The heuristic vulnerability model: fragility curves for masonry buildings

AbstractIn the framework of seismic risk analyses at large scale, among the available methods for the vulnerability assessment the empirical and expert elicitation based ones still represent one of most widely used options. In fact, despite some drawbacks, they benefit of a direct correlation to the actual seismic behaviour of buildings and they are easy to handle also on huge stocks of buildings. Within this context, the paper illustrates a macroseismic vulnerability model for unreinforced masonry existing buildings that starts from the original proposal of Lagomarsino and Giovinazzi (Bull Earthquake Eng 4(4):445–463, 2006) and has further developed in recent years. The method may be classified as heuristic, in the sense that: (a) it is based on the expertise that is implicit in the European Macroseismic Scale (EMS98), with fuzzy assumptions on the binomial damage distribution; (b) it is calibrated on the observed damage in Italy, available in the database Da.D.O. developed by the Italian Department of Civil Protection (DPC). This approach guarantees a fairly well fitting with actual damage but, at the same time, ensures physically consistent results for both low and high values of the seismic intensity (for which observed data are incomplete or lacking). Moreover, the method provides a coherent distribution between the different damage levels. The valuable data in Da.D.O. allowed significant improvements of the method than its original version. The model has been recently applied in the context of ReLUIS project, funded by the DPC to support the development of Italian Risk Maps. To this aim, the vulnerability model has been applied for deriving fragility curves. This step requires to introduce a correlation law between the Macroseismic Intensity (adopted for the calibration of the model from a wide set of real damage data) and the Peak Ground Acceleration (at present, one of most used instrumental intensity measures); this conversion further increases the potential of the macroseismic method. As presented in the paper, the first applications of the model have produced plausible and consistent results at national scale, both in terms of damage scenarios and total risk (economic loss, consequences to people)

Seismic behavior of lisbon mixed masonry-rc buildings with historical value: A contribution for the practical assessment

The fact that linear analysis is still the most used procedure in the design engineering offices, studies which addresses issues associated to the estimation of the structural behavior factor values are relevant. In this study, the behavior factor of a particular type of mixed masonry-reinforced concrete buildings in Lisbon is estimated. The typology chosen in this study represents 30% of building stock in Lisbon; these buildings were built between 1930 and 1960 and thus were designed without considering the seismic-design requirements proposed in current codes. The evaluation of the behavior factors was based on the use of nonlinear static analyses, performed in the form of the sensitivity analysis and following the criteria proposed in the current seismic codes and literature. In the scope of the sensitivity analysis, aleatory and epistemic uncertainties have been considered in terms of the mechanical parameters and structural details, respectively with the aim to take into account different characteristics of the structures. In order to derive the most reliable values of the behavior factor for this typology, extensive research in terms of the historical information, structural characterization and definition of the mechanical parameters has been performed. The study indicates that the final values of behavior factor are low and depend most on the type of connections between structural walls. Although the obtained values of the behavior factor for this typology match well with the ones proposed in most recent seismic codes, it is recommended that the assessment of such factor of a specific class for a particular structural type building should always be careful evaluated

Seismic assessment of plan irregular masonry buildings with flexible diaphragms

The seismic Performance-Based assessment of existing masonry buildings requires the use of nonlinear models, in order to check the attainment of ultimate limit states. Incremental Dynamic Analysis represents the most accurate method but very few models areavailable which are able to describe the stiffness and strength degradation, which are typical of masonry buildings, as well as the hysteretic behaviour of piers and spandrels under cyclic actions. At engineering practice level, the Displacement-Based approach is widely adopted, through the use of nonlinear static analysis. However, the application in the case of irregular URM buildings with flexible horizontal diaphragms represents an open issue, due to various difficulties, for example in the transformation of the pushover curve of the original MDOF into the equivalent SDOForinthe definition of performance levels. A wide numerical investigation was made onsome case studies, in order to check the applicability of nonlinear static analyses and propose some newprocedures. Nonlinear dynamic analyses have been adopted as reference solution

Reliability of nonlinear static analysis in case of irregular URM buildings with flexible diaphragms

The seismicPerformance-Based assessment of existing masonry buildings requires the use of nonlinear models, in order to check the attainment of ultimate limit states. Incremental Dynamic Analysis represents the most accurate method but very few models are available which are able to describe the stiffness and strength degradation, which are typical of masonry buildings, as well as the hysteretic behaviour of piers and spandrels under cyclic actions. At engineering practice level, the Displacement-Based approach is widely adopted, through the use of nonlinear static analysis. However, the application in the case of irregular URMbuildings with flexible horizontal diaphragms represents an open issue,due to the various difficulties, for example in the selection of proper load pattern or the definition of performance levels. A wide numerical investigation was made of some case studies, in order to check the applicability of nonlinear static analyses and propose some newprocedures. Nonlinear dynamic analyses have been adopted as reference solution, by using the Proper Orthogonal Decomposition technique in order to catch the dominant behaviours to be compared with those obtained by pushover analysis

Influence of spandrel modelling on the seismic assessment of existing masonry buildings

