Elastic Spectral Acceleration Research Articles

A non-ergodic ground-motion model of Fourier amplitude spectra for France

We used an ergodic ground-motion model (GMM) of California of Bayless and Abrahamson (Bull Seismol Soc Am 109(5):2088–2105, 2019) as a backbone model and incorporated the varying-coefficient model (VCM), with a modification for anisotropic path effects, to develop a new non-ergodic GMM for France based on the French RESIF data set (1996–2016). Most of the earthquakes in this database have small-to-moderate magnitudes (M2.0 – M5.2). We developed the GMM for the smoothed effective amplitude spectrum (EAS) rather than for elastic spectral acceleration because it allows the use of small-magnitude data to constrain linear effects of the path and site without the complication of the scaling being affected by differences in the response spectral shape. For the VCM, the coefficients of GMM can vary by geographical location and they are estimated using Gaussian-process regression. There is a separate set of coefficients for each source and site coordinate, including both the mean coefficients and the epistemic uncertainty in the coefficients. We further modify the anelastic attenuation term of a GMM by the cell-specific approach of Dawood and Rodriguez-Marek (Bull Seismol Soc Am. 103 (2B): 1360–1372, 2013) and Kuehn et al. (Bull Seismol Soc Am 109 (2): 575–585, 2019) to allow for azimuth-dependent attenuation for each source which reduces the standard deviation of the residuals at long distances. As an example, we compute the 5 Hz seismic hazard for two sites using the non-ergodic EAS GMM. At the 1E-4 annual frequency of exceedance hazard level, there can be a large difference between the ergodic hazard and the non-ergodic hazard if the distance between the chosen site and the available data is smaller than the correlation length of the non-ergodic terms). The combination of the non-ergodic median ground motion and the reduced aleatory variability can have large implications for seismic-hazard estimation for long return periods. For some sites, the estimated hazard will increase and for other sites, the estimated hazard will decrease compared to the traditional ergodic GMM approach. Due to the skewed distribution of the epistemic uncertainty of the hazard, more of the sites will see a decrease in the mean hazard at the 1E−4 hazard level than will see an increase as a result of using the non-ergodic GMM.

Effectiveness of Instantaneous Power in predicting the collapse responses of structures under pulse-like ground motions by Esra ZENGİN

This study investigates the performance of the Instantaneous Power (IP(T1)) intensity measure (IM) for predicting the structural collapse of structures under near-fault pulse-like ground motions. The efficiency and sufficiency of vector IM consisting of elastic spectral acceleration at the fundamental period of the structure (Sa(T1)) and IP(T1) are compared with those obtained using Sa(T1), average spectral acceleration (Saavg), and spectral shape-based vector IMs. A proportional reduction in error, which quantifies to what extent the other ground-motion parameter eliminates the error in the collapse capacity prediction relative to IM of interest, is used to assess the sufficiency. Our findings reveal that [Sa(T1), IP(T1)] yields better collapse capacity prediction compared to all IMs considered and is found to be sufficient with respect to most of the seismological parameters, duration-related IMs, pulse period, and scale factor.

A vector‐valued intensity measure for near‐fault ground motions

SummaryNear‐fault ground motions containing high energy and large amplitude velocity pulses may cause severe damage to structures. The most widely used intensity measure (IM) is the elastic spectral acceleration at the fundamental period of the structure (Sa(T1)); however, Sa(T1) is not a sufficient IM with respect to the effects of the pulse‐like ground motions on structural response. For near‐fault ground motions, including pulse‐like and non–pulse‐like time histories, we propose a vector‐valued IM consisting of a new IM called instantaneous power (IP(T1)) and the Sa(T1). The IP(T1) is defined as the maximum power of the bandpass‐filtered velocity time series over a time interval of 0.5T1. The IP(T1) is period‐dependent because the velocity time series is filtered over a period range (0.2T1‐3T1). This allows the IP(T1) to represent the power of the near‐fault ground motions relevant to the response of the structure. Using two‐dimensional models of the 2‐ and 9‐story steel‐frame buildings, we show that the proposed [Sa(T1), IP(T1)] vector IM gives more accurate estimates of the maximum inter‐story drift and collapse capacity responses from near‐fault ground motions than using the vector IM consisting of the Sa(T1), the presence of the velocity pulse, and the period of the velocity pulse. Moreover, for the structures considered, for a given Sa(T1), the IP(T1) is more strongly correlated with structural damage from near‐fault ground motions than the combination of the velocity pulse and pulse period.

