# Seismic Risk Assessment of Urban Areas by a Hybrid Empirical-Analytical Procedure Based on Peak Ground Acceleration

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Methodology for Seismic Risk Evaluation

- Documentation of architectural, structural and material features by examining building codes, historical and archival sources, on-site visual inspection, and thermographic imaging;
- Creation of a database of buildings and visualization of input data by the web map in the GIS environment;
- Geophysical survey of the soil type;
- Definition of seismic hazard for the test site using available seismic hazard maps of Croatia and the results of geophysical survey;
- Seismic vulnerability assessment by vulnerability index method for the sample of the buildings;
- Extrapolation of the results for the seismic vulnerability index for the entire test site;
- Non-linear static analysis of the relevant buildings located in the test site and determination of the peak ground accelerations for damage limitation, significant damage and near collapse states;
- Development of vulnerability–peak ground acceleration curves for three limit states (damage limitation, significant damage, and near collapse) for the test site;
- Development of vulnerability curves that establish relations between damage, vulnerability and peak ground acceleration for the test site, and serve to estimate the structural damage for a given seismic action;
- Risk evaluation in terms of seismic damage for three return periods;
- Risk evaluation in terms of the index of seismic risk for three return periods;
- Visualization of hazard, vulnerability indices, damage indices and indices of seismic risk of the buildings in the web map.

## 3. Investigation of the Test Site

#### 3.1. Architectural, Material, and Structural Characteristics of Buildings

#### 3.2. Geophysical Survey of the Test Site

_{S,30}of the shallow subsurface along three seismic lines in Kaštel Kambelovac. The velocity V

_{S,30}was calculated as the average of the V

_{sH}velocities, measured from the surface to a depth of 30 m. The V

_{S,30}velocity, higher than 800 m/s, allowes us to classify the soil as A class according EN 1998-1:2011 [37] in all three lines. Considering that the investigated test site is relatively small, the soil type A was considered for all buildings in the test area.

## 4. Seismic Hazard of the Area

_{g}in the Kaštela area, is equal to 0.22 g, 0.17 g, and 0.11 g for the return periods of 475, 225, and 95 years, respectively, and ground type A.

## 5. Seismic Vulnerability Assessment of the Area

#### 5.1. Vulnerability Index Method

_{v}is obtained as follows:

_{vi}is the numerical score for each class, and w

_{i}is the weight of each parameter. The vulnerability index is normalized in a 0–100% range; the low index indicates high seismic resistance and low vulnerability, while a high vulnerability index is characteristic of the buildings with low seismic resistance and high vulnerability.

_{v}is 438.75.

#### 5.2. Application of Vulnerability Index Method at the Test Site

_{v}< 30, from medium to low vulnerability for 30 < I

_{v}< 45, from medium to high vulnerability for 45 < I

_{v}< 60, and high vulnerability for I

_{v}> 60. The range of the values of vulnerability indices are taken according to the GNDT vulnerability classification used in the study of reconstruction of the Municipality of Arsita following the seismic event of 6 April 2009 [2,43]. More insight into the vulnerability of buildings erected in the period 1950 to 2000 can be obtained from the division of the vulnerability index map into 10% intervals (Figure 7b). The lowest vulnerability index, equal to 2.6, belongs to a two-story house with regular layout and elevation, made as a confined masonry structure with horizontal and vertical confining elements (RC ties and RC columns) and rigid horizontal diaphragms, all designed according to EC-8. The highest vulnerability index, equal to 76.9, was obtained for the Cambi Tower, a stone masonry building dating from the 15th century. The Cambi Tower is characterized by having poorly connected walls, flexible floors, an irregular layout and elevation. A vulnerability index of 45 and beyond is ascribed to medium-high and high vulnerability buildings, respectively. Typically, high vulnerability buildings turn out being mainly located in the old city center and made of stonemasonry.

_{v}< 30%). Within this class, however, there are visible differences in vulnerability. Newer buildings with brick blocks and horizontal and vertical confinement generally have the lowest vulnerability (less than 10%). Older buildings with concrete blocks and horizontal confinement approximately have an index between 10% and 20%. Buildings without confinement or the aforementioned ones, but irregular in elevation and/or layout and with several annexes and additions, have an index mostly between 20% and 30%.

