Seismic Risk Assessment in School Buildings: A Comparative Study of Two Assessment Methods

Abstract

Seismic risk assessment in school buildings is critical for ensuring the safety and resilience of educational institutions against seismic events. This paper presents a new seismic risk methodology named MM Risk and comparative study with Adriseismic methodology used for seismic risk assessment. The study aims to provide insights into the effectiveness and reliability of these methods in evaluating the seismic vulnerability of school buildings. Through a comprehensive review of the existing literature and application on a dataset of 213 schools (367 buildings), this paper evaluates the strengths and limitations of each method in terms of accuracy, complexity, and practical applicability. The results show that by integrating the approach of Adriseismic methodology and incorporating extensions related to irregularities, the social risk component (number of users), and the ability to assess different types of structures, a comprehensive and tailored methodology for assessing seismic risk can be developed. This is important since these factors are strongly influencing the seismic risk of schools as connected systems. Furthermore, this paper explores the implications of these findings for improving seismic risk mitigation strategies in school buildings. MM Risk methodology places over 70% of school buildings in the medium seismic risk category and 27% in the high seismic risk category. On the other hand, the Adriseismic methodology is more stringent, classifying 60% of school buildings into high and very-high risk categories. This disparity undoubtedly influences the prioritization list for seismic risk mitigation measures. However, definitely the comparative analysis presented in this paper offers valuable guidance for engineers, policymakers, and stakeholders involved in the seismic retrofitting and design of school buildings, ultimately contributing to the enhancement of seismic resilience in educational infrastructure.

1. Introduction

Along with the increasing worldwide urban growth and the constant threat of seismic events, the vulnerability of vital infrastructure, notably educational institutions, to seismic hazards has emerged as a pressing issue [1]. The possibility of catastrophic earthquakes hitting heavily populated areas emphasizes the critical need to understand and mitigate the seismic risk linked with schools [2]. This study seeks to explore the seismic risk of schools, illuminating the potential aftermath of earthquakes on these buildings and suggesting methodologies for evaluating seismic risk.

Educational institutions play a central role in shaping the future of communities, acting as centers for education, creativity, and social unity. However, the vulnerability of schools to seismic events presents a notable hazard to the well-being of students, teachers, and the wider society they serve [3]. The consequences of inadequately prepared and structurally deficient school buildings extend beyond the immediate aftermath of earthquakes, affecting the social cohesion, economic stability, and overall resilience of a region [4]. The seismic risk related to schools is a complex challenge that requires a thorough examination of various elements, such as building integrity, geological features, and the efficacy of existing risk-reducing measures [5]. Efforts have been made to consolidate existing knowledge on methods for assessing seismic risk [6] and to examine case studies illustrating the seismic vulnerability of schools in different regions [7]. At the onset of this exploration into seismic risk concerning schools, it is crucial to acknowledge the interdisciplinary nature of this issue [8]. Cooperation among structural engineers, seismologists, educators, policymakers, and community members is vital to crafting comprehensive solutions that tackle the distinct vulnerabilities and complexities associated with educational institutions [9]. By improving the knowledge of seismic risk factors and implementing tailored mitigation strategies, we can strive to establish safer and more resilient learning environments for both current and future generations [10].

One of the ways to prepare better is to perform seismic risk assessment studies and obtain the information about the risk status of schools and then prioritize them for mitigation actions. One of the most comprehensive documents covering the topic of rapid visual screening of structures for the purpose of detecting seismic vulnerability, i.e., potential seismic hazards is the FEMA 154 Rapid Visual Screening of Buildings for Potential Seismic Hazards: A Handbook [11], and the accompanying publication FEMA 155: Supporting Documentation [12]. They provide a methodology for the rapid visual screening of buildings. The first edition of the FEMA 154 dates back to 1988 [13,14], followed by the second edition in 2002 [15,16], and the third, the most recent in 2015 [11,12]. The rapid visual screening (RVS) procedure developed in these documents is based on a scoring system included in the data collection forms in which data are collected by the visual observation of structures. These documents cover only structural behavior, and for non-structural evaluation FEMA E-74 [17] can be used.

In addition to the FEMA manuals, the RVS procedure based on scoring was also developed in Canada (NRCC 1993) [18]. The approach relies on several critical factors, encompassing seismic activity, soil characteristics, structural type, structural irregularities, and the presence of non-structural risks. Additionally, the significance of the building and its occupancy are considered. Data for each structure are gathered using a standard seismic screening form, generating a seismic priority index score for each. These scores are subsequently utilized to prioritize buildings in the inventory for thorough seismic assessment, effectively identifying those that necessitate further review.

The method outlined in the standard for seismic evaluation [19], originating from Japan, focuses exclusively on reinforced concrete (RC) structures. It relies on assessing a “seismic index” designated for the structure, reflecting its seismic performance, and a seismic index for non-structural elements, such as exterior walls, to gauge their seismic resilience.