An Improved Seismic Intensity Measure of Inelastic Spectral Acceleration Based on MPA to Reduce the Dispersion in IDA

We present a new seismic intensity measure (IM) to reduce the dispersion in incremental dynamic analysis (IDA), which commonly use the elastic spectral acceleration as the IM. We propose using the inelastic spectral acceleration based on the principles of modal pushover analysis (MPA) as the seismic IM of ground motion. Unlike other methods of computing inelastic spectral acceleration, this new metric is calculated from the result of equivalent single degree-of-freedom (SDF) systems under the lateral force mode using the uncoupled modal response history analysis procedure. These equivalent SDF systems consider the constantly changing elastic–plastic hysteretic behaviour of the structure itself with different seismic intensities. The results indicate that the improved IDA method can more accurately estimate nonlinear structural responses in many intensity levels covering the entire range of structural responses—all the way from elastic behaviour to global dynamic instability. When the structure enters into the inelastic range, the seismic performance of the IDA’s dispersion using the inelastic spectral acceleration as the seismic IM is better than that using peak ground acceleration or elastic spectral acceleration.

Wavelet analysis for relating soil amplification and liquefaction effects with seismic performance of precast structures

SummaryPrecast concrete structures are preferred for facilities with large open areas due to easiness in construction. Such structures are typically composed of individual columns and long‐span beams, and are quite flexible and of limited redundancy. In this paper, nonlinear dynamic analyses of a typical such structure are conducted using as excitation 54 ground motions recorded on top of a variety of soils (hard, soft, and liquefied soil sites). The results show that liquefaction‐affected level‐ground motions systematically impose a greater threat to precast‐concrete structures in terms of seismic demand, even when low values of elastic spectral acceleration prevail, as opposed to soft‐soil records and even more to hard‐soil ones. Thus, elastic spectral acceleration appears to be an insufficient engineering demand parameter for design. Soil effects, the “signature” of which is born on ground motions, are first uncovered using wavelet analysis to detect the evolution of the energy and frequency content of the ground motion in the time domain. From this, the changes in effective (“dominant”) excitation period are noted, persuasively attributed to the nature of the soil, and finally correlated with the observed structural behavior. Copyright © 2016 John Wiley & Sons, Ltd.

A variant of modal pushover analyses (VMPA) based on a non-incremental procedure

A variant of modal pushover analysis (VMPA) is presented to evaluate the seismic performance of the structures. The suggested procedure is based on an iterative process in which secant stiffnesses are used both at the element level and in the modal response. VMPA diverges from the existing modal pushover analyses for the following reasons: (1) mode compatible adaptive forces are applied to the structure at each iteration step, (2) the application of the equal displacement rule in combination with secant stiffness based linearization in the spectral displacement (Sd)—spectral acceleration (Sa) relation eliminates the necessity to produce a modal capacity diagram for each mode. The displacement controlled algorithm determines the single ordinate of the modal capacity diagram corresponding to the target displacement demand for the nth mode (Sdn_p, San_p) by reducing elastic spectral acceleration (San_e) to converge to the plastic acceleration (San_p). A Matlab based computer program known as DOC3D-v2 is developed to implement the proposed procedure. To verify the success of the suggested procedure, 9- and 20-storey LA SAC buildings are analysed, and the resulting demands are compared with several existing procedures, such as the extended N2, MPA and MMPA, as well as nonlinear time history analyses performed for two different set of acceleration records. VMPA yields enhanced results in terms of storey drifts, especially for the 20-storey LA building, compared with the other methods. Although the storey displacements and drifts are largely consistent with nonlinear time history analysis results, conservative estimates are obtained for the storey shear forces.

