Analytical solution for the saturation line in dry-stack tailings dams under cumulative rainfall infiltration for many years

The saturation line serves as the foundation for the safety analysis and seepage control design of tailings dams. The primary cause of the saturation line formation in dry-stack tailings dams is the cumulative infiltration of years of rainfall. Previous studies have indicated that, under the cumulative infiltration of years of rainfall, a relatively stable seepage field eventually forms within dry-stack tailings dams, but there is a lack of theoretical research on this seepage field. This paper aims to establish a theoretical solution for the saturation line of dry-stack tailings dams under the accumulation of rainfall over many years. Based on this, the gradual seepage differential equations of the saturation line in dry-stack tailings dams were derived using Darcy's law and the energy equation. By incorporating downstream boundary conditions and rainfall boundary conditions, an analytical solution for the saturation line of dry-stack tailings dams under multi-years rainfall conditions was derived. A comparison between the analytical solution and numerical simulation results was conducted, indicating that the analytical solution closely matches the numerical solution, with a maximum difference of 5.17%. The findings of study can fill the gap in the theoretical study of seepage fields in dry-stack tailings dams under the accumulation of rainfall over many years, which is of significant importance in enriching the theoretical framework of seepage in dry tailings dams. It can serve as the basis for drainage design and slope stability analysis of dry-stack tailings dams, and is crucial for designing safer and more efficient waste management practices in mining and construction.