1 Introduction

Seismic vulnerability assessments are essential for predicting and mitigating the impacts of earthquakes on urban infrastructure. Among the plethora of methodologies used worldwide, the RISK-UE approach, developed under the European RISK-EU project’s Work Package 4 (Milutinovic & Trendafiloski 2003), stands out for its comprehensive application to seven major European cities. This approach includes two distinct assessment methods: the empirical LM1 method and the mechanical LM2 method, each tailored to different urban and structural characteristics. The application of these methodologies has been demonstrated in various contexts, including the assessment of historical masonry churches and other heritage buildings (Giovinazzi 2005; Lestuzzi et al. 2017), which often present unique structural challenges due to their age and construction techniques.

"Place d’Arme," the old urban center of Annaba city, characterized by its historical masonry buildings predominantly from the colonial French era, was selected as the focal area for this study. While architecturally significant, these buildings pose substantial risks due to their construction age and methods. By employing the LM1 and LM2 methods, this research aims to comprehensively evaluate seismic vulnerability, identify high-risk areas and structures, and inform effective mitigation strategies.

The data underpinning this assessment originates from a comprehensive building-by-building detailed survey conducted by the CTC (CTC 2010), the official technical organization of Annaba city responsible for the Technical Control of Construction. This survey provided an extensive database of 380 buildings, including structural details, material composition, and historical modifications, indispensable for accurately applying the LM1 and LM2 methods. The credibility and depth of this survey data are vital, as they ensure that the seismic vulnerability assessments are based on reliable and current information, reflecting the proper condition of the building stock in Annaba’s “Place d’Arme.”

For this study, the LM1 method was selected for its adaptability and efficiency in environments where detailed site-specific seismic data might not be available but where adequate estimates of seismic intensity are present. This method utilizes scenarios based on macroseismic intensities VI and VII, which are the maximum intensities historically assigned to Annaba City according to various references. These intensities correspond to moderate and strong seismic activities, respectively, crucial for estimating potential damages across a broad spectrum of building typologies, enabling rapid, generalized vulnerability assessments—ideal for emergency planning in densely populated areas like Annaba City's historical center, "Place d’Arme".

Conversely, the LM2 method was chosen for its detailed, building-specific assessment capabilities in regions where comprehensive micro-seismicity data are available (Lestuzzi et al. 2017). This method employs seismic scenarios corresponding to Peak Ground Acceleration (PGA) values of 0.04g and 0.08g. These values, taken from an existing Probabilistic Seismic Hazard Analysis (PSHA) published in the literature, represent the expected ground motion for 100-year and 475-year return periods, respectively (Hamdache et al. 2012)The PGA values allow for a nuanced understanding of how individual buildings are likely to perform under varying levels of seismic forces and are pivotal for planning targeted retrofitting and strengthening interventions for highly vulnerable buildings.

In this study, a comparison between the LM1 scenarios of intensities VI and VII with LM2 scenarios of PGA 0.04g and 0.08g is performed. This comparative analysis uniquely positions the study to evaluate both short-term (100-year return period corresponding to intensity V) and long-term (475-year return period corresponding to intensity VI) seismic risks, providing comprehensive insights into the seismic vulnerability of buildings in "Place d’Arme." This comparison will be conducted through a detailed examination of the damage probabilities across the entire study area and on a building-by-building basis, ensuring a thorough evaluation of both methods. Despite the differences in damage terminology between the two methods, a correspondence has been adapted to allow for a meaningful comparison of results. This adaptation ensures that similarities in outcomes can be accurately highlighted, providing a robust basis for validating the effectiveness of both methodologies in assessing seismic vulnerability.

The significance of this study lies in several key aspects. Firstly, it represents one of the first comprehensive seismic vulnerability assessments of historical masonry buildings in Annaba City, providing crucial insights for urban planning and risk mitigation in this important Algerian urban center. Secondly, applying both LM1 and LM2 methods from the RISK-UE framework offers a unique opportunity to compare and validate these approaches in the Algerian context, potentially informing future vulnerability assessments in similar urban environments across North Africa. Thirdly, by focusing on the historical "Place d'Arme" district, this study contributes to the preservation of cultural heritage through informed seismic risk management. Lastly, the findings of this research have direct implications for policy-making, urban resilience strategies, and public safety measures, making it a valuable resource for local authorities and urban planners. Overall, this study bridges a critical gap in our understanding of seismic vulnerabilities in Algerian cities and provides a methodological framework that can be adapted for use in other urban areas with similar architectural and seismic characteristics.

2 The RISK-UE WP4

The RISK-UE methodology offers a structured framework for assessing seismic vulnerability at the urban scale. Developed through collaborative efforts across European research institutions, this approach incorporates two distinct methods: the LM1 or "macroseismic" method and the LM2 or "mechanical" method, each catering to different urban environments and data availability scenarios (Milutinovic & Trendafiloski 2003).

The RISK-UE methodologies have been effectively utilized in Algeria and other non-European countries, which supports their broader applicability beyond European cities. Notably, the RISK-UE approaches were applied in Algeria in various studies, such as Senouci et al. (2013) in Oran, Guettiche et al. (2017) in Constantine, Boutaraa et al. (2018) in Chlef, and Soltane et al. (2022) in Skikda demonstrating the methodologies' effectiveness in a non-European context. Senouci et al. (2013) specifically indicated that the selection of RISK-UE approaches was due to the similarities in the architectural and constructive characteristics of existing buildings in Algeria and the northern side of the Mediterranean Sea. Additionally, the RISK-UE methodologies have been successfully adapted for use in other non-European countries, including Tunisia (Mansour et al. 2013), Morocco (Cherif et al. 2017), and China (Liu et al. 2019, 2023), confirming the methodologies' adaptability and relevance across different urban environments with similar architectural and seismic characteristics. These examples illustrate that with appropriate regional adjustments, the RISK-UE typologies and vulnerability values are valid and effective for buildings outside European contexts, thus supporting their use in the present study.

While the RISK-UE LM1 and LM2 methods provide valuable insights, it is important to acknowledge their constraints. For instance, the LM1 method relies on empirical data and expert judgment, which may introduce some subjectivity in vulnerability assessments. The LM2 method assumes idealized capacity curves that may not fully capture the complex behavior of the historic masonry structures. Additionally, both methods use simplified soil classifications that may not account for all local site effects. Future work could address these limitations through more detailed soil investigations, advanced structural modeling, and uncertainty quantification such as those conducted by Alexandruand et al. (2018) and Matari et al. (2023).