In New Zealand, the current approach to seismic assessment of structures is grounded in the latest manual, which dates back to 2017: The Seismic Assessment of Existing Buildings [20]. This manual supersedes the previous versions issued in 2006 and 2016. Seismic evaluation can be qualitative, offering a broad indication of a building’s earthquake rating and providing an overall perspective on its structural weaknesses, ultimately assigning a qualitative earthquake rating. While this method is described as simpler, it necessitates skilled engineers capable of identifying critical issues likely to impact seismic performance and possessing a solid understanding of building code requirements.

FEMA 154 [11] and FEMA 155 [12] have been used throughout the world as a baseline document for developing or modifying the methodology for the specific structural characteristics, building practice, and provided building code levels of safety. It has been used both as a case level study aiming to cover only a specific local area or specific type of structure, as well as in various building types. Some examples of national practices based on the FEMA approach are India [21,22], Turkey [23,24,25], Indonesia [26], Myanmar [27], Austria [28], Peru [29], the Philippines [30], etc.

Moreover, several approaches have been suggested to enhance the aforementioned RVS, aiming to increase cost-effectiveness and reduce subjective errors during the survey. Some researchers classify these approaches into two categories [31]: those rooted in statistical and machine learning methodologies, and those centered around fuzzy-based methods. Statistical approaches establish (linear) connections between input variables and seismic risk, whereas machine learning methods still encounter reliability issues with constrained datasets. Conversely, fuzzy systems incorporate expert opinions and capture ambiguity using fuzzy set theory.

Several methods, drawing from statistical approaches, have been developed, including those employing linear regression [21]. However, with the recent advancements in machine learning, an alternative automated strategy has emerged. This method automatically gathers street view images from Google Maps and utilizes deep learning methods to detect and categorize soft-story buildings within these images [32]. Compared to traditional screening methods, this proposed approach offers advantages in terms of cost efficiency, scalability, and consistency in evaluation.

Another enhancement to the RVS method involves the development of a smartphone app based on a multi-criteria decision-making tool for assessing and prioritizing building vulnerability. This improvement incorporates a global sensitivity analysis to explore the interactions between input parameters [33]. Additionally, artificial neural networks have been employed, leveraging a “training” dataset to predict seismic damage for data not included in the training set. Depending on the dataset’s variability, these networks can reliably predict the seismic damage state [34,35].

Furthermore, fuzzy logic approaches have been utilized in determining seismic vulnerability. These include type 1 approaches, which consider only vagueness in the membership functions, and type 2 approaches, where the membership functions themselves are treated as fuzzy [36,37].

Considering schools as structures whose seismic vulnerability could pose a significant societal impact, several comprehensive studies have been conducted in Europe [38,39,40,41,42,43,44]. Also, a fair amount of RVS studies have been performed specifically on this type of structure [45,46,47]. Some studies focused on qualitative surveys aimed to identify the most vulnerable school buildings among the dataset [45,46], where an appropriate methodology was developed accommodated to local conditions in the form of standardized questionaries. There are also examples of direct implementation of the FEMA approach for the seismic vulnerability assessment of schools in Peru [29] and the Philippines [30], or combination of developing fragility curves and RVS questionnaires [47].

Important input for every seismic risk assessment is the seismic hazard. The territory of the Republic of Serbia is located in a seismically active area. This is a fact that is not so socially current and represented and is very quickly forgotten after the earthquake. The fact is that in the territory of Serbia, seismic effects due to earthquakes of significant intensity occurr relatively rarely. Social awareness of the importance of earthquakes was suddenly awakened after the devastating earthquake in Skopje in 1963. The significance of the earthquake in Skopje is far wider, because after that seismic event, the technical regulation dealing with seismic design was introduced for the first time. The relevance of earthquake engineering at all levels of society was declining until the earthquakes in Banja Luka (1969) and Montenegro (1979). The earthquakes in Kopaonik (1985), Mionica (1998 and 1999), and Kraljevo (2010) were not enough to pay the necessary attention to earthquakes in Serbia in all segments of society. In the territory of the Republic of Serbia, the level of seismic hazard is largely determined by the occurrence of local low to moderate earthquakes. Central Serbia is home to the largest number of strong earthquakes and the highest seismic hazard. The effects of earthquakes are the greatest, due to the influence of the local soil, in river valleys, and on steep mountain slopes. In Western Serbia, the hazard is controlled by local earthquakes near Krupanj, Bajina Bašta, and Sjenica with magnitudes around 5. For the southern part of the Pannonian Basin, there are only historical data on strong earthquakes with certain accuracy, and the seismic activity in the Pannonian Basin is extremely low. This means that strong earthquakes occur with a long return period, which makes it difficult to reliably define the seismic hazard. The strong earthquakes of Vrancea (Romania) are significant for the area of Eastern Serbia. The situation is similar in the area of Southeast Serbia, where there are no strong local earthquakes. The hazard in this area has its causes in the catastrophic earthquakes that occurred in Bulgaria and Macedonia. The key problem in defining the seismic hazard in the territory of Serbia is insufficient study of the fault activity, which is of particular importance for defining the danger for our largest cities, Belgrade, Novi Sad, and Niš. Figure 1 shows a seismic hazard map for the Republic of Serbia, where the PGA values for soil type A can be seen.