#### 5.3. Vulnerability Index Method as a Basis for Seismic Risk Evaluation

## 6. Evaluation of PGA Values for Specific Limit States by Pushover Analysis

#### 6.1. Detection of Specific Limit States

- Near collapse NC—global capacity of the building is taken to be equal to the ultimate displacement capacity;
- Significant damage SD—global capacity of the building is taken to be equal to ¾ of the ultimate displacement capacity;
- Damage limitation DL—the capacity for global assessment is defined as a yield point of the idealized elasto-perfectly plastic force-displacement relationship of the equivalent SDOF.

_{DL =}μ

_{y}, μ

_{SD}and μ

_{NC}= μ

_{u}represents damage limitation, significant damage, and near collapse ductility coefficients.

_{B}, T

_{C}, and T

_{D}divide the elastic response spectrum [37] into four spectral acceleration branches represented with the functions f

_{i}(i = 1, …, 4). Therefore, it can be expressed as follows:

_{g}is peak ground acceleration and T is the period of the structure. Each limit state (DL, SD, and NC) is characterized with the following peak ground accelerations:

^{3}.

_{1}= 1.2 and the design ground acceleration a

_{g}= 0.22 g. Figure 9 illustrates the results of the pushover analyses for x and y direction.

_{DL}= 0.093 g = 0.422a

_{g}, PGA

_{SD}= 0.116 g = 0.527a

_{g}, PGA

_{NC}= 0.147 g = 0.668a

_{g}; (a) y direction—PGA

_{DL}= 0.030 g = 0.136a

_{g}, PGA

_{SD}= 0.059 g = 0.268a

_{g}, PGA

_{NC}= 0.078 g = 0.355a

_{g}. For completeness, the design ground acceleration a

_{g}= 0.22 g has been obtained based on the seismic hazard map for the return period of 475 years.

#### 6.2. Results of Pushover Analysis of the Buildings

## 7. Vulnerability Index—PGA Relations

_{g}= 0.22 g for T = 475 yearsin both the x and y directions. Moreover, in the simulations, a conspicuous number of buildings reached the collapse at accelerations that are lower than the demand acceleration of a

_{g}= 0.11 g for a return period T = 95 years. The local mechanism failure induced by a lack of connection among perpendicular walls, and poor connections between floors/roofs and walls, was also analyzed for few stone masonry buildings in the old city center, where out-of-plane effect can be expected. The lowest acceleration was achieved for the global response of the buildings [33]. Buildings outside of the center are made of concrete or brick masonry with horizontal RC confining elements or both with horizontal and vertical confining elements and rigid horizontal diaphragms. Therefore, the failure of the structure caused by local mechanisms is not expected and the behavior of the buildings represented by capacity accelerations will be analyzed assuming the global failure of the structure.

_{v}and the critical peak ground accelerations associated with the DL, SD, and NC limits. The trend lines I

_{v}–PGA

_{DL}, I

_{v}–PGA

_{SD}and I

_{v}–PGA

_{NC}for three limit states were obtained and are shown in Figure 14. The exponential functions were chosen as the most representative. They are used to approximate the yield, significant damage, and collapse peak ground accelerations for the entire test site. The values of yield and collapse accelerations are the basis for deriving vulnerability curves.

## 8. Vulnerability Curves and Damage Index Distribution

_{i}, and at the collapse, PGA

_{c}. In this study, instead of a post-earthquake damage observation, the acceleration for the yield and collapse states were calculated by the pushover analysis [27,33]. Then, using the vulnerability indices and yield and collapse accelerations, a new damage–vulnerability–peak ground acceleration relationship was derived. The damage index is expressed in the (0–1) interval via a tri-linear law, analogously to [4] though defined through two parameters: yield acceleration PGA

_{y}, which corresponds the beginning of the damage (d = 0), and collapse acceleration PGA

_{c}(d = 1).