2.1 LM1: The Macroseismic Method

The LM1 method, integral to the RISK-UE methodology, employs a macroseismic approach based on the European Macroseismic Scale (EMS-98), which categorizes buildings according to five damage states: Slight, Moderate, Substantial to Heavy, Very Heavy, and Destruction (Grünthal 1998). This classification system is crucial as it allows for a standardized assessment of potential damage across different building types found in the Euro-Mediterranean area.

Originally developed as part of the European project Risk-UE, the LM1 method is tailored to address the various construction types prevalent in this region. It requires seismic action to be defined in terms of macroseismic intensity, a measure that describes the observable effects of an earthquake at a specific location. This method facilitates the assessment of building vulnerability through the use of a vulnerability index (Eq. 1), which provides a quantitative measure of a building's susceptibility to damage.

$$ V_{I} = V_{{}}^{*} + \Delta V_{m} + \Delta V_{r} $$
(1)

where V* is the vulnerability index corresponding to the building's typology, ΔVm the seismic behavior modifier that includes other aspects that affect the building's seismic performance, ΔVr represents a regional modifier that takes into account the particular quality of some building types at a regional level.

According to the obtained value of the VI, the building can be then classified into one of the six vulnerability classes (Table 1), which correspond to the EMS-98 vulnerability classes (Martínez-Cuevas & Gaspar-Escribano 2016).

Table 1 Relation between VI and EMS-98 class
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2.1.1 Typological vulnerability index

To evaluate this vulnerability index accurately, the LM1 method introduces a typological index V*, defined as its most probable value. This index is derived from the Building Typology Matrix (BTM), which includes 15 principal building classes (Milutinovic & Trendafiloski 2003). These classes are grouped by structural types and construction materials, ensuring a comprehensive representation of typical building forms. Specifically, among these, there are 7 typologies dedicated to masonry buildings, which are predominant in the Euro-Mediterranean regions and similarly prevalent in Annaba's urban fabric (Table 2).

Table 2 Masonry building classification in Risk-UE and the representative values of \({V}^{*}\) (Lagomarsino & Giovinazzi 2006)
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In Table 1, \({V}^{-}\) and \({V}^{+}\) represent the negative and the positive plausible bounds for the range of \({V}^{*}\) a specific building type. \({V}^{-}\) and \({V}^{++}\) correspond to the upper and lower bounds of the possible values of the final vulnerability index value VI (Lagomarsino & Giovinazzi 2006).

2.1.2 The behavior modifier

The typological vulnerability index, V*, for each typology may be adjusted upwards or downwards using the behavior modifiers Vm (Eq. 2). These modifiers account for various factors that influence the building's seismic performance, such as the number of floors, the state of preservation, and irregularities in the horizontal and vertical layouts (see Table 3). Additionally, the height variation between neighboring buildings and their placement within the aggregate block are also considered (Milutinovic & Trendafiloski 2003).

$$ \Delta V_{m} = \sum {} V_{m} $$
(2)
Table 3 Scores for the vulnerability factors \({V}_{m}\) (Milutinovic and Trendafiloski 2003)
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2.1.3 The regional vulnerability factor

Regional building typologies are accounted for by introducing a regional vulnerability factor (ΔVr). This factor adjusts the VI typological vulnerability index to reflect the qualities of building types unique to certain regions. The determination of ΔVr is based on expert judgment or observed vulnerability, allowing for a more accurate representation of regional construction practices and associated vulnerabilities.

Oliveira & Mendes Victor (1984) investigated a massive stone typology in Lisbon and suggested a ΔVr value of 0.12, indicating better behavior than the average value. For Georgia, Tsereteli et al. (2014) recommended regional vulnerability factors based on expert judgment and actual inventory observations, with values for pre-code low-rise and mid-rise masonry structures with RC floors ranging from 0.12 to 0.15, while the highest values were given to the masonry buildings made of simple stone in the amount of 0.25 (Ademović et al. 2020).

Despite the benefits of incorporating the ΔVr factor, we opted not to include it in our study due to the lack of comprehensive, region-specific data that accurately reflects the unique seismic and architectural characteristics of Annaba City. Including an imprecise regional vulnerability term could have introduced significant uncertainties into our results, potentially undermining their accuracy and reliability. Moreover, similar studies conducted in Algeria using RISK-UE LM1 approach, such as those by Senouci et al. (2013) in Oran, Soltane et al. (2022) in Skikda, Guettiche et al. (2017) in Constantine, and Boutaraa et al. (2018) in Chlef, also did not use the regional vulnerability factor ΔVr for similar reasons. These researchers found that excluding this term did not significantly compromise the assessment's effectiveness​.

Additionally, studies conducted in other North African countries have followed a similar approach. For instance, Mansour et al. (2013) in Tunis, Tunisia, and Cherif et al. (2017) in Al Hoceima, Morocco, also did not incorporate the regional vulnerability factor in their seismic vulnerability assessments. These researchers similarly concluded that excluding the ΔVr factor did not adversely affect the reliability of their findings.

2.1.4 Estimation of the damage distribution

After determining the final vulnerability index, the LM1 methodology specifies the use of mean semi-empirical vulnerability functions for practical application (Eq. 3). These functions establish a correlation between the average damage grade μD, the macroseismic intensity I, and the vulnerability index VI (Milutinovic & Trendafiloski 2003).

$$ \mu_{D} = 2.5\left[ {1 + \tanh \left( {\frac{{I_{EMS - 98} + 6.25V_{I} - 13.1}}{2.3}} \right)} \right] $$
(3)

The damage probability distribution can be then easily obtained based on Beta distribution given by Eq. (4) (Milutinovic & Trendafiloski 2003).

$$ \begin{gathered} PDF:P_{\beta } \left( x \right) = \frac{\Gamma \left( t \right)}{{\Gamma \left( r \right)\Gamma \left( {t - r} \right)}}\frac{{\left( {x - a} \right)^{r - 1} \left( {b - x} \right)^{t - r - 1} }}{{\left( {b - a} \right)^{t - 1} }}\begin{array}{*{20}c} {} & {} & {a \, \le x < \, b} \\ \end{array} \hfill \\ \hfill \\ CDF:P_{\beta } \left( x \right) = \int\limits_{a}^{x} {p_{\beta } \left( \varepsilon \right)d\varepsilon } \hfill \\ \end{gathered} $$
(4)

