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Starting from considerations on the high seismic vulnerability of nonstructural elements, and at the same time the scarce consideration of their performance at the different stages of the design and assessment process, this paper proposes a very simple and ready-to-use seismic classification scheme for nonstructural elements. The proposed approach is based on a limited set of information, which may take advantage of the availability of a numerical model of the building and its results, although it may also rely on code formulations and evaluations of seismic performance from the literature. The different seismic classes are assigned to nonstructural elements by quantifying their expected seismic performance by means of fragility curves. This classification may be applied to newly designed nonstructural elements to help identify the best typology for the site and building of interest, and also for existing nonstructural elements that are already installed in existing buildings. In the latter case, the classification may help in defining a prioritization scheme for interventions required to make nonstructural elements safer for the building of concern. The feasibility of the proposed procedure is demonstrated by its application to two case studies, referring to existing buildings located at different seismicity sites.

In this paper, empirical fragility curves for reinforced concrete buildings are derived, based on post-earthquake damage data collected in the aftermath of earthquakes occurred in Italy in the period 1976–2012. These data, made available through an online platform called Da.D.O., provide information on building position, building characteristics and damage detected on different structural components. A critical review of this huge amount of data is carried out to guarantee the consistency among all the considered databases. Then, an in-depth analysis of the degree of completeness of the survey campaign is made, aiming at the identification of the Municipalities subjected to a partial survey campaign, which are discarded from fragility analysis. At the end of this stage, only the Irpinia 1980 and L’Aquila 2009 databases are considered for further elaborations, as fully complying with these criteria. The resulting database is then integrated with non-inspected buildings sited in less affected areas (assumed undamaged), to account for the negative evidence of damage. The PGA evaluated from the shakemaps of the Italian National Institute of Geophysics and Volcanology (INGV) and a metric based on six damage levels according to EMS-98 are used for fragility analysis. The damage levels are obtained from observed damage collected during post-earthquake inspections through existing conversion rules, considering damage to vertical structures and infills/partitions. The maximum damage level observed on vertical structures and infills/partitions is then associated to the whole building. Fragility curves for two vulnerability classes, C2 and D, further subdivided into three classes of building height, are obtained from those derived for specific structural typologies (identified based on building height and type of design), using their frequency of occurrence at national level as weights.

The homogeneity of standard Italian railway stations in terms of period of construction (second half of the 19th century), architectural and structural features, typical dimensions and morphology (...

This paper illustrates the derivation of an empirical fragility model for residential unreinforced masonry (URM) buildings, calibrated on Italian post-earthquake damage data and compatible with the key features of the Italian national seismic risk platform. Seismic vulnerability is described by fragility functions for three vulnerability classes, then refined based on the building height. To this aim, a clustering strategy is implemented to merge predefined building typologies into vulnerability classes, based on the similarity of the observed seismic fragility. On the other side, a specific procedure is built up to determine the vulnerability composition of the exposed URM building stock, starting from national census data. The empirically-derived model was implemented into the national seismic risk platform and used, together with other vulnerability models, for assessing seismic risk in Italy. The results presented in this paper, consisting of refined typological fragility curves and fragility curves for vulnerability classes, can be also exploited for estimating both expected seismic damage and risk in sites with similar seismic hazard and building inventory.

The Department of Civil Protection (DPC), in compliance with the EU decision 1313/2013 and at the request of the Sendai Framework for Disaster Risk Reduction 2015–2030 to update the disaster risk assessments by various countries, released the latest National Risk Assessment for Italy at the end of 2018. Specifically, as regards the seismic risk assessment, six research units belonging to two centres of competence of the DPC collaborated under its guidance to update the risk maps of the Italian residential heritage. This extensive collaboration complied with the recent Italian code for Civil Protection, which requires a broad scientific consensus for risk assessment. During this research activity, six fragility models were developed, according to some common criteria (four for masonry buildings and two for RC buildings). These models were then implemented by the DPC for the definition of the national seismic risk. Within this context, the aim of this paper is to evaluate the risk results provided by these models, compare their features, and assess and validate their prediction capabilities. In particular, this paper shows the comparison of predicted and observed damage scenarios and consequences on building stock and the population of two seismic events, i.e. L’Aquila 2009 and Amatrice 2016. Furthermore, the paper provides some interesting damage and risk predictions at a national level. Overall, the forecasts and comparisons made in this study demonstrate the validity of the approach adopted by the DPC for the assessment of national seismic risk.

