# A Quantitative Flood-Related Building Damage Evaluation Method Using Airborne LiDAR Data and 2-D Hydraulic Model

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Dataset

#### 2.1. Study Area

^{2}, consists of basin-shaped lakes and plains surrounded by mountains. Dongting Lake has an intricate system of feeder drainages distributed in a fan shape, but only has one outlet from which the Yangtze River continues downstream. Due to its special geographical location and complex morphology, this area has always been prone to flooding and requires intense seasonal management. A large amount of human, material, and financial resources are spent on dike management (during winter) and flood control (during summer). There are 266 dikes of different sizes stretching a total of 5812 km; the primary and secondary dikes are 3471 and 1509 km long, respectively. However, flood damages in the Dongting Lake area remain very severe: direct economic losses in 1996 and 1998 reached 15 billion yuan and 8.9 billion yuan, respectively. These impacts, along with the heavy repair and protection burden, have significantly limited the area’s socio-economic development.

^{2}(of which cultivated land accounts for 157.6 km

^{2}), the total dike length is 121.74 km, and the area’s population is 164,200. Due to its large population, the occurrence of a flood disaster would inevitably cause major losses to the local economy, so it is of great significance to carry out flood damage evaluations in this area.

#### 2.2. Dataset

## 3. Methods

#### 3.1. Building Extraction

#### 3.2. 2-D Hydraulic Model

^{2}+gh

^{2}/2,huv]T is the flux vector in the x direction; and g(q) = [hv,huv,hv

^{2}+gh

^{2}/2]T is the flux vector in the y direction. Here, h is the water depth; u and v are the vertical mean uniform flow velocity components of the x direction and the y direction, respectively; and g is the acceleration of gravity. The source–sink item b(q) is:

_{0x}and s

_{fx}are the river slope and friction slope in the x direction, respectively; s

_{0y}and s

_{fy}are the river slope and friction slope in the y direction, respectively; q

_{w}is the net rain depth per unit time; and the friction slope in the model is estimated by Manning’s formula.

^{j}is the length of the j

^{th}side in the unit; b*(q) is the source term. The flux in the direction normal ${\mathrm{F}}_{\mathrm{n}}^{\mathrm{j}}\left(\mathrm{q}\right)$, ${\mathrm{F}}_{\mathrm{n}}\left(\mathrm{q}\right)$ in short, is defined as follows:

^{−1}are the geometrical transform matrix and its inverse matrix, respectively, that is:

^{3}/s, the water level impact was minimum on Chenglingji. For the 30-year flood in 1954, the study determined that the maximum flood discharge flow of the Gongshuangcha flood diversion sluice was 3630 m

^{3}/s and the designed flood discharge water level was 33.10 m.

^{3}/s; when 31.63 < H < 32.60 m, the flow was at the submerged outflow stage and its rate was 3050 m

^{3}/s; when 32.60 < H < 33.65 m, a temporary flood diversion sluice was required.

#### 3.3. Construction of Building Flood Loss Rate Curves

#### 3.3.1. Building Classification

#### 3.3.2. Establishment of Flood Loss Rate

_{1}can be obtained by linear regression.

#### 3.4. Calculation of Building Replacement Cost

## 4. Results and Discussion

#### 4.1. Results

_{water level}= Max(H

_{cell1}+ H

_{cell2}+ …… + H

_{celln})/n, where n is the number of DEM cells inside the building and H

_{celln}is the water depth of the nth cell inside the building. Using this approach, the flood statistics for brick–concrete and brick–wood buildings at different water depths are shown in Table 3 and an example map is given in Figure 12.

_{brick−wood}and F

_{brick−concrete}represent the number of floors; H is the building height; P

_{brick−wood}and P

_{brick−concrete}are the per square meter replacement cost in yuan; and A

_{brick−wood}and A

_{brick−concrete}represent the footprint area of a single building. In this study, the feature roof coordinate points were expressed in 3-D coordinate points and the polygon area formed by the plane projection coordinates can be used to obtain the footprint area of the building.

_{brick−wood}and Y

_{brick−concrete}represent the flood loss rate function and H is the submerged water depth. Finally, the building flood damage in the study area can be calculated as follows:

#### 4.2. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 6.**The finite volume Ω. $\overline{\mathrm{x}}$ is left side of boundary, $\overline{\mathrm{y}}$ is right side of the boundary, ${\mathrm{f}}_{\mathrm{LR}}$ is flux, $\mathsf{\Phi}$ is the angle in the normal direction of the boundary.

**Figure 12.**Example map showing submerged buildings of both types; yellow indicates a water depth of 2–4 m, orange 4–6 m, and red >6 m.

