# Innovative Vulnerability and Risk Assessment of Urban Areas against Flood Events: Prognosis of Structural Damage with a New Approach Considering Flow Velocity

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Basic Elements of the Procedure

#### 2.1. Damage Data

#### 2.1.1. EDAC Flood Damage Database

_{max}≈ 2.5 m/s, which corresponds to moderate water movement typical of river floods. Data on damage cases caused by higher flow velocities (such as those that occur with flash floods) were not available. Therefore, an unconventional but innovative approach had to be implemented in the INNOVARU project. The damage data of the 2011 Tohoku earthquake tsunami were included, assuming that tsunamis represent an extreme form of (cyclic) flooding.

#### 2.1.2. Tsunami Damage Data

#### 2.2. Investigation Areas

^{®}) were integrated into EQUIP and linked to the internal database of the program (Figure 2). The database fields can be activated in the program by simply selecting of the relevant building plan. Predefined selection fields and the option of entering free text enable exceedingly efficient data input. The various background maps that can be activated (satellite, street map or hybrid view), in combination with the display of the present location (on GPS-capable tablet PCs), simplify orientation in the investigation area. For the identification and classification of flood-prone buildings in the investigation areas, and an established building typology approach (cf. [12,30]) is used.

^{®}.

#### 2.3. Flood Scenarios

## 3. Flood Damage and Vulnerability of Buildings

#### 3.1. Damage Scale for Flooding

#### 3.2. Flood Vulnerability Classes

**H**igh

**W**ater”) usually consist of reinforced concrete or masonry in a flood-resistant design and are characterized by a separation of vulnerable building parts from the flood water level, for instance, by raising the ground floor onto storey-high columns of steel or reinforced concrete [10]. Vulnerability class HW-F (newly introduced in [31]) is related to constructions such as floating homes (e.g., [36]), which represent a construction method specially adapted to floods.

_{m}) of similar impact levels.

_{m}) for the various main building types depending on the impact (inundation) level. Owing to these differences, damageability levels could be defined that are assumed to be typical for the vulnerability classes HW-A to HW-D. New or previously unclassified construction methods are classified based on their mean damage grades (D

_{m}) for the corresponding impact level [10].

#### 3.3. Prognosis of Structural Damage

_{m}) in the original interval (1 to 5; D1 to D5) depending on the vulnerability class.

#### 3.4. Loss Prediction

_{m}) into relative losses. For all of the developed damage functions, the number of storeys and the presence of a cellar is considered [9]. An exponential approach is selected as a mathematical formulation of the various specific damage functions [9,10,23].

## 4. Improved Prognosis of Structural Damages

#### 4.1. Consideration of Inundation Level and Flow Velocity

_{m}) of the clustered damage data for vulnerability classes HW-B and HW-C is shown in Figure 6a,b, respectively. Due to the simplified relationship between inundation level and flow velocity, the tsunami damage data follow a clearly defined area with respect to the impact level. However, assuming a plausible mathematical regression model, a realistic damage model can be derived. For this purpose, the previous approach of a hyperbolic tangent function for prognosis of the mean damage grades (D

_{m}) is extended to intervals 1 to 6 (D1 to D6) according to Equation (4).

- Variant V1 only converts the existing approach from [18] to the six-stage damage scale;
- Variant V2 uses the inundation level (h
_{gl}) and flood intensity (I_{fl}= h_{gl}× v_{fl}) from the so-called “Swiss model”, representing a combination of inundation level and flow velocity but without an extended physical background; - Variant V3 includes the inundation level (h
_{gl}) and the momentum flux (h_{gl}× v_{fl}^{2}) (which is related to the hydrodynamic forces); - Variant V4 considers only the momentum flux as a physically based input parameter;
- Variant V5 is similar to Variant 3 but weights the influence of the inundation level in a differentiated way.

_{gl}) + flood intensity (h

_{gl}× v

_{fl}):

_{gl}) + momentum flux (h

_{gl}× v

_{fl}

^{2}):

_{gl}× v

_{fl}

^{2}):

_{gl}) + momentum flux (h

_{gl}× v

_{fl}

^{2}):

_{1}, C

_{2}, >C

_{3}–Regression parameters (coefficients)

_{m}) starts with values >D1, even at the 0 m inundation level above ground level, as groundwater inundation could also cause structural damage. Figure 7 graphically demonstrates that there are (practically) implausible relationships in some variants. Here, the physically consistent variants prove to be problematic with respect to their qualitative course (cf. [11]):

_{gl}= 0 m with increasing flow velocities (which cannot occur here).

