Analytical Seismic Vulnerability and Performance Assessment of a Special-Importance Steel Building: Application Under the NCSE-02 Code

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This work demonstrates how analytical models integrating hazard characterisation, modal testing, nonlinear analysis, and retrofitting assessment can be applied to evaluate and optimise the seismic performance of essential infrastructure. The methodology assists practitioners in refining vulnerability definitions and strengthening strategies for buildings that must remain operational after earthquakes.

Abstract

This study develops a comprehensive workflow for the analytical seismic vulnerability and structural performance assessment of a special-importance steel building located in a region of elevated seismic hazard in southern Spain. The work addresses the need for reliable analytical methodologies for facilities that must remain operational during earthquakes. The proposed framework integrates a probabilistic seismic hazard assessment, including uniform hazard spectra and hazard disaggregation to identify control earthquakes. Additionally, an analytical vulnerability assessment under the Spanish seismic design code, NCSE-02, is performed. Operational modal analysis and nonlinear analysis are combined to retrofit the numerical model of the building and capture the building’s realistic seismic response. The resulting demand spectra are derived from site-specific ground-motion scenarios for Los Barrios (Cádiz, Spain). Retrofitting strategies are designed and assessed to ensure compliance with the code-defined performance requirements. Results indicate that the retrofitted model reproduces the building’s dynamic behaviour with improved reliability, and that the strengthening interventions enhance seismic performance while still allowing moderate damage in specific components. These findings highlight the importance of analytical vulnerability approaches and code-oriented retrofitting when evaluating the seismic performance and vulnerability of essential facilities. The study demonstrates that rigorous analytical methods provide a robust basis for defining seismic vulnerability in special-importance buildings and support improved decision-making for structural safety and resilience.

1. Introduction

Natural phenomena are one of the main channels of interaction between the Earth and socioeconomic systems, causing significant material, economic, and human losses. These natural disasters have intensified dramatically over the last few decades [1], with a major economic impact [2,3]. Throughout 2022, earthquakes caused a total of 1626 deaths, ranking as the fourth most deadly natural phenomenon [4]. In the same year, an earthquake in Afghanistan caused 1036 deaths and one in Indonesia caused 334. Between 1998 and 2017, 56% of deaths caused by natural phenomena were associated with earthquakes [5]. These data reflect the magnitude of the impact that earthquakes continue to have on today’s society, especially in regions with vulnerable infrastructure and buildings lacking seismic engineering design [6].

Throughout history, it has been shown that large earthquakes can cause minor or moderate damage in regions with low vulnerability, while smaller earthquakes have caused devastating catastrophes. For example, the 2010 Haiti earthquake, with a moment magnitude of Mw 7.0, destroyed approximately a quarter of the buildings in the city of Port-au-Prince and caused around 223,000 deaths [7]. In contrast, in the same year, an earthquake with a moment magnitude of Mw 8.8 in Chile caused 525 fatalities. If the magnitude is translated in terms of energy released, the Chilean earthquake was 500 times greater than the one in Haiti, yet it caused less than 1% of the casualties. This difference shows that the degree of structural and social vulnerability, construction quality, the existence of earthquake-resistant design codes, and emergency preparedness have a decisive influence on the final impact of an earthquake [8,9].

Therefore, seismic risk assessment requires the integration of three fundamental components: seismic hazard, which describes the expected ground motion in a given region [10]; structural vulnerability, which measures a building’s ability to withstand damage; and exposure, associated with population and infrastructure density in the area [11]. Seismic hazard depends on geotectonic factors, such as location relative to active faults or plate boundaries, and the depth at which the earthquake originates. However, these natural factors would cause no damage if there were no buildings or population exposed. Consequently, vulnerability and exposure are the elements that transform a natural phenomenon into a disaster. In addition to the physical and social factors mentioned above, seismic risk analysis must incorporate an integrated view that considers the combined effects on infrastructure and the resilience of communities. In this context, several studies have highlighted that due to the significant losses caused by past earthquakes it is essential to comprehensively model regional seismic impact and community resilience, particularly in areas with vulnerable infrastructure and limited seismic planning [12].

Population density and the quality of structures significantly affect the level of seismic risk. The higher the concentration of individuals and buildings, the greater the exposure, which consequently elevates the risk [13,14]. Conversely, implementing earthquake-resistant standards and utilizing suitable construction materials and methods can significantly mitigate the impact of an earthquake. Structures designed with principles of ductility, redundancy, and energy dissipation exhibit superior performance during seismic events, thereby decreasing their structural vulnerability.

In addition to physical factors, social elements also play a crucial role in mitigating seismic risk. Public readiness and awareness, the presence of emergency plans, drills, public education, and effective urban planning all contribute substantially to minimizing the effects of earthquakes. In this regard, alleviating seismic risk necessitates a comprehensive strategy that integrates prevention, preparedness, and response, engaging governments and communities along with scientists and engineering and construction experts [15].

Within structural measures, the precise definition of building and infrastructure characteristics is key. Therefore, to assess a building’s vulnerability and response capacity to an earthquake, it is essential to accurately determine its geometry, materials, foundation, mass distribution, and rigidity. A proper structural analysis not only contributes to occupant safety but also improves urban planning and decision-making regarding the use and maintenance of built heritage. However, the wide variety of architectural designs, construction materials, and regulations applied at different times complicates this task. On-site inspections allow for a direct evaluation of the structural and non-structural conditions of buildings, but they can be costly and labour-intensive, especially in large urban areas. On the other hand, seismic design codes provide technical criteria for the planning and construction of buildings capable of withstanding ground motion.

However, the reality of many cities includes a large building stock predating the application of modern regulations, which creates an adaptation challenge known as structural retrofitting. Retrofitting is defined as the process of structural and non-structural improvement aimed at strengthening existing buildings to make them safer and more efficient against seismic, thermal, or functional loads [16]. This type of intervention is essential to preserve the functionality of historic buildings or critical infrastructure, as well as to extend their service life in accordance with contemporary safety standards. Furthermore, it contributes to the sustainability and resilience of urban communities, ensuring that existing structures evolve in line with technological and regulatory advancements [17]. Structural retrofitting methods encompass a wide range of techniques: from incorporating reinforcements in critical elements to installing seismic isolation devices or energy dissipators [18]. The choice of the most appropriate strategy depends on the initial structural condition, local seismic characteristics, current regulations, and the functional requirements of the building.

Recent advances in seismic resilience research have focused on structural systems that dissipate energy during earthquakes and facilitate damage localisation for rapid after-earthquake repair. Experimental studies have demonstrated that integrating energy-dissipating components within steel frames enhances their seismic performance. For instance, novel replaceable energy-dissipation braces composed of steel tubes and plates have shown robust hysteretic behaviour and improved energy-dissipation capacity under quasi-static cyclic tests, with damage concentrated in replaceable elements rather than in primary members [19]. Similar results have been reported for sandwiched metallic fuse dampers that maintain stable hysteresis and high ductility, promoting enhanced deformation capacity and controlled damage distribution [20]. Moreover, studies on steel-braced frames with dissipative replaceable components indicate the systems can protect structural elements and permit recovery of energy-dissipation capacity simply by replacing the expendable parts [21].

Although the present study does not work with energy-dissipative devices, it shares the underlying objective of enhancing the seismic resilience of buildings. This work thus contributes to the broader performance-based design framework, where structural systems aim not only to satisfy code requirements, but also to minimize damage and facilitate efficient recovery after seismic events.