In this formula, a, b, and t are geometric parameters related to the damage distribution, and Γ represents the gamma function. The parameter x is a continuous variable that spans from a to b. The distribution is most stable when t = 8, with bounds set at a = 0 (indicating no damage) and b = 6 (indicating destruction). The parameter r (Eq. 5), which effectively serves as the variance, shapes the distribution and is calculated based on the parameter t and the average damage grade µD (Milutinovic & Trendafiloski 2003).

$$ r = t(0.007\mu_{D}^{3} - 0.052\mu_{D}^{2} + 0.2875\mu_{D} ) $$
(5)

The discrete beta density probability function is calculated from the probabilities associated with damage grades k and k + 1 (k = 0, 1, 2, 3, 4, 5), as follows (Eq. (6)) (Milutinovic and Trendafiloski 2003):

$$ P_{k} = p_{\beta } (k + 1) - p_{\beta } (k) $$
(6)

Using Eq. (7), fragility curves can be obtained directly from the physical building damage distributions derived from the beta probability function (Milutinovic and Trendafiloski 2003):

$$ p(D \ge D_{k} ) = 1 - p_{\beta } (k) $$
(7)

2.2 LM2: The Mechanical Method

The LM2 method is a sophisticated approach within the RISK-UE WP4 project that provides a detailed mechanical assessment of building vulnerability during seismic events. This method is driven by precise structural and soil data, which are crucial for accurately modeling the building's response to seismic forces. It uses the intersection point between the capacity curve of an equivalent nonlinear single degree of freedom (SDOF) system and the earthquake demand curve, representing both in a spectral acceleration versus displacement domain. This intersection point effectively determines the building's performance during a seismic event. Based on sufficiently detailed analysis and evaluation of the performance level of the buildings at a given level of earthquake ground motions, the conditional probability that buildings will reach a certain damage state shall be determined as presented in Fig. (1).

The method’s reliance on inelastic spectra, which need to define energy dissipation, is pivotal. This is achieved using the nonlinear SDOF system described by the following fundamental relationships between spectral displacement (Sd) and spectral acceleration (Sa) (Eqs. 8–9) (Athmani & Ademovic 2023)

$$ S_{a} = \frac{{S_{ae} }}{{R_{\mu } }} $$
(8)
$$ S_{d} = \mu \frac{{T^{2} }}{{4\pi^{2} }}S_{a} $$
(9)

Here, Sae​ is the elastic spectral acceleration, and T represents the natural period of vibration of the building. The ductility coefficient, μ, the ratio of the maximum displacement to the displacement at yield, is critical in these calculations. The Rμ​ parameter, representing the strength reduction factor due to ductility, can be calculated as shown in Eq. (10):

$$ R_{\mu } = \frac{{S_{ae} }}{{S_{ay} }} $$
(10)

Additionally, Rμ can be approximated as a function of the ductility coefficient μ with the following relationship (Eq. 11) (Athmani 2020):

$$ \left\{ {\begin{array}{*{20}l} {R_{\mu } = \left( {\mu - 1} \right)\frac{T}{{T_{2} }} + 1\begin{array}{*{20}c} {} & {} \\ \end{array} } \hfill & {T < T_{2} } \hfill \\ {R_{\mu } = \mu } \hfill & {T \ge T_{2} } \hfill \\ \end{array} } \right. $$
(11)

where T2 represents the period defining the right edge of the acceleration spectra plateau, equivalent to Tc used in Eurocode 8.

2.2.1 The seismic demand curves

For the framework of the seismic risk analysis of the Algerian urban areas, the seismic demand is represented in this section in compliance with the Algerian seismic code (RPA 2004) (Eq. 12).

$$ \frac{{S_{a} }}{g} = \left\{ {\begin{array}{*{20}c} {1.25A\left( {1 + \frac{T}{{T_{1} }}\left( {2.5\eta \frac{Q}{R} - 1} \right)} \right)} & {0 \le T \le T_{1} } \\ {2.5\eta \left( {1.25A} \right)\frac{Q}{R}} & {T_{1} \le T \le T_{2} } \\ {2.5\eta \left( {1.25A} \right)\frac{Q}{R}\left( {\frac{{T_{2} }}{T}} \right)^{2/3} } & {T_{2} \le T \le 3.0s} \\ {2.5\eta \left( {1.25A} \right)\left( {\frac{{T_{2} }}{3}} \right)^{2/3} \left( \frac{3}{T} \right)^{5/3} \frac{Q}{R}} & {T \ge 3.0s} \\ \end{array} } \right. $$
(12)

where Sa denotes the spectral acceleration, g is the acceleration due to gravity, and A is the Acceleration coefficient. T1 and T2 are the lower and upper limits of the period defining the horizontal spectral acceleration branch for the specific geologic and geotechnical soil conditions, respectively. The elastic response spectrum Sae(T), used in the LM2 method, is derived by setting the quality factor Q, the behavior factor R, and the structural damping at 5%, which results in the damping correction factor η also being set to 1 (Q = R = η = 1) (Athmani 2020).

2.2.2 Building capacity curve

Once again, the crucial reason for using the N2 method is that it is considered to be the most suitable when the capacity curve is derived in an Elastic-Perfectly plastic form (Milutinovic and Trendafiloski 2003). In fact, by neglecting the hardening and softening behaviors, the capacity of the non-linear S.D.O.F system is equivalent to a studied building typology. Table 4 presents the parameters that determine the capacity curve for various building typologies, categorized by height class (three classes: “L” for Low-Rise with 1–2 floors, “M” for Mid-Rise with 3–5 floors, and “H” for High-Rise with 6 or more floors). These parameters include yield and ultimate displacement, ductility, acceleration, and corresponding periods, which are essential for describing the non-linear response of each building type during seismic events:

  • Yield and Ultimate Displacement (dy, du)

  • Acceleration at Yield and Ultimate (ay, au)

  • Ductility (μ)

  • Characteristic Period (T)

