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.     

Intensity measures for probabilistic assessment of non‐structural components acceleration demand

A fundamental issue in the framework of seismic probabilistic risk analysis is the choice of ground motion intensity measures (IMs). Based on the floor response spectrum method, the present contribution focuses on the ability of IMs to predict non‐structural components (NSCs) horizontal acceleration demand. A large panel of IMs is examined and a new IM, namely equipment relative average spectral acceleration (E‐ASA_R), is proposed for the purpose of NSCs acceleration demand prediction. The IMs efficiency and sufficiency comparisons are based on (i) the use of a large dataset of recorded earthquake ground motions; (ii) numerical analyses performed on three‐dimensional numerical models, representing actual structural wall and frame buildings; and (iii) systematic statistical analysis of the results. From the comparative study, the herein introduced E‐ASA_R shows high efficiency with respect to the estimation of maximum floor response spectra ordinates. Such efficiency is particularly remarkable in the case of structural wall buildings. Besides, the sufficiency and the simple formulation allowing the use of existing ground motion prediction models make the E‐ASA_R a promising IMs for seismic probabilistic risk assessment. Copyright © 2015 John Wiley & Sons, Ltd.     

Prediction of spatially distributed seismic demands in specific structures: Ground motion and structural response

The efficacy of various ground motion intensity measures (IMs) in the prediction of spatially distributed seismic demands (engineering demand parameters, (EDPs)) within a structure is investigated. This has direct implications to building‐specific seismic loss estimation, where the seismic demand on different components is dependent on the location of the component in the structure. Several common IMs are investigated in terms of their ability to predict the spatially distributed demands in a 10‐storey office building, which is measured in terms of maximum interstorey drift ratios and maximum floor accelerations. It is found that the ability of an IM to efficiently predict a specific EDP depends on the similarity between the frequency range of the ground motion that controls the IM and that of the EDP. An IMs predictability has a direct effect on the median response demands for ground motions scaled to a specified probability of exceedance from a ground motion hazard curve. All of the IMs investigated were found to be insufficient with respect to at least one of magnitude, source‐to‐site distance, or epsilon when predicting all peak interstorey drifts and peak floor accelerations in a 10‐storey reinforced concrete frame structure. Careful ground motion selection and/or seismic demand modification is therefore required to predict such a spatially distributed demands without significant bias. Copyright © 2009 John Wiley & Sons, Ltd.     

Rocking amplification and strong‐motion duration

This paper characterizes the ability of natural ground motions to induce rocking demands on rigid structures. In particular, focusing on rocking blocks of different size and slenderness subjected to a large number of historic earthquake records, the study unveils the predominant importance of the strong‐motion duration to rocking amplification (ie, peak rocking response without overturning). It proposes original dimensionless intensity measures (IMs), which capture the total duration (or total impulse accordingly) of the time intervals during which the ground motion is capable of triggering rocking motion. The results show that the proposed duration‐based IMs outperform all other examined (intensity, frequency, duration, and/or energy‐based) scalar IMs in terms of both “efficiency” and “sufficiency.” Further, the pertinent probabilistic seismic demand models offer a prediction of the peak rocking demand, which is adequately “universal” and of satisfactory accuracy. Lastly, the analysis shows that an IM that “efficiently” captures rocking amplification is not necessarily an “efficient” IM for predicting rocking overturning, which is dominated by the velocity characteristics (eg, peak velocity) of the ground motion.     

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.     

