Validation of physics-based ground shaking scenarios for empirical fragility studies: the case study of the 2009 L’Aquila earthquake

Validation of physics-based ground shaking scenarios for empirical fragility studies: the case study of the 2009 L’Aquila earthquake | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Validation of physics-based ground shaking scenarios for empirical fragility studies: the case study of the 2009 L’Aquila earthquake Annalisa Rosti, Chiara Smerzini, Roberto Paolucci, Andrea Penna, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1536660/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract This paper explores and validates the use of ground shaking scenarios generated via 3D physics-based numerical simulations (PBS) for seismic fragility studies. The 2009 L’Aquila seismic event is selected as case-study application, given the availability of a robust and exhaustive post-earthquake database, gathering observed seismic damages detected on several building typologies representative of the Italian built environment, and of a validated numerical model for PBS ground shaking scenarios. Empirical fragility curves are derived as a function of different seismic intensity measures, by taking advantage of an improved statistical technique, overcoming possible uncertainties in the resulting estimates entailed by data aggregation. PBS-based fragility functions are compared to the corresponding sets of curves relying on updated ShakeMaps. The predictive capability of the adopted simulation strategies is then verified in terms of seismic damage scenarios, by respectively coupling PBS- and ShakeMap-based fragility models with the corresponding ground shaking scenarios. Comparison of observed and predicted damage distributions highlights the suitability of PBS for region-specific seismic vulnerability and risk applications. Fragility curves Seismic vulnerability Physics-based ground motion simulation ShakeMap Post-earthquake damage data Damage scenarios Seismic risk Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 1 Introduction With the ever-increasing computational power, 3D physics-based numerical simulations (PBS) are becoming a more and more appealing tool to provide realistic site-specific scenarios of earthquake ground motion, in alternative to the commonly used empirical ground motion prediction equations (GMPE), based on statistical regressions from regional or worldwide records. More specifically, PBS are the key approach towards generation of urban and regional risk scenarios, as it is the case for the ShakeOut (Porter et al., 2011) and Haywired (USGS, 2017a and 2017b) experiments in California, as well as for the Scenario Earthquake Shaking Maps (available at https://www.j-shis.bosai.go.jp ) suitable for prefecture emergency plans in Japan, in order to pinpoint target areas and target facilities needing maintenance for earthquake disaster prevention. As pointed out by Hirata (2017), the predicted damage in the Kumamoto prefecture, prior to the earthquake sequence of 2016, was in good agreement with the observed one, although countermeasures were not yet made effective at the time the earthquake occurred. In spite of their exceptional interest in the context of seismic risk evaluations at urban scale (see e.g., Smerzini and Pitilakis 2018; Stupazzini et al., 2021; Riaño et al. 2021), the applicability of PBS ground motion scenarios is questioned because of their high-frequency limitations, both because of computational limits, that prevent using excessively fine numerical meshes and solve short propagation wavelengths, and because of missing details in the geological model description. To solve these issues, hybrid approaches have been proposed to couple results of low-frequency (LF) PBS with high-frequency (HF) components from stochastic or empirical Green’s functions based approaches (Irikura and Miyake, 2011). However, since the hybrid approaches have the limitation of disregarding the correlation between LF and HF portions of motion, new approaches have been devised that, based on machine learning techniques (Paolucci et al., 2018; Okazaki et al., 2021), aim at solving this issue. Recently, Paolucci et al. (2021) have published the BB-SPEEDset, a dataset including several hundreds of simulated near-source broadband accelerograms from validated case studies, that proved to have statistical properties similar to the NEar-Source Strong-motion records dataset NESS2 (Sgobba et al., 2021). Validation of PBS results for engineering applications has already found considerable attention (e.g., Galasso et al. 2013; Bijelić et al. 2018; Tsioulou and Galasso 2018; Petrone et al., 2021a;b). However, in view of the seismic risk applications mentioned previously, it is also crucial to verify whether a PBS scenario is suitable to provide not only a reliable prediction of the level of damage observed in an urban area during a historical earthquake, but also a suitable basis for calibration of empirical fragility curves when instrumental information on ground shaking is not sufficient to reliably correlate the observed level of damage to the estimated ground motion intensity. As a matter of fact, the spatial distribution of ground motion intensity is typically inferred either by ShakeMaps (Worden et al. 2020; Wald et al. 2021), in case a sufficient number of records is available, or by empirical GMPEs (Erdik 2017), as it is often the case for historical earthquake with no instrumental records. In all such cases, there is a large level of uncertainty when a ground motion level is associated with the specific site where an earthquake effect is observed. Besides, the estimated ground motion is typically available only through its peak values, without information on other parameters related to the time history itself, such as duration and frequency content. Instead, once suitably validated, the PBS ground motion scenario may provide a complete picture of the variability of the ground motion waveforms, supporting the derivation of empirical fragility curves conditioned on a wider set of intensity measures (IM), including multi-component input. Motivated by these considerations, the primary goal of this paper is to investigate and validate the use of PBS ground shaking scenarios as input description for the derivation of empirical fragility curves, with application to a well-known case study for Italy, namely, the Mw6.2, Apr 6 2009, L’Aquila earthquake. This case study is selected because of the availability, on one side, of a database of post-earthquake damage surveys with an unprecedented level of detail (Dolce et al. 2019; Rosti et al. 2021a;b), and, on the other side, of a validated numerical model for PBS ground motion scenarios (Smerzini and Villani, 2012; Evangelista et al., 2017; Di Michele et al. 2022). Within this primary objective, a secondary objective of the paper is to propose up-to-date empirical fragility curves for L’Aquila, which distinguish from already published results owing to: (i) the use of the up-to-date version of the ShakeMap for the L’Aquila earthquake (v4 of Michelini et al. 2020 with respect to v3 of Michelini et al. 2008); (ii) the use of an enhanced statistical approach, which uses the Bernoulli distribution to characterize the random component of the probability model, overcoming possible uncertainty in the resulting fragility estimates driven by data binning; (iii) the adoption of alternative seismic intensity measures for the definition of the explanatory variable of the fragility functions. This paper is organised as follows. In Sections 2 and 3 , the case study of the L’Aquila earthquake is introduced, with emphasis on the presentation of the detailed damage database used for the empirical fragility study, as well as of the ground shaking scenarios obtained by PBS through the high-performance numerical code SPEED (Mazzieri et al. 2013), as opposed to those provided by the ShakeMaps approach (Michelini et al. 2020). Then, Section 4 presents and compares two different sets of typological fragility curves, obtained on the basis of either the latest version of the ShakeMaps or the PBS of the L’Aquila earthquake. Finally, in Section 5, the total building damage observed during the L’Aquila earthquake is compared with the predictions obtained by coupling both the ShakeMaps and the PBS ground motion maps with the corresponding set of fragility curves. 2 Case Study: The 2009 L’aquila Earthquake On April 6, 2009, a Mw 6.2 earthquake hit the city of L’Aquila, one of the largest urban centers in the Abruzzo region (Central Italy) with about 70,000 inhabitants, causing 308 deaths and vast destruction in the town itself and surrounding areas. The earthquake represents one of the largest shocks in Italy since the beginning of the instrumental age, after the 1980 Mw 6.9 Irpinia, the 2016 Mw 6.5 Norcia, the 1976 Mw 6.4 Friuli earthquake. The earthquake was generated by the seismic rupture of the Paganica segment of Upper Aterno Valley - Paganica fault system consisting of four NW-SE trending normal fault segments (Galadini et al. 2018). The causative fault borders the eastern side of the Aterno River Valley, a geological depression of tectonic origin related to the extensional tectonic stresses acting in Central Italy, as depicted in Fig. 1 . Note that the L’Aquila historical center is located on the surface projection of the causative fault inside the Aterno valley, at only about 2 km from the epicenter of the earthquake, suffering therefore from the largest ground shaking owing to the close proximity to the seismic source and to the site amplification effects of the valley sediments. The post-earthquake macroseismic survey revealed a maximum intensity degree of IX-X in the Mercalli-Cancani-Sieberg (MCS) scale in the towns of Onna and Paganica, while other 14 towns and villages, including L’Aquila, reached an intensity degree between VIII and IX (Galli et al. 2009). The isoseismal lines of maximum intensity showed a pattern strongly elongated in the NW-SE direction, from the epicenter toward the southern part of the Aterno Valley. This pattern reflects the geometry and the dynamics of the fault rupture, with prevailing directivity effects in the direction SE of the epicenter (see discussion in Section 3 ). After the earthquake, a comprehensive survey campaign, coordinated by the Italian Department of Civil Protection (DPC), was carried out with the aim of collecting damage and usability information on the affected building stock. This information was then conveyed in a damage database (Rosti et al. 2018; 2020a; 2021a, b; 2022), now available in the Observed Damage Database – Da.D.O. (Dolce et al. 2019). This is a web-GIS tool, operated by the Italian DPC, collecting and archiving data on the construction and structural characteristics, as well as on seismic damage, of ordinary buildings inspected after seismic crises of national importance, from 1976 onwards. The final L’Aquila database, including only data regarding residential buildings in municipalities which were completely surveyed (with completeness ratio larger than 90%, see discussion in Rosti et al. 2021a, b), consists of about 37000 buildings, which are shown in Fig. 1 . For each inspected building, the database collects information on the geographical coordinates, the construction material (masonry or RC), the typological building classification according to Table 1 , the number of storeys (see height classification in Table 2 ), the construction age, the Damage State (DS) according to the European Macroseismic Scale EMS (Grünthal et al. 1998). Furthermore, as clarified in the following section, the database has been enriched by associating to each damaged building a value of ground motion IM coming from both the ShakeMap and the PBS computations. Referring to Rosti et al. (2018) for further details on the criteria for the attribution of the damage grade, it is important to underline herein that a global damage level is assigned to each building based on the maximum damage observed on the most damaged building component. For the objective of this study, which is to compare the effect of different approaches for the characterization of ground shaking in the empirical fragility analysis, a subset of the damage dataset, corresponding to the detailed study area in Fig. 1 encompassing the L’Aquila municipality, is considered. An area of limited extent is studied mainly because of the computational limits associated with the generation of simulated broadband time histories over a dense grid of sites covering the entire area of the SPEED model. Furthermore, the detailed study area covers the region of larger engineering interest, because of the high density of severely damaged buildings. The considered dataset, hereafter referred to as detailed dataset, counts 7987 residential buildings, 4564 (57%) of which refer to masonry, whereas 3423 (43%) are RC buildings (Fig. 2 a). Note that in Table 1 the number of buildings belonging to each typological class is specified. Figure 2 shows the spatial distribution and percentage of the different damage levels, from 0 (no damage) to 5 (collapse), for both masonry (b) and RC buildings (c). Figure 3 shows the frequency of buildings in each damage state according to the different building typological and height classes: buildings are grouped into four main classes - a) Irregular layout or poor-quality masonry, with flexible or rigid diaphragms, w/wo connecting devices (e.g. tie-rods and/or tie-beams); b) Regular layout and good-quality masonry, with flexible or rigid diaphragms, w/wo connecting devices; c) RC seismically designed, pre 1981; d) RC seismically designed, post 1981 – and the corresponding height classes are considered to compute the statistics. The histograms indicate, as expected, that passing from more vulnerable classes, such as irregular masonry buildings, to less vulnerable classes (RC post 1981), there is a decrease of the percentage of higher damage states (DS4-DS5). Furthermore, there is a positive correlation between the percentage of DS4-DS5 with the height of the building, for any building class. In the territories more distant from the earthquake source, post-earthquake surveys tend to be limited to damaged buildings, as they are carried out only upon the owners’ request. As a consequence, resulting damage distributions could be biased by an underestimated number of undamaged buildings. To counteract this issue and to suitably account for the negative evidence of damage in sites less affected by the ground shaking, the post-earthquake dataset was integrated by 197’528 non-inspected buildings, located in the non-surveyed and partially-surveyed (with completeness ratio lower than 10%) municipalities, which were reasonably assumed undamaged (e.g. Rosti et al. 2022). The number of undamaged buildings was retrieved from national building census (ISTAT 2001). Allocation of undamaged RC buildings to predefined building types was immediate, as national building census classifies buildings based on construction material, construction age and number of stories. Differently, mapping of undamaged masonry buildings, identified by census parameters, to predefined building typologies was performed via the empirical correlation between census and typological building attributes reported in Rosti et al. (2022). Table 1 Typological building classification according to Rosti et al. (2021a;b). In the first column, the percentage of buildings belonging to each class within the detailed study area are reported into brackets. Building typology Construction Material Masonry type Intermediate diaphragm Connecting Devices? Design Level IRR/F/NCD (18.5%) Masonry Irregular layout or poor-quality (IRR) Flexible (F) No (NCD) - IRR/F/CD (6.8%) Yes (CD) - IRR/R/NCD (2.5%) Rigid (R) No - IRR/R/CD (3.8%) Yes - REG/F/NCD (4.6%) Regular layout and good-quality (REG) Flexible (F) No - REG/F/CD (3.1%) Yes - REG/R/NCD (3.2%) Rigid (R) No - REG/R/CD (14.7%) Yes - RC/Seismic-Pre81 (17.7%) RC - - - Seismic-Pre 1981 RC/Seismic-Post81 (25.1%) - - Seismic-Post 1981 Table 2 Building height classes for masonry and RC buildings. Construction material Height class No. storeys Masonry L 1–2 MH >2 RC L 1–2 M 3–4 H >4 3 3d Physics-based Simulation Of L’aquila Earthquake Ground Motion A 3D physics-based numerical approach, through the spectral element code SPEED (Mazzieri et al. 2013, http://speed.mox.polimi.it/ ), is used to simulate the seismic wave propagation during the L’Aquila earthquake and, hence, to construct the ground shaking scenario for fragility analysis. The 3D spectral element model of the L’Aquila earthquake derives from previous studies (Smerzini and Villani 2012; Evangelista et al. 2017) aimed at performing the calibration and the validation of the numerical model against the available recordings. The same model presented in Evangelista et al. 2017 is used in this work, apart from some modifications to the seismic velocity profile of the outcropping bedrock layer of the crustal model, as clarified in the following. Figure 4 shows an overview of the SPEED model of the L’Aquila earthquake to highlight its main inputs. The model extends over a volume of 58 km x 58 km x 20 km (see also box in Fig. 1 ) and it is discretized using an unstructured hexahedral mesh capable of propagating frequencies up to about 2 Hz. To simulate the earthquake rupture, a kinematic finite fault model is adopted using the slip distribution proposed by Ameri et al. (2012), as documented in Evangelista et al. (2017). The seismic velocity model (see inset in Fig. 4 ), calibrated based on the available seismic microzonation data, is constructed by combing a horizontally layered crustal model and a 3D model of the Aterno River valley. With respect to Evangelista et al. (2017), where the outcropping bedrock layer consists of very hard rock with shear wave velocity V S = 1700 m/s, the updated crustal model features a first layer (see Crust 1 in Fig. 4 ) with a parabolic gradient of V S from a minimum value of 800 m/s up to a value of 1700 m/s at 1000 m depth from the topographical surface. The modified velocity profile implies a V S30 value of 900 m/s, which is more consistent with the current knowledge on the average distribution of V S30 values for the rock formations of Central Italy (Forte et al. 2019). In Fig. 4 , a representative cross-section of the velocity model (see yellow line A-A’ superimposed on the mesh), passing through the L’Aquila downtown, is also shown to highlight the complexity of the wave propagation model. Note that ground topography is also accounted for in the SPEED simulation. To overcome the frequency limit of the numerical model, the ANN2BB technique proposed by Paolucci et al. (2018) and further improved in Paolucci et al. (2021), is used to enrich the PBS signals at high frequency. The essence of this technique is the use of an Artificial Neural Network, trained on a strong-motion recorded dataset, to predict short-period spectral ordinates starting from the long-period spectral ordinates of the SPEED signal. The procedure allows for the generation of broadband ground motions which preserve the features of the SPEED signals at low frequencies and, at high frequency, provide a realistic (i.e. consistent with