In a European context, Eurocode 8 (EC8) provides the technical framework for evaluating and improving the seismic resistance of existing structures [22,23]. Eurocode 8 establishes specific principles for retrofitting, including the following:

• Evaluation of existing seismic capacity through analysis of the strength and stiffness of structural elements and their energy-dissipation capacity.
• Seismic design criteria that ensure compliance with safety and structural performance standards.
• Identification of vulnerable areas within the structure to target reinforcement measures to critical areas.
• Structural documentation and verification to ensure that implemented improvements meet design and seismic performance requirements.

In Spain, the Norma de Construcción Sismorresiste de España (NCSE-02-Seismic design construction code) also establishes design and evaluation criteria for structures under seismic activity, defined as buildings of special importance, i.e., those whose destruction could disrupt essential services or generate catastrophic effects [24]. This group includes hospitals, educational centres, communication infrastructure, security force buildings, historical heritage sites, and any facility intended for mass occupancy [25]. These buildings require higher levels of safety and must remain operational during and after a seismic event. In this context, seismic risk reduction requires a comprehensive approach that prioritizes structural design and improvement using updated codes, combined with advanced analytical methodologies based on scientific research. The development of analytical vulnerability models allows for the accurate representation of building behaviour under seismic activity, to optimize reinforcement strategies and contribute to mitigating damage to critical infrastructure.

Seismic behaviour studies at the building level are important and essential in the case of structures of special importance. These studies provide information on structural behaviour and damage concentration and allow for analysis of code compliance under specific seismic scenarios. Therefore, the objectives of this work are as follows: (1) to define a workflow based on building models for estimating seismic vulnerability in buildings of special importance; (2) to analyze the seismic behaviour of a special-importance building in an area with higher seismicity than for which it was designed.

Scope and Limitations of the Study

This study focuses on the analytical assessment of the seismic vulnerability and structural behaviour of a steel building of special importance. A step-by-step methodology is proposed to provide a rigorous definition of a building’s seismic vulnerability. This methodology is necessary to estimate seismic vulnerability when faced with the problem of increased acceleration values in a region where buildings already exist. Seismic design regulations consider regional acceleration values. These acceleration values vary over time due to updates in hazard assessments. As a result, regional parameters and considerations are modified. In this case, existing buildings should be reinforced to meet regional seismic hazard and comply with design regulations. To examine this hypothesis, the building is virtually moved to a different region from the one in which it is currently constructed. Once relocated, the building is adapted to Spanish building seismic design code to comply with the code in the new study region. The hypothetical transfer presented in this study serves as an example to test what would happen if the estimated acceleration values in the region where the building is located were to increase.

The study does not include fragility curves, exceedance probabilities for damage states, or loss metrics, such as economic losses or human losses. Seismic exposure is also excluded, as the analysis considers a single structure rather than an urban or regional real estate portfolio. In conclusion, the contribution of this work is to provide an analytical framework for defining seismic vulnerability for special-importance buildings.

2. Methodology

According to the definition adopted by the United Nations Disaster Relief Coordinator [11], seismic risk in a given area depends on multiple interrelated factors: (1) the seismic hazard, which describes the expected ground motion in a specific geographic region for a defined probability and time window; (2) the structural vulnerability, or the capacity of buildings to withstand damage; (3) the exposure, including the density and distribution of buildings and population; and (4) the repair cost or the associated economic losses.

The research presented in this paper includes three phases with regard to the seismic performance of the building (Figure 1). First, the seismic hazard in a region of south-western Spain, Cádiz, is estimated. Next, a digital structural model of a real building set in central Spain, Madrid, is developed. Specifically, it is a steel building of special importance. The building is modelled following the proposed step-by-step methodology. Finally, the seismic performance of the building is estimated as if it were built in the study region, Cádiz.

Section 2 covers the proposed methodology and is divided into three subsections: probabilistic seismic hazard assessment, seismic vulnerability assessment, and seismic building performance. The first and third phases consist of applying methodologies that already exist in the literature. However, the second phase is the innovation presented in this work. It outlines the different steps for estimating the seismic vulnerability of a building of special importance.

2.1. Probabilistic Seismic Hazard Assessment

The first phase focuses on characterizing the seismic hazard. A probabilistic zonation-based methodology expressed in Equation (1) is adopted. The hazard H describes the probability P of exceeding a specified ground motion level A within a given exposure period t. The calculation integrates all earthquakes historically recorded within a 300 km radius of the site of interest. The variable a represents the estimated ground motion, expressed as peak ground acceleration (PGA, in g or cm/s²) or spectral acceleration (SA(T), in g or cm/s²).

H (a, t) = P (a ≥ A, in t years)

(1)

Classical probabilistic methodologies [26] assume that seismicity occurs within sources or seismogenic zones of homogeneous seismic potential. In order to model this phenomenon, seismic hazard evaluations utilize zoned models predicated on the assumption that earthquakes are randomly distributed across both temporal and spatial dimensions within each designated zone. Under this hypothesis, a Poisson model is employed to characterize earthquake occurrences, signifying the spatial and temporal independence of events occurring within the same zone. Equation (2) delineates the exceedance probability in relation to the Poisson occurrence rate.

P (a > A in t years) = 1 − e^{(−λ(a>A)t)}

(2)

where P (a > A in t years) is the probability of exceedance in t years; t is the exposure period; and λ is the annual rate of exceedance.

The return period (T_R) is a statistical concept defined as the inverse of the annual probability of exceedance of a specific acceleration ground value, Equation (3) [27]. The requisite T_R is contingent upon the significance of the structure: structures of greater importance necessitate lower exceedance probabilities, thereby resulting in extended return periods. For example, for an exposure time of 50 years, Equation (3) yields a 10% probability of exceeding the seismic motion associated with a 475-year return period, and a 5% probability for a 975-year T_R (Equations (4) and (5)).

P (a > A in t years) = 1 − e^(−t/T_R)

(3)

where P (a > A in t years) is the probability of exceedance in t years

P (a > A in t years) = 1 − e^(−50/475) = 0.10

(4)

P (a > A in t years) = 1 − e^(−50/975) = 0.05

(5)

The probabilistic framework yields hazard curves that articulate the exceedance probability of PGA or SA(T). These curves provide the essential input for the subsequent structural vulnerability assessment and ultimately define the demand spectra for the selected hazard scenarios.

Probabilistic methods for estimating seismic hazard rely on assumptions concerning both seismic sources and wave-propagation models (Figure 2). Because real sources and propagation models remain uncertain, probabilistic seismic hazard assessment (PSHA) [28,29] incorporates different hypotheses regarding seismic catalogues, the geometry and characterization of source zones, the spatial, temporal, and magnitude distribution of earthquakes (recurrence models), and ground-motion attenuation models. It also includes explicit treatment of associated uncertainties. A logic tree combines all modelling options selected at each stage of the analysis.

2.1.1. Uniform Hazard Spectra

The seismic hazard was estimated using a dual approach:

• Probabilistic. A zoned source model was used and recurrence models for seismogenic zones and active faults were considered. This method provides ground-motion values associated with a given exceedance probability by aggregating contributions from all possible earthquakes within the influence area. Consequently, the findings are not aligned with any specific seismic scenario.
• Probabilistic–deterministic. Specific seismic scenarios were identified by disaggregating the probabilistic hazard results. This process yields the control earthquakes, the events that contribute most to the probabilistic hazard for a given spectral frequency. Control earthquakes are characterized by three parameters: magnitude, distance, and epsilon (M, R, and ε).

