Code-based ground motion selection and scaling for seismic assessment: Application to two masonry building case studies

Code-based ground motion selection and scaling for seismic assessment: Application to two masonry building case studies Daniel Caicedo a,* , Igor Tomi´ c b , Shaghayegh Karimzadeh a , Vasco Bernardo c , Katrin Beyer b , Paulo B. Lourenço a a University of Minho, ISISE, ARISE, Department of Civil Engineering, Guimar˜ aes, Portugal b ´ Ecole Polytechnique F´ ed´ erale de Lausanne (EPFL), Earthquake Engineering and Structural Dynamics Laboratory (EESD), Lausanne, Switzerland c Earthquake Engineering and Structural Dynamics Unit (Structures Department), National Laboratory for Civil Engineering (LNEC), Lisbon, Portugal ARTICLE INFO Keywords: Old masonry buildings Eurocode 8 Ground motion selection and scaling Non-linear analysis Out-of-plane (OOP) response ABSTRACT This paper investigates the applicability and limitations of the guidelines for ground motion selection and scaling provided in the firstand second-generation of Eurocode 8 for the assessment of two unreinforced masonry buildings subjected to bi-directional loading. The numerical case studies consist of two unreinforced masonry buildings: one representative of stiff, monumental structures, and the other characterising tall, slender masonry typologies. Both structures are modelled in OpenSees using three-dimensional macroelements to capture the in-plane (IP) and out-of-plane (OOP) mechanisms, while also incorporating the effects of non-linear floor-to-wall connections and wall-to-wall interlocking. A total of ten sets of accelerograms are defined following the code-based requirements. These suites of accelerograms differ according to the version of Eurocode 8, seismological constraints, the range of matching, and the matching strategy, either uniform scaling or spectral matching. In addition to the bedrock case, soil classes B and C, defined according to Eurocode 8 prescriptions, are investigated. Subsequently, nonlinear time history analyses are conducted for each building. The non-linear response obtained after the action of each set is thoroughly analysed in terms of mean and dispersion. Furthermore, the minimum number of records recommended in the code to characterise the mean seismic demand and its dispersion is examined. Finally, important remarks are drawn regarding ground motion selection and scaling guidelines, specifically oriented to the case of old masonry constructions. 1. Introduction Old masonry constructions denote a major part of the building stock in Europe’s historic centres [1]. On top of that, many of them are representative landmarks of cultural heritage whose preservation is imperative for the development and growth of social-economic activity. Particularly, these kinds of buildings are highly vulnerable to seismic damage mainly due to their exposure in regions with medium to major seismic hazard levels [2] in addition to their inherent characteristics, including the mechanical properties (i.e., low tensile strength, low ductility, poor energy dissipation capacity, etc.), irregular configuration, or geometric irregularities [3–6]. Because of that, elastic approaches like response spectrum analysis are likely to lead to unrealistic estimations. Thus, other techniques, * Corresponding author. E-mail address: [email protected] (D. Caicedo). Contents lists available at ScienceDirect Journal of Building Engineering journal homepage: www.elsevier.com/locate/jobe https://doi.org/10.1016/j.jobe.2025.113558 Received 6 March 2025; Received in revised form 20 July 2025; Accepted 21 July 2025 Journal of Building Engineering 111 (2025) 113558 Available online 23 July 2025 2352-7102/© 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). such as non-linear static (either standard or multi-modal pushover) or non-linear response history analyses, are needed for proper seismic evaluation of pre-code masonry buildings. Thanks to the latest innovations and improvements in computing power, it is conceivable to assess complex structural systems through non-linear dynamic analyses accounting for potential sources of uncertainty stemming from material or structural modelling parameters [7] and record-to-record variability [8]. Among these sources of uncertainty, the latter has shown a significant influence on the variability of structural response [9,10]. In this sense, the selection and scaling of ground motion records have been recognised as a major source of bias and uncertainty in the assessment of engineering structures through non-linear dynamic analyses [11]. Two major state-of-the-art reviews have presented the principal methodologies for the selection of ‘appropriate’ sets of records to be used for the dynamic analysis of structural systems, first by Katsanos et al. [12] and, more recently, by Caicedo et al. [11]. In general, both revisions addressed common topics including the selection and scaling of real records matching a target spectrum defined by code provisions or different targets such as the uniform hazard spectrum (UHS) [13,14] and the conditional mean spectrum (CMS) [15,16] along with selection of motions based on scalar or vector-valued intensity measures (IMs) for probabilistic assessment [17–22] and the usage of simulated signals as an alternative to ground motion selection and scaling [23–28]. Unfortunately, due to their large complexity or excessive time consumption, in the case of probabilistic approaches, almost none of the above-mentioned techniques are commonly used in conventional engineering practice. To overcome this limitation, seismic codes, such as Eurocode 8 [29], American Standards ASCE/SEI 41-13 [30] and ASCE/SEI 7–10 [31], or the New Zealand Standard NZS 1170.5:2004 [32], provided generalised guidelines to be adopted by practitioners for selection and scaling of input motions. Yet, there are few investigations available in the literature that address seismic safety-checking through code-compliant sets of records. In line with investigating the effects of ground motion selection and scaling, Sextos et al. [33] quantified the impact of the Eurocode 8’s approach on the structural performance of an existing irregular reinforced concrete (RC) building damaged during the Lefkada 2003 earthquake in Greece. Significant intra-set scatter was observed in the inelastic response, leading, in consequence, to an erroneous estimation of the mean response. Koboevic et al. [34] studied the influence of selection and scaling, matched to the UHS of the 2005 National Building Code of Canada (NBCC 2005) [35], on the median inelastic brace deformations of a four-story concentrically braced steel frame. After comparing the effect of amplitude-scaled historical records, the authors encouraged the implementation of source-based simulated records [36]. Likewise, Lin et al. [37] examined different methodologies to derive spectrum-compatible input records for the analysis of three building types ranging from low-medium to high-rise (i.e., 4-, 10-, and 16-storey, respectively). On this occasion, the preference for real accelerograms, selected from earthquakes that occurred in regions with similar seismological characteristics to the target location and adequately scaled to match the design spectrum closely, was highlighted for performing time-history analyses of buildings. Michaud and L´ eger [38] evaluated the effectiveness of seven scaling methods and two spectral matching approaches using the NBCC 2005 