1 Introduction

Portugal is a country with low to moderate earthquake hazard (Silva et al. 2014c; Sousa and Costa 2016), whose past has been marked by several destructive events. These include the 1755 M ~ 8.5 Great Lisbon earthquake that caused heavy damage in the Southwest of the country (Oliveira et al. 1998), the 1969 M7.8 Algarve earthquake that damaged the old masonry building stock, and several destructive events that affected the Azores Archipelago in 1980 (M6.8 Terceira and Sao Jorge islands—Hirn et al. 1980) and 1998 (Mw6.2 Faial and Pico islands—Matias et al. 2007). Despite the low earthquake risk awareness of the population (Januário 2023), several initiatives have been supported by the Portuguese government to promote better construction practices (e.g., RESIST, 2023), to regulate structural modifications of the building stock, or to retrofit specific public buildings such as schools and hospitals (Estêvão et al. 2018). The development and implementation of such risk management measures must be supported by up-to-date and reliable probabilistic seismic risk models or realistic earthquake scenarios.

Probabilistic seismic risk models characterize the probability of an earthquake occurring in a specific location and the potential impact on the affected area. The development of such models requires three main components: (1) a seismic hazard characterizing the probability of ground shaking intensity at a set of locations, (2) an exposure model defining the location, value, occupants, and vulnerability class of the elements exposed to the seismic hazard, and (3) a set of vulnerability or fragility functions establishing the probability of damage or loss conditional on a ground shaking intensity measure. In the last decade, several seismic hazard and vulnerability models covering the Portuguese territory have been released, and some have been used for probabilistic seismic risk assessment (e.g., Silva et al. 2014b; Sousa and Costa 2016). Moreover, the Portuguese National Institute of Statistics (INE) has recently released data regarding the National Housing Census carried out in 2021, which provides fundamental information regarding the current status of the Portuguese residential building stock. Finally, there have been important methodological developments in the assessment of earthquake risk that are enabling the scientific community to evaluate risk metrics beyond the usual economic losses (e.g., Erdik 2017; Ward et al. 2020). These scientific advancements and the availability of new data represent a strong argument for the re-assessment of the potential impact of earthquakes in the country. This study advances the understanding of earthquake risk in Portugal by addressing the following five gaps and limitations:

  1. 1.

    Obsolete exposure information: previous risk assessment efforts used housing data from 2011 national census. Portugal has undergone significant changes in terms of its demographics, exposure, and built environment over the past decade (INE 2021). The construction of new buildings, population growth, inflation, and shifts in urbanization patterns have altered the landscape of the country. In this study, we have developed a novel exposure model using the 2021 housing census. Moreover, this study also includes commercial and industrial buildings, as described in Crowley et al. (2020).

  2. 2.

    Insufficient risk metrics: with the exception of some past studies (e.g., Sousa 2007; Sousa et al. 2007), most assessments have primarily focused on economic losses, with limited emphasis on metrics such as buildings lost or damaged, built-up area lost, and population affected. Such metrics are fundamental for the development of risk management and preparedness policies (e.g., Mendes-Victor et al. 1994). This study covers five fundamental risk metrics: economic losses, buildings lost, built-up area lost, fatalities, and population left homeless. Moreover, we disaggregated the losses according to the type of use (i.e., residential, commercial, and industrial) and components (i.e., structural/non-structural components and contents).

  3. 3.

    Lack of geographical coverage: most studies have focused on seismic hazard and risk assessment for continental (or mainland) Portugal and neglected the impact of earthquakes in the Azores and Madeira archipelagos. The former archipelago is comprised of 9 islands, has a population of over 240,000 people, and has been affected by several destructive events in the last century (Fontiela et al. 2018). The entire Portuguese territory has been considered in this study.

  4. 4.

    Out-of-date seismic hazard: recent developments in seismic hazard modelling have led to the release of a new seismic source model covering the Portuguese territory and several ground motion models applicable to the tectonic environment of this region. The hazard considered herein was developed within the scope of the European H2020 SERA (Seismology and Earthquake Engineering Research Infrastructure Alliance for Europe) project, and includes a number of novelties, as further described in Sect. 3.

  5. 5.

    Need to better characterise seismic vulnerability: previous studies on seismic risk for Portugal used vulnerability models whose damage criterion was based on structural damage (i.e., maximum global drift), and neglected the vulnerability of other elements that tend to be damaged due to high accelerations (i.e. acceleration-sensitive components) (e.g., Silva et al. 2014b). Moreover, past efforts used different approaches for the vulnerability assessment of reinforced concrete structures and masonry buildings. In this study, we used the model proposed by Martins and Silva (2021) that provides vulnerability functions for the different components and follows a uniform methodology for all building classes, as further described in Sect. 5.

