Tools, methodologies and discussions about single-site, multi-site and sequence-based probabilistic seismic hazard analysis.

In the framework of performance-based earthquake engineering (Cornell and Krawinkler, 2000), actions the structures must withstand are based on probabilistic seismic hazard analysis (PSHA). Classical formulation of PSHA goes back to the second half of the twentieth century (Cornell, 1968), but its implementation can still be demanding for engineers dealing with practical applications. Moreover, in the last years, a number of developments of PSHA have been introduced; e.g., vector-valued and advanced ground motion intensity measure (IM) hazard, the inclusion of the effect of aftershocks in single-site hazard assessment, and multi-site analysis requiring the characterization of random fields of spatially cross-correlated IMs. Although several software to carry out PSHA have been available since quite some time (see Danciu et al., 2010), generally, they do not feature a user-friendly interface and do not embed most of the recent methodologies relevant from the earthquake engineering perspective. These are the main motivations behind the development of a practice-oriented software, namely REgionAl, Single-SitE and Scenario-based Seismic hazard analysis (REASSESS V2.0). The tool, which has been developed within the activities of the AXA-DiSt 2014-2017 research program of AXA-Matrix Risk Consultants, Milan, Italy and Dipartimento di Strutture per l’Ingegneria e l’Architettura, is one main results of the thesis and has been used to develop all the other studies introduced in the following. In the most advanced countries, where PSHA is adopted for the definition of the design seismic actions, the code typically provides them in the form of hazard maps for different pseudo-spectral accelerations and return periods. In other words, for each of the sites the design spectrum is derived from the uniform hazard spectrum in which all the ordinates have the same return period of exceedance (the return period is usually a function of the design limit-state). PSHA has also been often questioned (e.g., Castanos and Lomnitz, 2002; Stein et al., 2003; Reiter, 2004; Musson et al., 2005; Wang, 2012). The ongoing debate on the adequacy of PSHA is (often) feed by the actually-observed seismic actions on structures. For example, when an earthquake occurs at a site, researchers typically compare the design spectrum with the recorded counterpart (e.g., Masi and Chiauzzi, 2009). In this sense, several studies show that the cases where the design spectra are exceeded are not rare (see, for example, Crowley et al., 2009). Another relevant issue concerning PSHA is that it is often implemented neglecting the effect of aftershocks, that can also be strong (e.g., Masi et al., 2011), in order to describe the occurrence of earthquakes according to the homogeneous Poisson process; as a consequence, seismic codes at the state-of-the-art worldwide implicitly assume that the effect of aftershocks is negligible and do not consider that failure of structures can be due to an aftershock rather than by a mainshock (i.e., the event of highest magnitude within a sequence). Finally, in the recent years, PSHA estimates have been confirmed or disproved through hazard validation studies performing formal tests against observed ground motions at multiple sites over the years (e.g., Schorlemmer et al., 2007; Albarello and D’Amico, 2008); the nature and form of these studies implies that results they provide are sensitive to the adopted hypothesis of spatial dependence/independence between ground motions at the sites and, also important, require a careful evaluation of the involved data. For these reasons, the thesis proposes a study which, not questioning PSHA (which is a rational method to quantify the seismic threat for a site), recalls some of the recent advances in the seismic hazard assessment to deepen the above-introduced issues. To do so, the whole discussion is addressed with reference to the case-study of Italy and adopting the same source model used to develop the national seismic hazard. In particular, PSHA is herein studied under three non-conventional points of view, by means of which: • it is demonstrated that the exceedance of design spectrum in the epicentral areas of earthquakes of even moderate magnitude is well expected, identifying the seismic scenarios for which such exceedance is more probable, and quantifying the expected amount of the exceedance when such exceedance occurs; • profiting of sequence-based PSHA (SPSHA) introduced by Iervolino et al. (2014), it is quantitatively shown that the hazard increase due to aftershocks for structural design is not very high, even if it is not negligible. It is also illustrated that the contribution of aftershocks to hazard for a site can strongly vary with return period and that, given the return period, it is different from site to site; • profiting of multi-site PSHA (MSPSHA; Giorgio and Iervolino, 2016), it is demonstrated that hazard validation studies via observed exceedances at multiple sites over the years should always consider the spatial dependence existing between ground motions at the sites generated by a common earthquake, to avoid erroneous conclusions about the inadequateness of PSHA