This paper presents the application of two methodologies on a dataset of 213 schools (367 buildings) in Serbia. The recently developed MM Risk methodology is presented and applied to the dataset. Then, the results are compared with the results of the Adriseismic methodology [49,50,51]. The aim of such studies is to derive the prioritization list.

2. Description of the Seismic Risk Assessment Methodologies

To prioritize seismic risk assessment for school buildings in Serbia, the aim was to utilize an empirical technique tailored to the region’s characteristics and construction practices. However, currently, there is not a fully suitable empirical methodology for rapidly estimating seismic risk in Serbia. Thus, the authors developed the MM Risk methodology, which was then compared to the Adriseismic methodology [49,50,51], previously validated in various instances [51]. The Adriseismic methodology was designed for the quick assessment of seismic risk in countries neighboring the Adriatic Sea, including Serbia, Greece, Albania, Italy, Croatia, and Slovenia. While this methodology provides a solid foundation, it requires refinement and adjustments to adequately address Serbia’s seismic activity and building structures. To facilitate field data collection and seismic risk evaluation, the MM Risk methodology was created, with a primary focus on preventing any casualties. Both methodologies are described in this section.

2.1. Adriseismic Methodology

The Adriseismic methodology [49,50,51] offers a rapid approach to evaluating the seismic vulnerability and risk of buildings. This methodology revolves around gathering essential building data and entering them into designated Excel forms (Figure 2). Once the data are inputted, background calculations are performed within the spreadsheet, resulting in an assessment. The methodology is designed to assess both masonry and reinforced concrete structures, hence providing two Excel templates—one for masonry buildings and another for concrete buildings (Figure 2). The core concept involves initially collecting necessary data, primarily through visual inspections of the structures and, when available, documentation pertaining to the buildings. The general structure of the Adriseismic methodology is given in Figure 2.

The initial step involves selecting the building’s foundation, floors, roofs, and wall types. The subsequent phase includes categorizing each construction parameter that influences the outcome into one of three categories. The final step entails specifying the building’s use, the ground category it sits on, and the horizontal ground acceleration, derived from seismic hazard maps relevant to the facility’s location. Once all necessary data are inputted (such as soil type, PGA, masonry size, mortar type, column dimensions, plan and height irregularities, etc.), an automatic calculation occurs in the background of the Excel document, generating the result. The result comprises three components: the seismic behavior index, indicating the building’s quality and readiness to withstand future earthquakes; the seismic risk level, indicating the likelihood of damage in the event of a future earthquake in the area; and the anticipated mechanism of the building’s failure.

This methodology classifies building structures into masonry and concrete frame structures, offering two distinct Excel sheets for data input and results display. It is important to highlight that although these two types of buildings are common in Serbia, the methodology does not cover other types such as wooden structures, steel structures, or mixed masonry and concrete systems. Moreover, the methodology exclusively concentrates on the frame system of reinforced concrete structures and does not address buildings with reinforced concrete walls or dual-reinforced concrete walls and frames.

For masonry structures, the input data required for the assessment can be categorized into 5 sections: general data (assessment date, address, and GPS coordinates), construction characteristics (type of foundation, walls, floor slab, and roof of the considered structure), masonry quality (type of masonry as well as choosing one of three levels of masonry quality and the quality of its execution), building characteristics (predominant use of the structure, the number of floors above ground in the building, the connection between structural elements, as well as the quantity level for irregularities in the plan, transversal wall distance, wall thickness, floor height, irregularities in height, expected ductility, permanent floor loads, thrusts due to arches or vaults at floor level and thrusts due to arches or vaults at roof level), and site data (three input parameters that pertain to the seismic zone of the building site in accordance with the specifications outlined in Eurocode 8) [52,53].

Resulting from the assessment for masonry structures, the following output parameters are derived:

• Masonry category: Determined by the quality of masonry, expressed as the letters A, B, or C, indicating the masonry’s capacity to withstand vertical, in-plane, and out-of-plane loads.
• Index of structural response: Influenced by both masonry quality and building characteristics, this index signifies the seismic vulnerability of the structure. It is presented as a decimal number ranging from 0 to 1, alongside corresponding categories from I to VI. A higher number or category suggests lower seismic vulnerability.
• Probable collapse mechanism: Categorized into three groups based on identified collapse mechanisms.
• Seismic risk: Derived from masonry quality, building characteristics, and site data, expressed as a decimal number equal to or greater than 0. A higher decimal number indicates a higher risk level, accompanied by categories such as “none,” “low,” “medium,” “high,” and “very high.”
• Retrofitting: Based on identified structural vulnerabilities, this parameter allows for the selection of materials and methods for structural retrofitting to implement mitigation measures.

