Exploring seismic fragility and strengthening of masonry built heritage in Lisbon (Portugal) via the Applied Element Method

Exploring seismic fragility and strengthening of masonry built heritage in Lisbon (Portugal) via the Applied Element Method Matteo Salvalaggio 1 , Vasco Bernardo *,2 , Paulo B. Lourenço 3 Institute for Sustainability and Innovation in Structures Engineering (ISISE), ARISE, Department of Civil Engineering, University of Minho, Guimar˜ aes, Portugal ARTICLE INFO Keywords: Unreinforced masonry buildings Fragility analysis Vulnerability assessment Seismic retrofit Applied Element Method ABSTRACT Although mainland Portugal has been spared from large magnitude earthquakes in recent years, it faces a threat due to the presence of several active fault systems. In such a framework, Portuguese pre-code masonry construction is believed to be the most vulnerable in the existing building stock. Given the lack of information on earthquake damage to this stock, the use of detailed numerical models is a viable strategy to comprehend its seismic behavior. This paper provides an updated fragility characterization of Lisbon pre-code masonry buildings based on their seismic assessment through the Applied Element Method. To limit the computational time, a promising pushover strategy, known as Incremental Ground Acceleration, was adopted. After the characterization of the current fragility, two retrofit layouts based on piers strengthening were modeled and assessed for the building stock whose seismic capacity does not meet expected demand. The aim of the paper is to derive updated fragility curves for the Lisbon region to support risk analysis incorporating the latest hazard studies and to offer insights into potential retrofit interventions. 1. Introduction Fragility curves play an important role in seismic risk studies by providing the likelihood of a structure to reach a certain level of damage due to earthquakes. This probability is influenced by the unpredictability of seismic ground motion and structure response. Fragility curves could belong to four main categories [1–6]: (i) empirical, derived through on post-earthquake damage observations [7–11]; (ii) expert judgement, if the relationship between the damage and the seismic intensity level is given based on expert opinion [12]; (iii) analytical, derived from numerical strategies based on mechanical models (e.g., rigid body model) or non-linear analyses [13–17]; (iv) hybrid, when some of previous methods are combined [18–20]. Although mainland Portugal has not been the target of large magnitude earthquakes in recent years, its geographical location makes it susceptible, as evidenced by historical events such as the devastating 1755 Lisbon earthquake (M w =8.5), 1909 Benavente earthquake (M w = 6.3) and the 1969 Algarve earthquake (M w =7.8). The seismic events caused extensive damage, especially in masonry constructions [21]. Furthermore, no seismic design has been considered until the first Portuguese regulation emerged in RSCCS 1958 [22]. The present study aims to develop analytical fragility curves based on the results obtained from numerical analyses conducted using the Applied Element Method (AEM). The analyses are specifically targeted to the pre-code masonry buildings situated in the Metropolitan Area of Lisbon (MAL), which is the region in Portugal with the highest seismic risk [23–25]. These studies developed fragility and vulnerability functions to characterize the building stock essentially based on statistical data and expert opinion, along with empirical methods. Other studies were recently developed for the region of Lisbon based on numerical models, emphasizing the high vulnerability of masonry buildings to moderate seismic intensity levels, amongst which the following are highlighted: Milosevic, Cattari and Bento 2020 [26] and Sim˜ oes et al., 2020 [27] developed fragility curves for typical prototypes of pre-code masonry buildings in the Lisbon region accounting for the uncertainty in the material properties. Their study considered a range of scaled response spectra compatible with the seismic action defined in [28] (Portuguese version of Eurocode 8 – EC8–3) for a 475-year return * Corresponding author. E-mail address: [email protected] (V. Bernardo). 