Derivation of seismic fragility curves through mechanical-analytical approaches: the case study of the URM school buildings in Friuli-Venezia Giulia region (Italy)

Cattari S., Alfano S., Manfredi V., Borzi B., Faravelli M., Di Meo A., da Porto F., Saler E., Dall’Asta A., Gioiella L., Di Ludovico M., Del Vecchio C., Del Gaudio C., Verderame G., Gattesco N., et. al.

Cocco G., Spacone E., Brando G.

This paper aims at giving a contribution to the topic concerning the preservation of valuable adobe buildings, by setting a methodology for assessing their seismic vulnerability at the urban scale by means of analytical and numerical models, accounting for both their in-plane and out-of-plane behaviors. To this purpose, the valuable historical center of Cusco (Peru) is considered as representative case study. The city center of Cusco is an extraordinary example of colonial architecture that preserves essential aspects of its origins, it being representative of a large plethora of historical centers in South America and the Caribbean, where most of the residential buildings are made of adobe masonry. First, archetypes, representative of the whole historical center, are identified in order to get a manageable stock of buildings for which the analyses can be addressed to. The structural capacity of each archetype is then given in terms of capacity curves for both out-of-plane and in-plane mechanisms. Subsequently, these curves are compared with the likely seismic demands to assess the probability of attaining pre-established damage states for different seismic intensities. The obtained probabilities are collected into Damage Probability Matrices (DPMs) and, finally, cumulated to plot the fitting fragility curves.

Sbrogiò L., Saretta Y., Valluzzi M.R.

Giusto S., Cattari S., Lagomarsino S.

This paper presents, firstly, an overview of the nonlinear static procedures (NSPs) given in different codes and research studies available in the literature, followed by the results achieved by the authors to evaluate the reliability of the safety level that they guarantee. The latter is estimated by adopting the fragility curve concept. In particular, 125 models of a masonry building case study are generated through a Monte Carlo process to obtain numerical fragility curves by applying various NSPs. More specifically, among the NSPs, the N2 method (based on the use of inelastic response spectra) with different alternatives and the capacity spectrum method (CSM)—based on the use of overdamped response spectra—are investigated. As a reference solution to estimate the reliability of the nonlinear static approach, nonlinear dynamic analyses (NLDAs) are carried out using the cloud method and a set of 125 accelerograms; the results are post-processed to derive fragility curves under the assumption of a lognormal distribution. The focus of this investigation is to quantify the influence that the NSP method’s choices imply, such as the criteria adopted to calculate the displacement demand of a structure or those for the bilinearization of the pushover curve. The results show that the N2 methods are all non-conservative. The only method that provides a good approximation of the capacity of the analyzed URM structures as derived from NLDAs is the CSM. In particular, bilinearization is proven to have a relevant impact on the results when using the N2 method to calculate displacement capacities, whereas the CSM method is not affected at all by such an assumption. The results obtained may have a significant impact on engineering practice and in outlining future directions regarding the methods to be recommended in codes.

Follador V., Carpanese P., Donà M., Alfano S., Cattari S., Lagomarsino S., da Porto F.

Seismic events that have occurred in Italy in recent decades have shown the significant vulnerability of the Italian building stock. In particular, residential masonry buildings have suffered serious damage, highlighting the need to plan effective mitigation strategies as soon as possible. In this context, this study aims to evaluate the effectiveness of possible retrofit interventions for masonry buildings. Fragility curves of macro-classes of residential masonry buildings have been developed in both as-built and retrofitted conditions within the DPC-ReLUIS agreement (Department of Civil Protection—Network of University Laboratories for Earthquake Engineering). In particular, three sets of fragility curves, developed by the University of Padova (UniPD) and the University of Genova (UniGEa and UniGEb) are discussed and compared herein. The three models show similar estimates of the expected structural improvements for the examined retrofit interventions when applied to the building macro-classes, although some differences, due to the different analysis approaches, can be observed.

Labò S., Cademartori S., Marini A.

