Seismic fragility curves for the Italian RC residential buildings based on non-linear dynamic analyses

In the present paper, Fragility Curves (FCs) of Reinforced Concrete (RC) building types with moment-resisting frame structure representative of the existing Italian building stock have been derived through an analytical approach. The proposed methodology is based on Non-Linear Dynamic Analyses encompassing all the steps required to bring about reliable as well realistic fragility results. First, prototype building types have been selected by considering the main attributes affecting the seismic vulnerability of existing RC buildings, that is: age of construction (i.e. ‘50 s, ‘70 s and ‘90 s), number of storeys (i.e. 2, 4 and 6 storeys), arrangement in elevation of infills (i.e. Bare-, Infilled-, Pilotis-frame) and design level (i.e. seismic or gravity loads). A simulated design has been used for detailing the building types at hand, whose non-linear dynamic response has been computed by using a large set of signals. The signals have been purposely selected in order to approach the elastic design spectra provided in the Italian seismic code for different return periods, being able to take into account also record-to-record variability and soil-amplification effects. A specific relationship between the considered engineering demand parameter (i.e. inter-storey drift ratio) and all damage levels proposed in the EMS-98 scale have been defined on the basis of empirical data and expert judgement. A set of FCs in terms of peak ground acceleration are finally derived and compared to point out the role of the considered vulnerability attributes.


Introduction
Italy is one of the European countries with the highest seismic hazard, both in terms of frequency and intensity of events. In the last 50 years, earthquakes have caused about 5000 fatalities and monetary losses of about €200 billion (DPC 2018). Moreover, they have damaged or destroyed a significant amount of historical and artistic heritage whose losses are * V. Manfredi vincenzo.manfredi@unibas.it 1 School of Engineering, University of Basilicata, Viale dell'Ateneo Lucano, 10, 85100 Potenza, Italy priceless. These dramatic effects stress the need and the urgency for comprehensive seismic risk assessments aimed at defining prevention and mitigation strategies at national, regional and local level. To this end, accounting for the massive scale of the problem, one of main goals is the identification of the areas in which intervention actions are primarily needed to reduce the seismic vulnerability of the built environment. In fact, it is worth emphasizing that the huge losses due to the past major events, e.g. Irpinia-Basilicata 1980, Abruzzo 2009and Central Italy 2016, mainly depend on the high vulnerability of the existing building stock, including both masonry and Reinforced Concrete (RC) buildings (e.g. Dolce and Goretti 2015;Masi et al. 2019a), which were mostly designed only for gravity loads or using low lateral forces and inadequate anti-seismic criteria. Hence, a reliable assessment of the seismic vulnerability of existing buildings is a crucial step in order to define realistic loss estimations and effective mitigation strategies in earthquake-prone areas.
Seismic vulnerability assessment can be performed through different methods based on (i) collection and analysis of observed damage data from past earthquakes (empirical approach), (ii) numerical analysis of mechanical models (analytical approach), and (iii) combination of analytical and empirical data (hybrid approach). A comprehensive overview of the available methods can be found in Calvi et al. (2006).
Empirical methods define fragility functions on the basis of the statistical analysis of damage data from post-earthquake surveys (e.g., Dolce et al. 2003;Rossetto and Elnashai 2003;Rota et al. 2008;Rosti et al. 2020;Del Gaudio et al. 2020;Spence et al. 2021). These methods make it possible to consider the variability of both building types and earthquake characteristics, which are important in case of large-scale risk assessments. However, the reliability of fragility functions is strongly affected by the quality and completeness of the database. Regarding this latter, large efforts were made in Italy with the development of a web-based platform, Da.D.O. (Observed Damage Database), collecting the great amount of data of post-earthquake surveys performed in the last 50 years (Dolce et al. 2019). Nevertheless, limited observational data are available for high-magnitude events with severe and widespread damage, especially for RC buildings. Moreover, undamaged buildings are generally not inspected in Italian post-earthquake usability surveys, thereby leading to a non-homogeneous availability of data throughout the different seismic intensities. If these data are not properly included in the analyses, fragility can be overestimated (Pitilakis et al. 2014).
Heuristic methods are part of the family of empirical approaches being based on the expertise of macroseismic methods adequately calibrated by using empirical data . In order to define fragility functions in terms of instrumental measures, the large amount of macroseismic data available in the historical database needs to be converted according to specific relationships (e.g. Masi et al. 2020).
Analytical methods are based on numerical analyses of structural prototypes representative of some building types (e.g., Masi et al., 2015;Del Gaudio et al. 2015;D'Ayala et al. 2015;Borzi et al. 2021). These methods make it possible to explicitly analyze all the main attributes of the building stock under examination together with the corresponding uncertainties. The proper identification of different sources of uncertainty (e.g. variability due to different characteristics of the real buildings with respect to the selected representative building type (inter-building variability) and within the same building (intra-building variability), record-to record variability, damage level definition) and their quantification can affect the reliability of analytical results (Rossetto et al. 2014). The main limitations of the analytical methods are the capability of a prototype or a set of structures to represent a complex building stock, the simplifications inevitably introduced by structural modelling and the damage level assignation based on one or more response parameters. On the contrary, analytical approaches allow simulation of the seismic response of different building types, also considering high intensity values, for which poor empirical data are generally available.
Different methods are generally used for deriving analytical fragility functions, whose choice mainly derives from a compromise between reliability of structural response and computational time demand. In this regard, despite its greater computational effort and the tricky issues related to the appropriate selection of records (e.g. Bommer and Acevedo 2004) and the choice of suitable intensity measures (e.g. Luco and Cornell 2007), Non-Linear Dynamic Analysis (NLDA) is considered as a reference analysis method.
In order to overcome some limitations inherent to the empirical and analytical approaches taken individually, they can be properly combined in the framework of hybrid methods (e.g. Kappos et al. 2016).
In the last decades, several projects, such as RISK-UE (Mouroux and Le Brun 2006), LESSLOSS (Calvi and Pinho 2004), SYNER-G (Pitilakis et al. 2014), and GEM (Yepes et al. 2016), aimed to develop and collect fragility functions for the built environment of different countries. As for Italy, in 2018 the Civil Protection Department (DPC) involved two Centers of Competence on seismic risk, that is ReLUIS (Network of University Laboratories for Earthquake Engineering) and Eucentre (European Centre for Training and Research in Earthquake Engineering), in order to prepare a state-of-the art version of the National Risk Assessment (NRA, Dolce et al. 2021) based on the more recent advancements made in seismic hazard definition, vulnerability assessment methods and loss estimation. After this, with the aim of updating the previous NRA results and extending the seismic risk analyses to other types of buildings/constructions (i.e. schools, churches, bridges), DPC supported a new research project for the period 2019-2021, named WP4 "Seismic Risk Maps-MARS" (Masi et al. 2021a). One of the main objectives of WP4-MARS is to enrich the vulnerability models adopted in the 2018 NRA by deriving additional Fragility Curves (FCs) through different approaches. This was especially required for RC buildings, since the previous FCs were mainly based on (poor) empirical data.
The present paper aims to describe the methodological framework used for deriving analytical FCs of a wide set of the RC existing building types with moment-resisting frame (MRF) structure mostly widespread in Italy through NLDAs. Several attributes mainly affecting seismic vulnerability have been considered in the selection of RC building types, that are: number of storeys (i.e. Low-rise, Mid-rise and High-rise type), presence/arrangement of infills (i.e. Regularly Infilled-frame, Pilotis-frame and Bare frame types), construction period (i.e.'50 s,'70 s and '90 s) and design level (i.e. buildings designed only for gravity loads, GLD, or buildings with earthquake resistant design, ERD). NLDAs have been performed by using a large suite of records purposely selected in order to be consistent with the Italian seismic hazard, also accounting for the role of amplification effects, thus permitting the generation of site-and building-independent FCs. In this context, Peak Ground Acceleration (PGA) was selected as intensity measure. A specific relationship between the considered Earthquake Demand Parameter (i.e. interstorey drift) and six damage levels (based on the EMS-98 European Macroseismic Scale, Grünthal 1998) has been defined mainly on the basis of experimental results.
After describing the methodology adopted to derive FCs using NLDAs, the results for the RC building types have been described and analyzed in order to emphasize the role of the main vulnerability parameters on seismic fragility.