UHS, considering both historical and simulated records. The results of non-linear dynamic analyses of various single-degree-of-freedom (SDOF) structures and a 4-storey steel frame revealed that spectral matching does not reduce the dispersion of the response, and its implementation is effective in reducing the number of records in seismic safety assessment. Ergun and Ates [39] highlighted the large variability with respect to scaled sets of far-field and near-field ground motions following the criteria for time-domain scaling provided in ASCE 7-05 and Eurocode 8. Araújo et al. [40] compared code-based selection methods [29–32] with an emphasis on the number of records required for estimating the mean seismic response. An additional spectral mismatch limit (±50 %) was proposed for each record to reduce the record-to-record variability within the matching period range. This constraint was further described and mathematically supported in the research by Macedo and Castro [41], where SelEQ was introduced as a web-based tool for the selection and scaling of ground motion records. A similar formulation was presented more recently in the research by Kayhan et al. [42]. Reyes et al. [43] proposed an adjustment to the ASCE/SEI 7–10 scaling based on spectral shape and an additional scale factor applied to the entire record set, which led to significant improvements in estimating the structural response of multi-storey plan-asymmetric buildings. Karimzadeh et al. [44] investigated the effects of ASCE/SEI 7–16 and Eurocode 8 selection criteria on estimating the seismic demand of an unreinforced masonry shear wall. Eurocode 8-based selection led to higher demand in terms of global displacements. More recently, Jalayer et al. [45] pointed out that the average code-based safety-checking could end up being unconservative with respect to performance-based procedures because of epistemic uncertainties referred to as the record-to-record variability (i.e., when the number of records is small). This paper explores the seismic safety verification of old masonry buildings subjected to bi-directional loading while comparing the code-based guidelines for earthquake selection and scaling provided in the firstand second-generation Eurocode 8 [46]. Within this framework, mechanical and geometric uncertainties are disregarded in the study. Two unreinforced masonry constructions are adopted as case studies. The first one corresponds to a two-storey stiff monumental heritage structure, and the second is representative of tall and slender masonry residential buildings. The numerical modelling is carried out in OpenSees [47] using three-dimensional macroelements [48] to account for the in-plane (IP) and out-of-plane (OOP) mechanisms. The effects of non-linear floor-to-wall connections and wall-to-wall interlocking are also considered in the models [49]. After selecting key parameters for the definition of the target spectra, a total of ten sets of accelerograms are specified. These sets differ according to the version of Eurocode 8, seismological constraints, range of matching, and matching strategy (i.e., uniform scaling, US, or spectral matching, SM). Like the study by Valente [50], which investigated the influence of spectrum-compatible accelerograms on the seismic response of historical masonry bell towers for different soil types, in this study, the effect of soil classes A, B, and C on the seismic response of unreinforced masonry constructions is investigated. The non-linear response obtained through time-history analyses is thoroughly investigated in terms of mean and dispersion for each set and soil class. Based on previous results from performance-based assessment [51], this research seeks to answer whether the minimum number of records recommended in the code is a reasonable assumption for the characterisation of the mean seismic demand and its dispersion. Lastly, important remarks are drawn, based on the findings of this research, concerning D. Caicedo et al. Journal of Building Engineering 111 (2025) 113558 2 the ground motion selection and scaling oriented to the safety-checking of unreinforced masonry buildings. 2. Overview of the numerical case studies In this study, two old masonry buildings are adopted as case studies. Both structures were first analysed by Tomi´ c et al. [7] and extended in the research by Caicedo et al. [51,52]. The numerical models of the buildings developed in OpenSees [47] are available in the online repository https://doi.org/10.5281/zenodo.12531709. Next, a brief description of the buildings’ topology and general assumptions for the modelling strategy are provided. 2.1. Description of the buildings’ topology The Holsteiner Hof building is a 2-storey stone masonry building representative of stiff monumental heritage structures. According to the Swiss Inventory of Cultural Property of National and Regional Significance, this building is a landmark of cultural heritage. The plan of the building is regular, with dimensions of 26.00 m ×14.00 m. The height of each storey is 4.50 m. Wall and spandrel thicknesses are 0.60 m and 0.30 m, respectively. Gables at the top have a thickness of 0.45 m. The floor system is composed of timber beams, simply supported on the walls in the shorter direction, and a layer of planks nailed directly to the beams. Consequently, horizontal forces are transferred as friction forces. The roof system is composed of a wooden truss structure. Minor retrofitting interventions were reported during the period 1976–1979 without significant modifications to the structural system. On the other side, the Lausanne Malley is a 6-storey structure representative of tall and slender masonry residential buildings. The building is regular in plan with dimensions of 14.00 m ×12.00 m. The storey height varies between 2.80 and 3.20 m, while the wall thickness gradually decreases from 0.60 to 0.25 m with the increasing of the building height. As with the Holsteiner Hof, the floor system is composed of timber beams, simply supported on the walls in the shorter direction, and a layer of planks nailed directly to the beams. The roof system is composed of a wooden truss structure. Soundproofing retrofitting measures were implemented recently and reported by Michel et al. [53]. The description of the two masonry building case studies is summarised in Table 1. 2.2. Modelling approach Both buildings are idealised through the equivalent frame model (EFM) approach by discretising façades into piers, spandrels, and rigid nodes using beams or macroelements [54,55]. The numerical models are carried out in OpenSees [47] using the recent macroelement formulation by Vanin et al. [48] to account for the IP and OOP mechanisms. The macroelement is formulated as a one-dimensional element with two nodes at the element ends and one additional node at the midspan. It can capture the IP and OOP response through three sectional models applied at the element ends and at the central section (See Fig. 1a). P-Δ formulation is selected as geometric transformation in OpenSees to capture second-order non-linear effects. Drift values are calculated individually for flexural and shear deformations based on the rotations and lumped shear deformations at the central node. Exceeding the limits in drift values will lead to the loss of lateral strength of the element. The floor system is modelled using orthotropic elastic membranes with higher stiffness in the direction of the beam span and lower stiffness in the perpendicular