Utilizing these control earthquakes, the uniform hazard spectra (UHS) were derived, which delineate the anticipated SA with consistent probability for a designated return period.

2.1.2. Hazard Disaggregation and Identification of Control Earthquakes

Seismic hazard assessment requires summing the contributions of all potential seismic scenarios, expressed as magnitude–distance pairs, that contribute to the exceedance of a target ground-motion value. However, a hazard curve does not reveal which earthquake characteristics (size and location) are most likely to cause exceedance at the site. The control earthquake was identified for the spectral frequency considered.

To ascertain its attributes, the triplet magnitude, distance, and epsilon (M, R, and ε) that most significantly contributes to the aggregate hazard was identified. This necessitates the disaggregation of the comprehensive hazard into its partial contributions, a methodology recognized as hazard disaggregation [29,30].

2.1.3. Hybrid Probabilistic–Deterministic Specific Scenarios

The final phase of the seismic hazard assessment develops specific hazard scenarios using the previously identified control earthquakes. These earthquakes represent characteristic events concerning magnitude, distance, and exceedance probability, thereby serving as the foundation for scenario definition.

When establishing these scenarios, the characteristics of the control earthquakes were linked to the seismic sources that display similar properties and fulfil the magnitude and distance conditions identified during disaggregation. These sources may pertain to discrete geological fault segments, tectonic regions, or any other identifiable origins of seismic activity.

By linking control earthquake characteristics with specific seismic sources, realistic and comprehensive scenarios for seismic building performance are constructed. The resulting specific spectra form the demand curves used in the subsequent building assessment.

2.2. Seismic Vulnerability Assessment

In this study, an analytical approach to define the seismic vulnerability of the building is developed. Current standards emphasize the need to characterize in detail the seismic vulnerability of structures of special importance. Below, the workflow followed to characterize seismic vulnerability is explained in detail (Figure 3).

2.2.1. Building Model

First, detailed data on the structure is collected to create the digital model of the building. To do this, we considered the architectural and structural plans, construction project reports, information on the materials used, and the geometric characteristics of the elements that make up the building, which involves on-site visits to the target building.

Using the collected documentation, a numerical model of the building was created. This model reproduces the structural layout, the mass distribution, the stiffness characteristics, and the material properties. If the building is divided into modules, as in the case study, the absence of diaphragm action between modules must be ensured when developing individual models. Moreover, after analyzing the independent modules, the potential interaction due to dissimilar dynamic responses should be assessed using a multi-module model—either complex or simplified when justified—to verify the code compliance of the complete building.

2.2.2. Integrated Analyses for Building Model: Initial Scenario

The proposed methodology consists of three analyses to define the building model: modal, operational modal, and limit state analysis.

Modal analysis. This analysis allows the evaluation of the dynamic characteristics of the structure. The process consists of determining the natural modal forms of vibration of the structure and the associated frequencies. Recent studies demonstrate that integrating ambient-vibration modal identification with analytical modelling improves the reliability of the calibrated structural models [31].

During the operational modal analysis, henceforth OMA, the building’s vibration response was measured at several locations using accelerometers. These recordings provide the natural vibration modes, frequencies, and modal shapes of a building under actual load and operating conditions [32,33,34].

Limit state analysis. In this step, all actions and forces affecting the structure were evaluated to confirm its load-bearing capacity and overall stability. It is necessary to ensure whether the building meets the safety limits established in current design codes.

2.2.3. Integrated Analyses for Building Model: Secondary Scenario

The case study presented in this manuscript relocates the building of interest to a region with greater seismic hazard than the one for which it was built. For this reason, the methodology proposes steps to validate the building’s capacity in its new location. To do this, we first repeat the limit state analysis considering the parameters of the current seismic regulations in the hypothetical relocation scenario proposed.

Secondly, the building’s capacity curve is defined. The resulting curve shows how the base shear varies with the displacement of a control node at roof level. To obtain the capacity curve, a nonlinear static analysis, pushover, is developed. This analysis applies a parameterised force to the building that has the same shape as the force caused by an earthquake on the building.

The performed nonlinear analyses only consider the bare building with the main structural elements. Non-structural elements are not considered, but it is important to note that they play an important role in the seismic response of the building. Components such as partitions, façade elements, pipe systems, and infills increase stiffness, reduce effective vibration periods and modify the dynamic response of the building. Therefore, their omission in numerical models can lead to differences between the analytically predicted dynamic properties and those identified experimentally.

In addition, non-structural components often suffer damage at lower seismic intensities than the main structural system. This means that, even though it is not a region with a high seismic threat, significant material and economic losses can occur [31,35,36]. As a result, neglecting non-structural elements can lead to underestimating the consequences related to damage in seismic building performances and seismic risk assessments, especially in the case of buildings of special importance, which must continue to function after an earthquake.

After performing the two previous analyses, limit state and pushover, the behaviour of the building in the new scenario is known. If the building has deformations and displacements greater than those acceptable according to regulations, it must be reinforced so that it complies with the codes of the region under study.

Retrofitting techniques are used to improve and reinforce buildings in accordance with regulations. Retrofitting a building improves the load-bearing capacity of its structures. There are various retrofitting techniques. For example, beams and columns can be strengthened using additional materials, including new elements, or modifying the distribution of loads. The budget available for retrofitting is the main factor in selecting the technique. In order to improve and reinforce an existing building, the following key aspects must be taken into account: the definition of the system’s load paths, the overall rigidity and strength of the building, irregularities in floor plan and height, the torsional behaviour, the ductility of the elements, the performance of the connections, the foundations, the anchoring of non-structural elements, and the possible interactions with adjacent buildings. These aspects are normally defined in the structural design phase of a building when it is to be constructed.

2.2.4. Seismic Building Performance

Based on the validated structural model, the building’s response to seismic actions is defined using a nonlinear dynamic analysis (NLDA). This method allows the definition of the maximum displacement reached by the building, considering plastification. Therefore, it is possible to characterize the building’s damage. To apply the method, it is necessary to establish the building’s hinges and thus ensure its ductility. Updated and in-force standards and codes must be considered to define the hinges.

NLDA is performed using a single synthetic accelerogram compatible with the target response spectrum, adopted as a demonstrative input to evaluate structural response under code-consistent seismic demand. The Spanish seismic design standard, NCSE-02, considers an importance factor of 1.3. This factor transforms the estimated seismic action for a T_R of 475 years to another action corresponding to a T_R of 975 years. It is necessary to use this factor because Spanish regulations establish that the T_R for buildings of special importance is 975 years. This T_R means that the assumed exceedance probability is 5% in 50 years.