Ductility‐dependent intensity measure that accounts for ground‐motion spectral shape and duration

The calculated nonlinear structural responses of a building can vary greatly, even if recorded ground motions are scaled to the same spectral acceleration at a building's fundamental period. To reduce the variation in structural response at a particular ground‐motion intensity, this paper proposes an intensity measure (IM_comb) that accounts for the combined effects of spectral acceleration, ground‐motion duration, and response spectrum shape. The intensity measure includes a new measure of spectral shape that integrates the spectrum over a period range that depends on the structure's ductility. The new IM is efficient, sufficient, scalable, transparent, and versatile. These features make it suitable for evaluating the intensities of measured and simulated ground motions. The efficiency and sufficiency of the new IM is demonstrated for the following: (i) elastic‐perfectly plastic single‐degree‐of‐freedom (SDOF) oscillators with a variety of ductility demands and periods; (ii) ductile and brittle deteriorating SDOF systems with a variety of periods; and (iii) collapse analysis for 30 previously designed frames. The efficiency is attributable to the inclusion of duration and to the ductility dependence of the spectral shape measure. For each of these systems, the transparency of the intensity measure made it possible to identify the sensitivity of structural response to the various characteristics of the ground motion. Spectral shape affected all structures, but in particular, ductile structures. Duration only affected structures with cyclic deterioration. 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.     

Effect of peak ground velocity on deformation demands for SDOF systems

The effect of peak ground velocity (PGV) on single‐degree‐of‐freedom (SDOF) deformation demands and for certain ground‐motion features is described by using a total of 60 soil site records with source‐to‐site distances less than 23 km and moment magnitudes between 5.5 and 7.6. The observations based on these records indicate that PGV correlates well with the earthquake magnitude and provides useful information about the ground‐motion frequency content and strong‐motion duration that can play a role on the seismic demand of structures. The statistical results computed from non‐linear response history analyses of different hysteretic models highlight that PGV correlates better with the deformation demands with respect to other ground motion intensity measures. The choice of PGV as ground motion intensity decreases the dispersion due to record‐to‐record variability of SDOF deformation demands, particularly in the short period range. The central tendencies of deformation demands are sensitive to PGV and they may vary considerably as a function of the hysteretic model and structural period. The results provided in this study suggest a consideration of PGV as a stable candidate for ground motion intensity measure in simplified seismic assessment methods that are used to estimate structural performance for earthquake hazard analysis. Copyright © 2005 John Wiley & Sons, Ltd.     

Spectral shape,epsilon and record selection

Selection of earthquake ground motions is considered with the goal of accurately estimating the response of a structure at a specified ground motion intensity, as measured by spectral acceleration at the first‐mode period of the structure, Sa(T₁). Consideration is given to the magnitude, distance and epsilon (ε) values of ground motions. First, it is seen that selecting records based on their ε values is more effective than selecting records based on magnitude and distance. Second, a method is discussed for finding the conditional response spectrum of a ground motion, given a level of Sa(T₁) and its associated mean (disaggregation‐based) causal magnitude, distance and ε value. Records can then be selected to match the mean of this target spectrum, and the same benefits are achieved as when records are selected based on ε. This mean target spectrum differs from a Uniform Hazard Spectrum, and it is argued that this new spectrum is a more appropriate target for record selection. When properly selecting records based on either spectral shape or ε, the reductions in bias and variance of resulting structural response estimates are comparable to the reductions achieved by using a vector‐valued measure of earthquake intensity. Copyright © 2006 John Wiley & Sons, Ltd.     

On the treatment of uncertainties in the development of fragility functions for earthquake loss estimation of building portfolios

State‐of‐the‐art methods for the assessment of building fragility consider the structural capacity and seismic demand variability in the estimation of the probability of exceeding different damage states. However, questions remain regarding the appropriate treatment of such sources of uncertainty from a statistical significance perspective. In this study, material, geometrical and mechanical properties of a number of building classes are simulated by means of a Monte Carlo sampling process in which the statistical distribution of the aforementioned parameters is taken into consideration. Record selection is performed in accordance with hazard‐consistent distributions of a comprehensive set of intensity measures, and issues related with sufficiency, efficiency, predictability and scaling robustness are addressed. Based on the appraised minimum number of ground motion records required to achieve statistically meaningful estimates of response variability conditioned on different levels of seismic intensity, the concept of conditional fragility functions is presented. These functions translate the probability of exceeding a set of damage states as a function of a secondary sufficient intensity measure, when records are selected and scaled for a particular level of primary seismic intensity parameter. It is demonstrated that this process allows a hazard‐consistent and statistically meaningful representation of uncertainty and correlation in the estimation of intensity‐dependent damage exceedance probabilities. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic motion and response prediction alternatives