1 0000-0002-0234-3272 2 0000-0002-5071-8155 3 0000-0001-8459-0199 Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct https://doi.org/10.1016/j.engstruct.2024.118890 Received 5 May 2024; Received in revised form 31 July 2024; Accepted 27 August 2024 Engineering Structures 320 (2024) 118890 Available online 3 September 2024 0141-0296/© 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). period. Bernardo et al., 2022 [16] derived fragility curves and time-based vulnerability functions for seismic assessment in compliance with EC8–3, considering a large synthetic database of representative buildings to couple with uncertainty in both materials and geometry. The present study considers the database of representative buildings for the region of Lisbon [16] and derives fragility curves compatible with more recent PSHA studies [29]. Detailed tridimensional numerical models were built and analyzed via the Applied Element Method (AEM), through Incremental Ground Acceleration (IGA) [30,31]. The response of the structures was computed for different hazard quantiles and return periods to evaluate the dispersion in demand. Based on the results obtained, the buildings with higher vulnerability were retrofitted and the Fig. 1. Benchmarking AEM against EFM: capacity curves and failure configurations derived from pushover analyses according to uniform load (top) and triangular load (bottom) distributions. Fig. 2. AEM models of archetypes A1, A3, B2, C1, C3 with 3 stories high. Table 1 Statistical properties for the geometric parameters [57]. Parameters L x [m] L y [m] IWD [-] H 0 [m] H n [m] OR F [-] OR B [-] Th 1 [m] Th 2 [m] Th 3 [m] Th 4 [m] Value 12.6 12.1 0.054 3.00 3.01 0.23 0.21 0.47 0.34 0.21 0.14 Note: L x and L y – building in plan dimensions; IWD – interior walls density; H 0 and H n – ground and upper floor stories height; OR – openings ratio: front (OR F ) and back (OR B ) façade; Th – walls thickness: main façades (1), lateral façades (2), inner (3), partition (4) M. Salvalaggio et al. Engineering Structures 320 (2024) 118890 2 corresponding fragility curves updated, for which a consistent improvement of seismic performance was found. The integration of fragility curves with the retrofit adopted is useful to support risk studies and enhance the resilience of structures against earthquake-induced damage. 2. The use of AEM for the modeling of URM structures Discontinuous strategies have proved to be effective for the simulation of existing masonry components [32,33]. In such a framework, promising findings were found through the use of the AEM. The method is based on the discretization of structures using rigid blocks, connected by a series of nonlinear springs whose behavior is based on material laws assigned, until a certain separation-strain threshold is reached [34,35]. The capability of AEM for simulating masonry components has been validated at pier scale, reducedand fullbuilding scales. Malomo et al., 2018 [36] benchmarked the in-plane behavior against three calcium-silicate brick masonry piers derived from Dutch typologies, subjected to shear-compression cyclic tests. Micro-modeling technique of masonry texture according to [37] was adopted, implementing both bricks and mortar properties. A satisfactory matching between experimental and numerical outcomes was found in terms of energy dissipation, crack pattern and drift value. The benchmarking of calcium-silicate masonry was extended to full scale shaking-table tests in Malomo et al., 2020 [38]. Khattak et al., 2023 [39] benchmarked AEM for the simulation of in-plane (IP) and out-of-plane (OOP) behaviors of stone and brick masonry, based on an U-shaped test carried out in the LNEC facilities [40]. It was found that the tool is capable of simulating such behaviors also in the nonlinear dynamic range, although an overestimation of displacements was found for lower intensities of motion. Bernardo et al., 2022 [41] discussed the simulation of masonry aggregate buildings through AEM, once their properties were calibrated against pier-scale cyclic tests and modal behavior based on Ambient Vibration Tests (AVT). A discretization procedure based on homogeneous masonry properties was used, with a regular block mesh (so-called normal in the framework of [37]), on the contrary to micro-modeling in [36,38,39]. The potential of AEM for the simulation of URM retrofit techniques was also assessed. Bernardo et al., 2019 [42] modeled a double-jacketing intervention based on hydraulic mortar NHL 3.5 with glass fiber-reinforced polymers, linked to URM substrate via 7 cm-long plastic connectors with 40 cm and 50 cm spacing, along horizontal and vertical directions, respectively. AEM was able to reproduce the behavior of both bare and retrofitted specimens int terms of displacement and force capacities, i.e., the envelope of experimental hysteretic cycles. Moreover, Adhikari and D’Ayala 2020 [43] showed that AEM can be successfully used for the study of heritage masonry structures. Rubble stone masonry samples derived by masonry textures surveyed in Nepal were tested and calibrated, adopting a micro-modeling strategy with triangular-based parallelepiped, which simulate both i) failure of units through sub-elements and ii) failure of units-to-units interfaces. A similar strategy was also applied of the simulation of confined clay brick masonry [31]. 