# Damage Evaluation and Seismic Assessment of a Typical Historical Unreinforced Masonry Building in the Zagreb 2020 Earthquake: A Case Study—Part I

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. As-Built State of the Case Study Building and Seismic Hazard at the Site

^{2}and total gross area of the building of around 2440 m

^{2}. The building consists of a basement, ground floor, three stories, and an attic (Figure 4). The basement has a height of 3 m, while the ground and first floors are 3.5 m high. The total height of the building is 22.70 m. The annexes on the courtyard side of the existing building are connected to its main part, which faces the street. The floor plan of the building is relatively irregular, with heterogeneous floor structures.

## 3. Preliminary Assessment of the Building’s Vulnerability

## 4. Experimental Measurements

#### 4.1. Mechanical Properties

_{KL3}= 1. In general, this is often not possible due to the availability of the position/location during the investigation, so the number and position are often chosen based on previous experience. The purpose of the selected in situ test is to determine the shear strength between two horizontal bed joints bounding a single brick unit. This method is a modification of the well-known “shove test”, which takes into account the control of vertical stress in accordance with the procedure and the ASTM C1531-16 standard [46]. Taking into account the linear regression, it is possible to determine the shear strength without the normal compressive stress (f

_{v}

_{0}) according to Coulomb’s law

_{v}is the shear strength of the masonry, µ is the coefficient of friction, σ

_{0}is the normal compressive strength, F

_{h}is the experimentally determined shear force at the time of shear failure, and A

_{u}and A

_{l}are the upper and lower areas of the brick. With the selected in situ method, it is possible to obtain f

_{v}

_{0}. First, f

_{v}must be determined experimentally, and then the value of the friction coefficient can be assumed to be 0.4 (HRN EN 1998-3) and the vertical compressive stress can be obtained from the numerical model. The advantage of the chosen method is that it can be carried out in a short time (45 min/location). However, the disadvantage of the method lies in the assumptions already mentioned. In this study, the protective layer of the plaster was removed at a total of eleven locations, a shear test was performed at seven locations, and the remaining four locations were only used for visual identification of the masonry. All shear tests were carried out approximately 100 centimeters above the floor, on the locations shown in Figure 7. The results of the shear test and compressive strength we performed are summarized in Table 2.

^{3}were determined on two extracted solid brick samples.

#### 4.2. Determination of the Structural Modal Parameters

## 5. Numerical Models and Analysis Methods

#### 5.1. Model Description

^{2}in all floor levels except for the basement, where it was 3.5 kN/m

^{2}. The additional permanent load was taken to be 1.5 kN/m

^{2}, and the imposed load was 2 kN/m

^{2}. Finally, the total estimated mass of the building above the foundation was about 3222 t.

#### 5.2. Vertical Loading Analysis

#### 5.3. Dynamic Properties of the Building

#### 5.4. Linear Analysis: Response Spectrum Method

_{g}= 0.125 g).

_{g}at which the structure meets the required seismic capacity. For this purpose, design of the elements was carried out for the shear forces induced by the ground acceleration in the range of a

_{g}= 0.025 g to a

_{g}= 0.125 g. The allowable redistribution of internal forces was also considered in the calculations. Since this is a linear calculation, and some of the shear forces induced by the seismic lateral force changed linearly with the change in a

_{g}, no new calculations needed to be performed. The results of the parametric calculation are shown in Figure 15. In the table, for each story of the building, the critical element utilization (calculated as the ratio of demand and capacity for lateral force) is given with respect to the peak ground acceleration in the soil category A. The same is shown in the diagram on the right, where the x-axis indicates the peak ground acceleration a

_{g}value and the ordinate indicates the coefficient of capacity. The critical elements for each floor are marked in the floor plan and in the diagram.

_{g}= 0.125 g. The SD limit state of critical elements on the 1st and 2nd floors was then found to be 58%, while in the basement and on the ground floor, we found it to be 76% of the 95-year return period ground acceleration.

