Ground motion sample size vs estimation uncertainty in seismic risk

In the context of seismic risk assessment as per the performance-based earthquake engineering paradigm, a probabilistic description of structural vulnerability is often obtained via dynamic analysis of a nonlinear numerical model. It typically involves subjecting the structural model to a suite of ground-motions that are representative, as a sample, of possible seismic shaking at the site of interest. The analyses results are used to calibrate a stochastic model describing structural response as a function of seismic intensity. The sample size of ground motion records used is, nowadays, usually governed by computation-time constraintson the other hand, it directly affects the estimation uncertainty which is inherent in risk analysis carried out in this way. Recent studies have suggested methodologies for the quantification of estimation uncertainty, to be used as tools for determining the appropriate number of records for each application on an objective basis. The present study uses one of these simulation-based methodologies, based on standard statistical inference methods and the derivation of structural fragility via incremental dynamic analysis, to investigate the accuracy of the risk estimate (e.g., the annual failure rate) vs the size of ground motion samples. These investigations consider various scalar intensity measures and confirm that that the number of records required to achieve a given level of accuracy for annual failure rate depends not only on the dispersion of structural responses, but also on the shape of the hazard curve at the site. This indicates that the efficiency of some frequently-used intensity measures is not only structure-specific but also site-specific.The study presented in this paper was developed within the activities of ReLUIS (Rete dei Laboratori Universitari di Ingegneria Sismica) for the project ReLUIS-DPC 2014–2018, as well as within the H2020-MSCA-RISE-2015 research project EXCHANGE-Risk (Grant Agreement Number 691213)

SPO2FRAG V1.0: SOFTWARE FOR PUSHOVER-BASED DERIVATION OF SEISMIC FRAGILITY CURVES

This article presents SPO2FRAG V1.0, the fi rst (beta) version of the Static PushOver to FRAGility software. The SPO2F RAG software is an interactive and user-friendly tool that can be used for approximate, computer-aided calc ulation of building seis mic fragility functions, based on static pushover analysis. It is coded in MATLAB ® environment and is currently under development at the Department of Structures for Engineering and Architecture of the University of Naples Federico II. At the core of the SPO2FRAG tool lies the SPO2IDA algorithm, which permits analytical predictions fo r incremental dynamic analysis summary fractiles at the sin- gle-degree-of-freedom system le vel. By effectively interfacing SPO2IDA with a series of oper- ations, intended to link the results of static pus hover analysis with the va riability that typically characterizes non-linear dynamic structural re sponse, SPO2FRAG provides an expedient so- lution to the computationally demanding task of analytically evaluati ng seismic building fra- gility, which would otherwise require a la rge number of non-linear dynamic analyses

REXELweb: a tool for selection of ground-motion records from the Engineering Strong Motion database (ESM)

This paper illustrates REXELweb, an updated online version of REXEL, which is a tool for the automatic selection and scaling of spectrum-compatible ground- motions for dynamic analysis of structures. REXELweb allows to define target spectra according to user-definition or design provisions (Eurocode 8 and Italian building code), as well as to uniform hazard spectra (UHS) based on a European hazard model. REXELweb implements all functionalities and options of REXEL through web-services that are accessible either via a MATHWORKS-MATLAB script or a user-friendly web-interface. The program selects records from the Engineering Strong Motion database (ESM), which is a daily-updated Pan-European repository of high-quality ground-motion records. These features make REXELweb a potentially useful tool for researchers and practitioners.Associazione Geotecnica ItalianaPublishedRome5T. Sismologia, geofisica e geologia per l'ingegneria sismic