direction (i.e., membrane definition is given by the two moduli of elasticity in the orthogonal directions, shear modulus, and thickness of the diaphragm). The roof truss structure is not explicitly modelled, similar to the floor system, elastic membrane elements with an adequate roof pitch are implemented and assumed to transmit only vertical loads to the underlying walls. Non-linear floor-to-wall connections are modelled through zero-length elements and a simple material model for frictional interfaces. Sliding is allowed in the perpendicular direction to the wall, ruled by a friction coefficient, μ , and no cohesion, as shown in Fig. 1b. The material can fail and lead to the loss of load-bearing capacity if a maximum slip is exceeded in the positive local “y” direction. The beam pounding effect is modelled when the relative slip in the negative direction “y” or in any direction “z” direction exceeds a predefined “gap” threshold. The failure of the connection at the beam support can lead to the OOP failure of a pier element. Similarly, wall-to-wall interlocking is modelled through zero-length elements following a uniaxial material law to simulate the formation of vertical cracks and separation of the orthogonal walls, which might trigger the OOP failure of macroelements. Fig. 1c depicts the material’s linear elastic behaviour in compression without crushing, and a finite tensile strength followed by exponential softening. As in Caicedo et al. [51], material and modelling parameters are deterministic and taken either from the mean of a normal distribution or the median of a lognormal distribution from various experimental campaigns reported in [7]. For simplicity, those values Table 1 Description of the buildings’ topology. Building Holsteiner Hof Lausanne Malley General Stiff monumental heritage structure Tall and slender residential masonry building Nº storeys 2 6 Dimensions in plan 26.00 m ×14.00 m 14.00 m ×12.00 m Storey height 4.50 m 3.20–2.80 m Wall thickness 0.60–0.30 m 0.60–0.25 m Floor system Timber beams and planks Timber beams and planks Roof system Secondary wooden truss structure Secondary wooden truss structure Retrofit Minor during 1976–1979 Soundproofing and seismic performance [53] D. Caicedo et al. Journal of Building Engineering 111 (2025) 113558 3 are summarised in Table 2. The drift capacities in flexure and shear, δ C,flexure and δ C,shear , represent the ultimate flexural and shear drift limits at which the lateral stiffness of the macroelement is set to zero, as defined by Vanin et al. [56]. The Rayleigh damping model is assumed for response-history analyses, proportional to mass and secant stiffness, and calibrated at 5 % on the first and sixth frequencies for both buildings. The secant-stiffness approach introduces a correction term to the initial stiffness matrix used in the classical Fig. 1. General assumptions for the modelling strategy. Table 2 Material and modelling parameters (Caicedo et al. [51,52]). Parameter Unit Definition Mean value Masonry Parameters E m [Pa] Modulus of elasticity [61–63] 3.5 ×10 9 G m [Pa] Shear modulus [61–63] 1.5 ×10 9 * f’ cm [Pa] Compressive strength [61–63] 1.3 ×10 6 c m [Pa] Cohesion [61–63] 2.3 ×10 5 * μ m [−] Friction coefficient [61–63] 0.25* ρ [kg/m 3 ] Density [61–63] 2000 Modelling Parameters δ C,flexure [−] Drift capacity in flexure [56] 0.01035* δ C,shear [−] Drift capacity in shear [56] 0.007* ζ[−] Damping ratio [49] 0.05 Note: (*) median value taken from a lognormal distribution. D. Caicedo et al. Journal of Building Engineering 111 (2025) 113558 4 Rayleigh damping. This approach approximates the behaviour of the secant-stiffness proportional damping model, with the correction term being updated at each converged analysis step. By employing secant-stiffness proportional damping, the model achieves a more accurate simulation of OOP rocking behaviour, closely aligning with experimental data and classical rocking formulations [57,58]. A 5 % damping ratio was also adopted in previous studies by Caicedo et al. [51,52], based on the consideration that the damping ratio of masonry structures increases with damage, compared to the undamaged state, which has been experimentally shown to be around 3 % [59,60]. An additional aspect influencing the OOP dynamic response of the macroelement is the damping model, which governs energy dissipation during rocking oscillations. The macroelement accounts for dissipative phenomena at the sectional level, and through viscous and numerical damping. Since significant crushing at the section edge does not occur under moderate axial loads, the dissipative behaviour during rocking oscillations is primarily attributed to damping mechanisms rather than material failure [48]. Fig. 2 shows the numerical modelling implementation of the Holsteiner Hof and Lausanne Malley buildings. The fundamental vibration periods of the structures that will be needed subsequently for earthquake selection in Section 3.4 are 0.16 s and 0.50 s for the Holsteiner Hof and Lausanne Malley buildings, respectively. Fig. 2. Numerical modelling implementation. D. Caicedo et al. Journal of Building Engineering 111 (2025) 113558 5 3. Ground motion selection and scaling strategies This study aims to contrast the guidelines provided in the “EN 1998-1-1:2004” and the latest “EN 1998-1-1:2024” of the Eurocode 8, Part 1, for the alternative representation of the seismic action using input motions for response history analysis. These differences lie in the definition of the elastic response spectra and the criteria for the selection and scaling of input motions. The following subsections provide a comparison of the elastic response spectra defined in the firstand second-generation of the Eurocode 8. Then, the rules for selection and scaling are summarised for both versions of the code, and the formulation of the algorithm for selection and scaling is presented. Lastly, the different suites of records are shown for each version of Eurocode 8, seismological constraints, range of matching, and matching. 3.1. Target elastic response spectrum The elastic response spectrum, S e , defined in EN 1998-1-1:2004 [29] for the horizontal components of the seismic action is given in Fig. 3a, and defined by: Se(T) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ agS[1+T TB ( η 2.5-1)];if 0≤T≤TB agS η 2.5;if TB≤T≤TC agS η 2.5[TC T];if TC≤T≤TD agS η 2.5[TCTD T2];if TD≤T≤4s (1) where T is the vibration period of a linear SDOF system; a g is the design ground acceleration on type A ground, a gR , multiplied by an importance factor γ I ; T B and T C are the lower and upper limits of the period in the constant spectral acceleration branch; T D is the value defining the beginning of the constant displacement response range of the spectrum; S is the soil factor; and η is the damping correction factor with a reference value of η =1 for 5 % viscous damping. The values of S, T B , T C , and T D are tabulated within the code for the Type 1 spectrum (high-magnitude, distant earthquakes with strong energy release) and the Type 2 spectrum recommended when the earthquakes that contribute most to the seismic hazard have low-to-moderate surface-wave magnitude, M s , not greater than 5.5; while the value of a gR can be taken from peak ground acceleration (PGA) maps. In general, the shape defined in the present version of Eurocode 8, Part 1, is well-known and easy to reproduce by practitioners in the fields of structural and earthquake engineering. Recently, the new