#### 5.5. Nonlinear Static Method (Pushover)

#### 5.6. Building Capacity Curves for X Direction

#### 5.7. Building Capacity Curves for Y Direction

#### 5.8. Calculation of Capacity and Demand of the Building

#### 5.9. Out-of-Plane Mechanisms (OOPs)

_{0}was determined through the application of the virtual work method and by determining effective mass ratio e* of the equivalent SDOF system. The corresponding spectral acceleration that activates the mechanism is given by ${\mathsf{\alpha}}_{0}^{*}={\mathsf{\alpha}}_{0}g/{F}_{C}{e}^{*}$, where Fc is the confidence factor equal to 1.35 for the rigid block assumption. For the subject building, local mechanisms selected for the OOP analysis are shown in Figure 21a and Figure 22a. The first wall (wall_1) is the south gable wall, selected due to its slenderness and because on the portion of the gable, it has no connection with perpendicular elements. The other is the west courtyard wall of the annex (wall_2), selected because of presence of the near and large number of openings on the side walls and, similarly to the gable wall, because it is loaded only by its own weight (timber joists oriented parallel to the wall) and because prior global analysis showed that this wall could be significantly damaged by seismic actions. The main presumption for this mechanism is the failure of spandrels on the side walls.

## 6. Discussion

_{g}= 0.125 g. The SD limit state of critical elements on the first and second floors occurred at 58%, while in the basement and on the ground floor, it was at 76% of the ground acceleration for a return period of 95 years.

