# Optimal Selection of Short- and Long-Term Mitigation Strategies for Buildings within Communities under Flooding Hazard

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## Abstract

**:**

## 1. Introduction

## 2. Research Methodology

#### 2.1. Flood Risk and Mitigation Model

_{f}(IM = x) = is the total building fragility-based flood losses in monetary terms at intensity measure IM = x (replacement or repair cost), P(DS

_{i}|IM = x) = is the exceedance probability of DS

_{i}at IM = x, P(DS

_{i+1}) = is the exceedance probability of DS

_{i+1}at IM = x, Lr

_{ci}= is the cumulative replacement cost ratio corresponding to DS

_{i}, and V

_{t}= is the total building cost (replacement cost).

#### 2.2. Optimization Model

#### 2.2.1. Objective of the Optimization Model

#### 2.2.2. Constraints of the Optimization Model

## 3. Illustrative Example of Lumberton, NC

#### 3.1. Flood Hazard and Damage Analysis Results

#### 3.2. Comparative Analysis of Short- and Long-Term Mitigation Strategies

## 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 2.**The relationship between flood depth and failure probability (

**a**), exceedance probability (

**b**), loss of components (

**c**), and percentage total building loss (

**d**) for a one-story residential building on a slab-on-grade foundation.

**Figure 3.**The spatial location of Lumberton city and its buildings with respect to the state of North Carolina: (

**a**) the physical boundary of North Carolina; (

**b**) the spatial locations of the buildings within Lumberton color-coded based on their archetypes; (

**c**) the spatial location of Lumberton city with respect to the state of North Carolina.

**Figure 4.**The simulated flood hazard for the flooding event in Lumberton, NC after Hurricane Matthew in 2016 and the exposed buildings: (

**a**) the flood hazard map in terms of the flood extent and flood inundation measured from ground elevation (m); (

**b**) the flood-exposed buildings color-coded based on their archetypes.

**Figure 5.**Location of buildings based on long-term strategy implementation when the total investment is $20 million (

**a**), $50 million (

**b**), $150 million (

**c**), and $280 million (

**d**).

**Figure 6.**Locations of buildings based on short-term strategy implementation when the total investment is $20 million (

**a**), $50 million (

**b**), $150 million (

**c**), and $280 million (

**d**).

**Figure 7.**Locations of buildings based on short- and long-term strategy implementation when the total investment is $20 million (

**a**), $50 million (

**b**), $150 million (

**c**), and $280 million (

**d**).

Damage State Level | Functionality | Damage Scale | Loss Ratio |
---|---|---|---|

DS-0 | Operational | Insignificant | 0.00–0.03 |

DS-1 | Limited Occupancy | Slight | 0.03–0.15 |

DS-2 | Restricted Occupancy | Moderate | 0.15–0.50 |

DS-3 | Restricted Use | Extensive | 0.50–0.70 |

DS-4 | Restricted Entry | Complete | 0.70–1.00 |

**Table 2.**The number of exposed buildings by archetype along with their current replacement value and base flood loss.

Archetype | Number of Buildings | Total Current Replacement Value | Total Base Flood Losses |
---|---|---|---|

F1: One-Story Single-Family Residential Building | 665 | $37,527,864 | $10,097,519 |

F2: One-Story Multi-Family Residential Building | 1741 | $194,990,289 | $80,651,358 |

F3: Two-Story Single-Family Residential Building The | 7 | $1,059,617 | $316,074 |

F4: Two-Story Multi-Family Residential Building | 96 | $21,174,848 | $5,548,556 |

F5: Small Grocery Store/Gas Station with a Convenience Store | 157 | $62,855,685 | $7,921,982 |

F6: Multi-Unit Retail Building (Strip Mall) | 1 | $7,195,517 | $0 |

F7: Small Multi-Unit Commercial Building | 1 | $256,600 | $157,864 |

F8: Super Retail Center The | 2 | $408,318 | $176,194 |

F9: Industrial Building | 62 | $124,562,628 | $12,002,943 |

F10: One-Story School | 8 | $7,429,091 | $2,495,461 |

F11: Two-Story School | 3 | $23,456,627 | $3,621,603 |

F12: Hospital/Clinic The | 0 | $0 | $0 |

F13: Community Center (Place of Worship) | 44 | $23,381,452 | $6,720,040 |

F14: Office Building | 17 | $8,782,066 | $2,565,452 |

F15: Warehouse (Small/Large Box) | 53 | $40,975,016 | $860,940 |

Exceedance Probability of a DS (Fragility) | Number of Buildings (Total = 2858) | ||||
---|---|---|---|---|---|

DS0 | DS1 | DS2 | DS3 | DS4 | |

0% < P_DS < 20% | 2201 | 396 | 567 | 2071 | 2822 |

20% < P_DS < 40% | 5 | 72 | 115 | 355 | 25 |

40% < P_DS < 60% | 7 | 72 | 144 | 293 | 7 |

60% < P_DS < 80% | 30 | 108 | 290 | 121 | 3 |

80% < P_DS < 100% | 614 | 2209 | 1741 | 17 | 0 |

Number of Buildings Mitigated | |||||
---|---|---|---|---|---|

Budget (Million) | No Intervention | Elevate 5 ft (1.5 m) | Elevate 10 ft (3 m) | Total # of Mitigated Buildings | Economic Loss |