Probabilistic seismic response analysis of a 3-D reinforced concrete building

This paper presents the probabilistic seismic demand analysis with respect to seismic input uncertainty only of a 3-D reinforced concrete building model subjected to three-component earthquake ground motion excitation. Response history analyses are carried out on a nonlinear frame model. Probability distributions are assumed for the ground motion Intensity Measure (IM) taken as the linear 5% damped elastic spectral acceleration at the fundamental period of the structure. Part of the framework of the so-called Performance Based Earthquake Engineering (PBEE) methodology developed by the Pacific Earthquake Engineering Research (PEER) Center is used in this study. This paper has two main objectives. The first objective is to perform a probabilistic demand analysis of an existing building conditional on the ground motion IM. The second objective is to use the results obtained from this existing testbed, with real-world complexities, to demonstrate the deficiency of the PEER PBEE methodology when using a scalar ground motion IM for 3-D structural models. This last objective shows the need for improving the definition of the seismic IM in the PBEE methodology for the general case of 3-D structures subjected to multi-directional input ground motions. To this effect, an ensemble of natural ground motion records is used to represent the inherent randomness in ground motion time-histories (i.e., record-to-record variability). The statistical correlation of different Engineering Demand Parameters (EDPs) with a set of IMs, taken as the 5% damped spectral accelerations at different periods for two horizontal ground motion components, is investigated in order to assess the dispersion in the EDPs due to different ground motion records. Some statistical correlation coefficients are found to be high, indicating that the dispersion of the EDPs is heavily influenced by the spectral content at periods different from the fundamental period. This result points to the need for using vector-valued ground motion Intensity Measures in the PBEE methodology currently proposed by PEER.

Spatial Correlation of Spectral Acceleration in European Data

Abstract Quantification of regional seismic risk is based on spatially correlated random fields and requires modeling of the joint distribution of ground‐motion intensity measures at all sites of interest. In particular, when a portfolio of buildings or a transportation/distribution network (lifeline) is of concern, correlation models for elastic spectral acceleration (SA) may also be required in order to estimate the expected loss in case of seismic events. The presented study focuses on semi‐empirical estimation of spatial correlation as a function of intersite separation distance. In fact, this paper complements, and is based on, preceding work of the authors referring to spatial correlation of peak ground acceleration and velocity (Esposito and Iervolino, 2011). The evaluation of correlation for ground‐motion residuals was performed on data from multiple earthquakes, considering different ground‐motion prediction equations fitted to the same records. Correlation analyses, carried out through geostatistical tools, considered two datasets: the Italian Accelerometric Archive and the European Strong‐Motion Database. Results appear generally consistent with previous research on the same topic. Finally, simple relationships providing the correlation range of intraevent residuals of SA, as a function of structural period, were derived for each dataset. The developed models are useful for earthquake engineering applications where spatial correlation of peak ground motion is required.

Cracking an Open Safe: Uncertainty in HAZUS-Based Seismic Vulnerability Functions

The “cracking an open safe” methodology has been used to tabulate HAZUS-based seismic vulnerability as functions of structure-independent intensity, while avoiding iteration in the structural analysis. The vulnerability functions give mean damage factor (MDF, defined here as mean repair cost as a fraction of replacement cost) versus 5%-damped elastic spectral acceleration response at 0.3-second and 1.0-second periods, for every combination of occupancy type, model building type, design level, magnitude, distance, site soil classification, etc. Like HAZUS-MH, these prior seismic vulnerability functions give no estimate of uncertainty in damage factor. The coefficient of variation (COV) of damage factor is readily calculated by taking advantage of the fact that that at any level of excitation there is a probability mass function of damage state and an implicit distribution of repair cost conditioned on damage state. COV is calculated here for each combination of occupancy type, model building type, etc., tabulated alongside MDF, and the tables presented for public use at www.risk-agora.org . It is found that a HAZUS-based COV generally decreases with increasing MDF (as has been observed using other analytical vulnerability methods), and the standard deviation of damage factor generally increases with increasing MDF.