## 7. Conclusions

- The building was severely damaged in a relatively moderate earthquake, which proves its significant seismic vulnerability and the need for further research on this type of building.
- When measuring the ambient vibrations before and after the earthquake, a change in natural frequencies of about 10% was observed, which proved that some of the load-bearing walls of the building are damaged and that they are in a cracking condition.
- Analysis using the response spectrum method provided significantly conservative values of the load-bearing capacity. Also, the mechanism of structural failure could not be reliably determined. The main reason for this was that the distribution of forces was carried out exclusively according to the stiffness of the elements, and the behavior factor was constant (equal to 1.5) for the entire building.
- According to the response spectrum method, the limit state of the SD was determined by the critical primary elements on the third floor, which was only 43% of the requirement for a
_{g}= 0.125 g (95-year return period earthquake). - When using the pushover method with various shapes and directions of loading, it was regularly found that the spandrels were the first elements to be damaged and later fail. Moreover, the appearance of wall damage was mainly observed on the higher floors of the building, which was the result of the low axial force and the absence of a rigid diaphragm.
- For the direction of action X, the influence of eccentricity and torsion on the overall load-bearing capacity of the building was characteristic. The failure mechanism was initiated by damage to the first and second floors of the western courtyard wall, which was a consequence of the torsional effects caused by the asymmetry of the building’s floor plan and the eccentricity of the lateral force. The analysis showed that the influence of eccentricity was significant for certain elements.
- When implementing the N2 method, we found that the structure met the requirement for peak ground acceleration of approximately 0.125 g (95-year return period earthquake), which corresponds to the required level of seismic resistance according to CTRBS.
- Out-of-plane analysis pointed to the key problem of this type of building. The analysis of the gable wall and the west wall showed that it was a critical failure mechanism. Similar patterns of damage and failure were also shown in the earthquake. Even for small earthquake intensities, it is likely that there will be out-of-plane damage to the walls due to the absence of floor panels that properly connect the walls in the floor plan.
- The main problem of this typology can be highlighted, which is the lack of rigid transverse walls of the building to connect the main load-bearing longitudinal walls. The gable walls are long and without openings, but they are relatively thin and are not connected to the floor structures, and they are quite distant from each other. Apart from those, there are staircase walls in the transverse direction, but they generally have many openings and do not significantly contribute to the lateral load transfer.
- Finally, an unfavorable circumstance is the partially divided floor plan of the building, which forms two units (the eastern unit facing the street and the western unit facing the courtyard). The location of the staircase at the intersection of these two units creates the risk that, in the event of an earthquake, these two units will respond separately. Their separation could have significant consequences for the building.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Uroš, M.; Todorić, M.; Crnogorac, M.; Atalić, J.; Šavor Novak, M.; Lakušić, S. Potresno Inženjerstvo—Obnova Zidanih Zgrada; University of Zagreb, Faculty of Civil Engineering: Zagreb, Croatia, 2021. [Google Scholar]
- So, E.; Babić, A.; Majetic, H.; Putrino, V.; Verrucci, E.; Contreras Mojica, D.; Rossetto, T.; Wilkinson, S.; Keogh, C.; D’Ayala, D. The Zagreb Earthquake of 22 March 2020; EEFIT: London, UK, 2020. [Google Scholar]
- Miranda, E.; Brzev, S.; Bijelic, N.; Arbanas, Ž.; Bartolac, M.; Jagodnik, V.; Lazarević, D.; Mihalić Arbanas, S.; Zlatović, S.; Acosta, A.; et al. Petrinja, Croatia December 29, 2020, Mw 6.4 Earthquake Joint Reconnaissance Report (JRR); ETH: Zurich, Switzerland, 2021. [Google Scholar]
- Šavor Novak, M.; Uroš, M.; Atalić, J.; Herak, M.; Demšić, M.; Baniček, M.; Lazarević, D.; Bijelić, N.; Crnogorac, M.; Todorić, M. Zagreb earthquake of 22 March 2020—Preliminary report on seismologic aspects and damage to buildings. Građevinar
**2020**, 72, 843–867. [Google Scholar] [CrossRef] - Atalić, J.; Uroš, M.; Šavor Novak, M.; Demšić, M.; Nastev, M. The Mw5.4 Zagreb (Croatia) earthquake of March 22, 2020: Impacts and response. Bull. Earthq. Eng.
**2021**, 19, 3461–3489. [Google Scholar] [CrossRef] - Available online: https://www.pmf.unizg.hr/geof/seizmoloska_sluzba/potresi_kod_petrinje?@=1m6dc#news_118053 (accessed on 5 May 2023).
- Atalić, J.; Demšić, M.; Baniček, M.; Uroš, M.; Dasović, I.; Prevolnik, S.; Kadić, A.; Šavor Novak, M.; Nastev, M. The December 2020 magnitude (Mw) 6.4 Petrinja earthquake, Croatia: Seismological aspects, emergency response and impacts. Bull. Earthq. Eng.