standard shape depicted in Fig. 3b was introduced in the latest EN 1998-1-1:2024 version of Eurocode 8, Part 1. On this occasion, the definition of horizontal components of the seismic action relies on the estimation, from hazard maps of spectral accelerations for two periods, namely S α (i.e., maximum response spectral acceleration, for 5 % damping, at the constant acceleration range of the elastic response spectrum) and S β (5 %-damped response spectral acceleration at the vibration period T β =1 s). The new S e shape can be defined then by: Fig. 3. Elastic response spectrum shape, Eurocode 8, Part 1. D. Caicedo et al. Journal of Building Engineering 111 (2025) 113558 6 Se(T) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ S α FA ;if 0≤T<TA S α TB-TA[ η (T-TA) + TB-T FA];if TA≤T<TB η S α ;if TB≤T<TC η SβTβ T;if TC≤T<TD η TD SβTβ T2;if T ≥TD (2) S α =FTF α S α ,RP (3) Sβ=FTFβSβ,RP (4) where F T is the topography amplification factor; T A is the short-period cut-off associated with the zero-period spectral acceleration (i. e., PGA); and F A is the ratio of S α to the zero-period spectral acceleration. Additionally, the corner frequency values can be calculated as: TB= ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ TC x;if 0.05 s ≤TC x≤0.10 s 0.05 s ;if TC x<0.05 s 0.10 s ;if TC x>0.10 s (5) TC=SβTβ S α (6) TD={2;if Sβ,RP ≤1 m/s2 1+Sβ,RP ;if Sβ,RP >1 m/s2(7) Here, x is used to define the lower corner period, T B , as a fraction of the upper one, T C , which is defined in equation (6). The values of T A , F A , and x are tabulated for the definition of the standard elastic spectrum. Likewise, F α and F β , corresponding to the amplification factors in the short and intermediate periods, can be calculated according to the site category. Finally, the values of S α ,RP and S β,RP are taken directly from spectral acceleration maps. The new spectral shape provides a more consistent representation of the seismic action at a given location by accounting for the mapped characterisation of the seismic hazard. The site-specific seismic hazard evaluation is a key advantage of the new seismic code, leading to more reasonable evaluations of structural performance. 3.2. First-generation eurocode 8 guidelines EN 1998-1-1:2004 established that the seismic motion may be represented in terms of ground acceleration time-histories. It is also specified that for three-dimensional analyses, the same accelerogram cannot be used simultaneously along both horizontal directions, and the description of the seismic motion may be made using artificial, recorded, or simulated accelerograms. The suite of accelerograms should meet the following conditions: −A minimum of three accelerograms should be used. −The mean of the zero-period spectral response acceleration values (calculated from the individual time histories) should not be smaller than the value of a g S for the site in question. −In the range of periods between 0.2T 1 and 2T 1 , where T 1 is the fundamental period of the structure in the direction where the accelerogram will be applied, the mean 5 % damped elastic spectrum, calculated from all ground motion time histories, should not be less than 90 % of the corresponding value of the 5 % damped elastic response spectrum. Moreover, section 4.3.3.4.3 of the code states that if the response is obtained from at least seven non-linear time-history analyses, the average of the response quantities from all these analyses should be assumed as the structural demand. Otherwise, the most unfavourable value of the response quantity among the analyses should be used. 3.3. Second-generation eurocode 8 guidelines Unlike the previous version, Annex D, within the EN 1998-1-1:2024 edition, provides detailed criteria for the selection and scaling of input accelerograms for response-history analyses. The new code version explicitly mentions that the minimum number of input D. Caicedo et al. Journal of Building Engineering 111 (2025) 113558 7 motions may be reduced to three, considering the maximum response, only for low and very low seismic action classes, considering the most unfavourable peak response; otherwise, a minimum of seven sets of input motions must be used, and the average peak response should be considered for estimating the seismic action effects. Simulated and artificial accelerograms are both allowed in the EN 19981-1:2024 edition. Real ones are preferred in regions with available records from qualified strong-motion databases. Yet, ground motion simulations are encouraged in areas lacking seismic stations or having a limited history of large-magnitude and potentially destructive earthquakes. Furthermore, the selection should account, as far as possible, for the regional tectonic environment, earthquake magnitude (M w ), source-to-site distance, and local conditions of the recording site, relevant to the return period of the seismic actions of interest. Subsequently, the following numerical constraints can be identified in the Annex to the code: −The spectral accelerations of the selected accelerograms should approach the elastic response spectrum in the matching range of 0.2 T 1 to 1.5 T 1 . −The scaling factor should not be larger than 2.0 nor smaller than 0.5 in the context of geotechnical applications or in the case of highly non-linear structural response. −In the matching range 0.2T 1 —1.5T 1 , the ratio of the average response spectrum to the target response spectrum should fall within the band from 0.75 to 1.3 and should have an average value larger than 0.95. −In the matching range 0.2T 1 —1.5T 1 , the individual spectrum of each accelerogram of the suite should not be out of the ±50 % of the target spectrum. −The suite of motions should not contain simultaneously two components of the same record and no more than two records from the same earthquake. These rules refer mainly to constant-amplitude or US scaling, in which the record is scaled in the time domain by a constant factor. Nevertheless, the second-generation guidelines allow for spectral-matching scaling, in which modifications are made in the frequency domain by adding wavelets until the response spectrum of the modified record approaches the target. Regarding multi-dimensional analyses, it is specified that compatibility of the horizontal components to the target spectrum should be verified based on the geometric mean of the horizontal spectral accelerations of records, and the orientation of the horizontal components with respect to the principal directions of the structure may be arbitrarily selected. It should be noted that as an alternative to the elastic response spectrum, UHS or CMS are allowed as targets. However, the present study focuses only on the comparison of the standard shapes proposed in both versions of the Eurocode 8, as depicted in Fig. 3. 