records) distribution of several IMs (Paolucci et al. 2021), as well as of the spatial variability (Infantino et al. 2021). The last feature is particularly relevant when generating ground shaking scenarios for seismic risk studies, because it ensures that realistic features of spatial correlation and coherency are maintained at both long and short periods. Referring the reader to the relevant publications for a thorough discussion of the features and results of the numerical model, some selected results are presented herein in relation with the main scope of this paper, which is the use of PBS ground shaking scenarios for the derivation of empirical fragility curves. For this purpose, Fig. 5 shows the map of Peak Ground Velocity (PGV) obtained from PBS (left) and from the up-to-date version (v4) of the ShakeMap according to Michelini et al. (2020) (right). The maximum horizontal component (Hmax) is shown to enable a consistent comparison between the two approaches, since ShakeMaps are released only for the Hmax component. To understand the differences between PBS and ShakeMap, it is worth recalling that the former is derived by computing the peak values directly from the waveforms simulated by SPEED on an arbitrarily dense grid of receivers, while the latter is generated by combining, through suitable geospatial interpolation algorithms, the ground motion values recorded at the available stations with the GMPEs predictions, where data are not available. Note that, for L’Aquila case study, in the area in Fig. 5 , only 6 stations (3 of which in the epicentral area) are used to adjust the field given by the GMPEs. On both maps, the MCS intensity field available in the Macroseismic Intensity Database (DBMI15, Locati et al. 2021) is superimposed. On the SPEED map, at two selected stations, namely AQK and AQV, the simulated velocity waveform is compared with the recorded one (NS and EW component, respectively). From the comparison of Fig. 5 the following remarks can be made: A good agreement is found between simulated and recorded waveforms in terms of peak values, frequency content and duration, although, at the stations of the Aterno river transect AQV-AQG-AQA (not reported herein for sake of brevity, see Evangelista et al. 2017), simulations tend to provide lower amplitudes than recorded, most likely because of inaccuracies of the source model; The simulated PGV pattern is in satisfactory agreement with the MCS intensity field: the areas of maximum PGV, which are found on the surface projection of the fault and inside the alluvial basin, correspond approximately to the sites with the highest intensity degrees. Consistently with the observed macroseismic field, the SPEED map shows a pattern oriented in the NW-SE direction with higher shaking toward SE, mainly because of the coupling of rupture propagation effects with site effects in the Aterno basin; On the other hand, the ShakeMap is excessively homogeneous, being based predominantly on median estimates from GMPEs, and it fails to predict the strong anisotropy of ground shaking in the SE direction. Instead, the largest PGV values of the ShakeMap are found in the North sector of the Aterno Valley (where the relatively high peak values recorded at the AQV-AQG-AQA array constrain the ShakeMap), in disagreement with corresponding MCS intensities of relatively modest degree (not larger than VII). Focusing on the detailed study area of Fig. 2 , relevant for the fragility analysis presented in the following sections, the comparison between PBS and ShakeMap in terms of both PGA-Hmax and PGV-Hmax appears as in Fig. 6 . To derive these maps, about 560 three-component broadband ground motion time histories are generated through the ANN2BB procedure on a regularly 500m spaced grid of receivers. Starting from the simulated waveforms, a wide set of IMs, including Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV), Peak Ground Displacement (PGD), Spectral Acceleration (SA) at different periods from 0s to 3s, Arias Intensity (I A ), Cumulative Absolute Velocity (CAV) and Housner Intensity (HI), is computed. Finally, by applying a spline spatial interpolation, it is possible to associate to each building of the detailed damage database the corresponding IM value from PBS. Note that the availability of the entire ground motion time history allows to derive a broader set of IMs: more specifically, not only the standard peak measures as used in the ShakeMap (namely, PGA, PGV and SA at 0.3 s, 1.0 s and 3.0s), but also integral measures which may offer further insights into their correlation with seismic damage. Although in this work we consider only PGA, PGV and SA, to enable a direct comparison with the standard approach based on ShakeMap, future studies will aim at evaluating the sensitivity of the fragility curves with respect to a larger set of IMs. The maps of Fig. 6 highlight further the differences in the spatial variability of ground shaking estimated by the two approaches. As shown in Paolucci et al. (2018), the PBS enriched by the ANN2BB technique at high frequencies provides a realistic spatial correlation of the peak ground motion values, with a relevant small-scale spatial variability, which reflects the physical features of the source rupture (not homogeneous across the fault plane) and of local site response characteristics. Furthermore, from a qualitative point of view, the spatial distribution of PGA shows a lower spatial correlation, as expected for short period IMs (Infantino et al. 2021). On the other hand, the ShakeMap provides a smooth pattern with limited spatial variability. To quantify these differences, Fig. 7 shows the histograms of the PGA-Hmax (left) and PGV-Hmax (right) values computed from both approaches at the building locations of the detailed damage database. It is clear that the ShakeMap values have a more limited variability than PBS: standard deviation (in log10 units) decreases from 0.14 to 0.07 for PGA and from 0.12 to 0.04 for PGV. 4 Derivation Of Fragility Curves 4.1 Statistical approach and fitting technique The derivation of fragility functions requires an appropriate statistical model and fitting technique to approximate observational data as a function of the ground motion severity. A statistical model is defined by a systematic and a random component. The systematic component, i.e. the fragility function, is the mean of the response variable (i.e. damage in this study) as a function of the explanatory variable (i.e. the selected ground motion IM). The random component instead represents the conditional probability distribution of the response variable given the explanatory one. In line with existing literature studies (e.g. Rota et al. 2008; Del Gaudio et al. 2017; Ader et al. 2020), the cumulative lognormal distribution is adopted for describing the probability of reaching or exceeding a preselected damage level, as a function of the seismic intensity measure: \({p}_{ij}=P \left(DS\ge {ds}_{i}|IM=i{m}_{j}\right)= {\Phi }\left[\frac{\text{l}\text{o}\text{g}(i{m}_{j}/{{\theta }_{ds}}_{i})}{\beta }\right]\) (1) where θ dsi is the median value of the selected intensity measure associated with damage level ds i whereas β denotes the logarithmic standard deviation. Given the availability of building-by-building data, the Bernoulli distribution (e.g. Rossetto et al. 2014; Ioannou et al. 2015) is selected for characterizing the random component of the statistical model: (2) where Y ij is the damage response given the intensity measure threshold im j , n j is equal to 1, p ij is the exceedance probability defined by Eq. (1). The term Y ij is modelled as a binary outcome taking the value of 1 if the selected damage level is sustained (i.e. DS ≥ ds i ) and 0 otherwise (i.e. DS < ds i ). The adoption of the Bernoulli distribution, which is a special case of the binomial distribution, allows for avoiding aggregation of damage data, which may introduce uncertainty in the resulting fragility estimates (e.g. Rossetto et al. 2014; Ioannou et al. 2015). Fragility functions are simultaneoulsy fitted via the maximum likelihood estimate (MLE) approach and a unique constant dispersion value ( β ) is assumed for all damage states to prevent intersecting fragility curves (e.g. Lallemant et al. 2015; Porter et al. 2021; Nguyen and Lallemant 2021; Rosti et al. 2021a, b). For each building typology, optimal parameters of the fragility model (i.e. θ dsi and β ) result from maximising the logarithm of the likelihood function: \(\left({\theta }_{dsi},\beta \right)=\text{arg}\text{m}\text{a}\text{x}[\text{log}\left(L\left({\theta }_{dsi},\beta \right)\right]=\text{arg}\text{max}\left[\text{l}\text{o}\text{g}\left(\prod _{i=1}^{nDS}\prod _{j=1}^{N}\frac{{n}_{j}!}{{y}_{ij}!\left({n}_{j}-{y}_{ij}\right)!}{{p}_{ij}}^{{y}_{ij}}{\left(1-{p}_{ij}\right)}^{\left({n}_{j}-{y}_{ij}\right)}\right)\right]\) (3) where nDS is the number of damage levels and N is the number of data points. 4.2 Fragility curves for PGA estimated from PBS and ShakeMap Taking advantage of the statistical modelling discussed in Section 4.1, empirical fragility curves are derived for a wide catalogue of building typologies. Considering its extensive use in seismic vulnerability and risk applications (e.g. da Porto et al. 2021; Dolce et al. 2021), PGA is first selected for representing the severity of the ground motion shaking. As previously commented, for consistency between the PBS- and ShakeMap-based approaches, the Hmax component is considered. To overcome the lack of PBS results outside the detailed study area, a hybrid strategy, exploiting the results from both PBS and ShakeMaps, is pursued for defining seismic input at different building locations of the damage database. Specifically, the ground shaking is locally estimated using PBS at buildings sited in the detailed study area (see Fig. 6 a), whereas the ShakeMap is used for estimating seismic input at undamaged buildings in the non-surveyed and partially-surveyed (with completeness ratio < 10%) municipalities (Section 2). Table 3 collects the parameters (i.e. median values and logarithmic standard deviation) of the typological fragility functions in terms of PGA, estimated on the basis of PBS, supplemented by ShakeMap estimates in the territories less affected by the ground shaking. Typological fragility curves fully relying on ShakeMap estimates are also derived (Table 3 ). Comparisons between sets of fragility curves resulting from PBS and those entirely based on the ShakeMap are shown in Fig. 8 , Fig. 9 , Fig. 10 . These comparisons serve as validation of the use of ground shaking scenarios from PBS to construct empirical fragility. The two sets of curves (PBS Vs ShakeMap) turn out to be consistent, although some differences are found. Specifically, PBS-derived fragility curves tend to be less conservative for masonry buildings (especially for the MH class), while a reverse trend is found for RC buildings (especially for post 1981 class). Table 3 Parameters (i.e. median and logarithmic standard deviation) of the typological fragility curves. IM: PGA from PBS and from ShakeMap IM estimation: PBS ShakeMap Building typology θ DS1 [m/s 2 ] θ DS2 [m/s 2 ] θ DS3 [m/s 2 ] θ DS4 [m/s 2 ] θ DS5 [m/s 2 ] β [-] θ DS1 [m/s 2 ] θ DS2 [m/s 2 ] θ DS3 [m/s 2 ] θ DS4 [m/s 2 ] θ DS5 [m/s 2 ] β [-] IRR/F/NCD/L 2.30 2.71 2.96 3.74 5.75 0.670 2.23 2.63 2.86 3.60 5.43 0.645 IRR/F/NCD/MH 1.57 1.95 2.27 2.95 5.37 0.723 1.51 1.86 2.15 2.75 4.85 0.697 IRR/F/CD/L 2.56 3.11 3.47 4.28 6.60 0.664 2.48 3.02 3.36 4.11 6.14 0.630 IRR/F/CD/MH 1.54 2.05 2.42 3.20 6.06 0.653 1.48 1.95 2.28 2.94 5.32 0.618 IRR/R/NCD/L 2.57 3.17 3.69 4.80 8.79 0.738 2.46 3.07 3.60 4.67 8.12 0.691 IRR/R/NCD/MH 1.69 2.23 2.79 4.14 7.55 0.654 1.60 2.11 2.61 3.74 6.29 0.604 IRR/R/CD/L 3.24 4.51 5.17 6.70 9.07 0.831 3.25 4.57 5.26 6.74 9.09 0.810 IRR/R/CD/MH 2.12 3.11 3.88 5.05 10.79 0.797 2.07 3.01 3.71 4.73 9.66 0.761 REG/F/NCD/L 4.47 6.22 7.20 10.11 19.87 0.952 4.46 6.25 7.24 10.20 19.88 0.934 REG/F/NCD/MH 2.33 3.56 4.36 6.36 11.77 0.870 2.25 3.48 4.27 6.10 11.08 0.832 REG/F/CD/L 4.31 8.12 9.17 12.17 26.70 0.802 4.34 8.08 9.08 12.00 26.82 0.795 REG/F/CD/MH 2.52 3.91 4.74 6.19 15.53 0.856 2.40 3.71 4.49 5.81 13.58 0.814 REG/R/NCD/L 4.18 5.90 7.23 10.05 14.33 0.827 4.22 5.93 7.26 10.07 14.25 0.811 REG/R/NCD/MH 2.84 4.68 5.64 8.88 12.04 0.938 2.93 4.87 5.82 9.09 12.11 0.923 REG/R/CD/L 5.31 9.23 11.77 15.11 20.35 0.867 5.38 9.26 11.61 14.89 19.71 0.833 REG/R/CD/MH 3.43 7.14 9.43 13.32 18.65 0.957 3.65 7.57 9.83 13.59 18.66 0.928 RC/Seismic-Pre81/L 3.20 4.55 6.40 9.45 17.31 0.654 3.28 4.71 6.60 9.58 17.31 0.648 RC/Seismic-Pre81/M 1.86 3.11 4.26 6.32 11.50 0.593 1.91 3.21 4.32 6.25 11.00 0.560 RC/Seismic-Pre81/H 1.34 2.31 3.50 7.91 14.56 0.650 1.29 2.17 3.21 6.93 12.32 0.603 RC/Seismic-Post81/L 3.40 6.91 10.15 16.06 24.87 0.722 3.67 7.51 10.80 16.63 24.79 0.684 RC/Seismic-Post81/M 1.86 4.23 7.17 13.03 33.40 0.827 2.23 4.89 7.65 12.44 27.85 0.711 RC/Seismic-Post81/H 1.35 2.28 4.02 9.50 19.12 0.695 1.53 2.63 4.50 9.93 18.96 0.637 4.3 Fragility curves for alternative seismic intensity measures One of the unquestionable advantages of PBS is the possibility of generating ground motion time-histories at predefined grid points, thus permitting to locally characterize the ground shaking by a broad catalog of IMs, including peak, spectral and integral intensity measures. To exploit this potentiality, empirical fragility curves are also derived for IMs alternative to PGA, namely, PGV and average spectral acceleration (SAavg), defined as average of spectral acceleration values evaluated at 0 s, 0.3 s and 1 s, suitably weighted based on the width of the associated period interval (i.e. weights equal to 0.15 for PGA, 0.5 for spectral acceleration at 0.3 s and 0.35 for spectral acceleration at 1 s). The reason of selecting PGV and SAavg among several intensity measures derives from the need of using the ShakeMaps, which are released only for PGA, PGV and SA at 0.3 s, 1 s and 3 s, for better constraining the tails of the fragility functions in the lower ground motion range. With respect to spectral intensity measures evaluated at the building fundamental period (e.g. Rossetto and Elnashai 2003), spectral ordinates averaged over a range of periods allow for accounting for the variety of structural configurations within a given building typology. Furthermore, the adoption of the average spectral acceleration accounts for period elongation associated with structural damage and higher modes contributions (e.g. Rosti et al. 2020a). Analogously to Section 4.2, the ground motion IMs, represented by PGV and SAavg, respectively, are characterized by PBS in the area close to the L’Aquila municipality and by the ShakeMap in the less affected municipalities. Based on the statistical procedure outlined in Section 4.1, sets of fragility functions are derived for each building typology, as a function of PGV (Table 4 ) and SAavg (Table 5 ). In the tables, parameters of the typological fragility functions entirely resting on ShakeMap estimates are also reported for comparison. Figure 11 shows empirically-derived fragility curves of some selected building typologies, as a function of different IMs, estimated by PBS (solid lines) and ShakeMap (dashed lines). As observed for PGA, PBS-derived fragility curves of URM building typologies are generally less conservative than the corresponding ShakeMap-based ones. Difference between sets of PBS- and ShakeMap-based fragility functions is more significant when PGV and SAavg are considered (Fig. 11 ). PBS-based fragility curves of RC buildings seismically designed after 1981 are slightly more conservative in the lower ground motion range than the corresponding ShakeMap-based ones. For a given IM, the overall trend of PBS- and ShakeMap-derived fragility functions is nevertheless very similar, suggesting a general consistency among resulting fragility curves. Table 4 Parameters (i.e. median and logarithmic standard deviation) of the typological fragility curves. IM: PGV from PBS and from ShakeMap IM estimation: PBS ShakeMap Building typology θ DS1 [m/s] θ DS2 [m/s] θ DS3 [m/s] θ DS4 [m/s] θ DS5 [m/s] β [-] θ DS1 [m/s] θ DS2 [m/s] θ DS3 [m/s] θ DS4 [m/s] θ DS5 [m/s] β [-] IRR/F/NCD/L 0.230 0.266 0.287 0.353 0.520 0.614 0.214 0.246 0.265 0.322 0.460 0.573 IRR/F/NCD/MH 0.166 0.200 0.227 0.286 0.492 0.661 0.153 0.183 0.207 0.255 0.420 0.618 IRR/F/CD/L 0.250 0.297 0.328 0.396 0.587 0.594 0.232 0.275 0.301 0.358 0.507 0.547 IRR/F/CD/MH 0.159 0.207 0.240 0.308 0.539 0.571 0.148 0.189 0.217 0.271 0.451 0.530 IRR/R/NCD/L 0.254 0.306 0.350 0.443 0.755 0.666 0.234 0.282 0.323 0.405 0.655 0.610 IRR/R/NCD/MH 0.179 0.228 0.280 0.402 0.689 0.606 0.161 0.203 0.245 0.337 0.533 0.533 IRR/R/CD/L 0.312 0.415 0.465 0.582 0.761 0.749 0.296 0.395 0.444 0.548 0.708 0.706 IRR/R/CD/MH 0.209 0.294 0.358 0.452 0.874 0.689 0.199 0.274 0.328 0.404 0.746 0.653 REG/F/NCD/L 0.442 0.592 0.673 0.914 1.705 0.881 0.398 0.530 0.599 0.803 1.437 0.826 REG/F/NCD/MH 0.239 0.345 0.414 0.583 1.030 0.791 0.215 0.311 0.371 0.505 0.848 0.723 REG/F/CD/L 0.413 0.730 0.816 1.067 2.161 0.738 0.371 0.630 0.696 0.882 1.717 0.676 REG/F/CD/MH 0.253 0.373 0.445 0.564 1.275 0.758 0.226 0.327 0.386 0.479 0.988 0.694 REG/R/NCD/L 0.405 0.547 0.655 0.875 1.217 0.757 0.366 0.488 0.579 0.762 1.027 0.696 REG/R/NCD/MH 0.284 0.441 0.519 0.776 1.018 0.844 0.268 0.414 0.482 0.705 0.902 0.797 REG/R/CD/L 0.493 0.804 0.996 1.252 1.632 0.782 0.443 0.698 0.844 1.041 1.314 0.703 REG/R/CD/MH 0.335 0.632 0.809 1.098 1.489 0.869 0.320 0.592 0.738 0.970 1.268 0.788 RC/Seismic-Pre81/L 0.312 0.427 0.578 0.832 1.476 0.608 0.291 0.394 0.524 0.719 1.187 0.551 RC/Seismic-Pre81/M 0.187 0.292 0.387 0.556 0.993 0.559 0.184 0.286 0.366 0.499 0.801 0.471 RC/Seismic-Pre81/H 0.136 0.220 0.322 0.684 1.234 0.606 0.131 0.207 0.289 0.564 0.932 0.528 RC/Seismic-Post81/L 0.336 0.630 0.895 1.380 2.035 0.671 0.317 0.575 0.780 1.116 1.554 0.574 RC/Seismic-Post81/M 0.190 0.393 0.620 1.042 2.412 0.735 0.208 0.401 0.581 0.869 1.684 0.594 RC/Seismic-Post81/H 0.134 0.212 0.357 0.816 1.618 0.675 0.151 0.237 0.373 0.735 1.277 0.552 Table 5 Parameters (i.e. median and logarithmic standard deviation) of the typological fragility curves. IM: SAavg from PBS and from ShakeMap IM estimation: PBS ShakeMap Building typology θ DS1 [m/s 2 ] θ DS2 [m/s 2 ] θ DS3 [m/s 2 ] θ DS4 [m/s 2 ] θ DS5 [m/s 2 ] β [-] θ DS1 [m/s 2 ] θ DS2 [m/s 2 ] θ DS3 [m/s 2 ] θ DS4 [m/s 2 ] θ DS5 [m/s 2 ] β [-] IRR/F/NCD/L 3.71 4.34 4.71 5.87 8.90 0.644 3.50 4.08 4.42 5.48 8.06 0.601 IRR/F/NCD/MH 2.61 3.18 3.66 4.67 8.25 0.687 2.45 2.97 3.40 4.28 7.25 0.647 IRR/F/CD/L 4.14 4.97 5.52 6.75 10.25 0.646 3.87 4.65 5.14 6.21 9.04 0.585 IRR/F/CD/MH 2.53 3.28 3.82 4.98 9.13 0.620 2.40 3.11 3.60 4.57 7.91 0.570 IRR/R/NCD/L 4.05 4.94 5.69 7.32 13.02 0.696 3.84 4.73 5.48 7.00 11.74 0.645 IRR/R/NCD/MH 2.80 3.61 4.45 6.46 11.50 0.632 2.59 3.35 4.09 5.73 9.32 0.563 IRR/R/CD/L 5.13 6.99 7.96 10.15 13.60 0.792 4.95 6.81 7.75 9.78 12.93 0.751 IRR/R/CD/MH 3.45 4.90 6.04 7.75 16.03 0.768 3.28 4.65 5.65 7.09 13.72 0.704 REG/F/NCD/L 7.06 9.63 11.07 15.27 29.03 0.912 6.68 9.16 10.49 14.46 26.95 0.870 REG/F/NCD/MH 3.85 5.71 6.91 9.90 17.80 0.839 3.55 5.31 6.44 8.97 15.60 0.771 REG/F/CD/L 6.95 12.88 14.60 19.25 41.50 0.784 6.51 11.63 12.97 16.82 35.20 0.738 REG/F/CD/MH 