Buildings with load-bearing structures made of hollow clay blocks with horizontal holes and cement-based mortar are quite common in Italy, yet the current design standards do not consider specific modeling issues to be addressed by practicing engineers. In the absence of peculiar specifications, the prescriptions given for ordinary masonry walls are thus commonly adopted. However, experimental tests proved that walls built with hollow brick masonry performed quite differently from ordinary masonry walls. Considering the in-plane flexural behavior under horizontal loads, unlike ordinary masonry walls that exhibit some ductility, this construction typology performs quite poorly, showing very little deformation capacity and ductility. In recent experimental campaigns, a brittle collapse mechanism was observed due to the toe crush, which entailed the inability of the wall to further withstand the vertical loads. In this paper, the effects of incorrect modeling choices on the characterization of the in-plane behavior of this construction typology and the consequences related to overestimating ductility are discussed; the effects of the reduced ductility on the reliability of the assessment of an existing building as well as on the conceptual design of possible structural retrofit measures are investigated. From the critical discussion, the need emerged to accurately model the in-plane flexural behavior and to update the code provisions to explicitly consider masonry walls with hollow clay bricks with horizontal holes.

Gioiella L., Morici M., Dall’Asta A.

Schools should be safe places where children and young people are hosted during their training years to develop their abilities and skills and to receive an education that makes them prepared to become the future of the nations where they live. Even though these aspects are of paramount importance and widespread recognized, the same importance does not seem to be equally ensured to school facilities. Educational institutes, indeed, are often old and realized without recent safety Standards, becoming consequently non-resilient, nor robust structures towards multiple natural hazards. This aspect concerns lots of countries worldwide, without making distinction among their richness level. In this paper empirical models for the prediction of damage and retrofit costs expected after earthquakes are presented. These probabilistic models relate seismic intensity to expected damage and economic losses, through the definition of continuous indexes, and are based on data collected after a recent earthquake occurred in Central Italy. Empirical data, required to define the probabilistic models, have been obtained by combining information coming from shaking maps, provided by the National Institute for Geophysics and Volcanology (INGV), information on the building properties (e.g. locations, dimensions, construction typology), provided by the Ministry of Education, and data about the damage suffered by constructions and funding for retrofit actions including damage repairing and seismic upgrading, provided by the Reconstruction Office. Proposed models provide the opportunity to directly derive fragility curves, to make it possible the use of the research outcomes in risk frameworks based on a discrete description of the damages and losses. Model parameters have been calibrated for the considered set of available data, but the methodology is general and can be also applied to different contexts, given data are available. Finally, the proposed models have been used to simulate the post-earthquake damage and losses scenario following a seismic event. A proposal for the analyses of probabilistic outputs have been developed to provide information useful to decision making purpose.

Angiolilli M., Brunelli A., Cattari S.

AbstractThe seismic evaluation of masonry buildings in aggregate, largely diffused within the existing Italian and European building stock, represents a difficult and open task that has not been exhaustively investigated so far. The study proposes a procedure aimed at evaluating the potential impact of the combination of local mechanisms and site-amplification in terms of fragility curves on an existing unreinforced masonry (URM) aggregate which is made of five adjacent structural units mutually interacting with each other during seismic sequences. The case study is inspired by built heritage of the historic centre of Visso struck by the Central Italy 2016/2017 earthquakes. The in-plane (IP) response of URM buildings was simulated through nonlinear dynamic analyses performed on a 3D equivalent frame model of the structure, whereas out-of-plane (OOP) mechanisms were analysed by adopting the rigid-block assumption but assuming, as seismic input, the floor accelerations derived from the post-processing of data derived from the global 3D model. An innovative procedure considering the pounding effect to the global response of the building is also presented. Two soil conditions were assumed with (freefield) and without (bedrock) site amplification. The results showed that site effects strongly affected the seismic vulnerability of the aggregate, also altering the combination between IP and OOP mechanisms. In fact, for bedrock condition, especially for medium–high damage levels, local mechanisms were prevailing with respect to the IP response. Conversely, for freefield condition, IP mainly governed the overall behaviour for all the damage levels, consistently with the field evidence.

Scala S.A., Del Gaudio C., Verderame G.M.