**2023**, 21, 5767–5808. [Google Scholar] [CrossRef] - Atalić, J.; Šavor Novak, M.; Uroš, M. Updated Risk Assessment of Natural Disasters in Republic of Croatia—Seismic Risk Assessment; Faculty of Civil Engineering in collaboration with Ministry of Construction and Physical Planning and National Protection and Rescue Directorate: Zagreb, Croatia, 2018. (In Croatian) [Google Scholar]
- Simović, V. Potresi na zagrebačkom području. Građevinar
**2000**, 52, 637–645. [Google Scholar] - Markušić, S.; Stanko, D.; Korbar, T.; Belić, N.; Penava, D.; Kordić, B. The Zagreb (Croatia) M5.5 Earthquake on 22 March 2020. Geosciences
**2020**, 10, 252. [Google Scholar] [CrossRef] - Crnogorac, M.; Todorić, M.; Uroš, M.; Atalić, J. Emergency seismic reconstruction program—UPPO; Faculty of Civil Engineering, University of Zagreb: Zagreb, Croatia; Croatian Association of Civil Engineers: Zagreb, Croatia, 2020. (In Croatian) [Google Scholar]
- Uroš, M.; Šavor Novak, M.; Atalić, J.; Sigmund, Z.; Baniček, M.; Demšić, M.; Hak, S. Post-earthquake damage assessment of buildings—Procedure for conducting building inspections. J. Croat. Assoc. Civ. Eng.
**2021**, 72, 1089–1115. [Google Scholar] [CrossRef] - Atalić, J.; Demšić, M.; Lazarević, D.; Uroš, M.; Baniček, M.; Todorić, M. Report on the Assessment of the Existing Condition of the Zagreb University Building; University of Zagreb: Zagreb, Croatia, 2021. (In Croatian) [Google Scholar]
- Pinasco, S.; Cattari, S.; Lagomarsino, A.; Demšić, M.; Šavor Novak, M.; Uroš, M. Numerical investigation of the seismic response of an unreinforced masonry residential buildings hit by Zagreb earthquake in 2020. In Proceedings of the 2nd Croatian Conference on Earthquake Engineering 2023, Zagreb, Croatia, 22–24 March 2023. [Google Scholar] [CrossRef]
- Moretić, A.; Chieffo, N.; Stepinac, M.; Lourenço, P.B. Vulnerability assessment of historical building aggregates in Zagreb: Implementation of a macroseismic approach. Bull. Earthq. Eng.
**2022**, 21, 2045–2065. [Google Scholar] [CrossRef] - Stepinac, M.; Lourenço, P.B.; Atalić, J.; Kišiček, T.; Uroš, M.; Baniček, M.; Šavor Novak, M. Damage classification of residential buildings in historical downtown after the ML5.5 earthquake in Zagreb, Croatia in 2020. Int. J. Disaster Risk Reduct.
**2021**, 56, 102140. [Google Scholar] [CrossRef] - Acito, M.; Buzzetti, M.; Cundari, G.A.; Milani, G. General methodological approach for the seismic assessment of masonry aggregates. Structures
**2023**, 57, 105177. [Google Scholar] [CrossRef] - Tomić, I.; Penna, A.; DeJong, M.; Butenweg, C.; Correia, A.A.; Candeias, P.X.; Senaldi, I.; Guerrini, G.; Malomo, D.; Wilding, B.; et al. Shake-table testing of a stone masonry building aggregate: Overview of blind prediction study. Bull. Earthq. Eng.
**2023**. [Google Scholar] [CrossRef] - Ferreira, T.M.; Costa, A.A.; Costa, A. Analysis of the Out-Of-Plane Seismic Behavior of Unreinforced Masonry: A Literature Review. Int. J. Arch. Heritage
**2014**, 9, 949–972. [Google Scholar] [CrossRef] - D’altri, A.M.; Sarhosis, V.; Milani, G.; Rots, J.; Cattari, S.; Lagomarsino, S.; Sacco, E.; Tralli, A.; Castellazzi, G.; de Miranda, S. Modeling Strategies for the Computational Analysis of Unreinforced Masonry Structures: Review and Classification. Arch. Comput. Methods Eng.
**2019**, 27, 1153–1185. [Google Scholar] [CrossRef] - Betti, M.; Galano, L.; Vignoli, A. Comparative analysis on the seismic behaviour of unreinforced masonry buildings with flexible diaphragms. Eng. Struct.
**2014**, 61, 195–208. [Google Scholar] [CrossRef] - Ottonelli, D.; Manzini, C.F.; Marano, C.; Cordasco, E.A.; Cattari, S. A comparative study on a complex URM building: Part I—Sensitivity of the seismic response to different modelling options in the equivalent frame models. Bull. Earthq. Eng.
**2021**, 20, 2115–2158. [Google Scholar] [CrossRef] - Cattari, S.; Calderoni, B.; Caliò, I.; Camata, G.; de Miranda, S.; Magenes, G.; Milani, G.; Saetta, A. Nonlinear modeling of the seismic response of masonry structures: Critical review and open issues towards engineering practice. Bull. Earthq. Eng.
**2021**, 20, 1939–1997. [Google Scholar] [CrossRef] - Cattari, S.; Magenes, G. Benchmarking the software packages to model and assess the seismic response of unreinforced masonry existing buildings through nonlinear static analyses. Bull. Earthq. Eng.
**2021**, 20, 1901–1936. [Google Scholar] [CrossRef] - Lagomarsino, S.; Camilletti, D.; Cattari, S.; Marino, S. Seismic assessment of existing irregular masonry buildings by nonlinear static and dynamic analyses. In Recent Advances in Earthquake Engineering in Europe: 16th European Conference on Earthquake Engineering, Thessaloniki, Greece, 18–21 June 2018; Springer International Publishing: Cham, Switzerland, 2018; pp. 123–151. [Google Scholar] [CrossRef]
- Tomić, I.; Vanin, F.; Beyer, K. Uncertainties in the Seismic Assessment of Historical Masonry Buildings. Appl. Sci.