**Figure 13.**Example of final flood loss distribution map for brick–wood buildings, each marked with their loss value.

**Figure 14.**Example of adjoining buildings. (

**a**) is vector data of buildings and (

**b**) is remote sensing image of buildings.

Building Type | Height (m) | Count |
---|---|---|

Brick–wood | <3 | 1577 |

3–6 | 18,302 | |

Brick–concrete | 6–9 | 6718 |

9–12 | 3259 | |

12–15 | 591 | |

15–18 | 90 | |

18–21 | 12 | |

21–24 | 2 |

Submerged Water Depth (m) | <1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 | 4.5 | 5.0 |
---|---|---|---|---|---|---|---|---|---|

Rural house flood loss rate (%) | 33 | 38 | 43 | 48 | 55 | 62 | 70 | 80 | 92 |

33 | 38 | 42 | 49 | 55 | 70 | 70 | 70 | 70 | |

30 | 52 | 68 | 80 | 87 | 90 | 90 | 90 | 90 | |

46 | 60 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | |

25 | 67 | 80 | 80 | 80 | 80 | 80 | 80 | 80 | |

27 | 53 | 86 | 86 | 86 | 86 | 86 | 86 | 86 | |

Urban house flood loss rate (%) | 3 | 6 | 9 | 12 | 16 | 19 | 19 | 19 | 19 |

Water Depth | Not Flooded | <1 m | 1–2 m | 2–3 m | 3–4 m | 4–5 m | 5–6 m | 6–7 m | 7–8 m | 8–9 m |
---|---|---|---|---|---|---|---|---|---|---|

Number of brick–concrete buildings | 0 | 197 | 413 | 1088 | 2046 | 3615 | 2568 | 677 | 59 | 9 |

Number of brick–wood buildings | 0 | 336 | 787 | 1575 | 2717 | 5617 | 5672 | 3070 | 99 | 6 |

Category | Items | Loss Rate of Assets | Average Loss Rate | ||||||
---|---|---|---|---|---|---|---|---|---|

[41] | [42] | [43] | [44] | [45] | [43] | [46] | |||

Industries, commerce, and enterprises | Industrial assets | 60 | 38 | 54 | 80 | 60 | 60 | - | 58.7 |

Commercial assets | 60 | 64 | 68 | 80 | 60 | 60 | - | 65.3 | |

Post and telecommunication assets | 60 | 60 | 50 | 60 | - | 93 | 85 | 68 | |

Rural power system assets | 50 | 90 | 80 | 80 | 100 | 89 | 85 | 82 | |

Rural broadcasting assets | 100 | 100 | 80 | - | - | - | 85 | 91.3 | |

Healthcare assets | - | 80 | 70 | - | - | - | 60 | 70 | |

Culture and sports assets | - | 80 | 70 | - | - | 73 | 60 | 70.8 | |

School assets | 80 | 80 | 70 | 80 | - | - | 60 | 70.8 | |

Township assets | 70 | 70 | 60 | 60 | 70 | - | 60 | 65 | |

Village team assets | - | 80 | 60 | 60 | 60 | - | 60 | 64 | |

Township enterprise assets | 70 | 80 | 70 | 70 | - | - | - | 72.5 | |

Transportation assets | 50 | 60 | 50 | - | - | 27.8 | 30 | 43.6 | |

Residential property | Agricultural equipment | 60 | - | 50 | 60 | 50 | - | - | 55 |

Private properties | 80 | 68 | 75 | 80 | 80 | 74 | 80 | 76.7 | |

Cattles and horses | 10 | - | 20 | 10 | 10 | - | 30 | 16 | |

Pigs | 30 | - | 40 | 30 | 30 | - | 60 | 38 | |

Fowl | 100 | - | 100 | - | - | - | 90 | 96.7 | |

Engineering facilities | Pump stations | 50 | 60 | - | - | - | - | - | 55 |

Culverts and sluices | 50 | 20 | - | - | - | - | - | 35 | |

Basic farmland facilities | 50 | - | 100 | - | - | - | - | 75 | |

Roads and bridges | 50 | - | 50 | 50 | 50 | - | - | 50 | |

Agriculture, forestry, and fisheries | Agriculture | 100 | 100 | 100 | 100 | 100 | 89.3 | 90 | 97 |

Forestry | 20 | 57 | 52 | 25 | 20 | 51.9 | 37.7 | ||

Fisheries | 100 | 89 | 68 | 100 | 100 | 68.1 | 80 | 86.4 | |

Averages | 61.90 | 70.89 | 65.32 | 64.06 | 60.77 | 68.61 | 67.67 | 64.19 |

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## Share and Cite

**MDPI and ACS Style**

Shen, D.; Qian, T.; Chen, W.; Chi, Y.; Wang, J.
A Quantitative Flood-Related Building Damage Evaluation Method Using Airborne LiDAR Data and 2-D Hydraulic Model. *Water* **2019**, *11*, 987.
https://doi.org/10.3390/w11050987

**AMA Style**

Shen D, Qian T, Chen W, Chi Y, Wang J.
A Quantitative Flood-Related Building Damage Evaluation Method Using Airborne LiDAR Data and 2-D Hydraulic Model. *Water*. 2019; 11(5):987.
https://doi.org/10.3390/w11050987

**Chicago/Turabian Style**

Shen, Dingtao, Tianlu Qian, Wenlong Chen, Yao Chi, and Jiechen Wang.
2019. "A Quantitative Flood-Related Building Damage Evaluation Method Using Airborne LiDAR Data and 2-D Hydraulic Model" *Water* 11, no. 5: 987.
https://doi.org/10.3390/w11050987