The paper discusses different modelling assumptions for spandrels in equivalent frame models and their effect on the global response of the wall. The topic is motivated by the following issues: i) reliable and practice oriented numerical tools constitute a key instrument to support mitigation policies and plan effective (in terms of cost and impact) retrofit interventions; ii) spandrels have lately been increasingly recognized to play a significant role on the load bearing capacity of masonry walls; iii) despite the experimental evidence of last years that highlighted significant differences between spandrels and piers, numerical tools available in literature and recommendations of codes do not yet account properly for the progress achieved with regard to spandrel models. To deepen such issues, various strength criteria specifically formulated for spandrels and available in literature have been implemented in the Tremuri program, including those proposed by Beyer (2012) that have been recently incorporated in the updated release of the NZSEE recommendations. With the so enhanced program, parametric nonlinear static analyses on 2D masonry walls have been performed to quantitatively assess the influence of spandrel modelling

Modelling of two damaged unreinforced masonry buildings following the Canterbury earthquakes

The reported study focusedon modellingthe seismic response of two URM buildings that were damaged in the Canterbury earthquake sequence. Static and dynamic nonlinear analyses were undertakenusing the equivalent frame approach. Actual time-history records attained during the earthquakes where used to undertake dynamic analyses and facilitatedirect comparison to the observed building damage. The results showedthat use of the equivalent frame methodenabledpredictionof the seismic responseof the two case study buildings with ahigh level of accuracy

Proposta di un aggiornamento della formulazione NTC-08 per gli spettri di piano e sua applicabilit\ue0 nella verifica dei meccanismi locali

La valutazione della risposta sismica di un\u2019appendice non strutturale o di una porzione strutturaleposti in quota o sommit\ue0 rispetto alla struttura principale \ue8tradizionalmente affrontata seguendo due approcci: i) il \u201cFloor response spectrum approach\u201d, che si basa sull\u2019ipotesi di poter trascurare l\u2019interazione dinamica tra i due sistemi ed opera per sottostrutture; ii) il \u201cCombined Primary-Secondary system approach\u201d, che studia il sistema nel suo complesso includendo esplicitamente gli effetti di accoppiamento. Nell\u2019ambito del primo approccio, il problema si riduce alla corretta definizione dello spettro di piano, per il qualenumerose formulazioni analitiche semplificate sono proposte in letteratura ed adottate nelle normative nazionali ed internazionali. Tali espressioni includono tuttavia in alcuni casi la dipendenza da un numero molto limitato di parametri, non sufficiente a cogliere tutti gli aspetti fisici che possono influenzare il fenomeno di interazione. In questo contesto, l\u2019articolo si pone due obiettivi: i) la verifica dell\u2019attendibilit\ue0 e la definizione dei campi di applicabilit\ue0 delle tradizionali procedure per sottostrutture; ii) il confronto tra alcune formulazioni proposte in letteratura per gli spettri di piano e la proposta di un aggiornamento di quella proposta in Lagomarsino 2015(e da cui deriva la formulazione NTC-08), che si \ue8 dimostrata dal confronto quella pi\uf9 affidabile

Masonry Italian Code-Conforming Buildings. Part 2: Nonlinear Modelling and Time-History Analysis

open6The 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 realized using an equivalent frame approach and by adopting two different constitutive laws. Both the effect of record-to-record variability and of epistemic and aleatory uncertainties in modelling were explored. The achieved results constitute the basis for the evaluation of the risk level implicit in Italian code-conforming buildings. Two main performance conditions are considered, namely usability-preventing damage and global collapse limit statesopenSerena Cattari, Daniela Camilletti, Sergio Lagomarsino , Stefano Bracchi, Maria Rota, Andrea PennaCattari, Serena; Camilletti, Daniela; Lagomarsino, Sergio; Bracchi, Stefano; Rota, Maria; Penna, Andre

Valutazione della risposta sismica di edifici in muratura irregolari in pianta e con solai flessibili

E\u2019 ormai consolidato, non solo a livello della ricerca ma anche nella pratica professionale, l\u2019uso dell\u2019analisi statica non lineare per la verifica della sicurezza sismica degli edifici esistenti in muratura secondo un approccio prestazionale agli stati limite. Come noto, tali metodi di analisi e verifica sono stati originariamente sviluppati per altre tipologie (calcestruzzo armato e acciaio), tipicamente sotto l\u2019ipotesi di solai rigidi e regolarit\ue0 strutturale; nell\u2019ultimo decennio sonopoistate formulate ulteriori proposte, ancora per tali tipologie, per includere gli effetti indotti da irregolarit\ue0 planimetriche e/o altimetriche ed il contributo dei modi superiori. Viceversa, nel caso degli edifici in muratura irregolari e con solaiflessibili l\u2019affidabilit\ue0 di tali metodi non \ue8 stata ancora valutata in maniera sistematica. In tale contesto, il presente articolo si propone di verificare l\u2019affidabilit\ue0 dell\u2019approccio statico non lineare edi suoi eventuali limiti di applicabilit\ue0 al variare di crescenti caratteristiche di irregolarit\ue0 planimetrica e flessibilit\ue0 dei solai, con particolare riferimento all\u2019uso di diverse distribuzioni di forze mantenute invarianti durante l\u2019analisi. A tale scopo sono state eseguite analisi parametriche su dieciconfigurazioni prototipo di un edificio in muratura ordinaria di tre piani. I risultati ottenuti da analisi dinamiche non lineari incrementali sono stati assunti come soluzione di riferimento e di validazione dell\u2019approccio statico