Probabilistic seismic performance evaluation of non-seismic RC frame buildings

In this paper, probabilistic seismic performance assessment of a typical non-seismic RC frame building representative of a large inventory of existing buildings in developing countries is conducted. Nonlinear time-history analyses of the sample building are performed with 20 large-magnitude medium distance ground motions scaled to different levels of intensity represented by peak ground acceleration and 5% damped elastic spectral acceleration at the first mode period of the building. The hysteretic model used in the analyses accommodates stiffness degradation, ductility-based strength decay, hysteretic energy-based strength decay and pinching due to gap opening and closing. The maximum inter story drift ratios obtained from the time-history analyses are plotted against the ground motion intensities. A method is defined for obtaining the yielding and collapse capacity of the analyzed structure using these curves. The fragility curves for yielding and collapse damage levels are developed by statistically interpreting the results of the time-history analyses. Hazard-survival curves are generated by changing the horizontal axis of the fragility curves from ground motion intensities to their annual probability of exceedance using the log-log linear ground motion hazard model. The results express at a glance the probabilities of yielding and collapse against various levels of ground motion intensities.

Probabilistic seismic demand analysis using advanced ground motion intensity measures

AbstractOne of the objectives in performance‐based earthquake engineering is to quantify the seismic reliability of a structure at a site. For that purpose, probabilistic seismic demand analysis (PSDA) is used as a tool to estimate the mean annual frequency of exceeding a specified value of a structural demand parameter (e.g. interstorey drift). This paper compares and contrasts the use, in PSDA, of certain advanced scalar versus vector and conventional scalar ground motion intensity measures (IMs). One of the benefits of using a well‐chosen IM is that more accurate evaluations of seismic performance are achieved without the need to perform detailed ground motion record selection for the nonlinear dynamic structural analyses involved in PSDA (e.g. record selection with respect to seismic parameters such as earthquake magnitude, source‐to‐site distance, and ground motion epsilon). For structural demands that are dominated by a first mode of vibration, using inelastic spectral displacement (Sdi) can be advantageous relative to the conventionally used elastic spectral acceleration (Sa) and the vector IM consisting of Sa and epsilon (ε). This paper demonstrates that this is true for ordinary and for near‐source pulse‐like earthquake records. The latter ground motions cannot be adequately characterized by either Sa alone or the vector of Sa and ε. For structural demands with significant higher‐mode contributions (under either of the two types of ground motions), even Sdi (alone) is not sufficient, so an advanced scalar IM that additionally incorporates higher modes is used. Published in 2007 by John Wiley & Sons, Ltd.

Reply to "Comment on 'Nonlinear Soil-Site Effects in Probabilistic Seismic-Hazard Analysis' by Paolo Bazzurro and C. Allin Cornell," by Jonathan P. Stewart and Christine A. Goulet

We thank Stewart and Goulet for taking an interest in our work and for bringing to our attention the article by Baturay and Stewart (2003), which should have been included in our reference list. Unlike the approach presented in our article, the article by Baturay and Stewart tackles the problem of quantifying the effects of local soil to the incipient seismic waves using an empirical rather than an analytical procedure. We certainly agree with the conclusions reached by Stewart and Goulet stating the applicability of both methodologies for seismic-hazard estimation of critical facilities. Our approach, which is predominantly analytical, undoubtedly benefits from a comparison with a procedure that is based on observations. In Figure 1 of their discussion, Stewart and Goulet provide a useful comparison of the record- to-record variability, ![Graphic][1] , of the elastic spectral acceleration at the soil surface, ![Graphic][2] , for f = 3.33 Hz, conditional on the level of peak ground acceleration (pga) at the bedrock that derives from the application of both procedures to different National Earthquake Hazards Reduction Program (nehrp) soil categories and to soft-soil sites. We were pleased to see that this comparison is very favorable and that the values from both approaches appear to be statistically indistinguishable. This enhanced the credibility of both procedures. Note, however, that the values of ![Graphic][3] in Figure 1 computed using the analytical method by Bazzurro and Cornell could potentially be reduced. Of course, reducing the variability in the surface spectral acceleration is important because … [1]: /embed/inline-graphic-1.gif [2]: /embed/inline-graphic-2.gif [3]: /embed/inline-graphic-3.gif