For concrete structures, the input data needed for assessment can be divided into three sections: general data, building characteristics, and site data. The input in the general data and site data sections are the same as for masonry structures, while the building characteristics category one selects the use of the structure, the number of floors above ground, the presence of large spans, as well as the choice of the quantity level (I, II, or III) for irregularities in the plan and height, expected ductility, concrete strength, steel strength, column dimensions, transversal reinforcement (column), and longitudinal reinforcement (column).

As a result of the assessment for concrete structures, the following 4 parameters are obtained: the index of structural response, probable collapse mechanism, seismic risk, and retrofitting. The interpretation of the index of structural response, seismic risk, and retrofitting aligns with the previously provided explanation for masonry structures. Possible failure mechanisms for concrete structures, according to this methodology are a soft story mechanism, brittle column failure due to combined tension and shear, brittle column failure due to combined compression and shear, compression failure of columns, failure due to torsional effects, and ductile column failure.

While the initial Adriseismic methodology provided a solid foundation for risk assessment, adjustments were necessary to ensure its comprehensive applicability to the unique conditions in Serbia. Originally developed for Italian construction practices and conditions, the Adriseismic methodology required certain alterations for the Serbian context. It is crucial to note that construction in practice in Serbia, although having European roots, can differ from the Italian construction sector, especially for the older buildings. Also, the influence of the economy and culture on construction, interior arrangement practice, and architectural aspects can diverge. These modifications were achieved through the calibration of coefficients related to the impact of design horizontal ground acceleration, transversal wall distance, floors above ground, wall thickness for masonry structures, and expected ductility on seismic risk. Additionally, the methodology incorporated the influence of building extensions, a factor not considered in the initial methodology but crucial in Serbia due to a significant number of extended structures. For masonry structures, the coefficients associated with material quality and construction method remained unchanged, as these aspects were deemed adequately addressed in well-established Italian standards. The modification process involved several iterations, with the calibration and adjustments thoroughly documented and presented in [54].

2.2. MM Risk Methodology

The basic principles of the MM Risk methodology are as follows:

• The absolute priority is to avoid the scenario of even one causality; therefore, life safety is the main criterion of the methodology.
• The large number of school objects brings the necessity to standardize criteria for ranking in order to plan investment (structural and non-structural) for the buildings at the highest risk.
• The methodology considers the correlation of earthquakes to other hazards that can occur as a secondary effect (damage or explosion of water and gas installations, landslide…).

The total risk score consists of a technical score and social score, where the technical score weighs 60% in the total score and the social score weighing factor is 40%. The technical risk score is computed by considering the seismic hazard, structural seismic vulnerability, required repairs, overall impression (engineering judgment), condition of non-structural elements, and installations and equipment. The weighting factors for these categories are detailed in

Table 1. Weighting factors for calculation of the technical seismic risk score.

Structural Seismic Vulnerability	Condition of Non-Structural Elements	Condition of Installations and Equipment	Needed Repairs	General Impression
30%	30%	10%	20%	10%

. The scores for each category are multiplied by these weighting factors before being summed. It is important to mention that weighting factors were selected based on the engineering judgment and empirical experience on the topic, after consultations with practitioners, architects, and colleagues conducting risk assessments in insurance companies. Subsequently, the score is further multiplied by the ratio of PGA (peak ground acceleration) at the school’s location to the maximum PGA for Serbia, which stands at 0.24 g as per the official seismic maps provided by the Seismological Survey of Serbia (Figure 1). To gather field data, a questionnaire (report) was developed, encompassing sections regarding general information about the school building, data about other school buildings at different locations, school geometry (irregularity in height and plane), year of construction, number of floors, structural type, soil type at the school’s location, photos from field visits, checklists, comments, etc. Using these data, the score for structural seismic vulnerability was computed. Soil type was taken into account only as a factor as in the response spectrum analysis, but not specifically considering landslides and the possibility of soil liquefaction, since these data were not available. A scoring table from FEMA P-154 [11] served as the basis for this calculation, with a maximum score of 3.6. Hence, the structural seismic vulnerability score is the ratio of the calculated value to the maximum value (3.6). The score for needed repairs is determined based on the average price per square meter, considering the school’s location (urban, suburban, or rural), and the extent of repairs required. A crucial aspect of the questionnaire (report) is a table containing information about the structural condition and any current damage to structural and non-structural elements. Special attention is given to non-structural elements and furniture in the school buildings, which may not directly contribute to building collapse but can impact injuries and casualties. The final step involves the engineer providing a general impression of the school building. The overall impression is included as a factor to take into account possible degradation of element strength (concrete due to corrosion, masonry due to lower material quality, etc.), as well as some interventions made during the use of schools that could influence the structural response under earthquakes (such as creating openings in the floor). These five categories are summed up to create a score that is then divided by the total gross area of the school building to form the final value of the technical score.

The conditions of the non-structural elements and installations and equipment can together form a non-structural score and thus the non-structural risk. The same structural seismic vulnerability of needed repairs and engineering as a general impression can form a structural score and risk.