4.00 6.02 7.22 9.32 22.66 0.806 3.78 5.68 6.79 8.61 18.96 0.757 REG/R/NCD/L 6.69 9.27 11.23 15.41 21.69 0.808 6.35 8.74 10.54 14.29 19.77 0.756 REG/R/NCD/MH 4.53 7.29 8.72 13.48 17.96 0.881 4.54 7.27 8.58 12.96 16.90 0.855 REG/R/CD/L 8.50 14.47 18.38 23.49 31.59 0.852 7.94 13.16 16.23 20.45 26.50 0.772 REG/R/CD/MH 5.56 11.18 14.62 20.45 28.38 0.930 5.57 10.94 13.93 18.78 25.19 0.858 RC/Seismic-Pre81/L 5.09 7.20 10.13 15.10 26.80 0.633 4.95 6.95 9.54 13.51 23.34 0.600 RC/Seismic-Pre81/M 3.06 5.05 6.95 10.38 19.32 0.609 3.02 4.93 6.49 9.12 15.36 0.519 RC/Seismic-Pre81/H 2.22 3.73 5.69 13.20 24.81 0.670 2.11 3.45 4.96 10.13 17.26 0.562 RC/Seismic-Post81/L 5.48 10.94 15.97 25.43 39.27 0.710 5.55 10.82 15.14 22.56 32.57 0.634 RC/Seismic-Post81/M 3.06 6.85 11.63 21.15 54.24 0.829 3.53 7.28 10.95 17.05 35.42 0.651 RC/Seismic-Post81/H 2.27 3.85 6.94 17.16 35.47 0.731 2.47 4.08 6.70 13.90 25.19 0.591 5 Validation Against Observed Damage Ground shaking scenarios from PBS and ShakeMap are respectively coupled with the corresponding fragility models for PGA, to verify their predictive capability in the context of seismic risk assessment. Referring to the detailed study area, building-by-building seismic scenarios are simulated in terms of physical damage. The availability of building-by-building data allows for a punctual definition of both seismic input and damage, avoiding the uncertainty driven by aggregated models (e.g. Nievas et al. 2022). The physics-based ground motion scenario in terms of PGA is combined with the fragility model resulting from the hybrid strategy (PBS + ShakeMap). The ShakeMap ground shaking scenario (Michelini et al. 2020) is instead coupled with fragility functions fully resting on ShakeMap ground motion estimates. Figure 12 shows the spatial distribution of damage to buildings sited in the detailed study area (Fig. 12 a) and in the L’Aquila historical centre (Fig. 12 b), resulting from the joint use of ground shaking scenarios and consistent fragility models. Results are displayed in terms of probability of exceedance of preselected damage levels (i.e. DS1, DS3 and DS4), evaluated at the building level. In the figure, bar plots represent the frequency distribution of the exceedance probability values of each damage level. Bar colours correspond to the exceedance probability ranges of the discretization adopted in the legend. For each building, a synthetic representation of damage (e.g. Dolce et al. 2003; Lagomarsino and Giovinazzi 2006; Rosti et al 2020b) is also provided in terms of mean damage ( µ D ), defined as weighted average of the expected probabilities of occurrence ( p k ) of the different damage levels ( DS k ): \({\mu }_{D}= \sum _{k=0}^{5}k{p}_{k}\) (4) Figure 13 shows the spatial and frequency distribution of mean damage in the study area and in the L’Aquila historical centre, resulting from the adopted simulation strategies. Besides contributing to the development of empirical fragility models, post-earthquake damage data (e.g. Dolce et al. 2019) are a unique opportunity for testing the adequacy of seismic vulnerability and risk models for territorial applications (e.g. Smerzini and Pitilakis 2018; da Porto et al. 2021; Riga et al. 2021). In this study, the accuracy of the adopted simulation procedures to reproduce the observed seismic damage is globally assessed in terms of damage distribution within the detailed study area (Fig. 14 ). In the figure, predicted global damage distributions for masonry, RC and all buildings (without distinction of the construction material) are compared to the observed ones. Predicted damage distributions are obtained by using PBS and ShakeMap ground motion scenarios, respectively, with consistent fragility models. In Fig. 15 , damage predictions are directly plotted against observations, highlighting possible overestimation or underestimation of the adopted simulation strategies with respect to each level of damage. Results show that both the adopted simulation procedures generally well reproduce the observed seismic damage in the detailed study area. Both procedures tend to slightly overestimate null damage (DS0) to the detriment of slight damage (DS1). Nevertheless, predictions are aligned with observations for all levels of damage from DS2 to DS5, indicating the general fitness of both procedures to reproduce observed seismic damage. Comparison between observed and predicted damage distributions is also detailed for each building typology (Fig. 16 ). In line with previous considerations, both simulation procedures allow to well reproduce the frequency of occurrence of damage levels from DS2 to DS5, which provide higher contribution to consequences estimation (e.g. da Porto et al. 2021). Slight damage is instead slightly underestimated in favour of null damage. This last finding can be explained by the need of constraining the tails of the fragility functions in the lower ground motion range, allowing for reliable seismic risk estimates (e.g. Rosti et al. 2021a, b; 2022). 6 Conclusions This work validates the use of ground shaking scenarios obtained by 3D PBS as a basis to constrain the intensity measures for empirical fragility analyses from past earthquakes. The selected case study is the 2009 L’Aquila earthquake, for which a comprehensive database of post-earthquake damage observations is available, together with relatively detailed ShakeMaps, constrained by few accelerometric records, to be used as a verification benchmark. In addition, a 3D numerical model, validated on the recordings of the event, is available encompassing a finite-fault kinematic source model as well as a detailed source-to-site wave propagation model embedding the topography of the region and the Aterno valley (Evangelista et al. 2017). To the authors’ knowledge, this work represents the first attempt to test the capability of the 3D physics-based numerical approach, which has attracted considerable research efforts in the last years, to provide region-specific ground shaking scenarios, to be used as input for the calibration of empirical fragility curves, as opposed to standard approaches relying on ShakeMaps or GMPEs. A novel set of fragility curves is empirically-derived by statistical processing of the L’Aquila post-earthquake damage database for several masonry and RC building typologies representative of the Italian building stock. The use of an improved statistical technique, relying on the Bernoulli distribution for modelling the random component of the statistical model and assuming a constant dispersion value for all damage states, allows for overcoming possible uncertainties in the resulting fragility estimates driven by data aggregation and for ensuring the ordinal nature of damage. Fragility curves are calibrated by characterizing the ground motion intensity at the buildings located within the L’Aquila municipality, i.e. the area severely affected by the earthquake, using the broadband shaking scenarios from the PBS. The ground motion IMs selected for the fragility analysis include PGA, which is the reference ground motion intensity measure used in the Italian national platform for seismic risk assessment (Borzi et al. 2021), as well as less standard intensity measures, such as PGV and SAavg (weighted average spectral acceleration in the range 0-1s). The fragility curves obtained from the PBS are compared for each building typology with the ones obtained, through the same statistical approach, using the latest version of the ShakeMap (v4), released by the National Institute of Geophysics and Volcanology of Italy. This comparison serves as a first validation of the use of physics-based ground motion scenario for empirical fragility studies, as it highlights that the two sets of fragility curves are in very good agreement, without any systematic biases. Finally, the two sets of fragility models, from PBS and ShakeMap, are coupled with the corresponding ground shaking scenarios to check the consistency of the predicted damage levels building-by-building and of their spatial distribution in the L’Aquila municipality area, with respect to the observed ones. Results point out that both approaches for ground shaking estimation well reproduce the observed distribution of damage among the different classes, especially for damage states from DS2 to DS5, which are expected to contribute the most to the loss estimation. Instead, slight discrepancies are found for lower damage states (DS0 and DS1). Besides having provided a novel validated set of empirical fragility curves for different common building typologies in Italy, this study sheds light on potential advantages of simulation-based seismic shaking scenarios for empirical fragility studies, particularly when strong-motion recordings are insufficient, or not available at all, to derive reliable shaking maps, as for historical earthquakes. More specifically, this work highlights the following main advantages related to the application of PBS to the problem at hand: PBS are suitable to provide ground shaking scenarios with a realistic spatial correlation, reflecting the specificity of the regional seismic wave propagation features (e.g. alluvial basins, topography) as well as of the seismic fault rupture. Figure 6 and Fig. 7 clearly demonstrate the capability of the PBS approach in providing a ground shaking scenario which, on the one hand, is more consistent with the observed macroseismic pattern owing to the coupling of rupture propagation effects with local site response, and, on the other hand, is characterized by a sound spatial correlation structure. The latter is typically neglected by standard approaches for ground motion characterization, although it may affect results in the lower and upper intensity measure range (Rosti et al. 2020a). Contrary to standard empirical models, from a 3D PBS the entire ground motion time history is available for any building site. This means that a wider portfolio of ground motion IMs can be computed, including not only peak values, as conventionally adopted in ShakeMaps (PGA, PGA and SA), but also integral measures (CAV, HI, I A ), which reflect in greater detail the variability of seismic shaking in amplitude, frequency and duration. It is, in fact, recognized that non-conventional or vector-valued ground motion intensity measures may improve the correlation with damage observations (e.g. Gehl et al. 2013; Masi et al. 2020). The sensitivity of fragility curves with respect to other intensity measures will be the subject of future studies. PBS may provide the opportunity for fully site-specific deterministic seismic damage/risk scenarios, where the simulated seismic input is used for calibrating consistent specific fragility models. Declarations Acknowledgements This work has been carried out in the framework of the 2019-2021 and 2022-2023 DPC-ReLUIS Project WP4 “MARS – Seismic Risk Maps” funded by the Italian Civil Protection Department. The authors would like to acknowledge Guido Corti for his support in the initial stage of this work. Funding The work has been funded by the Italian Department of Civil Protection under the 2019-2021 and 2022-2023 DPC-ReLUIS Project WP4 “MARS – Seismic Risk Maps”. Competing interests The authors declare that they have no competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data Availability The L’Aquila damage dataset is available in the Da.D.O. platform at http://egeos.eucentre.it/danno_osservato/web/danno_osservato?lang=EN. The SPEED code is available at http://speed.mox.polimi.it. The datasets generated during the current study are available from the corresponding author on reasonable request. 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Istituto Nazionale di Geofisica e Vulcanologia (INGV). https://doi.org/10.13127/DBMI/DBMI15.3 Masi, A., Chiauzzi, L., Nicodemo, G., Manfredi, V. (2020) Correlations between macroseismic intensity estimations and ground motion measures of seismic events. Bull Earthquake Eng 18, 1899–1932 (2020). https://doi.org/10.1007/s10518-019-00782-2 Mazzieri I, Stupazzini M, Guidotti R, Smerzini C (2013) SPEED: SPectral Elements in Elastodynamics with Discontinuous Galerkin: a non-conforming approach for 3D multi-scale problems, Int J Numer Meth Eng 95, no. 12, 991–1010 Michelini A, Faenza L, Lauciani V, Malagnini L (2008) Shakemap Implementation in Italy. Seismol Research Letters. 79 (5): 688–697. doi: https://doi.org/10.1785/gssrl.79.5.688 Michelini A, Faenza L, Lanzano G, Lauciani V, Jozinovic D, Puglia R, Luzi L (2020) The New ShakeMap in Italy: Progress and Advances in the Last 10 Yr. Seismol Research Letters, 91(1): 317-333. Nievas CI, Pilz M, Prehn K, Schorlemmer D, Weatherill G, Cotton F (2022) Calculating earthquake damage building by building: the case of the city of Cologne, Germany. Bull Earthq Eng, 20: 1519-1565. Nguyen M, Lallemant D (2021) Order matters: the benefits of ordinal fragility curves for damage and loss estimation. Risk Analysis, DOI: 10.1111/risa.13815. Okazaki T, Hachiya H, Iwaki A, Maeda T, Fujiwara H, Ueda N (2021). Simulation of broad-band ground motions with consistent long-period and short-period components using the Wasserstein interpolation of acceleration envelopes. Geophysical Journal International, 227: 333–349. Paolucci R, Gatti F, Infantino M, Smerzini C, Ozcebe AG, Stupazzini M (2018). Broadband Ground Motions from 3D Physics-Based Numerical Simulations Using Artificial Neural Networks, Bull. Seism. Soc. Am., 108(3A): 1272–1286. Paolucci R, Smerzini C, Vanini M (2021). BB-SPEEDset: A Validated Dataset of Broadband Near-Source Earthquake Ground Motions from 3D Physics-Based Numerical Simulations, Bull. Seism. Soc. Am., 111(5): 2527-2545. Petrone F, Abrahamson N, McCallen D, Miah M (2021a). Validation of (not-historical) large-event near-fault ground-motion simulations for use in civil engineering applications, Earthquake Engng Struct Dyn. 50:116–134. Petrone F, Abrahamson N, McCallen D, Pitarka A, Rodgers A (2021b) Engineering evaluation of the EQSIM simulated ground-motion database: The San Francisco Bay Area region, Earthquake Engng Struct Dyn. 50(15): 3939 – 3961. Porter K, Jones L, Cox D, Goltz J, Hudnut K, Mileti D, Perry S, Ponti D, Reichle M, Rose AZ, Scawthorn CR, Seligson HA, Shoaf KI, Treiman J, Wein A (2011). The ShakeOut Scenario: A Hypothetical Mw7.8 Earthquake on the Southern San Andreas Fault. Earthquake Spectra 27(2): 239-261. Porter K (2021). A Beginner’s Guide to Fragility, Vulnerability, and Risk. University of Colorado Boulder, 139 pp., http://www.sparisk.com/pubs/Porter-beginners-guide.pdf. Riaño AC, Reyes JC, Yamín LE, Bielak J, Taborda R, Restrepo D (2021) Integration of 3D large-scale earthquake simulations into the assessment of the seismic risk of Bogota, Colombia, Earthquake Engng Struct Dyn; 50(1): 155– 176, https://doi.org/10.1002/eqe.3373 Riga E, Karatzetzou A, Apostolaki S, Crowley H, Pitilakis K (2021) Verification of seismic risk models using observed damages from past earthquake events. Bull Earthq Eng, 19: 713-744. Rossetto T, Elnashai A (2003) Derivation of vulnerability functions for European-type RC structures based on observational data. Eng Struct, 25(10):1241–63. Rossetto T, Ioannou I, Grant DN, Maqsood T (2014) Guidelines for the empirical vulnerability assessment, GEM Techincal Report 2014-X, GEM Foundation, Pavia. Rosti A, Rota M, Penna A (2018) Damage classification and derivation of damage probability matrices from L’Aquila (2009) post-earthquake survey data. Bull Earthquake Eng, 16: 3687–3720 https://doi.org/10.1007/s10518-018-0352-6 Rosti A, Rota M, Penna A (2020a) Influence of seismic input characterisation on empirical damage probability matrices for the 2009 L’Aquila event. Soil Dyn Earthq Eng, 128, https://doi.org/10.1016/j.soildyn.2019.105870. Rosti A, Del Gaudio C, Di Ludovico M, Magenes G, Penna A, Polese M, Prota A, Ricci P, Rota M, Verderame GM (2020b) Empirical vulnerability curves for Italian residential buildings. Boll Geofis Teor Appl, 61(3): 357-374. Rosti A, Rota M, Penna A (2021a) Empirical fragility curves for Italian URM buildings. Bull Earthq Eng, 19: 3057-3076. Rosti A, Del Gaudio C, Rota M, Ricci P, Di Ludovico M, Penna A, Verderame GM (2021b) Empirical fragility curves for Italian residential RC buildings. Bull Earthq Eng, 19: 3165-3183. Rosti A, Rota M, Penna A (2022) An empirical seismic vulnerability model. Bull Earthq Eng, https://doi.org/10.1007/s10518-022-01374-3. Rota M, Penna A, Strobbia CL (2008) Processing Italian damage data to derive typological fragility curves. Soil Dyn Earthq Eng, 28(10): 933-947. Sgobba S, Felicetta C, Lanzano G, Ramadan F, D’Amico M, Pacor F (2021). NESS2.0: An Updated Version of the Worldwide Dataset for Calibrating and Adjusting Ground‐Motion Models in Near Source, Bull. Seism. Soc. Am., 111(5): 2358–2378. Smerzini C, Villani M (2012) Broadband numerical simulations in complex near-field geological configurations: the case of the 2009 Mw6.3 L’Aquila earthquake, Bull. Seism. Soc. Am., 102(6): 2436-2451. Smerzini C, Pitilakis K. (2018) Seismic risk assessment at urban scale from 3D physics-based numerical modeling: the case of Thessaloniki, Bull. Earthq Eng, 16(7): 2609-2631. Stupazzini M, Infantino M, Allmann A, Paolucci R (2021) Physics-based probabilistic seismic hazard and loss assessment in large urban areas: a simplified application to Istanbul. Earthquake Engng Struct Dyn. 50: 99-115. Tsioulou A, Galasso C (2018) Information theory measures for the engineering validation of ground-motion simulations. Earthquake Engng Struct Dyn. 47: 1095–1104. https://doi.org/10.1002/eqe.3015 USGS (2017a) The HayWired Earthquake Scenario—Earthquake Hazards. Scientific Investigations Report 2017–5013–A–H. USGS (2017b) The HayWired Earthquake Scenario—Engineering Implications. Scientific Investigations Report 2017–5013–I–Q. Wald DJ, Worden CB, Thompson EM, Hearne M. (2021) ShakeMap operations, policies, and procedures. Earthquake Spectra, doi:10.1177/87552930211030298 Worden CB, Thompson EM, Hearne M and Wald DJ (2020) ShakeMap Manual Online: Technical Manual, User’s Guide, and Software Guide. DOI: 10.5066/F7D21VPQ Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 23 May, 2022 Reviews received at journal 11 Apr, 2022 Reviewers invited by journal 09 Apr, 2022 Editor assigned by journal 08 Apr, 2022 First submitted to journal 08 Apr, 2022 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-1536660","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":97335040,"identity":"258f0f3e-bcc4-4d92-8270-8c8ae0c84e18","order_by":0,"name":"Annalisa Rosti","email":"","orcid":"","institution":"University of Pavia: Universita degli Studi di Pavia","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Annalisa","middleName":"","lastName":"Rosti","suffix":""},{"id":97335041,"identity":"061143a4-df22-4942-97a2-fb5c5a1a696b","order_by":1,"name":"Chiara Smerzini","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+ElEQVRIiWNgGAWjYDACCcYGBCeBQUKOgYG54QCDAQMP0VqMGRgYIVpw6pFA4yc2MEANwaWFf3Zz4+eKGgZ73fbexx8e7rBI387e2HjoRgGDjD0uS+4cbJY8c4whcduZ4wYGiWckcnf2HGw4nIPHYQYSiQ2SDWwMCWY30hgSEtskcjfcSCSopflnwz8Ge7P7zxgOALWkGxChpU2ysY2BcdsNNsYGoJYEglokbiS2WTb2SQD9ksbMANRiCPWLBA/PARwhNiP98c2Gbzb2ZsePMX/82VYnb87efPhzzh8be/YGHNZALUNyKoYIQWBAgtpRMApGwSgYGQAASjhZOTUT1QwAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0003-4357-6934","institution":"Politecnico di Milano","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Chiara","middleName":"","lastName":"Smerzini","suffix":""},{"id":97335042,"identity":"86eb16cf-0748-44ca-aac0-9213d0375716","order_by":2,"name":"Roberto Paolucci","email":"","orcid":"","institution":"Politecnico di Milano","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Roberto","middleName":"","lastName":"Paolucci","suffix":""},{"id":97335043,"identity":"38570967-2e29-4d81-be17-57f345586633","order_by":3,"name":"Andrea Penna","email":"","orcid":"","institution":"University of Pavia: Universita degli Studi di Pavia","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Andrea","middleName":"","lastName":"Penna","suffix":""},{"id":97335044,"identity":"01a33657-2b7c-4ce0-8be5-6110b63f9e68","order_by":4,"name":"Maria Rota","email":"","orcid":"","institution":"Eucentre","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Maria","middleName":"","lastName":"Rota","suffix":""}],"badges":[],"createdAt":"2022-04-08 09:48:54","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1536660/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1536660/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":20250661,"identity":"cbf66c7c-5fbf-473b-8497-6155fd49c80d","added_by":"auto","created_at":"2022-04-12 14:41:29","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":901439,"visible":true,"origin":"","legend":"\u003cp\u003eOverview of the case study: epicenter and fault of the 2009 L’Aquila earthquake, shape of the Aterno river valley, surveyed buildings, size of the SPEED model and of the detailed study area. \u0026nbsp;\u003c/p\u003e","description":"","filename":"fig1.png","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/6c68f7dfc07a611ea1801047.png"},{"id":20251698,"identity":"6a6a357c-b29e-4e3d-9a97-29f0ec5f2949","added_by":"auto","created_at":"2022-04-12 14:46:29","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1218264,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Detailed building dataset with identification of the construction material; distribution of damage levels in the masonry (b) and RC (c) buildings of the dataset.