Structural performance evaluation in near-source conditions

The present thesis confronts the problem of evaluating the seismic performance of structures in near-source conditions, when said structures are designed for inelastic response to strong ground motion. What sets near-source seismic input apart and causes it to merit particular attention, is the fact that NS ground motions often contain significant wave pulses. Therefore, a dataset of previously identified impulsive near-source records is used to derive an analytical-form relationship for the inelastic displacement ratio by means of regression analysis. It is found that a double-opposite-bumps form is required to match the empirical data as function of the structural period over the pulse period ratio, similar to what has been proposed in the literature for soft soil sites. The relationship consistently builds on previous studies on the topic, yet displays different shape with respect to the most common equations for static structural assessment procedures. This reveals that inelastic seismic demand of near-source pulse-like ground motions can exhibit different trends than ordinary records i.e., records not identified as pulse-like. Subsequently, the extension of non-linear static procedures for seismic design and assessment is discussed, with respect to the inelastic demand associated with forward directivity. In this context, a methodology is presented for the implementation of the Displacement Coefficient Method towards estimating near-source seismic demand. This method makes use of the results of near-source probabilistic seismic hazard analysis and the semi-empirical equation for pulse-like inelastic displacement ratio. An illustrative application of the Displacement Coefficient Method, with explicit inclusion of near-source, pulse-like effects, is given for a set of typical, plane, reinforced concrete frames, designed under Eurocode provisions. Different scenarios are considered in the application and non-linear dynamic analysis results are obtained and discussed with respect to the static procedure estimates. Conclusions drawn from the results help to assess the importance of incorporating near-source effects in performance-based seismic design. Finally, the seismic demand of oscillators with more complex, trilinear, backbone curves to near-source pulse-like ground motions is examined. This study is motivated by the need for seismic demand estimates by nonlinear static procedures that delve deeper into the inelastic range and arrive at quantifying dynamic collapse capacity, which has already set researchers on this path for ordinary ground motions. Thus, this chapter closely follows the methodology of Vamvatsikos and Cornell (2006), employing incremental dynamic analysis and the suite of one hundred and thirty pulse-like-identified ground motions, in order to develop an elaborate reduction factor-ductility-period relation for pulse-like near-source motions and oscillators characterized by generic trilinear backbones. The resulting analytical model captures both central tendency and dispersion of near-source pulse-like seismic demand. The model also makes the important inclusion of pulse period as a predictor variable, whose importance is demonstrated in an illustrative application

Near-source pulse-like seismic demand for multi-linear backbone oscillators

Nonlinear static procedures, which relate the seismic demand of a structure to that of an equivalent single-degree-of-freedom (SDOF) oscillator, are well-established tools in the performance based earthquake engineering framework and have gradually found their way into modern codes for seismic design and assessment. Initially, such procedures made recourse to inelastic spectra derived for simple elastic-plastic or bilinear oscillators, but the request for demand estimates, which delve deeper into the inelastic range, shifted the trend towards inves-tigating the seismic demand of oscillators with more complex backbone curves. Meanwhile, the engineering relevance of near-source (NS) pulse-like ground motions has been receiving increased attention, since it has been recognized that such ground motions can induce a distinctive type of inelastic demand. Pulse-like NS ground motions are usually the result of rupture directivity, where seismic waves generated at different points along the rupture front arrive at a site at the same time, leading to a double-sided velocity pulse, which delivers most of the seismic energy. Recent research has led to a methodology being proposed for incorpo-rating this NS effect in the implementation of nonlinear static procedures. Both of the aforementioned lines of earthquake engineering research motivate the present study, which investigates the ductility demands imposed by pulse-like NS ground motions on SDOF oscillators who feature pinching hysteretic behavior with trilinear backbone curves. This in-vestigation uses incremental dynamic analysis (IDA) considering a suite of one hundred and thirty pulse-like-identified ground motions. Median, as well as 16% and 84% fractile, IDA curves are calculated, on which an analytical model is fitted. Least-squares estimates are ob-tained for the model parameters, which importantly include pulse period Tp. The resulting equa-tions effectively constitute an R-μ-T/Tp relation for pulse-like NS motions. A potential application of this result is briefly demonstrated in an illustrative example of NS seismic de-mand estimation

La selezione di registrazioni accelerometriche a due componenti secondo le NTC18 e la circolare applicativa

