Evolution Pattern of Tailings Flow from Dam Failure and the Bu ﬀ ering E ﬀ ect of Debris Blocking Dams

: Tailings ponds are the indispensable facilities in the mine production and operation. Once the dam is destabilized and damaged, it will pose a serious threat on the life and property of the downstream population and could also potentially cause an environmental disaster. With an engineering background, this paper dynamically and numerically simulates the evolution process of tailings ﬂow from dam failure and the inﬂuence scope of any resulting disaster in context. The evolution characteristics of leaked tailings ﬂow are analyzed at various downstream riverbed slopes and debris blocking dam settings. In addition, parameters such as ﬂow rate, impact force and deposition range of leaked tailings ﬂow at downstream arrival are studied, as well as their correlations. The results indicate that the ﬂat terrains upstream and downstream of passage zone show a relatively larger area of inundation by tailings ﬂow. Both the maximum and ﬁnal downstream inundated ranges increase with the elevating slope of downstream riverbed, and the leaked tailings are deposited mainly in the nearby villages in front of the dam and the ﬂat terrains of the downstream passage zone. Additionally, rational establishment of debris blocking dams on the downstream side is e ﬀ ective in diminishing the damage of tailings ﬂow to the downstream section. This study can also provide an important basis for the quantitative evaluation of post-disaster inﬂuence scope for tailings pond as well as for the design of dam body. the evolution process of tailings ﬂow erent downstream riverbed slopes and debris blocking dam construction parameters. the same time, the evolution pattern, sedimentary characteristics and energy loss of tailings ﬂow during evolution are analyzed. In addition, the e ﬀ ects of downstream riverbed slope debris blocking construction on the tailings ﬂow characteristics also


Introduction
Tailings ponds are the artificial hazard sources with high potential energy. In the event of an accident, the resulting tailings flow might bring huge losses to the life and property of downstream populations while also polluting the ecological environment severely [1][2][3]. Tailings are the kinds of solid wastes generated from mineral separation. Tailings are also a special kind of soil, generally structured with single granule and beehive. Due to the poor comprehensive utilization of tailings, the majority of them are stored in the tailings ponds aside from the cases of beneficiation, mine filling and building material recovery [4][5][6]. With the continuous exploration by mine companies as well as the growing demand for mineral products, the dam height and storage volume of tailings ponds have

Simulation Model and Boundary Conditions
Digital Elevation Model (DEM) is created by collecting the digital elevation data within the scope of studied tailings pond combined with in situ investigation. The studied tailings pond dam has a crest elevation of 2005 m (the height above sea level), a fill dam height of 30 m, an initial dam height of 32 m, a total dam height of 62 m, a whole storage capacity of 3.996 million m 3 , and an effective storage capacity of 3.197 million m 3 , and it is located in Huili Country of Liangshan, Sichuan Province of China. The tailings pond adopts upstream damming, in which the height of each sub-dam is 5 m, the ratio of sub-dam to outer slope is 1:3.5, and the total slope ratio is 1:4.233. The objective of the sub-dams located upstream of the main dam is the deposition of tailings upstream of the sub-dams and, consequently, the increase of the storage capacity of the tailings ponds and the decrease of the streambed slope. Besides the storage capacity, maximum pond water level at overtopping, basic mechanical parameters of dam tailings and flow hydrograph range (Figure 1) of the tailings pond are determined based on the data collected in situ and the information provided by mining companies.
Dam failure computation models are built through in situ investigation at three downstream riverbed slopes, i.e., original terrain slope (average slope ratio of 4.2% along the valley bottom), elevation by 5% (average slope ratio of 9.2% along the valley bottom) and elevation by 10% (average slope ratio of 14.2% along the valley bottom), which can be found in Figure 2 Dam failure computation models are built through in situ investigation at three downstream riverbed slopes, i.e., original terrain slope (average slope ratio of 4.2% along the valley bottom), elevation by 5% (average slope ratio of 9.2% along the valley bottom) and elevation by 10% (average slope ratio of 14.2% along the valley bottom), which can be found in Figure 2.

