A generalized conditional intensity measure approach and holistic ground‐motion selection

A generalized conditional intensity measure (GCIM) approach is proposed for use in the holistic selection of ground motions for any form of seismic response analysis. The essence of the method is the construction of the multivariate distribution of any set of ground‐motion intensity measures conditioned on the occurrence of a specific ground‐motion intensity measure (commonly obtained from probabilistic seismic hazard analysis). The approach therefore allows any number of ground‐motion intensity measures identified as important in a particular seismic response problem to be considered. A holistic method of ground‐motion selection is also proposed based on the statistical comparison, for each intensity measure, of the empirical distribution of the ground‐motion suite with the ‘target’ GCIM distribution. A simple procedure to estimate the magnitude of potential bias in the results of seismic response analyses when the ground‐motion suite does not conform to the GCIM distribution is also demonstrated. The combination of these three features of the approach make it entirely holistic in that: any level of complexity in ground‐motion selection for any seismic response analysis can be exercised; users explicitly understand the simplifications made in the selected suite of ground motions; and an approximate estimate of any bias associated with such simplifications is obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

A ground motion selection algorithm based on the generalized conditional intensity measure approach

An algorithm is presented for the selection of ground motions for use in seismic response analysis. The algorithm is based on the use of random realizations from the conditional multivariate distribution of ground motion intensity measures, IM|IM_j, obtained from the generalized conditional intensity measure (GCIM) approach. The algorithm can be applied to the selection of both as-recorded amplitude-scaled and synthetic/simulated ground motions. A key feature is that the generality of the GCIM methodology allows for ground motion selection based on only explicit measures of the ground motions themselves, as represented by the various IM’s considered, rather than implicit causal parameters (e.g., source magnitude, source-to-site distance) which are presently used in other contemporary ground motion selection procedures. Several examples are used to illustrate the salient features of the algorithm, including: the effect of intensity measures considered; and the properties of ground motions selected for multiple exceedance probabilities. The flexibility of the proposed algorithm coupled with the GCIM methodology allows for objective and consistent ground motion selection as a natural extension of seismic hazard analysis.     

Ground motion selection for scenario ruptures using the generalised conditional intensity measure (GCIM) method

In this paper, the generalised conditional intensity measure (GCIM) method is extended to ground motion selection for scenario earthquake ruptures. The selection algorithm is based on generating random realisations of the considered intensity measure (IM) distributions for a specific rupture scenario and then finding the prospective ground motions that best fit the realisations using an optimal amplitude scale factor. Using different rupture scenarios and site conditions, two important aspects of the GCIM methodology are scrutinised: (i) different weight vectors for the various IMs considered and (ii) quantifying the importance of replicate selections for ensembles with different numbers of desired ground motions. It is demonstrated that considering only spectral acceleration (SA) ordinates in the selection process, as is common in many conventional selection procedures, may result in selected motions with a biased representation for duration and cumulative ground motion effects. In contrast, considering IMs other than SA ordinates (in particular, significant duration, cumulative absolute velocity, and Arias intensity) results in ensembles with an appropriate representation of these IMs, without a practically significant effect on SA ordinates. The benefit of conducting replicate selections to obtain a suite of motions with an improved representation for the distribution of the considered IMs is demonstrated, and a minimum number of replicates are suggested for different ground motion ensemble sizes. Copyright © 2015 John Wiley & Sons, Ltd.     