_{fl}= 0 m/s.

#### 4.2. Consideration of Inundation Level, Flow Velocity and the Number of Storeys

_{gl}) the mean damage grade (D

_{m}) tends to decrease with an increasing number of storeys (n

_{st}) due to the higher static requirements of multi-storey buildings.

_{gl}≥ 3.5 m), some outliers are visible.

_{m}), which is considered and weighted via the natural logarithm in the corresponding term in the simplified vulnerability functions acc. to Equation (10).

_{fl}= 0 and that the vulnerability functions presented in Section 4.1 are also valid for two-storey buildings.

_{st}> 5 are also possible.

_{gl}) + flood intensity (h

_{gl}× v

_{fl}):

_{gl}) + momentum flux (h

_{gl}× v

_{fl}

^{2}):

_{gl}× v

_{fl}

^{2}):

_{gl}) + momentum flux (h

_{gl}× v

_{fl}

^{2}):

_{1}, C

_{2}, C

_{3}, C

_{4}– Regression parameters (coefficients).

## 5. Validation of the Improved Model

_{fl}= 0 m/s).

_{m}) for the 2002 flood (see Section 2.3) were calculated for the individual affected buildings in the investigation areas. Because a comparison with the observed damage only makes sense for a larger number of buildings, the calculation results are aggregated at the level of land-use units. Therefore, comparison of the calculated and observed mean damage grades (MD

_{m}) in the land-use areas (which are composed by the calculated mean damage grades (D

_{m}) or the observed damage grades (D

_{i}) for the individual buildings) is based on the land-use areas according to the “Official topographic-cartographic information system” (Amtliches Topographisch-Kartographisches Informationssystem-ATKIS

^{®}) for Germany (cf. procedure in [10]).

^{®}land-use areas suitable for the investigation areas of Döbeln, Eilenburg, Flöha and Grimma are available from previous research projects with state of the year 2009.

^{®}land-use areas are much more coarsely or overlapping subdivided and therefore not suitable for aggregation of the calculation results at the land-use level. In contrast, the usable areas that are currently contained in the datasets of the “Official real estate cadaster information system-ALKIS

^{®}” (Amtliches Liegenschaftskataster_Informationssystem) are much more finely divided. Therefore, these are also considered unsuitable for validation purposes. Alternatively, the built-up areas were subdivided independently into area units that provide a sufficient number of buildings/damage cases for the Pirna and Freital investigation areas.

_{m,calc}) in comparison with the observed mean damage grades (MD

_{m,obs}) for the investigated variants for Grimma for Level II.

_{gl}= 0 m (e.g., with penetrating groundwater), variant V1 shows an increase in the mean damage grade (D

_{m}) as the flow velocity increases (see Figure 7a). Because practically no increase in the flow velocity can occur at h

_{gl}= 0 m, no increase in D

_{m}should be forecast here either. In contrast, variant V4 predicts a constant mean damage grade (D

_{m}) with standing water (v

_{fl}= 0 m/s), even with an increase in the inundation level (see Figure 7d).

_{gl}× v

_{fl}

^{2}).

_{m,calc}) for variant V2 at Levels I and II and the observed mean damage grades (MD

_{m,obs}) for the investigation areas of Döbeln, Eilenburg, Freital and Pirna. A slight increase in the calculated mean damage grades (MD

_{m,calc}) caused by the flow velocity at Level II is visible.

## 6. Conclusions

## 7. Outlook

_{m}), and a large scatter of flood damage cannot be considered.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Investigation areas in the Free State of Saxony (cf. [11]).

**Figure 2.**EDAC EQUIP survey tool for the documentation of building parameters (with background maps from Bing Maps

^{®}).

**Figure 4.**Inundation levels and flow velocities in the investigation areas: (

**a**) Grimma; (

**b**) Freital; (

**c**) Pirna.

**Figure 7.**Vulnerability functions for flood vulnerability classes depending on inundation level (h

_{gl}) and flow velocity (v

_{fl}): (

**a**) variant V1; (

**b**) variant V2; (

**c**) variant V3; (

**d**) variant V4; (

**e**) variant V5 (taken from [11]).

**Figure 8.**Damage data and simplified vulnerability functions for HW-C considering the inundation level above ground level (h

_{gl}) and the number of storeys (n

_{st}) (taken from [11]).

