# Risk Assessment for Critical Flood Height of Pedestrian Escape in Subway Station

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model and Method

#### 2.1. Model of Subway Station

#### 2.2. Construction of Pedestrian Number and Speed Factor Based on Monte Carlo

^{2}/person. By setting a larger range of pedestrian density and expanding the range of evacuated pedestrians, the applicability and correctness of the model are improved. The specific parameters can be determined according to the specific conditions of the city and the station. Assuming that the pedestrian density is 1.5 m

^{2}/person, the total number of pedestrians involved in the evacuation is 20,731.4/1.5 = 13,821.

^{2}/person). The training model is more feasible by setting a larger range of pedestrian’s density to expand the range of evacuated pedestrians. For the walking speed, in the event of a disaster, it should be taken into account that some pedestrians are running at a faster pace or that some injured pedestrians are walking slower than normal. Therefore, the basic walking speed of each group is multiplied by the speed factor, and the coefficient range is between 0.5 and 3. Setting a larger speed factor range can meet the fast or slow walking speeds of pedestrians in different states. In total, 30 groups of data parameters were input and simulated, and the simulated parameters and evacuation time of each group are shown in Table 3.

#### 2.3. Introduction to the Principle of Support Vector Machine

## 3. Result Analysis

#### 3.1. Analysis of Pedestrian Escape Time and Number in Each Sample

#### 3.2. Analysis of Pedestrian Passage Time and Number at Different Exits

#### 3.3. Calculation of Minimum Pedestrian Escape Speed Based on SVM

#### 3.4. Calculation of Critical Water Level Height Based on Minimum Escape Speed

^{2}), W represents the buoyancy of the pedestrian in flood, and the specific expression of buoyancy W is:

^{2}, ρ = 1000 kg/m3, f = 0.5 [35], are substituted into Equations (3) and (4). The friction force between the pedestrian and the ground at different flood heights is calculated and compared with the flood resistance of the pedestrian. Table 11 shows the comparison results, and Figure 22, Figure 23 and Figure 24 show the comparison curve.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 14.**(

**a**) Density of export pedestrians during saturation period; (

**b**) Density of export pedestrians in unsaturated period.

**Figure 19.**Hydrodynamic pressure of adult walking at a minimum safe speed at different flood heights.

**Figure 20.**Hydrodynamic pressure of child walking at a minimum safe speed at different flood heights.

**Figure 21.**Hydrodynamic pressure of elder walking at a minimum safe speed at different flood heights.

Pedestrian Group | Distribution | Min (m) | Max (m) | Average (m) | Standard Deviation (m) |
---|---|---|---|---|---|

Adult | Normal distribution | 1.55 | 1.85 | 1.73 | 0.05 |

Child | Normal distribution | 1.0 | 1.6 | 1.4 | 0.05 |

Elder | Normal distribution | 1.5 | 1.75 | 1.61 | 0.05 |

Pedestrian Group | Distribution | Min (m) | Max (m) | Average (m) | Standard Deviation (m) |
---|---|---|---|---|---|

Adult | Normal distribution | 0.42 | 0.55 | 0.48 | 0.03 |

Child | Normal distribution | 0.34 | 0.48 | 0.38 | 0.03 |

Elder | Normal distribution | 0.39 | 0.51 | 0.44 | 0.03 |

Case | Space Occupation (m^{2}/pers) | Density (pers/m^{2}) | Speed Factor | Number of Pedestrians (per) | Evacuation Time (s) |
---|---|---|---|---|---|