3. Methodological Application

The proposed methodological approach consists of estimating the seismic performance of a special importance building that is currently built and operational. The building is selected because it is considered a good case study for two reasons: (1) information about its structure is available, and (2) field campaigns can be carried out to correctly define the model. The building serves to illustrate the workflow proposed in Section 2 of the manuscript. It provides insight into the behaviour of a building when seismic hazard increases in the study region. It is the Escuela Técnica Superior de Ingenieros en Topografía, Geodesia y Cartografía (ETSITGC—Higher Technical School of Surveying, Geodesy, and Cartography Engineering), located in Madrid (Spain). The seismic hazard in the study area is very low. The map in the existing NCSE-02 [21] standard provides a basic acceleration of less than 0.04 g. Therefore, the standard only prescribes the need for seismic design in Madrid due to the fact the building is of special importance. Nonetheless, the seismic risk and performance assessment of the building in this actual location have shown this is not governing, as wind lateral action effects overcome those of seismic loads. Therefore, this building could constitute a representative example of a special-importance building not designed for withstanding relevant seismic loads.

Therefore, to comply with the points for which the methodology was designed, an increase in the seismic hazard demand is considered. This is pedagogically performed in this example by changing the location of the building so the new location is of interest from a hazard perspective. Nonetheless, the increment of seismic hazard demands typically occurs due to updates to codes or the realization of improved hazard studies, as stated before. The new region is influenced by both near and distant earthquakes. To test the proposed methodology under realistic seismic demand conditions, the building is hypothetically relocated from its actual location in Madrid to Los Barrios (Cádiz), while preserving its original structural configuration and material properties.

Accordingly, the key aspect of current study is that this is a special-importance building that must satisfy the requirements associated with a higher seismic hazard level than that assumed in its original design. Hence, the updated hazard level is therefore explicitly considered, and retrofit measures are evaluated to meet the applicable design criteria for the new scenario.

3.1. Probabilistic Seismic Hazard Assessment

The new study area in which the building is located is in the city of Los Barrios (Cadiz, Spain). Specifically, it is located at the Los Barrios Endesa Generación S.A. port. Please refer to the Supplementary Material Figure S1 to see the location map of the study region.

In this project, a first family of spectra has been obtained that includes UHS for return periods of 475 and 975 years. Subsequently, a second family of specific spectra was obtained from the control earthquakes obtained by disaggregating the seismic hazard results. Both families of spectra include the local effect derived from a specific study carried out in situ in Los Barrios, considering the geotechnical and geophysical characteristics of the site. In addition, for the development of the research, the spectra generated from the seismic hazard assessment (UHS and specific) were compared with those proposed by the Spanish seismic design standard, NCSE-02.

Below is a detailed description of each of the phases that have been undertaken to estimate seismic hazard.

3.1.1. Seismic Catalogue

The seismic catalogue was defined based on the catalogue prepared for the Actualización de mapas de peligrosidad sísmica de España 2012 (Update of seismic hazard maps for Spain 2012) [37]. The catalogue was updated to October 2020; it contains earthquakes with depths greater than 65 km and with magnitudes less than Mw 3.0. In this way, earthquakes that were relevant to the seismic hazard of the study area were considered, including results from various Spanish sources of information [38,39].

Homogenization and refinement processes were applied to the seismic catalogue. Homogenization was performed using the moment magnitude scale (Mw) and Reduced Major Axis (RMA) linear regressions [40]. Subsequently, the catalogue was refined. This approach eliminates repeated events, aftershocks, and foreshocks [26]. To do this, space–time windows were used around the main earthquakes [41,42]. In addition, the Monte Carlo method was applied to incorporate uncertainties associated with the Mw magnitude by simulating 1000 synthetic catalogues. In this way, the frequency of each earthquake classified as an aftershock is estimated.

Finally, a completeness analysis was conducted to determine the reference years from which the catalogue could be considered complete for different magnitude ranges [43]. Based on this analysis, the earthquake occurrence rate was established and the hypothetical number of earthquakes that occurred during the study period was estimated.

The final study catalogue consists of 8230 earthquakes that occurred between 1 January 1048, and 15 October 2020. The earthquakes in the catalog have a minimum Mw of 3.0, a maximum Mw of 8.5, and a maximum depth of 65 km.

3.1.2. Seismic Sources Characterization

In this study, the official model of the Instituto Geológico y Minero de España (IGME-Spanish Geological and Mining Institute) was adopted, of the Iberian Peninsula and surrounding areas (ZESIS). This model was developed in [44]. The seismicity pattern of the seismic zones, its recurrence law, and the maximum magnitude that each source can generate were characterized. This analysis was performed for sources within a 320 km radius from the centre of the study site. The site of interest is located in the seismic zone that includes the Strait of Gibraltar and the Spanish and Moroccan mainland and marine areas, the Gibraltar Arc. This seismic zone has a predominant strike slip focal mechanism and is associated with a relatively high hazard level.

Subsequently, the recurrence laws and seismic parameters of each seismic zone were estimated. The modified Gutenberg–Richter model was used to calculate the recurrence law [45]. The model establishes a linear correlation between the natural logarithm of the number of earthquakes (N) and the magnitude (M). Equation (6) saw the Gutenberg–Richter correlation.

Ln(N) = α – β·M

(6)

where α is a coefficient that represents the number of earthquakes exceeding a minimum magnitude, and β represents the ratio between big and small earthquakes. The minimum magnitude for calculating the rate was Mw 4.0 for all zones. Please refer to the Supplementary Material Table S2 to consult the parameters that characterize the seismic sources.

3.1.3. Ground Motion Prediction Equations and Logic Tree

Ground Motion Prediction Equations (GMPEs) define the expected ground motion due to the occurrence of earthquakes within each seismic zone. There are only a few models in the Iberian Peninsula developed for magnitudes greater than Mw 5.1. This is due to the lack of sufficient accelerometric data for magnitudes greater than Mw 5.1. For this reason, the present study uses a combination of models. The selected models are updated, developed on a global scale, and consistent with the magnitude and distance characteristics of the catalogue used in this study.

Table 1. Ground Motion Prediction Equations (GMPEs) considered in the current study.

GMPE	Abbreviated Name	Periods/Magnitudes (Mw)
[46]	ASK13	Short periods
[47]	CB14	Short periods
[48]	CY14	Long periods
[49]	MP11	Mw < 5.1
[50]	AB10	Mw > 5.1

include selected models selected for the current study:

Finally, a logic tree was developed to include different combinations between GMPEs (Figure 4). In this way, the epistemological uncertainties inherent in the GMPEs are included in the seismic hazard study. The tree consists of three input data nodes. The first node is for the study catalogue. The second node is for the seismic zones model considered (ZESIS). The third node has four branches of GMPEs combinations.

3.2. Seismic Vulnerability Assessment

3.2.1. Building Model

The object of study for the seismic performance assessment is the ETSITGC building (Figure 5). It is a steel building constructed in 1977. It has six floors above ground and a built area of 9645 m². The structure is divided by two expansion joints, which means that the building is composed of four modules. As stiffening elements, the building has braces on two of its masonry facades. The foundation is composed of concrete slabs on columns.

The digital model of the building’s structure was created using information from three data sources. First, the architectural plans which provided precise details on the layout and fundamental geometric characteristics of the building were used. Second, valuable information on some structural details was extracted from a report on the condition of the building issued in 2019. Finally, several field campaigns were conducted to collect data regarding the materials and elements’ dimensions.

Table 2. Geometry and dimensions of the building’s structural elements.