3 2 Methodology
Analytical fragility curves of RC types with moment-resisting frame (MRF) structure representative of Italian existing building stock have been derived by following a properlydefined methodology based on 10 main steps, as listed below: 1. Identification of building classes 2. Selection of building types 3. Simulated design 4. Modelling 5. Selection of Intensity Measure 6. Ground-motion records 7. Definition of "structural response-damage level" relationship 8. Non-linear dynamic analyses 9. Treatment of uncertainties 10. Derivation of analytical fragility curves In the next sub-sections, each step is described by highlighting the most relevant features.

Identification of building classes
Building classes have been identified on the basis of the main attributes affecting RC seismic vulnerability. Among these, period of construction is one of the most adopted parameters because it accounts for improvement over the years in terms of material properties, code requirements etc. In Italy, two macro-periods can be identified for RC buildings, i.e. before 1971and after 1971. Indeed, in 1971 Law 1086 introduced new significant rules related to both design and construction phase, thus fostering an overall improvement of the structural quality. Before that, Royal Decree 2229/1939 provided very poor structural requirements and low mechanical properties of materials were permitted. Specifically, it considered three types of steel quality, i.e. low-carbon, medium-carbon and high-carbon steel, whose nominal tensile stress values at yielding are in the range of 230-310 MPa. Note that only smooth bars were produced during that period. In the '70 s, due to a more flexible code upgrading process permitted by Law 1086/1971, several Ministerial Decrees were issued. In addition to a general upgrading of structural requirements, they permitted increasing material strength to be used in design practice. Specifically for steel, deformed bars were introduced with yield stress values ranging from 380 to 440 MPa. In the '90 s, the structural quality of construction was further increased due to the use of resistant schemes deriving from anti-seismic design (i.e. frames along the two in-plane directions) and a larger use of computer-aided design.
Other than design code upgrading, over the years seismic classification (i.e. territory where seismic rules are mandatory in design practice) has also improved. Specifically, from the 1908 Reggio Calabria-Messina earthquake to 2003 (OPCM 3274/2003), all the Italian territory was progressively classified as seismic, although with different hazard intensities. More specifically, up to the early 2000s, i.e. when modern anti-seismic codes along with a new seismic zonation were introduced by Ordinance 3274/2003, only two main seismic categories were defined in terms of horizontal loads equal to either 7% or 10% of the "seismic weight", respectively for I and II categories. It is also worth noting that before 3274/2003 Ordinance, seismic design rules differed from gravity ones only for lateral load intensities to be considered in the structural analysis, while no adequate anti-seismic details were prescribed. In De , a detailed description on the evolution of both seismic classification and design code prescriptions is reported.
Keeping in mind the key role of infills on seismic performance, in particular for types designed only for gravity loads, in Italy different types can be found over the years. whose characteristics mainly depend on the increasing requirements due to codes on energy demand reduction. Specifically, in accordance with available studies on infill typologies in Italy, (e.g. the TABULA and EPISCOPE project, Corrado et al. 2014;Braga et al. 2011;Manfredi and Masi 2018), '50 s infills were typically made up of a single layer of solid bricks (25 cm thick) or two layers (made up by solid/hollow clay bricks) and empty cavity (cavity wall type). The latter type was also commonly found in the '70 s, consisting of an external layer (12 cm thick), an internal one (8 cm thick) and empty cavity (10 cm thick) with a total thickness of about 30 cm. As a consequence of the first Italian rule addressing thermal insulation criteria in buildings (Law 91/1991), the two layers of hollow bricks have a greater thickness, particularly the external one (15-20 cm thick). A single layer (25-30 cm thick) of hollow blocks has also been adopted.
As for infill configuration along the height, three configurations can be generally observed: (i) "Fully infilled" (i.e. frames with effective infill panels regularly arranged at each level along the height), (ii) "Pilotis" (i.e. frames with infills having large openings or absent at the ground floor), and (iii) "Bare" (i.e. frames without effective infills due to large openings and/or badly connected to resisting members).
Several studies pointed out how infills regularly arranged offer a significant contribution to lateral capacity whereas, on the contrary, poor performance is generally experienced in case of irregular (pilotis) configuration in elevation (e.g. Dolšek and Fajfar 2001;Masi 2003;Repapis et al. 2006;Ricci et al. 2013;Jeon et al. 2015a).
In Italy, data on the above-described attributes can be obtained from several sources such as building-by-building surveys (Masi et al. 2021b), post-earthquake inspections (Da.D.O. database, Dolce et al. 2019), interview-based surveys (Zuccaro et al. 2015) or census of population and houses (ISTAT 2011). Although the data from the first two sources are more reliable since they are generally collected by technicians according to a more riskoriented approach which allows better highlighting of local distinctive vulnerability features , the low amount of data obtained from these activities does not permit extending results to the entire Italian territory. On the contrary, although ISTAT census (2011) provides poor data generally collected by non-technical operators, it covers all the Italian territory. According to it, the Italian building stock amounts to about 12 million buildings, most of which are masonry structures (more than 7 million) while about 4 million are RC ones. As shown in Fig. 1a, about 64% of the RC building stock was built in the period 1961-90 with a prevalence of 2 storeys (about 44%). Note that, according to ISTAT 2011, only four classes in terms of number of storeys are considered, thus comprising taller buildings in the " ≥ 4" class.
As for design level (Fig. 1b), buildings with only gravity load design are predominant (about 73%) compared to those designed by considering lateral forces (about 27%). This latter type mainly comprises buildings designed with seismic intensity deriving from the 2nd seismic category.