Table 4 Capacity curves defining parameters for unreinforced masonry building typologies (Giovinazzi 2005)
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2.2.3 Estimation of the Performance Point

As already indicated, this method describes the building capacity in terms of bilinear capacity curves established for each building typology and the demand in terms of inelastic response spectra. The performance point (Sd*), critical for assessing the seismic performance of the building, is obtained through the N2 method by a closed analytical function, eliminating the need for graphical representation and making the LM2 method particularly effective for detailed, technical assessments of building vulnerabilities. According to Athmani (2020), for the Algerian context, the performance point can be estimated as follows (Eq. 13):

$$ S_{d*} = \left\{ {\begin{array}{*{20}l} {\frac{{S_{de} }}{{R_{\mu } }}\left[ {1 + \left( {R_{\mu } - 1} \right)\frac{{T_{2} }}{T}} \right]\begin{array}{*{20}c} {} & {} \\ \end{array} } \hfill & {T < T_{2} } \hfill \\ {\begin{array}{*{20}c} {} \\ {S_{de} } \\ \end{array} } \hfill & {\begin{array}{*{20}c} {} \\ {T_{2} \le T} \\ \end{array} } \hfill \\ \end{array} } \right. $$
(13)

2.2.4 Fragility and damage distribution

Fragility curves are used to evaluate the damage conditions of a building affected by an earthquake. These curves represent the probability of reaching or exceeding a specific damage state, DSk, under a given seismic action. This is achieved by applying a lognormal cumulative probability function (Eq. 14).

$$ P\left[ {D_{SK} \left| {S_{d*} } \right.} \right] = \Phi \left[ {\frac{1}{\beta }\ln \left( {\frac{{S_{d*} }}{{S_{d,k} }}} \right)} \right] $$
(14)

where ϕ represents the standard lognormal cumulative distribution function, and Sd* is the spectral displacement at the performance point. The parameter β is the standard deviation of the natural logarithm of the displacement threshold Sd,k, which is defined as a function of the ductility μ from the capacity curve (Eq. 15). This definition allows for a variation in the damage distributions that is equivalent to the scatter observed in actual damage (Lagomarsino and Giovinazzi 2006).

$$ \begin{array}{*{20}c} {\beta = 0.4\ln \mu } & {\left( {k = 1,2,3,4} \right)} \\ \end{array} $$
(15)

The parameter Sd,k represents the median value of spectral displacement at which the building reaches a specific damage state threshold, denoted as DSk. The LM2 method identifies four damage states: Minor, Moderate, Severe, and Collapse, corresponding to k = 1,2,3, and 4, respectively. According to Athmani (2020), the damage limit states Sd,k adopted for the Algerian masonry buildings are defined in Eq. (16):

$$ \begin{array}{*{20}l} {S_{d,1} = 0.7d_{y} } \hfill \\ {S_{d,2} = 1.5d_{y} } \hfill \\ {S_{d,3} = 0.5\left( {d_{y} + d_{u} } \right)} \hfill \\ {S_{d,4} = d_{u} } \hfill \\ \end{array} $$
(16)

The probability histograms of the damage limit states are directly derived from the cumulative distribution as (Eq. 17) (Athmani 2020):

$$ \begin{array}{*{20}l} {p_{S4} = P\left[ {D_{S4} \left| {S_{d*} } \right.} \right]} \hfill & {} \hfill \\ {p_{Sk} = P\left[ {D_{Sk} \left| {S_{d*} } \right.} \right] - P\left[ {D_{Sk + 1} \left| {S_{d*} } \right.} \right],\begin{array}{*{20}c} {} & {} \\ \end{array} } \hfill & {k = 1/3} \hfill \\ {p_{S0} = 1 - P\left[ {D_{S1} \left| {S_{d*} } \right.} \right]} \hfill & {} \hfill \\ \end{array} $$
(17)

3 Case Study: Annaba City

3.1 Context and Selection of Pilot Area

Annaba City, with a population of over 260,199 according to the 2011 census, is an exemplary urban center that embodies the architectural heritage and urban challenges typical of northeastern Algeria. The old historical center of Annaba, often referred to as "Place d’Arme" (Fig. 1) is distinguished by its dense residential and commercial districts characterized by narrow alleys and streets, primarily constructed during the colonial French era between 1830 and 1962. These buildings, which dominate the urban landscape, represent a vital yet vulnerable segment of the city's heritage, contributing cultural value and significant seismic risk due to their structural conditions (Fig. 2).

Fig. 1
figure 1

Damage Estimation Process in the LM2 method (Milutinovic and Trendafiloski 2003)

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Fig. 2
figure 2

Google maps location and aerial view of the old city center in Annaba

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The building stock in "Place d’Arme" is primarily residential and known for its significant degradation, with 380 masonry buildings that reflect a range of structural types and materials characteristic of the colonial period. This area, housing about 12,000 people, is one of the city's first settlement areas. It is now a critical focus for seismic vulnerability assessment due to the poor conservation status of the buildings and the high risk they pose to their inhabitants.

3.2 Data Collection and Building Typologies

In the seismic vulnerability assessment of Annaba City’s historical masonry buildings, a meticulously structured data collection approach is paramount to obtaining precise and actionable insights. The Technical Control of Construction (CTC) in Annaba employs a comprehensive diagnostic datasheet that is the backbone for this process. This datasheet systematically captures a wide array of critical data spanning general building characteristics, structural and non-structural elements, geometrical features, and the current state of degradation. Each category is crucial for evaluating seismic resilience and determining the appropriate intervention strategies for the buildings in "Place d’Arme". Four parts are composed of the CTC’s datasheets (CTC 2010):

  • Description Section: This segment captures essential information about masonry buildings, such as the year of construction, materials used (focusing on various types of masonry), usage, and general slope of the site. The details regarding structural and non-structural elements, such as different types of masonry bonds and techniques, are tailored to those commonly found in masonry constructions.

  • Detailed Diagnosis of the Elements' State: The diagnosis section delves into the condition of both structural and non-structural masonry components. It assesses the integrity of masonry walls, the presence of any cracks or degradation, and the condition of other masonry-related features like chimneys and facades.

  • Conclusion and Recommendations: Based on the diagnostic outcomes, this part categorizes masonry buildings into different intervention classes (slight, moderate, heavy) depending on their degradation state (from good to highly degraded). Recommendations are specifically geared towards masonry preservation and strengthening techniques, including repointing, grouting, or retrofitting with modern materials.