Rarity, proximity, and design actions: mapping strong earthquakes in Italy

At the state-of-the-art of structural codes, seismic design actions are based on probabilistic seismic hazard analysis (PSHA). In the performance-based earthquake engineering framework, the return period of exceedance of the reference ground motion is established based on the desired performance of the structure. It is easy to show and recognize that exceedance of elastic spectra, for the most common return periods considered for design, is very likely for some earthquakes if they occur close to the site of interest, and that this does not necessarily contradict the results of PSHA. Therefore, it might be relevant to gather insights about: (i) the probability that the site is in proximity of earthquakes of magnitude that can imply exceedance; (ii) the probability that earthquakes occurring close cause exceedance of design actions; (iii) the minimum magnitude of close-by events that are likely to cause exceedance of design actions, which are then referred to as the strong earthquakes; (iv) the accelerations that structures could be exposed to in the case of exceedance of design spectra. These results, which are produced for Italy in this study, may be considered by-products of PSHA, and are helpful in determining what to expect in terms of elastic actions for code-conforming structures in countries where probabilistic seismic hazard lies at the basis of structural design

Sequence-based hazard analysis for Italy considering a grid seismic source model

Earthquakes are usually clustered in both time and space and, within each cluster, the event of highest magnitude is conventionally identified as the mainshock, while the foreshocks and the aftershocks are the events that occur before and after it, respectively. Mainshocks are the earthquakes considered in the classical formulation of the probabilistic seismic hazard analysis (PSHA), where the contribution of foreshocks and aftershocks is usually neglected. In fact, it has been shown that it is possible to rigorously, within the hypotheses of the model, account for the effect of mainshock-aftershocks sequences by means of the sequence-based PSHA (i.e., SPSHA). SPSHA extends the usability of the homogeneous Poisson process, adopted for mainshocks within PSHA, to also describe the occurrence of clusters maintaining the same input data of PSHA; i.e., the seismic rates derived by a declustered catalog. The aftershocks’ occurrences are accounted for by means of conditional non-homogeneous Poisson processes based on the modified Omori law. The seismic source model for Italy has been recently investigated, and the objective of the study herein presented is to include and evaluate the effect of aftershocks, by means of SPSHA, based on a new grid model. In the paper, the results of PSHA and SPSHA are compared, considering the spectral and return periods that are of typical interest for earthquake engineering. Finally, a comparison with the SPSHA map based on a well- established source model for Italy is also provided

Exceedance of design actions in epicentral areas: insights from the ShakeMap envelopes for the 2016–2017 central Italy sequence

AbstractShakeMap is the tool to evaluate the ground motion effect of earthquakes in vast areas. It is useful to delimit the zones where the shaking is expected to have been most significant, for civil defense rapid response. From the earthquake engineering point of view, it can be used to infer the seismic actions on the built environment to calibrate vulnerability models or to define the reconstruction policies based on observed damage vs shaking. In the case of long-lasting seismic sequences, it can be useful to develop ShakeMap envelopes, that is, maps of the largest ground intensity among those from the ShakeMap of (selected) events of a seismic sequence, to delimit areas where the effects of the whole sequence have been of structural engineering relevance. This study introduces ShakeMap envelopes and discusses them for the central Italy 2016–2017 seismic sequence. The specific goals of the study are: (i) to compare the envelopes and the ShakeMap of the main events of the sequence to make the case for sequence-based maps; (ii) to quantify the exceedance of design seismic actions based on the envelopes; (iii) to make envelopes available for further studies and the reconstruction planning; (iv) to gather insights on the (repeated) exceedance of design seismic actions at some sites. Results, which include considerations of uncertainty in ShakeMap, show that the sequence caused exceedance of design hazard in thousands of square kilometers. The most relevant effects of the sequence are, as expected, due to the mainshock, yet seismic actions larger than those enforced by the code for structural design are found also around the epicenters of the smaller magnitude events. At some locations, the succession of ground-shaking that has excited structures, provides insights on structural damage accumulation that has likely taken place; something that is not accounted for explicitly in modern seismic design. The envelopes developed are available as supplemental material

Comparing alternative models for multisite probabilistic seismic risk analysis

The risk assessment for a building portfolio or a spatially distributed infrastructure requires multi-site probabilistic seismic hazard analysis (MSPSHA). In fact, MSPSHA accounts for the stochastic dependency between the ground motion intensity measures (IMs) at the sites. Multi-site hazard needs to define the correlation structure for the same IM at different sites (spatial correlation), that of different IMs at the same site (cross-correlation) and that of different IMs at different sites (spatial-cross-correlation). Literature shows that such models usually require a significant amount of regional data to be semi-empirically calibrated. An approximated yet simpler-to-model alternative option is the conditional-hazard approach. The latter, originally developed for single-site analyses as an alternative to vector-valued PSHA, allows computing the distribution of a secondary IM given the occurrence or exceedance of a value of a primary IM. Conditional hazard considers the spatial correlation of the primary IM and the cross-correlation at each site for the two IMs, thus, if it is adopted for MSPSHA, the spatial correlation of the secondary IM as well as the spatial-cross-correlation between the two IMs descends from these two models. In the study, the conditional hazard procedure for MSPSHA is discussed and implemented in an illustrative application. Results in terms of distribution of the total number of exceedances of selected thresholds at the sites in a given time interval are compared with the case of complete formulation of MSPSHA and the differences are quantified. It appears that conditional hazard is a solid, yet simpler alternative for MSPSHA, at least in the considered cases.This paper was developed within the H2020-MSCA-RISE-2015 research project EXCHANGE-Risk (Grant Agreement No. 691213)