3. Numerical modeling of Lisbon masonry buildings 3.1. Modelling strategy and assumptions The structural models have been constructed according to the numerical AEM strategy in the Extreme Loading for Structures (ELS) software implementation [44], which has proved to be effective and efficient for the simulation of unreinforced masonry structures (Section 2). The structural components are discretized through rigid blocks, with nonlinearity lumped at interface springs. Linear normal k n and shear stiffness k s are derived from Young’s modulus E, shear modulus G, contact area A and block height (perpendicular to contact surface) as per Eqs. (1) and (2), according to [34]. kn=EA h(1) ks=GA h(2) A meso-modeling homogeneous discretization strategy [41,45–47] was adopted for masonry components, with pseudo-cubic 8-noded rigid blocks of average 0.3 m size and the generation of 5 ×5 (i.e., 25) nonlinear springs per each contact surface, according to [34,36,38]. The size of the blocks was derived by a previous study [41], where a mesh Table 2 Material properties (MP) of masonry – outer (Out) and inner (Int) walls. Masonry set Mechanical properties E [GPa] G [GPa] f c [MPa] τ 0 [MPa] f t [MPa] Friction [-] w [kN/m 3 ] Out Int Out Int Out Int Out Int Out Int Out Int Out Int MP1 5.6 2.2 2.38 0.91 7.00 2.80 0.21 0.21 0.315 0.315 0.8 0.8 1.8 1.2 MP2 4.0 1.6 1.70 0.65 5.00 2.00 0.15 0.15 0.225 0.225 0.8 0.8 1.8 1.2 MP3 3.0 1.3 1.28 0.55 3.75 1.63 0.11 0.11 0.165 0.165 0.8 0.8 1.8 1.2 MP4 2.0 1.0 0.85 0.45 2.50 1.25 0.07 0.07 0.105 0.105 0.8 0.8 1.8 1.2 MP5 0.8 0.4 0.34 0.18 1.00 0.5 0.03 0.03 0.042 0.042 0.8 0.8 1.8 1.2 Note: E – Young’s modulus, G – shear modulus, f c – compressive strength, τ 0 – cohesion, f t – tensile strength, Friction – tangent value of friction angle, w – density. Table 3 Properties assumed for retrofit layer (mortar and fibers as a whole), based on Bernardo et al., 2019 [42]. Property E [GPa] G [GPa] Yield stress [MPa] τ 0 [MPa] Ultimate stress [MPa] Friction [-] Ultimate strain [-] w [kN/m 3 ] Retrofit layer 15 6.5 2.5 0.21 3.83 0.8 0.2 1.85 Table 4 Properties assumed for retrofit-to-masonry interface, based on Bernardo et al., 2019 [42]. Connection E [GPa] G [GPa] f c [MPa] τ 0 [MPa] f t [MPa] Friction [-] Retrofit-to-masonry interface 4.0 1.6 4.65 0 0.465 0.8 M. Salvalaggio et al. Engineering Structures 320 (2024) 118890 3 convergence analysis was carried out for a similar building typology. The nonlinear behavior of masonry vertical structures is described through the Concrete Maekawa model [48], assuming a pseudo-parabolic compressive envelope and a tension cut-off, and the Mohr-Coulomb yielding model for shear. Once the threshold separation strain is reached, material springs are deleted and contact springs are generated [49]. Diaphragms and lintel elements were modeled through linear brittle models in tension and compression, although no material failures were expected (and also detected in the postprocessing of results). Rigid floor diaphragms is a common typology in the MAL region and evaluated in previous case studies, high vulnerability to moderate and high seismicity levels was found [16,26,41]. 3.2. Validation of the modeling strategy Advanced numerical tools such as AEM, although promising in replicating with good approximation the behavior of structural Fig. 3. Capacity curves for archetypes A1, A3, B2, C1, and C3, with 3, 4 and 5 stories high, for X longitudinal direction, with markers for LS1 (green square), LS2 (yellow triangle), LS3 (orange diamond), LS4 (red circle). M. Salvalaggio et al. Engineering Structures 320 (2024) 118890 4 elements, require a detailed characterization of material laws and mechanical parameters. As an example, the estimation of the shear stiffness of the springs may be tricky in the framework of masonry discontinuous models, since ratios varying