**Figure 9.**Vulnerability functions (variant V2) depending on inundation level (h

_{gl}), flow velocity (v

_{fl}) and number of storeys (n

_{st}): (

**a**) HW-A; (

**b**) HW-B; (

**c**) HW-C; (

**d**) HW-D (variant V3 is shown in [11]).

**Figure 10.**Comparison of the calculated mean damage grades MD

_{m,calc}in the land-use areas (micro-scale damage calculation) and the observed damages (MD

_{m,obs}) in Grimma (Level 2): (

**a**) variant V1; (

**b**) variant V2; (

**c**) variant V3; (

**d**) variant V4; (

**e**) variant V5; (

**f**) observed damage.

**Figure 12.**Comparison of the calculated mean damage grades (MD

_{m,calc}) in the land-use areas and the observed damage (MD

_{m,obs}) in the Döbeln investigation area: (

**a**) calculated mean damage grades (MD

_{m,calc}), Level I; (

**b**) calculated mean damage grades (MD

_{m,calc}), Level II; (

**c**) observed mean damage grades (MD

_{m,obs}).

**Figure 13.**Comparison of the calculated mean damage grades (MD

_{m,calc}) in the land-use areas and the observed damages (MD

_{m,obs}) in the Eilenburg investigation area: (

**a**) calculated mean damage grades (MD

_{m,calc}), Level I; (

**b**) calculated mean damage grades (MD

_{m,calc}), Level II; (

**c**) observed mean damage grades (MD

_{m,obs}).

**Figure 14.**Comparison of the calculated mean damage grades (MD

_{m,calc}) in the land-use areas and the observed damages (MD

_{m,obs}) in the Freital investigation area: (

**a**) calculated mean damage grades (MD

_{m,calc}), Level I; (

**b**) calculated mean damage grades (MD

_{m,calc}), Level II; (

**c**) observed mean damage grades (MD

_{m,obs}).

**Figure 15.**Comparison of the calculated mean damage grades (MD

_{m,calc}) in the land-use areas and the observed damage grades (MD

_{m,obs}) in the Pirna investigation area: (

**a**) calculated mean damage grades (MD

_{m,calc}), Level I; (

**b**) calculated mean damage grades (MD

_{m,calc}), Level II; (

**c**) observed mean damage grades (MD

_{m,obs}).

**Table 1.**Overview of the investigation areas (for interim state cf. [11]).

Investigation Area | Buildings Inspected (Affected) ^{1} | Damage Cases: SAB ^{2} (EDAC) ^{3} | Year(s) of Survey | |
---|---|---|---|---|

Residential | Total | |||

Pirna | 1209 (938) | 1405 (1067) | 1148 (366) | 2008 |

Grimma | 773 (690) | 1280 (1186) | 616 (306) | 2009, 2017 |

Freital | 1048 (946) | 2096 (1842) | 865 (277) | 2019 |

Eilenburg | 1041 (1028) | 2184 (2149) | 961 (551) | 2003, 2004 |

Döbeln | 832 (788) | 1429 (1348) | 681 (276) | 2004 |

Flöha | 734 (721) | 1872 (1828) | 582 (154) | 2009 |

^{1}Acc. to flood scenarios (see Section 2.3).

^{2}Reported to Saxonian Relief Bank (SAB) [14].

^{3}Included in EDAC flood damage database.

**Table 2.**Overview of the 2002 flood scenarios (for interim state cf. [11]).

Investigation Area | 2D Model Approach | Grid Size (m × m) ^{1} | Inundation Level h_{gl} (m) ^{2} | Flow Velocity v_{fl} (m/s) ^{2} |
---|---|---|---|---|

Pirna | detailed | variable | 0–4.1 | 0–5.3 |

Grimma | detailed | 5 × 5 (h_{gl})1 × 1 (v _{fl}) | 0–5.0 | 0–2.7 |

Freital | detailed | 2 × 2 | 0–3.5 | 0–4.5 |

Eilenburg | mean roughness | 25 × 25 | 0–3.5 | 0–1.9 |

Döbeln | detailed | variable | 0–4.7 | 0–2.4 |

Flöha | mean roughness | 5 × 5 | 0–2.8 | 0–2.3 |

^{1}Output from hydraulic calculation.

^{2}At building location.