  • Accompanying Photos: Visual evidence showcases typical damage patterns found in masonry buildings, providing an apparent reference for identifying similar issues in other structures.

The CTC's methodical approach to data collection, as depicted in the figure, provides a robust foundation for our seismic vulnerability assessment. The detailed breakdown of structural and non-structural elements, geometric features, and a clear classification of degradation and intervention needs enable a holistic understanding of each building's condition and vulnerabilities. In applying the LM1 and LM2 methods, such comprehensive data is instrumental in accurately modeling seismic responses and planning effective mitigation strategies.

For our study in "Place d’Arme," this level of detail allows for the precise application of both macroseismic and mechanical assessment methods, ensuring that the resulting vulnerability profiles are as accurate as possible. Furthermore, categorizing intervention needs enhances seismic resilience by providing clear directives for strengthening efforts, making it an essential component of the urban seismic risk management strategy.

Incorporating this structured approach validates the assessments' reliability and reinforces the necessity for systematic data collection and analysis in seismic vulnerability studies. This enhanced data collection framework can serve as a model for similar urban assessments, particularly in regions with historic building stocks that require detailed examination to inform effective conservation and risk mitigation efforts.

The comprehensive survey conducted in “Place d’Arme” focused on the detailed architectural and structural characteristics of these buildings. About 54% of these structures are constructed using stone, while 33% utilize adobe. The floors often feature timber structures, sometimes supported on stone or brick vaults that are not well attached to the walls. Mixed floors with steel beams sometimes support brick masonry arches and concrete slabs.

The range of buildings includes predominantly low- to mid-rise structures, with 42% being 1–2 storeys and 56% between 3–5 storeys. High-rise buildings, though less common, represent about 2% of the building stock. This diverse range of structures offers a unique insight into the typical construction practices and the associated seismic risks in Annaba's historical center.

The state of these buildings, as recorded in the CTC database, underscores their vulnerability. Most are fully occupied despite their poor conservation state, highlighting the urgent need for effective seismic risk management strategies tailored to these high-density, historically significant urban environments.

The collected data encompass geometrical features, geographical location, type of construction, year of construction, state of preservation, and other relevant parameters. This detailed characterization is crucial for accurately assessing the seismic vulnerability and developing interventions that can mitigate the risk of catastrophic failures during seismic events.

3.3 Seismic context of the study area

Annaba, a city in northeastern Algeria, is located near two significant seismogenic zones: Guelma and Constantine (Fig. 3).

Fig. 3
figure 3

Example of the degradation state of the Place d’Arme district (CTC 2010)

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Several seismic events that occurred in the surrounding region may have strong to damaging effects on Annaba city (Boudebouda et al. 2024; Khemis & Athmani 2023). In terms of intensity, generally, an intensity of VI is attributed to Annaba city and does not exceed VII as also reported by Yelles-Chaouche et al. (2006)On the other hand, the seismic hazard of Annaba city was also studied in terms of spectral values through the probabilistic seismic hazard analysis performed by Hamdache et al. (2012). The outcomes in terms of peak ground acceleration (PGA) are found to be 0.040 g and 0.08 g for the return periods 100 and 475 years, respectively.

4 Developing the seismic scenarios

4.1 Implementation of the LM1 Method

The implementation of the LM1 macroseismic method in the historical center of Annaba, specifically "Place d’Arme," involved a comprehensive assessment of the traditional masonry building stock. This assessment was guided by the calculated typological vulnerability index (V*), which considers both general and specific structural factors affecting each building's seismic vulnerability. Figure 4 and Table 5 show the distribution of the building typologies for the studied area according to the LM1 method. In the heart of this neighborhood, 199 buildings in the residential core, which is 52% of the total, with the Rubble Stone structures (M1). Their presence not only has a firm shadow thrown down for historical reliance on traditional building materials but also provokes questions about their resilience to seismic activities if potential earthquakes were to occur.

Fig. 4
figure 4

Seismic map around Annaba city; squares denote historical earthquakes, while circles represent instrumental earthquake

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Table 5 Distribution of the building typologies according to the RISK-UE LM1 method
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Adjacent to these, the constructions in Adobe (M2) sum to 121 buildings, which is 32% and seem to emanate an aspect of the vernacular architecture of the region. Their vulnerability to seismic events due to the materials used is a big concern when assessing vulnerability.

Further added to the tapestry are the U Masonry (old bricks) (M5) and Massive stone (M4) buildings, although they are on a lower scale but part of architectural diversity. Their inclusion in the study highlights the necessity for comprehensive knowledge of seismic vulnerability in all building typologies.

Further down, a mix of traditional and modern types of construction can be seen, such as reinforced concrete slabs (M6), which account for 16 buildings or 4% of the total.

In conclusion, the distribution of masonry building typologies in 'Place d'Arme' offers a nuanced perspective on the seismic vulnerability of Annaba city's architectural heritage. By examining each building type within the framework of the LM1 method, this study seeks to inform proactive measures aimed at enhancing the seismic resilience of the neighbourhood while preserving its rich cultural legacy.

In the context of seismic vulnerability assessments, the impact of soil conditions, often referred to as site effects, is a critical factor influencing ground motion and, consequently, the structural response of buildings during an earthquake (Ademovic et al. 2022; Amendola & Pitilakis 2023; Brunelli et al. 2022; Chieffo & Formisano 2020; De Risi et al. 2019). This study deliberately excluded site effects from the seismic vulnerability analysis due to the specific soil characteristics in Annaba City’s “Place d’Arme” district. The soil in this area is classified as stiff to very stiff (DUAC 2006), a condition that typically results in minimal amplification of seismic waves (Bazzurro & Cornell 2004). This assessment is supported by Senouci et al. (2012), who found similar soil conditions in Oran, Algeria, indicating that the primary determinant of seismic damage is the inherent vulnerability of the buildings themselves rather than variations in soil response. Previous studies conducted in Algeria using the RISK-UE LM1 method, such as those in Constantine (Guettiche et al. 2017), Chelef (Boutaraa et al. 2018), Skikda (Soltane et al. 2022), as well as the study by Sabeur et al. (2023) in Mostaganem similarly neglected site effects to concentrate on structural vulnerabilities. These studies have demonstrated that focusing on the inherent vulnerabilities of buildings provides reliable insights into seismic risk, supporting the methodology used in this assessment. By focusing on the structural vulnerabilities, our methodology ensures that the seismic vulnerability assessment remains robust and reliable, providing actionable insights for mitigating risks in Annaba City's historic urban landscape.