from 1.0 to 0.5 of the normal stiffness are commonly found in literature, e.g., 1.0 [50], 0.55 [51,52], 0.5 [45], 0.29 [53]. Based on the validation framework for AEM models provided in [47], the AEM models were firstly validated through the benchmarking of capacity curves against the ones obtained from a previous study for the same building’s typology employing the Equivalent Frame Model (EFM) in the TreMuri research software [54]. The previous calibration of EFM models, based on cyclic experimental tests performed on sone masonry panels with the mean material properties adopted [42], is discussed in [41]. In the scope of this work, AEM tridimensional models starting from the mean material properties and geometry were built. To cover the uncertainty in both geometry and materials [16], a probabilistic framework to represent the building stock in the area under investigation was conducted. Therefore, the set of material properties selected, Fig. 4. Capacity curves for archetypes A1, A3, B2, C1, and C3, with 3, 4 and 5 stories high, for Y transverse direction, with markers for LS1 (green square), LS2 (yellow triangle), LS3 (orange diamond), LS4 (red circle). M. Salvalaggio et al. Engineering Structures 320 (2024) 118890 5 corresponding to the different quantiles of [16], intends to reflect their influence in the buildings global response, providing a scatter for the limit states defined and the values of PGA demand. The results were used to derive fragility curves for the building stock. Hence, for benchmarking purposes, pushover analyses were carried out for both AEM and EFM, i.e., ELS and TreMuri, according to triangular and uniform load distributions along the height of the building. The average displacement of roof was assumed as the control point. The obtained base shear-displacement capacity curves and failure configurations are reported in Fig. 1, labelled as AEM and TREMURI. The comparison reveals a good agreement between the two strategies, with similar nonlinear envelope and peak shear force, with a slight overestimation of the ultimate displacement of AEM compared to EFM. In order to match the outcomes of TreMuri, the input shear modulus in ELS had to be reduced through a 0.8 multiplier with respect to original formulation given in (Eq. (2)). The ratio between shear and normal springs stiffnesses found was hence equal to 0.32. The AEM model was then considered calibrated. Finally, in the scope of the present work, Incremental Ground Acceleration (IGA) analyses [30,31,41,43] were carried out by giving an horizontal increasing acceleration at the ground. The effectiveness of this strategy in predicting the seismic behavior of masonry structures has been benchmarked against Incremental Dynamic Analysis (IDA) in [56], where IGA was proven to be capable of predicting the capacity curves with higher accuracy than conventional pushover load distributions. IGA capacity curves were found closer to uniform-derived than triangular-derived capacity curves, with a slightly higher maximum base shear force (less than 20 % difference) (Fig. 1). 3.3. Geometrical layouts, material properties and boundary conditions The geometric features (i.e., plan layout, stories height, openings ratio, walls thickness and floor type) were statistically obtained based on a population of 100 pre-code buildings (built before 1960s), as described in [16,57]. From the nine archetypes derived in [16], five were selected for this study, namely A1, A3, B2, C1, C3, considering different material and geometrical properties, up to 5 stories high. Fig. 2 presents the layout of these archetypes for 3 stories high. Table 1 summarizes the geometrical parameters and value adopted for the archetypes. Based on the mean size configuration of B2 archetype (12.6 ×12.1 m), the remaining four archetypes were derived assuming a dispersion equals to one standard deviation, i.e., the length of longitudinal façades parallel to X axis L x =12.6 ±5.0 m and the length of transverse façades parallel to Y axis L y =12.1 ±4.1 m. The total in plan area ranges approximately between 60.0 m 2 and 285.0 m 2 . The mean thickness values for the façade walls were assumed, whilst for the inner walls the mode (i.e., most common) values were adopted (representative of more than 60 % of the buildings surveyed according to [57]). The definition of material mechanical properties was based on the wide range of properties selected in [16], where property uncertainties were taken into account through Monte