Columns
	Material: rolled steel Profile: double UPN box section Height: 415 cm per level Dimensions per level. Basement: 26 × 18 × 1.4 cm; Ground floor: 24 × 17 × 1.3 cm, First floor: 22 × 16 × 1.25 cm; Second floor: 22 × 16 × 1.25 cm; Third floor: 20 × 15 × 1.5 cm; Fourth floor: 20 × 15 × 1.5 cm
Beams
	Material: rolled steel Profile: IPE450 Dimensions: 45 × 17 cm
Expansion joints
	Two expansion joints divide the building into four modules.

shows photographs of certain parts or elements of the building that have facilitated the definition of its geometric characteristics and construction materials.

The main structure of the building consists of rolled steel frames. The columns are 415 cm high and are double UPN box sections of different dimensions depending on the floor (Table 2). The beams are IPE450 sections and the slabs are one-way and 20 cm thick. The building is divided internally by walls made of hollow bricks that are 15 cm thick. In addition, the facades are made of masonry. The east and west facades have St. Andrew’s crosses as bracing elements.

AutoCAD v2024 was utilized to create a precise model of the distribution of structural elements. This model was subsequently used as a solid basis for structural modelling. SAP2000 was utilized to integrate the geometry and material characteristics of all of the structural elements. This advanced structural analysis software enabled the creation of a complete three-dimensional model (Figure 6). To define the capacity curve of the bare structure and estimate the seismic damage, the backbone parameters to define the hinges, their acceptance criteria, and key characteristics were assigned considering [51]. For columns and beams, the criteria presented in Table 9-7.1 in [51] were considered. Hinges were assigned at a 0.05 and 0.95 clear length to avoid the areas of physical interaction between elements or joints. On the one hand, the plastic hinges for columns allow the consideration of the effects of the interaction between axial force and moment in both directions. On the other hand, the plastic hinges for beams allow the definition of the effect of the moment in the direction of maximum inertia. The plastic hinges for steel diagonals allow the definition of the effect of axial forces. Axial behaviour was modelled using plastic hinges in SAP2000. Hinges were defined according to Table 9-8 in [51]. The resulting axial backbone is asymmetric in tension and compression and includes post-buckling strength reduction through the capping/residual branch, which is critical for braced frames. The post-ultimate option was set to drop load after the ultimate point. Brace end releases were modelled as pinned. An isotropic hysteresis model was adopted; therefore, explicit cyclic degradation of strength and stiffness was not modelled and is acknowledged as a limitation for applications requiring detailed cyclic deterioration.

As mentioned above, the building under study has two expansion joints which are built to ensure no diaphragm interaction (see Table 2, figure expansion joints). The building is considered to be divided into four modules (Figure 7). For this reason, it is recommended to perform a comprehensive analysis of each module independently and afterwards, check the potential interaction between modules due to the dissimilar modules’ movement.

The present study focuses exclusively on a single module. Analyzing only one module allows the improvement of the understanding of the seismic behaviour of a particular section of the building. Furthermore, working with a single module allows the proposed methodology to be applied to a specific scenario. Based on this application, the results can be checked and the methodology validated. In the future, the approach can be extrapolated to other modules or buildings.

For the present research, the central module of the ETSITGC building was selected as the object of the study. It is the blue module in Figure 7, hereafter referred to as Mod1 (Figure 8). Mod1 was selected for different reasons. On the one hand, due to its central position, Mod1 interacts with the other modules of the building. Therefore, its behaviour directly impacts the overall seismic response of the structure. On the other hand, despite its slenderness, Mod1 lacks bracing elements such as diagonals, shear walls, or St. Andrew’s crosses, which play a fundamental role in the lateral stability of a structure. When a slender building lacks these elements, its ability to resist horizontal forces, such as those produced by strong winds or seismic movements, may be reduced. This fact could affect the structural and functional integrity of the building.

3.2.2. Integrated Analyses for Building Model: Initial Scenario

Initially, a modal analysis is performed, considering the bare structure of Mod1 of the ETSITGC building. According to design standards applicable at the time of construction, 100% of the permanent masses and 60% of the remaining masses are considered for the modal analysis. This analysis provides the characteristic vibration modes of the Mod1.

Secondly, an OMA was conducted. This campaign captured the building’s response under real seismic or dynamic excitation conditions, including non-structural elements. During the field campaign, ambient vibrations were measured using a Tromino Engy 3G+, 3D velocity sensor, MoHo S.L.R., Marghera, Venice, Italy (Figure 9).

The vibration data was recorded for ten minutes at a total of 10 points strategically distributed throughout all floors of the building (Figure 10). It is important to note that these measurement points were consistently located in the same horizontal position on all floors.

The Standard Spectral Ratio (SSR) methodology [52] was implemented to analyze the results and obtain the fundamental frequencies. This is a widely accepted and used method for evaluating a building’s environmental vibration response. The method defines the building’s response as the ratio between the Fourier amplitude spectra of the ground oscillations recorded at a given site and at a nearby rocky site, originating from the same earthquake and movement component [53]. It is recommended to take simultaneous measurements at all points of interest, as this allows for more accurate phase information to be obtained. The characterization of the Mod1 building was carried out with a single station, as the necessary equipment for simultaneous measurements was not available. Despite this limitation, all necessary precautions and considerations were taken [52,54,55] to ensure the validity of the measurement method used. The main precautionary measure taken into account was to perform the measurements on the same day to ensure equal noise conditions in the building (occupancy and wind). Therefore, it can be assumed that the maximum amplitude responses are the same between measurements and the reliability of the results obtained in terms of the building’s fundamental vibration periods can be ensured.

Finally, a limit state analysis of the building was performed. The seismic design codes and the standards at the time of construction of the building and for the region in which it was built were considered. In other words, the design conditions of the building at the time and place where it was actually designed (1977, in Madrid) were recreated. For clarity in the following descriptions, the initial scenario will be named as SR1 (Madrid, 1977).

The standards, technical codes and regulations considered in SR1 are PDS-1 [56], MV 101-1962 [57], and MV 103-1972 [58]. Please refer to the Supplementary Material Table S2 to consult the parameters considered for permanent and accidental actions involved in the limit state analysis on Mod1 for SR1. In addition, load cases are established that consider both permanent and variable actions. Load cases are based on the ultimate limit state (ULS). Please refer to the Supplementary Material Table S4 to consult the established load cases established for the limit state analysis for scenario SR1. For the spectral analysis, 5% damping was set and the modes considered all needed to reach more than 90% of the building mass.

3.2.3. Integrated Analyses for Building Model: Secondary Scenario

In the secondary scenario, the design codes and the standards at the time of the present study and for the region under study were considered. In this way, the aim is to “transfer” the building spatially and temporally and adapt it to the design standards in the hypothetical scenario assumed (2021, in Los Barrios, Cádiz). For clarity in the following descriptions, the secondary scenario will be named SR2 (Los Barrios, 2021).

The standards, technical codes and regulations considered in SR2 are NCSE-02 [24], CE-21 [59], and DB SE AE [60]. Please refer to the Supplementary Material Table S3 to consult the parameters considered for permanent and accidental actions involved in the limit state analysis on Mod1 for SR2. These parameters consist of the self-weights of the structural elements, the characteristic value of the service overload, and the simultaneity coefficients for the occurrence of variable actions. In addition, load cases are established that consider both permanent and variable actions. Load cases are based on the ultimate limit state (ULS). Please refer to the Supplementary Material Table S5 to consult established load cases established for the limit state analysis for scenario SR2. The spectral analysis was executed in accordance with the NCSE-02 [24] load combinations in different directions for each case. In the one hand, 100% of the spectrum in the two main orthogonal directions. On the other hand, 30% of the spectrum in the secondary direction. Additionally, a third direction was tested, forming 45° with the building. All the combinations allow the analysis of the influence of directionality. The most results were employed for the retrofitting. As for the initial scenario, the damping was considered 5% and the modes considered all needed to reach more than 90% of the building mass with an SSR combination of modes.