For this study, two seismic scenarios were constructed based on macroseismic intensities VI and VII of the EMS-98 scale (Grünthal 1998). These intensities were chosen considering their relevance to the seismic activity typically expected in the region and other similar urban areas in Algeria. A vulnerability index (VI) was then assigned to each building to quantify its susceptibility to damage under these scenarios.

The distribution of vulnerability indexes across the 380 surveyed masonry buildings revealed significant findings. The mean vulnerability index was determined to be 0.93, ranging from a minimum of 0.55 to a maximum of 1.02. The outcomes of this vulnerability assessment were visually represented through seismic vulnerability maps, as shown in Fig. 5, which illustrates the spatial distribution of seismic vulnerability indices and unreinforced masonry (URM) typologies in the "Place d'Arme" district of Annaba City. This visual representation is crucial for identifying high-risk areas, guiding retrofitting efforts, and informing urban planning and emergency preparedness strategies.

Fig. 5
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Distribution of the building typologies according to the LM1 method

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After assigning the final vulnerability index (VI) to each masonry building, the expected mean damage grade can be calculated using Eq. (2). Figures 6 and 7 illustrate the spatial distribution map of the mean damage grades (μD​) for seismic intensities VI and VII, respectively, and the building occupancy of Annaba City’s “Place d’Arme” district. By identifying areas with higher damage grades and occupancy levels, authorities can prioritize interventions, enhance emergency response plans, and allocate resources effectively to mitigate risks and improve community safety.

Fig. 6
figure 6

Spatial distribution of the vulnerability index together with the URM typologies according to the RISK-UE LM1 method

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Fig. 7
figure 7

Spatial distribution of building occupancy and the mean damage grade according to LM1 for seismic scenario VI

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After calculating the average damage grade for the buildings under each seismic scenario, the probability of damage can be determined. Figure 8 the histograms of damage probability for both seismic scenarios using the LM1 method.

Fig. 8
figure 8

Spatial distribution of building occupancy and the mean damage grade according to LM1 for seismic scenario VII

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At intensity VI, the highest probability is for slight damage (D1) at 0.363, followed by moderate damage (D2) at 0.254, suggesting that most buildings will experience some repairable structural impact. As the intensity increases to VII, there's a noticeable shift towards more severe damage; the probabilities for moderate (D2) and substantial to heavy damage (D3) are the highest at 0.312 and 0.272, respectively, indicating a significant likelihood of considerable structural impairments, that could limit building usability and safety. The distribution shows that with escalating seismic intensity, the risk and severity of damage increase markedly, underlining the urgent need for enhanced structural reinforcement and preparedness measures to mitigate these risks effectively in higher seismic scenarios. These findings highlight the vulnerability of the building stock to seismic events and the critical necessity for implementing robust seismic resilience strategies in the region.

4.2 Implementation of the LM2 method

In the implementation of the RISK-UE LM2 method for assessing the seismic vulnerability of Annaba City, two distinct seismic scenarios were developed, corresponding to Peak Ground Acceleration (PGA) values of 0.04 g and 0.08 g. These scenarios are analogous to the macroseismic intensities VI and VII, respectively, as used in the LM1 method. This alignment allows for a coherent comparison between the outcomes of the two methods, providing a comprehensive understanding of building vulnerability under varying seismic conditions.

The seismic demand for each scenario was defined using a 5% damped elastic response spectrum (Sae(T)), as prescribed by the Algerian seismic code (RPA 2004). The PGA values of 0.04 g and 0.08 g are incorporated into the A parameter of the response spectrum, ensuring that the seismic forces are accurately represented for the conditions in Annaba. Additionally, the response spectrum was specifically adapted to reflect the local soil conditions prevalent in the study area. Annaba City is characterized by stiff to very stiff soil (DUAC 2006), classified under RPA99/2003 as firm soil. The typical periods T1 and T2 (Eq. 12) for this soil type are 0.15 and 0.4 s, respectively (RPA 2004). These parameters ensure that the seismic input accurately reflects the specific geotechnical features of the study area, thereby enhancing the precision of the vulnerability assessment.

Furthermore, the distribution of building typologies, as presented in Table 6 and Fig. 9, is based on the typologies outlined in Table 4 provided by the RISK-UE LM2 framework. These predefined typologies are crucial for capturing the existing building types in Annaba, particularly the unreinforced masonry (URM) typologies, which are prevalent in the area. By utilizing these standardized typologies, the study benefits from a consistent and comparable approach across different assessments.

Table 6 Distribution of the building typologies according to the RISK-UE LM2 method
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Fig. 9
figure 9

Damage probability distribution for both seismic scenarios of the LM1 method

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By utilizing the capacity curve for each building typology, the intersection with the response spectrum allows for the evaluation of the performance point of each structure. This intersection provides critical insights into how a building is expected to perform under seismic loading, highlighting its potential vulnerabilities. Once the performance point is determined, the probability of damage for each building typology can be evaluated. This process is illustrated in Fig. 9, which visually demonstrates how the intersection of the capacity curve and the response spectrum informs the seismic performance assessment and subsequent probability of damage estimation. This approach ensures a comprehensive understanding of the seismic risk faced by the building stock in Annaba City.

Figure 10 displays the probabilities of damage grades for masonry buildings in the study area using the LM2 method under two different Peak Ground Acceleration (PGA) scenarios: 0.04 g and 0.08 g. At the lower PGA of 0.04 g, the distribution indicates a higher probability of slight damage (Ds1) at 0.379, with moderate damage (Ds2) also significant at 0.266, suggesting that many buildings might require some level of intervention but generally retain their structural integrity. As the PGA increases to 0.08 g, there is a clear shift towards more severe damage: the probability of moderate damage (Ds2) increases dramatically to 0.411, and substantial damage (Ds3) also rises to 0.184. The shift in damage probabilities with higher PGA underscores a greater likelihood of significant structural impairments that could critically impact building usability and safety, highlighting the escalating risk with stronger seismic events. This information is crucial for understanding the severity of potential structural failures and the need for enhanced preventive measures and targeted strengthening strategies in anticipation of higher seismic intensities.