\u0026nbsp;\u003c/p\u003e","description":"","filename":"fig2.png","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/cbf38d67354e7afbfb36b5e3.png"},{"id":20252217,"identity":"392c10a0-7908-41f3-9441-9f04e1160976","added_by":"auto","created_at":"2022-04-12 14:51:29","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":72681,"visible":true,"origin":"","legend":"\u003cp\u003eStatistics of the building dataset: damage distribution for masonry buildings – (a) irregular, (b) regular – and RC buildings – (c) Pre-1981, (b) Post-1981 seismic design – for the different height classes.\u0026nbsp;\u003c/p\u003e","description":"","filename":"fig3.png","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/ebd8fe770837faa95c81c9d7.png"},{"id":20250656,"identity":"4b4f7ad1-ac8c-4782-af46-68d2e6f795dc","added_by":"auto","created_at":"2022-04-12 14:41:29","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":449583,"visible":true,"origin":"","legend":"\u003cp\u003e3D numerical model for the L’Aquila earthquake.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"fig4.png","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/92a83b58010413011ef32145.png"},{"id":20250658,"identity":"4ad14c22-831e-4145-8aae-657942d64a34","added_by":"auto","created_at":"2022-04-12 14:41:29","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":268438,"visible":true,"origin":"","legend":"\u003cp\u003eMaximum of horizontal components (Hmax) of Peak Ground Velocity (PGV) from PBS (left) and from ShakeMap (right) in comparison with the macroseismic MCS intensity field (from DBMI15 v3.0). On the PBS map, the broadband simulated and recorded velocity time histories at stations AQK (NS component) and AQV (EW component) are shown. The superimposed triangles denote the available strong-motion recordings used for the generation of the ShakeMap.\u0026nbsp;\u003c/p\u003e","description":"","filename":"fig5.png","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/cd2c04d3d56b4c4d0501d851.png"},{"id":20252755,"identity":"f7e7e176-d300-4baa-9c2d-3e712c7255ee","added_by":"auto","created_at":"2022-04-12 14:56:29","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":245787,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of PGA-Hmax (a) and PGV-Hmax (b) maps from PBS (left) and from ShakeMap (right) within the detailed study area. The thick contour denotes the location of the L’Aquila historical center.\u0026nbsp;\u003c/p\u003e","description":"","filename":"fig6.png","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/11946b19a7340ed9790f2171.png"},{"id":20250662,"identity":"9ae5abc5-a480-4b5e-ac12-df1ebc00abcc","added_by":"auto","created_at":"2022-04-12 14:41:30","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":52368,"visible":true,"origin":"","legend":"\u003cp\u003eHistograms of PGA-Hmax (left) and PGV-Hmax (right) values at the building locations in the detailed study area from SPEED (red) and ShakeMap (green).\u0026nbsp;\u003c/p\u003e","description":"","filename":"fig7.png","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/59785ab24c717cba3c43b1bb.png"},{"id":20252756,"identity":"0f87346f-9165-4267-9041-acc394ed4719","added_by":"auto","created_at":"2022-04-12 14:56:30","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":96415,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of empirically-derived fragility curves of low-rise masonry building typologies. IM: PGA estimated from PBS (solid lines) and by ShakeMap (dashed lines)\u0026nbsp;\u003c/p\u003e","description":"","filename":"fig8.png","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/44ba057ddd31597c214aae1c.png"},{"id":20251705,"identity":"01afa3dd-e848-4409-b05f-e723d129585f","added_by":"auto","created_at":"2022-04-12 14:46:30","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":103890,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of empirically-derived fragility curves of mid-/high-rise masonry building typologies. IM: PGA estimated from PBS (solid lines) and by ShakeMap (dashed lines)\u003c/p\u003e","description":"","filename":"fig9.png","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/e70234a00884ec8a07088eb7.png"},{"id":20250668,"identity":"8cad3d14-5737-448c-a439-5031e3a5f301","added_by":"auto","created_at":"2022-04-12 14:41:30","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":69245,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of empirically-derived fragility curves of RC building typologies. IM: PGA estimated from PBS (solid lines) and by ShakeMap (dashed lines)\u003c/p\u003e","description":"","filename":"fig10.png","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/08cf23a564076f3002770b3e.png"},{"id":20252758,"identity":"7a2a0972-c3fa-46ed-8ec7-a23009390ec6","added_by":"auto","created_at":"2022-04-12 14:56:30","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":97780,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of empirically-derived fragility curves of selected building typologies as a function of different IMs, estimated from PBS (solid lines) and by ShakeMap (dashed lines)\u003c/p\u003e","description":"","filename":"fig11.png","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/7455e7bfba58027c35a74bfc.png"},{"id":20251704,"identity":"aa305579-18bb-4b99-853d-4aa99f53d657","added_by":"auto","created_at":"2022-04-12 14:46:30","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":632916,"visible":true,"origin":"","legend":"\u003cp\u003eExpected probability of exceedance of preselected damage levels: study area (a) and L’Aquila historical centre (b).\u003c/p\u003e","description":"","filename":"fig12.png","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/b6f5897b931854eb69e8b35a.png"},{"id":20250671,"identity":"3456ee79-ce72-46eb-90d9-41d35fc122f9","added_by":"auto","created_at":"2022-04-12 14:41:30","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":384865,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of mean damage predictions obtained from the two alternative simulation procedures: study area and L’Aquila historical centre.\u0026nbsp;\u003c/p\u003e","description":"","filename":"fig13.png","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/2ced0671dde724e21851ff8a.png"},{"id":20251701,"identity":"473aca04-8528-4234-a205-f638171c3e36","added_by":"auto","created_at":"2022-04-12 14:46:30","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":35941,"visible":true,"origin":"","legend":"\u003cp\u003eObserved and predicted global damage distributions for masonry, RC and all buildings in the detailed study area.\u0026nbsp;\u003c/p\u003e","description":"","filename":"fig14.png","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/daa172489e023598e181452f.png"},{"id":20252219,"identity":"30c6e862-ca3e-41fc-be4b-e78c8ef800c7","added_by":"auto","created_at":"2022-04-12 14:51:30","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":40467,"visible":true,"origin":"","legend":"\u003cp\u003e Predicted versus observed frequency of occurrence of damage levels along with the 1-to-1 line: masonry, RC and all buildings in the detailed study area.\u003c/p\u003e","description":"","filename":"fig15.png","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/8e75c2a2acc64de5ba007d9b.png"},{"id":20250665,"identity":"f6a2d7c2-d962-4395-9da3-166ced389ec4","added_by":"auto","created_at":"2022-04-12 14:41:30","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":125147,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of observed and predicted damage distributions for masonry and RC building typologies.\u0026nbsp;\u0026nbsp;\u003c/p\u003e","description":"","filename":"fig16.png","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/2aa95890192eee28781eac70.png"},{"id":20252759,"identity":"fa7e6105-12b3-4637-adba-d51e3078170e","added_by":"auto","created_at":"2022-04-12 14:56:35","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2690376,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1536660/v1/58ffe49c-4dd6-459c-b212-49793cb2d7ee.pdf"}],"financialInterests":"","formattedTitle":"Validation of physics-based ground shaking scenarios for empirical fragility studies: the case study of the 2009 L’Aquila earthquake","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eWith the ever-increasing computational power, 3D physics-based numerical simulations (PBS) are becoming a more and more appealing tool to provide realistic site-specific scenarios of earthquake ground motion, in alternative to the commonly used empirical ground motion prediction equations (GMPE), based on statistical regressions from regional or worldwide records. More specifically, PBS are the key approach towards generation of urban and regional risk scenarios, as it is the case for the ShakeOut (Porter et al., 2011) and Haywired (USGS, 2017a and 2017b) experiments in California, as well as for the Scenario Earthquake Shaking Maps (available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.j-shis.bosai.go.jp\u003c/span\u003e\u003cspan address=\"https://www.j-shis.bosai.go.jp\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) suitable for prefecture emergency plans in Japan, in order to pinpoint target areas and target facilities needing maintenance for earthquake disaster prevention. As pointed out by Hirata (2017), the predicted damage in the Kumamoto prefecture, prior to the earthquake sequence of 2016, was in good agreement with the observed one, although countermeasures were not yet made effective at the time the earthquake occurred.\u003c/p\u003e \u003cp\u003eIn spite of their exceptional interest in the context of seismic risk evaluations at urban scale (see e.g., Smerzini and Pitilakis 2018; Stupazzini et al., 2021; Ria\u0026ntilde;o et al. 2021), the applicability of PBS ground motion scenarios is questioned because of their high-frequency limitations, both because of computational limits, that prevent using excessively fine numerical meshes and solve short propagation wavelengths, and because of missing details in the geological model description. To solve these issues, hybrid approaches have been proposed to couple results of low-frequency (LF) PBS with high-frequency (HF) components from stochastic or empirical Green\u0026rsquo;s functions based approaches (Irikura and Miyake, 2011). However, since the hybrid approaches have the limitation of disregarding the correlation between LF and HF portions of motion, new approaches have been devised that, based on machine learning techniques (Paolucci et al., 2018; Okazaki et al., 2021), aim at solving this issue. Recently, Paolucci et al. (2021) have published the BB-SPEEDset, a dataset including several hundreds of simulated near-source broadband accelerograms from validated case studies, that proved to have statistical properties similar to the NEar-Source Strong-motion records dataset NESS2 (Sgobba et al., 2021).\u003c/p\u003e \u003cp\u003eValidation of PBS results for engineering applications has already found considerable attention (e.g., Galasso et al. 2013; Bijelić et al. 2018; Tsioulou and Galasso 2018; Petrone et al., 2021a;b). However, in view of the seismic risk applications mentioned previously, it is also crucial to verify whether a PBS scenario is suitable to provide not only a reliable prediction of the level of damage observed in an urban area during a historical earthquake, but also a suitable basis for calibration of empirical fragility curves when instrumental information on ground shaking is not sufficient to reliably correlate the observed level of damage to the estimated ground motion intensity.\u003c/p\u003e \u003cp\u003eAs a matter of fact, the spatial distribution of ground motion intensity is typically inferred either by ShakeMaps (Worden et al. 2020; Wald et al. 2021), in case a sufficient number of records is available, or by empirical GMPEs (Erdik 2017), as it is often the case for historical earthquake with no instrumental records. In all such cases, there is a large level of uncertainty when a ground motion level is associated with the specific site where an earthquake effect is observed. Besides, the estimated ground motion is typically available only through its peak values, without information on other parameters related to the time history itself, such as duration and frequency content. Instead, once suitably validated, the PBS ground motion scenario may provide a complete picture of the variability of the ground motion waveforms, supporting the derivation of empirical fragility curves conditioned on a wider set of intensity measures (IM), including multi-component input.\u003c/p\u003e \u003cp\u003eMotivated by these considerations, the primary goal of this paper is to investigate and validate the use of PBS ground shaking scenarios as input description for the derivation of empirical fragility curves, with application to a well-known case study for Italy, namely, the Mw6.2, Apr 6 2009, L\u0026rsquo;Aquila earthquake. This case study is selected because of the availability, on one side, of a database of post-earthquake damage surveys with an unprecedented level of detail (Dolce et al. 2019; Rosti et al. 2021a;b), and, on the other side, of a validated numerical model for PBS ground motion scenarios (Smerzini and Villani, 2012; Evangelista et al., 2017; Di Michele et al. 2022). Within this primary objective, a secondary objective of the paper is to propose up-to-date empirical fragility curves for L\u0026rsquo;Aquila, which distinguish from already published results owing to: (i) the use of the up-to-date version of the ShakeMap for the L\u0026rsquo;Aquila earthquake (v4 of Michelini et al. 2020 with respect to v3 of Michelini et al. 2008); (ii) the use of an enhanced statistical approach, which uses the Bernoulli distribution to characterize the random component of the probability model, overcoming possible uncertainty in the resulting fragility estimates driven by data binning; (iii) the adoption of alternative seismic intensity measures for the definition of the explanatory variable of the fragility functions.\u003c/p\u003e \u003cp\u003eThis paper is organised as follows. In Sections 2 and \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the case study of the L\u0026rsquo;Aquila earthquake is introduced, with emphasis on the presentation of the detailed damage database used for the empirical fragility study, as well as of the ground shaking scenarios obtained by PBS through the high-performance numerical code SPEED (Mazzieri et al. 2013), as opposed to those provided by the ShakeMaps approach (Michelini et al. 2020). Then, Section 4 presents and compares two different sets of typological fragility curves, obtained on the basis of either the latest version of the ShakeMaps or the PBS of the L\u0026rsquo;Aquila earthquake. Finally, in Section 5, the total building damage observed during the L\u0026rsquo;Aquila earthquake is compared with the predictions obtained by coupling both the ShakeMaps and the PBS ground motion maps with the corresponding set of fragility curves.\u003c/p\u003e"},{"header":"2 Case Study: The 2009 L’aquila Earthquake","content":"\u003cp\u003eOn April 6, 2009, a Mw 6.2 earthquake hit the city of L\u0026rsquo;Aquila, one of the largest urban centers in the Abruzzo region (Central Italy) with about 70,000 inhabitants, causing 308 deaths and vast destruction in the town itself and surrounding areas. The earthquake represents one of the largest shocks in Italy since the beginning of the instrumental age, after the 1980 Mw 6.9 Irpinia, the 2016 Mw 6.5 Norcia, the 1976 Mw 6.4 Friuli earthquake. The earthquake was generated by the seismic rupture of the Paganica segment of Upper Aterno Valley - Paganica fault system consisting of four NW-SE trending normal fault segments (Galadini et al. 2018). The causative fault borders the eastern side of the Aterno River Valley, a geological depression of tectonic origin related to the extensional tectonic stresses acting in Central Italy, as depicted in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. Note that the L\u0026rsquo;Aquila historical center is located on the surface projection of the causative fault inside the Aterno valley, at only about 2 km from the epicenter of the earthquake, suffering therefore from the largest ground shaking owing to the close proximity to the seismic source and to the site amplification effects of the valley sediments.\u003c/p\u003e\n\u003cp\u003eThe post-earthquake macroseismic survey revealed a maximum intensity degree of IX-X in the Mercalli-Cancani-Sieberg (MCS) scale in the towns of Onna and Paganica, while other 14 towns and villages, including L\u0026rsquo;Aquila, reached an intensity degree between VIII and IX (Galli et al. 2009). The isoseismal lines of maximum intensity showed a pattern strongly elongated in the NW-SE direction, from the epicenter toward the southern part of the Aterno Valley. This pattern reflects the geometry and the dynamics of the fault rupture, with prevailing directivity effects in the direction SE of the epicenter (see discussion in Section \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eAfter the earthquake, a comprehensive survey campaign, coordinated by the Italian Department of Civil Protection (DPC), was carried out with the aim of collecting damage and usability information on the affected building stock. This information was then conveyed in a damage database (Rosti et al. 2018; 2020a; 2021a, b; 2022), now available in the Observed Damage Database \u0026ndash; Da.D.O. (Dolce et al. 2019). This is a web-GIS tool, operated by the Italian DPC, collecting and archiving data on the construction and structural characteristics, as well as on seismic damage, of ordinary buildings inspected after seismic crises of national importance, from 1976 onwards.