# Post-Earthquake Damage Assessment—Case Study of the Educational Building after the Zagreb Earthquake

^{*}

## Abstract

**:**

## 1. Introduction

_{L}= 5.5, and intensity of VII, in the epicenter, according to the EMS-98 scale [1]. At 7 h 1 min followed the strongest subsequent earthquake of magnitude M

_{L}= 5.0 and intensity of VI. The main earthquake damaged most of the buildings in the Lower Town, including residential buildings, universities, schools, kindergartens, hospitals and public buildings. The vast majority of buildings built after the first mandatory earthquake regulations in former Yugoslavia (1964) [2,3] either remained intact or suffered small damage. Nonetheless, the larger part of the city’s historical center (Upper and Lower Town) was severely damaged because the buildings in the center were built before any seismic regulations. The damage to historical buildings is enormous. Numerous museums, churches and university buildings have been severely damaged (Figure 1). At the end of the year, Croatia was hit by another devastating earthquake with an epicenter in Petrinja, located approx. 50 km from Zagreb (M

_{L}= 6.3). The quake caused subsequent damage to already damaged buildings, but to a lesser extent.

## 2. The Case Study

^{2}. The building consists of a basement, first, second, third floor and attic. According to the Croatian seismic hazard map [24], the building is located in the area of peak ground acceleration intensity of a

_{gR}= 0.255 g for a return period of 475 years. The building serves as an educational-scientific institution. The condition of the building before the earthquake, regarding the vertical loads, was satisfactory, and the building was regularly maintained.

## 3. Methodology

#### 3.1. Assessment Procedure

#### 3.2. Rapid Preliminary Assessment Results

- Separation and local decay of plaster;
- Minor local damage is visible on structural elements (walls, columns, arches);
- In the eastern part of the building, diagonal cracks are visible on the load-bearing walls.

#### 3.3. Detailed Assessment Results

#### 3.4. In Situ Masonry Shear Strength Tests

#### Results of the Shear Strength Tests

_{umax}acting on one brick at the time of reaching the shear strength in that brick and the corresponding mortar area on both sides of the shear is transmitted (Ag + Ad). The test method can be seen in Figure 17 and photographs (Figure 18 and Figure 19).

_{v}with the contribution of σ

_{0}—vertical stress. During the test, each measuring position is precisely located to calculate the vertical load (G

_{0}), that is, vertical stress (σ

_{0}) from the numerical model. Therefore, for each test site, in addition to the floor plan position, the height of the measuring position from the upper edge of the ceiling structure (h) is recorded. When analyzing the shear strength of mortar, the vertical constant load is taken into account, that is, vertical stresses at a particular test position. Shear strength according to Mohr–Coulomb law is calculated by Equation (1).

_{vm}= μ · σ

_{0}+ f

_{vm0}

_{vm0}= 0.32 MPa > 0.10 MPa). The results show that the quality of masonry is good in contrast to similar buildings from that period.

#### 3.5. Numerical Modeling

_{I}= 1.2. Three PGA values are used for two limit states. According to the new law “Law on the Reconstruction of Earthquake-Damaged Buildings in the City of Zagreb, Krapina-Zagorje County and Zagreb County (NN 102/2020)” [54], ultimate limit state return period can be different depending on the level of strengthening for old masonry buildings damaged in the recent earthquakes. Limit state of significant damage with a return period of 475 and limit state of damage limitation with a return period of 95 years were checked [55]. In the new law [54], the return period of 225 years which corresponds to a probability of exceedance of 20% in 50 years is introduced for a limit state of significant damage.

_{C}, the target displacement is determined by the procedure for short periods shown in Figure 29. Buildings with short natural periods of vibration do not comply with the equal displacement rule [56] as buildings with medium-long and long natural periods of vibration.

_{Rd}/M

_{Ed}ratio is greater than or equal to 1.0. In Figure 30, walls that did not satisfy the check are colored red.

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References and Note

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**Figure 1.**Typical damage to educational buildings after the Zagreb earthquake (photo credit: M. Stepinac).

**Figure 2.**Protected zones A and B with the location of the case study inside the Lower Town of Zagreb (yellow dashed line).

**Figure 7.**1st floor plan with load-bearing walls in red. The floor plan of the 2nd floor is identical to the 1st floor plan.