1 | 0.844 | 1.185 | 1.241 | 24,567 | 897.6 |

2 | 3.704 | 0.270 | 0.972 | 5597 | 410 |

3 | 4.216 | 0.237 | 0.959 | 4913 | 396.9 |

4 | 2.456 | 0.407 | 2.064 | 8438 | 279.9 |

5 | 1.448 | 0.691 | 0.703 | 14,325 | 1006.8 |

6 | 4.352 | 0.230 | 2.439 | 4768 | 152.3 |

7 | 1.694 | 0.509 | 2.323 | 12,240 | 286.4 |

8 | 3.760 | 0.266 | 1.266 | 5515 | 307.3 |

9 | 3.216 | 0.311 | 1.777 | 6447 | 274.6 |

10 | 1.968 | 0.508 | 2.487 | 10,532 | 280.2 |

11 | 0.652 | 1.534 | 1.447 | 31,802 | 870.1 |

12 | 4.152 | 0.241 | 1.832 | 4996 | 222.6 |

13 | 1.876 | 0.533 | 2.594 | 11,053 | 271.9 |

14 | 1.563 | 0.640 | 2.167 | 13,266 | 327.6 |

15 | 1.048 | 0.954 | 1.968 | 19,778 | 456.3 |

16 | 0.928 | 1.078 | 1.253 | 22,348 | 753.4 |

17 | 2.476 | 0.404 | 1.076 | 8375 | 491.5 |

18 | 3.360 | 0.298 | 0.987 | 6178 | 439.7 |

19 | 4.416 | 0.226 | 1.297 | 4685 | 295.9 |

20 | 3.296 | 0.303 | 1.589 | 6282 | 281.1 |

21 | 0.624 | 1.603 | 2.808 | 33,232 | 480 |

22 | 2.500 | 0.400 | 0.962 | 8293 | 560.8 |

23 | 4.120 | 0.243 | 2.949 | 5033 | 134 |

24 | 2.972 | 0.336 | 0.778 | 6966 | 623.7 |

25 | 3.720 | 0.269 | 1.522 | 5577 | 274 |

26 | 1.232 | 0.812 | 1.156 | 16,834 | 668.1 |

27 | 4.048 | 0.247 | 2.278 | 5121 | 201.3 |

28 | 3.028 | 0.330 | 0.794 | 6833 | 563.3 |

29 | 4.064 | 0.246 | 0.927 | 5100 | 400.6 |

30 | 0.740 | 1.351 | 1.770 | 28,008 | 648 |

Number of Pedestrians | Group | Sample Serial Number |
---|---|---|

0~10,000 | A | 2, 3, 4, 6, 8, 9, 12, 17, 18, 19, 20, 22, 23, 24, 25, 27, 28, 29 |

10,000~20,000 | B | 5, 7, 10, 13, 14, 15, 26 |

More than 20,000 | C | 1, 11, 16, 21, 30 |

Exit | Number of Pedestrians (per) | Proportion (%) | Evacuation Time (s) |
---|---|---|---|

1 | 448 | 8.90 | 51 |

2 | 309 | 6.14 | 50 |

3 | 586 | 11.64 | 59 |

4 | 112 | 2.23 | 26 |

5 | 1292 | 25.67 | 105 |

6 | 658 | 13.07 | 88 |

7 | 441 | 8.76 | 68 |

8 | 307 | 6.10 | 135 |

9 | 271 | 5.38 | 27 |

10 | 502 | 9.98 | 76 |

11 | 39 | 0.78 | 29 |

12 | 68 | 1.35 | 32 |

Exit | Number of Pedestrians (per) | Proportion (%) | Evacuation Time (s) |
---|---|---|---|

1 | 544 | 7.97 | 202 |

2 | 399 | 5.84 | 165 |

3 | 885 | 12.95 | 259 |

4 | 133 | 1.95 | 79 |

5 | 1592 | 23.30 | 450 |

6 | 1109 | 16.23 | 404 |

7 | 536 | 7.84 | 206 |

8 | 484 | 7.08 | 536 |

9 | 375 | 5.49 | 108 |

10 | 701 | 10.26 | 259 |

11 | 23 | 0.33 | 51 |

12 | 52 | 0.76 | 66 |

Escape Result | Sample Serial Number | |
---|---|---|

Failed to escape (time ≤ 330) | Success | 4, 6,7, 8, 9, 10, 12, 13,14, 19 20, 23, 25, 27 |

Escape success (time > 330) | Fail | 1, 2, 3, 5, 11, 15, 16, 17, 18, 21, 22, 24, 26, 28, 29, 30 |

Sample Serial Number | Simulation Results | SVM Classification Results |
---|---|---|