\u003c/p\u003e\n\u003cp\u003eThe final L\u0026rsquo;Aquila database, including only data regarding residential buildings in municipalities which were completely surveyed (with completeness ratio larger than 90%, see discussion in Rosti et al. 2021a, b), consists of about 37000 buildings, which are shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. For each inspected building, the database collects information on the geographical coordinates, the construction material (masonry or RC), the typological building classification according to Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, the number of storeys (see height classification in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e), the construction age, the Damage State (DS) according to the European Macroseismic Scale EMS (Gr\u0026uuml;nthal et al. 1998). Furthermore, as clarified in the following section, the database has been enriched by associating to each damaged building a value of ground motion IM coming from both the ShakeMap and the PBS computations. Referring to Rosti et al. (2018) for further details on the criteria for the attribution of the damage grade, it is important to underline herein that a global damage level is assigned to each building based on the maximum damage observed on the most damaged building component.\u003c/p\u003e\n\u003cp\u003eFor the objective of this study, which is to compare the effect of different approaches for the characterization of ground shaking in the empirical fragility analysis, a subset of the damage dataset, corresponding to the detailed study area in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e encompassing the L\u0026rsquo;Aquila municipality, is considered. An area of limited extent is studied mainly because of the computational limits associated with the generation of simulated broadband time histories over a dense grid of sites covering the entire area of the SPEED model. Furthermore, the detailed study area covers the region of larger engineering interest, because of the high density of severely damaged buildings. The considered dataset, hereafter referred to as detailed dataset, counts 7987 residential buildings, 4564 (57%) of which refer to masonry, whereas 3423 (43%) are RC buildings (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea). Note that in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e the number of buildings belonging to each typological class is specified. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e shows the spatial distribution and percentage of the different damage levels, from 0 (no damage) to 5 (collapse), for both masonry (b) and RC buildings (c).\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e shows the frequency of buildings in each damage state according to the different building typological and height classes: buildings are grouped into four main classes - a) Irregular layout or poor-quality masonry, with flexible or rigid diaphragms, w/wo connecting devices (e.g. tie-rods and/or tie-beams); b) Regular layout and good-quality masonry, with flexible or rigid diaphragms, w/wo connecting devices; c) RC seismically designed, pre 1981; d) RC seismically designed, post 1981 \u0026ndash; and the corresponding height classes are considered to compute the statistics. The histograms indicate, as expected, that passing from more vulnerable classes, such as irregular masonry buildings, to less vulnerable classes (RC post 1981), there is a decrease of the percentage of higher damage states (DS4-DS5). Furthermore, there is a positive correlation between the percentage of DS4-DS5 with the height of the building, for any building class.\u003c/p\u003e\n\u003cp\u003eIn the territories more distant from the earthquake source, post-earthquake surveys tend to be limited to damaged buildings, as they are carried out only upon the owners\u0026rsquo; request. As a consequence, resulting damage distributions could be biased by an underestimated number of undamaged buildings. To counteract this issue and to suitably account for the negative evidence of damage in sites less affected by the ground shaking, the post-earthquake dataset was integrated by 197\u0026rsquo;528 non-inspected buildings, located in the non-surveyed and partially-surveyed (with completeness ratio lower than 10%) municipalities, which were reasonably assumed undamaged (e.g. Rosti et al. 2022). The number of undamaged buildings was retrieved from national building census (ISTAT 2001). Allocation of undamaged RC buildings to predefined building types was immediate, as national building census classifies buildings based on construction material, construction age and number of stories. Differently, mapping of undamaged masonry buildings, identified by census parameters, to predefined building typologies was performed via the empirical correlation between census and typological building attributes reported in Rosti et al. (2022).\u003c/p\u003e\n\u003ctable border=\"1\" id=\"Tab1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eTypological building classification according to Rosti et al. (2021a;b). In the first column, the percentage of buildings belonging to each class within the detailed study area are reported into brackets.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBuilding\u003c/p\u003e\n \u003cp\u003etypology\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eConstruction\u003c/p\u003e\n \u003cp\u003eMaterial\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMasonry\u003c/p\u003e\n \u003cp\u003etype\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eIntermediate\u003c/p\u003e\n \u003cp\u003ediaphragm\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eConnecting\u003c/p\u003e\n \u003cp\u003eDevices?\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDesign\u003c/p\u003e\n \u003cp\u003eLevel\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/F/NCD (18.5%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"8\"\u003e\n \u003cp\u003eMasonry\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"4\"\u003e\n \u003cp\u003eIrregular layout or poor-quality (IRR)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eFlexible (F)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo (NCD)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/F/CD (6.8%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eYes (CD)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/R/NCD (2.5%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eRigid (R)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/R/CD (3.8%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/F/NCD (4.6%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"4\"\u003e\n \u003cp\u003eRegular layout and good-quality (REG)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eFlexible (F)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/F/CD (3.1%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/R/NCD (3.2%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eRigid (R)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/R/CD (14.7%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Pre81 (17.7%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eRC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSeismic-Pre 1981\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Post81 (25.1%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSeismic-Post 1981\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003ctable border=\"1\" id=\"Tab2\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eBuilding height classes for masonry and RC buildings.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eConstruction material\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eHeight class\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNo. storeys\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eMasonry\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eL\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u0026ndash;2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026gt;2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eRC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eL\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u0026ndash;2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u0026ndash;4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026gt;4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e"},{"header":"3 3d Physics-based Simulation Of L’aquila Earthquake Ground Motion","content":"\u003cp\u003eA 3D physics-based numerical approach, through the spectral element code SPEED (Mazzieri et al. 2013, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://speed.mox.polimi.it/\u003c/span\u003e\u003c/span\u003e), is used to simulate the seismic wave propagation during the L\u0026rsquo;Aquila earthquake and, hence, to construct the ground shaking scenario for fragility analysis. The 3D spectral element model of the L\u0026rsquo;Aquila earthquake derives from previous studies (Smerzini and Villani 2012; Evangelista et al. 2017) aimed at performing the calibration and the validation of the numerical model against the available recordings. The same model presented in Evangelista et al. 2017 is used in this work, apart from some modifications to the seismic velocity profile of the outcropping bedrock layer of the crustal model, as clarified in the following.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e shows an overview of the SPEED model of the L\u0026rsquo;Aquila earthquake to highlight its main inputs. The model extends over a volume of 58 km x 58 km x 20 km (see also box in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e) and it is discretized using an unstructured hexahedral mesh capable of propagating frequencies up to about 2 Hz. To simulate the earthquake rupture, a kinematic finite fault model is adopted using the slip distribution proposed by Ameri et al. (2012), as documented in Evangelista et al. (2017). The seismic velocity model (see inset in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e), calibrated based on the available seismic microzonation data, is constructed by combing a horizontally layered crustal model and a 3D model of the Aterno River valley. With respect to Evangelista et al. (2017), where the outcropping bedrock layer consists of very hard rock with shear wave velocity V\u003csub\u003eS\u003c/sub\u003e = 1700 m/s, the updated crustal model features a first layer (see Crust 1 in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e) with a parabolic gradient of V\u003csub\u003eS\u003c/sub\u003e from a minimum value of 800 m/s up to a value of 1700 m/s at 1000 m depth from the topographical surface. The modified velocity profile implies a V\u003csub\u003eS30\u003c/sub\u003e value of 900 m/s, which is more consistent with the current knowledge on the average distribution of V\u003csub\u003eS30\u003c/sub\u003e values for the rock formations of Central Italy (Forte et al. 2019). In Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e, a representative cross-section of the velocity model (see yellow line A-A\u0026rsquo; superimposed on the mesh), passing through the L\u0026rsquo;Aquila downtown, is also shown to highlight the complexity of the wave propagation model. Note that ground topography is also accounted for in the SPEED simulation.\u003c/p\u003e\n\u003cp\u003eTo overcome the frequency limit of the numerical model, the ANN2BB technique proposed by Paolucci et al. (2018) and further improved in Paolucci et al. (2021), is used to enrich the PBS signals at high frequency. The essence of this technique is the use of an Artificial Neural Network, trained on a strong-motion recorded dataset, to predict short-period spectral ordinates starting from the long-period spectral ordinates of the SPEED signal. The procedure allows for the generation of broadband ground motions which preserve the features of the SPEED signals at low frequencies and, at high frequency, provide a realistic (i.e. consistent with records) distribution of several IMs (Paolucci et al. 2021), as well as of the spatial variability (Infantino et al. 2021). The last feature is particularly relevant when generating ground shaking scenarios for seismic risk studies, because it ensures that realistic features of spatial correlation and coherency are maintained at both long and short periods.\u003c/p\u003e\n\u003cp\u003eReferring the reader to the relevant publications for a thorough discussion of the features and results of the numerical model, some selected results are presented herein in relation with the main scope of this paper, which is the use of PBS ground shaking scenarios for the derivation of empirical fragility curves. For this purpose, Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e shows the map of Peak Ground Velocity (PGV) obtained from PBS (left) and from the up-to-date version (v4) of the ShakeMap according to Michelini et al. (2020) (right). The maximum horizontal component (Hmax) is shown to enable a consistent comparison between the two approaches, since ShakeMaps are released only for the Hmax component. To understand the differences between PBS and ShakeMap, it is worth recalling that the former is derived by computing the peak values directly from the waveforms simulated by SPEED on an arbitrarily dense grid of receivers, while the latter is generated by combining, through suitable geospatial interpolation algorithms, the ground motion values recorded at the available stations with the GMPEs predictions, where data are not available. Note that, for L\u0026rsquo;Aquila case study, in the area in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e, only 6 stations (3 of which in the epicentral area) are used to adjust the field given by the GMPEs. On both maps, the MCS intensity field available in the Macroseismic Intensity Database (DBMI15, Locati et al. 2021) is superimposed. On the SPEED map, at two selected stations, namely AQK and AQV, the simulated velocity waveform is compared with the recorded one (NS and EW component, respectively). From the comparison of Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e the following remarks can be made:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eA good agreement is found between simulated and recorded waveforms in terms of peak values, frequency content and duration, although, at the stations of the Aterno river transect AQV-AQG-AQA (not reported herein for sake of brevity, see Evangelista et al. 2017), simulations tend to provide lower amplitudes than recorded, most likely because of inaccuracies of the source model;\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eThe simulated PGV pattern is in satisfactory agreement with the MCS intensity field: the areas of maximum PGV, which are found on the surface projection of the fault and inside the alluvial basin, correspond approximately to the sites with the highest intensity degrees. Consistently with the observed macroseismic field, the SPEED map shows a pattern oriented in the NW-SE direction with higher shaking toward SE, mainly because of the coupling of rupture propagation effects with site effects in the Aterno basin;\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eOn the other hand, the ShakeMap is excessively homogeneous, being based predominantly on median estimates from GMPEs, and it fails to predict the strong anisotropy of ground shaking in the SE direction. Instead, the largest PGV values of the ShakeMap are found in the North sector of the Aterno Valley (where the relatively high peak values recorded at the AQV-AQG-AQA array constrain the ShakeMap), in disagreement with corresponding MCS intensities of relatively modest degree (not larger than VII).\u003c/p\u003e\n \u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eFocusing on the detailed study area of Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, relevant for the fragility analysis presented in the following sections, the comparison between PBS and ShakeMap in terms of both PGA-Hmax and PGV-Hmax appears as in Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e. To derive these maps, about 560 three-component broadband ground motion time histories are generated through the ANN2BB procedure on a regularly 500m spaced grid of receivers. Starting from the simulated waveforms, a wide set of IMs, including Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV), Peak Ground Displacement (PGD), Spectral Acceleration (SA) at different periods from 0s to 3s, Arias Intensity (I\u003csub\u003eA\u003c/sub\u003e), Cumulative Absolute Velocity (CAV) and Housner Intensity (HI), is computed. Finally, by applying a spline spatial interpolation, it is possible to associate to each building of the detailed damage database the corresponding IM value from PBS. Note that the availability of the entire ground motion time history allows to derive a broader set of IMs: more specifically, not only the standard peak measures as used in the ShakeMap (namely, PGA, PGV and SA at 0.3 s, 1.0 s and 3.0s), but also integral measures which may offer further insights into their correlation with seismic damage. Although in this work we consider only PGA, PGV and SA, to enable a direct comparison with the standard approach based on ShakeMap, future studies will aim at evaluating the sensitivity of the fragility curves with respect to a larger set of IMs.\u003c/p\u003e\n\u003cp\u003eThe maps of Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e highlight further the differences in the spatial variability of ground shaking estimated by the two approaches. As shown in Paolucci et al. (2018), the PBS enriched by the ANN2BB technique at high frequencies provides a realistic spatial correlation of the peak ground motion values, with a relevant small-scale spatial variability, which reflects the physical features of the source rupture (not homogeneous across the fault plane) and of local site response characteristics. Furthermore, from a qualitative point of view, the spatial distribution of PGA shows a lower spatial correlation, as expected for short period IMs (Infantino et al. 2021). On the other hand, the ShakeMap provides a smooth pattern with limited spatial variability. To quantify these differences, Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e shows the histograms of the PGA-Hmax (left) and PGV-Hmax (right) values computed from both approaches at the building locations of the detailed damage database. It is clear that the ShakeMap values have a more limited variability than PBS: standard deviation (in log10 units) decreases from 0.14 to 0.07 for PGA and from 0.12 to 0.04 for PGV.