To conclude the vulnerability assessment of Mod1, the capacity curve was defined by performing a pushover analysis of scenario SR2. The result after the limit state analysis and the pushover for Mod1 in scenario SR2 has accurately identified the specific elements that require structural reinforcement. Some retrofitting techniques were implemented to these critical elements.

The selection of the appropriate retrofitting solution varies significantly depending on several factors: the knowledge and experience of the professional in charge of the project, the available budget, or the regional construction materials and techniques, among others. Therefore, a single and standard retrofitting approach is not proposed in the manuscript. In this study, diagonals in two directions with articulated joints and welded steel plates that transmit force to reinforce critical elements of Mod1 were included (Figure 11). To dimension the reinforcement plates, the instructions of the Spanish steel standard for welded joints that transmit force are considered [61]. Bracing frames with articulated joints in the diagonals have been established in accordance with the specifications for frames in the previous regulations.

3.2.4. Seismic Building Performance

In this section, the seismic performance of the reinforced Mod1 in scenario SR2 was estimated. The seismic demand resulting from the seismic hazard assessment in Section 3.1 was considered. This section involves exposing the building to the seismic activity of the ad hoc seismic hazard study in Los Barrios and assessing its performance, assuming that it is designed in accordance with the current Spanish standard, NCSE-02. To do this, a synthetic accelerogram is generated (Figure 12). This accelerogram is compatible with the response spectrum resulting from the hazard study, shown in Section 4.1.4.

4. Results and Discussion

4.1. Probabilistic Seismic Hazard Assessment

4.1.1. Uniform Hazard Spectra

The seismic hazard has been estimated in terms of PGA and SA for 14 structural periods (T). The estimate has been expressed in units of g. First, the seismic hazard was assessed considering generic rock sites. Subsequently, the rock results were projected onto soil transfer functions. The transfer functions were obtained from a study of the local effect of the terrain using geophysical methods in the area of interest. As a result, the UHS was obtained for a T_R of 975 years (Figure 13), with a value 0.1 g for the PGA. This approach is consistent with recent methodologies that integrate probabilistic hazard, local site response characterization, and soil–structure dynamic interaction when assessing expected seismic motions at specific sites [62].

4.1.2. Control Earthquakes and Probabilistic–Deterministic Specific Scenarios

For the disaggregation, the PGA and SA(2 s) movements for the T_R of 975 years were considered. The current study employs a three-dimensional approach for risk disaggregation (magnitude, distance, and epsilon). Target ground motion levels have been established at different selected spectral ordinates. For each target spectral acceleration, the combinations of magnitude, distance, and epsilon that contribute most to the estimated seismic hazard were identified. After analyzing the results of the disaggregation, an epsilon equal to 3 was considered and three control earthquakes were established (

Table 3. Control earthquakes obtained by disaggregating seismic hazard results in the Los Barrios project.

Control Earthquake	Spectral Acceleration	Magnitude (Mw)	Distance R (km)
Control earthquake 1	2 s	6.5–7.0	120–140
Control earthquake 2	PGA	4.5–5.0	0–20
Control earthquake 3	2 s	6.0–6.5	80–160

).

In order to define the seismic scenarios, the selected control earthquakes were associated with the specific seismic sources. The seismic sources that are compatible with the control earthquakes were selected. Seismic sources should have associated distance and magnitude parameters that include the properties of the control earthquakes.

Table 4. Seismic scenarios identified for the control earthquake.

Scenario	Location 1	Magnitude (Mw)	Distance R (km)
Scenario 1	Tofiño bank fault	7.0	120
Scenario 2	Neotectonics map fault	5.0	15
Scenario 3	El Acebuchal fault	6.4	80

¹ For the location of the seismic events, see Figure S2 in the Supplementary Material.

includes the main characteristics of the seismic scenarios.

4.1.3. Specific Response Spectra for the Deterministic Specific Scenarios

Three response spectra were estimated from the three seismic scenarios. The resulting response spectra were compared with the spectrum in the current Spanish seismic design code NCSE-02. Based on this standard, the basic seismic acceleration for the municipality of Los Barrios is 0.04 g. Given that the current study considers a building of special importance, the basic acceleration for Los Barrios was multiplied by the importance factor of 1.3. Below, the spectra for each scenario are included.

Response-specific spectrum for scenario 1 (S1). Scenario 1 is characterized by a magnitude of Mw 7.0 and a source-site distance of 120 km. Figure 14 shows the response spectrum obtained from the transfer models estimated in the geophysical measurement campaign and the NCSE-02 spectrum. For the development of the NCSE-02 spectrum, a terrain coefficient equal to 2 and an importance factor of 1.3, corresponding to a T_R of 975 years, were considered.

Response-specific spectrum for scenario 2 (S2). Scenario 2 is characterized by a magnitude of Mw 5.0 and a source-site distance of 15 km. Figure 15 shows the response spectrum obtained from the transfer models estimated in the geophysical measurement campaign and the NCSE-02 spectrum.

Response-specific spectrum for scenario 3 (S3). Scenario 3 is characterized by a magnitude of Mw 6.4 and a source-site distance of 80 km. Figure 16 shows the response spectrum obtained from the transfer models estimated in the geophysical measurement campaign and the NCSE-02 spectrum.

4.1.4. Discussion

As a summary of the results generated in the seismic hazard assessment for Los Barrios, four response spectra were obtained: one UHS for T_R 975 years, and three specific spectra derived from the disaggregation analysis. All the spectra were obtained for both rock surface and considering the local effect. Figure 17 shows the four estimated spectra and the one according to NCSE-02 for a special-importance coefficient of 1.3 (T_R 975 years) and a terrain coefficient C = 2. The NCSE-02 spectrum is considered as the basis for the design of the building at Los Barrios site. However, the other response spectra represent the seismic action to be expected according to the recent study carried out ad hoc for the site where the building is considered to be located.

To define the spectrum for studying the seismic performance of the building, the UHS, the specific scenario spectra, and the spectrum according to NCSE-02 are analyzed together. Figure 17 shows all the spectra. The figure shows that the UHS is always above the specific spectra. Therefore, the UHS is the most conservative and should be used for the seismic performance study. However, it can also be seen that, from the 0.2 s period onwards, the NCSE-02 spectrum is above the UHS (Figure 18).

The NCSE-02 establishes the following: the spectral ordinates shall in no case be lower than those obtained by the general procedure described in the code. For this reason, the final spectrum for the study is a combination of the UHS and the NCSE-02 spectrum. The spectrum to be used for the study of the seismic performance of the building is shown in Figure 19. The final spectrum has two segments. The first segment goes up to 0.2 s and corresponds to the UHS. From 0.2 s onwards, the second segment corresponds to the spectrum based on NCSE-02.

4.2. Seismic Vulnerability Assessment

4.2.1. Integrated Analyses for Building Model: Initial Scenario

The results of the modal analysis obtained for the Mod1 module reveal a vibration period of 2.4 s in the X direction for the second vibration mode, with a significant mass contribution of 70%. Similarly, in the Y direction, a period of 2.7 s was obtained for the first vibration mode and a mass contribution of 71% (Figure 20). These period values and the corresponding mass contributions are essential indicators of the dynamic behaviour of the structure under seismic excitation.