Selection of building types
Starting from the above-described building classes, some prototypes representative of the Italian building stock have been selected by using typological data deriving from the review of technical documentations and large building-by-building surveys involving some Italian towns (Dolce et al. 2003;Masi et al. 2021b). First of all, two different "regular" inplane layouts have been considered, i.e. "small" for LR types and "large" for both MR and HR types. Both types have rectangular in-plane shape ( Fig. 2) with different dimensions and number of bays along the two orthogonal directions. Specifically, the first one (i.e. "small" ERD in-plane layout of LR (f) and MR-HR (g) types layout) has total dimensions 12.15 × 8.70 m 2 with three bays along the X directions and two bays along X; the second one (i.e. "large" layout) has total dimensions 20.95 × 11.75 m 2 with five and three bays, respectively for the X and Y directions. In elevation, three different numbers of storeys, that is 2, 4 and 6 storeys, have been considered as representative of LR, MR and HR building classes, respectively. For all prototypes, a constant inter-storey height equal to 3.05 m is assumed.
As a consequence of both code requirements and common practice, different lateral resisting schemes have been considered over the years. Specifically, for the older building types, no significant differences in terms of structural scheme can be found for buildings designed with/without lateral forces. Consequently, both GLD and ERD types belonging to the '50 s and '70 s have lateral load resisting frames with rigid beams only along the X direction while, along the Y transversal direction, beams are present only in the exterior frames. Contrarily, ERD types designed in accordance with '90 s codes have frames along the two in-plane directions, with internal flexible beams and rigid beams along the perimeter. In the '90 s, as a consequence of the widespread awareness deriving from the increasing areas classified as seismic, an ERD-like resisting scheme is frequently observed also in the case of only gravity load design (i.e. GLD).
For all building prototypes, staircase sub-structure is placed in a symmetric position in relation to the Y direction. Making reference to the available handbooks and the typical current practice of the periods under study, staircase structure is made up of two knee beams at each storey with cantilevered steps and mid-height stepping slabs.
Floor slabs are made up of one-way RC joists (50 cm spaced with 10 cm width and 20 cm height), a concrete cover plate with 5 cm thickness and hollow clay bricks, setting a total slab thickness equal to 25 cm. Dead load, also including non-structural floor components, is equal to 6.3 kN/m 2 while, in accordance with the considered technical codes, live load is assumed equal to 2.0 kN/m 2 .
As for infills, double-layer type with hollow clay bricks (arranged with horizontal holes) and empty cavity has been considered for all prototypes, albeit with different thickness values for the external layer (the internal one is fixed to 8 cm). Specifically, the external layer is 12 cm thick for both'50 s and '70 s types while it is 20 cm for '90 s ones. As a result, the "effective" thickness values (i.e. the values considered in infill modelling) are 20 cm (as obtained by summing thickness values of the two layers, 8 + 12 cm) for both'50 s and '70 s types and 28 cm (8 + 20 cm) for '90 s ones.
At the end, by combining 3 periods, 2 design levels, 3 number of storeys, 3 arrangements of infills, 54 models have been considered, as shown in Fig. 3.

Simulated design
For each building prototype, cross-section dimensions and reinforcement details have been determined by means of simulated design (Masi 2003), considering the code in force at the different periods, the usual design practice and the typical properties of materials. In the following, these three aspects have been separately described.

Technical codes
As regards GLD types, Royal Decree 2229/1939 has been adopted for '50 s building stock. It was enforced up to the early '70 s, when Ministerial Decree 30 May 1972 was issued, herein used to design '70 s types. Finally, Ministerial Decree 1 April 1983 has been considered for the earlier considered period, i.e. '90 s. Along with the above-mentioned codes used for gravity load design, three additional codes for ERD types have been considered in order to comply with the specific requirements for buildings in seismic classified areas, that is Royal Decree 640/1935, Law 1684/1962 and Ministerial Decree 24 January 1986, respectively for the '50 s, '70 s and '90 s. As reported below, the codes used for ERD types mainly provide prescriptions on seismic load modelling while no specific anti-seismic detail is required. Due to the prevalence of buildings located in areas with low-seismic classification, lateral forces for ERD types have been calculated according to the requirements for the 2nd seismic category.

Materials and reinforcement details
In accordance with the codes used for GLD, concrete with compressive strength value equal to 12.0 MPa (only for members under axial loads) and 22.5 MPa (for flexural members) have been considered for '50 s types. As for (smooth) reinforcement bars, steel has low-carbon quality with yielding tensile strength value of 140 MPa. A better quality of materials was permitted by the '70 s codes, with "characteristic" compressive strength of concrete equal to 25 MPa and FeB38k steel quality (i.e. deformed bars with tensile strength at yielding equal to 380 MPa). Finally, for '90 s types, the same concrete quality has been adopted as for the '70 s types while a higher quality of steel reinforcement bars, i.e. FeB44k having tensile strength at yielding equal to 440 MPa. Note that the above-described materials have been used also for ERD types.
As for reinforcement details, slight differences can be found over the considered codes. In particular, for columns, the minimum percentage of longitudinal reinforcement (with respect to the cross-section area of concrete) ranges from 0.6 to 0.8% while the spacing of stirrups is obtained as the minimum value between 10 (or 15) times the diameter of the longitudinal bars and half of the minimum dimension of the cross section (or 25 cm). For beams, more restrictive requirements were provided by Ministerial Decree 1 April 1983 with respect to the previous codes. Indeed, incline bars previously adopted for shear stress were not permitted and the minimum values of stirrup spacing decreased (i.e. at the beam end sections, no greater than 12 times the minimum diameter value of the longitudinal bars). It worth noting that the above-reported minimum requirements also apply to lateral (seismic) force design, i.e. ERD types, since no further anti-seismic details are required in the considered seismic codes, e.g. transverse reinforcement in beam-column joints.
For the sake of clearness, Table 1 summarizes the main requirements of the considered codes.

