# Seismic Vulnerability Assessment of Historical Masonry Buildings in Croatian Coastal Area

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{y}, which represents the beginning of the damage, and the acceleration of the collapse of the building, PGA

_{c}.

## 2. Seismic Vulnerability Assessment of the Test Site

#### 2.1. Description of the Test Site

^{2}and includes more than 400 buildings. The settlement consists of a historical core with stone masonry buildings built between the 15th and 19th centuries (Figure 2) and of the parts outside the historical core dating from the beginning of the 20th century to the present (the north, east and, west parts are shown in Figure 3). These buildings were constructed in different periods according to different technical regulations. The oldest buildings were constructed before 1948; then, some blocks were erected from 1949 to 1964, from 1964 to 1982, and from 1982 to 2005. The most modern buildings have been built from 2005 onwards.

#### 2.2. Collection of the Geometrical, Material, and Structural Data

- Investigation of the buildings using historical documentation [40] and archival documentation of the town of Kaštela;
- Detailed survey of geometrical characteristics, architectural measurements, and creation of architectural drawings (floor plans and cross sections);
- Identification of structural systems and materials through visual inspection, using archive documentation, literature, and thermographic imaging in the several specific cases where, due to non-documented reconstructions, it was not possible to recognize the material and structural characteristics of the buildings;
- Characterization of the soil type by means of a geophysical survey.

#### 2.3. Seismic Vulnerability Assessment Using the Vulnerability Index Method

_{v}is calculated in the form:

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

_{i}is the weight of each parameter. This vulnerability index is then normalized in a 0–100% range. A low index means that the structure is not particularly vulnerable and has a high capacity under seismic action, whereas a high index shows that the structure is vulnerable and has low seismic capacity.

_{v}is 438.75.

#### 2.4. Seismicity of the Area

_{g}= 0.22 g and a

_{g}= 0.11 g for the return periods of 475 and 95 years, respectively. In Croatia, the type 1 response spectrum for an earthquake magnitude higher than 5.5 was adopted.

_{S,30}map along each line was also computed by averaging the vertical V

_{sH}tomographic values from the surface to a depth of 30 m. Relatively high obtained values, between 1.2 and 1.7 km/s, indicate the presence of shallow hard rock [14], which can be classified as soil type A according EN 1998-1:2011 [46]. Considering the results obtained along the three investigated lines and given the size of the test area, the seismic hazard was assumed to be constant for all buildings in the area.

#### 2.5. Vulnerability Index Results

#### Historical Core

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

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

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

_{v}> 60. Figure 7 shows the vulnerability map of the area, whereas the distribution of the vulnerability is shown in Figure 8. Most buildings in the historical core belonged to the high vulnerability class (25%) and to the medium-high vulnerability class (47%). A small number of buildings were classified as medium-low vulnerability (21%). Only a few buildings were of low vulnerability (7%), and these were old stone buildings that were reconstructed. Buildings with vulnerability index of 45 and larger were considered highly vulnerable, as expected, given the age of the town center. The indexes ranged from 11.1, corresponding to one of the newer houses that was completely renovated at the boundary of the core, to 76.9, the vulnerability index of the Cambi tower. Houses made of poorly connected walls, with flexible floor structures, irregular in layout and height, were revealed to be more endangered. In addition to these basic aspects, the degree of general preservation of the building and the presence of subsequent reconstructions significantly affected the vulnerability indexes.

## 3. Development and Calibration of Vulnerability Model

#### 3.1. Vulnerability Model

_{i}, and to the collapse, PGA

_{c}, as follows:

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

_{c}(d = 1).

#### 3.2. Static-Nonlinear Pushover Analysis of Representative Buildings

_{x}and u

_{y}), which are associated with a warping direction. This enables us to model both flexible and rigid floors.