**Figure 10.**Six categories of usability divided into three original labels (in Croatian) [30].

**Figure 12.**Cracks on the eastern staircase: exterior (

**a**) and interior (

**b**) (photo credit: I. Hafner).

**Figure 13.**Diagonal cracks on the central staircase: exterior (

**a**) and interior (

**b**) (photo credit: I. Hafner).

**Figure 18.**Masonry shear strength tests at measuring positions PS-PR-1 (

**a**) and PS-PR-2 (

**b**) on the ground floor (photo credit: L. Lulić).

**Figure 19.**Masonry shear strength tests at measuring positions PS-1-1 (

**a**) and PS-1-3 (

**b**) on the 1st floor (photo credit: L. Lulić).

Floor | Testing Site | h (cm) | A_{h} (cm^{2}) | H_{u, max} (kN) | Shear Strength f _{v} (MPa) |
---|---|---|---|---|---|

Ground floor | PS-PR-1 | 45 | 784 | 55.5 | 0.708 |

PS-PR-2 | 60 | 812 | 58.3 | 0.717 | |

PS-PR-3 | 75 | - | - | - | |

PS-PR-4 | 60 | - | - | - | |

PS-PR-5 | 60 | 504 | 16.3 | 0.323 | |

1st floor | PS-1-1 | 50 | 448 | 17.6 | 0.393 |

PS-1-2 | 50 | 728 | 121.9 | 1.675 | |

PS-1-3 | 70 | 526 | 24.4 | 0.464 | |

2nd floor | PS-2-1 | 45 | 783 | 44.7 | 0.571 |

PS-2-2 | 55 | 812 | 40.6 | 0.500 | |

PS-2-3 | 55 | 840 | 94.8 | 1.129 |

Material Characteristic | Value |
---|---|

Modulus of elasticity | 3000 N/mm^{2} |

Shear modulus | 1200 N/mm^{2} |

Specific weight | 18 kN/m^{3} |

Mean compressive strength of masonry | 6.63 N/mm^{2} |

Shear strength | 0.14 N/mm^{2} |

Characteristic compressive strength of masonry | 5.53 N/mm^{2} |

Confidence factor | 1.2 |

Partial safety factor for material | 1 |

Shear drift | 0.0053 |

Bending drift | 0.0107 |

Final creep coefficient | 0.5 |

Parameter | Value (x-Direction) | Value (y-Direction) |
---|---|---|

T* (s) | 0.411 | 0.433 |

m* (kg) | 2,725,590 | 2,339,506 |

w (kN) | 45,733 | 45,733 |

M (kg) | 4,661,901 | 4,661,901 |

m*/M (%) | 58.47 | 50.18 |

Γ | 1.31 | 1.41 |

F*y (kN) | 6719 | 3736 |

d*y (cm) | 1.06 | 0.76 |

d*m (cm) | 3.91 | 1.81 |

Return Period | α (x-Direction) | α (y-Direction) |
---|---|---|

475 | 0.633 | 0.291 |

225 | 0.894 | 0.411 |

95 | 0.560 | 0.363 |

Local Mechanism | α |
---|---|

LM1 | 4.93 |

LM2 | 2.10 |

LM3 | 0.53 |

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Lulić, L.; Ožić, K.; Kišiček, T.; Hafner, I.; Stepinac, M.
Post-Earthquake Damage Assessment—Case Study of the Educational Building after the Zagreb Earthquake. *Sustainability* **2021**, *13*, 6353.
https://doi.org/10.3390/su13116353

**AMA Style**

Lulić L, Ožić K, Kišiček T, Hafner I, Stepinac M.
Post-Earthquake Damage Assessment—Case Study of the Educational Building after the Zagreb Earthquake. *Sustainability*. 2021; 13(11):6353.
https://doi.org/10.3390/su13116353

**Chicago/Turabian Style**

Lulić, Luka, Karlo Ožić, Tomislav Kišiček, Ivan Hafner, and Mislav Stepinac.
2021. "Post-Earthquake Damage Assessment—Case Study of the Educational Building after the Zagreb Earthquake" *Sustainability* 13, no. 11: 6353.
https://doi.org/10.3390/su13116353