\u003c/p\u003e"},{"header":"4 Derivation Of Fragility Curves","content":"\u003cdiv class=\"Section2\" id=\"Sec5\"\u003e\n \u003ch2\u003e4.1 Statistical approach and fitting technique\u003c/h2\u003e\n \u003cp\u003eThe derivation of fragility functions requires an appropriate statistical model and fitting technique to approximate observational data as a function of the ground motion severity.\u003c/p\u003e\n \u003cp\u003eA statistical model is defined by a systematic and a random component. The systematic component, i.e. the fragility function, is the mean of the response variable (i.e. damage in this study) as a function of the explanatory variable (i.e. the selected ground motion IM). The random component instead represents the conditional probability distribution of the response variable given the explanatory one.\u003c/p\u003e\n \u003cp\u003eIn line with existing literature studies (e.g. Rota et al. 2008; Del Gaudio et al. 2017; Ader et al. 2020), the cumulative lognormal distribution is adopted for describing the probability of reaching or exceeding a preselected damage level, as a function of the seismic intensity measure:\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({p}_{ij}=P \\left(DS\\ge {ds}_{i}|IM=i{m}_{j}\\right)= {\\Phi }\\left[\\frac{\\text{l}\\text{o}\\text{g}(i{m}_{j}/{{\\theta }_{ds}}_{i})}{\\beta }\\right]\\)\u003c/span\u003e\u003c/span\u003e(1)\u003c/p\u003e\n \u003cp\u003ewhere \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003e\u003cem\u003edsi\u003c/em\u003e\u003c/sub\u003e is the median value of the selected intensity measure associated with damage level \u003cem\u003eds\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e whereas \u003cem\u003e\u0026beta;\u003c/em\u003e denotes the logarithmic standard deviation.\u003c/p\u003e\n \u003cp\u003eGiven the availability of building-by-building data, the Bernoulli distribution (e.g. Rossetto et al. 2014; Ioannou et al. 2015) is selected for characterizing the random component of the statistical model:\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\"\u003e (2)\u003c/p\u003e\n \u003cp\u003ewhere \u003cem\u003eY\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e is the damage response given the intensity measure threshold \u003cem\u003eim\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e is equal to 1, \u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e is the exceedance probability defined by Eq. (1). The term \u003cem\u003eY\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e is modelled as a binary outcome taking the value of 1 if the selected damage level is sustained (i.e. \u003cem\u003eDS\u003c/em\u003e\u0026thinsp;\u0026ge;\u0026thinsp;\u003cem\u003eds\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e) and 0 otherwise (i.e. \u003cem\u003eDS\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;\u003cem\u003eds\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e). The adoption of the Bernoulli distribution, which is a special case of the binomial distribution, allows for avoiding aggregation of damage data, which may introduce uncertainty in the resulting fragility estimates (e.g. Rossetto et al. 2014; Ioannou et al. 2015).\u003c/p\u003e\n \u003cp\u003eFragility functions are simultaneoulsy fitted via the maximum likelihood estimate (MLE) approach and a unique constant dispersion value (\u003cem\u003e\u0026beta;\u003c/em\u003e) is assumed for all damage states to prevent intersecting fragility curves (e.g. Lallemant et al. 2015; Porter et al. 2021; Nguyen and Lallemant 2021; Rosti et al. 2021a, b).\u003c/p\u003e\n \u003cp\u003eFor each building typology, optimal parameters of the fragility model (i.e. \u003cem\u003e\u0026theta;\u003c/em\u003e\u003csub\u003e\u003cem\u003edsi\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003e\u0026beta;\u003c/em\u003e) result from maximising the logarithm of the likelihood function:\u003c/p\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left({\\theta }_{dsi},\\beta \\right)=\\text{arg}\\text{m}\\text{a}\\text{x}[\\text{log}\\left(L\\left({\\theta }_{dsi},\\beta \\right)\\right]=\\text{arg}\\text{max}\\left[\\text{l}\\text{o}\\text{g}\\left(\\prod _{i=1}^{nDS}\\prod _{j=1}^{N}\\frac{{n}_{j}!}{{y}_{ij}!\\left({n}_{j}-{y}_{ij}\\right)!}{{p}_{ij}}^{{y}_{ij}}{\\left(1-{p}_{ij}\\right)}^{\\left({n}_{j}-{y}_{ij}\\right)}\\right)\\right]\\) \u003c/span\u003e\u003c/span\u003e(3)\u003c/p\u003ewhere \u003cem\u003enDS\u003c/em\u003e is the number of damage levels and \u003cem\u003eN\u003c/em\u003eis the number of data points.\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec6\"\u003e\n \u003ch2\u003e4.2 Fragility curves for PGA estimated from PBS and ShakeMap\u003c/h2\u003e\n \u003cp\u003eTaking advantage of the statistical modelling discussed in Section 4.1, empirical fragility curves are derived for a wide catalogue of building typologies. Considering its extensive use in seismic vulnerability and risk applications (e.g. da Porto et al. 2021; Dolce et al. 2021), PGA is first selected for representing the severity of the ground motion shaking. As previously commented, for consistency between the PBS- and ShakeMap-based approaches, the Hmax component is considered. To overcome the lack of PBS results outside the detailed study area, a hybrid strategy, exploiting the results from both PBS and ShakeMaps, is pursued for defining seismic input at different building locations of the damage database. Specifically, the ground shaking is locally estimated using PBS at buildings sited in the detailed study area (see Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ea), whereas the ShakeMap is used for estimating seismic input at undamaged buildings in the non-surveyed and partially-surveyed (with completeness ratio\u0026thinsp;\u0026lt;\u0026thinsp;10%) municipalities (Section 2).\u003c/p\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e collects the parameters (i.e. median values and logarithmic standard deviation) of the typological fragility functions in terms of PGA, estimated on the basis of PBS, supplemented by ShakeMap estimates in the territories less affected by the ground shaking. Typological fragility curves fully relying on ShakeMap estimates are also derived (Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). Comparisons between sets of fragility curves resulting from PBS and those entirely based on the ShakeMap are shown in Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e, Fig. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e, Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003eThese comparisons serve as validation of the use of ground shaking scenarios from PBS to construct empirical fragility. The two sets of curves (PBS Vs ShakeMap) turn out to be consistent, although some differences are found. Specifically, PBS-derived fragility curves tend to be less conservative for masonry buildings (especially for the MH class), while a reverse trend is found for RC buildings (especially for post 1981 class).\u003c/p\u003e\n \u003ctable border=\"1\" id=\"Tab3\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eParameters (i.e. median and logarithmic standard deviation) of the typological fragility curves. IM: PGA from PBS and from ShakeMap\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eIM estimation:\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"6\"\u003e\n \u003cp\u003ePBS\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"6\"\u003e\n \u003cp\u003eShakeMap\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eBuilding typology\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS1\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS2\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS3\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS4\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS5\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026beta; [-]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS1\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS2\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS3\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS4\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS5\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026beta; [-]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/F/NCD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.670\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.645\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/F/NCD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.723\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.697\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/F/CD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.664\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.630\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/F/CD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.653\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.618\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/R/NCD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.738\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.691\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/R/NCD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.654\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.604\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/R/CD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.831\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.810\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/R/CD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.797\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.761\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/F/NCD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.952\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.934\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/F/NCD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.870\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.832\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/F/CD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e26.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.802\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.34\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e26.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.795\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/F/CD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.856\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.814\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/R/NCD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.827\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.811\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/R/NCD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.938\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.923\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/R/CD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.867\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.833\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/R/CD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.957\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.928\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Pre81/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.654\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.648\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Pre81/M\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.593\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.560\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Pre81/H\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.34\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.650\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.603\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Post81/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e24.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.722\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e24.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.684\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Post81/M\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e33.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.827\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e27.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.711\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Post81/H\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.695\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.637\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec7\"\u003e\n \u003ch2\u003e4.3 Fragility curves for alternative seismic intensity measures\u003c/h2\u003e\n \u003cp\u003eOne of the unquestionable advantages of PBS is the possibility of generating ground motion time-histories at predefined grid points, thus permitting to locally characterize the ground shaking by a broad catalog of IMs, including peak, spectral and integral intensity measures. To exploit this potentiality, empirical fragility curves are also derived for IMs alternative to PGA, namely, PGV and average spectral acceleration (SAavg), defined as average of spectral acceleration values evaluated at 0 s, 0.3 s and 1 s, suitably weighted based on the width of the associated period interval (i.e. weights equal to 0.15 for PGA, 0.5 for spectral acceleration at 0.3 s and 0.35 for spectral acceleration at 1 s). The reason of selecting PGV and SAavg among several intensity measures derives from the need of using the ShakeMaps, which are released only for PGA, PGV and SA at 0.3 s, 1 s and 3 s, for better constraining the tails of the fragility functions in the lower ground motion range. With respect to spectral intensity measures evaluated at the building fundamental period (e.g. Rossetto and Elnashai 2003), spectral ordinates averaged over a range of periods allow for accounting for the variety of structural configurations within a given building typology. Furthermore, the adoption of the average spectral acceleration accounts for period elongation associated with structural damage and higher modes contributions (e.g. Rosti et al. 2020a).\u003c/p\u003e\n \u003cp\u003eAnalogously to Section 4.2, the ground motion IMs, represented by PGV and SAavg, respectively, are characterized by PBS in the area close to the L\u0026rsquo;Aquila municipality and by the ShakeMap in the less affected municipalities.\u003c/p\u003e\n \u003cp\u003eBased on the statistical procedure outlined in Section 4.1, sets of fragility functions are derived for each building typology, as a function of PGV (Table \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e) and SAavg (Table \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e). In the tables, parameters of the typological fragility functions entirely resting on ShakeMap estimates are also reported for comparison.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e shows empirically-derived fragility curves of some selected building typologies, as a function of different IMs, estimated by PBS (solid lines) and ShakeMap (dashed lines). As observed for PGA, PBS-derived fragility curves of URM building typologies are generally less conservative than the corresponding ShakeMap-based ones. Difference between sets of PBS- and ShakeMap-based fragility functions is more significant when PGV and SAavg are considered (Fig. \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e). PBS-based fragility curves of RC buildings seismically designed after 1981 are slightly more conservative in the lower ground motion range than the corresponding ShakeMap-based ones. For a given IM, the overall trend of PBS- and ShakeMap-derived fragility functions is nevertheless very similar, suggesting a general consistency among resulting fragility curves.\u003c/p\u003e\n\u003ctable border=\"1\" id=\"Tab4\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eParameters (i.e. median and logarithmic standard deviation) of the typological fragility curves. IM: PGV from PBS and from ShakeMap\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eIM estimation:\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"6\"\u003e\n \u003cp\u003ePBS\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"6\"\u003e\n \u003cp\u003eShakeMap\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eBuilding typology\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS1\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e[m/s]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS2\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS3\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e[m/s]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS4\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS5\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026beta; [-]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS1\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS2\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS3\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS4\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS5\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026beta; [-]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/F/NCD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.230\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.266\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.287\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.353\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.520\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.614\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.214\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.246\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.265\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.322\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.460\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.573\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/F/NCD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.166\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.200\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.227\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.286\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.492\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.661\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.153\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.183\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.207\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.255\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.420\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.618\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/F/CD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.297\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.328\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.396\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.587\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.594\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.232\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.275\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.301\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.358\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.507\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.547\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/F/CD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