The social score, which accounts for 40% of the total score, reflects the ratio of the social index to the maximum social index across all investigated schools. It provides a ranking of schools based on the social index. The social index is calculated by multiplying the score of the users by the distance of the school from other schools. To incorporate the number of pupils in the seismic risk assessment, the score for users is determined by ranking all investigated schools according to the number of pupils. The schools with the highest number of pupils receive a higher component of the seismic risk score in this regard. The index for distance is also derived from ranking schools based on the furthest distance to neighboring schools. Consequently, schools without another nearby school receive a higher risk score because in the case of an earthquake it is more difficult to find the substituting school for their pupils. School halls are documented, but their presence is not taken as a factor influencing the social or technical score of the school. This is conducted because they can be used as shelters, not only for pupils but also for all the people from that area and therefore there is a low possibility that halls could be used for teaching or as a substituting place for classrooms. During the field work, information about the shift work in schools was fortunately collected and then used to calculate the social score. Namely, the number of shifts (one or two) was used as a multiplication factor for the social score; since the schools with two shifts have a two-times higher risk of earthquake occurrence when the school is in use by pupils and staff.

The technical, social, and total score are transformed into the risk level by ranking as follows:

• “High” for the values of the score lower than 25;
• “Medium” for the values of the score between 25 and 50;
• “Low” for the values of the score higher than 50.

3. Dataset of School

Within this chapter, the results of detailed research will be presented, which included a database of 213 primary and secondary schools in parts of Serbia with a high seismic hazard. The research included an analysis of the current state of the schools and the preparation of detailed reports. These reports are the basis for seismic risk analysis.

Certain schools were extended as the need for school capacity increased from year to year, and from decade to decade. Therefore, the dataset consists of 367 buildings, from which old school buildings, new school buildings, and sports halls can be distinguished. For every school, its location (GPS coordinates) was collected and marked on the map, together with the satellite photo (Figure 3). Furthermore, photos of the school facade were taken (Figure 4), as well as photos from the inside of the school (Figure 5), and placed into the report. Special attention in the technical questionnaire/report was paid to the non-structural and furniture elements in the school buildings that are not related to the building collapse but can affect injuries and causalities.

During the collection of the data on the field, the available technical documentation was collected (Figure 6) with the aim of supporting the classification of the structural system. Technical documentation often presented a valuable source for finding the year of construction, type of slab, footprint area, etc. During the field work, investigations about the quality of the materials (destructive and non-destructive tests) were not performed since this was not in the scope of the work; therefore, conclusions about the material type and quality (concrete, mortar, bricks, etc.) can only be made based on the assumptions related to the construction type and year.

Analyzing the reports of each school individually, the buildings were divided according to pre-defined categories:

• Construction period;
• Footprint shape;
• Type of vertical structural system;
• Type of floors/slabs;
• Number of floors;
• Total gross area of facilities;
• Presence of a sports hall.

All the abovementioned categories were processed and evaluated within the database. Figure 7 shows the construction period and the percentage share of buildings, according to predetermined ranges of years of construction. Here, it can be seen that the largest number of buildings (171) were built in the period from 1961 to 1980, that is, almost 50% of the buildings from the database.

The next criteria by which objects were classified was the building footprint shape. What should definitely be pointed out is that in addition to the usual building footprint shapes such as rectangular, L, H, and T, there were also shapes that are assigned to the category called “other” (Figure 8). These were the shapes of the letters X, F, E, etc. Figure 8 shows the shapes and the percentage share of those footprint shapes. Of the investigated 367 objects, 50% have a rectangular base, while also a significant number have a footprint in the form of the letter “L”. (This shape can be undesirable in terms of the effect of seismic forces, if no seismic joint is constructed; therefore, information about the presence of seismic joints was documented as well and taken into account in the technical score by improving it to the factor for rectangular shape if a seismic joint was present.)

One of the most important criteria is the type of structural system, i.e., its predominant supporting vertical structure and predominant horizontal structure (floors/slabs). In the case of a vertical supporting structure, in the database we can distinguish between RC (reinforced concrete frames, walls and dual systems), masonry (unreinforced and confined), timber, steel, prefabricated and combined (for example, masonry and RC, masonry and timber, etc.). Whereas, in the case of floors/slabs, several systems were identified: vaults, flexible floors (wooden), semi-rigid (steel beams), rigid (reinforced concrete), and others. Figure 9 and Figure 10 show the distribution in numbers and percentage of the vertical and horizontal structural systems.

Based on previous charts, it can be concluded that the most dominant are reinforced concrete and masonry structures. Therefore, it is interesting to notice their dominant periods of construction (Figure 11). Most of the buildings with a predominant masonry structure were built in the period from 1901 to 1940. (40%), while the majority of those with an RC structure were in the period from 1961 to 1980 (56%).

