# Risk Evaluation Model of Life Loss Caused by Dam-Break Flood and Its Application

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Risk Formation Path of Life Loss Caused by Dam-break Flood Based on the Disaster Process

#### 2.2. Evaluation Indicator System of Life Loss Caused by Dam-Break Flood.

_{R}), flood intensity (S

_{F}), time of dam breaking (T

_{B}), time of warning (T

_{W}), and an understanding of the level of flood severity (U

_{B}). In addition, it can be seen from the risk formation path that other factors, such as dam height (H

_{D}), reservoir capacity (C

_{R}), distance from the dam (L

_{D}), and self-rescue capability (R

_{C}), directly or indirectly affect the disaster damage of human lives. Therefore, in this manuscript, the hazard indicators select dam height, reservoir capacity, and flood strength (the product of water depth and flow velocity) as important factors. The exposure factors can be divided into natural geography conditions and other external environments. Considering the difficulty in data acquisition and the influence on the evaluation results, the main factors in the exposure indicator are the distance from the broken dam, time of warning, and time of breaking. The vulnerability factors select the population at risk, understanding of flood severity and the self-rescue capability which have great influence and are easy to calculate. Table 1 shows the evaluation indicator system.

#### 2.3. Risk Classification Standard of Life Loss Risk Indicators

#### 2.4. Variable Fuzzy Evaluation Model of Life Loss Risk

#### 2.4.1. Determining the Matrix of the Sample Eigenvalue

_{1}, X

_{2}, ···, X

_{n}}, each sample has m indicator eigenvalues, then the matrix of the sample eigenvalue to be evaluated can be expressed as:

_{ij}is the measured eigenvalue of Indicator i of Sample j; i = 1, 2, ... , m; j = 1, 2, ... , n.

#### 2.4.2. Determining the Matrix of the Standard Interval of Indicators

_{ih}, b

_{ih}] is the standard interval of Indicators i of Level h, and a

_{ih}, b

_{ih}are the upper and lower limits of the interval.

#### 2.4.3. Determining the Matrix of Standard Interval Point Value

_{ih}is the point value when Indicator i in the standard interval [a

_{ih}, b

_{ih}] has a relative membership degree of 1 to the Level h, M

_{ih}can be determined based on the physical meaning and the actual situation. Since M

_{ih}(h = 1, 2, ···, c) is an important parameter, for Level 1 M

_{i1}= a

_{i1}, for Level c M

_{ic}= a

_{ic}, for intermediate level l, when c is odd, M

_{il}= (a

_{il}+ b

_{il})/2c. The general model of the point value M

_{ih}satisfying the above conditions is

_{i1}= a

_{i1}; for h = c, M

_{ic}= a

_{ic}, for $h=\text{}l=\text{}\frac{c+1}{2}{,\text{}M}_{\mathit{il}}\text{}=\frac{{a}_{\mathit{il}}{+b}_{\mathit{il}}}{2}$. By Formula (3), Matrix $\text{}M\text{}=\text{}\left({M}_{\mathit{ih}}\right)$ can be obtained from the Matrix Y.

#### 2.4.4. Determining the Matrix of Relative Membership Degree of the Indicator x_{ij} to Each Level

_{ij}of the sample u

_{j}falls into [M

_{ih}, M

_{i(h}

_{+1)}], the interval between the adjacent two levels of the matrix M, Level h and Level (h + 1), then the relative membership degree of Indicator i to Level h can be calculated by the following formula:

_{ij}falls outside the range of M

_{i1}and M

_{ic}, according to the physical concept: ${\text{}\mu}_{i1}\left({u}_{j}\right){\text{}=\text{}\mu}_{\mathit{ic}}\left({u}_{j}\right)\text{}=\text{}1$.

#### 2.4.5. Determining the Comprehensive Membership Degree of the Indicator

_{j}of the evaluation object x

_{ij}to the Level h is calculated according to the following formula:

#### 2.4.6. Calculating the Comprehensive Evaluation of Grade Eigenvalue

## 3. Case Study

^{4}. Considering the data authenticity, content comprehensiveness, and sample representativeness, the eight selected dams could meet the needs of the risk evaluation. The qualitative indicator is reasonably assigned according to the situation of the dam-break investigation and the classification of the evaluation indicator. The basic data of the sample data are shown in Table 3.