Carlo simulations (MCS). In order to decrease the computational time of AEM analyses, five different percentiles (10 %, 16 %, 50 %, 84 % and 90 %) of the material properties (MP) sampled were extracted from the previous MCS to cover the variability considered. Table 2 depicts masonry properties (MP) MP1 to MP5 corresponding to very good, good, medium, low and very low MP, respectively. Masonry material was assumed as a homogeneous medium, with equivalent material properties. The mean macroscopic mechanical parameters adopted, namely the Young’s modulus E and shear modulus G, were derived using a strain-based first-order homogenization technique applied to the properties of small representative specimens and obtained from laboratory destructive tests. Further details can be found in Krejˇ cí et al. 2021 [58] and Bernardo et al., 2022 [41]. Floor diaphragms were modelled using 12 cm-thick rigid blocks and springs, with Young’s modulus E of 30 GPa and shear modulus G of 13 GPa, as derived for the Lisbon stock in [16]. Timber lintels above openings were modeled trough rigid blocks and springs as well, according to [38]. C14 timber mechanical properties were assumed, as per [47], since no detailed characterization is available and the elements are not expected to exceed linear behavior. The adopted properties include a Table 5 Maximum crack width of masonry components measured in function of Limit States and comparison with some reference studies. Stories Crack width [mm] and (Coefficient of Variation [-]) LS1 LS2 ¼DS LS3 ¼SD LS4 ¼NC 1 0.52 (0.63) 0.97 (0.44) 6.97 (0.86) 14.04 (0.82) 2 0.93 (0.13) 1.32 (0.16) 9.82 (0.85) 12.62 (0.79) 3 1.16 (0.17) 1.62 (0.19) 10.23 (0.83) 13.16 (0.74) 4 1.46 (0.16) 1.89 (0.16) 10.83 (0.84) 12.28 (0.75) 5 1.54 (0.15) 2.04 (0.18) 11.16 (0.85) 13.22 (0.67) Average 1.12 1.57 9.80 13.06 Adhikari and D’Ayala 2020; Adhikari 2021[43,56] 1 5 10 >10 Giardina et al., 2013[67] ≤1≤5 5 −15 15 −25 Fig. 5. Crack pattern for B2P3 model and MP3 material properties set, for the main limit states. Crack width thresholds corresponding to LS1 (green), LS2 (yellow), LS3 (orange), LS4 (red), as per Table 5. M. Salvalaggio et al. Engineering Structures 320 (2024) 118890 6 Young’s modulus E of 7000 MPa and shear modulus G of 440 MPa, tensile strength f t of 10 MPa and density of 350 kg/m 3 . The wall thickness was adopted for the lintel, together with a height equal to 15 cm and a support length (i.e., length of lateral insertion inside the wall) equal to 15 cm. The floor-to-wall interfaces were assumed equal to floor ones, in order to guarantee a good connection with respect to masonry properties (i.e., failure was expected on wall side and not at interface) and ensure equal planar displacements. The interfaces between the various masonry walls and masonry-to-lintels were assumed equal to the outer wall properties, different for each masonry set. The model was considered fixed at the base in all degrees of freedom. Masonry permanent loads were calculated through distributed density assigned. Diaphragms permanent loads were equal to 3.78 kN/ m 2 , while live loads equal to 2.0 kN/m 2 were assumed for category A (residential use) [59]. The adopted seismic load combination was considered, as per [60]. 3.4. Choice and modeling of the strengthening intervention A wide range of techniques are available for the retrofit of masonry structures, based on units texture and design [61,62]. When masonry is sound and monolithic behavior can be assumed, the application of composite strips (polymer matrix with fibers) onto wall surfaces is an effective method to enhance their tensile and shear strength [63]. Composites have gained widespread recognition in the retrofitting and Fig. 6. Capacity curves for archetypes A3, B2, and C1, with 3, 4 and 5 stories high, for X longitudinal direction, in function of retrofit layout. Markers for LS1 (green square), LS2 (yellow triangle), LS3 (orange diamond), LS4 (red circle). M. Salvalaggio et al. Engineering Structures 320 (2024) 118890 7 conservation of built heritage, attributed to their favorable strength-to-weight ratio and ease of application. It is advisable, however, to install them with compatible mortars rather than resins, ensuring more reversible and durable interventions [64–66]. This type of intervention is currently widespread among professional practice and common retrofit interventions of existing buildings. To this intervention type belongs the one provided in [42], which has been tested on masonry