.159\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.207\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.240\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.308\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.539\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.571\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.148\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.189\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.217\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.271\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.451\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.530\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/R/NCD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.254\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.306\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.350\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.443\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.755\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.666\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.234\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.282\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.323\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.405\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.655\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.610\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/R/NCD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.179\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.228\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.280\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.402\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.689\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.606\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.161\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.203\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.245\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.337\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.533\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.533\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/R/CD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.312\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.415\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.465\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.582\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.761\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.749\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.296\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.395\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.444\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.548\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.708\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.706\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/R/CD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.209\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.294\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.358\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.452\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.874\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.689\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.199\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.274\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.328\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.404\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.746\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.653\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/F/NCD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.442\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.592\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.673\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.914\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.705\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.881\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.398\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.530\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.599\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.803\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.437\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.826\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/F/NCD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.239\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.345\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.414\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.583\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.030\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.791\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.215\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.311\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.371\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.505\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.848\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.723\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/F/CD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.413\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.730\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.816\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.067\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.161\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.738\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.371\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.630\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.696\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.882\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.717\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.676\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/F/CD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.253\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.373\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.445\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.564\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.275\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.758\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.226\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.327\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.386\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.479\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.988\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.694\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/R/NCD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.405\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.547\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.655\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.875\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.217\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.757\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.366\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.488\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.579\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.762\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.027\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.696\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/R/NCD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.284\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.441\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.519\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.776\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.018\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.844\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.268\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.414\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.482\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.705\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.902\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.797\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/R/CD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.493\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.804\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.996\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.252\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.632\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.782\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.443\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.698\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.844\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.041\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.314\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.703\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/R/CD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.335\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.632\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.809\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.098\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.489\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.869\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.320\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.592\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.738\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.970\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.268\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.788\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Pre81/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.312\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.427\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.578\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.832\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.476\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.608\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.291\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.394\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.524\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.719\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.187\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.551\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Pre81/M\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.187\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.292\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.387\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.556\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.993\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.559\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.184\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.286\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.366\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.499\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.801\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.471\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Pre81/H\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.136\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.220\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.322\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.684\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.234\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.606\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.131\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.207\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.289\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.564\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.932\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.528\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Post81/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.336\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.630\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.895\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.380\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.035\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.671\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.317\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.575\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.780\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.116\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.554\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.574\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Post81/M\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.190\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.393\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.620\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.042\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.412\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.735\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.208\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.401\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.581\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.869\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.684\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.594\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Post81/H\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.134\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.212\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.357\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.816\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.618\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.675\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.151\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.237\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.373\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.735\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.277\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.552\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cdiv class=\"gridtable\"\u003e\u003ctable border=\"1\" id=\"Tab5\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eParameters (i.e. median and logarithmic standard deviation) of the typological fragility curves. IM: SAavg from PBS and from ShakeMap\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eIM estimation:\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"6\"\u003e\n \u003cp\u003ePBS\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"6\"\u003e\n \u003cp\u003eShakeMap\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eBuilding typology\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS1\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS2\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS3\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS4\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS5\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026beta; [-]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS1\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS2\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS3\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS4\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026theta;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eDS5\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e[m/s\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026beta; [-]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/F/NCD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.34\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.644\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.601\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/F/NCD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.687\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.647\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/F/CD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.646\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.585\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/F/CD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.620\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.570\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/R/NCD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.696\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.645\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/R/NCD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.632\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.563\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/R/CD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.792\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.751\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIRR/R/CD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.768\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.704\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/F/NCD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e29.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.912\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e26.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.870\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/F/NCD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.839\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.771\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/F/CD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e41.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.784\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e35.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.738\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/F/CD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e22.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.806\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.757\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/R/NCD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e21.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.808\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.756\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/R/NCD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.881\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.855\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/R/CD/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e23.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e31.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.852\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e26.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.772\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eREG/R/CD/MH\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e28.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.930\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e25.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.858\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Pre81/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e26.