21 | Fail | Fail |

22 | Fail | Fail |

23 | Success | Success |

24 | Fail | Fail |

25 | Success | Success |

26 | Fail | Fail |

27 | Success | Success |

28 | Fail | Fail |

29 | Fail | Fail |

30 | Fail | Fail |

Flood Height (cm) | Adult | Child | Elder |
---|---|---|---|

10 | 3.6 N | 2.0 N | 2.9 N |

20 | 6.4 N | 6.7 N | 9.7 N |

30 | 21.6 N | 15.3 N | 18.8 N |

40 | 40.9 N | 30.8 N | 36.6 N |

50 | 67.9 N | 48.4 N | 59.8 N |

60 | 94.9 N | 73.9 N | 86.3 N |

70 | 116.5 N | 116.4 N | 124.2 N |

80 | 162.3 N | 175.8 N | 172.7 N |

90 | 261.3 N | 252.0 N | 269.0 N |

100 | 372.2 | 275.6 | 386.2 |

Flood Height (cm) | Adult | Child | Elder |
---|---|---|---|

10 | 0.00136 m^{3} | 0.00106 m^{3} | 0.00124 m^{3} |

20 | 0.0024 m^{3} | 0.0019 m^{3} | 0.0022 m^{3} |

30 | 0.0036 m^{3} | 0.0031 m^{3} | 0.0034 m^{3} |

40 | 0.0054 m^{3} | 0.0047 m^{3} | 0.0051 m^{3} |

50 | 0.0073 m^{3} | 0.0062 m^{3} | 0.0069 m^{3} |

60 | 0.0092 m^{3} | 0.0080 m^{3} | 0.0087 m^{3} |

70 | 0.0113 m^{3} | 0.0104 m^{3} | 0.0109 m^{3} |

80 | 0.014 m^{3} | 0.0128 m^{3} | 0.0136 m^{3} |

90 | 0.017 m^{3} | 0.0150 m^{3} | 0.0164 m^{3} |

100 | 0.02 m^{3} | 0.0170 m^{3} | 0.0190 m^{3} |

**Table 11.**Friction and flood resistance of all groups when walking at a critical speed at different flood heights.

Flood Height (cm) | Adult | Child | Elder | |||
---|---|---|---|---|---|---|

Friction | Flood Resistance | Friction | Flood Resistance | Friction | Flood Resistance | |

10 | 308.4 | 3.6 | 201.5 | 2.0 | 266.8 | 2.9 |

20 | 303.3 | 6.4 | 197.4 | 6.7 | 262.1 | 9.7 |

30 | 297.4 | 21.6 | 191.5 | 15.3 | 256.2 | 18.8 |

40 | 288.6 | 40.9 | 183.7 | 30.8 | 247.9 | 36.6 |

50 | 279.3 | 67.9 | 176.4 | 48.4 | 239.1 | 59.8 |

60 | 269.9 | 94.9 | 167.5 | 73.9 | 230.3 | 86.3 |

70 | 259.7 | 116.5 | 155.8 | 116.4 | 219.5 | 124.2 |

80 | 246.4 | 162.3 | 144.0 | 175.8 | 206.2 | 172.7 |

90 | 231.7 | 261.3 | 133.2 | 252.0 | 192.5 | 269.0 |

100 | 217.0 | 372.2 | 123.4 | 275.6 | 179.8 | 386.2 |

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**MDPI and ACS Style**

Tang, Y.; Zhou, T.; Zhong, Y.; Hu, S.; Lin, J.; Lin, Z.; Liu, H.; Liu, B.; Zhao, Y.; Wang, Y.; Lin, H. Risk Assessment for Critical Flood Height of Pedestrian Escape in Subway Station. *Water* **2022**, *14*, 3409.
https://doi.org/10.3390/w14213409

**AMA Style**

Tang Y, Zhou T, Zhong Y, Hu S, Lin J, Lin Z, Liu H, Liu B, Zhao Y, Wang Y, Lin H. Risk Assessment for Critical Flood Height of Pedestrian Escape in Subway Station. *Water*. 2022; 14(21):3409.
https://doi.org/10.3390/w14213409

**Chicago/Turabian Style**

Tang, Yi, Tianzhong Zhou, Youxin Zhong, Shengbin Hu, Jing Lin, Zhiyu Lin, Hongwei Liu, Baohua Liu, Yanlin Zhao, Yixian Wang, and Hang Lin. 2022. "Risk Assessment for Critical Flood Height of Pedestrian Escape in Subway Station" *Water* 14, no. 21: 3409.
https://doi.org/10.3390/w14213409