Statistical methods are available which predict the maximum response of simple oscillators given the peak acceleration (A_p), peak velocity (V_p) or peak displacement (D_p) of seismic ground motions. An alternative parameter, namely an ordinate (or ordinates) of the Fourier amplitude spectrum of ground motion acceleration, FS(f), may in fact be a preferred predictor of peak response, especially in a frequency range close to f. Other statistical methods (attenuation laws) use distance R and other parameters such as magnitude (M), Modified Mercalli epicentral Intensity (I_o) and Modified Mercalli site Intensity (MMI or I_s) to predict spectral velocity (S_v(f)), etc. In using such approaches, it is most desirable to know the total uncertainty in the predicted peak response of the system given the starting parameter values. An extensive strong motion data set is used to study these questions, The most direct prediction models are found to be preferable (have lower prediction dispersion) but data may not be available in all regions to permit their use.     

Seismic demand sensitivity of reinforced concrete shear‐wall building using FOSM method

The uncertainty in the seismic demand of a structure (referred to as the engineering demand parameter, EDP) needs to be properly characterized in performance‐based earthquake engineering. Uncertainties in the ground motion and in structural properties are responsible for EDP uncertainty. In this study, sensitivity of EDPs to major uncertain variables is investigated using the first‐order second‐moment method for a case study building. This method is shown to be simple and efficient for estimating the sensitivity of seismic demand. The EDP uncertainty induced by each uncertain variable is used to determine which variables are most significant. Results show that the uncertainties in ground motion are more significant for global EDPs, namely peak roof acceleration and displacement, and maximum inter‐storey drift ratio, than those in structural properties. Uncertainty in the intensity measure (IM) of ground motion is the dominant variable for uncertainties in local EDPs such as the curvature demand at critical cross‐sections. Conditional sensitivity of global and local EDPs given IM is also estimated. It is observed that the combined effect of uncertainties in structural properties is more significant than uncertainty in ground motion profile at lower IM levels, while the opposite is true at higher IM levels. Copyright © 2005 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.     

Filtered incremental velocity: A novel approach in intensity measures for seismic collapse estimation

This study evaluates the performance of a new intensity measure, referred to as filtered incremental velocity FIV3, which is computed using time-domain features extracted from an acceleration time series and is aimed at the evaluation of structural collapse. This novel approach focuses on the area under a small number of acceleration pulses in the ground motion instead of focusing on the peak response of linear elastic oscillators as in many recently proposed measures of ground motion intensity. FIV3 is developed based on previous research that has highlighted the close relation between the incremental velocity of a ground motion and its potential to induce large inelastic incursions on structures. However, unlike the original definition of incremental velocity which provides a single level of intensity for a ground motion, this new intensity measure is period-dependent and computed as the sum of the three largest incremental velocities obtained from a low-pass filtered ground acceleration time series. Efficiency and sufficiency with respect to several ground motion parameters such as magnitude, source-to-site-distance, spectral shape, scale factor, and duration are carefully evaluated and compared against those computed with some traditional and recently proposed intensity measures using collapse results from a four-story reinforced concrete frame. Results indicate that FIV3 leads to lower variability of collapse estimates and therefore higher efficiency as well as high sufficiency compared with those of other ground motion intensity parameters indicating that this new intensity measure is a promising parameter for structural collapse risk assessment.     