The objectives of this study are to propose a new probabilistic seismic risk model for Portugal leveraging upon recently released models and datasets, and to identify the regions in the country with the highest seismic risk according to five risk metrics. The outcomes from this study are useful for the development of risk management measures, or to transfer the financial risk to the international (re)insurance market.

2 Review of existing studies

Over the past decades, several studies covering Portugal have been devoted to the various aspects of earthquake hazard and risk. In this section, we summarize some of the most relevant studies that have influenced the model proposed herein.

Regarding seismic hazard assessment, at the regional scale the SHARE project (2009–2013) (Woessner et al. 2015) aimed at establishing a uniform and consistent seismic hazard model for Europe. This involved selecting a set of ground motion models compatible with the European tectonic environment and generating a harmonized seismic source model. Later, within the scope of the European H2020 SERA project, Danciu et al. (2021) presented an update of the European Seismic Hazard Model (ESHM20), which has been officially adopted as an “acceptable representation of the seismic hazard in Europe” in the revision of Eurocode 8. At national level, one of the first comprehensive seismic hazard assessments for Portugal was carried out by Oliveira and Costa (1984). This assessment served as the foundation for the seismic hazard maps endorsed by the Portuguese design code of 1983 (RSA 1983). Additional studies were conducted within the scope of the National Annex for the Eurocode 8 (CEN 2010), resulting in seismic hazard maps for moderate and large magnitude events at different distances. Two notable studies by Sousa et al. (2006) and Vilanova and Fonseca (2007) have proposed a probabilistic seismic hazard model for mainland Portugal and have been used in seismic risk assessment (Silva et al. 2014c; Sousa and Costa 2016). Duarte et al. (2018) proposed a new model for the occurrences of earthquakes in the south of the Continent that may in the future be considered. In this study, we used the latest seismic hazard model covering Portugal (ESHM20), and compared the losses calculated herein with those of the previous risk studies. Other studies that contributed towards the understanding of the seismic hazard for the country include Sousa and Oliveira (1997), (Oliveira et al. 2000), Oliveira et al. (2004), (Carvalho et al. 2009), Muir-Wood and Mignan (2009), Estevão (2012), Catita et al. (2019), Teves-Costa et al. (2019) and (Karimzadeh et al. 2024).

For what concerns the development of exposure models at the European scale, building data from national housing censuses was collected within the NERA project (2010–2014) (NERA 2014) for all European countries. Later in the European SERA project, a pan-European exposure model was developed covering the residential, commercial, and industrial building stock (Crowley et al. 2020). At the national scale, Silva et al. (2014a) and Sousa and Costa (2016) developed an exposure model for mainland Portugal based on the national housing census from 2011 and building statistics from the Portuguese National Institute for Statistics. Other exposure models at the local level have been developed for Lisbon (Oliveira et al. 1997; D’Ayala et al. 1997; Santos and Ferreira 2023), Coimbra (Vicente et al. 2011), and Seixal (Santos et al. 2013). Such models tend to use detailed information at the building level or from cadastral datasets, which can be used to verify and calibrate models at the regional or national level. Mota de Sá (2016) and Mota de Sá et al. (2018) developed theoretical work for the Lisbon City Council to obtain an “indicator of seismic vulnerability” for existing buildings, which has been applied to more than a hundred buildings (Oliveira et al. 2023).

Regarding the vulnerability of the building stock, at the European scale, Spence et al. (2008) investigated the practices and methodologies for assessing seismic vulnerability of existing buildings in Europe, particularly in areas with moderate to high seismic hazard. This study involved collecting and reviewing analytical fragility curves from the literature and evaluating them based on a qualitative criterion. More recently, the European Syner-G project (2009–2013) (Pitilakis et al. 2014) compiled a database of structural fragility of buildings, infrastructures, and networks. It also defined a unified methodology for evaluating both the physical and socio-economic vulnerability. At the national scale, Silva et al. (2014b) proposed a new vulnerability model for reinforced concrete moment frames with infills for Portugal. At the local scale, Lamego et al. (2017) studied the vulnerability of old buildings in a neighbourhood in Lisbon, comprising three common Portuguese building types: stone masonry, “placa”, and reinforced concrete buildings. More recently, Martins and Silva (2021) have developed a uniform methodology to develop fragility and vulnerability functions for over 1000 building classes. This model is particularly important for the purposes of this project since it covers the most predominant construction typologies in Portugal, and it separates the losses according to building components (i.e., structural/non-structural and contents). As a good calibration of any loss simulator, the work of Pereira (2009), obtaining an estimation for losses in 1755 Lisbon earthquake, is an extremely good challenger for new models. Azzaro et al. (2018) also prepared a simulation for non-structural elements in a neighbourhood of Lisbon.