The next criterion by which the buildings were classified was the number of floors of the school buildings (Figure 12). The largest number of buildings have only a ground floor and GF+1 floor. As we move towards three, four, and five stories, masonry structures are less and RC load-bearing structures are becoming more common.

The size of the school (total gross area) and the presence of the sports hall represents important information for the purpose of providing a shelter in case of natural disasters. However, the total gross area was not used as a factor influencing the seismic risk score. It was more important for the decision makers to estimate potential costs, if they decided to agree to the retrofit. Therefore, these data were collected as well, and Figure 13 shows that most of the school buildings have a total gross area of up to 1000–1500 m², and that unfortunately most of them (70%) do not have a sports hall as a separate building, but a classroom adapted to serve as an improvised sports hall for sport classes during the wintertime. The same type of data (year of construction, structural type, etc.) were collected for the sports halls as well.

All these characteristics are important for the behavior of the structures under earthquake loading; therefore, these data present a valuable input for determining the seismic risk of the buildings from the dataset of schools.

4. Application of the Two Methodologies on the Dataset

The research included the collection of archival data and data in the field, then their processing, and filling in the forms of the mentioned methodology. Based on calculations using the methodologies, the results were obtained—data on the seismic risk of all 213 schools (367 buildings). In the following sections, the results from both methodologies are presented, followed by their comparison.

4.1. Adriseismic

The investigated schools are distributed throughout various parts of Serbia, encompassing both urban and rural areas. During observations, reinforced concrete, masonry, prefabricated, steel, wooden, and combined systems were identified in all considered schools. While this methodology is applicable to masonry and reinforced concrete frame structures, which constitute the majority of schools, it was not feasible to apply it to steel and wooden schools, resulting in their exclusion from consideration. There were a total of 18 steel buildings and 7 wooden buildings. Combined systems, such as a combination of reinforced concrete and masonry, reinforced concrete and wooden, or reinforced concrete and steel, were also encountered. For combined reinforced concrete and masonry systems, evaluations were conducted separately for masonry and concrete, with the less favorable result adopted. Combined reinforced concrete and wooden systems, as well as combined reinforced concrete and steel systems, were assessed using the concrete system form. In cases where structural vertical elements were concrete and slabs were wooden, the minimum ductility of the building was assumed (q = 1.5). Some schools had multiple buildings on the same parcel, including old and new schools, gymnasiums, kitchens, etc. If these buildings were physically separated or had seismic divisions, their plan irregularity was assessed based solely on their individual shapes. Otherwise, irregularity was evaluated for all connected buildings as if they were one structure.

Figure 14 shows the result of the modified Adriseismic methodology. The seismic risk of buildings is expressed on a scale of none–low–medium–high–very high. It can be seen that more than 1/3 are in a category of medium seismic risk and 60% are in the categories of high and very-high seismic risk.

4.2. MM Risk

It is interesting to show the results of MM Risk methodology for different categories. First, the technical risk is shown on Figure 15 (left). It can be seen that more than 96% of schools have a medium or high seismic risk related to the structures itself. However, it is crucial to remember that technical risk comprises both structural and non-structural elements. Thus, Figure 16 illustrates the outcomes concerning the risks associated with these components. Structural risk factors in seismic hazards include vulnerability, necessary repairs, and overall assessment (engineering judgment), while non-structural risk accounts for seismic hazards, the condition of non-structural elements, and installations. The seismic risk results for structural and non-structural components show similarities, albeit with slightly higher percentages in the medium risk category for non-structural elements compared to structural ones.

As detailed in the MM Risk methodology, the seismic risk assessment for schools integrates both technical and social scores, with a weighting of 60% and 40%, respectively. The social score considers factors such as the proximity of the school to others and the student population, enriching the overall understanding of seismic risk for schools. Figure 15 (right) illustrates that over two-thirds of schools fall into the medium social seismic risk category. When technical and social risks are combined (Figure 17, left), it reveals that the majority (72%) of schools are categorized as having a medium seismic risk. Only 1% are classified as low risk, while 27% require mitigation measures due to being in a high risk category. On Figure 18, a map of Serbia with circles of different colors that characterize a certain level of seismic risk by school (green circle—low risk; yellow circle—medium risk; and red circle—high risk) can be seen. The map gives a good overview of the prioritization for seismic risk mitigation activities. Furthermore, this is strongly supported by the number of school users per seismic risk category, showing that more than 40 thousand pupils and school staff are in a high seismic risk category. This brings some alerts and therefore it helps in deciding on seismic risk reduction activities.

5. Comparison of the Results and Discussion

The seismic risk assessment was conducted for all school buildings in the dataset using the two mentioned methodologies. The assessment results are illustrated in the preceding figures, presenting the distribution of examined buildings based on their seismic risk levels for each methodology. While the Adriseismic methodology typically provides four types of results, this presentation focuses solely on seismic risk levels. It is noteworthy that the Adriseismic methodology indicates that a significant portion of school buildings fall into the high and very-high seismic risk categories, a finding that may seem somewhat unexpected.