**2021**, 11, 2280. [Google Scholar] [CrossRef] - Angiolilli, M.; Brunelli, A.; Cattari, S. Fragility curves of masonry buildings in aggregate accounting for local mechanisms and site effects. Bull. Earthq. Eng.
**2023**, 21, 2877–2919. [Google Scholar] [CrossRef] - Brunelli, A.; de Silva, F.; Cattari, S. Site effects and soil-foundation-structure interaction: Derivation of fragility curves and comparison with Codes-conforming approaches for a masonry school. Soil Dyn. Earthq. Eng.
**2021**, 154, 107125. [Google Scholar] [CrossRef] - D’Ayala, D.; Speranza, E. Definition of Collapse Mechanisms and Seismic Vulnerability of Historic Masonry Buildings. Earthq. Spectra
**2003**, 19, 479–509. [Google Scholar] [CrossRef] - NIKER Project—Critical Review of Methodologies and Tools for Assessment of Failure Mechanisms and Interventions, Deliverable 3.3, WORKPACKAGE 3: Damage Based Selection of Technologies; NIKER Project: Padova, Italy, 2010.
- Ferreira, T.M.; Costa, A.A.; Arêde, A.; Gomes, A.; Costa, A. Experimental characterization of the out-of-plane performance of regular stone masonry walls, including test setups and axial load influence. Bull. Earthq. Eng.
**2015**, 13, 2667–2692. [Google Scholar] [CrossRef] - de Felice, G. Out-of-Plane Seismic Capacity of Masonry Depending on Wall Section Morphology. Int. J. Arch. Heritage
**2011**, 5, 466–482. [Google Scholar] [CrossRef] - Costa, A.A.; Arêde, A.; Costa, A.; Oliveira, C.S. Out-of-plane behaviour of existing stone masonry buildings: Experimental evaluation. Bull. Earthq. Eng.
**2011**, 10, 93–111. [Google Scholar] [CrossRef] - Costa, A.A.; Arêde, A.; Costa, A.C.; Penna, A.; Costa, A. Out-of-plane behaviour of a full scale stone masonry façade. Part 1: Specimen and ground motion selection. Earthq. Eng. Struct. Dyn.
**2013**, 42, 2081–2095. [Google Scholar] [CrossRef] - Costa, A.A.; Arêde, A.; Costa, A.C.; Penna, A.; Costa, A. Out-of-plane behaviour of a full scale stone masonry façade. Part 2: Shaking table tests. Earthq. Eng Struct. Dyn.
**2013**, 42, 2097–2111. [Google Scholar] [CrossRef] - Degli Abbati, S.; Rossi, M.; Lagomarsino, S. Out-of-plane experimental tests on masonry panels. In Proceedings of the 2nd European Conference on Earthquake Engineering and Seismology, Istanbul, Turkey, 25–29 August 2014. [Google Scholar]
- Grillanda, N.; Valente, M.; Milani, G. ANUB-Aggregates: A fully automatic NURBS-based software for advanced local failure analyses of historical masonry aggregates. Bull. Earthq. Eng.
**2020**, 18, 3935–3961. [Google Scholar] [CrossRef] - Funari, M.F.; Mehrotra, A.; Lourenço, P.B. A Tool for the Rapid Seismic Assessment of Historic Masonry Structures Based on Limit Analysis Optimisation and Rocking Dynamics. Appl. Sci.
**2021**, 11, 942. [Google Scholar] [CrossRef] - Mercuri, M.; Pathirage, M.; Gregori, A.; Cusatis, G. Computational modeling of the out-of-plane behavior of unreinforced irregular masonry. Eng. Struct.
**2020**, 223, 111181. [Google Scholar] [CrossRef] - Aşıkoğlu, A.; Vasconcelos, G.; Lourenço, P.B.; Pantò, B. Pushover analysis of unreinforced irregular masonry buildings: Lessons from different modeling approaches. Eng. Struct.
**2020**, 218, 110830. [Google Scholar] [CrossRef] - Herak, M.; Allegretti, I.; Herak, D.; Ivančić, I.; Kuk, V.; Marić, K.; Markušić, S.; Sović, I. Republika Hrvatska, Karta potresnih Područja. 2011. Available online: http://seizkarta.gfz.hr (accessed on 5 May 2023).
- Milutinovic, Z.; Trendafilovski, G. An Advanced Approach to Earthquake risk Scenarios with Applications to Different European Towns—WP4: Vulnerability of Current Buildings; RISK-EU; Bureau de Recherches Géologiques et Minières: Orleans, France, 2003; 110p. [Google Scholar]
- Lagomarsino, S.; Giovinazzi, S. Macroseismic and mechanical models for the vulnerability and damage assessment of current buildings. Bull. Earthq. Eng.
**2006**, 4, 415–443. [Google Scholar] [CrossRef] - Grünthal, G. European Macroseismic Scale 1998 (EMS-98); Cahiers du Centre Européen de Géodynamique et de Séismologie 15; Centre Européen de Géodynamique et de Séismologie: Luxembourg, 1998. [Google Scholar]
- HRN EN 1998-3; Eurocode 8: Design of Structures for Earthquake Resistance—Part 3: Assessment and Retrofitting of Buildings. HZN: Zagreb, Croatia, 2011. (In Croatian)
- ASTM C1531-16; Standard Test Methods for In Situ Measurement of Masonry Mortar Joint Shear Strength Index. ASTM: West Conshohocken, PA, USA, 2016.
- CSI. CSI Analysis Reference Manual for SAP2000, ETABS, SAFE and CSiBridge; Computers and Structures Inc.: Berkeley, CA, USA, 2017. [Google Scholar]
- ASCE/SEI 41-13; Seismic Rehabilitation of Existing Buildings. American Society of Civil Engineers: Reston, VA, USA, 2014; ISBN 9780784412855.
- Fajfar, P.; Gašperšič, P. The N2 method for the seismic damage analysis of RC buildings. Earthq. Eng. Struct. Dyn.
**1996**, 25, 31–46. [Google Scholar] [CrossRef] - Fajfar, P. A nonlinear analysis method for performance-based seismic design. Earthq. Spectra
**2000**, 16, 573–592. [Google Scholar] [CrossRef]