Computational Parameters
After vertical integration, the controlling equations can be reduced to a 2D format [28], which is described by the Navier-Stokes equations. The simplified controlling equations are shown below.
The continuity equation: The equations of motion: Dam failure computation models are built through in situ investigation at three downstream riverbed slopes, i.e., original terrain slope (average slope ratio of 4.2% along the valley bottom), elevation by 5% (average slope ratio of 9.2% along the valley bottom) and elevation by 10% (average slope ratio of 14.2% along the valley bottom), which can be found in Figure 2.

Computational Parameters
After vertical integration, the controlling equations can be reduced to a 2D format [28], which is described by the Navier-Stokes equations. The simplified controlling equations are shown below.
The continuity equation: The equations of motion:

Computational Parameters
After vertical integration, the controlling equations can be reduced to a 2D format [28], which is described by the Navier-Stokes equations. The simplified controlling equations are shown below.
The continuity equation: The equations of motion: where h denotes the draining tailing flow depth (m), I is the drop in the water surface per unit distance within the simulated range and is called the hydraulic gradient (%), u and v refer to the flow rate in the horizontal and vertical directions (m/s), respectively; S f x and S f y are the differences in the unit distance of the frictional resistance in the x and y directions, respectively, and are called the frictional slope (%), S ox and S oy are the differences in elevation within a unit distance in the x and y directions, respectively, and are called the riverbed slope (%). When the flood or tailings flow is simulated by the FLO-2D, it can be performed in the dynamic wave mode or the diffused wave mode. According to the similarity criterion, Equation (1) is a mass conservation equation, while Equation (2) and Equation (3) are the momentum conservation equations.
Additionally, the evolution process of leaked tailings flow can be described by the rheological equation for high sediment concentration, which is proposed by O'Brien [29], as shown below.
where S f , S y , S v and S td represent frictional slope, yield slope, viscous slope and turbulence-distribution slope, respectively. τ y denotes the yield stress of the fluid during the flow, γ m denotes the fluid specific gravity, η is the viscous coefficient of fluid, K is the laminar flow resistance coefficient, and n refers to the Manning coefficient representing the roughness of ground surface.
Yield stress in the current study refers to the Bingham yield stress, which is reflected primarily as the internal stress pattern of viscous tailings flow and present in the form of viscous force [30][31][32]. The viscous force is a resistance produced by the interaction between shear and tensile stresses of fluid [33,34]. As a result, the Bingham viscosity coefficient and viscous force are closely correlated in the present work, and the increase in fluid volume concentration leads to exponential increases in the Bingham yield stress and Bingham viscosity coefficient [35,36].
The relationship between the yield stress and the volume concentration is shown in Equation (5).
and the relational expression between the Bingham viscous coefficient and the volume concentration is presented in Equation (6).
where volume concentration (C V ) indicates the percentage of soil and debris like aggregate and gravel in the leaked tailings flow over the entire tailings flow volume. α 1 , β 1 , α 2 and β 2 are the empirical coefficients of the yield stress and viscous force, which can be derived experimentally. On this basis, Table 1 provides the relevant parameters used in the present numerical simulation.

Simulation Parameters Values
Fluid relative density γ m (g/cm 3

Flow Depth of Leaked Tailings
This study chooses the passage zone downstream of the tailings pond as the simulation target. As presented in Figure 3, the leaked tailings all flow downstream along the valley bottom (lowest point) within the passage zone after collapse of tailings pond in three different slope conditions.