Table 5. Record length (s), analysis window length (s), frequency resolution (Hz) defined and periods (s) obtained after SSR analysis of the ETSITGC building. The points are organized in the table by modules to facilitate interpretation of the results.

Module	Record Length (s)	Window Length (s)	Frequency Resolution (Hz)	Point	Period SSR (s)
					UX	UY
Mod1	600	20	0.05	Pont 1	0.46 ± 0.05	0.41 ± 0.02
	600	20	0.05	Point 4	0.46 ± 0.07	0.41 ± 0.05
Mod2	600	20	0.05	Point 3	0.41 ± 0.03	0.46 ± 0.08
	600	20	0.05	Point 5	0.41 ± 0.03	0.46 ± 0.10
	600	20	0.05	Point 11	0.31 ± 0.02	0.33 ± 0.03
	600	20	0.05	Point 12	0.33 ± 0.03	0.33 ± 0.05
Mod3	600	20	0.05	Point 6	0.46 ± 0.02	0.41 ± 0.02
	600	20	0.05	Point 7	0.33 ± 0.12	0.28 ± 0.12
Mod4	600	20	0.05	Point 2	0.46 ± 0.03	0.40 ± 0.03
	600	20	0.05	Point 10	0.33 ± 0.02	0.29 ± 0.06

shows the results of frequencies and periods obtained after applying the SSR method to all points measured in the ETSITGC building during the OMA campaign. On the one hand, Mod1 presents similar periods in both directions. On the other hand, Mod2 exhibits significant variation between the periods of its points. This means possible differences in stiffness and dynamic behaviour within this module. It is the module with the greatest irregularity in the floor plan. Finally, Mod3 and Mod4 show great variability in the UY direction. The points where the shortest period were identified are those located at the corners of these last two modules. This fact could be related to the possible influence of rotation on the dynamic response, something that should be verified with a more detailed modal analysis for these modules. The corners of a building are often critical areas in terms of stress and deformation distribution.

Table 6. Mod1 periods after the SSR analysis and modal analysis.

Period (s)
SSR		Modal analysis
UX	UY	UX	UY
0.46	0.41	2.4	2.7

shows the results obtained specifically for Mod1 of the OMA, calculated by applying SSR to the modal analysis carried out with SAP2000. The periods obtained after the modal analysis are up to 2.5 times greater than those obtained from the OMA records. The value of the fundamental period depends on two factors. On the one hand, the stiffness of the building. For example, the type of foundation considered, the non-consideration of non-structural elements, or the definition of structural elements with a certain degree of uncertainty, among others, imply an increase or decrease in the stiffness of the designed structural model. On the other hand, the definition of the fundamental period is also due to the estimated mass of the building. If the mass considered for the calculation of the building’s resistance increases significantly, so does the period, since both values are directly proportional to each other.

The differences observed between the OMA results and the modal structural analyses are consistent with the previous published research. In [33], the influence of non-structural walls on steel-frame buildings was studied. When considering different distributions of interior walls, the authors found that the periods calculated considering non-structural elements were significantly lower compared to those that only considered structural elements. This finding supports the idea that the inclusion of non-structural elements can significantly affect the dynamic response of the structure. Similarly, the study by [32] provides additional insight by exploring the effect of temperature on a steel building. They identified the lack of partition walls in the numerical model as the main reason for the discrepancies between experimentally and numerically obtained dynamic properties. The omission of interior walls in the numerical model led to lower frequencies (longer periods) compared to the OMA results. In [63], fundamental periods were calculated according to ASCE-7 standards and the methodology proposed by Uang and Smith and compared with experimental results. The periods obtained numerically were significantly longer, in some cases more than double the experimental periods (OMA). This fact supports the variability that can arise between methods.

Taken together, these studies support the validity of the differences observed in the results obtained for the present study. The discrepancies between the results obtained using OMA and modal structural analysis are known to occur and have been documented. These differences are attributed to the omission of details and non-structural elements in numerical models, which is consistent with the inherent complexity of the dynamic responses of real structures.

Figure 21 shows the spectrum considered for the current study, resulting from the previous hazard assessment. The fundamental periods obtained for Mod1 after the modal analysis and the OMA are included. The OMA period has an associated acceleration value of 0.26 g (orange in Figure 21). The modal analysis period has an associated acceleration value of 0.10 g (purple in Figure 21).

Figure 22 shows the results for the limit state analysis considering the spectrum for the scenario SR1 (1977, in Madrid). Each structural element has a colour which corresponds to the element utilization index. This index is a ratio which indicates the relationship between the maximum stress experienced by a specific element and its resistance capacity. It is a measure of the “structural safety” of the element. For this reason, a ratio equal or close to 1 indicates that the element is being stressed to its limit capacity. This fact could mean a critical element that requires greater attention in terms of design or reinforcement.

All structural elements have a ratio below unity. Therefore, the profiles of the elements used in the structural modelling for Mod1 in SR1 are consistent with the design specifications in force during the construction period. Furthermore, the applied loads do not exceed their theoretical resistance capacity. Therefore, the defined model is accepted.

4.2.2. Integrated Analyses for Building Model: Secondary Scenario

Figure 23 shows the results for the ultimate limit state analysis considering the spectrum for Mod1 in the scenario SR2 (Los Barrios, 2021). A total of 27 columns and 10 beams with a ratio value greater than 1 have been identified. This finding can be the consequence of the variability in the distance between columns, which ranges from 3 m to 9.5 m. This fact reflects the influence of the increase in demand, the workflow key, in the ratio of element utilization.

Finally, a nonlinear static analysis, pushover, was developed. The analysis was performed on Mod1 in scenario SR2. The increasing parametric loads were defined proportional to the first and second mode of vibration and define the vertical loads for the seismic combination ultimate limit state (ULS) of NCSE-02. Quality assurance was performed using the monitored displacement of a control point located on the roof. The pushover was run in SAP2000 v24 using the default nonlinear solution controls: SAP2000’s default approach is a hybrid method designed for robustness. It combines the efficiency of constant-stiffness with the accuracy of the Newton–Raphson method. Therefore, the capacity curve of Mod1 (Figure 24) reflects the bending behaviour in terms of resistance and stiffness, in both main orthogonal directions. The main difference between the two capacity curves is the inherent ductility of the building in each of the directions evaluated. The building is more ductile in the X direction. In addition, the performance point has been indicated on the capacity curve. The performance point is represented by a displacement value, in m, and a base shear value, in kN. This point is used to determine the safety and load-bearing capacity of a structure during a seismic event.

According to NCSE-02, the maximum deformation that can be considered acceptable for the studied building is 9 cm. After the pushover analysis, a deformation value of 13 cm in the X direction and 16 cm in the Y direction is obtained. Both deformation values are well above the maximum permitted and are therefore not considered adequate. Based on the obtained result after the limit state analysis and the pushover, it is considered necessary to apply retrofitting in Mod1.