A site‐consistent method to quantify sufficiency of alternative IMs in relation to PSDA

In probabilistic seismic demand analysis, evaluation of the sufficiency of an intensity measure (IM) is an important criterion to avoid biased assessment of the demand hazard. However, there exists no metric to quantify the degree of sufficiency as per the criterion of Luco and Cornell (2007). This paper proposes a site‐specific unified measure for degree of sufficiency from all seismological parameters under consideration using a total information gain metric. This unified metric for sufficiency supports not only comparison of the performance of different IMs given a response quantity but also assessment of the performance of a particular IM across different response quantities. The proposed sufficiency metric was evaluated for a 4‐story steel moment frame building, and the influence of ground motion selection on the degree of sufficiency was investigated. It was observed that ground motion selection can have a significant impact on IM sufficiency. Because computing the total information gain requires continuous deaggregation across the IM space, an approximate deaggregation technique that allows for a more practical estimation of marginal deaggregation probabilities is proposed. It is expected that the total information gain metric proposed in this paper will aid in understanding the efficiency‐sufficiency relation, thus enabling the selection of a proper scalar IM for a given site and application in probabilistic seismic demand analysis.     

Direct use of PGV for estimating peak nonlinear oscillator displacements

A predictive model is presented for estimating the peak inelastic oscillator displacements (S_d,ie) from peak ground velocity (PGV). The proposed model accounts for the variation of S_d,ie for bilinear hysteretic behavior under constant ductility (µ) and normalized lateral strength ratio (R) associated with postyield stiffness ratios of α=0 and 5%. The regression coefficients are based on a ground‐motion database that contains dense‐to‐stiff soil site recordings at distances of up to 30 km from the causative fault. The moment magnitude ( M ) range of the database is 5.2? M ?7.6 and the ground motions do not exhibit pulse‐dominant signals. Confined to the limitations imposed by the ground‐motion database, the model can estimate S_d,ie by employing the PGV predictions obtained from the attenuation relationships (ground‐motion prediction equations). In this way, the influence of important seismological parameters can be incorporated to the variation of S_d,ie in a fairly rationale manner. This feature of the predictive model advocates its implementation in the probabilistic seismic hazard analysis that employs scalar ground‐motion intensity indices. Various case studies are presented to show the consistent estimations of S_d,ie by the proposed model. The error propagation in the S_d,ie estimations is also discussed when the proposed model is associated with attenuation relationships. Copyright © 2008 John Wiley & Sons, Ltd.     

Impact of hazard‐consistent ground motion duration in structural collapse risk assessment

This study evaluates the effect of considering ground motion duration when selecting hazard‐consistent ground motions for structural collapse risk assessment. A procedure to compute source‐specific probability distributions of the durations of ground motions anticipated at a site, based on the generalized conditional intensity measure framework, is developed. Targets are computed for three sites in Western USA, located in distinct tectonic settings: Seattle, Eugene, and San Francisco. The effect of considering duration when estimating the collapse risk of a ductile reinforced concrete moment frame building, designed for a site in Seattle, is quantified by conducting multiple stripe analyses using groups of ground motions selected using different procedures. The mean annual frequency of collapse (λ_collapse) in Seattle is found to be underestimated by 29% when using typical‐duration ground motions from the PEER NGA‐West2 database. The effect of duration is even more important in sites like Eugene (λ_collapse underestimated by 59%), where the seismic hazard is dominated by large magnitude interface earthquakes, and less important in sites like San Francisco (λ_collapse underestimated by 7%), where the seismic hazard is dominated by crustal earthquakes. Ground motion selection procedures that employ causal parameters like magnitude, distance, and Vs₃₀ as surrogates for ground motion duration are also evaluated. These procedures are found to produce poor fits to the duration and response spectrum targets because of the limited number of records that satisfy typical constraints imposed on the ranges of the causal parameters. As a consequence, ground motions selected based on causal parameters are found to overestimate λ_collapse by 53%. Copyright © 2016 John Wiley & Sons, Ltd.     