Damage Grade | Damage | Description | Drawing | Example ^{1} | |
---|---|---|---|---|---|

Structural | Non-Structural | ||||

D1 | none | light | moisture damage, dirt | ||

D2 | light | moderate | slight cracking of loadbearing walls doors/windows pushed in washing out of foundations contamination replacement of finshings necessary | ||

D3 | moderate | heavy | larger cracking in loadbearing walls and slabs settlements collapse of non-loadbearing walls replacement of non-loadbearing building elements necessary | ||

D4 | heavy | very heavy | collapse of loadbearing walls, slabs replacement of loadbearing walls, slabs | ||

D5 | very heavy | very heavy | collapse of larger parts of building | ||

D6 | very heavy | very heavy | dislocation: building completely washed away, toppled or displaced from foundation |

^{1}Photos of D1 to D6 damage taken by EDAC (D1 to D5: flood in 2002; D6: flood in 2021, cf. [3]).

**Table 4.**Classification of building types in vulnerability classes and identification of ranges of scatter [31].

Building Type | Vulnerability Class HW- | |||||
---|---|---|---|---|---|---|

A | B | C | D | E | F | |

Clay | ||||||

Prefabricated timber frame | ||||||

Timber frame with masonry or clay infill | ||||||

Masonry | ||||||

Reinforced concrete | ||||||

Flood-resistant design | ||||||

Flood-evasive design |

Variant | VC | Coefficients | Coefficient of Determination (R^{2}) | ||
---|---|---|---|---|---|

C_{1} | C_{2} | C_{3} | |||

V1 | HW-A ^{1} | 0.351 | −0.730 | - | - |

HW-B | 0.292 | −0.853 | - | 0.72 | |

HW-C | 0.238 | −0.914 | - | 0.84 | |

HW-D ^{2} | 0.189 | −0.920 | - | 0.76 | |

V2 | HW-A ^{1} | 0.255 | 0.066 | −0.572 | - |

HW-B | 0.135 | 0.053 | −0.621 | 0.78 | |

HW-C | 0.062 | 0.042 | −0.647 | 0.88 | |

HW-D ^{2} | 0.035 | 0.030 | −0.650 | 0.84 | |

V3 | HW-A ^{1} | 0.230 | 0.017 | −0.496 | - |

HW-B | 0.143 | 0.011 | −0.571 | 0.79 | |

HW-C | 0.090 | 0.007 | −0.623 | 0.85 | |

HW-D ^{2} | 0.071 | 0.004 | −0.650 | 0.79 | |

V4 | HW-A ^{1} | 0.017 | 0.105 | - | - |

HW-B | 0.013 | −0.250 | - | 0.74 | |

HW-C | 0.009 | −0.456 | - | 0.83 | |

HW-D | 0.005 | −0.512 | - | 0.78 | |

V5 | HW-A ^{1,2} | 0.578 | 0.017 | −0.800 | - |

HW-B ^{2} | 0.381 | 0.011 | −0.800 | 0.79 | |

HW-C ^{2} | 0.264 | 0.007 | −0.800 | 0.86 | |

HW-D ^{2} | 0.227 | 0.004 | −0.800 | 0.80 |

^{1}For HW-A, the coefficients were extrapolated from vulnerability classes HW-B, HW-C and HW-D.

^{2}Coefficients slightly modified.

Variant | VC | Coefficients | |||
---|---|---|---|---|---|

C_{1} | C_{2} | C_{3} | C_{4} | ||

V1 | HW-A | 0.351 | −0.155 | −0.622 | - |

HW-B | 0.292 | −0.064 | −0.809 | - | |

HW-C | 0.238 | −0.127 | −0.829 | - | |

HW-D | 0.189 | −0.074 | −0.869 | - | |

V2 | HW-A | 0.255 | 0.066 | −0.155 | −0.465 |

HW-B | 0.135 | 0.053 | −0.064 | −0.577 | |

HW-C | 0.062 | 0.042 | −0.127 | −0.559 | |

HW-D | 0.035 | 0.030 | −0.074 | −0.599 | |

V3 | HW-A | 0.230 | 0.017 | −0.155 | −0.388 |

HW-B | 0.143 | 0.011 | −0.064 | −0.527 | |

HW-C | 0.090 | 0.007 | −0.127 | −0.535 | |

HW-D | 0.071 | 0.004 | −0.074 | −0.599 | |

V4 | HW-A | 0.017 | −0.155 | 0.212 | - |

HW-B | 0.013 | −0.064 | −0.206 | - | |

HW-C | 0.009 | −0.127 | −0.368 | - | |

HW-D | 0.005 | −0.074 | −0.460 | - | |

V5 | HW-A | 0.578 | 0.017 | −0.155 | −0.693 |

HW-B | 0.381 | 0.011 | −0.064 | −0.756 | |

HW-C | 0.264 | 0.007 | −0.127 | −0.712 | |

HW-D | 0.227 | 0.004 | −0.074 | −0.749 |

Investigation Area | MAE | RMSE | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