_{i}Φ

_{i}/Σm

_{i}Φ

_{i}

^{2}, where Φ

_{i}is the i-th component of the eigenvector and m

_{i}is the mass of the node i. For the actual base shear force F and the corresponding top displacement of the structure d of the MDOF system, the values F

^{*}= F/Γ and d

^{*}= d/Γ represent the base shear force and the displacement of the equivalent SDOF system, respectively.

_{y}

^{*}, representing the actual strength of an idealized system, is equal to the base-shear force at the formation of the plastic mechanism. The initial stiffness was determined assuming an area equivalence between the equivalent and the bilinear system. The yield displacement of the bilinear SDOF system d

_{y}

^{*}= 2(d

_{m}

^{*}− E

_{m}

^{*}/F

_{y}

^{*}) was obtained from the deformation energy E

_{m}

^{*}up to the formation of the plastic mechanism. The mass m

^{*}, the stiffness k

^{*}, and the period T

^{*}of the equivalent SDOF system can be obtained as follows:

_{ay}and the elastic spectral acceleration S

_{ae}of an elastic SDOF with period T

^{*}are calculated as:

_{μ}is expressed as:

_{ai}and displacement S

_{di}were derived as follows:

_{y}and collapse acceleration PGA

_{c}are calculated from the corresponding displacements according to the following procedure.

_{r}

^{*}was cast as a function of the spectral elastic displacement S

_{de}(T

^{*}) using the following analytical relationship:

_{y}

^{*}is associated with the early damage state and ultimate displacement d

_{u}

^{*}with the collapse; the early damage ductility μ

_{y}and collapse ductility μ

_{c}are expressed as:

_{g}is peak ground acceleration, whereas f

_{i}(i = 1, …, 4) represents the function which defines four different branches of the elastic response spectrum and depends on the period T, soil factor S, and damping correction factor η, and the characteristics periods T

_{B}, T

_{C}, and T

_{D}represent the lower and upper limits of each spectral acceleration branch. The peak ground accelerations PGA

_{y}and PGA

_{c}, corresponding to the yield displacement and to the ultimate displacement, respectively, can now be calculated in the form:

^{3}. A limited knowledge level (KL1) of the building and a confidence factor of CF = 1.35 according to EC8-3 [48] were assumed.

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

_{g}= 0.22 g, and the soil factor S = 1.0. Figure 13 shows the results of a total of 36 pushover analyses. The behavior was different along the two main directions and depended on the direction of the lateral loads.

_{c}in the x and y directions are shown in Figure 14, together with their bilinear idealizations, which are essential for capacity identification. The lowest capacity in both directions was obtained for the linear distribution.

_{g}) in the x direction and 0.079 g (0.363 a

_{g}) in the y direction, where a

_{g}represents the design ground acceleration, defined by the seismic hazard map for the return period of 475 years, and it is equal to a

_{g}= 0.22 g.

_{y}, corresponding to the yield point. It is worth mentioning that the lowest values of PGA

_{y}and PGA

_{c}do not necessarily correspond to the same distribution of lateral forces. In this case, the capacity acceleration in terms of the yield is equal to 0.048 g (0.218 a

_{g}) in the x-direction and 0.028 g (0.130 a

_{g}) in the y-direction.

_{v}–PGA

_{y}and I

_{v}–PGA

_{c}for the yield and collapse states were obtained. The most representative functions were chosen. They can be used to approximately evaluate the yield and collapse peak ground accelerations for the historic center of Kaštel Kambelovac.

_{y}and PGA

_{c}, obtained through Equation (2) and using the relation shown in Figure 16. As PGA

_{y}and PGA

_{c}are functions of the vulnerability index I

_{v}, the values of PGA

_{y}, corresponding to damage d = 0, and PGA

_{c}, corresponding to damage d = 1, can be computed for each value of I

_{v}. These vulnerability curves are shown in Figure 18.

_{g}= 0.22 g and a

_{g}= 0.11 g for soil type A, respectively.