Some studies have combined these three components to assess economic or human losses for Portugal. At the global scale, the Global Earthquake Model Foundation (GEM – Silva et al. 2020) combined the previously mentioned SHARE hazard model with the exposure model from Silva et al. (2014b) to compute normalized economic losses. At the European scale, Crowley et al. (2021) presented the development of an earthquake risk model for the European territory, which resulted in the calculation of a risk index that combined economic and human losses. Additionally, Gkatzogias et al. (2022) assessed the impact of different seismic strengthening and energy renovation interventions for existing buildings. At the national scale, in addition to the previously mentioned studies by Silva et al. (2014b) and Sousa and Costa (2016), it is also worth mentioning the work by Sousa et al. (2022) that focused on the assessment of direct and indirect economic losses to the precast reinforced concrete industrial building stock in mainland Portugal. At the local or urban level, Xofi et al. (2022, 2023) focused on the assessment of seismic risk of the Metropolitan Area of Lisbon (MAL) using data from the 2011 national census. Additional studies covering Portugal (or specific regions or cities) can be found in Oliveira (2013).

3 Seismic hazard assessment

3.1 Overview

As previously described, a few seismic hazard models have been developed in the past for Portugal, partially due to the need to include a seismic hazard zonation in design regulations, or within the scope of European projects (e.g., SHARE, SERA). From the review of the previous studies, we decided to adopt the latest European Seismic Hazard Model (ESHM20—Danciu et al. 2021). Unlike the previously released models, this proposal has not been properly applied in seismic risk analysis for Portugal, and it incorporates a number of relevant novelties, as further described in this section.

3.2 Description of the seismic hazard model components

The European Seismic Hazard Model is comprised of three main components: a seismogenic source model, a ground motion model (GMM) logic tree, and a site model characterizing ground shaking amplification in the European territory.

The seismogenic source model includes an area source model and a smoothed seismicity plus faults model. The epistemic uncertainty is handled through a complex logic tree model to account for different choices or assumptions in the seismogenic process such as different parameters in the magnitude-frequency distributions or maximum magnitudes. The various branches were assigned probabilities based on available geological, geophysical, and seismological data, as well as the independence between datasets, assumptions made in model building, and the likelihood of each branch being the true model. All modelling assumptions are thoroughly described in Danciu et al. (2021), and the input models in the OpenQuake format (Pagani et al. 2014) are available in the European Facilities for Earthquake Hazard and Risk (EFEHR) platform (http://hazard.efehr.org).

The development of the ground motion model logic tree followed a different approach from its predecessor, in which instead of selecting a set of best suited ground motion models for each tectonic region (e.g., Delavaud et al. 2012), a single ground motion model was calibrated for the entire region, and adjustment factors were defined for several regions in Europe. A comprehensive description of the process followed to develop this scaled backbone ground motion model can be found in Weatherill et al. (2023), and the logic tree file is available in the EFEHR portal.

Finally, a site response model compatible with the backbone ground motion model was developed by Weatherill et al. (2023). This model departed from the traditional practice of simply combining average shear wave velocity in the top 30 m layer (VS30—e.g., Wald and Allen 2007) with amplification factors embedded within the ground motion model, to utilize directly topographic slope and geological data, and amplification functions developed using station data recorded in Europe. This model is supported by several datasets including a harmonized map of superficial geology, a new European model of VS30 constructed from slope and geology, and a database of VS30 measurements, all available in the EFEHR portal (http://risk.efehr.org/site-model).

We combined these three main components within the OpenQuake engine (Pagani et al. 2014) to compute seismic hazard curves, seismic hazard maps, and to generate a large stochastic event set for seismic risk analysis, as described in Sect. 3.2 and 6.

3.3 Seismic hazard results

The seismic hazard assessment was performed utilizing the OpenQuake engine (Pagani et al. 2014), an open-source software for seismic hazard and risk analysis. For this section, we specifically employed the Classical PSHA-based hazard calculator. Hazard calculations were performed using a smoothed hexagonal point grid with a spatial resolution of 0.03 decimal degrees, for a total of 9871 grid points. Figure 1 shows the mean seismic hazard map for Portugal in terms of peak ground acceleration (PGA—in g) expected to be exceeded with a 10% probability in 50 years (equivalent to a return period of 475 years)—a commonly used reference in seismic design regulations.

Fig. 1
figure 1

Mean seismic hazard map in terms of peak ground acceleration (g) for a probability of exceedance of 10% in 50 years (equivalent to a return period of 475 years)

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The mean hazard map indicates PGA values ranging from 0.04 to 0.55 g, in line with past studies for the Southwest of the territory (e.g., Vilanova and Fonseca 2007). The map reveals that the southern and central-west regions of mainland Portugal have the highest seismic hazard, with PGA values ranging from 0.14 to 0.55 g. The northern part of the country is characterized by low to moderate seismic hazard, ranging from 0.04 to 0.15 g. While the seismic hazard in the Madeira islands is considerably lower, the Azores archipelago has high seismic hazard, due to its geographic location in the junction of the Eurasian, North-American and Nubian plates, with values ranging from 0.22 to 0.47 g.