**Figure 1.**Geographical location of the Zagreb region with location of the building and the epicenters of the 2020 earthquakes.

**Figure 2.**Damage to residential and commercial–residential buildings on: (

**a**) a perspective view of the city of Zagreb according to usability tags (colors) and gross floor areas of buildings (heights of columns) and (

**b**) a perspective view of the historical center according to buildings’ usability tags from the GIS-based Building Usability Database (source: Croatian Centre for Earthquake Engineering—CCEE).

**Figure 3.**Photographs of the case study building: (

**a**) south- and street-facing facade; (

**b**) side view; (

**c**) aerial view.

**Figure 5.**Cross-section and timber floor structure. (

**a**) cross-section of the building; (

**b**) layers of the timber floor structure; (

**c**) photograph of the timber floor structure.

**Figure 7.**(

**a**) Characteristic floor plan and locations of the shear test, (

**b**) shear test of mortar without control of vertical stress, (

**c**) samples for determination of compressive strengths of solid bricks.

**Figure 8.**Measurement point locations (

**a**) in cross-section and (

**b**) in floor plan. (

**c**) Characteristic record of frequency domain decomposition (FDD) for the determination of natural frequencies.

**Figure 9.**Experimentally obtained (

**a**) first (dominant) translation mode shape in y direction, and (

**b**) second translation mode shape in X direction. The blue lines represent the undeformed shape, while the red lines represent the deformed shape.

**Figure 10.**Numerical model of a building created in ETABS v.17. Vertical load-bearing system of masonry walls with dimensions by floors. (