## 4. Result and Discussions

#### 4.1. Model Calculation

#### 4.2. Results Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Ge, W.; Li, Z.; Liang, R.Y.; Li, W.; Cai, Y. Methodology for Establishing Risk Criteria for Dams in Developing Countries, Case Study of China. Water Resour. Manag.
**2017**, 31, 4063–4074. [Google Scholar] [CrossRef] - Matalas, N.C.; Jr, C.F.N. Ministry of Water Resources of the People’s Republic of China. First National Water Conservancy Survey Bulletin; China Water Resources and Hydropower Press: Beijing, China, 2013. [Google Scholar]
- Li, L.; Wang, R.; Sheng, J. Risk Assessment and Risk Management of Mycotoxins in Food; China Water Resources and Hydropower Press: Beijing, China, 2006. [Google Scholar]
- Fan, Q.; Tian, Z.; Wang, W. Study on risk assessment and early warning of flood-affected areas when a dam break occurs in a mountain river. Water
**2018**, 10, 1369. [Google Scholar] [CrossRef] - Li, Z.; Ge, W.; Wang, J.; Li, W. Strategic consideration of dam safety management and risk management in China. Adv. Water Resour.
**2015**, 26, 589–595. [Google Scholar] [CrossRef] - Álvarez, M.; Puertas, J.; Peña, E.; Bermúdez, M. Two-dimensional dam-break flood analysis in data-scarce regions: The case study of Chipembe dam, Mozambique. Water
**2017**, 9, 432. [Google Scholar] [CrossRef] - Brown, C.A.; Graham, W.J. Assessing the threat to life from dam failure. J. Am. Water Resour. Assoc.
**1988**, 24, 1303–1309. [Google Scholar] [CrossRef] - Reiter, P. Loss of Life Caused by Dam Failure: The RESCDAM LOL Method and Its Application to Kyrkosjarvi Dam in Seinajoki; Final Report of PR Water Consulting Ltd.: Helsinki, Finland, 2001. [Google Scholar]
- Assaf, H.; Hartford, D. A virtual reality approach to public protection and emergency preparedness planning in dam safety analysis. Proceedings of Canadian Dam Association, Victoria, BC, Canada, October 2002. [Google Scholar]
- Aboelata, M.; Bowles, D.S.; McClelland, D.M. A model for estimating dam failure life loss. In Proceedings of the Australian Committee on Large Dams Risk Workshop, Launceston, Tasmania, Australia, October 2003. [Google Scholar]
- Dekay, M.L.; Mcclelland, G.H. Predicting loss of life in cases of dam failure and flash flood. Insur. Math Econ.
**1993**, 13, 193–205. [Google Scholar] [CrossRef] - Lee, J.S. Uncertainties in the predicted number of life loss due to the dam breach floods. KSCE J. Civ. Eng.
**2003**, 7, 81–91. [Google Scholar] [CrossRef] - Jonkman, S.N.; Godfroy, M.; Sebastian, A.; Kolen, B. Brief communication: Post-event analysis of loss of life due to hurricane Harvey. Nat. Hazards
**2018**, 18, 1073–1078. [Google Scholar] [CrossRef] - Jonkman, S.N.; Vrijling, J.K.; Vrouwenvelder, A.C.W.M. Methods for the estimation of loss of life due to floods: a literature review and a proposal for a new method. Nat. Hazards
**2008**, 46, 353–389. [Google Scholar] [CrossRef][Green Version] - Li, L.; Zhou, K. Research Status of Life Loss Estimation Methods Caused by Dam Breakdown. Adv. Water Resour.
**2006**, 26, 76–80. [Google Scholar] - Sun, Y.; Zhong, D.; Mingchao, L.I.; Ying, L.I. Theory and Application of Loss of Life Risk Analysis for Dam Break. J. Tianjin Univ., Sci. Technol.
**2010**, 16, 383–387. [Google Scholar] [CrossRef] - Peng, M.; Zhang, L.M. Analysis of human risks due to dam-break floods—part 1: A new model based on Bayesian networks. Nat. Hazards
**2012**, 64, 903–933. [Google Scholar] [CrossRef] - Peng, M.; Zhang, L.M. Analysis of human risks due to dam break floods—part 2: Application to Tangjiashan landslide dam failure. Nat. Hazards
**2012**, 64, 1899–1923. [Google Scholar] [CrossRef] - Wu, M.; Ge, W.; Li, Z.; Wu, Z.; Zhang, H.; Li, J.; Pan, Y. Improved Set Pair Analysis and Its Application to Environmental Impact Evaluation of Dam Break. Water
**2019**, 11, 82. [Google Scholar] [CrossRef] - Li, Z.; Li, W.; Ge, W. Weight analysis of influencing factors of dam break risk consequences. Nat. Hazard Earth Syst.
**2018**, 18, 3355–3362. [Google Scholar] [CrossRef][Green Version] - Gu, S.; Zheng, X.; Ren, L.; Xie, H.; Huang, Y.; Wei, J.; Shao, S. SWE-SPHysics simulation of dam break flows at South-Gate Gorges Reservoir. Water
**2017**, 9, 387. [Google Scholar] [CrossRef] - Ragas, A.M.; Huijbregts, M.A.; Henning De Jong, I.; Leuven, R.S. Uncertainty in environmental risk assessment: implications for risk-based management of river basins. Integr. Environ. Asses.
**2010**, 5, 27–37. [Google Scholar] [CrossRef] - Zhou, Z.Y.; Wang, X.L.; Sun, R.R.; Ao, X.F.; Sun, X.P.; Song, M.R. Study of the comprehensive risk analysis of dam-break flooding based on the numerical simulation of flood routing. Part II: Model application and results. Nat. Hazards
**2014**, 72, 675–700. [Google Scholar] [CrossRef] - Latrubesse, E.M.; Arima, E.Y.; Dunne, T.; Park, E.; Baker, V.R.; D’Horta, F.M.; Wight, C.; Wittmann, F.; Zuanon, J.; Baker, P.A. Damming the rivers of the Amazon basin. Nature
**2017**, 546, 363–369. [Google Scholar] [CrossRef] - Dutta, D.; Herath, S.; Musiake, K. A mathematical model for flood loss estimation. J. Hydrol.
**2003**, 277, 24–49. [Google Scholar] [CrossRef] - Zhou, K. Research on Analysis Method of Life Loss of Dam Failure; Nanjing Hydraulic Research Institute: Nanjing, China, 2006. [Google Scholar]
- Huang, D.; Yu, Z.; Li, Y.; Han, D.; Zhao, L.; Chu, Q. Calculation method and application of loss of life caused by dam break in China. Nat. Hazards
**2017**, 85, 39–57. [Google Scholar] [CrossRef] - Chen, S.Y.; Xue, Z.C.; Li, M.; Zhu, X.P. Variable sets method for urban flood vulnerability assessment. Sci. China
**2013**, 56, 3129–3136. [Google Scholar] [CrossRef] - Chen, S.Y.; Xue, Z.C.; Min, L.I. Variable Sets principle and method for flood classification. Sci. China Technol. Sci.
**2013**, 56, 2343–2348. [Google Scholar] [CrossRef] - Li, Z.; Li, W.; Ge, W.; Xu, H. Dam Breach Environmental Impact Evaluation Based on Set Pair Analysis-Variable Fuzzy Set Coupling Model. J. Tianjin U. (Sci. Technol.)
**2019**, 3, 269–276. [Google Scholar]