V1 | V2 | V3 | V4 | V5 | V1 | V2 | V3 | V4 | V5 | |

Döbeln | 0.38 | 0.34 | 0.41 | 0.44 | 0.41 | 0.48 | 0.48 | 0.51 | 0.54 | 0.51 |

Eilenburg | 0.48 | 0.41 | 0.49 | 0.51 | 0.50 | 0.75 | 0.68 | 0.70 | 0.68 | 0.71 |

Flöha | 0.23 | 0.26 | 0.34 | 0.44 | 0.33 | 0.32 | 0.34 | 0.40 | 0.50 | 0.40 |

Freital | 0.28 | 0.24 | 0.28 | 0.43 | 0.26 | 0.42 | 0.38 | 0.41 | 0.52 | 0.40 |

Grimma | 0.40 | 0.39 | 0.33 | 0.37 | 0.34 | 0.51 | 0.52 | 0.46 | 0.51 | 0.47 |

Pirna | 0.36 | 0.21 | 0.32 | 0.34 | 0.33 | 0.40 | 0.23 | 0.35 | 0.37 | 0.37 |

Total | 0.36 | 0.31 | 0.36 | 0.42 | 0.36 | 0.48 | 0.44 | 0.47 | 0.52 | 0.48 |

Investigation Area | MAE | RMSE | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

V1 | V2 | V3 | V4 | V5 | V1 | V2 | V3 | V4 | V5 | |

Döbeln | 0.35 | 0.34 | 0.39 | 0.42 | 0.39 | 0.46 | 0.47 | 0.49 | 0.52 | 0.49 |

Eilenburg | 0.49 | 0.43 | 0.49 | 0.52 | 0.50 | 0.65 | 0.60 | 0.62 | 0.62 | 0.63 |

Flöha | 0.25 | 0.30 | 0.34 | 0.45 | 0.34 | 0.31 | 0.36 | 0.40 | 0.50 | 0.40 |

Freital | 0.27 | 0.24 | 0.26 | 0.41 | 0.25 | 0.42 | 0.39 | 0.40 | 0.50 | 0.39 |

Grimma | 0.41 | 0.35 | 0.34 | 0.37 | 0.34 | 0.51 | 0.48 | 0.46 | 0.50 | 0.47 |

Pirna | 0.33 | 0.23 | 0.28 | 0.30 | 0.29 | 0.37 | 0.25 | 0.31 | 0.33 | 0.33 |

Total | 0.35 | 0.32 | 0.35 | 0.41 | 0.35 | 0.45 | 0.43 | 0.44 | 0.50 | 0.45 |

No. | Type/ Location | Description | Flow Direction | Scheme |
---|---|---|---|---|

1 | Stand-alone | Direct | ||

2a | Front house | Beginning of a row of houses | Direct/flow around | |

2b | End house | End of a row of houses | Flow around/circulation | |

2c | Front/end house | Beginning/end of a row of houses | Orthogonal/circulation | |

3a | Central house | In the middle of a row of houses | Tangential | |

3b | Central house | In the middle of a row of houses | Direct/orthogonal | |

4 | Corner house | Cross situation | Flow around/circulation |

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## Share and Cite

**MDPI and ACS Style**

Maiwald, H.; Schwarz, J.; Kaufmann, C.; Langhammer, T.; Golz, S.; Wehner, T.
Innovative Vulnerability and Risk Assessment of Urban Areas against Flood Events: Prognosis of Structural Damage with a New Approach Considering Flow Velocity. *Water* **2022**, *14*, 2793.
https://doi.org/10.3390/w14182793

**AMA Style**

Maiwald H, Schwarz J, Kaufmann C, Langhammer T, Golz S, Wehner T.
Innovative Vulnerability and Risk Assessment of Urban Areas against Flood Events: Prognosis of Structural Damage with a New Approach Considering Flow Velocity. *Water*. 2022; 14(18):2793.
https://doi.org/10.3390/w14182793

**Chicago/Turabian Style**

Maiwald, Holger, Jochen Schwarz, Christian Kaufmann, Tobias Langhammer, Sebastian Golz, and Theresa Wehner.
2022. "Innovative Vulnerability and Risk Assessment of Urban Areas against Flood Events: Prognosis of Structural Damage with a New Approach Considering Flow Velocity" *Water* 14, no. 18: 2793.
https://doi.org/10.3390/w14182793