## 6 Conclusions  
To satisfy the needs of the mining industry for extending its tailings pond storage capacity, a new drainage method was suggested to effectively decrease the phre  
Figure 17: The stability analysis results for the tailings dam (cases **a–h**).  
-drainage system was successfully implemented in designing a seepage-proof system for the higher Xigou tailings dam where the seepage damage may increase. In this study, the MPSO-BP method was used to back-analyze the real permeability coefficients at the site, and a systematic case study of the seepage field analysis was performed using the substructure technique and the variational inequality formulation of Signorini's type in a three-dimensional finite element model. The major conclusions are summarized as follows:  
1. Compared with only setting horizontal drainage pipes or with no drainage pipes, the performance of the new drainage system not only effectively reduced the seepage pressure and depressed the water table but also improved the overall groundwater movement trend and the local seepage field.
2. A stochastic simulation analysis was carried out for analyzing the local failure of the new drainage system, in which 5% and 10% of local blockages have a marginal influence on the seepage field, and the upper and lower envelopes show a lower deviation from the free surface without local failure. The maximum seepage gradients reached 1.43 for the 5% local failure case and 1.57 for the 10% local failure case, but these values were still within the permissive seepage gradient.
3. The sensitivity analysis of the tailings material showed that the performance of the seepage control system was insensitive to the change in the horizontal and vertical permeability coefficients. The sensitivity analysis of the drainage spacing indicated that the designed 10 m pipe spacing was suitable for the drainage pipe arrangement.
4. Utilizing the LEM, the potential failure surface was evaluated, and the corresponding FOSs were obtained at different water levels. Comparing the FOSs under various drainage system conditions, it was obvious that the cases without drainage and with horizontal drainage seemed to lead to an unstable tailings dam under the normal water level or the extremely high water level. However, when the new drainage system was implemented properly, the tailings dam was safe under a variety of working conditions.  
[PERSON] and [PERSON] designed the framework and wrote the manuscript. [PERSON] and [PERSON] collected the data. [PERSON] and [PERSON] mainly responsible for the simulation analysis. [PERSON] and [PERSON] verified the results of our wor. [PERSON] and [PERSON] discussed the results and contributed to the final manuscript.  
This research was funded by the Project of the National Natural Science Foundation of China/Yalong River Joint Fund grant number U1765205, the Project of the National Natural Science Foundation of China grant number 51609073, a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions grant number YS11001, and the CRSRI Open Research Program grant number CKWV2017515/KY.  
The authors declare no conflict of interest.