**Figure 4.**Sketch map of life-loss risk grade results and mortality rate in the “Large Population” group.

**Figure 5.**Sketch map of life-loss risk grade results and mortality rate in the “Small Population” group.

Categories | Indicators | Indicator Meaning | Selecting Reason |
---|---|---|---|

Hazards indicators X _{1} | X_{11} | Dam height H _{D}/(m) | Dam height and reservoir capacity often determine the severity of the flood, affecting the downstream submerged range and duration. With increasing flood intensity, the flexibility and stability of human bodies in the water get worse. |

X_{12} | Dam capacity C _{R}/(10^{5} m^{3}) | ||

X_{13} | Flood intensity S _{F}/(m^{2}/s) | ||

Exposure indicators X _{2} | X_{21} | Distance from dam L_{D}/(km) | The farther away from the dam location, the less the population is affected. The prompt warning will win time for the downstream evacuation, and the breaking time affects the prompt warning capability and the dynamic distribution of the downstream population. |

X_{22} | Time of warning T _{W}/(h) | ||

X_{23} | Time of breaking T _{B} | ||

Vulnerability indicators X _{3} | X_{31} | Population at risk P_{R}/(person) | The more the population at risk is, the greater the threat of life loss in the region is. The more serious the understanding of the severity of the flood, the higher the probability of escape. Self-rescue capability refers to the escape conditions and methods that may be taken when the dam breaks, expressed as the success rate of the rescue. |

X_{32} | Understanding level of flood severity U _{B} | ||

X_{33} | Self-rescue capability R_{C}/(%) |

Categories | Indicators | Level 1 | Level 2 | Level 3 | Level 4 | Level 5 |
---|---|---|---|---|---|---|

Slight | General | Medium | Serious | Extremely Serious | ||

Hazards indicator X _{1} | H_{D} (X_{11}) | 0–10 | 10–30 | 30–70 | 70–100 | >100 |

C_{R} (X_{12}) | 1–10 | 10–10^{2} | 10^{2}–10^{3} | 10^{3}–10^{4} | >10^{4} | |

S_{F} (X_{13}) | 0–0.5 | 0.5–4.6 | 4.6–12.0 | 12.0–15.0 | >15.0 | |

Exposure indicator X _{2} | L_{D} (X_{21}) | >50 | 50–20 | 20–10 | 10–5 | 5–0 |

T_{W} (X_{22}) | >1 | 1–0.75 | 0.75–0.5 | 0.5–0.25 | 0.25–0 | |

T_{B} (X_{23}) | daytime | weeknight | holiday night | early morning on workday | early morning on holiday | |