_{y}, and collapse peak ground acceleration PGA

_{c}, obtained by the pushover analysis for 18 analyzed buildings, as shown in Table 2. Yield acceleration PGA

_{y}is assigned to PGA

_{DL}and collapse acceleration PGA

_{c}to PGA

_{NC}limit states, respectively. As PGA

_{y}and PGA

_{c}depend on the vulnerability index I

_{v}, the values of PGA

_{y}, associated with damage d = 0, and PGA

_{c}, associated with damage d = 1, can be calculated for each value of I

_{v}.

## 9. Seismic Risk Distribution in Terms of the Index of Seismic Risk

_{C}associated to the structural capacity and the demand ground acceleration PGA

_{D}. It is expressed in the following form:

_{C}is equal to PGA

_{NC}.

- a
_{g}—peak ground horizontal acceleration on type A soil, ${\mathrm{a}}_{\mathrm{g}}={\mathrm{\gamma}}_{\mathrm{I}}{\mathrm{a}}_{\mathrm{g}\mathrm{R}}$, where ${\mathrm{\gamma}}_{\mathrm{I}}$ depends on the importance of the building; - S—soil parameter.

_{D}obtained from the seismic hazard map for the selected return period is given as $\mathrm{P}\mathrm{G}{\mathrm{A}}_{\mathrm{D}}={\mathrm{a}}_{\mathrm{g}}\mathrm{S}$.

## 10. Discussion

_{g}= 0.22 g for T = 475 years in either directions. Moreover, several buildings reached the structural collapse at peak ground accelerations that are lower than the demand acceleration of a

_{g}= 0.11 g for a return period T = 95 years. It should be noted that capacity accelerations have been obtained for the global structural response. Although local failure mechanisms can be critical for the buildings with flexible floors and weak connection between the walls, the analysis of local mechanisms of many buildings showed that the lowest accelerations have been reached for the global analysis of the buildings. Considering that the aim of the study is a vulnerability assessment of the settlement, critical acceleration has been determined on all buildings for the global response of the structure. The capacity of the buildings typical for the structures outside of the historical center varied depending on the applied materials and construction rules. Unreinforced concrete masonry buildings built before the first seismic regulation in 1964, concrete masonry with horizontal RC ring ties typical for the period between 1964 and 1980, and confined concrete masonry both with horizontal and vertical RC confining elements built between 1980 and 2005 do not meet seismic demands of a

_{g}= 0.22 g for T = 475 years. Only the buildings made of confined brick masonry, designed according to Eurocode 8, meet the seismic demand.

## 11. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**City of Kaštela: (

**a**) geographical position of the city in the Kaštela Bay; (

**b**) historical center of Kaštel Kambelovac [34].

**Figure 5.**Thermographic examination of unreinforced stone masonry building partially covered with plaster, and significant cracks in a gable wall [39].