Conditional spectrum‐based ground motion selection. Part I: Hazard consistency for risk‐based assessments

The conditional spectrum (CS, with mean and variability) is a target response spectrum that links nonlinear dynamic analysis back to probabilistic seismic hazard analysis for ground motion selection. The CS is computed on the basis of a specified conditioning period, whereas structures under consideration may be sensitive to response spectral amplitudes at multiple periods of excitation. Questions remain regarding the appropriate choice of conditioning period when utilizing the CS as the target spectrum. This paper focuses on risk‐based assessments, which estimate the annual rate of exceeding a specified structural response amplitude. Seismic hazard analysis, ground motion selection, and nonlinear dynamic analysis are performed, using the conditional spectra with varying conditioning periods, to assess the performance of a 20‐story reinforced concrete frame structure. It is shown here that risk‐based assessments are relatively insensitive to the choice of conditioning period when the ground motions are carefully selected to ensure hazard consistency. This observed insensitivity to the conditioning period comes from the fact that, when CS‐based ground motion selection is used, the distributions of response spectra of the selected ground motions are consistent with the site ground motion hazard curves at all relevant periods; this consistency with the site hazard curves is independent of the conditioning period. The importance of an exact CS (which incorporates multiple causal earthquakes and ground motion prediction models) to achieve the appropriate spectral variability at periods away from the conditioning period is also highlighted. The findings of this paper are expected theoretically but have not been empirically demonstrated previously. Copyright © 2013 John Wiley & Sons, Ltd.     

A ground motion selection procedure for enforcing hazard consistency and estimating seismic demand hazard curves

This paper develops a procedure to select unscaled ground motions for estimating seismic demand hazard curves (SDHCs) in performance‐based earthquake engineering. Currently, SDHCs are estimated from a probabilistic seismic demand analysis, where several ensembles of ground motions are selected and scaled to a user‐specified scalar conditioning intensity measure (IM). In contrast, the procedure developed herein provides a way to select a single ensemble of unscaled ground motions for estimating the SDHC. In the context of unscaled motions, the proposed procedure requires three inputs: (i) database of unscaled ground motions, (ii) I M , the vector of IMs for selecting ground motions, and (iii) sample size, n; in the context of scaled motions, two additional inputs are needed: (i) a maximum acceptable scale factor, SF_max, and (ii) a target fraction of scaled ground motions, γ. Using a recently developed approach for evaluating ground motion selection and modification procedures, the proposed procedure is evaluated for a variety of inputs and is demonstrated to provide accurate estimates of the SDHC when the vector of IMs chosen to select ground motions is sufficient for the response quantity of interest. Copyright © 2015 John Wiley & Sons, Ltd.     

Conditional spectrum‐based ground motion selection. Part II: Intensity‐based assessments and evaluation of alternative target spectra

In a companion paper, an overview and problem definition was presented for ground motion selection on the basis of the conditional spectrum (CS), to perform risk‐based assessments (which estimate the annual rate of exceeding a specified structural response amplitude) for a 20‐story reinforced concrete frame structure. Here, the methodology is repeated for intensity‐based assessments (which estimate structural response for ground motions with a specified intensity level) to determine the effect of conditioning period. Additionally, intensity‐based and risk‐based assessments are evaluated for two other possible target spectra, specifically the uniform hazard spectrum (UHS) and the conditional mean spectrum (CMS, without variability).It is demonstrated for the structure considered that the choice of conditioning period in the CS can substantially impact structural response estimates in an intensity‐based assessment. When used for intensity‐based assessments, the UHS typically results in equal or higher median estimates of structural response than the CS; the CMS results in similar median estimates of structural response compared with the CS but exhibits lower dispersion because of the omission of variability. The choice of target spectrum is then evaluated for risk‐based assessments, showing that the UHS results in overestimation of structural response hazard, whereas the CMS results in underestimation. Additional analyses are completed for other structures to confirm the generality of the conclusions here. These findings have potentially important implications both for the intensity‐based seismic assessments using the CS in future building codes and the risk‐based seismic assessments typically used in performance‐based earthquake engineering applications. Copyright © 2013 John Wiley & Sons, Ltd.     