**a**) 3d numerical model; (

**b**) layout of the walls on the ground floor; (

**c**) layout of the walls in the first floor.

**Figure 11.**Normal stress distribution and soil stresses (for permanent vertical load). (

**a**) stress distribution in the basement walls. (

**b**) stress distribution in the ground floor walls. (

**c**) soil stresses.

**Figure 12.**Natural mode shapes of the building: (

**a**) adapted model for ambient vibrations, and (

**b**) model of SD limit state.

**Figure 13.**Response spectrum method results: (

**a**) maximum story displacements. (

**b**) maximum story inter-story drifts. (

**c**) seismic lateral forces in the X and Y directions for a 95-year return period.

**Figure 14.**Summary of the wall shear capacity for seismic action with a 95-year return period (behavior factor 1.5) (

**a**) without and (

**b**) with redistribution performed.

**Figure 15.**Parametric analysis results for a

_{g}. (

**a**) critical element utilization by story. (

**b**) demand/capacity of the primary critical wall in each story.

**Figure 16.**(

**a**) Characteristic points on the 3rd floor; (

**b**) distribution pattern of acceleration; (

**c**) eccentricity of lateral force.

**Figure 17.**Relevant capacity curves of the building: (

**a**) in the +X direction. (

**b**) in the −X direction.

**Figure 18.**Relevant capacity curves of the building: (

**a**) in the +Y direction. (

**b**) in the −Y direction.

**Figure 19.**Number of elements that have reached the limit state SD as a function of the control point displacement.

**Figure 20.**Relevant capacity curves of the building: linear load distribution directions X (

**a**) and Y (

**d**). shear load distribution directions X (

**b**) and Y (

**e**). lateral load method distribution directions X (

**c**) and Y (

**f**).

**Figure 21.**(

**a**) Solid model of the case study building and selected overturning local mechanisms in Rhinocheros; (

**b**) activation factor; (

**c**) spectral acceleration that activates mechanism; (

**d**) minimum demanded value for the spectral acceleration over the building height; and (

**e**) safety factor value for the 95-year return period of seismic action.

**Figure 22.**(

**a**) Solid model of the one-story (wall_3) and two-story (wall_4) bending local mechanisms in Rhinocheros; (

**b**) activation factor; (

**c**) spectral acceleration that activates mechanism; and (

**d**) safety factor value for the 95-year return period of seismic action.

Average story height [cm] | 330 |

Ground floor level relative to actual ground [cm] | 120 |

Total height (ground to rooftop) [m] | 22.7 |

Number of stories | 5 |

Material used for load-bearing structure | Masonry (full brick with lime mortar) |

Technology of construction | In situ |

Load-bearing system | Wall system |

Presence of tie-columns | No |

Presence of tie-beams | No |

Foundation type | Strip foundations—unconnected |

Foundation material | Masonry |

Foundations at different levels | No |

Material of floor structure | Wood |

Type of floor structure | Wooden beams with a heavy soft plate (gravel and wood planks, etc.) |

Material of roof structure | Wood |

Roof shape | Gable roof |

Position in aggregate | At the end of a row |

Interaction with adjacent building | Next to a lower building |

Floor levels relative to the adjacent building | Irregular |

Floorplan shape | Irregular |

Structural regularity in elevation | No irregularities |

Soft story | No |

Regularity in plan | Torsional eccentricity |

Year of reconstruction | 0 |

Reconstruction | Negligible |

Added stories | Yes |

Total ground floor area [m^{2}] | 380 |

Total floorplan area of the building [m^{2}] | 1900 |

Ground floor wall area in X direction [m^{2}] | 23.82 |

Ground floor wall area in Y direction [m^{2}] | 30.36 |

Ground floor wall area percentage in X direction | 6 |

Ground floor wall area percentage in Y direction | 8 |

ag475 [g] | 0.25 |

ag95 [g] | 0.13 |

Total building weight [kN]—without basement | 31,608 |

Behavior factor q | 1.5 |

Soil category according to EC8 | C |

Estimated first period T1 [s] | 0.362 |

Response spectrum ordinate for T1—A(T1) [g] | 0.498 |

Lateral force Fb [kN] | 10,654 |

Lateral force coefficient—BS [-] | 0.337 |

Average shear stress τ_{X} [MPa] | 0.447 |

Average shear stress τ_{Y} [MPa] | 0.351 |

Building type (RISK UE) | M31H |

V_{I}^{c} | 0.74 |

Maintenance | −0.04 |

Number of stories | 0.06 |

Structural system | 0.02 |

Soft story | 0 |

Floorplan irregularities | 0.04 |

Irregularities in height | 0 |

Added stories | 0.04 |

Roof (heavy roof with thrust) | 0.04 |

Reconstruction | 0 |

Position in aggregate | 0.06 |

Buildings of different heights in the aggregate | 0.02 |

Staggered floors of buildings in the aggregate | 0.02 |

Foundations | 0 |

Terrain morphology | 0 |

V_{R} | 0 |

V_{I}^{z} | 1.00 |

μ_{D}(VIII) | 3.58 |

μ_{D}(IX) | 4.24 |

Floor Location | Label | Notes | Shear Strength f_{v} [MPa] | Compressive Strength [MPa] |
---|---|---|---|---|