Figure 2 shows the mean hazard curves for six cities in Portugal, depicting the probability of exceedance in 50 years of four ground shaking intensity measures: PGA and spectral acceleration at three periods of vibration (Sa(0.3), Sa(0.6), and Sa(1.0)). These intensity measures are used by the vulnerability model employed in this study.

Fig. 2
figure 2

Comparison of the mean hazard curves for four ground shaking intensity measures for six cities in Portugal

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These results indicate that Faro, located in the southern region of mainland Portugal, has the highest seismic hazard among the selected locations. Ponta Delgada, in the Azores islands, and Lisbon, in the central-west region of mainland Portugal, also have significant seismic hazard. Notably, these three top locations have been affected by destructive events in the last centuries (Ferrão et al. 2016).

4 Exposure model

4.1 Overview

Exposure models include detailed information about the spatial distribution of the built environment, namely its geographical location, number of buildings, structural properties, replacement costs, and number of occupants. The exposure models for Portugal used in previous risk studies were developed using information from the 2011 national housing census (Silva et al. 2014c; Sousa and Costa 2016), and neglected the commercial and industrial building stock. With the release of new data collected in the context of the 2021 national housing census (https://censos.ine.pt/), it is now important to update the existing model and understand how this new information can impact the risk estimates. Moreover, within the scope of the European H2020 SERA project, an exposure model for the commercial and industrial building stock covering Portugal was developed (Crowley et al. 2020). In this section, we describe how the new exposure model for the residential building stock was developed, and we summarize the main features of the commercial and industrial building stock released as part of the SERA project.

4.2 Residential building stock

The latest housing census for Portugal captures detailed information about the residential building stock, including the number of buildings and dwellings disaggregated by the number of storeys and year of construction. Although this information is collected at the building level, currently the 2021 data is available at the parish level (freguesia), which is the smallest administrative division in Portugal. In contrast with the previous census data (2011), which provided the housing data considering simultaneously three variables (i.e., type of construction, number of storeys and age of construction), this newer survey did not include the type of construction of each building (i.e., reinforced concrete, masonry with a slab, masonry walls without slab, adobe walls or loose stone masonry, and other), which is fundamental to categorize each building into a vulnerability class. For this reason, the information about the number of buildings within each construction type from 2011 was used in the development of the new model. To adjust these values to the current number of buildings, we calculated the difference in the number of buildings between 2011 and 2021. Then, for each parish (freguesia), it was assumed that if this difference is negative (i.e., the number of buildings in 2021 is lower than in 2011), the buildings that were demolished were either masonry or older buildings, and therefore these were excluded from the model. On the other hand, when there was an increase in the number of buildings, we assumed that the new buildings were constructed using reinforced concrete. This process was rather challenging due to the fact that between the two housing censuses, some parishes were merged, one new parish was created (Parque das Nações) and some administrative boundaries were adjusted. The reorganization of the parishes is described in a “Administrative Reorganisation of the Parishes” table, released by the Ministry of Internal Affairs in 2013. Based on this information, we reviewed each parish and either summed their building stock (when two parishes were merged), or split their building stock proportional to the population (i.e., Parque das Nações). When the boundaries of a parish were modified, it was not possible to identify specifically which buildings should be moved to the new parish. Some parishes that were affected by this change include: Gafanha da Nazaré, Buarcos or Ajuda. We understand that this is a limitation of the proposed exposure model, but also do not expect any significant impact in the resulting risk metrics given the scale of the current study.

The housing census of 2021 reports approximately 3.5 million residential buildings, comprising 6 million dwellings. Considering the attributes available for each building (type of construction, year of construction and number of storeys), the building portfolio was divided into different building classes following the GEM building taxonomy (Silva et al. 2022). According to the type of construction, the buildings were categorized into 5 main classes: reinforced concrete (CR) buildings, brick/stone masonry (with wooden floors (MUR + FW), or with concrete floors (MUR + FC), adobe masonry buildings (MUR + ADO), and other/unknown typologies (UNK). As shown in Fig. 3, the majority of the building stock is made of reinforced concrete (53.7%), housing around 63% of the population.