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.633\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e23.34\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.600\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Pre81/M\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.609\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.519\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Pre81/H\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e24.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.670\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.562\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Post81/L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e25.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e39.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.710\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e22.56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e32.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.634\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Post81/M\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e21.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e54.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.829\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e35.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.651\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC/Seismic-Post81/H\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e35.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.731\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e25.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.591\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"5 Validation Against Observed Damage","content":"\u003cp\u003eGround shaking scenarios from PBS and ShakeMap are respectively coupled with the corresponding fragility models for PGA, to verify their predictive capability in the context of seismic risk assessment. Referring to the detailed study area, building-by-building seismic scenarios are simulated in terms of physical damage. The availability of building-by-building data allows for a punctual definition of both seismic input and damage, avoiding the uncertainty driven by aggregated models (e.g. Nievas et al. 2022). The physics-based ground motion scenario in terms of PGA is combined with the fragility model resulting from the hybrid strategy (PBS\u0026thinsp;+\u0026thinsp;ShakeMap). The ShakeMap ground shaking scenario (Michelini et al. 2020) is instead coupled with fragility functions fully resting on ShakeMap ground motion estimates. Figure \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e shows the spatial distribution of damage to buildings sited in the detailed study area (Fig. \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003ea) and in the L\u0026rsquo;Aquila historical centre (Fig. \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003eb), resulting from the joint use of ground shaking scenarios and consistent fragility models. Results are displayed in terms of probability of exceedance of preselected damage levels (i.e. DS1, DS3 and DS4), evaluated at the building level. In the figure, bar plots represent the frequency distribution of the exceedance probability values of each damage level. Bar colours correspond to the exceedance probability ranges of the discretization adopted in the legend.\u003c/p\u003e\n\u003cp\u003eFor each building, a synthetic representation of damage (e.g. Dolce et al. 2003; Lagomarsino and Giovinazzi 2006; Rosti et al 2020b) is also provided in terms of mean damage (\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003eD\u003c/em\u003e\u003c/sub\u003e), defined as weighted average of the expected probabilities of occurrence (\u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003ek\u003c/em\u003e\u003c/sub\u003e) of the different damage levels (\u003cem\u003eDS\u003c/em\u003e\u003csub\u003e\u003cem\u003ek\u003c/em\u003e\u003c/sub\u003e):\u003c/p\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }_{D}= \\sum _{k=0}^{5}k{p}_{k}\\) \u003c/span\u003e\u003c/span\u003e(4)\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e shows the spatial and frequency distribution of mean damage in the study area and in the L\u0026rsquo;Aquila historical centre, resulting from the adopted simulation strategies.\u003c/p\u003e\n\u003cp\u003eBesides contributing to the development of empirical fragility models, post-earthquake damage data (e.g. Dolce et al. 2019) are a unique opportunity for testing the adequacy of seismic vulnerability and risk models for territorial applications (e.g. Smerzini and Pitilakis 2018; da Porto et al. 2021; Riga et al. 2021). In this study, the accuracy of the adopted simulation procedures to reproduce the observed seismic damage is globally assessed in terms of damage distribution within the detailed study area (Fig. \u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e). In the figure, predicted global damage distributions for masonry, RC and all buildings (without distinction of the construction material) are compared to the observed ones. Predicted damage distributions are obtained by using PBS and ShakeMap ground motion scenarios, respectively, with consistent fragility models. In Fig. \u003cspan class=\"InternalRef\"\u003e15\u003c/span\u003e, damage predictions are directly plotted against observations, highlighting possible overestimation or underestimation of the adopted simulation strategies with respect to each level of damage. Results show that both the adopted simulation procedures generally well reproduce the observed seismic damage in the detailed study area. Both procedures tend to slightly overestimate null damage (DS0) to the detriment of slight damage (DS1). Nevertheless, predictions are aligned with observations for all levels of damage from DS2 to DS5, indicating the general fitness of both procedures to reproduce observed seismic damage.\u003c/p\u003e\n\u003cp\u003eComparison between observed and predicted damage distributions is also detailed for each building typology (Fig. \u003cspan class=\"InternalRef\"\u003e16\u003c/span\u003e). In line with previous considerations, both simulation procedures allow to well reproduce the frequency of occurrence of damage levels from DS2 to DS5, which provide higher contribution to consequences estimation (e.g. da Porto et al. 2021). Slight damage is instead slightly underestimated in favour of null damage. This last finding can be explained by the need of constraining the tails of the fragility functions in the lower ground motion range, allowing for reliable seismic risk estimates (e.g. Rosti et al. 2021a, b; 2022).\u003c/p\u003e"},{"header":"6 Conclusions","content":"\u003cp\u003eThis work validates the use of ground shaking scenarios obtained by 3D PBS as a basis to constrain the intensity measures for empirical fragility analyses from past earthquakes. The selected case study is the 2009 L\u0026rsquo;Aquila earthquake, for which a comprehensive database of post-earthquake damage observations is available, together with relatively detailed ShakeMaps, constrained by few accelerometric records, to be used as a verification benchmark. In addition, a 3D numerical model, validated on the recordings of the event, is available encompassing a finite-fault kinematic source model as well as a detailed source-to-site wave propagation model embedding the topography of the region and the Aterno valley (Evangelista et al. 2017).\u003c/p\u003e\n\u003cp\u003eTo the authors\u0026rsquo; knowledge, this work represents the first attempt to test the capability of the 3D physics-based numerical approach, which has attracted considerable research efforts in the last years, to provide region-specific ground shaking scenarios, to be used as input for the calibration of empirical fragility curves, as opposed to standard approaches relying on ShakeMaps or GMPEs.\u003c/p\u003e\n\u003cp\u003eA novel set of fragility curves is empirically-derived by statistical processing of the L\u0026rsquo;Aquila post-earthquake damage database for several masonry and RC building typologies representative of the Italian building stock. The use of an improved statistical technique, relying on the Bernoulli distribution for modelling the random component of the statistical model and assuming a constant dispersion value for all damage states, allows for overcoming possible uncertainties in the resulting fragility estimates driven by data aggregation and for ensuring the ordinal nature of damage.\u003c/p\u003e\n\u003cp\u003eFragility curves are calibrated by characterizing the ground motion intensity at the buildings located within the L\u0026rsquo;Aquila municipality, i.e. the area severely affected by the earthquake, using the broadband shaking scenarios from the PBS. The ground motion IMs selected for the fragility analysis include PGA, which is the reference ground motion intensity measure used in the Italian national platform for seismic risk assessment (Borzi et al. 2021), as well as less standard intensity measures, such as PGV and SAavg (weighted average spectral acceleration in the range 0-1s). The fragility curves obtained from the PBS are compared for each building typology with the ones obtained, through the same statistical approach, using the latest version of the ShakeMap (v4), released by the National Institute of Geophysics and Volcanology of Italy. This comparison serves as a first validation of the use of physics-based ground motion scenario for empirical fragility studies, as it highlights that the two sets of fragility curves are in very good agreement, without any systematic biases. Finally, the two sets of fragility models, from PBS and ShakeMap, are coupled with the corresponding ground shaking scenarios to check the consistency of the predicted damage levels building-by-building and of their spatial distribution in the L\u0026rsquo;Aquila municipality area, with respect to the observed ones. Results point out that both approaches for ground shaking estimation well reproduce the observed distribution of damage among the different classes, especially for damage states from DS2 to DS5, which are expected to contribute the most to the loss estimation. Instead, slight discrepancies are found for lower damage states (DS0 and DS1).\u003c/p\u003e\n\u003cp\u003eBesides having provided a novel validated set of empirical fragility curves for different common building typologies in Italy, this study sheds light on potential advantages of simulation-based seismic shaking scenarios for empirical fragility studies, particularly when strong-motion recordings are insufficient, or not available at all, to derive reliable shaking maps, as for historical earthquakes. More specifically, this work highlights the following main advantages related to the application of PBS to the problem at hand:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\n \u003cp\u003ePBS are suitable to provide ground shaking scenarios with a realistic spatial correlation, reflecting the specificity of the regional seismic wave propagation features (e.g. alluvial basins, topography) as well as of the seismic fault rupture. Figure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e and Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e clearly demonstrate the capability of the PBS approach in providing a ground shaking scenario which, on the one hand, is more consistent with the observed macroseismic pattern owing to the coupling of rupture propagation effects with local site response, and, on the other hand, is characterized by a sound spatial correlation structure. The latter is typically neglected by standard approaches for ground motion characterization, although it may affect results in the lower and upper intensity measure range (Rosti et al. 2020a).\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eContrary to standard empirical models, from a 3D PBS the entire ground motion time history is available for any building site. This means that a wider portfolio of ground motion IMs can be computed, including not only peak values, as conventionally adopted in ShakeMaps (PGA, PGA and SA), but also integral measures (CAV, HI, I\u003csub\u003eA\u003c/sub\u003e), which reflect in greater detail the variability of seismic shaking in amplitude, frequency and duration. It is, in fact, recognized that non-conventional or vector-valued ground motion intensity measures may improve the correlation with damage observations (e.g. Gehl et al. 2013; Masi et al. 2020). The sensitivity of fragility curves with respect to other intensity measures will be the subject of future studies.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003ePBS may provide the opportunity for fully site-specific deterministic seismic damage/risk scenarios, where the simulated seismic input is used for calibrating consistent specific fragility models.\u003c/p\u003e\n \u003c/li\u003e\n\u003c/ul\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis work has been carried out in the framework of the 2019-2021 and 2022-2023 DPC-ReLUIS Project WP4 \u0026ldquo;MARS \u0026ndash; Seismic Risk Maps\u0026rdquo; funded by the Italian Civil Protection Department. The authors would like to acknowledge Guido Corti for his support in the initial stage of this work.\u0026nbsp;\u003c/p\u003e\u003cp\u003eFunding\u003c/p\u003e\n\u003cp\u003eThe work has been funded by the Italian Department of Civil Protection under the 2019-2021 and 2022-2023 DPC-ReLUIS Project WP4 \u0026ldquo;MARS \u0026ndash; Seismic Risk Maps\u0026rdquo;.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eCompeting interests\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003eData Availability\u003c/p\u003e\n\u003cp\u003eThe L\u0026rsquo;Aquila damage dataset is available in the Da.D.O. platform at http://egeos.eucentre.it/danno_osservato/web/danno_osservato?lang=EN. The SPEED code is available at http://speed.mox.polimi.it. The datasets generated during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAder T, Grant DN, Free M, Villani M, Lopez J, Spence R (2020) An unbiased estimation of empirical lognormal fragility functions with uncertainties on the ground motion intensity measure. J Earthq Eng, 24(7): 1115-1133.\u003c/li\u003e\n \u003cli\u003eAmeri G, Gallovic F, Pacor F (2012) Complexity of the Mw 6.3 2009 L\u0026rsquo;Aquila (central Italy) earthquake: Broadband strong motion modeling. J Geophys Res 117: B04308\u003c/li\u003e\n \u003cli\u003eBijelić N, Lin T, Deierlein GG. 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Earthq Eng, 16(7): 2609-2631.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eStupazzini M, Infantino M, Allmann A, Paolucci R (2021) Physics-based probabilistic seismic hazard and loss assessment in large urban areas: a simplified application to Istanbul. Earthquake Engng Struct Dyn. 50: 99-115.\u003c/li\u003e\n \u003cli\u003eTsioulou A, Galasso C (2018) Information theory measures for the engineering validation of ground-motion simulations. Earthquake Engng Struct Dyn. 47: 1095\u0026ndash;1104. https://doi.org/10.1002/eqe.3015\u003c/li\u003e\n \u003cli\u003eUSGS (2017a) The HayWired Earthquake Scenario\u0026mdash;Earthquake Hazards. Scientific Investigations Report 2017\u0026ndash;5013\u0026ndash;A\u0026ndash;H.\u003c/li\u003e\n \u003cli\u003eUSGS (2017b) The HayWired Earthquake Scenario\u0026mdash;Engineering Implications. Scientific Investigations Report 2017\u0026ndash;5013\u0026ndash;I\u0026ndash;Q.\u003c/li\u003e\n \u003cli\u003eWald DJ, Worden CB, Thompson EM, Hearne M. (2021) ShakeMap operations, policies, and procedures. Earthquake Spectra, doi:10.1177/87552930211030298\u003c/li\u003e\n \u003cli\u003eWorden CB, Thompson EM, Hearne M and Wald DJ (2020) ShakeMap Manual Online: Technical Manual, User\u0026rsquo;s Guide, and Software Guide. DOI: 10.5066/F7D21VPQ\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bulletin-of-earthquake-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"beee","sideBox":"Learn more about [Bulletin of Earthquake Engineering](https://www.springer.com/journal/10518)","snPcode":"10518","submissionUrl":"https://submission.nature.com/new-submission/10518/3","title":"Bulletin of Earthquake Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Fragility curves, Seismic vulnerability, Physics-based ground motion simulation, ShakeMap, Post-earthquake damage data, Damage scenarios, Seismic risk","lastPublishedDoi":"10.21203/rs.3.rs-1536660/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1536660/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper explores and validates the use of ground shaking scenarios generated via 3D physics-based numerical simulations (PBS) for seismic fragility studies. The 2009 L\u0026rsquo;Aquila seismic event is selected as case-study application, given the availability of a robust and exhaustive post-earthquake database, gathering observed seismic damages detected on several building typologies representative of the Italian built environment, and of a validated numerical model for PBS ground shaking scenarios. Empirical fragility curves are derived as a function of different seismic intensity measures, by taking advantage of an improved statistical technique, overcoming possible uncertainties in the resulting estimates entailed by data aggregation. PBS-based fragility functions are compared to the corresponding sets of curves relying on updated ShakeMaps. The predictive capability of the adopted simulation strategies is then verified in terms of seismic damage scenarios, by respectively coupling PBS- and ShakeMap-based fragility models with the corresponding ground shaking scenarios. Comparison of observed and predicted damage distributions highlights the suitability of PBS for region-specific seismic vulnerability and risk applications.\u003c/p\u003e","manuscriptTitle":"Validation of physics-based ground shaking scenarios for empirical fragility studies: the case study of the 2009 L’Aquila earthquake","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-04-12 14:41:27","doi":"10.21203/rs.3.rs-1536660/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2022-05-23T22:04:42+00:00","index":0,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2022-04-11T05:29:32+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2022-04-09T07:18:10+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2022-04-08T11:43:49+00:00","index":"","fulltext":""},{"type":"submitted","content":"Bulletin of Earthquake Engineering","date":"2022-04-08T05:39:24+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bulletin-of-earthquake-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"beee","sideBox":"Learn more about [Bulletin of Earthquake Engineering](https://www.springer.com/journal/10518)","snPcode":"10518","submissionUrl":"https://submission.nature.com/new-submission/10518/3","title":"Bulletin of Earthquake Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"8beb374d-163b-46ad-869f-f500e8db79fe","owner":[],"postedDate":"April 12th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2022-10-20T07:18:37+00:00","versionOfRecord":[],"versionCreatedAt":"2022-04-12 14:41:27","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-1536660","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-1536660","identity":"rs-1536660","version":["v1"]},"buildId":"rHA-KDH7Qsr4HCuvH75dn","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}