Flow Depth of Leaked Tailings
This study chooses the passage zone downstream of the tailings pond as the simulation target. As presented in Figure 3, the leaked tailings all flow downstream along the valley bottom (lowest point) within the passage zone after collapse of tailings pond in three different slope conditions. Due to the presence of fluted or relatively flat terrains upstream and downstream of the passage zone, the inundated areas by leaked tailings flow are larger on the upstream and downstream sections than the midstream section, where the terrain changes more drastically. The inundated ranges increase with the increasing slope of downstream riverbed, which maximize at 2.8 × 10 5 m 2 , 3.7 × 10 5 m 2 and 4.9 × 10 5 m 2 , respectively. In the earlier stage of dam failure, the volume of water in the leaked tailings flow is considerably higher than the volume of tailings. As the dam breach opening develops further, the content of tailings increases. In the meanwhile, the impact height increases gradually with the descending terrain, and the influence scope on downstream section accordingly increases. The elevated content of tailings in the leaked tailings flow leads to a corresponding increase in the fluid viscosity. In the later stage of dam failure, the water content in leaked tailings flow declines gradually, and the drag force of tailings flow decreases. By contrast, the frictional resistance increases to ultimately attain equilibrium of forces and maximization of flow rate. With further increase in the frictional resistance, the flow rate of leaked tailings flow declines to zero to achieve the maximum inundated area. This result is consistent with the energy storage-dissipation-deposition process during physical motion [37].  Due to the presence of fluted or relatively flat terrains upstream and downstream of the passage zone, the inundated areas by leaked tailings flow are larger on the upstream and downstream sections than the midstream section, where the terrain changes more drastically. The inundated ranges increase with the increasing slope of downstream riverbed, which maximize at 2.8 × 10 5 m 2 , 3.7 × 10 5 m 2 and 4.9 × 10 5 m 2 , respectively. In the earlier stage of dam failure, the volume of water in the leaked tailings flow is considerably higher than the volume of tailings. As the dam breach opening develops further, the content of tailings increases. In the meanwhile, the impact height increases gradually with the descending terrain, and the influence scope on downstream section accordingly increases. The elevated content of tailings in the leaked tailings flow leads to a corresponding increase in the fluid viscosity. In the later stage of dam failure, the water content in leaked tailings flow declines gradually, and the drag force of tailings flow decreases. By contrast, the frictional resistance increases to ultimately attain equilibrium of forces and maximization of flow rate. With further increase in the frictional resistance, the flow rate of leaked tailings flow declines to zero to achieve the maximum inundated area. This result is consistent with the energy storage-dissipation-deposition process during physical motion [37]. Figure 4 presents a diagram of maximum impact height of leaked tailings flow along the valley bottom downstream of dam in the earlier stage. In the original terrain scenario, the tailings in leaked tailings flow are deposited substantially within the valleys or flat terrains on the upstream 150-650 m section and the downstream 1200-1800 m section after the failure of tailings pond, while deposited slightly within the areas with sharp slope changes on the midstream section. After terrain elevation by 5% and 10% separately on the basis of original topography, significant reduction of tailings storage capacity is noted for both the upstream and downstream sections with the rising terrain, as well as substantial decline in the amount and depth of deposition.
Water 2019, 11, x FOR PEER REVIEW 6 of 13 elevation by 5% and 10% separately on the basis of original topography, significant reduction of tailings storage capacity is noted for both the upstream and downstream sections with the rising terrain, as well as substantial decline in the amount and depth of deposition. Maximum depth of tailings deposition decreases gradually with the elevating slope of downstream riverbed. Maximum impact height is found near Village I for the original terrain (14.43 m). After terrain elevation by 5% (4.97 m), the maximum impact height is found at the valley downstream of Village III; and after terrain elevation by 10% (3.30 m), the maximum impact height is found also at the valley downstream of Village III. Deepest sedimentation point of tailings is developed downstream, and the deposition thickness also decreases accordingly.

Flow Rate of Leaked Tailings
As shown in Figure 5, the maximum velocities of tailings flow are all located downstream of initial dam, and the maximum evolution velocities of tailings flow increase with the elevating terrain, which are 10 m/s, 10.9 m/s and 13.5 m/s, respectively. In the original terrain scenario, the terrain and altitude difference decrease sharply within the areas downstream of initial dam and upstream of Village III after dam failure, thus enabling fast evolution of the leaked tailings flow. At the downstream section of Village III, however, the altitude difference changes little and the evolution distance is long. Therefore, a gradual decline of flow rate is noted with the increasing evolution distance. According to Figure 5, after elevating terrain by 5% and 10%, the altitude difference changes rather greatly for a scope from the initial dam to the 1000 m downstream section, and the flow rate of leaked tailings continues to heighten. The velocity tends to stabilize when the downstream altitude difference narrows down.