On occurrence disaggregation of probabilistic seismic hazard

Disaggregation of probabilistic seismic hazard allows to quantify how much one or more earthquake scenarios contribute to the occurrence [exceedance] of a ground motion intensity measure threshold of interest (x) at the construction site. The scenario is usually defined in terms of magnitude (M), source-to-site distance (R), and possibly includes the standardized residual (ε) of the ground motion model considered in the hazard analysis. Analytically, in case occurrence is of interest, disaggregation provides the joint probability density function of or conditional on the event, that is, or . Occurrence disaggregation is important for a number of earthquake engineering applications, and it is typically addressed in the literature in an approximated manner, considering as the conditioning event , with being an arbitrary finite width of the interval. This short communication undertakes a deeper examination of occurrence disaggregation clarifying that: (i) no approximation is needed in the case of disaggregation in terms of magnitude and distance (i.e., when is sought); (ii) is theoretically degenerate, and as such, its approximation via finite can lead to misleading results; (iii) if is chosen coherently with the discretization of the domain used in the hazard integral, it leads to approximated , enabling the conclusion that occurrence disaggregation does not add information with respect to disaggregation

Testing three seismic hazard models for Italy via multi-site observations.

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

The peak over the design threshold in strong earthquakes

In state-of-the-art seismic design, reference seismic actions are based on probabilistic seismic hazard assessment, which provides the ground-motion intensity corresponding to a reference return period of exceedance at the site. Exceedance of elastic actions, which is systematically observed in the epicentral areas of strong earthquakes, does not necessarily mean violation of the structural design limit-state; nevertheless, in such a case, the safety margins inherent to design are left to other factors beyond the elastic spectrum, which are, in general, not explicitly controlled. Therefore, it might be useful to quantify the expected (i.e., mean) amount of ground-motion intensity exceedance in earthquakes for which the design spectrum is not conservative. In fact, this study, with reference to Italy, provides and discusses the map of the expected value of acceleration, given the exceedance of the design spectra at any site in the country. It is shown, among other results, that: (1) the expected exceedance varies significantly from site-to-site across the country despite the same return period of the threshold is considered everywhere, (2) its pattern is opposite to that of the from disaggregation, and (3) the peak-over-the-threshold can be larger than 2.5 times than the corresponding ordinate of the design spectrum with 475 years return period. These results may be informative about what to expect for code-conforming structures in terms of seismic actions during strong earthquakes, that is, those able to cause exceedance of design elastic spectra

REASSESS V1.0: a computationally-efficient software for probabilistic seismic hazard analysis

A stand-alone software for the probabilistic assessment of seismic hazard is devel- oping. In its final version, it shall be structured in thre e modules for: (i) site-specific, (ii) sce- nario-based and (iii) multi-site (regional) anal yses. This paper focuses on (i), which is devoted to single-site probabilisti c seismic hazard analysis (PSHA). Seismic sources can be either z ones or individual faults. The algorithm to compute PSHA is implemented assuming, classically, that the process of occurrence of earthquakes on each seismic source follows a homogeneous Poisson pr ocess; the processes for different sources are independent. The required input data are: (1) the source(s) geometry and the annual rate(s) of occurrence of earthquakes in the magnitude interval of interest; (2) the distribution of magnitude given the occurrence of one earthquake; (3) the ground motion propagation model (GMPM); (4) the soil classification at the site for which haz ard is evaluated. Regarding (1-3), the user is aided by some library impl emented in the software. REASSESS also is able to account for model uncer tainty, in fact, logic trees can be built based on alternatives for the source’s annual ra te of earthquake occurrence, magnitude dis- tribution and GMPM. The strength of REASSESS, beyond the user-friendly interface, stays in the PSHA computation algorithms. These have been coded in MATLAB®, targeting accuracy and reduced computing time. Its potential for ea rthquake engineering and engineering seismology applications is il- lustrated by a few applications discussed in the paper

Macroseismic intensity hazard maps for Italy based on a recent grid source model

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