A framework for the evaluation of ground motion selection and modification procedures

This study develops a framework to evaluate ground motion selection and modification (GMSM) procedures. The context is probabilistic seismic demand analysis, where response history analyses of a given structure, using ground motions determined by a GMSM procedure, are performed in order to estimate the seismic demand hazard curve (SDHC) for the structure at a given site. Currently, a GMSM procedure is evaluated in this context by comparing several resulting estimates of the SDHC, each derived from a different definition of the conditioning intensity measure (IM). Using a simple case study, we demonstrate that conclusions from such an approach are not always definitive; therefore, an alternative approach is desirable. In the alternative proposed herein, all estimates of the SDHC from GMSM procedures are compared against a benchmark SDHC, under a common set of ground motion information. This benchmark SDHC is determined by incorporating a prediction model for the seismic demand into the probabilistic seismic hazard analysis calculations. To develop an understanding of why one GMSM procedure may provide more accurate estimates of the SDHC than another procedure, we identify the role of ‘IM sufficiency’ in the relationship between (i) bias in the SDHC estimate and (ii) ‘hazard consistency’ of the corresponding ground motions obtained from a GMSM procedure. Finally, we provide examples of how misleading conclusions may potentially be obtained from erroneous implementations of the proposed framework. Copyright © 2014 John Wiley & Sons, Ltd.     

The effect of causal parameter bounds in PSHA‐based ground motion selection

In this paper the effect of causal parameter bounds (e.g. magnitude, source‐to‐site distance, and site condition) on ground motion selection, based on probabilistic seismic hazard analysis (PSHA) results, is investigated. Despite the prevalent application of causal parameter bounds in ground motion selection, present literature on the topic is cast in the context of a scenario earthquake of interest, and thus specific bounds for use in ground motion selection based on PSHA, and the implications of such bounds, is yet to be examined. Thirty‐six PSHA cases, which cover a wide range of causal rupture deaggregation distributions and site conditions, are considered to empirically investigate the effects of various causal parameter bounds on the characteristics of selected ground motions based on the generalized conditional intensity measure (GCIM) approach. It is demonstrated that the application of relatively ‘wide’ bounds on causal parameters effectively removes ground motions with drastically different characteristics with respect to the target seismic hazard and results in an improved representation of the target causal parameters. In contrast, the use of excessively ‘narrow’ bounds can lead to ground motion ensembles with a poor representation of the target intensity measure distributions, typically as a result of an insufficient number of prospective ground motions. Quantitative criteria for specifying bounds for general PSHA cases are provided, which are expected to be sufficient in the majority of problems encountered in ground motion selection for seismic demand analyses. Copyright © 2016 John Wiley & Sons, Ltd.     

Empirical equations for the prediction of displacement spectrum intensity and its correlation with other intensity measures

Displacement spectrum intensity (DSI), defined as the integral of a ground motion's displacement response spectrum from 2.0 to 5.0 s, is proposed as an indicator of the severity of the long period content of a ground motion. It is demonstrated how the distribution of DSI can be predicted using existing ground motion prediction equations for (pseudo) spectral accelerations, which is necessary for it to be a useful intensity measure (IM) in either probabilistic or deterministic seismic hazard analysis. Empirical correlation equations between DSI and other common ground motion IMs are developed for active shallow crustal earthquakes using a dataset of ground motions from active shallow crustal earthquakes. The ability of DSI to account for near-source ground motions exhibiting forward directivity, potentially damaging far-source long-period ground motion, and its use with other spectrum intensity parameters to characterise short, medium, and long period severity of ground motions is discussed. The developed ground motion prediction and correlation equations enable DSI to be utilised in rigorous ground motion selection frameworks such as the generalised conditional intensity measure (GCIM) approach.     

Seismic hazard disaggregation in performance‐based earthquake engineering: occurrence or exceedance?

Seismic hazard disaggregation is commonly used as an aid in ground‐motion selection for the seismic response analysis of structures. This short communication investigates two different approaches to disaggregation related to the exceedance and occurrence of a particular intensity. The impact the different approaches might have on a subsequent structural analysis at a given intensity is explored through the calculation of conditional spectra. It is found that the exceedance approach results in conditional spectra that will be conservative when used as targets for ground‐motion selection. It is however argued that the use of the occurrence disaggregation is more consistent with the objectives of seismic response analyses in the context of performance‐based earthquake engineering. Copyright © 2015 John Wiley & Sons, Ltd.     

