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

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## Abstract

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## 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

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**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 |

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**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