As defined in Section 3.2.3, once the two retrofitting techniques have been applied, the limit state analysis was developed again. As a result of this analysis, a validated Mod1 model is obtained in which all profiles show a ratio between the resistant capacity and the load demands of less than 1 (Figure 25). Mod1 is capable of resisting external forces and guarantees its stability and structural safety under various load conditions. Finally, the building is analyzed for deformations. According to NCSE-02, the maximum deformation that can be considered acceptable for the Mod1 building is 9 cm. After the deformation analysis, a deformation value of 3.4 cm in the X direction and 1 cm in the Y direction is obtained. Both deformation values are below the maximum allowed and are therefore considered adequate.

4.2.3. Seismic Building Performance

At this stage of the study, two models have been developed that comply with current regulations for both scenario SR1 (1977, in Madrid) and SR2 (Los Barrios, 2021). Based on these valid models, NLDA is performed. To develop the NLDA, we used the published method in [64], P-delta effects and 5% damping.

The mentioned analysis reveals local collapses or specific elements for which retrofitting should be more deeply studied as they could compromise the operationally of the building. Figure 26 shows the damage results obtained after performing the NLDA for the reinforced Mod1 in the scenario SR2 (Los Barrios, 2021). On the one hand, slight damage (green dots) can be observed in some of the diagonals that were subject to the retrofitting process. This slight damage may manifest itself in the form of fissures or deformations that do not affect the structural integrity of the building. On the other hand, severe damage can be seen in two supports on one side of the Mod1 building (red dots). It is important to pay special attention to these elements and consider the possibility of applying retrofitting techniques to them in future studies. Severe damage means that the collapse of the elements in question must be prevented.

5. Conclusions

This study proposes a step-by-step analytical methodology for evaluating the seismic vulnerability and code-compliant structural performance of buildings of special importance under specific hazard scenarios. In this study, seismic performance is evaluated focusing on the structural response and damage state of a single exposed asset, rather than on regional loss estimation. This approach proposes the development of different integrated analyses to correctly define the vulnerability of the building, evaluating its resistance and deformation capacity. The proposed methodology allows for the estimation of the seismic behaviour of buildings in the event that seismic standards are updated and the hazard values of the region in which the building is constructed are increased.

In addition to the presented methodology, its application to a case study has been explained and the results obtained have been presented. The case study considers a special-importance building constructed in Madrid that is to be moved to Cadiz, a region with greater hazards for which the building was originally constructed. The methodology developed has made it possible to accurately define the vulnerability of the building under study, identify its capacity curve, and to establish critical areas of the building for which structural reinforcements are necessary in order to comply with regulatory requirements.

It is demonstrated that operational methods, OMA, and SSR offer a more complete perspective of the actual dynamics of the building. Overall, the results obtained in previous studies conducted by OMA on steel buildings support the validity of the differences observed in the present study results. The differences should be attributed to the omission of non-structural elements in the numerical building models. Therefore, it is due to the building mass considered, which is consistent with the complexity inherent in the dynamic responses of real structures.

In the context of modal analysis and OMA, the fundamental periods for each horizontal direction were estimated. The conservative approach is to consider the most unfavourable fundamental period. This means selecting the lowest period among those obtained in the different directions. The reason behind this choice is that the shortest period represents the dominant natural frequency of the structure and is crucial for evaluating its seismic response. Therefore, in the present case study, the fundamental period of 0.41 s is considered to be a representative value for the structure as a whole.

The resulting response spectrum consists of two sections (Figure 19). The first section (up to 0.20 s) coincides with the UHS for a T_R of 975 years, obtained after the PSHA. The second section (from 0.20 s onwards) forms part of the spectrum proposed by NCSE-02 for a building of special importance and a ground coefficient equal to 2. In the specific Mod1 study, the two fundamental periods indicated in Figure 21 have associated acceleration values that fall within the NCSE-02 spectrum segment. Therefore, the building is on the safe side. However, it is important to note that if it were a building with fewer floors, it would have shorter fundamental vibration periods, for instance less than 0.20 s. The building would be exposed to acceleration values associated with the first segment of the study spectrum, which are higher than those specified in the NCSE-02. This highlights the importance of conducting ad hoc hazard assessments for the area of interest, especially in the case of buildings of special importance. In this way, structural safety and compliance with the corresponding regulatory requirements can be guaranteed.

After analyzing the building limit state in the scenario SR1 (Madrid, 1977), it is concluded that the estimated loads applied to the structural model satisfy the resistance requirements established by the in-force regulations and codes in 1977. In addition, it is considered that the profile’s elements are mostly in line with the design standards applicable at the time of construction. Therefore, it can be said that the profile established for Mod1 SR1 is consistent with the time of construction and the region for which it was designed. However, as can be seen in Figure 23, the profile’s elements are not appropriate for an area of greater seismicity than originally considered. For this reason, it was necessary to modify the structure by increasing its stiffness through bracing systems in order to adapt it to scenario SR2. In addition to performing Mod1 limit state analyses for the different scenarios, the capacity curve for Mod1 in scenario SR2 before reinforcement was obtained.

Finally, a NLDA was performed considering an accelerogram compatible with the expected seismic motion, resulting from the ad hoc seismic hazard assessment. The results of the seismic performance assessment reveal elements with slight and severe damage, even though the structure has been adapted to the standard and code requirements of scenario SR2. Although retrofitting has improved the building’s seismic resistance, there are still areas that could benefit from further attention or reinforcement.

It is worth mentioning that a complete verification would require modelling and analyzing all four modules under the same set of actions, including potential inter-module interactions such as contact (pounding) induced by dynamic relative displacements.

The main contribution of this work lies in the step-by-step methodology proposed to define the seismic vulnerability of a building of special importance. In addition, we present a case study to put the proposed methodology into practice and consider an increase in seismic hazard in the study region due to updated seismic design regulations. This methodology can be applied to other existing buildings of special importance subject to updated or more demanding seismic scenarios.

6. Future Work and Research

The accurate definition of the seismic risk of a building is best achieved by applying specific fragility curves. When working with specific structures, it is preferable to use fragility curves based on local data and studies that reflect the specific conditions and properties of the region and the type of construction under consideration. However, in practice, obtaining local data and studies for each building can be extremely complicated and costly. For this reason, a direction for future work is the application of the methodology proposed in this study to buildings of the same structural type in a larger region. In this way, the methodology presented could be validated by extrapolating it from the application on a single building to several buildings. This approach allows for more generalizable results that are applicable to a wider range of buildings, facilitating seismic risk assessment on a regional or even national scale.

Once the detailed results and analysis for Mod1 have been obtained, as a future line of research we propose the application of the proposed methodology to the rest of the ETSITGC building’s modules. The information gathered and the considerations made during the analysis of the initial module will become a solid foundation for addressing the seismic performance and risk assessment of the other sections of the building. This step-by-step approach allows for a gradual and complete understanding of the seismic behaviour of the building as a whole and the effects of interaction between modules.

As the building is classified as special importance, post-earthquake functionality is a relevant requirement. In this study, functionality is addressed at a structural-safety level by verifying code compliance, strength and deformation limits, and by identifying structural components reaching severe damage in Nonlinear Time History Analysis (NLTHA). Nonetheless, non-structural elements and building systems can affect functionality. Therefore, the exclusion of non-structural elements is a limitation of this study. Future research should incorporate non-structural components into numerical models. This would improve the estimation of stiffness, damping and damage distribution in the building and the study of building functionality after the earthquake. The continuity of this research will ensure a comprehensive and rigorous assessment of the seismic risk in the building.