Design practice
By following the common practice mostly adopted before the advent of the personal computer, resisting members have been designed considering simplified models. For GLD types related to both the'50 s and '70 s, the columns have been designed taking into account only axial loads and adopting the minimum reinforcement details required by codes. The beams have been designed on the basis of the simplified model of continuous beam resting on simple supports.
For ERD types, internal forces have been analysed by considering single frames subjected to lateral force evaluated as a function of the gravity loads applied and neglecting any in-plane redistribution due to RC slabs. In accordance with the prescriptions provided by the codes considered for the 2 nd seismic category, lateral forces are equal to 7% of the "seismic weight" with a constant distribution along the height for both'50 s and '70 s types while an inverted triangular force distribution has been considered for the '90 s.
For this latter period, for both GLD and ERD prototypes, 3D modelling has been performed in a common framework of computer-aided structural analyses. In this way, reinforcement details for columns, in particular, have been determined by considering flexural moments around two orthogonal axes.
For all types, the staircase knee beams have been designed as a stand-alone structure taking into account internal forces due to only gravity loads.
Safety verifications have been carried out using the "allowable stress method" whose stress values have been evaluated as a function of the corresponding "nominal" properties of materials according to the adopted code.

Modelling
Structural response of the above-mentioned building prototypes has been simulated by 3D models implemented in the OpenSees platform (McKenna 2011). In order both to guarantee an adequate reliability of structural results and to reduce computational demand due to the several time history analyses to be performed, macro-modelling based on lumped plasticity approach has been adopted. Most of the failure mechanisms affecting existing   in the context of the RINTC project (Iervolino et al 2022). More specifically, in order to model flexural response, at both ends of each structural member, a bending moment-rotation (M-θ) relationship has been defined by adopting the trilinear Ibarra-Medina-Krawinkler model (IMK,  which is able to reliably simulate the softening behaviour of RC members as well as strength and stiffness degradation. The parameters of the IMK model have been evaluated by means of the empirical predictive equations by Haselton et al. (2008) which are obtained on the basis of a large set of RC columns with deformed bars. As a consequence, the IMK model along with Haselton's equations have been considered to model only RC members for both'70 s and '90 s structures. On the contrary, for '50 s types (which have plain bars), a quadrilinear model by Verderame and Ricci (2018) has been used to better simulate the different flexural response due to plain bars with respect to deformed ones. When brittle failure has been predicted (e.g. in the short columns of staircase structure), the above-mentioned M-θ relationship has been properly modified in order to take into consideration the possible premature failure in shear. More specifically, for each column member, the bending moment value has been calculated through equilibrium condition with ultimate shear strength, this latter evaluated using the Sezen and Moehle (2004) model. Due to the degrading behaviour as a function of ductility demand of the considered shear capacity model, by comparing the shear demand due to bending moment with the corresponding strength, three different failure modes can be expected, that are: (i) flexural mode (column fails in flexure), (ii) shear mode (column fails in shear before reaching yielding moment), and (iii) an intermediate condition (shear/flexural mode), in which column fails in flexure for a bending moment within yielding to capping values. More details can be found in De .
In order to consider the presence of infill panels into frames and their role on structural response, an equivalent single-strut approach has been adopted. Note that, due to the negligible contribution to the lateral capacity provided by infills with large openings and/ or badly connected to RC members, infill presence has not been considered for BF and at the ground floor of PF types. The cross-section area of each strut has been calculated by multiplying the panel thickness by an equivalent width determined through the expression originally proposed by Decanini and Fantin (1986). A trilinear backbone model described in Ricci et al. (2018) has been adopted to simulate in-plane infill response.
Due to the huge number of NLDAs to be performed, in order to find a compromise between computational time and required accuracy, both the local interaction infills-adjacent RC columns and the non-linear response of beam-column joints have not been considered in structural modelling.
In evaluating the capacity of RC members, typical mechanical properties found in real buildings have been assumed as a function of the periods under consideration. Specifically, starting from the results obtained by Masi et al. (2019b), who analysed the concrete strength of a large database of core tests extracted from RC Italian buildings, the mean compressive strength value has been set to 16, 20 and 25 MPa for'50 s,'70 s and '90 s building types, respectively. As for steel, on the basis of the results obtained by Verderame et al. (2012) and Masi and Digrisolo (2013)

Selection of intensity measure (IM)
One of the most important phases in deriving analytical fragility curves is the selection of an appropriate Intensity Measure (IM). As firstly introduced by Luco and Cornell (2007), IM selection needs to meet both efficiency and sufficiency criteria. Efficient IMs guarantee a low variability of the structural response, thus allowing a reduced number of analyses. Sufficient IMs render the computed structural response strictly dependent on the intensity values, thus low dependency from other earthquake parameters such as magnitude and source-to-source distance. Further criteria have been successively defined in order to evaluate the goodness of signal selection, among them practicality, effectiveness, robustness and computability (Pitilakis et al. 2014).
Despite these criteria for evaluating the best link between seismic hazard and structural response, selecting the optimal IM is still an open issue given that each IM inevitably presents pros and cons. For example, PGA and Sa(T 1 ) are widely adopted in fragility analyses due to the large availability of ground motion prediction equations (GMPEs) based on these IMs as well as to the simplicity of calculation. At the same time, they can be poorly correlated to the non-linear response of structures (e.g. Masi 2003;Haselton et al. 2012; O'Reilly 2021). On the contrary, integral parameters such as Housner intensity or a combination of spectral acceleration at different periods of vibration (e.g. Kazantzi and Vamvatisikos, 2015;Ebrahimian et al. 2015) reduce response variability but increase the complexity of the procedure.
Keeping the goal of this study in mind, the choice of the best IM has been made in order to satisfy two main criteria, namely: (i) to allow the derivation of fragility curves for different structural types covering a wide range of periods of vibration, (ii) to allow for site-independent analyses, i.e. derivation of fragility curves irrespective of the hazard characteristics of a specific site. In this context, PGA is an acceptable compromise between a good correlation with the non-linear seismic response and practical constraints, i.e. structure-and site-independence. Further, being the most used IM, PGA allows the proposed FCs to be compared with several studies available in literature.

Ground-motion records
A special attention has been paid to the selection of suitable ground motion records for NLDAs. In this context, two main criteria need to be satisfied, that are: (i) to provide a sufficiently large set of accelerograms consistent with the seismic hazard of the whole Italian territory by also taking into account the main soil amplification conditions, ii) to allow the derivation of fragility curves for different structural types considering all the damage levels according to the European Macroseismic Scale EMS-98 (Grunthal 1998).
As deeply described in Manfredi et al. (2022), signal selection has been made by means of a purposely defined tool, namely S&M-Select & Match, which provides recorded ground motions approaching a target spectrum according to user-defined criteria from a large database (SIMBAD-V06, Smerzini et al. 2014). To this purpose, eight Italian code-conforming spectra have been defined having increasing intensities (i.e. return period values going from 50 to 10,000 years) and, then, about 15 signals for each 1 3 return period (i.e. globally 125 records) have been selected. Each signal consists of two in-plane orthogonal components.
In order to consider amplification effects due to main soil conditions in Italy (Mori et al. 2020), signals refer to A/B categories according to Ministerial Decree 17 January 2018 (NTC 2018).
For very long return periods (i.e. 5000 and 10,000 years), no real signals are available in the considered database. Consequently, starting from the subset obtained for events with 2500 year return period, a spectral matching procedure available in S&M tool has been used to scale in the frequency domain real signals until its response spectrum matches the target one within a prescribed tolerance. More details on the spectrum matching method used by S&M can be found in Manfredi et al. (2022) while the list of considered accelerograms are in the Appendix.
With reference to Fig. 4a, the suite of recorded ground motions covers a wide range of magnitude values consistent with the Italian hazard going from 5.0 to 7.1, while the epicentral distances R epi are between 4 and 30 km. The average shear wave velocity in the top 30 m, V S30 , is about 540 m/s.
For the considered dataset, the frequency of PGA values is plotted in Fig. 4b, separately for the two in-plane components (i.e. H1 and H2). Note that, for each PGA bin, H1 and H2 components have similar percentages, with a relative prevalence (45%) of signals having intensities up to 0.3 g while the complementary percentage mainly consists of signals with intensity 0.3-0.75 g. Very high intensity signals are about 5%.