First floor | ST 1-1 | CLBW | 0.577 | 7.71 |

Second floor | ST 2-1 | ELBW | 0.593 | 6.84 |

ST 2-2 | CLBW | 0.500 | - | |

ST 2-3 | EGW | 0.259 | - | |

Third floor | ST 3-1 | CLBW | 0.304 | - |

ST 3-2 | ELBW | 0.389 | - | |

ST 3-3 | ELBW | 0.333 | - |

Natural Frequency ± St.dev (Hz) | Relative Damping ± St.dev (%) | ||
---|---|---|---|

October 2014 | September 2020 | October 2014 | September 2020 |

2.55 ± 0.02 | 1.98 ± 0.02 | 1.46 ± 1.02 | 2.87 ± 0.80 |

3.10 ± 0.03 | 2.63± 0.02 | 2.84 ± 1.75 | 2.76 ± 1.19 |

Compressive Strength | Initial Shear Strength | Young’s Modulus | Shear Modulus | Specific Weight | Tension Strength | |
---|---|---|---|---|---|---|

Masonry typology | f_{m} [MPa] | f_{vm}_{0} [MPa] | E [MPa] | G [MPa] | γ [kN/m^{3}] | f_{t} |

Masonry in bricks and lime mortar | 3.4 | 0.16 | 1500 | 500 | 18 | 0.114 |

In-Plane Failure Mechanisms | Analytic Expression |
---|---|

Crushing/bending | ${V}_{\mathrm{Rd},\mathrm{r}}=\mathsf{\psi}\frac{{\sigma}_{0}{t}_{w}{l}_{w}^{2}}{2\mathrm{h}}\left(1-\frac{{\sigma}_{0}}{{f}_{\mathrm{Mc}}}\right)$ |

Shear diagonal cracking | ${V}_{\mathrm{Rd},\mathrm{t}}={\mathrm{l}}_{w}{t}_{w}\frac{{f}_{\mathrm{Mt}}}{b}\sqrt{\left(1+\frac{{\sigma}_{0}}{{f}_{\mathrm{Mt}}}\right)}$ |

Shear sliding | ${V}_{\mathrm{Rd},\mathrm{ts}}={\mathrm{l}}_{wc}{t}_{w}\left({f}_{v0}+\mathsf{\mu}{\mathsf{\sigma}}_{d}\right)$ |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Uroš, M.; Demšić, M.; Šavor Novak, M.; Atalić, J.; Baniček, M.; Jevtić Rundek, R.; Duvnjak, I.; Košćak, J.; Pilipović, A.; Prevolnik, S.
Damage Evaluation and Seismic Assessment of a Typical Historical Unreinforced Masonry Building in the Zagreb 2020 Earthquake: A Case Study—Part I. *Buildings* **2024**, *14*, 474.
https://doi.org/10.3390/buildings14020474

**AMA Style**

Uroš M, Demšić M, Šavor Novak M, Atalić J, Baniček M, Jevtić Rundek R, Duvnjak I, Košćak J, Pilipović A, Prevolnik S.
Damage Evaluation and Seismic Assessment of a Typical Historical Unreinforced Masonry Building in the Zagreb 2020 Earthquake: A Case Study—Part I. *Buildings*. 2024; 14(2):474.
https://doi.org/10.3390/buildings14020474

**Chicago/Turabian Style**

Uroš, Mario, Marija Demšić, Marta Šavor Novak, Josip Atalić, Maja Baniček, Romano Jevtić Rundek, Ivan Duvnjak, Janko Košćak, Ante Pilipović, and Snježan Prevolnik.
2024. "Damage Evaluation and Seismic Assessment of a Typical Historical Unreinforced Masonry Building in the Zagreb 2020 Earthquake: A Case Study—Part I" *Buildings* 14, no. 2: 474.
https://doi.org/10.3390/buildings14020474