Ground motion selection for simulation‐based seismic hazard and structural reliability assessment

This paper examines four methods by which ground motions can be selected for dynamic seismic response analyses of engineered systems when the underlying seismic hazard is quantified via ground motion simulation rather than empirical ground motion prediction equations. Even with simulation‐based seismic hazard, a ground motion selection process is still required in order to extract a small number of time series from the much larger set developed as part of the hazard calculation. Four specific methods are presented for ground motion selection from simulation‐based seismic hazard analyses, and pros and cons of each are discussed via a simple and reproducible illustrative example. One of the four methods (method 1 ‘direct analysis’) provides a ‘benchmark’ result (i.e., using all simulated ground motions), enabling the consistency of the other three more efficient selection methods to be addressed. Method 2 (‘stratified sampling’) is a relatively simple way to achieve a significant reduction in the number of ground motions required through selecting subsets of ground motions binned based on an intensity measure, IM. Method 3 (‘simple multiple stripes’) has the benefit of being consistent with conventional seismic assessment practice using as‐recorded ground motions, but both methods 2 and 3 are strongly dependent on the efficiency of the conditioning IM to predict the seismic responses of interest. Method 4 (‘generalized conditional intensity measure‐based selection’) is consistent with ‘advanced’ selection methods used for as‐recorded ground motions and selects subsets of ground motions based on multiple IMs, thus overcoming this limitation in methods 2 and 3. Copyright © 2015 John Wiley & Sons, Ltd.     

Markov chain Monte Carlo ground‐motion selection algorithms for conditional intensity measure targets

Two new algorithms are presented for efficiently selecting suites of ground motions that match a target multivariate distribution or conditional intensity measure target. The first algorithm is a Markov chain Monte Carlo (MCMC) approach in which records are sequentially added to a selected set such that the joint probability density function (PDF) of the target distribution is progressively approximated by the discrete distribution of the selected records. The second algorithm derives from the concept of the acceptance ratio within MCMC but does not involve any sampling. The first method takes advantage of MCMC's ability to efficiently explore a sampling distribution through the implementation of a traditional MCMC algorithm. This method is shown to enable very good matches to multivariate targets to be obtained when the numbers of records to be selected is relatively large. A weaker performance for fewer records can be circumvented by the second method that uses greedy optimisation to impose additional constraints upon properties of the target distribution. A preselection approach based upon values of the multivariate PDF is proposed that enables near‐optimal record sets to be identified with a very close match to the target. Both methods are applied for a number response analyses associated with different sizes of record sets and rupture scenarios. Comparisons are made throughout with the Generalised Conditional Intensity Measure (GCIM) approach. The first method provides similar results to GCIM but with slightly worse performance for small record sets, while the second method outperforms method 1 and GCIM for all considered cases.     

Evaluation of ground motion selection and modification procedures using synthetic ground motions

This study presents a novel approach for evaluating ground motion selection and modification (GMSM) procedures in the context of probabilistic seismic demand analysis. In essence, synthetic ground motions are employed to derive the benchmark seismic demand hazard curve (SDHC), for any structure and response quantity of interest, and to establish the causal relationship between a GMSM procedure and the bias in its resulting estimate of the SDHC. An example is presented to illustrate how GMSM procedures may be evaluated using synthetic motions. To demonstrate the robustness of the proposed approach, two significantly different stochastic models for simulating ground motions are considered. By quantifying the bias in any estimate of the SDHC, the proposed approach enables the analyst to rank GMSM procedures in their ability to accurately estimate the SDHC, examine the sufficiency of intensity measures employed in ground motion selection, and assess the significance of the conditioning intensity measure in probabilistic seismic demand analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