Structural performance assessment under near‐source pulse‐like ground motions using advanced ground motion intensity measures

This paper demonstrates the effectiveness of utilizing advanced ground motion intensity measures (IMs) to evaluate the seismic performance of a structure subject to near‐source ground motions. Ordinary records are, in addition, utilized to demonstrate the robustness of the advanced IM with respect to record selection and scaling. To perform nonlinear dynamic analyses (NDAs), ground motions need to be selected; as a result, choosing records that are not representative of the site hazard can alter the seismic performance of structures. The median collapse capacity (in terms of IM), for example, can be systematically dictated by including a few aggressive or benign pulse‐like records into the record set used for analyses. In this paper, the elastic‐based IM such as the pseudo‐spectral acceleration (S_a) or a vector of S_a and epsilon has been demonstrated to be deficient to assess the structural responses subject to pulse‐like motions. Using advanced IMs can be, however, more accurate in terms of probabilistic response prediction. Scaling earthquake records using advanced IMs (e.g. inelastic spectral displacement, S_di, and IM _1I&2E; the latter is for the significant higher‐mode contribution structures) subject to ordinary and/or pulse‐like records is efficient, sufficient, and robust relative to record selection and scaling. As a result, detailed record selection is not necessary, and records with virtually any magnitude, distance, epsilon and pulse period can be selected for NDAs. Copyright © 2008 John Wiley & Sons, Ltd.     

Scaling of ductility and damage‐based strength reduction factors for horizontal motions

The conventional approach of obtaining the inelastic response spectra for the aseismic design of structures involves the reduction of elastic spectra via response modification factors. A response modification factor is usually taken as a product of (i) strength factor, R_S, (ii) ductility factor, R_μ, and (iii) redundancy factor, R_R. Ductility factor, also known as strength reduction factor (SRF), is considered to primarily depend on the initial time period of the single‐degree‐of‐freedom (SDOF) oscillator and the displacement ductility demand ratio for the ground motion. This study proposes a preliminary scaling model for estimating the SRFs of horizontal ground motions in terms of earthquake magnitude, strong motion duration and predominant period of the ground motion, geological site conditions, and ductility demand ratio, with a given level of confidence. The earlier models have not considered the simultaneous dependence of the SRFs on various governing parameters. Since the ductility demand ratio is not a complete measure of the cumulative damage in the structure during the earthquake‐induced vibrations, the existing definition of the SRF is sought to be modified with the introduction of damage‐based SRF (in place of ductility‐based SRF). A parallel scaling model has been proposed for estimating the damage‐based SRFs. This model considers damage and ductility supply ratio as parameters instead of ductility demand ratio. Through a parametric study on ductility‐based SRFs, it has been shown that the hitherto assumed insensitivity of earthquake magnitude and strong motion duration may not be always justified and that the initial time period of the oscillator plays an important role in the dependence of SRF on these parameters. Further, the damage‐based SRFs are found to show similar parametric dependence as observed in the case of the ductility‐based SRFs. Copyright © 2000 John Wiley & Sons, Ltd.     

A predictive model for Arias intensity at multiple sites and consideration of spatial correlations

Arias intensity, I_a, has been identified as an efficient intensity measure for the estimation of earthquake‐induced losses. In this paper, a new model for the prediction of Arias intensity, which incorporates nonlinear site response through the use of the average shear‐wave velocity and a heteroskedastic variance structure, is proposed. In order to estimate the effects of ground motions on spatially‐distributed systems, it is important to take into account the spatial correlation of the intensity measure. However, existing loss‐estimation models, which use I_a as an input, do not take this aspect of the ground motion into account. Therefore, the potential to model the spatial correlation of Arias intensity is also investigated. The empirical predictive model is developed using recordings from the Pacific Earthquake Engineering Research Center Next Generation of Attenuation database whereas the model for spatial correlation makes use of the well‐recorded events from this database, that is the Northridge and Chi‐Chi earthquakes. Copyright © 2011 John Wiley & Sons, Ltd.