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1. A new perspective on seismic intensity measures (IMs)

   Grigoriu, M. ( August 2019 , SEMC 2019)

   The usefulness of current intensity measures (IMs) and fragilities are assessed in a setting in which the probability law of the seismic ground acceleration process is known. It is shown that typical demand parameters and IMs are weakly dependent so that fragilities defined as functions of these measures provide limited information for seismic design. 

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2. An earthquake-source-based metric for seismic fragility analysis

   https://doi.org/10.1007/s10518-018-0341-9  

   Radu, Alin ; Grigoriu, Mircea ( February 2018 , Bulletin of Earthquake Engineering)

   The seismic fragility of a system is the probability that the system enters a damage state under seismic ground motions with specified characteristics. Plots of the seismic fragilities with respect to scalar ground motion intensity measures are called fragility curves. Recent studies show that fragility curves may not be satisfactory measures for structural seismic performance, since scalar intensity measures cannot comprehensively characterize site seismicity. The limitations of traditional seismic intensity measures, e.g., peak ground acceleration or pseudo-spectral acceleration, are shown and discussed in detail. A bivariate vector with coordinates moment magnitude m and source-to-site distance r is proposed as an alternative seismic intensity measure. Implicitly, fragility surfaces in the (m, r)-space could be used as graphical representations of seismic fragility. Unlike fragility curves, which are functions of scalar intensity measures, fragility surfaces are characterized by two earthquake-hazard parameters, (m, r). The calculation of fragility surfaces may be computationally expensive for complex systems. Thus, as solutions to this issue, a bi-variate log-normal parametric model and an efficient calculation method, based on stochastic-reduced-order models, for fragility surfaces are proposed. 

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3. Fragility modeling practices and their implications on risk and resilience analysis: From the structure to the network scale

   https://doi.org/10.1177/87552930231219220  

   Rincon, Raul ; Padgett, Jamie Ellen ( January 2024 , Earthquake Spectra)

   Although fragility function development for structures is a mature field, it has recently thrived on new algorithms propelled by machine learning (ML) methods along with heightened emphasis on functions tailored for community- to regional-scale application. This article seeks to critically assess the implications of adopting alternative traditional and emerging fragility modeling practices within seismic risk and resilience quantification to guide future analyses that span from the structure to infrastructure network scale. For example, this article probes the similarities and differences in traditional and ML techniques for demand modeling, discusses the shift from one-parameter to multiparameter fragility models, and assesses the variations in fragility outcomes via statistical distance concepts. Moreover, the previously unexplored influence of these practices on a range of performance measures (e.g. conditional probability of damage, risk of losses to individual structures, portfolio risks, and network recovery trajectories) is systematically evaluated via the posed statistical distance metrics. To this end, case studies using bridges and transportation networks are leveraged to systematically test the implications of alternative seismic fragility modeling practices. The results show that, contrary to the classically adopted archetype fragilities, parameterized ML-based models achieve similar results on individual risk metrics compared to structure-specific fragilities, promising to improve portfolio fragility definitions, deliver satisfactory risk and resilience outcomes at different scales, and pinpoint structures whose poor performance extends to the global network resilience estimates. Using flexible fragility models to depict heterogeneous portfolios is expected to support dynamic decisions that may take place at different scales, space, and time, throughout infrastructure systems.

    

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4. Multivariate return period‐based ground motion selection for improved hazard consistency over a vector of intensity measures

   https://doi.org/10.1002/eqe.3338  

   Du, Ao ; Padgett, Jamie E. ( August 2020 , Earthquake Engineering & Structural Dynamics)

   Ground motion selection is a crucial step in probabilistic seismic performance assessment of structural systems. Particularly, identifying ground motion records compatible with a specific hazard level has been the major focus of past studies. We propose a multivariate return period (MRP)‐based record selection methodology to further improve the multivariate hazard consistency over a vector of intensity measures (IMs). Unlike the traditional univariate return period anchored on a scalar IM, MRP generalizes the return period concept by accommodating the joint rate of exceedance of a vector of IMs, thereby providing more holistic seismic hazard characterization. By leveraging MRP in linking the seismic hazard to a vector IMs, the proposed MRP‐based ground motion selection methodology for the first time offers a mathematically rigorous yet practical solution for multivariate hazard consistency in ground motion selection. The merit of the MRP‐based ground motion selection is demonstrated by comparing the resulting target spectra and seismic demand estimates for several case‐study structures with other state‐of‐the‐art ground motion selection alternatives. From the results, the MRP‐based ground motion selection employing Kendall's distribution function turns out to be a promising alternative, offering favorable new features including (a) moderate target spectra intensity and moderately low target spectra standard deviation; (b) superior convergence with the increase of the conditioning IM dimension and ability to approximate higher‐dimensional multivariate hazard consistency with lower dimensional conditioning IMs; and (c) capability to realistically capture the multimodal spectral shape owing to the incorporation of multivariate Gaussian mixture distribution in generating target spectra.

    

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5. Are seismic fragility curves fragile?

   https://doi.org/doi.org/10.1016/j.probengmech.2020.103115  

   Grigoriu, M. and ( January 2021 , Probabilistic engineering mechanics)

   null (Ed.)

   A hypothetical seismic site is constructed for which the probability law of the seismic ground acceleration process 𝑋(𝑡) is specified. Since the seismic hazard is known, the performance of the incremental dynamic analysis- (IDA) and multiple stripe analysis- (MSA) based fragilities, which are used extensively in Earthquake Engineering, can be assessed without ambiguity. It is shown that the IDA- and MSA-based fragilities are unsatisfactory for moderate and large seismic events, are sensitive to the particular parameters used for their construction, and may or may not improve with the sample size. Also, the usefulness of the optimization algorithms for selecting ground motions records is questionable. 

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