The outcomes of the modified Adriseismic methodology are utilized for comparison with the results obtained from the MM Risk methodology. Comparing the results of these two methodologies poses significant challenges due to differences in their conceptual frameworks and outcomes. Adriseismic methodology categorizes seismic risk into five categories, whereas MM Risk methodology employs just three. Nonetheless, certain trends can be observed for both methodologies. The MM Risk methodology places over 70% of school buildings in the medium seismic risk category and 27% in the high seismic risk category. On the other hand, the Adriseismic methodology is more stringent, classifying 60% of school buildings into the high and very-high risk categories. This disparity undoubtedly influences the prioritization list for seismic risk mitigation measures.

The findings suggest that MM Risk methodology tends to assess seismic risk for buildings more cautiously than the modified Adriseismic methodology, possibly due to variations in the concepts and input parameters. While the conceptual disparities among the methodologies have been previously outlined, the distinctions in input parameters are discussed subsequently. The Adriseismic methodology incorporates the characteristics of the building materials, yielding diverse outcomes for reinforced concrete (RC) buildings with differing stirrup spacing in columns or embedded steel reinforcement featuring distinct yield stresses. Moreover, it distinguishes between masonry buildings constructed with brick or stone, and varying types of mortar. Conversely, the MM Risk methodology lacks provisions for assigning varying material qualities or construction techniques. Instead, it assumes that by specifying the building typology in the assessment form, the material and construction quality are predefined for a given structure. The Adriseismic methodology does not account for the building occupancy’s (number of users) influence on seismic risk, despite the generally higher risk associated with public buildings such as schools. Conversely, the MM Risk methodology incorporates the number of pupils and school staff into its assessment. The Adriseismic methodology exclusively evaluates masonry and RC frame buildings, whereas the MM Risk methodology boasts a broad applicability, extending to concrete, masonry, wood, steel, and prefabricated structures. It is clear that the MM Risk methodology delves deeper into the influence of building geometry and structural element arrangement (e.g., presence of irregularities) on seismic vulnerability compared to the Adriseismic methodology. It identifies various plan and elevation irregularities, while the Adriseismic methodology only recognizes three criteria of irregularity, treating buildings with two or three irregularity types as equally vulnerable. In contrast to the Adriseismic methodology, which incorporates the number of floors as a factor affecting seismic risk, the MM Risk methodology omits this consideration. All these differences in the concepts and input parameters of the methodologies can be the cause of the observed differences in results. It should be noted that for the development of a methodology for the region of Serbia, it is recommended to use the concept and input data of the modified Adriseismic methodology, with an expansion related to the types of irregularities and various construction typologies detailed at a high level by the MM Risk methodology.

The seismic risk methodologies give valuable support for decision making and the prioritization list of activities. Traditionally, every building can be studied in detail by modeling it and using the methods based on nonlinear seismic response analysis methods, including time-history analysis and pushover analysis, which offer comprehensive insights into the behavior of buildings under earthquake loads. They account for material nonlinearity and geometric imperfections, providing detailed assessments of structural performance [55,56]. On the other hand, approximate static analysis techniques such as the capacity spectrum method and equivalent static method provide efficient means to estimate the seismic demands on structures [57]. While these methods lack the precision of nonlinear approaches, they offer valuable preliminary assessments for seismic design and retrofitting, especially for simpler structures or in early design stages. In recent times, Incremental Dynamic Analysis (IDA) has surfaced in various iterations as a parametric analysis technique, aiming to provide a more comprehensive estimation of structural performance under seismic loads [58]. However, all these methods are quite demanding and time consuming and it is not feasible to apply them on all the schools in one country. Therefore, prioritizing is needed and this can be achieved by applying seismic risk methodologies.

It is very important to have the information about the seismic risk for schools, as they pose a threat for school users. Therefore, significant work has been conducted in developing seismic risk mitigation measures for schools. Calvi [59] outlined suitable strengthening intervention strategies that logically utilize available resources. Cost–benefit analysis, using the breakeven time as a metric, proves to be a valuable tool in determining the economic feasibility of retrofit strategies, as studied by Cardone et al. [60]. Moreover, the recent introduction of seismic risk classification guidelines in Italy [61] offers a simplified method for classifying existing buildings before and after strengthening interventions. Adhering to these guidelines may result in tax deductions as an incentive to enhance the seismic safety of the existing Italian school building stock, thereby fostering increased awareness of seismic safety and the significance of adequate seismic retrofitting among citizens. Incorporating seismic resilience measures during construction or retrofitting may initially increase the life cycle cost of buildings; however, these investments often result in significant long-term savings by mitigating potential damage and ensuring occupant safety during seismic events as shown in some studies [62]. Therefore, a comprehensive analysis that balances initial costs with potential future benefits is crucial for informed decision-making in building design and maintenance.