Vulnerability indicator X _{3} | P_{R} (X_{31}) | 1–10^{2} | 10^{2}–10^{3} | 10^{3}–10^{4} | 10^{4}–10^{5} | >10^{5} |

U_{B} (X_{32}) | very clear | clear | common | unclear | very unclear | |

R_{C} (X_{33}) | 100–80 | 80–60 | 60–40 | 40–20 | 20–0 |

No. | Dam Break Samples | Province | Date | Dam Type | Dam Height/m | Capacity/10^{5} m^{3} | Dam Break Time | Population at Risk |
---|---|---|---|---|---|---|---|---|

1 | Liujiatai | Hebei | 1963-08-08 | Clay core dam | 35.9 | 405.4 | 03:55 | 11,929 |

2 | Hengjiang | Guangdong | 1970-09-15 | Homogeneous earth dam | 48.4 | 787.9 | 08:00 | 2500 |

3 | Dongkoumiao | Zhejiang | 1971-06-02 | Homogeneous earth dam | 21.5 | 25.5 | 05:50 | 3500 |

4 | Lijiatsui | Gansu | 1973-04-29 | Homogeneous earth dam | 25.0 | 11.4 | 23:30 | 1034 |

5 | Shijiagou | Gansu | 1973-08-25 | Homogeneous earth dam | 28.6 | 8.6 | 05:30 | 300 |

6 | Banqiao | Henan | 1975-08-08 | Clay heart wall dam | 24.5 | 4920.0 | 01:00 | 180,000 |

7 | Shimantan | Henan | 1975-08-08 | Homogeneous earth dam | 25.0 | 918.0 | 00:00 | 72,422 |

8 | Gouhou | Qinghai | 1993-08-27 | Concrete face dam | 71.0 | 33.0 | 22:00 | 30,000 |

Indicator | X_{11} | X_{12} | X_{13} | X_{21} | X_{22} | X_{23} | X_{31} | X_{32} | X_{33} |
---|---|---|---|---|---|---|---|---|---|

Weights ${\omega}_{i}$ | 0.0135 | 0.0225 | 0.2282 | 0.0219 | 0.1722 | 0.0442 | 0.3210 | 0.0424 | 0.1341 |

No. | Dam Break Samples | Level Eigenvalue H | $\mathbf{Mean}\text{}\overline{\mathit{H}}$ | Loss of Life (people) | Mortality Rate (%) | |||
---|---|---|---|---|---|---|---|---|

$\mathit{\alpha}=\text{}1,\text{}\mathit{p}=\text{}1$ | $\mathit{\alpha}=\text{}1,\text{}\mathit{p}=\text{}2$ | $\mathit{\alpha}=\text{}2,\text{}\mathit{p}=\text{}1$ | $\mathit{\alpha}=\text{}2,\text{}\mathit{p}=\text{}2$ | |||||

1 | Liujiatai | 3.5850 | 3.6129 | 3.4846 | 3.6250 | 3.5769 | 60 | 0.50 |

2 | Hengjiang | 2.8345 | 3.0475 | 2.4262 | 2.6770 | 2.7463 | 20 | 0.80 |

3 | Dongkoumiao | 3.2366 | 3.2944 | 3.0324 | 3.1283 | 3.1729 | 154 | 4.40 |

4 | Lijiatsui | 3.8492 | 3.5430 | 4.4748 | 3.8165 | 3.9209 | 516 | 49.90 |

5 | Shijiagou | 3.3062 | 3.2151 | 3.3087 | 2.9489 | 3.1947 | 81 | 27.00 |

6 | Banqiao | 4.0103 | 3.9112 | 4.4435 | 4.2807 | 4.1614 | 15982 | 8.88 |

7 | Shimantan | 3.7725 | 3.6617 | 4.0104 | 3.8170 | 3.8154 | 1500 | 2.07 |

8 | Gouhou | 3.6652 | 3.6091 | 3.8517 | 3.7486 | 3.7186 | 320 | 1.07 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Li, W.; Li, Z.; Ge, W.; Wu, S.
Risk Evaluation Model of Life Loss Caused by Dam-Break Flood and Its Application. *Water* **2019**, *11*, 1359.
https://doi.org/10.3390/w11071359

**AMA Style**

Li W, Li Z, Ge W, Wu S.
Risk Evaluation Model of Life Loss Caused by Dam-Break Flood and Its Application. *Water*. 2019; 11(7):1359.
https://doi.org/10.3390/w11071359

**Chicago/Turabian Style**

Li, Wei, Zongkun Li, Wei Ge, and Sai Wu.
2019. "Risk Evaluation Model of Life Loss Caused by Dam-Break Flood and Its Application" *Water* 11, no. 7: 1359.
https://doi.org/10.3390/w11071359