Flow Rate of Leaked Tailings
As shown in Figure 5, the maximum velocities of tailings flow are all located downstream of initial dam, and the maximum evolution velocities of tailings flow increase with the elevating terrain, which are 10 m/s, 10.9 m/s and 13.5 m/s, respectively. In the original terrain scenario, the terrain and altitude difference decrease sharply within the areas downstream of initial dam and upstream of Village III after dam failure, thus enabling fast evolution of the leaked tailings flow. At the downstream section of Village III, however, the altitude difference changes little and the evolution distance is long. Therefore, a gradual decline of flow rate is noted with the increasing evolution distance. According to Figure 5, after elevating terrain by 5% and 10%, the altitude difference changes rather greatly for a scope from the initial dam to the 1000 m downstream section, and the flow rate of leaked tailings continues to heighten. The velocity tends to stabilize when the downstream altitude difference narrows down.

Impact Force of Leaked Tailings Flow
This study investigated the effect of the impact during the evolution process of leaked tailings flow on its downstream constructs, and the exerting range of impact force is the region that the discharged sediments flow through. The impact force of leaked tailings flow on the downstream constructs is calculated using Equation (7) through Equation (9) [27,[37][38][39][40]. Multiple factors, including the impact angle, flow rate and density of tailings flow, can affect the computational results by varying degrees [38][39][40]. υ is the flow rate of leaked tailings at arbitrary time; C w represents the weight concentration; e is a constant; and F is the impact force per unit width.
According to Equation (9), increases in the flow rate and depth lead to enhanced impact force per unit area.
From Figure 3 and Figure 6, it can be seen that the locations of maximum impact forces in three different conditions are all adjacent to the maximum evolution velocity location. In the original terrain condition, the maximum impact force is located downstream from the initial dam with the value of 706 kN/m. With the elevation of slope, the maximum impact force increases first and then decreases, which is 883 kN/m at an elevation by 5% and is 495 kN/m at an elevation by 10%, showing a value approximately 70% of the original terrain scenario.

Impact Force of Leaked Tailings Flow
This study investigated the effect of the impact during the evolution process of leaked tailings flow on its downstream constructs, and the exerting range of impact force is the region that the discharged sediments flow through. The impact force of leaked tailings flow on the downstream constructs is calculated using Equation (7) through Equation (9) [27,[37][38][39][40]. Multiple factors, including the impact angle, flow rate and density of tailings flow, can affect the computational results by varying degrees [38][39][40].
P i = kρ f υ 2 (7) where P i denotes the impact pressure imposed by leaked tailings flow on other objects within the flow region; ρ f refers to the fluid density of leaked tailings flow; h denotes the maximum depth of leaked tailings flow; k is the impact coefficient, and its value range from 1.261 to 3.427 [26,27]; υ is the flow rate of leaked tailings at arbitrary time; C w represents the weight concentration; e is a constant; and F is the impact force per unit width. According to Equation (9), increases in the flow rate and depth lead to enhanced impact force per unit area.
From Figures 3 and 6, it can be seen that the locations of maximum impact forces in three different conditions are all adjacent to the maximum evolution velocity location. In the original terrain condition, the maximum impact force is located downstream from the initial dam with the value of 706 kN/m. With the elevation of slope, the maximum impact force increases first and then decreases, which is 883 kN/m at an elevation by 5% and is 495 kN/m at an elevation by 10%, showing a value approximately 70% of the original terrain scenario.

Effects of Debris Blocking Dam on Tailings Flow
Debris blocking dams are set up at three characteristic locations downstream of initial dam in this study (Dam 1: valley mouth upstream of Village III, 1000 m away from the initial dam; Dam 2: valley mouth upstream of Village II, 600 m away from the initial dam; and Dam 3: valley mouth downstream of Village I, 400 m away from the initial dam). The height of these dams is 10 m.
According to the data collected in situ and the information provided by mining companies, there are villages downstream of these three locations, where the constructions of the debris blocking dams at these characteristic locations downstream are more conducive to reducing losses. Additionally, these three places are located at the top of the valley, the terrain on both sides is higher and the cost of dam constructions is relatively low.