Le moderne normative sismiche come l’Eurocodice 8 (EC8) o le Norme Tecniche per le Costruzioni (NTC), consentono la verifica del progetto strutturale tramite analisi dinamiche, utilizzando modelli tridimensionali delle strutture, sollecitate da due o tre componenti del moto del suolo (due componenti orizzontali ed una componente verticale). Tali registrazioni del moto sismico vanno scelte in modo che siano rappresentative della sismicità del sito di costruzione e gli spettri di risposta elastica, eventualmente scalati, devono rispettare alcuni requisiti di compatibilità con lo spettro elastico di progetto (spettro obiettivo). Le NTC impongono, come criterio di spettrocompatibilità, che la media degli spettri elastici delle componenti orizzontali dei segnali selezionati debba approssimare lo spettro elastico obiettivo entro una fissata soglia tolleranza in un determinato intervallo di periodi: tale prescrizione implicitamente permette che le due componenti orizzontali di una registrazione selezionata possano avere di fattori di scala diversi. La circolare applicativa delle NTC ha invece introdotto, similmente a quanto prescritto nello EC8–parte 2 (progettazione sismica di ponti), una procedura per cui preliminarmente vengono combinati gli spettri delle componenti orizzontali della singola registrazione tramite la radice quadrata della somma dei quadrati (SRSS) delle ordinate spettrali, viene poi calcolata la media degli spettri SRSS opportunamente scalati e confrontata con lo spettro obiettivo incrementato di una fissata quantità. Obiettivo di questo lavoro è valutare la compatibilità tra i risultati ottenuti con la procedura prescritta dalle nuove NTC e le indicazioni esposte in circolare. Un’ulteriore analisi condotta ha confrontato separatamente le medie delle componenti orizzontali con lo spettro obiettivo (e non complessivamente, come precedentemente esposto). I risultati ottenuti suggeriscono che le due procedure portano a selezioni tra loro compatibili. Inoltre, nella grande maggioranza dei casi trattati il soddisfacimento del criterio di compatibilità considerando la media complessiva di tutte le componenti delle registrazioni porta al soddisfacimento della compatibilità per componenti separate

Accounting for near-source effects in the displacement coefficient method for seismic structural assessment

Non-linear static procedures are well-established analytical tools for performance-based seismic design and assessment. On the other hand, near-source (NS) ground motions are emerging as relevant to structural engineering because they may be characterized by seismic demand larger and systematically different than that typically induced by so-called ordinary records. This is the result of phenomena such as rupture forward directivity (FD), which may lead to the appearance of distinct velocity pulses in the ground motion velocity time-history. Lately, effort was put towards the framework necessary for taking FD into ac-count in probabilistic seismic hazard analysis (PSHA). The objective of the present study is to discuss the extension of non-linear static procedures, such as the displacement coefficient method (DCM), with respect to the inelastic demand associated with FD. In this context, the DCM is implemented to estimate NS seismic demand by making use of the results of NS-PSHA, developed for single-fault-case scenarios. A predictive model for NS-FD inelastic displace-ment ratios, previously developed by the authors, is employed. An illustrative application of the DCM, with explicit inclusion of NS-pulse-like effects, is given for a plane R/C frame de-signed under modern code provisions

The displacement coefficient method in near-source conditions

The use of nonlinear static procedures for performance-based seismic design (PBSD) and assessment is a well-established practice, which has found its way into modern codes for quite some time. On the other hand, near-source (NS) ground motions are receiving increasing attention, because they can carry seismic demand systematically different and larger than that of the so-called ordinary records. This is due to phenomena such as rupture forward directivity (FD), which can lead to distinct pulses appearing in the velocity time-history of the ground motion. The framework necessary for taking FD into account in probabilistic seismic hazard analysis (PSHA) has recently been established. The objective of the present study is to discuss the extension of nonlinear static procedures, specifically the displacement coefficient method (DCM), with respect to the inelastic demand associated with FD. In this context, a methodology is presented for the implementation of the DCM toward estimating NS seismic demand, by making use of the results of NS-PSHA and a semi-empirical equation for NS-FD inelastic displacement ratio. An illustrative application of the DCM, with explicit inclusion of NS-pulse-like effects, is given for a set of typical plane R/C frames designed under Eurocode provisions. Different scenarios are considered in the application and nonlinear dynamic analysis results are obtained and discussed with respect to the static procedure estimates. Conclusions drawn from the results may help to assess the importance of incorporating NS effects in PBSD