## 4. Discussion

- Identification of architectural, structural, and material characteristics of the buildings through the investigation of historical and archival documentation, literature, visual inspection, and thermographic imaging;
- Characterization of the soil type through a geophysical survey;
- Calculation of seismic vulnerability indexes for all buildings in the area;
- Calculation of the peak ground accelerations for early damage and collapse states of the buildings through non-linear static (pushover) analysis of representative buildings;
- Development of a new damage–vulnerability–peak ground acceleration relationship, which estimates the damage of the buildings under specific seismic action;
- Risk analysis in terms of seismic damage;
- Demonstration of seismic vulnerability and seismic risk using seismic vulnerability index maps and damage index maps.

_{v}< 60) and high (I

_{v}> 60) vulnerability classes. The reasons for such a high vulnerability are that these buildings cannot effectively bear the seismic load due to the fact that they were constructed with unconfined stone masonry walls, flexible wooden floors and roofs, and poor connections between the walls and floors. Additionally, irregularities in the plan and elevation, age, and the degree of general preservation of the building contribute to their high vulnerability. It has also been shown that reconstructed buildings have significantly lower vulnerability indexes. For example, one of the reconstructed buildings has a vulnerability index of 11.1.

_{g}= 0.22 g for T = 475 years in either direction. Moreover, a significant number of buildings achieved collapse at accelerations that are lower than the demand acceleration of a

_{g}= 0.11 g for a return period T = 95 years. These evaluations rely on the analysis of the global structural response. Evaluation of the local failure mechanisms for the Public Library building and a few other buildings showed that the lowest critical acceleration was obtained for the global response. Therefore, the yield and collapse acceleration and the associated damage for all buildings were estimated based on the global response of the structure. The motivation for this is that, considering that our final aim is a large-scale vulnerability assessment of the area, a global structural analysis is acceptable.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Town of Kaštela: (