Flow Depth of Leaked Tailings
As presented in Figure 7, the leaked tailings flow evolves downstream along the topographically lowest point in the passage zone in all three different conditions. The tailings inundated area is larger for the upstream and downstream sections of passage zone than for the midstream section. Under three dam distance conditions, the maximum inundated ranges are 2.7 × 10 5 m 2 , 2.5 × 10 5 m 2 and 2.37 × 10 5 m 2 , respectively. Consequently, the downstream inundated area shrinks with the narrowing distance between debris blocking and initial dams.

Effects of Debris Blocking Dam on Tailings Flow
Debris blocking dams are set up at three characteristic locations downstream of initial dam in this study (Dam 1: valley mouth upstream of Village III, 1000 m away from the initial dam; Dam 2: valley mouth upstream of Village II, 600 m away from the initial dam; and Dam 3: valley mouth downstream of Village I, 400 m away from the initial dam). The height of these dams is 10 m.
According to the data collected in situ and the information provided by mining companies, there are villages downstream of these three locations, where the constructions of the debris blocking dams at these characteristic locations downstream are more conducive to reducing losses. Additionally, these three places are located at the top of the valley, the terrain on both sides is higher and the cost of dam constructions is relatively low.

Flow Depth of Leaked Tailings
As presented in Figure 7, the leaked tailings flow evolves downstream along the topographically lowest point in the passage zone in all three different conditions. The tailings inundated area is larger for the upstream and downstream sections of passage zone than for the midstream section. Under three dam distance conditions, the maximum inundated ranges are 2.7 × 10 5 m 2 , 2.5 × 10 5 m 2 and 2.37 × 10 5 m 2 , respectively. Consequently, the downstream inundated area shrinks with the narrowing distance between debris blocking and initial dams.
From Figure 8, it can be found that the deposition thicknesses of tailings crossing over the debris blocking dams decrease slightly compared with the case without such dams. The maximum sedimentation thicknesses are all found in front of the debris blocking dams, which increase with the shortening distance between initial and debris blocking dams and are all located in the valley near Village I. After flowing over the debris blocking dams, the tailings are deposited primarily in the valley near Village III, and the inundated height increases with the increasing of the distance between the debris blocking dam and the initial dam. From Figure 8, it can be found that the deposition thicknesses of tailings crossing over the debris blocking dams decrease slightly compared with the case without such dams. The maximum sedimentation thicknesses are all found in front of the debris blocking dams, which increase with the shortening distance between initial and debris blocking dams and are all located in the valley near Village I. After flowing over the debris blocking dams, the tailings are deposited primarily in the valley near Village III, and the inundated height increases with the increasing of the distance between the debris blocking dam and the initial dam.   From Figure 8, it can be found that the deposition thicknesses of tailings crossing over the debris blocking dams decrease slightly compared with the case without such dams. The maximum sedimentation thicknesses are all found in front of the debris blocking dams, which increase with the shortening distance between initial and debris blocking dams and are all located in the valley near Village I. After flowing over the debris blocking dams, the tailings are deposited primarily in the valley near Village III, and the inundated height increases with the increasing of the distance between the debris blocking dam and the initial dam.  Village I. Meanwhile, the maximum flow rates downstream of the debris blocking dams are all found at the valley mouth near the upstream side of Village III. After setting up the debris blocking dams, the maximum downstream flow rates also decrease accordingly.

Impact Force of Leaked Tailings Flow
As shown in Figure 7 and Figure 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.  Village I. Meanwhile, the maximum flow rates downstream of the debris blocking dams are all found at the valley mouth near the upstream side of Village III. After setting up the debris blocking dams, the maximum downstream flow rates also decrease accordingly.

Impact Force of Leaked Tailings Flow
As shown in Figure 7 and Figure 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.

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.