Earthquake demand parameter versus damage level relationship
When carrying out fragility studies, a key step is the definition of a proper relationship between the considered Earthquake Demand Parameter (EDP) and the corresponding description of building performance. EDPs generally refer to member forces/deformations, displacements (e.g. interstorey drift ratio, IDR) or energy-based indicators (e.g. Park and Ang 1985). Due to the inherent capability to establish a direct connection to damage, IDR is largely used (e.g. Cornell et al. 2002;Ellingwood et al. 2007;Krawinkler and Lignos 2009), particularly in the case of RC members with low ductility and displacement-sensitive components such as hollow clay infill walls.
In the present study IDR has been used as EDP and a relationship with the five (other than the "null" damage) damage levels according to the European Macroseismic Scale (EMS-98) has been defined. In this context, special attention has been paid to the performance of non-structural components. Indeed, as shown by past Italian earthquakes (e.g. Braga et al. 2011;Del Gaudio et al. 2018;Masi et al. 2019a;Di Ludovico et al 2019), damage to non-structural components is extensively experienced by RC buildings, with damage levels up to D3 mainly due to infill walls and interior partitions. Therefore, starting from the IDR vs EMS-98 relationship already proposed in Masi et al. (2015), IDR range values for the lower damage levels have been modified on the basis of prominent experimental databases available in the literature and consistent with the infill types considered in the present study. More specifically, De , further integrated by Del Gaudio et al. (2019), collected a large database of experimental data related to in-plane performance of infills, 36 of them refer to solid infills (i.e. without openings) made up by hollow clay with horizontal holes. Fragility curves were derived in terms of IDR for the damage levels consistent with the EMS-98 definition. Median and lognormal standard deviation values of IDR for the first three damage levels are, respectively, equal to 0.08% and 0.71 for D1, 0.33% and 0.41 for D2, 0.83% and 0.48 for D3.
An analogous study was carried out by Cardone and Perrone (2015). Median values evaluated for a sub-set of data (20 tests) related to solid infills with hollow clay bricks are 0.19% for D1, 0.57% for D2 and 1.09% for D3. As for lognormal standard deviation, the values are 0.37, 0.40 and 0.32, respectively for D1, D2 and D3 damage levels.
Finally, the IDR mean values obtained by  for three limit states consistent with the first three EMS-98 damage levels are 0.19%, 0.64% and 1.31%, while standard deviation values are equal to 0.09, 0.32 and 0.43.
In order to define the most likely range of IDR related to the three lower damage levels, for each distribution both 16th and 84th (for the upper value) percentiles have been calculated. Then, the bound values have been assumed equal to the mean value obtained for the 16th and 84th percentile, respectively for bottom and upper bounds. Table 2 summarizes the above-described results.
Finally, the IDR ranges have been modified by expert judgment in order to ensure the continuity and consistency of values over the ranges (i.e. the upper value of a given range and the bottom value of the next one have to be the same). Further, due to the inherent difficulty in distinguishing between slight damage (i.e. D1) and absence of damage (D0), the bottom bound value of D1 (which is 0.09% originally) has been set to 0.15%. Similarly, the upper bound value of D3 has been cut off to 1.2% because the value obtained from experimental data (about 1.5%) appears to be too high and inconsistent with the expected structural damage for the same damage level.
Although the above reported IDR values refer to infills without openings and effectively connected to resisting members (i.e. consistent with the definition of IF types), for the sake of simplicity, the same values have been also adopted for both BF and PF types.
For the most severe damage levels (i.e. D4-D5), only structural performance has been considered. Specifically for collapse (D5), the IDR values provided in Masi et al. (2015) have been updated by considering the results of a series of Incremental Dynamic Analyses (IDAs, Vamvatsikos and Cornell 2002) purposely performed in the present study for some of the structural types under examination. IDAs have been carried out by using 20 signals belonging to the sub-dataset obtained for the 50 year return period and scaled up to dynamic instability (i.e. displacements indefinitely increase for an infinitesimal increase of intensity). The IDR values related to D5 have been assumed as the 16th percentile of the data distribution at dynamic instability. Figure 5 shows IDA results performed for the

Non-linear dynamic analyses
Several approaches able to derive analytical fragility curves through nonlinear dynamic analyses (NLDAs) are available in literature. As summarized by Baker (2015), one of the most adopted approaches is the Incremental Dynamic Analysis (IDA, Vamvatsikos and Cornell 2002), in which a fixed suite of ground motions is incrementally scaled up to dynamic instability (i.e. when a small increment in ground motion intensity generates an excessive increase in structural response), consistent with structural collapse. The fragility parameters are determined on the basis of the IM intensity values associated with the onset of collapse (or any limit state) and then by computing their mean and standard deviation. A second approach is Multiple Stripes Analysis (MSA, Jalayer and Cornell 2009), where NLDAs are performed by using different sets of ground motions, each one referred to a specify IM value. In this case, data related to the fraction of ground motions at each IM value that cause collapse (or any limit state) are fitted though appropriate techniques. It is worth noting that, in the two above-mentioned approaches, ground motions need to be scaled and, especially for IDA, it can introduce bias on the structural performance estimation (e.g. Zacharenaki et al. 2014). Finally, in the Cloud analysis , EDP results from NLDAs performed by using a suite of recorded ground motions are fitted in the logarithmic scale with the corresponding IM ones in order to derive fragility parameters. In the present study, NLDAs have been performed through the Opensees software (McKenna 2011) by using a large suite of ground motion records (i.e. 125, see Sect. 2.6), most of which (85) are real (unscaled) signals, thus reducing the possible bias in the structural response evaluation due to scaling (e.g. Du et al 2019). For each building prototype described above, 125 NLDAs have been carried out by simultaneously using the two inplane components of signals. To this purpose, it is worth noting that, as a consequence of the adopted modelling (in which no interaction between axial force and flexural moments as well as between the flexural moments around the two orthogonal axes is considered) and the substantial in-plane building symmetry, structural response along the two orthogonal axes does not affect each other. In this way, two useful data are obtained from each analysis and properly considered in fragility curve derivation.
During analyses, for each storey, the displacement of the centre of mass has been recorded and then the maximum IDR value has been evaluated along the two in-plane directions. For each IDR value falling into a given range as defined in Sect. 2.7, the corresponding PGA value has been collected. The dataset of PGA values related to the different damage levels has been considered to derive fragility curve parameters (see Sect. 3).
For MR-GLD type, Fig. 6 shows the IDR-PGA points in a bi-logarithmic scale along with the threshold values of IDR. Note that, in the figure, the dynamic instability cases (for which no finite IDR value can be obtained from NLDA) are plotted by considering an arbitrarily high IDR value and marked in black edge. The treatment of the dynamic instability cases in deriving FCs for D5 damage level is described in Sect. 2.10.