Discussion on ‘a framework for the evaluation of ground motion selection and modification procedures’ by N. Simon Kwong,Anil K. Chopra,and Robin K. McGuire

The paper under discussion proposes a framework to evaluate ground motion selection and modification procedures and illustrates its application for two different procedures as applied to a non‐degrading bilinear inelastic single‐degree‐of‐freedom system. This discussion focuses on providing additional context that this writer feels is needed in relation to both the proposed framework and also its specific application in the paper, which are important for the conclusions made by the authors. Copyright © 2015 John Wiley & Sons, Ltd.     

Effect of ground motion selection methods on seismic collapse fragility of RC frame buildings

Variation in the seismic collapse fragility of reinforced concrete frame buildings predicted using different ground motion (GM) selection methods is investigated in this paper. To simulate the structural collapse, a fiber‐element modelling approach with path‐dependent cyclic nonlinear material models that account for concrete confinement and crushing, reinforcement buckling as well as low cycle fatigue is used. The adopted fiber analysis approach has been found to reliably predict the loss in vertical load carrying capacity of structural components in addition to the sidesway mode of collapse due to destabilizing P–Δ moments at large inelastic deflections. Multiple stripe analysis is performed by conducting response history analyses at various hazard levels to generate the collapse fragility curves. To select GMs at various hazard levels, two alternatives of uniform hazard spectrum (UHS), conditional mean spectrum (CMS) and generalized conditional intensity measure (GCIM) are used. Collapse analyses are repeated based on structural periods corresponding to initial un‐cracked stiffness and cracked stiffness of the frame members. A return period‐based intensity measure is then introduced and applied in estimating collapse fragility of frame buildings. In line with the results of previous research, it is shown that the choice of structural period significantly affects the collapse fragility predictions. Among the GM selection methods used in this study, GCIM and CMS methods predict similar collapse fragilities for the case study building investigated herein, and UHS provides the most conservative prediction of the collapse capacity, with approximately 40% smaller median collapse capacity compared to the CMS method. The results confirm that collapse probability prediction of buildings using UHS offers a higher level of conservatism in comparison to the other selection methods. Copyright © 2017 John Wiley & Sons, Ltd.     

The effect of amplitude scaling limits on conditional spectrum-based ground motion selection

Amplitude scaling is commonly used to select ground motions matching a target response spectrum. In this paper, the effect of scaling limits on ground motion selection, based on the conditional spectrum framework, is investigated. Target spectra are computed for four probabilistic seismic hazard cases in Western United States, and 16 ground motion suites are selected using different scaling limits (ie, 2, 5, 10, and 15). Comparison of spectral acceleration distributions of the selected ground motion suites demonstrates that the use of a scaling limit of 2 yields a relatively poor representation of the target spectra, because of the small limit leading to an insufficient number of available ground motions. It is also shown that increasing scaling limit results in selected ground motions with generally increased distributions of Arias intensity and significant duration Ds_5-75, implying that scaling limit consideration can significantly influence the cumulative and duration characteristics of selected ground motions. The ground motion suites selected are then used as input for slope displacement and structural dynamic analyses. Comparative results demonstrate that the consideration of scaling limits in ground motion selection has a notable influence on the distribution of the engineering demand parameters calculated (ie, slope displacement and interstory drift ratio). Finally, based on extensive analyses, a scaling limit range of 3 to 5 is recommended for general use when selecting ground motion records from the NGA-West2 database.     

