Abstract
Design ground motion intensities determine the actions for which structures are checked, in the conventional approach of seismic codes, not to fail the target performances. On the other ...hand, due to inherent characteristics of probabilistic seismic hazard analysis (PSHA), it is expected that site-specific design intensity based on PSHA is exceeded in the epicentral area of moderate-to-high magnitude earthquakes. In the context of regional seismic loss assessment and of the evolution of seismic codes from the regulator perspective, it is useful to gather insights about the extent of the zone around the earthquake source where code-conforming structures are expected to be systematically exposed to seismic actions larger than those accounted for in design. To assess such areal extent based on empirical evidence is the scope of the study presented in the paper. To this aim, peak ground acceleration ShakeMap data for Italian earthquakes from 2008 to 2020 were compared to the current design intensities in the same areas for which the maps are available. This allowed, first, to develop simple semi-empirical models of the exceedance area versus the magnitude of the earthquakes. Second, it allowed to model the probability that an earthquake of given magnitude causes exceedance of the design intensity via logistic regressions. Coupling the first and second class of models provides an approximation of the expected exceedance (logarithmic) area upon occurrence of an earthquake of given magnitude. Such an area can be of several thousand square kilometers for earthquakes occurring relatively frequently in countries such as Italy.
Probabilistic seismic hazard analysis (PSHA) is widely employed worldwide as the rational way to quantify the uncertainty associated to earthquake occurrence and effects. When PSHA is carried out for ...a whole country, its results are typically expressed in the form of maps of ground motion intensities that all have the same exceedance return period. Classical PSHA relies on data that continuously increase due to instrumental seismic monitoring, and on models that continuously evolve with the knowledge on each of its many aspects. Therefore, it can happen that different, equally legitimate, hazard maps for the same region can show apparently irreconcilable differences, sparking public debate. This situation is currently ongoing in Italy, where the process of governmental enforcement of a new hazard map is delayed. The discussion is complicated by the fact that the events of interest to hazard assessment are intentionally rare at any of the sites the maps refer to, thus impeding empirical validation at any specific site. The presented study, pursuing a regional approach instead, overcoming the issues of site specific PSHA validation, evaluated three different authoritative PSHA studies for Italy. Formal tests were performed directly testing the output of PSHA, that is probabilistic predictions, against the observed ground shaking exceedance frequencies, obtained from about fifty years of continuous monitoring of seismic activities across the country. The bulk of analyses reveals that, apparently alternative hazard maps are, in fact, hardly distinguishable in the light of observations.
Prioritization of seismic risk mitigation at a large scale requires rough-input methodologies able to provide an expedited, yet conventional, assessment of the seismic risk corresponding to the ...portfolio of interest. In fact, an evaluation of seismic vulnerability at regional level by means of mechanics-based methods is generally only feasible for a fraction of the portfolio, selected according to prioritization criteria, due to the sheer volume of information and computational effort required. Therefore, conventional assessment of seismic risk via simple indices has been proposed in literature and in some guidelines, mainly based on the comparison of code requirements at the time of design and current seismic demand. These indices represent an attempt to define a relative seismic risk measure for a rapid ranking to identify the part of the portfolio that deserves further investigation. Although these risk metrics are based on strong assumptions, they have the advantage of only requiring easy-to-retrieve data, such as design year and location as the bare minimum, making them suitable for applications within the risk analysis industry. Moreover, they can take both hazard and vulnerability into account, albeit conventionally, and can be manipulated in order to account for exposure in terms of individual or societal risks. In the present study, the main assumptions, limitations, and possible evolutions of existing prioritization approaches to nominal risk are reviewed, with specific reference to the Italian case. Furthermore, this article presents the software NODE (available to interested readers), which enables the computation of location-specific code-based seismic performance demands, according to the Italian code and the evolution of seismic classification since 1909. Finally, this study intends to contribute to the ongoing debate on strategies for large-scale seismic assessment for building stock management purposes.
Current seismic structural design makes use of a ground motion intensity that has a certain probability of being exceeded at a site of interest in a time interval or, equivalently, exceedance return ...period. The design intensities with the same return period are often collected in the form of maps deriving from probabilistic seismic hazard analysis (PSHA) for each of the sites of interest. Probability theory underlying PSHA dictates that, in any time interval, design intensities are expected to be exceeded in a fraction of sites that depends on the return period the map refers to. In the case of Italy, three different nationwide PSHA studies can be currently considered of relevance. In the study, the estimated areal fraction of the Italian territory exposed to exceedance of the design intensity from 2008 to 2019 was quantified for the three hazard models, based on ShakeMap data for instrumental earthquakes. In addition, the same fraction was calculated considering a sparse catalog of inferred ShakeMap for historical earthquakes that occurred over almost 1000 years. It was found that, despite the apparent differences in the hazard models, the estimated fraction of territory exposed to exceedance is comparable for all the considered hazard maps.