The aim of this study is the analysis of seismic fragility of residential masonry buildings, with particular emphasis to the evolution of seismic behaviour over the years. To this purpose, a detailed and comprehensive taxonomy has been established, considering a restricted selection of building's features, avoiding the ineffective fragmentation of the database. The fragility assessment has been performed based on the data collected after the L'Aquila 2009 earthquake and made available by the Italian Department of Civil Protection through the online platform Da.D.O. (Database of Observed Damage). The database has undergone a refinement process to guarantee the completeness of the information, avoiding possible bias in the subsequent fitting procedure for fragility analysis. Thus, PGA (peak ground acceleration) from the ShakeMap has been used for ground motion characterization and 5 + 1 damage levels defined according to the European Macroseismic Scale have been considered for damage classification. Different regression models have been adopted to determine the parameters of lognormal fragility curves, measuring their goodness of fit with the observed damage probability matrices. Starting from the unconstrained model, further regression constraints (i.e., a common value for logarithmic standard deviation and the respect of the hierarchy of median PGA with the construction age) have been introduced, thus leading to the definition of the constrained model. The benefits in the introduction of further regression constraints are counterposed to the effectiveness of constrained curves to model observational data through the comparison of the goodness of fit between the unconstrained and constrained models.

Brunelli A., de Silva F., Cattari S.

The paper focuses on the seismic response of masonry buildings in the historical centre of Visso, severely hit by the 2016–2017 Central Italy earthquake. This represents an emblematic case of site effects and, also, of soil-foundation-structure (SFS) interaction. Maps of the observed damage at urban scale are compared with those estimated from fragility curves derived for the building stock that characterizes the Visso municipality. Similarly to what is quite recurring in typical small historical centres in Italy and Europe, the key feature of Visso is to be mostly composed by unreinforced masonry (URM) buildings (85%), the majority of which is in aggregate (93%). Fragility curves were developed through a numerical procedure based on nonlinear dynamic analyses on 3D equivalent frame models, both fixed and compliant base, accounting for site effects and SFS interaction. The procedure aims at balancing the computational effort with the potential of defining fragility curves customized for the building under investigation and, thus, hopefully capable to improve the reliability of risk assessment. The fragility curves for URM buildings in aggregate explicitly account for the recurring failure mechanisms that post-earthquake evidence has testified, i.e. in-plane (IP) and out-of-plane (OOP) responses, as well as the interaction effects among adjacent units and pounding effects. The numerical procedure has been applied and validated in previous works of Authors on various archetypes representative either of an isolated school and one aggregate. In this work, additional archetypes have been analyzed and, then, the whole set of achieved fragility curves has been generalized to be applicable for a risk assessment at urban scale and develop damage scenarios of the Visso's urban settlement. To this aim, simplified modification factors have been proposed to be applied to fragility curves of rock soil condition to account for the possible effect of soft soil as well as the activation of OOP mechanisms. Results have shown that the match between the observed and simulated response improves when the interaction between the structure and the soil is considered.

Di Ludovico M., Cattari S., Verderame G., Del Vecchio C., Ottonelli D., Del Gaudio C., Prota A., Lagomarsino S.

Recent seismic events worldwide have demonstrated the high vulnerability of existing school buildings and the urgent need to have reliable tools for the rapid seismic performance assessment and damage and loss quantification. Indeed, the significant damage observed on structural and non-structural components may have a significant impact in terms of direct and indirect losses making critical the recovery of stricken communities. Although a significant amount of work has been done in developing fragility curves for the residential building stock, only few contributions clearly refer to school buildings that significantly differ in terms of the main characteristics from the residential ones. This research work proposes fragility curves for reinforced concrete and unreinforced masonry public school buildings typical of the Italian building stock, based on the damage observed in the aftermath of the 2009 L’Aquila earthquake. A comprehensive and unique database including data on damaged and undamaged school buildings (2037 records) in the Abruzzo region was built using data from four different sources. Due to limited amount of data, the fragility curves can be very sensitive to the method adopted for their derivation, thus three different approaches (i.e. empirical, empirical-binomial, heuristic) are considered in the paper and the results are compared. Finally, a direct comparison with fragility curves available in the literature for the Italian residential building stock is presented.

Lagomarsino S., Cattari S., Angiolilli M., Bracchi S., Rota M., Penna A.

Manfredi V., Masi A., Özcebe A.G., Paolucci R., Smerzini C.