3.4. Algorithm for selection and scaling Past investigations [41,42,64–73] addressed the selection procedure of acceleration records for non-linear dynamic analysis as a constrained optimisation problem; among them, some tools have been widely adopted for ground motion selection in code-based seismic analysis, namely SelEQ [41] and REXEL [73]. Similarly, this study proposes a general algorithm that is easy to adapt to the conditions established in both versions of the Eurocode 8. In this regard, the sum of square differences between the mean of the suite of records and the target spectrum is defined as: F(x) = ∑ j i=1(Sa,mean(Ti)-Sa,target(Ti))2(8) where j is equal to the number of vibration periods considered in the matching domain. F(x) denotes the main objective for minimising to achieve convergence with the target design spectrum. Nonetheless, additional constraints should be taken into consideration to create a global optimisation problem with penalty functions. In the first place, lower and upper bounds for the mean spectrum can also be defined to generalise the first constraint in the form: C1(x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ lower boundmean −min[Sa,mean(Ti)/Sa,target(Ti)];if min[Sa,mean(Ti)/Sa,target(Ti)]<lower boundmean max[Sa,mean(Ti)/Sa,target(Ti)]−upper boundmean;if max[Sa,mean(Ti)/Sa,target(Ti)]>upper boundmean 0;otherwise (9) In that way, the S a, mean (T)/S a, target (T) ratio is calculated, and a penalty cost is defined either as the difference between the lower bound for the mean spectrum and the minimum value of this ratio, or the difference between the maximum ratio with the upper bound of the mean spectrum, is added to the global optimisation problem in case that those minimum or maximum values of the ratio are out of the lower and upper bounds set for the mean spectrum. Analogously, a second constraint can be defined, this time for the lower and upper limits of each record: D. Caicedo et al. Journal of Building Engineering 111 (2025) 113558 8 C2(x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ lower boundind −min[Sa,ind(Ti)/Sa,target(Ti)];if min[Sa,ind(Ti)/Sa,target(Ti)]<lower boundind max[Sa,ind(Ti)/Sa,target(Ti)]−upper boundind;if max[Sa,ind(Ti)/Sa,target(Ti)]>upper boundind 0;otherwise (10) C 2 (x) will include an additional cost to the global optimisation problem every time that the S a, ind (T)/S a, target (T) ratio is out of the bounds established for the individual spectrum. This constraint was originally proposed by Macedo and Castro [41] to reduce the individual mismatch, commonly referred to as the so-called record-to-record variability. Thus, the global optimisation problem assumes the final form: F(x) = ∑ j i=1(Sa,mean(Ti)-Sa,target(Ti))2+C1(x) + C2(x)(11) In the research listed above [41,42], an additional penalty is imposed when the same ground motion, or event, is considered more than once in the selected set. However, a different approach is adopted herein to decrease the complexity of the objective function by reducing the number of constraints within the global optimisation problem. First, a series of seismological conditions (i.e., source mechanism, magnitude, source-to-site distance, and soil conditions) are considered to apply a first filter to the dataset of ground motion records. Then, the sum of squared errors (SSE) between the acceleration spectrum and the target spectrum is computed, considering the two main horizontal components of each record. Since this study focuses on the horizontal ground components affecting masonry buildings, the filtered set is reorganised by ranking the SSE of each record in the two directions of analysis from lowest to largest. To address the issue of selecting motions from the same record, only the component with the lowest SSE is retained for the next stage. Subsequently, to further resolve the same-event-record issue, records originating from the same event are excluded, conserving only the one with the highest (unscaled) compatibility with the target code spectrum. After all mathematical formulation is set regarding the objective function and additional constraints, the vector x is introduced as: x= {x1,x2⋯xN}T(12) where the value of x i denotes the ith scaling factor affecting the ith record in a set of N accelerograms in such a way that the S a, mean (T) is calculated as: Sa,mean(T) = ∑ N i=1 Sa,ind(T) N(13) Therefore, the optimisation problem is now aimed at determining the x i scaling factors that will reduce the total cost defined earlier in Equation (11), for which the differential evolution (DE) metaheuristic is adopted. This metaheuristic, introduced by Storn and Price [74], is part of evolutionary computing, and it is oriented to determine solutions for optimisation problems of real variables in continuous fields. A full description of the adaptation of the DE metaheuristic technique to a well-known civil engineering problem can be found in [75]. For the problem analysed herein, the conventional ’best1bin ′ DE strategy is selected. The initial population is set to 100 random solution vectors, and the mutation and recombination constants are fixed as 0.5 and 0.4, respectively, for a maximum of 100 iterations. 3.5. Sets of records The derived suites of records depend on the Eurocode 8 version in addition to the seismological constraints, range of matching, and matching strategy. The seismological constraints can be considered as “Fully” or “Relax”. When the “Fully” flag is activated, all seismological constraints referred to source mechanism, M w , Joyner-Boore distance (R JB ), and average shear wave velocity in the top Table 3 Definition of the suites of records for non-linear time-history analyses. Set Version Constraints Domain Strategy 1a First-generation Fully Range US 1b Second-generation Fully Range US 2a First-generation Relax Range US 2b Second-generation Relax Range US 3a First-generation Fully Entire US 3b Second-generation Fully Entire US 4a First-generation Relax Entire US 4b Second-generation Relax Entire US 5a First-generation Fully Entire SM 5b Second-generation Fully Entire SM D. Caicedo et al. Journal of Building Engineering 111 (2025) 113558 9 target can be linearly scaled to match target spectra at different limit states [40]. Table 4 summarises the target spectrum parameters adopted for reproducing the spectral shape defined in each code generation. Eurocode 8 does not impose the use of the vertical component of seismic action for the case of unreinforced masonry structures [46]. Its consideration is mandatory when the PGA is greater than 0.25g or in specific cases in which the modal response in the vertical direction is relevant to the global behaviour of the structure. Numerical evidence supports that records with predominant near-fault effects (i.e., R JB <10 km) significantly influence both horizontal and vertical seismic demands, particularly in low vibration periods. Since earthquake distances are bounded in the selection process as R JB ≥15 km, the vertical component of seismic action is neglected in this research, which is also supported by some experimental shake-table studies that reported a marginal effect of vertical components on the seismic performance of unreinforced masonry buildings [80]. Nevertheless, a recent study by Di Michele et al. [81] stressed the importance of the vertical component on unreinforced masonry buildings when near-fault records, particularly those from large magnitude (M w ≥6.5) earthquakes, are considered. Thus, further examination of this aspect is recommended for future research. The records are selected from a large catalogue, including accelerograms from the reference database for seismic ground motion in Europe (RESORCE) [82], the pan-European engineering strong motion (ESM) [83], the Turkish accelerometric database provided by disaster and emergency management presidency (AFAD) [84], and the Italian accelerometric archive (ITACA) [85]. The same databases have been adopted for earthquake selection to assess the case study buildings, as described in section 2.1, in the context of probabilistic seismic demand analysis (PSDA) [52] and incremental dynamic analysis (IDA) [51]. 