# Overtopping Failure of a Reinforced Tailings Dam: Laboratory Investigation and Forecasting Model of Dam Failure

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## Abstract

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## 1. Introduction

## 2. Experimental

#### 2.1. Experimental Facilities

#### 2.2. Experimental Materials and Procedures

- The tailings with 10% water content were prepared according to the test requirements (as shown in Figure 5a).
- Layer compaction method for construction tailings dam, each layer was 8 cm, the compactness of each layer is 85% (as shown in Figure 5b).
- Lay down the reinforcement and sensors (as shown in Figure 5c).
- The displacement monitoring mark were placed on the side of the dam every 10 cm according to the drawn grid lines (as shown in Figure 5d).
- Install the camera, and calibrate these equipment after their placement in the tailings dam.

## 3. Results and Discussion

#### 3.1. Reinforcement Density on Dam Displacement

#### 3.2. Reinforcement Layers and Flooding Time on the Phreatic Level

#### 3.3. Stress Change during Overtopping

#### 3.4. Analysis on Evolution of the Overtopping Failure Process

## 4. Prediction Model of Overtopping Failure

_{s}was the density of the tailings (kg/m

^{3}), C

_{t}was the erosion coefficient of tailings (kg/m

^{3}), $\mathsf{\Delta}b$ was the increment of breach width in $\mathsf{\Delta}t$(m), ν was the velocity of water in breach (m/s), and ν

_{k}was the velocity of impact resistance (m/s), which was related to the properties of the dam material.

_{sm}was the coefficient of submergence, k

_{sm}= 0.95, b was the breach width (m), h

_{0}was the breach depth (m), and in this paper, h

_{0}= z.

_{t}was the erosion coefficient of reinforced tailings dam. From the test results, it was found that the C

_{t}was changing with the number of reinforcement layers. The relationship between C

_{t}and the number of reinforcement layers (N) was shown in Table 4, which could be represented by Equation (5):

## 5. Conclusions

- The reinforcement layers significantly affected the phreatic level. As the number of reinforcement layers increased, the rate of the rise of the phreatic level was slowing down, but the final phreatic level became higher.
- The number of reinforcement layers had an impact on the final shape of dam breach after overtopping erosion. The final breach was shaped as a ladder with four reinforcement layers and an hourglass without reinforcement.
- The reinforcement layers could improve the anti-erosion capability of tailings dam. With the increase of reinforcement layers, the size of breach and the loss rate of stress were reduced significantly.
- Based on the erosion principle, a mathematical model including the number of reinforcement layers was proposed to predict the width and flow of the tailings dam breach.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**The schematic diagram of geo-grid laying. (

**a**) N = 0; (

**b**) N = 1; (

**c**) N = 2; (

**d**) N = 3; (

**e**) N = 4.

**Figure 5.**The procedures of tailings dam construction. (

**a**) Tailings sample; (

**b**) tailings dam construction; (

**c**) tailings dam construction; (

**d**) displacement monitor.

**Figure 6.**The final vertical and horizontal displacement of tracer points during overtopping for different reinforcement layers. (

**a**) Displacement of point W1; (

**b**) Displacement of point W8; (

**c**) Displacement of point W10.

**Figure 9.**The characteristics of dam internal stress, (

**a**) stress of sensor BX-201; (

**b**) stress of sensor BX-202, $SL=(SF-SP)/SP\times 100\%$.

**Figure 10.**The breach shape for different reinforcement layers. (

**a**) Before test; (

**b**) N = 0; (

**c**) N = 1; (

**d**) N = 2; (

**e**) N = 3; (

**f**) N = 4.

Type | Grid Size (mm) | Tensile Strength (kN·m^{−1}) | Elongation at Break (%) | ||
---|---|---|---|---|---|

Vertical | Horizontal | Longitudinal | Transverse | ||

JT1101 | 25 | 25 | 6.5 | 6.5 | 12.7 |

Index | Values |
---|---|

Specific gravity | 2.10 |

Moisture content (%) | 12.5 |

Porosity | 0.024 |

Modulus of compression (MPa) | 17.6 |

Coefficient of compressibility (MPa^{−1}) | 0.058 |

Permeability coefficient (×10^{−6} m·s^{−1}) | 5.86 |

Cohesion (kPa) | 7.52 |

Internal friction angle (Φ/°) | 31.2 |

Index | Values | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Time (s) | 0 | 20 | 40 | 60 | 80 | 100 | 120 | 140 | 160 | 180 | 200 | 220 | 240 | 280 | 300 | 320 | |

Breach Depth (cm) | N = 0 | 0 | 10 | 10 | 12 | 12.5 | 14 | 16 | 18 | 20 | 20 | 22 | 22 | 22 | 22 | 22 | 22 |

N = 1 | 0 | 6 | 8 | 11 | 11 | 13 | 13 | 15 | 15 | 17 | 17 | 20 | 20 | 20 | 20 | 20 | |

N = 2 | 0 | 4 | 6 | 7.2 | 8 | 8 | 8 | 8 | 10 | 12 | 14 | 14 | 14 | 14 | 14 | 14 | |

N = 3 | 0 | 3 | 3 | 3 | 4 | 4 | 6 | 7 | 8 | 8 | 9 | 10 | 10 | 10 | 10 | 10 | |

N = 4 | 0 | 2 | 2 | 2 | 4 | 4 | 5 | 7 | 7 | 8 | 8 | 10 | 10 | 10 | 10 | 10 |

Reinforcement Layers (N) | 0 | 1 | 2 | 3 | 4 |
---|---|---|---|---|---|

C_{t} (×10^{−4} kg/cm^{3}) | 38.62 | 13.51 | 9.92 | 6.10 | 5.59 |

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**MDPI and ACS Style**

Jing, X.; Chen, Y.; Williams, D.J.; Serna, M.L.; Zheng, H.
Overtopping Failure of a Reinforced Tailings Dam: Laboratory Investigation and Forecasting Model of Dam Failure. *Water* **2019**, *11*, 315.
https://doi.org/10.3390/w11020315

**AMA Style**

Jing X, Chen Y, Williams DJ, Serna ML, Zheng H.
Overtopping Failure of a Reinforced Tailings Dam: Laboratory Investigation and Forecasting Model of Dam Failure. *Water*. 2019; 11(2):315.
https://doi.org/10.3390/w11020315

**Chicago/Turabian Style**

Jing, Xiaofei, Yulong Chen, David J. Williams, Marcelo L. Serna, and Hengwei Zheng.
2019. "Overtopping Failure of a Reinforced Tailings Dam: Laboratory Investigation and Forecasting Model of Dam Failure" *Water* 11, no. 2: 315.
https://doi.org/10.3390/w11020315