Conditional spectrum‐based ground motion record selection using average spectral acceleration

The use of a seismic intensity measure (IM) is paramount in decoupling seismic hazard and structural response estimation when assessing the performance of structures. For this to be valid, the IM needs to be sufficient;that is, the engineering demand parameter (EDP) response should be independent of other ground motion characteristics when conditioned on the IM. Whenever non‐trivial dependence is found, such as in the case of the IM being the first‐mode spectral acceleration, ground motion selection must be employed to generate sets of ground motion records that are consistent vis‐à‐vis the hazard conditioned on the IM. Conditional spectrum record selection is such a method for choosing records that are consistent with the site‐dependent spectral shape conditioned on the first‐mode spectral acceleration. Based on a single structural period, however the result may be suboptimal, or insufficient, for EDPs influenced by different period values, for example, peak interstory drifts or peak floor accelerations at different floors, potentially requiring different record suites for each. Recently, the log‐average spectral acceleration over a period range, AvgSA, has emerged as an improved scalar IM for building response estimation whose hazard can be evaluated using existing ground motion prediction equations. Herein, we present a recasting of conditional spectrum record selection that is based on AvgSA over a period range as the conditioning IM. This procedure ensures increased efficiency and sufficiency in simultaneously estimating multiple EDPs by means of a single IM. Copyright © 2017 John Wiley & Sons, Ltd.     

Prediction of spatially distributed seismic demands in specific structures: Structural response to loss estimation

A companion paper has investigated the effects of intensity measure (IM) selection in the prediction of spatially distributed response in a multi‐degree‐of‐freedom structure. This paper extends from structural response prediction to performance assessment metrics such as probability of structural collapse; probability of exceeding a specified level of demand or direct repair cost; and the distribution of direct repair loss for a given level of ground motion. In addition, a method is proposed to account for the effect of varying seismological properties of ground motions on seismic demand that does not require different ground motion records to be used for each intensity level. Results illustrate that the conventional IM, spectral displacement at the first mode, S_de(T₁), produces higher risk estimates than alternative velocity‐based IM's, namely spectrum intensity, SI, and peak ground velocity, PGV, because of its high uncertainty in ground motion prediction and poor efficiency in predicting peak acceleration demands. Copyright © 2009 John Wiley & Sons, Ltd.     

Efficient sampling and data reduction techniques for probabilistic seismic lifeline risk assessment

Probabilistic seismic risk assessment for spatially distributed lifelines is less straightforward than for individual structures. While procedures such as the ‘PEER framework’ have been developed for risk assessment of individual structures, these are not easily applicable to distributed lifeline systems, due to difficulties in describing ground‐motion intensity (e.g. spectral acceleration) over a region (in contrast to ground‐motion intensity at a single site, which is easily quantified using Probabilistic Seismic Hazard Analysis), and since the link between the ground‐motion intensities and lifeline performance is usually not available in closed form. As a result, Monte Carlo simulation (MCS) and its variants are well suited for characterizing ground motions and computing resulting losses to lifelines. This paper proposes a simulation‐based framework for developing a small but stochastically representative catalog of earthquake ground‐motion intensity maps that can be used for lifeline risk assessment. In this framework, Importance Sampling is used to preferentially sample ‘important’ ground‐motion intensity maps, and K‐Means Clustering is used to identify and combine redundant maps in order to obtain a small catalog. The effects of sampling and clustering are accounted for through a weighting on each remaining map, so that the resulting catalog is still a probabilistically correct representation. The feasibility of the proposed simulation framework is illustrated by using it to assess the seismic risk of a simplified model of the San Francisco Bay Area transportation network. A catalog of just 150 intensity maps is generated to represent hazard at 1038 sites from 10 regional fault segments causing earthquakes with magnitudes between five and eight. The risk estimates obtained using these maps are consistent with those obtained using conventional MCS utilizing many orders of magnitudes more ground‐motion intensity maps. Therefore, the proposed technique can be used to drastically reduce the computational expense of a simulation‐based risk assessment, without compromising the accuracy of the risk estimates. This will facilitate computationally intensive risk analysis of systems such as transportation networks. Finally, the study shows that the uncertainties in the ground‐motion intensities and the spatial correlations between ground‐motion intensities at various sites must be modeled in order to obtain unbiased estimates of lifeline risk. Copyright © 2010 John Wiley & Sons, Ltd.