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.     

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.     

Evaluation of the exact conditional spectrum and generalized conditional intensity measure methods for ground motion selection

Two existing, contemporary ground motion selection and modification procedures – (i) exact conditional spectrum (CS‐exact) and (ii) generalized conditional intensity measure (GCIM) – are evaluated in their ability to accurately estimate seismic demand hazard curves (SDHCs) of a given structure at a specified site. The amount of effort involved in implementing these procedures to compute a single SDHC is studied, and a case study is chosen where rigorous benchmark SDHCs can be determined for evaluation purposes. By comparing estimates from ground motion selection and modification procedures with the benchmark, we conclude that estimates from CS‐exact are unbiased in many of the cases considered. The estimates from GCIM are even more accurate, as they are unbiased for most – but not all – of the cases where estimates from CS‐exact are biased. We find that it is possible to obtain biased SDHCs from GCIM, even after employing a very diverse collection of intensity measures to select ground motions and implementing its bias‐checking feature, because it is usually difficult to identify intensity measures that are truly ‘sufficient’ for the response of a complex, multi‐degree‐of‐freedom system. 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.     

A probabilistic framework for quantification of aftershock ground‐motion hazard in California: Methodology and parametric study

This paper presents a proposed method of aftershock probabilistic seismic hazard analysis (APSHA) similar to conventional ‘mainshock’ PSHA in that it estimates the likelihoods of ground motion intensity (in terms of peak ground accelerations, spectral accelerations or other ground motion intensity measures) due to aftershocks following a mainshock occurrence. This proposed methodology differs from the conventional mainshock PSHA in that mainshock occurrence rates remain constant for a conventional (homogeneous Poisson) earthquake occurrence model, whereas aftershock occurrence rates decrease with increased elapsed time from the initial occurrence of the mainshock. In addition, the aftershock ground motion hazard at a site depends on the magnitude and location of the causative mainshock, and the location of aftershocks is limited to an aftershock zone, which is also dependent on the location and magnitude of the initial mainshock. APSHA is useful for post‐earthquake safety evaluation where there is a need to quantify the rates of occurrence of ground motions caused by aftershocks following the initial rupture. This knowledge will permit, for example, more informed decisions to be made for building tagging and entry of damaged buildings for rescue, repair or normal occupancy. Copyright © 2008 John Wiley & Sons, Ltd.     

Improved seismic hazard model with application to probabilistic seismic demand analysis

An improved seismic hazard model for use in performance‐based earthquake engineering is presented. The model is an improved approximation from the so‐called ‘power law’ model, which is linear in log–log space. The mathematics of the model and uncertainty incorporation is briefly discussed. Various means of fitting the approximation to hazard data derived from probabilistic seismic hazard analysis are discussed, including the limitations of the model. Based on these ‘exact’ hazard data for major centres in New Zealand, the parameters for the proposed model are calibrated. To illustrate the significance of the proposed model, a performance‐based assessment is conducted on a typical bridge, via probabilistic seismic demand analysis. The new hazard model is compared to the current power law relationship to illustrate its effects on the risk assessment. The propagation of epistemic uncertainty in the seismic hazard is also considered. To allow further use of the model in conceptual calculations, a semi‐analytical method is proposed to calculate the demand hazard in closed form. For the case study shown, the resulting semi‐analytical closed form solution is shown to be significantly more accurate than the analytical closed‐form solution using the power law hazard model, capturing the ‘exact’ numerical integration solution to within 7% accuracy over the entire range of exceedance rate. Copyright © 2007 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.     

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.     

Effects of two alternative representations of ground‐motion uncertainty on probabilistic seismic demand assessment of structures

A probabilistic representation of the entire ground‐motion time history can be constructed based on a stochastic model that depends on seismic source parameters. An advanced stochastic simulation scheme known as Subset Simulation can then be used to efficiently compute the small failure probabilities corresponding to structural limit states. Alternatively, the uncertainty in the ground motion can be represented by adopting a parameter (or a vector of parameters) known as the intensity measure (IM) that captures the dominant features of the ground shaking. Structural performance assessment based on this representation can be broken down into two parts, namely, the structure‐specific part requiring performance assessment for a given value of the IM, and the site‐specific part requiring estimation of the likelihood that ground shaking with a given value of the IM takes place. The effect of these two alternative representations of ground‐motion uncertainty on probabilistic structural response is investigated for two hazard cases. In the first case, these two approaches are compared for a scenario earthquake event with a given magnitude and distance. In the second case, they are compared using a probabilistic seismic hazard analysis to take into account the potential of the surrounding faults to produce events with a range of possible magnitudes and distances. The two approaches are compared on the basis of the probabilistic response of an existing reinforced‐concrete frame structure, which is known to have suffered shear failure in its columns during the 1994 Northridge Earthquake in Los Angeles, California. Copyright © 2007 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.     

Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios

Probabilistic seismic demand models are a common and often essential step in generating analytical fragility curves for highway bridges. With these probabilistic models being traditionally conditioned on a single seismic intensity measure (IM), the degree of uncertainty in the models is dependent on the IM used. Selection of an optimal IM for conditioning these demand models is not a trivial matter and has been the focus of numerous studies. Unlike previous studies that consider a single structure for IM selection, this study evaluates optimal IMs for use when generating probabilistic seismic demand models for bridge portfolios such as would be found in HAZUS‐MH. Selection criteria such as efficiency, practicality, sufficiency, and hazard computability are considered in the selection process. A case study is performed considering the multi‐span simply supported steel girder bridge class. Probabilistic seismic demand models are generated considering variability in the geometric configurations and material properties, using two suites of ground motions—one synthetic and one recorded motion suite. Results show that of the 10 IMs considered, peak ground acceleration (PGA) and spectral acceleration at the fundamental period are the most optimal for the synthetic motions, and that cumulative absolute velocity is also a close contender when using recorded motions. However, when hazard computability is considered, PGA is selected as the IM of choice. Previous studies have shown that spectrally based quantities perform better than PGA for a given structure, but the findings of this study indicate that when a portfolio of bridges is considered, PGA should be used. Copyright © 2007 John Wiley & Sons, Ltd.     

Practice‐oriented estimation of the seismic demand hazard using ground motions at few intensity levels

This paper examines the calculation of the seismic demand hazard in a practice‐oriented manner via the use of seismic response analyses at few intensity levels. The seismic demand hazard is a more robust measure for quantifying seismic performance, when seismic hazard is represented in a probabilistic format, than intensity‐based assessments, which remain prevalent in seismic design codes. It is illustrated that, for a relatively complex bridge–foundation–soil system case study, the seismic demand hazard can be estimated with sufficient accuracy using as little as three intensity measure levels that have exceedance probabilities of 50%, 10% and 2% in 50 years which are already of interest in multi‐objective performance‐based design. Compared with the conventional use of the mean demand from an intensity‐based assessment(s), it is illustrated that, for the same number of seismic response analyses, a practice‐oriented ‘approximate’ seismic demand hazard is a more accurate and precise estimate of the ‘exact’ seismic demand hazard. Direct estimation of the seismic demand hazard also provides information of seismic performance at multiple exceedance rates. Thus, it is advocated that if seismic hazard is considered in a probabilistic format, then seismic performance assessment, and acceptance criteria, should be in terms of the seismic demand hazard and not intensity‐based assessments. Copyright © 2013 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.     

Seismic demand models for probabilistic risk analysis of near fault vertical ground motion effects on ordinary highway bridges

The influence of vertical ground motions on the seismic response of highway bridges is not very well understood. Recent studies suggest that vertical ground motions can substantially increase force and moment demands on bridge columns and girders and cannot be overlooked in seismic design of bridge structures. For an evaluation of vertical ground motion effects on the response of single‐bent two‐span highway bridges, a systematic study combining the critical engineering demand parameters (EDPs) and ground motion intensity measures (IMs) is required. Results of a parametric study examining a range of highway bridge configurations subjected to selected sets of horizontal and vertical ground motions are used to determine the structural parameters that are significantly amplified by the vertical excitations. The amplification in these parameters is modeled using simple equations that are functions of horizontal and vertical spectral accelerations at the corresponding horizontal and vertical fundamental periods of the bridge. This paper describes the derivation of seismic demand models developed for typical highway overcrossings by incorporating critical EDPs and combined effects of horizontal and vertical ground motion IMs depending on the type of the parameter and the period of the structure. These models may be used individually as risk‐based design tools to determine the probability of exceeding the critical levels of EDP for pre‐determined levels of ground shaking or may be included explicitly in probabilistic seismic risk assessments. Copyright © 2011 John Wiley & Sons, Ltd.     

