Refined multivariate return period-based ground motion selection and implications for seismic risk assessment
Introduction
In performance-based earthquake engineering (PBEE), the unconditional seismic risk (or annual rate of exceedance) of an engineering demand parameter (EDP), D, can be quantified via seismic risk assessment (SRA) as shown in Eq. (1) [1], [2], which convolves the probabilistic seismic hazard of a scalar or vector ground motion intensity measure (IM) with the conditional demand distribution:where: denotes the rate of occurrence of the IM. A scalar IM is typically considered and can be conveniently obtained from probabilistic seismic hazard analysis (PSHA); is the complementary cumulative distribution function (CCDF) of the EDP conditioned on the IM. Its evaluation requires intensity-based assessment, which provides structural seismic demand estimates subjected to ground motions at a given hazard level. Owing to the recent advances in ground motion selection, such as the Conditional Spectrum (CS)-based ground motion selection approaches [3], [4], [5] and the Generalized Conditional Intensity Measure (GCIM) approach [6], [7], hazard-consistent ground motions can be afforded to enable more efficient and reliable SRA [8], [9], [10], although the conditional demand estimates within the intensity-based assessment are yet sensitive to the selection of conditioning IMs [10], [11]. It should be noted that intensity-based assessment is still commonly suggested in performance-based seismic design procedures [12], and different demand estimates due to the adoption of different conditioning IMs cause confusions and difficulties in interpreting these results. For this reason, the “worst-case” envelope of intensity-based assessments based on the conditional mean spectrum of multiple conditioning IMs is suggested [10], [12], [13], which may lead to overly conservative demand estimates and increased number of required time history analyses. Essentially, such conditioning IM sensitivity of the abovementioned ground motion selection approaches can be traced back to the definition of return period, which is typically hinged on a scalar IM and is thus not able to holistically characterize the joint exceedance of higher-dimensional vector IMs [14]. A scalar IM only reflects part of the ground motion characteristics, and usually a vector of IMs are needed to offer more sufficient and holistic depiction of the ground motion.
To address the above-mentioned research gaps, the concept of multivariate return period (MRP) was recently introduced into PSHA by leveraging Kendall’s distribution function [15] as a stochastic ordering measure to holistically handle a vector of conditioning IMs, and a new MRP-based ground motion selection methodology was proposed accordingly [14]. This approach features several favorable properties that allow more objective ground motion selection for intensity-based assessment, including: (1) moderate target spectra intensity, and moderately low target spectra standard deviation across a wide range of IMs; (2) superior convergence with the increase of the conditioning vector IM dimension, and ability to approximate higher-dimensional hazard consistency with lower dimensional conditioning IMs; and (3) capability to realistically incorporate multiple causal earthquakes owing to the implementation of multivariate Gaussian mixture distribution in simulating the response spectra. Despite the above-mentioned advantages of the MRP-based ground motion selection, a large number of naïve Monte-Carlo simulations and joint cumulative distribution function (CDF) evaluations of the vector conditioning IMs are required, which constitute the major computational hurdle of this method especially when dealing with large return periods or high-dimensional conditioning IMs. In addition, the original study [14] only discussed the implementation of the MRP-based ground motion selection in the context of intensity-based assessment. To further extend its applicability into risk-based assessment, modification of the risk integral (Eq. (1)) is needed, and the unbiasedness in the resulting risk estimates is yet to be examined. Furthermore, despite the emerging research focus on leveraging advanced statistical learning enabled parameterized surrogate demand models (SDMs) for conditional seismic demand estimation [16], [17], [18], [19] as well as their increasing application into SRA [20], [21], [22], there is a dearth of study on investigating the influence of ground motion selection on the resulting risk estimates of the SDM-enabled SRA.