Treatment of uncertainties
In fragility studies, three main sources of uncertainty are generally considered which refer to seismic demand, building capacity and damage level definition. The first one reflects the aleatory of earthquake motion as physical phenomenon and the fact that there is no exact link between a given IM and the considered EDP. This source is commonly referred to as record-to-record variability. Uncertainty in capacity accounts for both intra-building and building-to-building variability deriving from different values of geometrical, mechanical, structural and modelling parameters. Finally, damage threshold uncertainty mainly accounts for the definition of the damage levels, the choice of the damage model, the damage index used to represent the damage levels of a structure, and the correlation with the chosen intensity measure (Maio and Tsionis 2016).
Since fragility curves are often expressed as lognormal cumulative distribution functions, uncertainty is estimated in terms of lognormal standard deviation β, also noted as dispersion.
In general, in analytical fragility studies, one source of uncertainty is numerically estimated while the others are assumed as deterministic from literature. In this way, recordto-record variability is usually considered because it can be easily evaluated by a suitable set of signals. For example, Kappos and Panagopoulos (2010) derived fragility curves for 54 building types representing most of the common types in Southern Europe designed according to different code levels. Record-to-record variability was evaluated by means of several NLDAs conducted by using 16 signals scaled up to collapse. On the contrary, as also suggested by FEMA (2022), capacity variability was assumed equal to 0.3 for lowcode buildings and 0.25 for high-code ones. The uncertainty in the definition of damage state is equal to 0.4 for all building types. Similar values were also considered by Celik and Ellingwood (2009) and Jeon et al. (2015b) for non-ductile RC frames. O'Reilly and Sullivan (2018) numerically evaluated both record-to-record and modelling variabilities for some Italian existing RC frames designed only for vertical loads. At collapse, the two sources of uncertainty have similar magnitude for all considered types. Specifically for 3 storey type and weak infills, dispersion value due to record-to-record variability is 0.32 while modelling variability is 0.34.
Under the hypothesis that variables related to the sources of uncertainty are stochastically independent and lognormally distributed, the total variability is typically modelled by a square root sum-of-the-squares (SRSS) combination, as follows: where β D , β C and β DS refer to seismic input demand, structural capacity and damage level definition, respectively.
In line with the above-described approach, in the present study β D has been numerically evaluated by NLDAs performed on a suite of records described in Sect. 2.6. The other two parameters have been accounted for by adding to β D deterministic values according to Eq. 1. The values have been selected on the basis of the above-described results from literature. More specifically, in order to better emphasize the lower variability in structural capacity due to "a more engineered" design generally obtained in the case of lateral (seismic) force design compared to that for only gravity loads, β C is assumed equal to 0.25 for ERD and 0.30 for GLD. Finally, accounting for the different factors affecting the uncertainty in defining damage threshold, β DS is set equal to 0.4for all types.

Generation of fragility curves
Fragility curves express the conditional probability of experiencing or exceeding a given damage level due to a given ground motion intensity. In the past, several authors have demonstrated that the lognormal cumulative distribution function (CDF) can be a reasonable choice to estimate structural and non-structural failure. As an example, Aslani and Miranda (2005) used a Kolmogorov-Smirnov test to verify the probability of occurrence of the maximum interstory drift ratio at the first story of an existing seven-story RC building subjected to a suite of 40 earthquake ground motions with increasing intensity. The goodness-of-fit test revealed that the results lie between the limits of acceptability, thus confirming that lognormal probability distribution assumption is reasonable for this kind of structural response. The same outcome was also found by  by using collapse data related to different structural systems, both single-degree-of-freedom (SDOF) systems and generic frames. In the present study, for a given damage level, the associated fragility curve has been derived by using the dataset of PGA values corresponding to the IDR data (obtained from NLDAs, see Sect. 2.8) falling within the IDR threshold values related to the considered damage level. For this PGA dataset, both median and logarithmic standard deviation values have been calculated and then CDF function is applied as follows: where P(Dk|PGA) is the probability of exceedance of the k-th damage level (Dk) given PGA value, Φ is the standard normal (Gaussian) cumulative distribution function, D,Dk and θ Dk denote the logarithmic standard deviation and median (i.e. 50% probability of not being exceeding) values of PGA related to Dk damage level, respectively.
In Eq. 2, D,Dk accounts for only the record-to-record variability due to earthquake ground motion as obtained from NLDAs. Consequently, in order to take into account the other sources of uncertainty, Eq. 1 is applied as described in Sect. 2.9.
Damage level D5 (i.e. collapse) requires a special treatment. More specifically, two cases can occur at collapse, that are: (1) drift value exceeding the considered threshold value at the end of analysis (hereafter C1 case), and (2) very large (infinite) IDR values determining global dynamic instability or nonconvergence of analysis (hereafter C2 case). It is noted that, in the C2 case, analysis is not completed and consequently Eq. 2 could provide incorrect/unrealistic results. Therefore, in order to properly take into account results from both C1 and C2 cases, the following expression, based on the total probability theorem, can be applied: where P(D5|PGA, C 1 ) is the conditional probability of having D5 damage level given a certain PGA value due to C1 case and computed by Eq. 2; P C 2 |PGA is the probability of occurrence of C2 case which can be predicted by a logistic regression model (Jalayer et al. 2017) as a function of PGA, as follows: where α 0 and α 1 are the logistic regression parameters.
Finally, as described in Porter et al. (2007), in order to avoid that fragility curves related to two (or more than two) damage levels intersect each other, it is appropriate to assume the same dispersion value that is typically calculated averaging the results obtained for all damage levels, as reported in the following Eq. 5. Consequently, median value for each damage level needs to be also revised, according to the following Eq. 6:

Seismic fragility results: description and analysis
The methodology described at Sect. 2 has been adopted to derive fragility curves for several building types selected and designed by varying different vulnerability attributes. In such a way, a comprehensive set of fragility curves able to represent the whole Italian existing building stock has been provided to be used for seismic risk analyses.
Tables 4 and 5 report all the fragility curve parameters, i.e. median and lognormal standard deviation (β) PGA values for GLD and ERD types, respectively. The tables also show the dispersion values β D due to record-to-record variability, as obtained by averaging over the values related to all damage levels.
Further, for the sake of brevity, only fragility curves (in the range of PGA 0 ÷ 1.5 g) for GLD and ERD types with regularly infilled (IF) configuration are displayed in Figs. 7 and 8, respectively. The diagrams with the FCs related to BF and PF configurations are reported in the Appendix.
Results firstly show that dispersion values (β) are in the range 0.54-0.67, with slightly higher values for GLD types (on average 0.62) compared to ERD types (on average 0.58). As for PGA median values, D1 damage level is reached at values around the range 0.1-0.2 g, almost irrespective of the design level, while greater differences are found for higher damage levels, e.g. for D3 it was found 0.2-0.45 g for GLD types with respect to 0.3-0.65 for ERD types.
The results are reported in more detail in Sects. 3.1-3.4 where the derived FCs are analyzed by considering the selected vulnerability attributes one by one, i.e. infill arrangement (Sect. 3.1), construction period (Sect. 3.2), number of storeys (Sect. 3.3) and design level (Sect. 3.4), so that the relative role of each attribute can be singled out.

Role of infill arrangement
On the basis of the results obtained from the analyses carried out on 4 storeys building prototypes (i.e. MR types) by considering both design levels (i.e. GLD and ERD) according to the '70 s codes, in Fig. 9a PGA median values related to two damage levels (i.e. D3 and D5, representative of moderate damage and collapse, respectively) are plotted by varying the infill configuration.
As expected, the presence of regularly arranged infills contributes to the lateral capacity as shown by the higher PGA values found for IF type with respect to BF and PF ones. This better performance is more significant at lower damage levels compared to higher ones.
To this regard, for GLD type, the relative difference between IF and BF (with respect to BF) in terms of PGA values is about + 54% at D3, i.e. when infills, even though damaged, contribute to the lateral capacity, while negligible difference are found at D5, i.e. when, due to the brittle behavior of infills, their contribution becomes almost negligible.
When infills are absent at the first (ground) floor as in case of PF type, poor performance has been evaluated in particular at D5. Specifically, for GLD type, PF configuration shows a similar PGA value (0.26 g) to BF (0.24 g) at D3 while, due to the soft storey mechanism, a remarkable reduction is found at D5 (0.65 g for PF against 0.72 g for BF and 0.73 for IF).
(6) Dk = exp 1.28 Dk − Dk + ln Dk These results could imply that infills need to be (accurately) modelled when fragility analyses focus on lower damage levels or in the case of building types with irregular configuration in elevation. On the contrary, infill modelling could be neglected in the case of collapse fragility of IF types.
Although ERD types were designed with low intensity lateral forces, significant differences can be found by comparing the median values related to ERD and GLD types, for all infill configurations. For example, for IF type, PGA median values at D3 increase from 0.37 g for GLD to 0.46 for ERD (about + 24%), while, at D5, they are equal to 0.73 g and 1.00 g (about + 37%), respectively.
As for dispersion (note that β values are assumed constant for all damage levels as computed by Eq. 5), IF types show β values appreciably lower than BF and PF ones for GLD Table 4 Parameters of the fragility curves for GLD types θ Dk is the PGA median value for the k-th (k = 1,…,5) damage level, β D is the dispersion value due to only record-to-record variability, β is the dispersion value evaluated by Eq. types, while being almost constant for ERD types (Fig. 9b). Differences between GLD and ERD types are more remarkable for PF configuration. As an example, for the same type considered before (i.e. MR and '70 s period), the dispersion value for PF is 0.67 for GLD and 0.59 for ERD (about −13%).

Role of construction period
The construction period also affects vulnerability results, in particular at higher damage levels, with PGA median values increasing from '50 s to '90 s types, regardless of infill arrangement and design level. For example, based on the results obtained from the analysis of building prototypes with 4 storeys (i.e. MR types), Fig. 10a shows the PGA median values related to D3 and D5 damage levels for both GLD and ERD types with BF configuration. At D3, median values increase going from '50 s to'90 s with a relative Specifically for GLD types, results depend on the combination of two main factors, that is material quality and lateral resisting system. Indeed, as a result of gravity load design, both geometric dimensions and reinforcement details of structural members do not significantly differ, in particular for '50 s and '70 s types. Consequently, the differences observed between the younger and the older types mainly depend on the better quality of materials (both concrete and steel) adopted in the NLDAs, which increase lateral capacity in terms of both stiffness (mainly affecting D3 results) and strength (mainly affecting D5 results). In addition to the influence of material quality, the 3D resisting scheme adopted for the '90 s types further increases seismic performance with respect to the'70 s types (whose structures are frames only along one direction).
As for ERD results, in particular at D5, a decreasing trend over the periods is found with lower relative differences compared to GLD ones. To this purpose, it is worth noting that, due to the different material quality adopted in the simulated design, the relative increment of reinforcement provided by lateral force design generally decreases with the periods. As a results, although the mechanical properties of materials adopted in NLDAs increases going from '50 s to '90 s types, the above-mentioned differences in terms of amount of reinforcement have a greater influence on the relative seismic performance over the periods and also with respect to GLD types. Similar trends are found for IF types (Fig. 10c). In this case, results also depend on the different effective infill thickness, which is 28 cm for '90 s types and 20 cm for both'50 and 70 s ones. As for dispersion (Fig. 10b, d, respectively for BF and IF configurations), the same values are obtained for the different construction periods, with a slight increase in the case of GLD types compared to ERD ones (e.g. 0.60 vs 0.56 for '50 s types) and for BF compared to IF (e.g. 0.64 vs 0.60 for '50 s types).

Role of number of storeys
In general, PGA median values decrease with the number of storeys, with more significant differences going from 2-storey (LR) to 4-storey (MR) types. As reported in Fig. 11a, for IF-'70 s and GLD design level, PGA median values at D3 are 0.47 g for LR type, 0.37 g for MR type (about − 27% with respect to LR) and 0.35 g for HR type (about − 5% with respect to MR). Similar relative differences can be found at D5. These results mainly depend on the minimum design requirements provided by the structural codes. Especially for low rise buildings (i.e. 1-2 storeys), these requirements lead to an over-design of the resisting members (in particular for columns) compared to the acting vertical loads, with the surplus capacity offering a greater contribution to sustain the lateral forces compared to MR and HR types.
In the context of large-scale studies, these results suggest that building types with a number of storeys greater than four could be condensed in a unique class, thus also reducing computational time demand required for structural analyses of taller buildings.
In Fig. 11a, PGA median values obtained for ERD types are also shown. As expected, comparing GLD with ERD results, higher PGA values for the ERD types are found, with higher differences at D5 (about + 36%, almost constant for all heights). On the contrary, at D3, differences show a decreasing trend going from LR to HR types, with very low differences (about 8%) between GLD and ERD values in case of HR type.
As for dispersion (Fig. 11b), β values slightly increase with the number of storeys, with a slight increase in the case of GLD type compared to ERD.