specimens representative of the built stock investigated in this paper. For this reason, such technique was chosen as reference to be simulated in this study. The strengthening intervention to archetypes consists in the application of the retrofit layer to the outer façades, addressed at improving their IP resistance. The OOP retrofitting is not considered since the boxlike behavior of the archetypes was already guaranteed in the bare layout, preventing OOP mechanisms from triggering. The strengthening solution adopted comprises a double-jacketing retrofit with mortar based on hydraulic lime NHL 3.5 and fiberglass mesh, with total thickness of 3 cm (2 cm for the leveling layer +1 cm for the finishing layer). The mesh was fixed to the masonry using plastic connectors, approximately 7 cm long, in a grid pattern of 40 cm width by 50 cm height. The solution was evaluated through experimental cyclic tests and used to calibrate the AEM formulation as described in [42]. In this study, retrofit was applied to façades parallel to X direction, since such archetypes for MP4 and MP5 properties were found the most vulnerable (see Section 3.3). Furthermore, two layouts were assessed, with retrofit in both outer and inner sides of façades (2S), and only in the inner sides of façades (1S). The former technique was assessed since the Portuguese historical building represented by the archetypes are often subjected to conservation laws which limit alterations of their outer aesthetics. It follows that complete (2S) retrofit of piers could be Fig. 6. (continued). M. Salvalaggio et al. Engineering Structures 320 (2024) 118890 8 challenging or forbidden. The retrofit layer was modeled through 3 cmthick blocks, with main dimensions equal to underneath masonry mesh. Retrofit and retrofit-to-wall springs were modeled as per [42], with properties listed in Table 3 and Table 4. 4. Seismic behavior of URM archetypes 4.1. Bare archetypes The outcomes of IGA-based pushover analyses are reported in this Section. The displacement capacity was assumed as the average of the values of top floor elements, while the shear was measured at the base up to reaching 20 % decay of the maximum peak strength (Near Collapse limit state – NC), as provided by the EC8–3 [28] for a global safety verification. The definition of limit states follows the provisions of EC8–3 [28], namely Damage Limitation (DL-LS2), Significant Damage (SD-LS3) and Near Collapse (NC-LS4). Additionally, Immediate Occupancy limit state (LS1) was also considered and assumed equal to 70 % of the displacement for LS2. The capacity curves normalized in terms of spectral acceleration S a and spectral displacement S d , and the corresponding limit states, for the archetypes A1, A3, B2, C1 and C3, with 3 to 5 stories high are presented in Fig. 3, for X longitudinal direction, and Fig. 4, for Y transverse direction. The S a values generally decrease when the number of stories and the material properties increase. For the X direction, the highest S a is detected for C archetypes with longer façades along X direction (L x > L y ), with beneficial effects of lower masses (C1 archetype). The capacity curves derived by medium size B2 archetype showed a different behavior compared to others, based on horizontal acceleration along X or Y direction. For Y direction (Fig. 4), B2 capacity curves were mainly placed in the average of the group, with A3 the upper bound, due to the highest L y with highest L y -on-mass ratio, and C1 the lower bound, due to lowest L y -on-mass ratio. Since the transverse façades do not have openings, the resisting shear mechanisms were directly proportional to L y . Instead, for the X direction (Fig. 3), the highest density of openings in the façades made the increase of capacity not directly proportional to length L x , with C1 the upper bound and A3 the lower bound, due to highest and lowest L x -on-mass ratio. However, B2 outcomes were generally closer to lower bounds A1 and A3, although some variations were found based on number of floors and property set. The displacement capacity was found higher for taller specimens. Low variability at archetype varying was found for X-direction capacity curves, although the dispersion increases when mechanical properties are scarce (Fig. 3). Higher variability was observed for Y-direction capacity curves, due to their dependance on wide piers. Such behavior also affected displacement limit states, with higher variability detected in Y direction than X, especially