Günaydin et al. [63] carried out structural condition assessment of a nineteenth-century historical masonry school building by conducting geometrical checking and seismic performance evaluation. They concluded that structural assessment requires the consideration of relevant code and guidelines; therefore, this has to be included in the seismic risk assessment of schools as well. Grant et al. [64] worked on a prioritization scheme for schools, deriving that the launch of a global campaign for safe schools and safe health structures in disaster-prone regions should first be undertaken. Second, measures should be taken to strengthen disaster-resilient public and private investments by implementing structural, non-structural, and functional disaster risk prevention and reduction measures in critical facilities, particularly schools and hospitals, as well as physical infrastructures. This includes prioritizing proper design and construction practices from the outset to withstand hazards, incorporating principles of universal design and the standardization of building materials, implementing retrofitting and rebuilding where necessary, fostering a culture of maintenance, and considering economic, social, structural, technological, and environmental impact assessments. Several retrofitting programs [65] and proposals have been developed [66,67,68,69,70], with the aim of improving the behavior of structures and schools as well. For all these tasks, seismic risk studies are a starting point. Therefore, the results of the studies presented in this paper give a solid basis for improving seismic safety in schools.

6. Conclusions

This paper introduces a new seismic risk methodology and demonstrates its application on a dataset of schools in Serbia. To evaluate its effectiveness, the results are compared with those obtained using the Adriseismic methodology. The objective is to identify the strengths of these methodologies, with the aim of informing the development of a new methodology for assessing the seismic risk of structures in Serbia that can be used for prioritization and appropriate risk mitigation.

Mitigating seismic risk in schools involves a comprehensive approach aimed at minimizing damage and ensuring the safety of pupils and staff during earthquakes. The first task is risk assessment. Conducting an assessment to identify potential vulnerabilities in school buildings and infrastructure to seismic activity is the starting task. This involves evaluating the structural integrity, soil conditions, and location-specific seismic hazards. After this, structural retrofitting can start. Therefore, before implementing structural enhancements to strengthen existing buildings against seismic forces, a seismic risk study has to be performed. This also influences a non-structural mitigation with the aim of securing non-structural elements such as furniture, equipment, and utilities to prevent injuries and damage during earthquakes. Seismic risk studies also support the emergency preparedness planning that aims to develop and implement emergency response plans tailored to seismic events. This includes establishing evacuation procedures, conducting drills, and educating students and staff on earthquake safety measures.

Both the Adriseismic and MM Risk methodologies were applied and analyzed in 213 schools comprising 367 buildings. It is observed that the original Adriseismic methodology is a good starting point for the risk assessment of buildings in Serbia, but it needs to be modified so that it fully corresponds to the application in the conditions of Serbia. The Adriseismic methodology was modified to suit the Serbian region. The results indicate that the modified Adriseismic methodology tends to estimate seismic risk more conservatively compared to the MM Risk methodology. The MM Risk methodology categorizes over 70% of school buildings as having a medium seismic risk, with 27% falling into the high risk category. In contrast, the Adriseismic methodology, being more stringent, places 60% of school buildings in the high and very-high risk categories. This difference significantly impacts the prioritization of seismic risk mitigation measures. Nonetheless, the comparative analysis outlined in this paper provides valuable insights for engineers, policymakers, and stakeholders engaged in the seismic retrofitting and design of school buildings, ultimately fostering improved seismic resilience in educational infrastructure.

Based on these findings, it can be concluded that a methodology for assessing seismic risk of structures in Serbia should have a similar conceptual framework and input parameters as the modified Adriseismic methodology. However, it should also incorporate extensions related to irregularities, the social risk component (number of users), and the ability to assess different types of structures, which the MM Risk methodology effectively covers. By integrating these aspects, a comprehensive and tailored methodology for assessing seismic risk in Serbia can be developed. The application of empirical methodologies emerges as an invaluable tool for swiftly and effectively assessing the seismic risk of buildings. This capability underscores the crucial importance of accurately determining such risks for the proper functioning of urban environments. By leveraging these methodologies, stakeholders can make informed decisions to enhance the resilience of structures and safeguard communities against the potential impact of seismic events. All of this is important for deriving a prioritization list and adequate mitigation strategies.

One of the most important activities where seismic risk studies can significantly help is the raising of public awareness and education. Raising awareness among stakeholders about seismic risks and the importance of preparedness involves community outreach initiatives, informational campaigns, and workshops to promote earthquake resilience. All of this needs the results of seismic risk studies. Afterwards, policy development and enforcement can start, such as enacting and enforcing building codes, regulations, and standards related to seismic resilience in school construction and maintenance. This ensures that new school buildings meet seismic safety requirements and existing ones are retrofitted as needed. And finally, without seismic risk studies of such a kind as presented in this paper, it is not possible to secure adequate funding and resources for implementing seismic risk mitigation measures in schools. This may involve seeking government grants, accessing disaster relief funds, or allocating budgetary resources at the local, state, or national level.

By addressing these tasks systematically, schools can enhance their resilience to seismic hazards and protect the lives and well-being of their occupants during earthquakes.