Fig. 3
figure 3

Distribution of buildings according to type of construction, construction period, and number of storeys

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The year of construction allows understanding the level of seismic design in place when the buildings were constructed. By comparing the construction year classes available in national housing census with the evolution of seismic codes in Portugal (e.g. Silva et al. 2014b), four design levels were defined. No-code (CDN) refers to buildings built before 1960, which marks the introduction of the first regulations with seismic provisions in Portugal (RSCCS 1958, RSEP 1961). Low code (CDL) covers buildings constructed between 1961 and 1980. The latter year is close to the year when a more modern design regulation was introduced in Portugal (RSA 1983). Moderate code (CDM) covers the period from 1981 until 2010, and high code (CDH) refers to structures built after 2011, already assumed to follow the Eurocodes. Additional information concerning the different design regulations in Portugal can be found in Barbosa (2019) or Crowley et al. (2021). It is relevant to note that around 36% of the building stock has been built before the introduction of the 1983 design code (RSA 1983). Figure 3 shows the distribution of buildings for each construction typology, according to the construction period and number of storeys. We note that even if an adobe (MUR + ADO) or unreinforced masonry building (MUR + FW or MUR + FC) was built recently (and would thus fall under the CDM or CDH category), the building is still assumed to have limited seismic capacity, as dictated by the vulnerability model described in the following section. From the distribution of the number of buildings according to the construction material and number of storeys (Fig. 3 right), it is possible to note that vulnerable unreinforced masonry building classes are mostly low rise (1 or 2 floor) buildings, while mid- and high-rise buildings are typically reinforced concrete structures.

For the estimation of economic losses, it is necessary to establish a replacement value for each building, which corresponds to the cost required to build a structure with the same characteristics and area, based on current construction costs. To calculate the total replacement cost of each building, we multiplied the average construction cost per square meter by the total area of the building. The area of each building was estimated considering the average number of dwellings per building and the average area per dwelling. From the 2011 census data it is possible to infer the distribution of the average number of dwellings for buildings with a specific number of storeys. As shown in Table 1, buildings with 3 storeys, for example, have on average 2.08 dwellings. We note that this data is also available at the parish level, but the differences across the country are not significant.

Table 1 Average number of dwellings per building per number of storeys
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Regarding the average area per dwelling, it is important to distinguish separated houses from apartment buildings, as the latter tends to have smaller areas. The National Statistical Office (INE) provides information concerning the area per dwelling for the seven areas defined by Coordinating Committee for Regional Development (CCRD) in Portugal, with an average value for the country of 101 m2. We assumed that this is a reasonable value for dwellings in apartment buildings. Moreover, according to the 2021 housing census, 93% of the buildings with 1 or 2 storeys are single family houses (i.e. contain only one dwelling). For separated houses, we reviewed hundreds of entries in real state web portals to define a reasonable dwelling area. From this review, we assumed that buildings with 1 storey or 2 storeys have an average area of 150 m2 and 120 m2 per dwelling, respectively, while buildings with 3 storeys or more are apartment buildings with an average area per dwelling of 100 m2.

The construction costs per square meter have important variations throughout the country, depending on the building location. The housing construction price in 2022, calculated according to the traditionally accepted method by the majority of insurers operating in Portugal, are divided in 3 zones. Zone I includes the district capitals, other major cities and the islands (830.03 €/m2), zone II includes counties located in urban areas (725.56 €/m2), and Zone III refers to counties located in rural areas (657.35 €/m2).

Having the number of dwellings per building, the average dwelling area, and the construction costs (according to the building location), the total cost per building was calculated by multiplying these three variables. This building cost includes the structural and non-structural components, but it does not include the cost of the contents (e.g., furniture, appliances, equipment, machinery). The total replacement cost for residential structures was obtained by considering the expected percentages of structural, non-structural, and contents costs presented in Table 2. These fractions were defined by reviewing construction cost books and the available literature, as described in Yepes-Estrada et al. (2023).

Table 2 Percentage of the economic costs (structural, non-structural, and contents) by type of construction for residential buildings
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Along with the economic impacts, estimating human consequences such as fatalities and population left homeless is fundamental to create post-disaster emergency plans and to inform disaster risk reduction and preparedness measures. To obtain these outputs, the exposure model must include information about the number of occupants inside each building, at different times of the day. To estimate the number of occupants in each building, we multiplied the average number of occupants per dwelling in each parish by the number of dwellings in each building. The average number of occupants per dwelling per parish was calculated by dividing the population by the number of dwellings in each parish.

4.3 Commercial and Industrial building stock

Information regarding the industrial and commercial building stock is far less detailed than the residential counterpart, both in terms of spatial resolution and construction attributes. This is a trend that is common to most countries (Yepes-Estrada et al. 2023), leaving exposure analysts with no alternative but to use simplified methodologies. In this study, commercial buildings include offices, wholesale, retail (trade), and hotels, while the industrial facilities cover manufacturing, mining, quarrying, and construction activities. As previously mentioned, we adopted the commercial and industrial building stock for Portugal developed within the scope of the H2020 European SERA project. We summarize herein the methodologies that were followed for the development of these models, and additional details regarding the derivation procedure and assumptions can be found in Crowley et al. (2020).