4. Analysis of results This section presents a detailed discussion of the results of non-linear time history analyses conducted for the two case study buildings subjected to the action of the ground motion sets presented in section 3. Since both structures are modelled through the equivalent frame model (EFM) approach, the analysis focuses on examining indicators of global behaviour. The idealisation of the structure in piers and spandrels usually leads to the definition of a mechanical system with a limited representation of damage (i.e., less realistic prediction of cracking patterns and local failure mechanisms). Therefore, the maximum average roof displacement, max(Δr), and maximum base shear, max(V b ), are selected as engineering demand parameters (EDPs) for the analysis of the global response. Further investigation on alternative EDPs that can capture local failure mechanisms should be conducted in future work (e.g., residual or peak displacement). The max(Δr) is selected as a critical indicator of damage and response in the non-linear range of structural elements. On the other hand, the max(V b ) represents the strength of the case study building by quantifying the total lateral force resisted at the base after seismic events. This serves as a measure of the overall seismic demand and potential damage to the structure. [63]. The reaction forces at the base nodes are computed at each step of the response history analysis and summed up individually for each direction (i.e., “x” and “y” axes). A resultant force vector is then obtained by calculating the square root of the sum of the squares of these directional components. The max(V b ) corresponds to the maximum value of the vector previously calculated. For a better representation of inertial properties, the macroelement formulation proposed by Vanin et al. [48], assumes a non-uniform distribution of the element’s mass to its three nodes (See Fig. 1a); 2/3 of the mass is assigned to the central node, while the remaining 1/3 portion of the mass is distributed evenly to the bottom and top nodes of the macroelement. The portion of the mass at the bottom nodes of the piers located at the ground level, near the foundation, is not accounted for in the computation of the base shear, as they are assumed to move solidly with the ground [86]. Particularly for the case of low-rise, short-period masonry structures, the max(V b ) is a good indicator of the record-to-record variability since ground motion sets with considerable PGA variability will lead to higher base shear dispersion. The selection of these global EDPs is in agreement with the analyses presented in Refs. [51,52]. Discussion is presented next separately for each case study building. Fig. 7. Box plot Holsteiner Hof — Soil type A. D. Caicedo et al. Journal of Building Engineering 111 (2025) 113558 16 4.1. Holsteiner Hof Figs. 7–9show the numerical results in terms of max(Δr) and max(V b ) for soil types A, B, and C, respectively. Box-whisker diagrams are employed to show the distribution of numerical data for each set of ground motion records. The shape of the box provides a clear representation of the general trend of the data, emphasizing the median values of each ground motion set. The whiskers (the lines extending from the box on both sides) extend to the minimum and maximum data values of EDP. Outliers are identified as the values that fall above or below the ends of the whiskers. Additionally, collapse and non-collapse observations are depicted independently within the plots to show a more consistent statistical representation of the data. It is noted that collapse is identified with a multiplier of record numbers in case more than one collapse is found. As in [52], asymptotic values of 40.00 mm and 4000 kN are set to represent the global collapse in terms of max(Δr) and max(V b ) metrics. These values denote the largest possible non-collapse data, and they are used to bound the collapse damage state. On bedrock, the median of max(Δr) ranges from 2.07 mm to 6.81 mm for Sets 2a and 4a, respectively (See Fig. 7a). These same sets produce the minimum and maximum base shear forces (max(V b )), corresponding to 1544 and 1836 kN. Relaxation of constraints in Sets 4a and 4b induces the largest variability in the results of max(Δr) and max(V b ), respectively. On the contrary, and regardless of the EDP, Set 5a and Set 5b drastically reduce the effects of the record-to-record variability in the dynamic response of the building. The extreme values of max(Δr) are 0.91 mm and 15.64 mm, observed in Set 3b and Set 4a. Similarly, the extreme values for the max(V b ), range from 1007 kN (Set 3b) to 2686 kN (Set 1a), followed closely by Sets 2a and 4a. In general, the extreme values of EDPs align with records showing extreme PGA. Except for the three collapse cases in Set 2a, Set 2b, and Set 5b, the Holsteiner Hof building remained mainly elastic after exposure to seismic records. This implies that low-intensity seismic events produce correspondingly low EDP values, while high-intensity records lead to increased EDP observations. For soil type B, the median of the max(Δr) ranges between 2.84 mm for set 2b and 11.54 mm for Set 4a (See Fig. 8a). The median of max(V b ) in Fig. 8b varies between 1640 kN and 2400 kN, for the same sets, Set 2b and Set 4a, respectively. Further, Set 1b and Set 2b (i. e., US with full and partial consideration of seismological constraints targeting the new shape of the soil B spectrum) lead to the highest dispersion in terms of max(Δr) and max(V b ). The highest number of non-collapse observations occurred in Set 4a and Set 3a, corresponding to max(Δr) =34.62 mm and max(V b ) =3763 kN. Likewise, the minimum values are max(Δr) =1.97 mm and max(V b ) = 1325 kN, both observed in Set 1a. In opposition, the lowest dispersion for both EDPs is achieved by Set 5a (i.e., SM to the old shape of Fig. 8. Box plot Holsteiner Hof — Soil type B. Fig. 9. Box plot Holsteiner Hof — Soil type C. D. Caicedo et al. Journal of Building Engineering 111 (2025) 113558 17 the soil B spectrum) with median values of max(Δr) =7.38 mm and max(V b ) =2240 kN. The amplification in soil shape C leads to more collapse cases, mainly in Set 2a and Set 1b. The median max(Δr) computed for soil type C varies from 2.64 mm in Set 1a up to 13.94 mm for Set 4b. Similarly, the median value of max(V b ) varies between 1660 kN for Set 1a and 2750 kN for Set 2b. The largest dispersion, or record-to-record variability, is observed within Set 4b and Set 2b for the max(Δr) and max(V b ), respectively. The peak value of max(Δr) corresponds to 29.63 mm, observed in Set 3b, although Set 2b and Set 3b lead to comparable values. Similarly, max(V b ) =3565 kN is computed within Set 1a. Minimum values of both EDPs are obtained in Set 2a, corresponding to max(Δr) =1.80 mm, and max(V b ) =1345 kN. Set 2a also leads to the lowest record-to-record variability in terms of max(Δr), although that distribution corresponds only to 4 non-collapse observations. Instead, when accounting for all seven records, Set 5a provides the smallest dispersion, as in the case of soil type B. In terms of max(V b ), Set 5b (i.e., spectral matching to the soil C spectrum shape) shows the lowest dispersion. Fig. 10 illustrates the capacity curves of the Holsteiner Hof building in terms of PGA derived from IDA. These curves, presented in [51], were generated using 21 input ground motions from the same database employed in this study to select earthquake record sets for non-linear response