$0 | 2858 | 0 | 0 | 0 | $133,135,992 |

$3.5 | 2837 | 17 | 4 | 21 | $127,398,555 |

$7 | 2818 | 33 | 7 | 40 | $124,164,674 |

$10.5 | 2787 | 57 | 14 | 71 | $121,268,774 |

$14 | 2762 | 81 | 16 | 97 | $118,517,884 |

$ 20 | 2718 | 123 | 18 | 141 | $114,017,769 |

$50 | 2524 | 288 | 46 | 334 | $94,973,886 |

$150 | 1797 | 726 | 335 | 1061 | $52,520,789 |

$280 | 1120 | 1329 | 409 | 1738 | $14,704,547 |

Number of Buildings Mitigated | |||||||||
---|---|---|---|---|---|---|---|---|---|

Number of Buildings Surrounded by a Barrier of Height (Hb) | |||||||||

Budget (Million) | No Intervention | Hb = 0.4 m | Hb = 0.5 m | Hb = 0.7 m | Hb = 1.0 m | Hb = 1.3 m | Hb = 1.5 m | Total # of Mitigated Buildings | Economic Loss |

$0 | 2858 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | $133,135,992 |

$3.5 | 2827 | 0 | 0 | 5 | 4 | 7 | 15 | 31 | $124,118,022 |

$7 | 2767 | 1 | 0 | 9 | 16 | 26 | 39 | 91 | $119,675,195 |

$10.5 | 2707 | 1 | 0 | 12 | 29 | 47 | 62 | 151 | $116,597,842 |

$14 | 2638 | 1 | 0 | 14 | 37 | 74 | 94 | 220 | $114,059,986 |

$20 | 2514 | 2 | 1 | 16 | 47 | 116 | 162 | 344 | $110,680,315 |

$50 | 2027 | 33 | 8 | 70 | 146 | 264 | 311 | 832 | $107,224,597 |

$150 | 2027 | 33 | 8 | 70 | 146 | 264 | 311 | 832 | $107,224,597 |

$280 | 2027 | 33 | 8 | 70 | 146 | 264 | 311 | 832 | $107,224,597 |

Number of Buildings Mitigated | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Number of Buildings Surrounded by a Barrier of Height (Hb) | |||||||||||

Budget (Million) | No Intervention | Hb = 0.4 m | Hb = 0.5 m | Hb = 0.7 m | Hb = 1.0 m | Hb = 1.3 m | Hb = 1.5 m | Elevate 5 ft | Elevate 10 ft | Total # of Mitigated Buildings | Economic Loss |

$0 | 2858 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | $133,135,992 |

$3.5 | 2834 | 0 | 0 | 4 | 3 | 4 | 9 | 3 | 1 | 24 | $ 123,380,846 |

$7 | 2788 | 1 | 0 | 7 | 8 | 15 | 28 | 8 | 3 | 70 | $ 118,059,178 |

$10.5 | 2746 | 1 | 0 | 9 | 16 | 28 | 39 | 15 | 4 | 112 | $ 114,175,819 |

$14 | 2716 | 1 | 0 | 10 | 22 | 34 | 44 | 24 | 7 | 142 | $ 110,893,178 |

$20 | 2650 | 1 | 0 | 10 | 27 | 45 | 60 | 51 | 14 | 208 | $ 105,849,491 |

$50 | 2378 | 2 | 1 | 14 | 39 | 80 | 106 | 212 | 26 | 480 | $ 84,368,342 |

$150 | 1539 | 2 | 1 | 18 | 53 | 131 | 184 | 601 | 329 | 1319 | $ 39,452,522 |

$280 | 788 | 5 | 3 | 23 | 75 | 185 | 239 | 1091 | 446 | 2067 | $ 4,539,084 |

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**MDPI and ACS Style**

Gupta, H.S.; Nofal, O.M.; González, A.D.; Nicholson, C.D.; van de Lindt, J.W.
Optimal Selection of Short- and Long-Term Mitigation Strategies for Buildings within Communities under Flooding Hazard. *Sustainability* **2022**, *14*, 9812.
https://doi.org/10.3390/su14169812

**AMA Style**

Gupta HS, Nofal OM, González AD, Nicholson CD, van de Lindt JW.
Optimal Selection of Short- and Long-Term Mitigation Strategies for Buildings within Communities under Flooding Hazard. *Sustainability*. 2022; 14(16):9812.
https://doi.org/10.3390/su14169812

**Chicago/Turabian Style**

Gupta, Himadri Sen, Omar M. Nofal, Andrés D. González, Charles D. Nicholson, and John W. van de Lindt.
2022. "Optimal Selection of Short- and Long-Term Mitigation Strategies for Buildings within Communities under Flooding Hazard" *Sustainability* 14, no. 16: 9812.
https://doi.org/10.3390/su14169812