For the development of the commercial building stock, socio-economic data was collected from the National Institute of Statistics (INE) regarding the number of (commercial) businesses. Assuming that each business requires a building or facility, this step led to the number of buildings at the second administrative level. Then, based on mapping schemes which describe the distribution of building classes for each commercial activity (offices, wholesale, retail and hotels), a building class was assigned to each asset. The cost of each asset was determined by assuming an average area and a construction cost, which again is dependent on the location of the building. We note that some commercial activities (in particular wholesale and retail) are located on the ground floor of residential buildings. These buildings of mixed use, which are identified within the national housing census (approximately 10% of the residential buildings in Portugal) were classified as residential buildings. This information was used to reduce the number of commercial buildings, to avoid double counting the construction area of this type of activity.

The development of the industrial building stock followed a different approach, as originally described in Sousa et al. (2017). For this type of buildings, an European land cover dataset (CORINE 2006) was used to identify the areas in Portugal where industrial buildings might exist, and the number of facilities were identified using data from OpenStreetMap (OSMF 2023). A statistical process was applied to understand which industrial areas had all buildings identified (within OpenStreetMap), and which areas were incomplete, and thus required the application of an extrapolation procedure based on the estimates derived for the complete areas. For the specific case of Portugal, this procedure was validated against detailed cadastral data regarding industrial buildings from 18 districts (Araújo 2018). The commercial and industrial exposure models are available in the EFEHR exposure repository (https://gitlab.seismo.ethz.ch/efehr/esrm20_exposure), along with all of the assumptions concerning areas, costs, and mapping schemes.

The distribution of the economic value amongst structural and non-structural components, as well as the estimation of the cost of contents, was performed using the percentages proposed by Yepes-Estrada et al. (2023), as previously presented for the residential building stock. These percentages are presented in Table 3 per type of occupancy and building class.

Table 3 Percentage of the economic costs (structural, non-structural, and contents) by type of construction for non-residential buildings
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Finally, it is fundamental to distribute the population at different times of the day across residential, commercial, and industrial buildings. To do so, we used the model proposed by Jaiswal et al. (2010) that provides occupancy rates based on the fraction of employed population and the type of activities within each administrative area (i.e., agriculture, industry, and services). The average occupancy rates during the day, night and transit hours are presented in Table 4. The same procedure was followed for the development of the European exposure model (Crowley et al. 2020).

Table 4 Occupancy rates for residential buildings during the day, night, and transit
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4.4 Appraisal of the exposure model for Portugal

Residential buildings represent most of the exposure model for Portugal, accounting for 92.4% of the number of buildings, while commercial and industrial building represent 4.8% and 2.8%, respectively. In terms of replacement cost, residential buildings represent a lower fraction (78.9%) due to the high costs of the contents in commercial and industrial buildings. These distributions are depicted in Fig. 4.

Fig. 4
figure 4

Distribution of the number of buildings (left) and replacement cost (right) by occupancy

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Figure 5 summarizes some of the main indicators of the exposure model aggregated at the district level, while Fig. 6 presents the economic value and number of buildings at the scale in which the data from the 2021 census were made available (i.e., freguesia). These results indicate that more than 50% of the economic value of the building stock is concentrated only in four districts (Lisbon, Porto, Setubal, and Braga), while the number of buildings is more uniformly distributed, with half of the building stock located in the top 6 districts. It is interesting to note the variation in the percentage of buildings with insufficient seismic provisions (from 42% in Madeira to 79% in Portalegre and Beja). It is also important to highlight that only 12% of the total number of buildings follow the most recent seismic regulation. These are important findings, as they allow identifying concentrations of exposure with an expected poor seismic performance, and thus where additional risk analyses should be performed.

Fig. 5
figure 5

Exposure indicators of the Portuguese building stock per district

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Fig. 6
figure 6

Economic value and number of buildings at the smallest available administrative division (i.e., freguesia)