history analyses. The results are summarised by the 50th percentile (median), 16th, and 84th quantiles, along with the performance points for Immediate Occupancy (IO) and Collapse Prevention (CP). These curves provide an approximation of the building’s “true” mean numerical response. Besides, the acceleration records used in [51] to derive the IDA curves are representative of soil profiles A, B, and C. The values of a g S (See Fig. 3a) denoting the target PGA in the old shape of the spectrum are 0.15, 0.18, and 0.17 g for soil types A, B, and C, respectively. Analogously, the values of S α /F A for the new shape, depicted in Fig. 3b, are 0.14, 0.18, and 0.21 g, for the same soil types, respectively. Subsequently, in the same order, the 50th fractile gives estimations of the median values of max(Δr) as 3.43, 6.24, and 5.54 mm for the old shape and 3.08, 5.83, and 8.89 mm for the new one. For the bedrock case, the closest estimations to the median response, matching the old shape of the target spectrum, are given by Set 3a and Set 5a with relative errors of 33.7 % and 5.62 %, respectively. Sets “b”, in general, provided good approximations to the median with a maximum relative error of 23.54 % in Set 1b; this is again attributed to the fact that the structure remained mainly elastic, and its response is proportional to the level of intensity in the signal. For soil type B, the closest approximation to the median is found in Sets 3a and Set 5b regarding the old and new shapes of the code-based spectrum, with relative errors of 5.5 % and 11.7 %, respectively. On the other hand, for soil type C and the previous code-based spectrum, Set 4a provides a close approximation to the median, with a relative error of 3.7 %, followed by Set 3a with a relative error of 6.7 %. For the new shape, the closest estimation of the median is given by Set 1b, emphasizing the importance of seismological constraints in the selection process of input motions whenever possible. 4.2. Lausanne Malley The results of non-linear time history analyses are consistent with the observations made in Refs. [51,52], where the Lausanne Malley was found to be a highly vulnerable building. A considerable part of the earthquake motions led the building to global collapse regardless of the relatively low-intensity levels in terms of PGA, as depicted in Figs. 4–6. Fig. 11 shows the scatter of EDPs for soil type A. Set 2b and Set 4a provide the lowest and highest estimation of the median values of EDP and as 11.33 mm and 30.61 mm for the max (Δr), and 3025 and 4068 kN for the max(V b ), respectively. The highest variability in the response is given by Set 3a and Set 3b for the max(Δr) and max(V b ), respectively. In contrast, Set 5a and Set 5b exhibit the lowest dispersion, regardless of the chosen EDP. As shown in Fig. 12, all motions within Sets 1a, 3b, 4b, and 5a for soil type B led the building to global collapse. Similarly, six out of seven records in Sets 2a, 2b, and 3a induced collapse. The non-collapse observations generated by the remaining recording in Fig. 12 correspond to max(Δr) =71.01 mm, max(V b ) =4829 kN; max(Δr) =20.40 mm, max(V b ) =3483 kN; and max(Δr) =55.30 mm, max (V b ) =4446 kN, for Sets 2a, 2b, and 3a respectively. For Sets 1b, 4a, and 5b, the median EDPs shown in Fig. 12 are max(Δr) =23.09 mm, max(V b ) =4050 kN; max(Δr) =68.40 mm, max(V b ) =4746 kN; and max(Δr) =31.55 mm, max(V b ) =4411 kN; out of which Set 1b and Set 4a induced the largest and lowest record-to-record variability for non-collapse data, respectively. Next, for soil type C (See Fig. 13), only Set 5b showed collapse for all ground motion records. For the other sets, the non-collapse median values of max(Δr) vary from 34.38 mm in Set 1b up to 49.98 mm in Set 4b. Similarly, the median max(V b ) varies between 3872 and 4788 kN. The minimum values of global EDPs correspond to the outlier in Set 2b, with max(Δr) =27.23 mm, and max(V b ) =3518 kN. Besides, the lowest Fig. 10. Capacity curve in terms of PGA — Holsteiner Hof (Caicedo et al. [51]). D. Caicedo et al. Journal of Building Engineering 111 (2025) 113558 18 variability is achieved by utilising Set 4a and Set 5a in terms of max(Δr) and max(V b ), respectively. Contrastingly, Set 1b induces the highest dispersion for both global metrics under analysis. Fig. 14 shows the IDA capacity curves in terms of PGA for the Lausanne Malley, indicating the PGA of each target in the selection. Under EN 1998-1-1:2004 spectrum, the median max(Δr) estimated from the target values of PGA are 31.44 mm, 66.58 mm, and 57.79 mm for soil types A, B, and C, respectively. In comparison, for EN 1998-1-1:2024 spectrum, the values are 28.10 mm for soil A, 61.46 mm for soil B, and greater than 90.00 mm (i.e., global collapse) for soil C. For soil type A, Set 4a and Set 4b deliver the best approximation to the median response by targeting the values of PGA from EN 1998-1-1:2004 and EN 1998-1-1:2024 with relative errors of 2.63 % and 16.20 %, respectively. For soil type B, the closest estimation of the median demand from a target value of PGA =0.18 g (EN 1998-1-1:2004) is observed in Set 4a with a relative error of 2.7 % regarding the non-collapse observations. In general, poor estimations are delivered by Sets “b” Fig. 11. Box plot Lausanne Malley — Soil type A. Fig. 12. Box plot Lausanne Malley — Soil type B. Fig. 13. Box plot Lausanne Malley — Soil type C. D. Caicedo et al. Journal of Building Engineering 111 (2025) 113558 19 (targeting the latest spectral shape), particularly for soil type B. In this sense, the closest value to the median is given by Set 5b with a relative error of 48.7 % (See Fig. 12a), indicating that more records are required to improve the accuracy of the estimations. Moving to soil type C, the best approximation to the median value from the old shape of the spectrum is delivered by Set 1a with a 16.8 % relative error, followed closely by Set 5a with a relative error of 21.3 %. Lastly, by targeting the EN 1998-1-1:2024 soil C spectrum, Sets 2b, 3b, and 5b are sufficient to provide reasonable estimations of collapse since the majority of records within the sets induced the global failure of the building. 4.3. Record-to-record variability In general, for both buildings, the highest record-to-record variability is observed for Set 1b and Set 2b. These sets have in common the matching range 0.2T 1 –1.5T 1 , while in Set 1a and Set 2a, with a broader matching range, the dispersion is less. This is even more noticeable for Sets “3”, “4”, and “5”, in which, regardless of the code version and constraint conditions, the dispersion decreases drastically when the selection process targets the spectra in the broader range. This is attributed to the participation of higher modes in the dynamic response as well as the elongation of the fundamental period, T 1, as a clear indicator of structural inelasticity because of damage accumulation. Thus, one important limitation of code-based selection approaches seems to be the narrow matching ranges, in terms of T 1, defined in the standards, e.g., 0.2 T 1 –2.0 T 1 in the former EN 1998 and 0.2 T 1 –1.5 T 1 in the later revision. Shaking table tests conducted on various examples of unreinforced masonry structures with flexible diaphragms support this claim. In these experiments, the first-mode period progressively elongated up to twice the undamaged fundamental period [86,87] or even 3.5 times of the undamaged T 1 in the worst-case scenario [88]. Another factor that can be