**a**) protected architectural heritage of the town of Kaštela; (

**b**) a view of an old historical core, Kastel Kambelovac [39].

**Figure 4.**Examples of wall textures of stone masonry buildings: (

**a**) non-squared roughly shaped stone masonry of various sizes arranged in chaotic manner; (

**b**) wall composed of disorganized roughly shaped stones; (

**c**) walls made of natural well-worked homogenous squared stones accurately executed; (

**d**) walls of St. Mihovil church, composed of well-organized cut blocks.

**Figure 5.**Current state of buildings in the historic centre: (

**a**) damage to Cambi tower; (

**b**) completely demolished building; (

**c**,

**d**) significant cracks in the load-bearing walls of residential buildings.

**Figure 6.**(

**a**) Location of the Kaštela City on the Dalmatian coast. (

**b**) Position of the seismic lines in the historic center of Kaštela [47].

**Figure 9.**Spatial distribution of the 11 parameters that comprise the seismic vulnerability index: (

**a**) type and organization of the resistant system; (

**b**) quality of the resistant system; (

**c**) conventional resistance; (

**d**) position of the building and foundation; (

**e**) typology of floors; (

**f**) planimetric configuration; (

**g**) elevation configuration; (

**h**) maximum distance among walls; (

**i**) roof; (

**j**) non-structural elements; (

**k**) state of conservation.

**Figure 12.**Public library: (

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

**b**) ground floor plan; (

**c**) section view; (

**d**) structural model used for non-linear seismic analysis.

**Figure 15.**Analyzed buildings: (

**a**) Cambi Tower; (

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

**c**) Public Library; (

**d**) Rowing club; (

**e**) Kindergarten; (

**f**) Ballet School; (

**g**) Dudan Palace; (

**h**) Folk Castle; (

**i**) Kumbat Towers; (

**j**) Residential building—Obala kralja Tomislava 1; (

**k**) Perišin house.

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 | var. |

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

Elevation configuration (P7) | 0 | 5 | 25 | 45 | var. |

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

Roof (P9) | 0 | 15 | 25 | 45 | var. |

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

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

Direction | Load | Eccentricity | PGA_{y}/g | PGA_{c}/g |
---|---|---|---|---|

+x | uniform | 0 | 0.063 | 0.148 |

+x | linear | 0 | 0.057 | 0.144 |

+x | modal | 0 | 0.257 | 0.264 |

−x | uniform | 0 | 0.121 | 0.188 |

−x | linear | 0 | 0.121 | 0.147 |

−x | modal | 0 | 0.235 | 0.257 |

+y | uniform | 0 | 0.046 | 0.095 |

+y | linear | 0 | 0.033 | 0.088 |

+y | modal | 0 | 0.051 | 0.168 |

−y | uniform | 0 | 0.054 | 0.132 |

−y | linear | 0 | 0.039 | 0.105 |

−y | modal | 0 | 0.060 | 0.173 |

+x | uniform | +5% | 0.052 | 0.130 |

+x | uniform | −5% | 0.079 | 0.171 |

+x | linear | +5% | 0.048 | 0.123 |

+x | linear | −5% | 0.072 | 0.166 |

+x | modal | +5% | 0.248 | 0.264 |

+x | modal | −5% | 0.231 | 0.245 |

−x | uniform | +5% | 0.109 | 0.151 |

−x | uniform | −5% | 0.143 | 0.553 |

−x | linear | +5% | 0.098 | 0.131 |

−x | linear | −5% | 0.136 | 0.557 |

−x | modal | +5% | 0.229 | 0.413 |

−x | modal | −5% | 0.207 | 0.208 |

+y | uniform | +5% | 0.040 | 0.089 |

+y | uniform | −5% | 0.055 | 0.107 |

+y | linear | +5% | 0.028 | 0.079 |

+y | linear | −5% | 0.038 | 0.100 |

+y | modal | +5% | 0.042 | 0.144 |

+y | modal | −5% | 0.066 | 0.212 |

−y | uniform | +5% | 0.048 | 0.118 |

−y | uniform | −5% | 0.063 | 0.146 |

−y | linear | +5% | 0.031 | 0.122 |

−y | linear | −5% | 0.045 | 0.115 |

−y | modal | +5% | 0.049 | 0.156 |

−y | modal | −5% | 0.071 | 0.194 |

Building | Vulnerability Index I _{V} [%] | Yield Acceleration PGA _{y} [g] | Collapse Acceleration PGA _{C} [g] |
---|---|---|---|

Cambi Tower | 76.9 | 0.030 | 0.078 |

St. Mihovil Church | 40.5 | 0.057 | 0.102 |

Public Library | 59.0 | 0.028 | 0.079 |

Rowing club | 40.2 | 0.064 | 0.141 |

Kindergarten | 41.0 | 0.059 | 0.092 |

Ballet School | 23.9 | 0.103 | 0.183 |

Dudan Palace | 50.1 | 0.051 | 0.083 |

Folk Castle | 58.7 | 0.081 | 0.080 |

Kumbat Towers | 65.2 | 0.057 | 0.103 |

Residential building | 34.8 | 0.081 | 0.152 |

Perišin house | 48.7 | 0.058 | 0.121 |

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**MDPI and ACS Style**

Nikolić, Ž.; Runjić, L.; Ostojić Škomrlj, N.; Benvenuti, E.
Seismic Vulnerability Assessment of Historical Masonry Buildings in Croatian Coastal Area. *Appl. Sci.* **2021**, *11*, 5997.
https://doi.org/10.3390/app11135997

**AMA Style**

Nikolić Ž, Runjić L, Ostojić Škomrlj N, Benvenuti E.
Seismic Vulnerability Assessment of Historical Masonry Buildings in Croatian Coastal Area. *Applied Sciences*. 2021; 11(13):5997.
https://doi.org/10.3390/app11135997

**Chicago/Turabian Style**

Nikolić, Željana, Luka Runjić, Nives Ostojić Škomrlj, and Elena Benvenuti.
2021. "Seismic Vulnerability Assessment of Historical Masonry Buildings in Croatian Coastal Area" *Applied Sciences* 11, no. 13: 5997.
https://doi.org/10.3390/app11135997