for LS4. Based on the strain diagrams corresponding to each Limit State, the maximum tensile crack widths on main façades were obtained, as reported in Table 5. The values found for the single-story layouts had the greatest discrepancy from the other stories ones, likely related to the lower capacity to redistribute seismic forces over the walls after local failures. Variation was lower from twoto five-stories instead. The dispersion of crack width values increased as damage status becomes more severe. A comparison with other crack width assumptions per limit state is also given in Table 5. Values derived from AEM modeling were found close to ones discussed in [43,56,67], although they were slightly higher for LS1 and lower for LS2. As per collapse shape, damage is lumped at the first floor. A representative incremental crack pattern for archetype B2P3 and MP3 material set, accounting seismic action along X direction, is shown in Fig. 5. Cracks appeared in the first-floor walls at LS1, growing larger and spreading to the second floor by LS2. Upon reaching LS3, shear cracks raised in the piers of the first floor, while horizontal cracks developed at the base of the transverse façades due to hinge formation. Finally, at LS4, severe shear cracks grew along the entire section of the piers on the first floor, with the crack pattern in the transverse walls extending further. 4.2. Retrofitted archetypes - MP4 and MP5 properties The outcomes of IGAs carried out for the five retrofitted archetypes, with properties MP4 and MP5, are discussed in this Section. Capacity curves were derived as per bare buildings discussed in Section 4.1. Figure 6 illustrates the capacity curves normalized in terms of spectral Fig. 7. Metropolitan Area of Lisbon (left) and seismic hazard curves for different return periods (right). Table 6 Gutenberg-Richter parameters and attenuation laws adopted. Seismogenic model a b m max Attenuation laws EC8 2.41 0.71 7.2 Ambraseys et al. 1996[72] ERSTA 3.03 0.79 7.1 Atkinson and Boore 2006[73] SERA 3.95 1.00 7.4 Akkar and Bommer 2010[74] Note: a is the intercept and b the slope of the logarithmic relationship between the number of earthquakes and their magnitudes. m max is the maximum magnitude of the truncated Gutenberg-Richter law. M. Salvalaggio et al. Engineering Structures 320 (2024) 118890 9 The damage reduction varied as a function of the limit states: DL ranged from 5 % to 22 %, SD from 6 % to 51 %, and NC from 60 % to 90 %, from the least improvement of one-sided strengthening to larger benefit provided by two-sided one. The fragility curves obtained can be employed in risk studies, also in the framework of a cost-benefit analysis. The outcomes of the retrofit solution adopted also provide relevant information about the estimation of overstrength coefficients and ductility factors to support the safety seismic assessment of in-plane strengthened masonry buildings using code-based approaches. Funding/Acknowledgment This work has received funding from multiple sources. This study has been funded by the STAND4HERITAGE project that has received funding from the European Research Council (ERC under the European Union’s Horizon 2020 research and innovation program (Grant agreement No. 833123), as an Advanced Grant. The national funds from FCT / MCTES under the R&D Unit Institute for Sustainability and Innovation in Structural Engineering (ISISE), reference UIDB/04029/2020 (doi. org/10.54499/UIDB/04029/2020), and the Associate Laboratory Advanced Production and Intelligent Systems ARISE, reference LA/P/ 0112/2020, have provided partial financial support for this study. Code availability Not applicable. Conflicts of interest/Competing interests No potential conflict of interest was reported by the authors. CRediT authorship contribution statement Paulo B. Lourenço: Writing – review & editing, Supervision, Funding acquisition. Vasco Bernardo: Writing – review & editing, Writing – original draft, Methodology, Formal analysis, Conceptualization. Matteo Salvalaggio: Writing – review & editing, Writing – original draft, Visualization, Methodology, Formal analysis, Conceptualization. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data Availability Data will be made available on request. References [1] Lagomarsino S, Cattari S. Fragility functions of masonry buildings. Geotech, Geol Earthq Eng 2014. https://doi.org/10.1007/978-94-007-7872-6_5. [2] Kappos AJ, Papanikolaou VK. 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