**Figure 7.**Vulnerability index map of the test site. (

**a**) Division into four vulnerability classes. (

**b**) 10% division intervals.

**Figure 8.**Cambi Tower: (

**a**) photo of the building; (

**b**) ground floor plan; (

**c**) section view; (

**d**) structural model.

**Figure 10.**Analyzed buildings in the historical centre: (

**a**) Cambi Tower; (

**b**) Cumbat Towers; (

**c**) Public Library; (

**d**) Folk Castle; (

**e**) Dudan Palace; (

**f**) Perišin house; (

**g**) St. Mihovil Church; (

**h**) rowing club; (

**i**) residential building; (

**j**) ballet school.

**Figure 11.**Typical configurations outside of the historical center: (

**a**) plan; (

**b**) section view P + 1; (

**c**) section view P + 2.

**Figure 13.**Peak ground accelerations for NC, SD, and DL limit states calculated by pushover analysis.

**Figure 17.**Damage index distribution at the test site: (

**a**) T = 95 years; (

**b**) T = 225 years; (

**c**) T = 475 years.

**Figure 18.**Risk maps in terms of index of seismic risk: (

**a**) T = 95 years; (

**b**) T = 225 years; (

**c**) T = 475 years.

Parameter | Score (s_{vi}) | Weight (w_{i}) | |||
---|---|---|---|---|---|

A | B | C | D | ||

Type and organization of the resistant system (P1) | 0 | 5 | 20 | 45 | 1.50 |

Quality of the resistant system (P2) | 0 | 5 | 25 | 45 | 0.25 |

Conventional resistance (P3) | 0 | 5 | 25 | 45 | 1.50 |

Position of the building and foundation (P4) | 0 | 5 | 25 | 45 | 0.75 |

Typology of floors (P5) | 0 | 5 | 15 | 45 | 0.50–1.25 |

Planimetric configuration (P6) | 0 | 5 | 25 | 45 | 0.50 |

Elevation configuration (P7) | 0 | 5 | 25 | 45 | 0.50–1.00 |

Maximum distance among the walls (P8) | 0 | 5 | 25 | 45 | 0.25 |

Roof (P9) | 0 | 15 | 25 | 45 | 0.5–1.5 |

Non-structural elements (P10) | 0 | 0 | 25 | 45 | 0.25 |

State of conservation (P11) | 0 | 5 | 25 | 45 | 1.00 |

No. | Building | I_{V} [%] | PGA_{DL} [g] | PGA_{SD} [g] | PGA_{NC} [g] |
---|---|---|---|---|---|

1 | Cambi Tower | 76.9 | 0.030 | 0.059 | 0.078 |

2 | Kumbat Towers | 65.2 | 0.057 | 0.087 | 0.103 |

3 | Public Library | 59.0 | 0.028 | 0.061 | 0.079 |

4 | Folk Castle | 58.7 | 0.081 | 0.061 | 0.080 |

5 | Dudan Palace | 50.1 | 0.051 | 0.068 | 0.083 |

6 | Perišin house | 48.7 | 0.058 | 0.061 | 0.121 |

7 | St. Mihovil Church | 40.5 | 0.057 | 0.086 | 0.102 |

8 | Rowing club | 40.2 | 0.064 | 0.110 | 0.141 |

9 | Residential building | 34.8 | 0.081 | 0.095 | 0.152 |

10 | Ballet school | 23.9 | 0.103 | 0.142 | 0.183 |

11 | Type 1 building P + 2 | 29.1 | 0.083 | 0.114 | 0.142 |

12 | Type 1 building P + 1 | 29.1 | 0.061 | 0.144 | 0.173 |

13 | Type 2 building P + 2 | 13.4 | 0.098 | 0.145 | 0.175 |

14 | Type 2 building P + 1 | 13.4 | 0.115 | 0.187 | 0.220 |

15 | Type 3 building P + 2 | 6.0 | 0.065 | 0.158 | 0.189 |

16 | Type 3 building P + 1 | 6.0 | 0.075 | 0.175 | 0.206 |

17 | Type 4 building P + 2 | 4.3 | 0.103 | 0.188 | 0.243 |

18 | Type 4 building P + 1 | 2.6 | 0.130 | 0.218 | 0.270 |

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**MDPI and ACS Style**

Nikolić, Ž.; Benvenuti, E.; Runjić, L.
Seismic Risk Assessment of Urban Areas by a Hybrid Empirical-Analytical Procedure Based on Peak Ground Acceleration. *Appl. Sci.* **2022**, *12*, 3585.
https://doi.org/10.3390/app12073585

**AMA Style**

Nikolić Ž, Benvenuti E, Runjić L.
Seismic Risk Assessment of Urban Areas by a Hybrid Empirical-Analytical Procedure Based on Peak Ground Acceleration. *Applied Sciences*. 2022; 12(7):3585.
https://doi.org/10.3390/app12073585

**Chicago/Turabian Style**

Nikolić, Željana, Elena Benvenuti, and Luka Runjić.
2022. "Seismic Risk Assessment of Urban Areas by a Hybrid Empirical-Analytical Procedure Based on Peak Ground Acceleration" *Applied Sciences* 12, no. 7: 3585.
https://doi.org/10.3390/app12073585