attributed to the reduction in dispersion, when matching a broader period range, is the contribution of higher modes and activation of potential OOP failure mechanisms due to earthquake excitations [89,90]. The advanced macroelement approach implemented in this research allows for the consideration of OOP local failure modes that, otherwise, would be impossible to consider with conventional macroelement approaches [91,92]. Previous applications of the three-dimensional macroelement showed how earthquake loads induced OOP failures (i.e., partial or total overturning of the façade), corresponding to OOP local modes that can occur at lower frequencies [49,52]. On the other hand, although dispersion decreases within Sets “3”, “4”, and “5”, they also lead to higher estimations of the median, which suggests that targeting the elastic response spectrum shape, either EN 1998-1-1:2004 or EN 1998-1-1:2024, is a rather conservative approach. Alternative targets, such as UHS and CMS, are likely to provide more realistic estimations of the median response as suggested in Refs. [93,94]. Generally, the closest approximation of the median response, derived from capacity curves, was achieved by datasets that incorporated seismological constraints during the preselection phase. This observation aligns with the findings of previous studies [33,40] since complying with the specific seismological and geological conditions will ensure spectral compatibility with hazard-consistent scenarios. The spectral shape is intrinsically influenced by seismological parameters, such as magnitude and distance (M, R) pairs [15], which are key parameters in more refined selection methodologies like those employed in Refs. [51,52]. Finally, it is worth noting that all analysed sets consist of seven acceleration records, which, in some cases, could not reach a satisfactory compatibility with the median demand estimated from IDA capacity curves. That is the case of EN 1998-1-1:2024 soil type B, where the best approximation resulted in a relative error approaching 50 %. These results imply the need to revise and validate the number of accelerograms required for a reliable estimation of the ’true’ mean seismic demand using probabilistic methods, specifically for pre-code unreinforced masonry constructions, where record-to-record variability plays a critical role. 5. Conclusions The seismic safety of old masonry buildings under bi-directional earthquake loads was addressed in this paper. Detailed threedimensional models of two buildings were developed in OpenSees, accounting for in-plane (IP) and out-of-plane (OOP) masonry wall effects, as well as non-linear wall and floor connections. Input motion targets were based on spectral shapes from EN 1998-11:2004 and EN 1998-1-1:2024, using a 475-year return period. A metaheuristic algorithm selected ten accelerogram suites, reflecting differences in Eurocode versions, seismological constraints, period-domain matching, and scaling strategies. Besides soil profile A, soil amplification effects were analysed for soil profiles B and C. Non-linear response history analyses were conducted to examine the Fig. 14. Capacity curve in terms of PGA — Lausanne Malley (Caicedo et al. [51]). D. Caicedo et al. Journal of Building Engineering 111 (2025) 113558 20 variability in structural response stemming from record-to-record uncertainty. Based on the numerical findings of this research, the following observations are valid for the code-based selection of earthquake motions for seismic evaluation of short-period old masonry buildings: •Whenever possible, seismological constraints should be accounted for in the preselection process of input motions to deliver a more realistic approximation of the seismic demand. •Aimed at reducing the dispersion of the seismic response, the matching strategy should fit the target spectrum in a broader matching range (i.e., 0.0 s ≤T ≤4.0 s) and not just a range defined around the fundamental elastic period, T 1 , since higher modes and period lengthening because of cumulative damage play a relevant role in the dynamic behaviour of pre-code masonry constructions. •Targeting the elastic design spectrum defined in either the EN 1998-1-1:2004 or the EN 1998-1-1:2024 editions of Eurocode 8 resulted in higher estimations of the median response, showing better accuracy when the spectral shape from the first-generation code edition was selected as the target. The effect of alternative, less conservative targets, such as the uniform hazard spectrum or conditional mean spectrum, on the seismic demand of unreinforced masonry buildings is encouraged to be examined in future research. Finally, the median response in terms of global EDPs may exhibit significant relative errors, reaching up to 50 % in the worst-case scenario (as shown for soil type B, EN 1998-1-1:2024). This underscores the need to revise and validate the minimum number of records required for a reliable estimation of the ’true’ mean seismic demand from a probabilistic perspective, specifically, for the case of pre-code masonry constructions, in which record-to-record variability significantly influences the outcomes. Future work should focus on the application of probabilistic methods on representative masonry archetypes, considering the mixed effect of record-torecord variability and quantification of model uncertainty (e.g., variation in mechanical properties), to provide complementary guidance for selecting earthquake ground motions, which is often based on engineering experience. CRediT authorship contribution statement Daniel Caicedo: Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Conceptualization. Igor Tomi´ c: Writing – review & editing, Visualization, Validation, Supervision, Software, Methodology, Investigation, Formal analysis, Conceptualization. Shaghayegh Karimzadeh: Writing – review & editing, Visualization, Validation, Resources, Methodology, Investigation, Conceptualization. Vasco Bernardo: Writing – review & editing, Visualization, Supervision, Methodology, Conceptualization. Katrin Beyer: Writing – review & editing, Visualization, Supervision, Resources, Project administration, Conceptualization. Paulo B. Lourenço: Writing – review & editing, Validation, Supervision, Resources, Project administration, Funding acquisition, 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. Acknowledgment This study has been partly 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. This work was also partly financed by FCT/MCTES through national funds (PIDDAC) under the R&D Unit Institute for Sustainability and Innovation in Structural Engineering (ISISE), under reference UIDB/04029/2020 (doi.org/10.54499/UIDB/04029/ 2020), and under the Associate Laboratory Advanced Production and Intelligent Systems ARISE under reference LA/P/0112/2020. This work is partly financed by national funds through FCT - Foundation for Science and Technology, under grant agreement 2023.01101.BD attributed to the first author. The second author was supported by the Swiss National Science Foundation through grant 200021_175903/1 Equivalent frame models for the in-plane and OOP response of unreinforced masonry buildings. Data availability The Python scripts for code-based ground motion selection and sets of motions used in this study are shared openly through the repository https://zenodo.org/records/15459442. References [1] M. Como, Statics of historic masonry constructions: an essay. 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