the factors leading to the change of seepage water in the dry-stack tailings pond (Note: residual water refers to the water that cannot be separated freely after tailings are dehydrated). By simultaneous Equations (1)-(3), the volume of water entering the tailings pond is calculated by Equation (4)  
\[\mathrm{d}V_{in}=Q_{m}\mathrm{d}t \tag{4}\]  
The volume of water drainage out of the seepage field is calculated by Formula (5),  
\[\mathrm{d}V_{out}=Q_{d1}\mathrm{d}t+Q_{d2}\mathrm{d}t+Q_{c}\mathrm{d}t+Q_{l} \mathrm{d}t \tag{5}\]  
where \(V_{out}\) is volume of water discharge out of the seepage field, \(Q_{d1}\) is rate of flow of water drainage through the initial dam, \(Q_{d2}\) is rate of flow of water drainage through a drainage pipe buried in the dam, \(Q_{c}\) is rate of flow of water evaporation, and \(Q_{l}\) is rate of flow of water leakage through the reservoir bottom. The initial dam of the tailings pond is generally a permeable dam, and it is the main way for seepage water discharging out of the tailings and it must be considered in the calculation. In the dry-stack tailings pond, drainage pipes buried in the dam body are mainly used to control the phreatic line. When the buried depth of the phreatic line is lower than the position of the drainage pipe, it cannot be considered in the calculation, thus the calculation result of the seepage field tends to be safer.