This paper describes the multivariate statistical model of the structure-related modelling uncertainty, developed with reference to reinforced concrete, masonry, steel, and seismically isolated buildings, within the framework of the RINTC project. The model describes the variability of material properties as well as the uncertainty associated with the adopted response models. Specific aspects of each structural typology are also discussed, with a focus on the statistical dependence of the random variables in the model. Finally, the paper describes also the efficient sampling procedure adopted. Effect of model uncertainty on response for each typology are discussed in the corresponding papers within this special issue dedicated to the RINTC project.

Post-earthquake damage data represent an invaluable source of information for the seismic vulnerability assessment of the exposed building stock, as they are a direct evidence of the actual buildings’ performance under real seismic events. This paper exploits a robust and homogeneous database of damage data collected after the 2009 L’Aquila (Italy) earthquake, to derive damage probability matrices for several building typologies representative of the Italian building stock. To this aim, the first part of the work investigates several issues related to the definition of damage to be associated with each inspected building. Different approaches and damage conversion rules are applied, pointing out advantages and weaknesses of each one. Considering the widespread seismic damage observed on masonry infill panels and partitions of reinforced concrete constructions, the impact of this type of non-structural damage on empirical damage and functional loss distributions is explored. The second part of the study proposes different possible interpretations of the repartition of the observed damage in the different damage levels, showing in some cases a bimodal trend. Two novel hybrid procedures are outlined and compared with the classical binomial approach for predicting the subdivision of damage in the different levels. The application of the proposed methodologies to the different building typologies allows the selection, for each one, of the method providing the best fit to empirical results. The parameters required for the application of the optimal approach are reported in the paper, so that results can be used for forecasting the expected seismic damage in sites with similar seismic hazard and exposed buildings.

The companion paper by Rota and Rosti (Bull Earthq Eng, 2017) illustrates a methodology for comparing PSH results with historical macroseismic observations at different scales, in terms of mean damage. This paper presents examples of application of the methodology, at the different considered scales, to the South-East quarter of France. This moderate seismicity region is characterised by a long history of civilization, which makes macroseismic observations available for a long time span, although they are highly approximated measures of the seismic action and they are affected by significant uncertainties. The first scale of application presented is at a single site, i.e. the city of Annecy. This example shows that, despite the seismic history of this city is characterised by a significant number of macroseismic observations spanning over a long time period, they mostly consist of very low intensity values and hence the comparison at a single site is not very meaningful. Therefore, the comparison is carried out on a set of seven aggregated sites, well distributed in the region of interest, providing interesting results and suggesting the opportunity of extending the comparison at an even larger scale. The comparison at the regional scale also allows some interesting observations, although it is obviously able to only provide general (average) indications on the PSH results. These comparisons were aimed at showing the applicability of the proposed methodology, pointing out advantages and drawbacks of the different application scales.

The need for verifying and/or validating the results of probabilistic seismic hazard studies has become evident, despite the absence of generally accepted methods for judging such results. This paper proposes a methodology for comparing the results of PSH with historical macroseismic observations, at different scale levels. The selected metric of the comparison is the mean damage, i.e. the average annually expected damage. Hence, a procedure for converting macroseismic observations and PGA levels, for which PSH estimates are provided, into mean damage values is first presented. The procedure is based on the macroseismic method for converting intensities into mean damage values, whereas it takes advantage of fragility curves (representative of the seismic vulnerability of the building stock at the time of historical observations) to transform the rates of occurrence of PGA values into the equivalent quantity in terms of mean damage. A methodology for site-specific comparison is first outlined. To overcome some of the limitations of the comparison at a single site, two procedures for aggregating several sites by sampling in space are then presented, with the aim of enlarging the available macroseismic dataset. Finally, a procedure for the comparison at the regional level is discussed. Applications of the proposed methodologies will be discussed in a companion paper (Rosti and Rota in Bull Earthq Eng, 2017).

