3.2.3. Impact Force of Leaked Tailings Flow

As shown in Figures 7 and 10, the locations of maximum impact forces after dam failure are all at the valley near Village I, whose values are all 1000 kN/m. Moreover, marked enhancement of impact force is observed in the vicinities of debris blocking dams. After crossing these dams, the impact forces of tailings flow decrease due to the decline in flow rate and depth. The locations of maximum impact forces are all at the valley mouth near the upstream side of Village III, which are adjacent to the maximum downstream flow rate locations.

**Figure 10.** The maximum impact force of leaked tailings flow downstream with debris blocking dams at different distances. (**a**) 1000 m away from initial dam; (**b**) 600 m away from initial dam; (**c**) 400 m away from initial dam.

#### **4. Conclusions**

In this study, different conditions of downstream riverbed slopes and debris blocking dam construction are analyzed for the tailings pond. The evolution characteristics and deposition laws of leaked tailings flow after dam failure are studied through simulation. During the evolution process, the overtopping flows carry the tailing particles towards the downstream, among the drag forces on

the tailing particles, the friction is greater than the resistance, the tailing particles therefore migrate downstream rapidly. When the friction of the drag forces is equal to its resistance, the flow rate of tailing particles reaches a maximum. With the decrease in water content in the discharged sediments, the uplift force is gradually reduced, the resistance is increased, and the flow rate of tailing particles is decreased. The tailing particles gradually deposit until the flow rate reaches the isolation rate, and they finally deposit completely.

The results demonstrate larger inundated area of tailings flow on the upstream and downstream sections than the midstream, where there are drastic terrain changes. With the elevation of downstream riverbed slope, the inundated area increases, while the maximum depth of tailings deposition decreases gradually. In addition, the deepest sedimentation point of tailings is developed downstream, and the deposition thickness also decreases accordingly. The maximum evolution velocity increases with the elevating terrain, and the maximum impact forces are all located adjacent to the locations of maximum evolution velocity or maximum flow depth.

Setting up debris blocking dams at different distances (characteristic locations) downstream of the initial dam leads to a decline in the maximum inundated range of leaked tailings flow with the shortening distance of these dams from the initial dam. After blockage by the dams, the energy storage-dissipation-deposition process needs to be repeated again. Both the flow rate and depth decrease after crossing the debris blocking dams, and the downstream inundated area is accordingly reduced. Thus, the downstream inundated area ultimately decreases with the shortening distance between initial and debris blocking dams.

**Author Contributions:** G.W. and S.T. designed the study, participated in data collection and analysis, carried out the statistical analyses, wrote the graph of the data and drafted the manuscript. Z.X. and X.K. participated in data collection, statistical analysis and drafted the manuscript. J.C. and B.H. participated in statistical analyses, and helped to interpret the data and draft the manuscript. All authors gave final approval for publication.

**Funding:** This research is supported by the Program for the National Key Research and Development Plan (2017YFC0804600), Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences (Z018017), Changjiang Scholars and Innovative Research Team in University (IRT\_17R112), National Natural Science Foundation of China (41602307; U1802243; 51904040), Open Issue with Key Laboratory of Mine Geological Hazards Mechanism and Control and Department of Natural Resources of Shaanxi Province (KF2018-09).

**Acknowledgments:** The authors would like to acknowledge the colleagues from the State Key Laboratory of Coal Mine Disaster Dynamics and Control for their perspectives and suggestions related to data collection and statistical analysis.

**Conflicts of Interest:** The authors declare no competing interests.