Fig. 10
figure 10

Spatial distribution of the building typologies according to the LM2 method

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4.3 Comparison between the RISK-UE LM1 and LM2 methods

Both LM1 and LM2 methodologies employ distinct scales for categorizing damage states, which are integral to interpreting the results of seismic vulnerability assessments.

  • LM1 Method: Recognizes a 'no-damage' state termed 'None', and five damage grades as defined by the EMS-98 scale: Slight, Moderate, Substantial to Heavy, Very Heavy, and Destruction. This method thus uses six categories (five damage + 'no damage') to describe the post-earthquake state of structures.

  • LM2 Method: It also recognizes a 'no-damage' state termed 'None' but uses a four-damage limit state scale: Minor, Moderate, Severe, and Collapse. Thus, the LM2 method has five categories (four damage + 'no damage') to qualify the damage after an earthquake.

Despite the differences in scaling and terminology, the first three damage grades of LM1 and the damage states of LM2 are directly correlated. The damage grades ‘Very Heavy’ and ‘Destruction’ of LM1 correspond to the ‘Collapse’ limit stat of LM2.

The comparison of damage probabilities for both methods under each seismic scenario provides a practical view of how these methodologies project the vulnerability of the building stock. The results presented in Table 7 detail the probability of each damage grade under two seismic intensities for LM1 and two PGA levels for LM2.

Table 7 Damage probability estimated in both methods for the two seismic scenarios
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The comparative analysis of the LM1 and LM2 methodologies under respective seismic conditions—Intensity VI matched with PGA 0.04g, and Intensity VII with PGA 0.08 g—reveals striking similarities across all damage grades, underscoring the consistency and reliability of both methods in assessing seismic vulnerability (Fig. 11). For both scenarios, probabilities for no damage (DG0) are closely aligned, increasing confidence in the minimal structural impact predictions at lower seismic intensities. As for slight and moderate damages (DG1 and DG2), both methods predict similar trends with a gradual increase in damage likelihood as seismic intensity escalates, indicating a realistic expectation of repairable to significant structural issues. The higher damage grades (DG3 and DG4), although less likely, show a significant rise in probabilities, especially under higher intensities or PGAs, suggesting both methods are well-calibrated to forecast substantial to severe damages effectively. This correlation between predicted damage outcomes from both macroseismic and mechanical perspectives reinforces their applicability for strategic urban planning and risk mitigation in Annaba City.

Fig. 11
figure 11

Damage probability distribution for both seismic scenarios of the LM2 method

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Further analysis of the LM1 and LM2 methodologies under respective seismic scenarios of VI and VII (LM1) compared to 0.04g and 0.08g (LM2) reveals a detailed perspective on the comparability of these methods in quantifying building vulnerabilities. For each building analyzed, the difference in the probabilities of damage across the damage states DG1, DG2, DG3, and DG4 was computed to quantify the consistency between the macroseismic and mechanical approaches.

The results, as depicted in the accompanying scatter plot (Figs. 12 and 13), illustrate that the variance between the corresponding damage probabilities of LM1 and LM2 for each building does not exceed 20% of a damage grade. This finding is consistent across all compared scenarios: from lower intensity/severity (LM1 VI vs. LM2 0.04 g) to higher intensity/severity (LM1 VII vs. LM2 0.08 g).

Fig. 12
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Comparison of the damage probabilities of the entire building stock according to LM1 and LM2 methods

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Fig. 13
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Residual probability damage value ΔP[DGi] computed for each damage level for the first seismic scenario

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Such a marginal difference underscores the reliability and comparability of both methods in assessing seismic vulnerability. Moreover, this close alignment in results between LM1 and LM2 methods indicates that despite their different technical approaches—LM1 being more generalized and LM2 providing a detailed mechanical analysis—both methods converge on similar conclusions regarding the seismic resilience or vulnerability of the analyzed buildings.

The comprehensive evaluation of seismic vulnerability in Annaba City's building stock, utilizing the RISK-UE methodologies, specifically the LM1 and LM2 methods, underscores the importance of aligning predicted vulnerabilities with the actual structural characteristics of the area. These methods were employed to ensure that the predicted vulnerabilities are not only theoretically sound but also practically relevant to the specific architectural and structural characteristics of the buildings in the area.

The LM1 method utilizes macroseismic intensity scenarios, while the LM2 method focuses on site-specific spectral responses, providing a comprehensive framework for assessing seismic vulnerabilities.

The study is grounded in data collected from 380 surveyed buildings, which include detailed information on structural types, materials, and historical modifications (CTC 2010). This data is crucial for accurately modeling the seismic performance of the buildings.

The LM1 method's use of macroseismic intensities VI and VII corresponds to the historical seismic activity levels experienced in Annaba, providing a realistic framework for assessing potential damage. Similarly, the LM2 method's scenarios of Peak Ground Acceleration (PGA) values of 0.04 g and 0.08 g reflect the expected ground motion for significant return periods, offering detailed insights into the structural performance under varying seismic forces.

The alignment between predicted vulnerabilities and the actual building stock is further demonstrated through the spatial distribution of vulnerability indexes and damage probabilities across the surveyed area. The seismic vulnerability maps generated from this study provide a clear visual representation of high-risk areas. For instance, the prevalence of rubble stone (M1) and adobe (M2) structures, which are known for their high susceptibility to seismic damage, was directly reflected in the high vulnerability assigned by both LM1 and LM2 methods.

By integrating empirical data with advanced seismic assessment techniques, this study offers a robust framework for enhancing seismic risk management strategies in Annaba City. This nuanced understanding of vulnerability not only validates the theoretical soundness of the methodologies used but also ensures their applicability to the specific architectural and structural characteristics of Annaba’s buildings."

4.4 Validation of results

In this study, the LM1 and LM2 methods from the RISK-UE WP4 project were utilized to assess the seismic vulnerability of historical masonry buildings in Annaba City. Several key factors underscore the validity of our predictive outcomes despite the inherent challenges in traditional validation due to data limitations in Algeria.