Several building codes propose methodologies to account for epistemic uncertainties in the seismic assessment of masonry buildings by selecting a knowledge level and reducing material strengths by means of the associated value of the confidence factor. Previous works showed that, in the case of masonry structures, this approach has various limitations, such as the lack of proper consideration of experimental tests performed. This article focuses on the issue of imperfect knowledge on material properties of existing masonry buildings and proposes a probabilistic methodology for the assessment, based on Bayesian updating of mechanical properties. The use of a Bayesian approach allows to update the values of the material properties assumed a priori as knowledge on the building increases, by taking into account all the experimental information gathered during the assessment process. A large number of simulated assessments is carried out and the values of the confidence factors on material properties are defined through the comparison between the obtained results and those of the reference structure, assumed to be perfectly known. These factors are useful in a more general framework for the assessment of masonry buildings accounting for different sources of uncertainty.

An experimental campaign aiming at investigating the seismic performance of unreinforced masonry low-density autoclaved aerated concrete blocks is presented. After characterization tests on blocks, mortar and wallettes, in-plane cyclic tests on six full-scale unreinforced masonry piers were performed to obtain a reliable description of the lateral cyclic behavior. Information regarding the displacement capacity and the correlation between experimental and analytical strengths were derived. The results show a limited in-plane displacement capacity of piers, strongly depending on the applied vertical load, and a good correlation between experimental and calculated lateral strengths. At the end of the cyclic tests, the residual vertical strength of some walls was also directly checked.

A suitable characterisation of seismic input at the sites where damage is reported is a key aspect of the study of empirical seismic fragility. The availability of a shakemap, specifically derived for the event of interest from recorded ground motions, allows considering site conditions, spatial variability and possible directivity effects. Whenever this is not available, alternative solutions must be considered, such as for example the use of ground motion prediction equations (GMPEs) or the generation of conditional spatially correlated ground motion random fields (CSCRFs). Each of these approaches bears several uncertainties, which obviously have an effect on the derived empirical damage probability matrices. This paper explores issues and procedures related with the ground motion characterisation and assesses their impact on empirical damage distributions derived from a comprehensive post-earthquake damage database, compiled after the 2009 L'Aquila (Italy) seismic event. Several GMPEs are qualitatively and quantitatively ranked with respect to the available accelerometric data and the damage probability matrices obtained with the best performing GMPE are then compared with results obtained using more refined ground motion characterisations.

The unreinforced masonry (URM) buildings designed to be conforming with the Italian building code, as illustrated in the companion paper, were analyzed by performing time-history analyses on models...

Experimental campaigns carried out in the past showed that the presence of truss bed-joint reinforcement provides a general improvement to the performance of masonry panels subjected to horizontal actions. The truss-like elements are effective in improving resistance and reducing damage and, therefore, they enhance the displacement capacity. The experimental tests available in the literature, performed on prototypes in different scale or in small number compared to the possible combinations of slenderness, axial load and boundary conditions, hardly allow drawing quantitative conclusions on the real benefit of the presence of horizontal reinforcement to the performance improvement for a specific masonry type. The experimental campaign presented in this paper includes a set of in-plane cyclic tests on Autoclaved Aerated Concrete (AAC) masonry panels with thin horizontal and vertical joints filled with thin layer mortar, made both in unreinforced and bed-joint reinforced masonry with flat-truss bed-joint reinforcement. The direct comparison of the results, along with specific tests performed on wallettes made with the two different construction technologies, allows the assessment of the effectiveness of the horizontal reinforcement in enhancing the in-plane seismic performance of AAC masonry.

The choice of modelling strategy and analysis options has a significant influence on the results of the seismic assessment of existing buildings and therefore it is very important to have an idea of the dispersion in the results due to different hypotheses regarding the structural model. This paper concentrates on pushover analysis, considered as the reference method currently adopted by engineers for the seismic assessment of existing masonry buildings, and on the equivalent-frame macro-element approach, assumed to be a satisfactory compromise between computational effort and accuracy in the results. A logic tree approach is used to treat the different considered options, including the definition of the geometry of the equivalent frame, the distribution of loads among the masonry piers and on the horizontal diaphragms, the degree of coupling between orthogonal walls, the definition of the cracked stiffness of structural elements and the modelling of masonry spandrels. By assigning a value of probability to each end branch of the tree, the distribution of the peak ground acceleration corresponding to the selected limit states can be obtained and, from this distribution, a quantitative estimate (in probabilistic terms) of the effect of modelling uncertainties on the seismic response of masonry structures is derived.