Ground motion selection is one of the most important phases in the derivation of fragility curves through non-linear dynamic analyses. In this context, an easy-to-use software, namely S&M—Select & Match, has been adopted for the selection and spectral matching of recorded ground motions approaching a target response spectrum in a broad period range. In this paper, after a brief description of the key features of the S&M tool, two sets of 125 accelerograms, separately for stiff (i.e. site classes A and B according to the Italian code) and soft soil (i.e. site classes C and D) conditions, have been selected on the basis of the elastic design spectra of the Italian seismic code defined for different return periods. The selected ground motions have been analysed and used for non-linear dynamic analysis of a case study representative of a common Italian RC building type designed only to gravity loads. Results have been analysed in order to check the capability of the considered signals to adequately cover all the damage levels generally adopted in seismic risk analyses, as well as the effects on seismic response due to the selection criteria permitted by the proposed tool.

Angiolilli M., Lagomarsino S., Cattari S., Degli Abbati S.

The paper describes the derivation of fragility curves useful for the seismic risk analyses of existing unreinforced masonry buildings inserted in aggregate. The L-shaped examined aggregate consists of three adjacent structural units that may mutually interact during seismic events. The seismic assessment is focused on the corner unit. The effects of different connection types between the adjacent units on the structural response were investigated. The seismic vulnerability of the masonry aggregate was assessed through nonlinear dynamic analyses (NDA) performed according to the multi-stripes approach. Both the in-plane and out-of-plane mechanisms were analyzed. The in-plane response of the corner unit is assessed through a 3D equivalent frame model of the entire aggregate, while the evaluation of its out-of-plane response makes use of the rigid-block assumption. Although evaluated in a separate way, the NDAs performed on the latter are based on the time histories derived from the global 3D model. The results are then processed in order to derive fragility curves, firstly, of the single failure mechanisms and, then, of the overall combined behavior. To this aim, various performance conditions are examined. For the reference building, the damage limit state is mainly governed by the in-plane behavior, while the collapse limit state by out-of-plane mechanisms. Moreover, the higher the connection level between adjacent structural units, the higher the interaction between in-plane and out-of-plane mechanisms at the collapse limit state. • Procedure for derivation of fragility curves by NLDA accounting for both in-plane and out-of-plane mechanisms. • The 3D equivalent frame model of the aggregate considers the interaction between buildings by proper joints. • Rigid block NLDAs of the OOP response use time histories derived from the 3D model of the aggregate. • For the corner building, damage limit state is governed by IP response while collapse by OOP mechanisms. • The higher the connection between structural units, the higher the interaction of IP and OOP at collapse.

Cattari S., Camilletti D., D'Altri A.M., Lagomarsino S.

The assessment of the seismic vulnerability of masonry buildings requires reliable and computationally efficient numerical models. Different modelling strategies can be adopted when studying the global response of these structures, such as Continuum Constitutive Laws Models (CCLM) belonging to Finite Element (FE) models, which may be very accurate but whose use in practice presents several issues (high computational burden, requirement of many input data), and Equivalent Frame (EF) Models, that, even if based on strong simplifications, are now widespread in engineering practice, thanks to their computational efficiency and the need of few mechanical parameters for the structural analysis. The paper discusses the consistent use of these modelling techniques for the seismic analysis of masonry structures . To this aim, a comparison of two approaches (CCL and EF models) is presented focusing at first the attention on the calibration of the constitutive laws through analyses on single panels and then moving to the validation of some simplified assumptions made in the EFM through the analysis of a 2D regular URM wall. For the aim of validation, the CCL model is considered as the reference solution making an accurate comparison with the EF model in terms of generalized forces, drift and damage occurred at element scale and of pushover curve at global scale. • A procedure for cross-calibrating the mechanical parameters in Finite Element (FE) and Equivalent Frame (EF) models is discussed in the paper. • The procedure guarantees a consistent use of two modelling approaches for the seismic assessment of URM buildings. • The reliability of EF model in case of regular 2D URM walls is confirmed through a very detailed comparison with the FE model. • Different rules for the EF idealization of regular URM walls are tested and criteria to orient the choice on the most reliable ones are proposed.