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5 Vulnerability model

We adopted the fragility and vulnerability functions proposed by Martins and Silva (2021), whose methodology is summarised herein. This study identified the most common building classes globally by reviewing technical reports, scientific articles, and World Housing Encyclopedia reports. For the particular case of European countries, the building classes were defined within the scope of the NERA and SERA projects, which involved dozens of European scientists, and technical workshops in Italy, Serbia, and Portugal to establish a comprehensive list of existing types of construction. The capacity of each building class was defined through a single-degree-of-freedom (SDOF) oscillator, whose structural and dynamic properties (e.g., yield and ultimate drifts, elastic and yield period, participation factor of the first mode of vibration) were defined based on the literature covering numerical studies, experimental tests, damage observations, and expert judgment. The response of the SDOF oscillators was evaluated through nonlinear time history analysis (performed using the open-source software for structural analysis OpenSees—McKenna et al. 2000), considering a wide range of ground motion records from the European, Mexican, and American strong motion databases. The estimation of the probability of exceeding a set of damage states (slight, moderate, extensive, and complete damage) was performed following the cloud analysis method originally proposed by Jalayer and Cornell (2009). As described in Martins and Silva (2021), a damage criterion based on the yielding and ultimate drift was assumed for the structural and drift-sensitive non-structural components. Then, the probability of exceeding each damage state was converted into loss ratios through a damage-to-loss (also known as consequence) model. Loss ratios of 0.05, 0.20, 0.60 and 1.00 were assumed for slight, moderate, extensive, and complete damage, respectively. For the acceleration sensitive non-structural components and contents, only the complete damage state was considered, as these elements will most likely be replaced if damaged. For this case, a set of acceleration thresholds were defined based on the level of ductility of the building class and type of use (residential, commercial, and industrial). The vulnerability analyses were performed using the Vulnerability Modelers Toolkit (VMTK—Martins et al. 2021) supported by the GEM Foundation. All the capacity parameters and fragility/vulnerability functions are publicly available in the repositories included in the associated publications. Additional information about the vulnerability methodology can be found in the online documentation (https://docs.openquake.org/vulnerability/), and the vulnerability process can be reproduced using the VMTK (https://github.com/GEMScienceTools).

For the assessment of probabilistic seismic risk for Portugal we used 580 vulnerability functions, covering 116 building classes and 5 risk metrics, as further described in the following section. As an example, Fig. 7 presents the vulnerability functions for 4 common building classes in Portugal.

Fig. 7
figure 7

Vulnerability curves for 4 common building classes in Portugal for four physical risk indicators (Economic losses, buildings/area lost, population left homeless) and fatalities

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6 Seismic Risk Assessment

The assessment of earthquake risk was performed using the Probabilistic Event-based Risk calculator of the OpenQuake-engine (Silva et al. 2014a). This calculator generates a large number of stochastic event sets (SES) using the probabilistic seismic hazard model. We used the hazard model described in Sect. 3 and generated 100,000 SESs with a one-year duration, randomly sampling different branches of the source model and ground motion logic tree according to the associated weights. For each event in the SES, a ground motion field was generated, considering both the spatial and inter-period correlation in the ground motion residuals using the correlation models from Jayaram and Baker (2010) and Goda and Atkinson (2009), respectively. The ground shaking at the location of each asset was combined with the associated vulnerability functions and exposure information to compute the expected loss for each event in the SES. These results were used to compute event loss tables, loss exceedance curves and average annualised losses. Additional information about the OpenQuake-engine can be found in the online documentation (https://docs.openquake.org/oq-engine/master/manual), while guidance regarding probabilistic event-based analysis is provided in Silva (2017).

Figure 8 presents the average annualised results aggregated at the district level for five risk metrics: economic losses, buildings with complete damage (or lost), built-up area lost, fatalities, and population left homeless. These results indicate that most of the earthquake risk in Portugal is concentrated in the districts of Lisbon, Setúbal, Santarém, Faro (i.e., Algarve) and in the Azores islands. This trend is due to the significant seismic hazard in these regions (as described in Sect. 3.3), associated with a high concentration of buildings, population, and economic value (see Figs. 5 and 6). Sousa (2007) carried out an identical assessment and ranked the districts according to the expected economic and human seismic losses. Although the values estimated in the referred study differ from our estimates, it is noticeable that the order of the four districts with highest economic losses is the same, and that four out of five districts with the most fatalities overlap between the two analyses.

Fig. 8
figure 8

Average annualised results aggregated at the district level for five risk metrics: a economic losses, b buildings with complete damage, c built-up area lost, d fatalities and e population left homeless

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Figure 9 presents four annualized risk metrics at the second administrative level (i.e., concelho). We note that the risk calculations were performed at a finer resolution (i.e., freguesia), but we decided to aggregate the results at a coarser division for the sake of clarity. The spatial pattern of the risk metrics indicates a higher potential for losses in the Southwest of the country, the Lower Tagus Valley, and the Azores Archipelago.

Fig. 9
figure 9

Average annualised losses at the second administrative division (i.e., concelho)

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Table 5 summarizes the selected earthquake risk metrics at the national level, in terms of average annualised losses (AAL). The AAL has also been normalized by the total exposed values to evaluate the average annualised loss ratio (AALR).