A comparison of intensity‐based demand distributions and the seismic demand hazard for seismic performance assessment

This paper compares the seismic demands obtained from an intensity‐based assessment, as conventionally considered in seismic design guidelines, with the seismic demand hazard. Intensity‐based assessments utilize the distribution of seismic demand from ground motions that have a specific value of some conditioning intensity measure, and the mean of this distribution is conventionally used in design verification. The seismic demand hazard provides the rate of exceedance of various seismic demand values and is obtained by integrating the distribution of seismic demand at multiple intensity levels with the seismic hazard curve. The seismic demand hazard is a more robust metric for quantifying seismic performance, because seismic demands from an intensity‐based assessment: (i) are not unique, with different values obtained using different conditioning intensity measures; and (ii) do not consider the possibility that demand values could be exceeded from different intensity ground motions. Empirical results, for a bridge‐foundation‐soil system, illustrate that the mean seismic demand from an intensity‐based assessment almost always underestimates the demand hazard value for the exceedance rate considered, on average by 17% and with a large variability. Furthermore, modification factors based on approximate theory are found to be unreliable. Adopting the maximum of the mean values from multiple intensity‐based assessments, with different conditional intensity measures, provides a less biased prediction of the seismic demand hazard value, but with still a large variability, and a proportional increase the required number of analyses. For an equivalent number of analyses, direct computation of the seismic demand hazard is a more logical choice and provides additional performance insight. Copyright © 2013 John Wiley & Sons, Ltd.     

A simulation‐based framework for risk assessment and probabilistic sensitivity analysis of base‐isolated structures

A versatile, simulation‐based framework for risk assessment and probabilistic sensitivity analysis of base‐isolated structures is discussed in this work. A probabilistic foundation is used to address the various sources of uncertainties, either excitation or structural, and to characterize seismic risk. This risk is given, in this stochastic setting, by some statistics of the system response over the adopted probability models and stochastic simulation is implemented for its evaluation. An efficient, sampling‐based approach is also introduced for establishing a probabilistic sensitivity analysis to identify the importance of each of the uncertain model parameters in affecting the overall risk. This framework facilitates use of complex models for the structural system and the excitation. The adopted structural model explicitly addresses nonlinear characteristics of the isolators and of any supplemental dampers, and the effect of seismic pounding of the base to the surrounding retaining walls. An efficient stochastic ground motion model is also discussed for characterizing future near‐fault ground motions and relating them to the seismic hazard for the structural site. An illustrative example is presented that emphasizes the results from the novel probabilistic sensitivity analysis and their dependence on seismic pounding occurrences and on addition of supplemental dampers. Copyright © 2011 John Wiley & Sons, Ltd.     

Alternative non‐linear demand estimation methods for probability‐based seismic assessments

Alternative non‐linear dynamic analysis procedures, using real ground motion records, can be used to make probability‐based seismic assessments. These procedures can be used both to obtain parameter estimates for specific probabilistic assessment criteria such as demand and capacity factored design and also to make direct probabilistic performance assessments using numerical methods. Multiple‐stripe analysis is a non‐linear dynamic analysis method that can be used for performance‐based assessments for a wide range of ground motion intensities and multiple performance objectives from onset of damage through global collapse. Alternatively, the amount of analysis effort needed in the performance assessments can be reduced by performing the structural analyses and estimating the main parameters in the region of ground motion intensity levels of interest. In particular, single‐stripe and double‐stripe analysis can provide local probabilistic demand assessments using minimal number of structural analyses (around 20 to 40). As a case study, the displacement‐based seismic performance of an older reinforced concrete frame structure, which is known to have suffered shear failure in its columns during the 1994 Northridge Earthquake, is evaluated. Copyright © 2008 John Wiley & Sons, Ltd.     

Merging energy‐based design criteria and reliability‐based methods: exploring a new concept

This paper examines the potential development of a probabilistic design methodology, considering hysteretic energy demand, within the framework of performance‐based seismic design of buildings. This article does not propose specific energy‐based criteria for design guidelines, but explores how such criteria can be treated from a probabilistic design perspective. Uniform hazard spectra for normalized hysteretic energy are constructed to characterize seismic demand at a specific site. These spectra, in combination with an equivalent systems methodology, are used to estimate hysteretic energy demand on real building structures. A design checking equation for a (hypothetical) probabilistic energy‐based performance criterion is developed by accounting for the randomness of the earthquake phenomenon, the uncertainties associated with the equivalent system analysis technique, and with the site soil factor. The developed design checking equation itself is deterministic, and requires no probabilistic analysis for use. The application of the proposed equation is demonstrated by applying it to a trial design of a three‐storey steel moment frame. The design checking equation represents a first step toward the development of a performance‐based seismic design procedure based on energy criterion, and additional works needed to fully implement this are discussed in brief at the end of the paper. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

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.