Firstly, our research encompassed an extensive survey of 380 historic masonry buildings, systematically categorized into five main masonry typologies and 12 sub-typologies. This comprehensive dataset provides a solid foundation for our vulnerability assessment. The diversity and scale of the buildings surveyed make individual simulations impractical, as this would require detailed architectural plans and specific mechanical properties for each structure. However, the consistent findings obtained through the LM1 and LM2 methods serve as a form of cross-validation. Despite their different technical approaches, both methods yielded similar conclusions regarding the seismic resilience or vulnerability of the analyzed buildings. This convergence of results reinforces the applicability and reliability of these methods for strategic urban planning and risk mitigation efforts in Annaba City.

Secondly, in Algeria, available damage data are limited to specific seismic events, such as the El Asnam earthquake in 1980, which impacted Chlef city and registered an intensity of IX to X (MM) (Ait-Meziane et al. 2018). The seismic vulnerability of unreinforced masonry (URM) buildings in Chlef was studied by Boutaraa et al. (2018) using the RISK-UE LM1 method. Their research focused exclusively on URM buildings classified as type C according to the EMS-98 scale, assigning them a maximum vulnerability index of 0.7. Given the lower seismic intensity in Annaba and the higher vulnerability of its historical masonry buildings compared to those in Chlef, direct comparisons are not feasible.

Similarly, Boukri et al. (2013) analyzed URM buildings in Boumerdès city using observed damage data from the Zemmouri earthquake in 2003, which recorded a seismic intensity of X on the EMS-98 scale (Ait-Meziane et al. 2018). However, their study lacks detailed typological distinctions and did not apply the RISK-UE methodology, making comparisons with Boumerdès data problematic. These differences in seismic intensity and the absence of specific URM typology assessments further complicate direct comparisons with our study in Annaba.

Finally, the only feasible comparison of our outcomes using the RISK-UE approach is with studies such as Soltane et al. (2022) in Skikda and Sabeur et al. (2023) in Mostaganem City, as they similarly focused on unreinforced masonry (URM) buildings using the RISK-UE LM1 methodology. For seismic intensity VI, a direct comparison is only possible with the study by Sabeur et al. (2023) in Mostaganem, as Soltane et al. (2022) in Skikda commenced their scenarios at intensity VII. Other studies, such as those by Senouci et al. (2013) in Oran and Guettiche et al. (2017) in Constantine, also examined URM buildings; however, they included additional typologies, such as steel and reinforced concrete buildings, in their analysis. These studies presented global outcomes of seismic vulnerability for the entire study area without disaggregating results by building typology. Consequently, a direct comparison of our outcomes with these studies is not possible despite their use of the RISK-UE LM1 method.

Figure 14 illustrates a comparative analysis of damage probabilities across different grades (D1 to D5) for seismic intensities VI and VII, focusing on our study in Annaba alongside studies conducted by Sabeur et al. (2023) in Mostaganem and Soltane et al. (2022) in Skikda.

Fig. 14
figure 14

Residual probability damage value ΔP[DGi] computed for each damage level for the second seismic scenario

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For intensity VI, our study in Annaba shows damage probabilities that align closely with those observed in Mostaganem by Sabeur et al. (2023). Specifically, while the damage probability for D1 in our study is slightly lower, the distribution across the other damage grades (D2 to D5) demonstrates similar trends, indicating that the expected damage in Annaba under intensity VI is comparable to that in Mostaganem (Fig. 15)

Fig. 15
figure 15

Damage probability validation using the RISK-UE LM1 method

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At intensity VII, the comparison becomes even more pertinent. The damage probabilities in Annaba, as observed in our study, fall within the range reported by both Soltane et al. (2022) in Skikda and Sabeur et al. (2023) in Mostaganem. For the lower damage grades (D1 and D2), our results are closely aligned with those from the other two cities, while for higher damage grades (D3 to D5), our study shows a moderate increase in damage probability that is consistent with the trends observed in Mostaganem and Skikda. This convergence of results across different regions supports the validity of our findings, indicating that the seismic vulnerability of historical masonry buildings in Annaba is similar to that of other Algerian cities under comparable seismic conditions. The consistent application of the RISK-UE LM1 methodology across these studies further reinforces the reliability of our predictive outcomes, thereby validating the applicability of our approach to Annaba.

5 Conclusions

This study provides a comprehensive evaluation of the seismic vulnerability of historical masonry buildings in Annaba City's "Place d’Arme" using the empirically based LM1 method and mechanically based LM2 methods from the RISK-UE WP4 framework. The application of these methodologies on a large scale in Annaba, particularly the LM2 method, represents a novel contribution to seismic vulnerability assessments in Algeria, where only the LM1 method has been previously applied.

The findings reveal a high vulnerability across most of the surveyed structures, with significant potential for damage under increased seismic activity. The comparative analysis and cross-validation of the LM1 and LM2 methods confirm the consistency and reliability of their predictive outcomes. Despite differences in scaling and terminology, both methods show striking similarities across all damage grades under respective seismic conditions. This dual-methodology approach validates the RISK-UE framework's robustness and demonstrates the complementary strengths of empirical and mechanical assessment techniques. Consequently, this research broadens the applicability of the RISK-UE methodologies beyond their traditional European settings by establishing a methodological framework that can be adapted for use in other Algerian cities and regions with similar characteristics.

The high vulnerability identified for many historical masonry buildings in Annaba's “Place d’Arme” district has significant implications for risk management policies. This study reveals an urgent need for targeted seismic strengthening interventions, especially for buildings at the highest risk. Local authorities should prioritize structures requiring immediate attention based on vulnerability and potential damage. Building codes need updating to include specific provisions for strengthening historical masonry structures, considering Annaba's unique architectural heritage. The spatial distribution of vulnerability should inform future urban planning, with special consideration given to areas containing clusters of highly vulnerable buildings. Given the high occupancy rates of many at-risk structures, public awareness campaigns and emergency preparedness programs are crucial to educate residents about seismic risks and proper response procedures. Financial incentives or assistance programs encourage private building owners to undertake necessary seismic upgrades. Moreover, the findings underscore the need for enhanced coordination between various governmental departments to ensure an integrated approach to risk management. Finally, establishing ongoing monitoring and periodic reassessment of building vulnerabilities will allow for evaluating implemented measures and identifying emerging risks over time, ensuring the long-term safety and resilience of Annaba's historical center.