Performance-based earthquake engineering, developed over the last decades for the design and assessment of other structures, can also be applied for masonry structures if the particularities of masonry are incorporated into the procedure. According to this methodology, structural performance can be assessed according to damage states which are identified through displacement/damage indicators. While various methods for the identification of limit states from the results of nonlinear static analyses exist, the identification of damage states from the results of nonlinear dynamic analyses is still uncertain. This article investigates a number of criteria allowing to identify the attainment of significant limit states from the results of time history analyses, in terms of appropriately identified response quantities. These criteria are applied to five building prototypes and their results are compared. A comparison with the limit states derived from nonlinear static analyses is also made.

An extensive experimental program was carried out at EUCENTRE, within a research project on the evaluation and reduction of the seismic vulnerability of stone masonry structures. The main part of the experimental program has been devoted to the shaking table tests on three full-scale, two-story, single-room prototype buildings made of undressed double-leaf stone masonry. The first building tested was representative of existing unreinforced stone masonry structures with flexible wooden diaphragms, without any specific anti-seismic design nor detailing. In the second and third buildings, strengthening interventions were simulated on structures theoretically identical to the first one, improving wall-to-floor and wall-to-roof connections and increasing diaphragm stiffness. In particular, in the third specimen, steel and r.c. ring beams were used to improve the diaphragm connection to the walls and collaborating r.c. slab and multi-layer plywood panels were used to stiffen floor and roof diaphragms, respectiv...

The Italian building code defines the seismic action in terms of elastic accel- eration response spectra derived from the results of a probabilistic seismic hazard study performed for the whole national territory. This representation of the seismic input is insuf- ficient for several situations (e.g. analysis of geotechnical systems or time-history analyses of structures), for which the seismic input needs to be specified in terms of accelerograms. This work illustrates a methodology for the seismic mesozonation of the Italian territory, with the aim of defining suites of 7 real accelerograms recorded at outcropping rock sites with flat topographic conditions and, most importantly, compatible with the elastic acceler- ation response spectrum defined by the Italian building code at any location in Italy. These accelerograms do not require any correction and can be directly used for nonlinear dynamic analyses of structures and geotechnical systems. The mesozonation is based on identification of groups of spectra with similar characteristics and shape. For each of these groups, a parent spectrum is defined and used for selecting real spectrum-compatible records. Limited linear scaling is then applied to these accelerograms to make them compatible with all the response spectra of the group. The results of this work for the 475-years return period are accessi- ble through the SEISM-HOME Web-GIS (www.eucentre.it/seismhome.html) providing, for any site in Italy, a suite of 7 real accelerograms spectrum-compatible, on average, with the acceleration response spectrum prescribed by the Italian building code. SEISM-HOME is a useful tool for practitioners needing ready-to-use time-histories for seismic analyses.

The assessment of existing masonry buildings is an important issue in earthquake prone countries like Italy. The current Italian building code, which adopts the approach proposed by Eurocode 8, includes an assessment procedure based on the use of confidence factors, whose values depend on the level of knowledge of the structure. These factors are intended to take into account all possible uncertainties related to the incomplete knowledge of the structure. This article investigates the reliability of the code-based procedure for the assessment of existing masonry buildings and pinpoints some problematic aspects. The approach followed is the simulation of the entire code-based assessment procedure, with the flow of decisions that an engineer would face in the assessment of an existing building schematized in the form of a logic tree. The proposed simulated procedure accounts for different sources of epistemic uncertainty like the selection of the level of knowledge, uncertainty in the results and location o...

Site response analysis is strongly influenced by the uncertainty associated to the definition of soil properties and model parameters. Deterministic, or even parametric analyses are unable to systematically assess such uncertainty, since the site characterisation can hardly be sufficiently accurate for a deterministic prediction of site response and alternative approaches are hence needed. A fully stochastic procedure for estimating the site amplification of ground motion is proposed and applied to a case study in central Italy. The methodology allows to take into account the record-to-record variability in an input ground motion and the uncertainty in dynamic soil properties and in the definition of the soil model. In particular, their effect on response spectra at the ground surface is evaluated.