In the present work, we will first develop a refined MRP-based ground motion selection approach to significantly improve its computational efficiency, by introducing a two-step adaptive refinement procedure. Afforded by this refinement, a MRP-based SRA framework is established to accommodate the MRP-based ground motion selection, thus closing the gap between its use in intensity-based assessment and risk-based assessment. Based on a series of case studies, the merit of the MRP-based ground motion selection in the context of SRA is thoroughly examined, offering valuable insights into the influence of ground motion selection and conditioning IM selection on the resulting risk estimate consistency.
Section snippets
Proposed refined MRP-based ground motion selection and SRA framework
In this section, the concept of return period and the original MRP-based ground motion selection method are briefly introduced, followed by detailed illustration of the refined MRP-based ground motion selection and SRA framework.
Case-study sites and seismic hazard
To demonstrate the efficacy the refined MRP-based ground motion selection and the risk consistency of the MRP-based SRA framework, two hypothetical sites, one located in Memphis, Tennessee (35.2°N, 89.9°W), and the other one located in Los Angeles (LA), California (34.1°N, 118.2°W) are considered. They respectively represent a stable continental tectonic setting with moderate seismicity and a shallow crustal tectonic setting with high seismicity.
Evaluation of the refined MRP-based ground motion selection
In this section, the efficacy of the proposed refinement for the MRP-based ground motion selection is thoroughly examined. For demonstration purpose, Sa at three spectral periods [0.05, 1, 5] (s) are considered as the conditioning vector IMs (IMC) for the MRP-based ground motion selection, which will be denotes as MRP-Sa hereafter. For the target spectra selection in this section, a 5% return period tolerance level is considered to define the target return period range. For sake of comparison,
Implications of the MRP-based ground motion selection for seismic risk assessment
Section 4 underscores the efficacy and computational efficiency of the proposed refined MRP-based ground motion selection. In this section, detailed examination of the merit of the MRP-based ground motion selection in the context of SRA is carried out.
Conclusions
This study advances the notion of multivariate return period (MRP) as a basis of both selecting ground motions for response assessment as well as enabling risk consistent seismic risk assessment (SRA), while addressing practical challenges of computational complexity and efficiency. Specifically, we improve the previously proposed MRP-based ground motion selection methodology [14] by introducing a two-step adaptive refinement procedure to substantially alleviate the computational cost for
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements:
The authors would like to thank the two anonymous reviewers for their constructive comments and suggestions, which further helped improve the quality of this manuscript. The authors gratefully acknowledge the support for this research by the National Science Foundation (NSF) through grants CMMI-1520817. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
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2022, Engineering StructuresCitation Excerpt :Besides using the surrogate model, another way to improve the accuracy of performance assessment is incorporating more hazard information in demand prediction. The scalar IM may not be adequate to reflect the complex characteristics of the ground motion time history [26] and it can result in biased estimation [27]. Vector IM contains more information on the ground motion and can reflect multiple characteristics of the earthquakes.
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2022, Soil Dynamics and Earthquake EngineeringCitation Excerpt :In this way, various damage states of highway bridges can be reached after the nonlinear time-history analysis. Note that if the results from the probabilistic seismic hazard analysis were available for the local bridge site, different methods of ground motion selections, namely the uniform hazard spectrum-based approach, conditional spectrum-based method [84,85] and multivariate return period-based methodology [86–89], should be implemented to improve the hazard consistency of the whole proposed methodology. Fig. 6 illustrates the characteristics of 170 ground motions selected in this paper, along with the response spectra and histogram of PGAs.
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2021, Engineering StructuresCitation Excerpt :As a result, the selected ground motions do not necessarily resemble the waveform characteristics pertaining to the site-specific seismic hazard, and also may not sufficiently cover a wide range of intensity levels to avoid extrapolation. Despite the recent advancements in hazard-consistent ground motion selection [18-21], they are yet to be integrated with the SDA procedures. The inelastic SDOF structures are then randomly paired with the above selected hazard-consistent ground motion sequences, and a total number of Nsim nonlinear time history analyses are carried out in OpenSees [44] for each of the four inelastic SDOF structures at each site listed in Table 1.