The increasing attention of stakeholders to extreme winds impacting the built environment is driving towards the adoption of probabilistic risk assessment methods, which aim at the stochastic ...modelling of three main risk components: hazard, vulnerability (or fragility), and exposure. Taking from seismic risk assessment, the hazard is typically expressed in terms of exceedance rate of an intensity measure of the natural event, usually related to wind speed, and the risk metric is the expected annual loss or the exceedance rate of the loss. On these premises the extreme wind risk assessment software, ERMESS, has been developed for risk assessment for portfolios of buildings. It integrates recent global- and regional-scale hazard maps for extreme wind events, that is, cyclones and tornadoes, and a database of more than five-thousand building- and component-level wind vulnerability and fragility functions from the literature. A procedure to develop building-level fragility models, based on existing component-level fragility functions, was also developed and embedded in ERMESS. Finally, the exposure (i.e. consequence) models are based on information provided by the insurance industry. The paper illustrates the software by means of proof-of-concept applications that show how ERMESS can be effective in wind risk assessment.
This technical note illustrates and makes available some simple procedures to assess the estimation uncertainty for the parameters of seismic fragility curves. The considered fragility fitting ...methods refer to the lognormal assumption and are supposed to be based on the results of multi-stripe dynamic analysis of a deterministic non-linear structural model, so that the uncertainty in the fragility parameters arises from the so-called record-to-record variability. The discussed procedures are based on the statistics approach of resampling with substitution, which is commonly referred to as bootstrap. It is also briefly discussed how the estimation uncertainty depends on the maximum value of the probability of failure given seismic intensity that is observed from structural analysis. This work may aid earthquake engineering practice because, both the curve fitting and estimation uncertainty algorithms are implemented in a major update of an application-ready software tool made available at https://www.reluis.it/it/progettazione/software/r2r-eu.html.
•Some procedures for the assessment of the estimation uncertainty in the seismic fragility parameters are illustrated.•A discussion of the effect, on the estimation uncertainty, of the maximum fragility value from structural analysis, is given.•The discussed algorithms are coded in a software made available through the technical note.
Seismic hazard maps from probabilistic seismic hazard analysis or PSHA collect, at different sites, the values of the (site-specific) ground motion intensity measures of interest that, ...taken individually, have the same exceedance return period. For large-scale analyses, a widely used intensity measure is the macroseismic (
MS
) intensity, that provides an assessment of the earthquake effect based on the observed consequences in the hit area. Hazard maps can be developed in terms of
MS
intensity, and some examples exist in this respect. In the case of Italy, the last
MS
hazard map is based on the same seismic source model (known as MPS04) adopted to derive the design seismic actions of the current building code, a study dating more than ten years ago. It provides results in terms of countrywide Mercalli–Cancani–Sieberg (MCS) intensity level with 475 years return period. This short paper presents and discusses MCS probabilistic seismic hazard maps for Italy based on a recent grid-seismicity source model, herein named MPS19, synthetizing the large effort of a wide scientific community. The results, which are obtained by means of classical PSHA, are given in the form of maps referring to the 475 years return period, and also others of earthquake engineering interest. Moreover, it is discussed that the return period does not univocally identifies the
MS
intensity because, although
MS
is, by definition, a discrete random variable, it is modelled, in a given earthquake, by means of a normal distribution, that is, treated as continuous. Thus, the maps of the minimum return period causing the occurrence or exceedance of different MCS intensities are also provided. Finally, the comparison between the 475 years return period hazard map presented and the one which is currently the point of reference in Italy, that is, computed using MPS04, is briefly discussed. All the computed maps are made available to the reader as supplemental material.
Hazard curves from probabilistic seismic hazard analysis (PSHA) are plots of the rate of earthquakes exceeding ground motion intensity values vs such threshold values, for a site of interest. In ...classical PSHA, these curves can be transformed to provide the probability of exceedance of ground motion intensity values in any time interval, utilizing the properties of the homogeneous Poisson process (HPP). In turn, these probability curves can be seen as the plot of the complementary cumulative distribution function of the maximum intensity observed, at the site, in the time interval of interest. One consequence of the HPP framework, within which PSHA is developed, is that, for large time intervals, it can be argued that these curves could asymptotically lead to a probabilistic model for extreme value (EV) random variables. This is discussed, with a simple engineering approach, in this short note, where it is found – via case studies – that exceedance hazard curves seem to converge towards an EV distribution (i.e., the EV type II or Fréchet), with a pace that is impacted by the discontinuity inherent to the curves. It is also seen that other common models, typically used to provide an analytical format to probabilistic curves, do not show the same level of convergence. Besides providing further insights on the results of PSHA, this study can possibly be useful for those cases where a closed-form equation for the hazard curve could be needed, such as reliability-based calibration of building codes, or seismic risk studies involving seismic hazard approximation/extrapolation.
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