A new analytical approach for the derivation of fragility curves for masonry buildings is proposed. The methodology is based on nonlinear stochastic analyses of building prototypes. Since such structures are assumed to be representative of wider typologies, the mechanical properties of the prototypes are considered as random variables, assumed to vary within appropriate ranges of values. Monte Carlo simulations are then used to generate input variables from the probability density functions of mechanical parameters. The model is defined and nonlinear analyses are performed. In particular, nonlinear static (pushover) analyses are used to define the probability distributions of each damage state whilst nonlinear dynamic analyses allow to determine the probability density function of the displacement demand corresponding to different levels of ground motion. Convolution of the complementary cumulative distribution of demand and the probability density function of each damage state allows to derive fragility curves.

Typological fragility curves have been derived from post-earthquake survey data on building damage, collected in the areas affected by the most relevant Italian earthquakes of the last three decades. A complex and time consuming codification and reinterpretation work has been done on a set of about 150,000 survey building records, in order to define empirical damage probability matrices for several building typologies, characteristic of the Italian building stock. The obtained data have then been processed by advanced nonlinear regression methods in order to derive typological fragility curves. These curves, organised in five damage levels, provide useful information both for relative comparisons among typologies and for seismic risk analyses at different scales. By combining hazard definitions, fragility curves and inventory data, complete earthquake risk scenario studies can be performed, but even the single convolution of hazard and fragility allows to obtain typological risk maps, both for single damage state definitions and for concise average loss parameters. The very high potential of these results is shown by some applications reported in the paper.

International audience; Notwithstanding its potential high level, the seismic vulnerability of masonry arch bridges has yet to completely perceived, possibly due to the relatively scarce damage evidence collected after recent eathquakes. The dearth of research studies on this topic is thus one of the main motivations behind the current endeavour, which aims at a better understanding of the dynamic interaction between the arch walls and the filling material of typical masonry arch bridges, and the consequent susceptibility of the latter to out-of-plane collapse mechanisms. Within this framework, a numerical model for the evaluation of the seismic out-of-plane capacity of bridge walls, including the effects of the infill material, is proposed. This methodology can be subdivided into three main components; computation of static earth pressure, eveluation of dynamic soil thrust, assesment of out-of-plane capacity of masonry wall. In addition, a congruent and relatively simple procedure for the estimation of the seismic demand on the arch wall is described. Finally, a parametric study is carried out with a view to appraise the seismic vulnerability associated to typical masonry arch bridge typologies.

The earthquake sequence started on May $$20$$ th 2012 in Emilia (Italy) affected a region where masonry constructions represent a large part of the existing building stock and the construction of new modern masonry buildings is a common practice. The paper is focused on the performance of common architectural configurations, typical for residential or business use. The large majority of old masonry buildings is made of fired clay bricks. The seismic performance of these buildings is particularly interesting since major past earthquakes in Italy affected areas with mainly stone masonry structures. Apart from examples showing systematic or peculiar structural deficiencies governing the vulnerability of several buildings, the overall seismic performance of these structures to repeated shaking, with PGA as large as 0.25–0.3 g was rather good, despite the major part of them were only conceived for carrying vertical loads. In fact, seismic design is mandatory in the area only since 2003. Modern low-rise masonry buildings erected after this date and incorporating seismic design and proper detailing resulted in most cases practically undamaged. The examples reported in the paper allow an evaluation of the superior performance of seismically designed modern masonry buildings in comparison to older ones.

The seismic capacity of a structure is a function of the characteristics of the system as well as of its state, which is mainly affected by previous damage and deterioration. The cumulative damage from repeated shocks (for example during a seismic sequence or due to multiple events affecting an unrepaired building stock) affects the vulnerability of masonry buildings for subsequent events. This paper proposes an analytical methodology for the derivation of state-dependent fragility curves, taking into account cumulated seismic damage, whilst neglecting possible ageing effects. The methodology is based on nonlinear dynamic analyses of an equivalent single degree of freedom system, properly calibrated to reproduce the static and dynamic behaviour of the structure. An application of the proposed methodology to an unreinforced masonry case study building is also presented. The effect of cumulated damage on the seismic response of this prototype masonry building is further studied by means of nonlinear dynamic analyses with the accelerograms recorded during a real earthquake sequence that occurred in Canterbury (New Zealand) between 2010 and 2012.