Role of design level
As already observed, design level has a remarkable role on seismic fragility. In order to better highlight how fragility parameters vary, also accounting for period of construction, additional comparisons between GLD and ERD types in terms of PGA median values have been made. Specifically, Fig. 12 shows the comparison GLD-ERD for the MR-IF types ERD types always show higher PGA median values than GLD ones, especially in the case of more severe damage levels, while lower differences can be found at D1-D3 levels. In order to understand these results, it is worth highlighting that, in the absence of design requirements specifically devoted to preventing non-structural damage (as for ERD types considered in this study), response at the lower seismic intensities (i.e. related to D1-D3 damage levels) considerably depends on infills, whose mechanical To this purpose, as mentioned in Sects. 2.2 and 2.4, although infill thickness values increase over the years, infills are generally made up by hollow clay bricks with horizontal holes, thus exhibiting similar mechanical characteristics (e.g. compressive strength value) and, consequently, similar performance under seismic actions. When seismic intensity increases (i.e. PGA values related to D4-D5 damage levels), the infills' contribution becomes more and more negligible and, consequently, seismic performance is mainly due to the capacity of structural members, which significantly differs between GLD and ERD types.
Note that, in deriving fragility curves for ERD types, these different structural capacities have also been taken into account by adopting higher IDR threshold values compared to GLD types (see Table 3).
Results also show that the relative differences between ERD and GLD types decrease with the construction period (i.e. from '50 s to '90 s). As an example, for GLD types, PGA median values at D5 are 0.68 g, 0.73 g and 0.97 g for '50 s, '70 s and '90 s types, respectively. The corresponding values obtained for ERD types are 0.93 g (about + 37% with respect to GLD), 1.00 g (about + 37%) and 1.14 g (about + 18%). In order to explain these results, it is worth noting that, in the '90 s, the common design practice was to adopt for GLD buildings a lateral resisting system similar to that required in the case of seismic design, that is, placing frames along both orthogonal in-plane directions.

Final remarks
Fragility curves are largely used worldwide for seismic risk analyses. In Italy, different approaches have been adopted within the Work Package WP4-MARS of the 2019-2021 DPC-ReLUIS research project to update the 2018 national risk assessment.
In the present paper, a comprehensive methodology purposely set up to derive analytical FCs through nonlinear dynamic analyses and based on ten main steps, has been carefully described by highlighting the main features of each step. Special attention has been firstly devoted to the identification of the main attributes affecting the seismic vulnerability of RC buildings with moment-resisting frame (MRF) structure and to the selection/design of the building prototypes. Specifically, several prototypes have been selected to properly represent the whole Italian building stock by varying period of construction (i.e. '50 s, '70 s and 90 s), number of storeys (i.e. 2, 4 and 6 storeys representative of Low-, LR, Mid-, MR, and High-rise types, HR), arrangement of infills in elevation (i.e. Bare-, Infilled-and Pilotisframe), and finally design level (i.e. seismic, ERD, representative of "Low-code" types, or gravity load design, GLD, representative of "Pre-code" types).
Further, a relationship between the selected demand parameter (i.e. IDR, interstorey drift ratio) values and the five damage levels proposed in the EMS-98 scale has been defined by considering experimental data, with particular attention to the role of nonstructural components. Non-linear dynamic analyses have been performed by using a set of 125 signals, properly selected to be consistent with the Italian seismic hazard, to derive site-independent fragility curves for all damage levels. Finally, the obtained fragility curves 1 3 have been described and analyzed in order to highlight the role of each considered vulnerability attribute.
Results show that infill configuration in elevation and design level are the most important attributes affecting fragility curve parameters, with the former having a greater role at the lower damage levels and the latter at the higher ones. As an example, for MR-GLD type, designed according to the '70 s code, the relative difference between IF and BF (with respect to BF) in terms of PGA median value is about + 54% at D3, i.e. when infill contribution to lateral capacity is still significant, while it becomes negligible (about + 1%) at D5, i.e. when infills are generally heavily damaged and their contribution vanishes.
For the same MR-'70 s type (with IF configuration), the difference between GLD and ERD in terms of PGA median values is + 24% at D3, while it increases to + 37% at D5. In order to understand these results, it is worth noting that both GLD and ERD types have the same infill type and, furthermore, no damage prevention requirements are considered in the design of ERD types, in accordance with the design rules of that period. As a consequence, as long as infill contribution to seismic response is significant, i.e. up to D3 damage level, lower differences can be found between GLD and ERD types. On the contrary, at D5, i.e. when infill contribution becomes almost negligible, seismic response only depends on the capacity of structural members, thus showing higher differences from gravity load to "seismic" design levels.
Comparing seismic fragility over the considered construction periods, it is found that the lateral force design adopted for the ERD types has a greater impact on the older types (i.e. belonging to '50 s) compared to the more recent ones (i.e. '90 s). To this regard, it is also worth noting that, in accordance with the design practice commonly adopted in the '90 s, GLD types have the same lateral resisting system (i.e. frames along the two orthogonal inplane directions) required by codes for ERD types.
The fragility curves proposed in this paper make an important contribution to a reliable seismic risk assessment of the Italian building stock. As a matter of fact, contrarily to masonry buildings, a small amount of observed damage data is generally available for RC buildings. Therefore, the derivation of fragility curves through analytical approaches becomes almost mandatory. In such a way, additional data on the fragility of RC buildings can be obtained by analysing their seismic response, also compared to higher intensity values and to structural types widely present in the Italian building stock but missing in the existing damage databases.
Additional developments of the study can be made and are currently in progress. Particularly, the reliability of the proposed fragility curves can be further improved by comparing the results with those obtained from real seismic events in terms of expected damage at different intensities. Some useful comparisons can also be made by considering other fragility functions obtained both from prominent literature studies and within the WP4-MARS project itself. In such a way, the damage prediction capability of the fragility curves obtained from different studies and/or approaches can be comparatively evaluated, thus highlighting their inherent pros and cons and, finally, allowing their results to be beneficially combined.    *Refers to frequency-scaled signals according to the spectral matching procedure described in Manfredi et al. (2022)