Table 5 Summary of the main earthquake risk metrics for Portugal
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The economic losses and loss ratios (i.e., losses normalized by the exposed values) were disaggregated based on the main types of construction (as described in Sect. 4) and components (structural/nonstructural components and contents), as illustrated in Fig. 10. More than half of the economic losses are due to damage in the reinforced concrete building stock, partially due to the fact that one third of these buildings were built before the introduction of the first modern seismic regulation in Portugal (i.e. 1983), but mostly due to the higher costs in comparison with the other typologies. In fact, when these losses are normalized by the economic value, it is clear that unreinforced masonry and adobe have a higher likelihood to suffer damage due to earthquakes. Regarding the occupancy class, the residential portfolio is the main contributor to the total economic losses (90.6%), followed by the industrial (5.1%) and commercial buildings (4.3%).

Fig. 10
figure 10

Distribution of the average annual economic losses (left) and loss ratios (right) for different types of construction and components

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Past studies such as Silva et al. (2014c) estimated an average annual loss of 288 M EUR, while Sousa (2006) indicated an annual loss of 257 M EUR, both for the residential building stock only. These estimates are considerably higher than the annual loss proposed herein (181 M EUR), in particular considering that the present study also covers commercial and industrial facilities, and losses due to damage to contents. One of the reasons for this reduction is the lower seismic hazard, especially for the Northeast of the country whose hazard is below 0.1 g (in terms of PGA) for the 475 years return period. The direct comparison of the vulnerability functions for 4 building classes presented in these studies also show a higher vulnerability for the past studies. Finally, it is also worth mentioning that despite the increase in the number of buildings from 2011 to 2021, the newer construction was assumed to follow modern design regulations, whose vulnerability is considerably lower. The AAL indicated by the work of Sousa and Costa (2016) (147 M EUR) is in line with the values presented herein, though again only the residential building stock was considered. Table 6 lists the AAL proposed by the current and past projects, with figures adjusted to 2022 using the consumer price index (CPI). The models used in the present study and their results are publicly available to allow further comparisons with future studies.

Table 6 Comparison of the average annual loss (AAL) from previous studies
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7 Conclusions

This study presented a new view of probabilistic seismic risk for Portugal, considering recently released models and datasets. In comparisons with past efforts, this study advanced the understand of earthquake risk by covering the entire territory of Portugal (continental and islands), considering commercial and industrial facilities, calculating risk metrics beyond economic losses, and disaggregating the risk geographically and according to the main construction material and building components.

The exposure model for the residential building stock derived herein using the 2021 Building Census data estimates the replacement cost for the Portuguese building stock at approximately 905 billion EUR, which is approximately 3.7 times the 2022 Portuguese gross domestic product. The majority of the building stock is located in the Metropolitan Area of Lisbon and Porto, with the seismic hazard (in terms of PGA) in the former area above 0.15 g for the 475 years return period. In terms of earthquake risk, the estimated average annual economic losses of 181 M EUR are considerable for the country. To put in perspective, this loss is equivalent to one third of the construction cost of the new hospital in Lisbon, one of the largest in the country. The human impact (average annual human losses) is relatively low, mostly due to the fact that the building stock is predominantly composed by structures with 1–2 storeys (84% of the buildings), which tend to have low volume loss and consequently low fatality rates. The seismic risk map highlights the Lower Tagus Valley, the South of Portugal, and the Azores islands as high-risk regions, with adobe and unreinforced masonry typologies identified as the most vulnerable.

It is important to note that the models used herein are characterized by large epistemic and aleatory uncertainties, and sensitivity analysis to further understand the impact of the variability of each component in the final risk estimates should be carried out. Moreover, we note that these losses only include damage due to ground shaking, and do not include the potential impact of tsunamis, landslides, liquefaction, or fire following. Eventual economic losses due to business disruption (e.g., Sousa et al. 2022) or post-loss amplification (Hoyos and Silva 2024) have also not been included, and could increase the losses considerably.

The results and findings from this study can be used to identify hotspots of earthquake risk in the country, and thus where additional risk studies should be supported, to ultimately result in the design and implementation of disaster risk measures, such as retrofitting campaigns, strategic urban planning, emergency plans, and risk awareness initiatives. The components of the model presented herein are also useful to perform earthquake scenarios considering the characteristics of historical events (e.g., Villar and Silva 2017), or for impact assessment shortly after the occurrence of destructive events (e.g., Silva and Horspool 2019). In the future, we plan to extend these analyses to demonstrate the importance of accounting for the impact of earthquake-triggered hazards (e.g., Daniell et al. 2017), disruption in the transportation system (Costa et al. 2020), and inclusion of the number of occupants and associated socio-economic conditions considering the vulnerability attributes of each building.

8 Conflict of interest

The authors declare that they have no conflicts of interest.