Evaluation of predictors of non‐linear seismic demands using ‘fishbone’ models of SMRF buildings

AbstractPredictors (or estimates) of seismic structural demands that are less computationally time‐consuming than non‐linear dynamic analysis can be useful for structural performance assessment and for design. In this paper, we evaluate the bias and precision of predictors that make use of, at most, (i) elastic modal vibration properties of the given structure, (ii) the results of a non‐linear static pushover analysis of the structure, and (iii) elastic and inelastic single‐degree‐of‐freedom time‐history analyses for the specified ground motion record. The main predictor of interest is an extension of first‐mode elastic spectral acceleration that additionally takes into account both the second‐mode contribution to (elastic) structural response and the effects of inelasticity. This predictor is evaluated with respect to non‐linear dynamic analysis results for ‘fishbone’ models of steel moment‐resisting frame (SMRF) buildings. The relatively small number of degrees of freedom for each fishbone model allows us to consider several short‐to‐long period buildings and numerous near‐ and far‐field earthquake ground motions of interest in both Japan and the U.S. Before doing so, though, we verify that estimates of the bias and precision of the predictor obtained using fishbone models are effectively equivalent to those based on typical ‘full‐frame’ models of the same buildings. Copyright © 2003 John Wiley & Sons, Ltd.

Sensitivity of Building Loss Estimates to Major Uncertain Variables

This paper examines the question of which sources of uncertainty most strongly affect the repair cost of a building in a future earthquake. Uncertainties examined here include spectral acceleration, ground-motion details, mass, damping, structural force-deformation behavior, building-component fragility, contractor costs, and the contractor's overhead and profit. We measure the variation (or swing) of the repair cost when each basic input variable except one is taken at its median value, and the remaining variable is taken at its 10th and at its 90th percentile. We perform this study using a 1960s highrise nonductile reinforced-concrete moment-frame building. Repair costs are estimated using the assembly-based vulnerability (ABV) method. We find that the top three contributors to uncertainty are assembly capacity (the structural response at which a component exceeds some damage state), shaking intensity (measured here in terms of damped elastic spectral acceleration, Sa), and details of the ground motion with a given Sa.

Application of inelastic response spectra derived from seismic hazard spectral ordinates for Canada: Discussion

In Fig. 3 of the paper, the authors have produced the mean strength reduction factors (R) for a range of target ductility values as a function of period, T (s), and they have noted that the use of elastic spectra with reduction factor involves considerable uncertainty. Because of this uncertainty, the authors prefer to obtain the design strength directly from inelastic response spectra corresponding to a range of values of the ductility (μ). The factor R may be considered as the ratio of the elastic spectral acceleration for a given period to the corresponding inelastic spectral acceleration associated with a specified inelastic damage level or ductility. The authors have used spectral curves for two different suites of records (one for high a/v ratio and the other for intermediate a/v ratio), scaled appropriately to derive two mean elastic response spectra to match reasonably with the target spectra. The same suites of record are then used to derive the inelastic response spectra for six different values of ductility. For use in the design code, curves are fitted to the inelastic spectra. The curve fitting parameters are given in Table 5. These parameters are then used in conjunction with eqs. [4] and [5] to calculate the elastic ( μ= 1) and inelastic (μ > 1) base shear values. The authors have used the spectral curves produced for the reference ground condition (RGC) described as “firm ground” in the GSC document (Adams et al. 1996). In this document, the seismic hazard values obtained for hard rock are amplified

Application of inelastic response spectra derived from seismic hazard spectral ordinates for Canada

The Geological Survey of Canada is currently producing a suite of new hazard maps for Canada. These maps take into account the additional recorded data obtained during the past 13 years, as well as the new geological and tectonic information that has recently become available. They provide elastic spectral acceleration values for a uniform probability of exceedance of 10% in 50 years. A method of using the uniform hazard spectral values to obtain design response spectral curves for different values of ductility is presented here. The method uses two spectral values obtained from the hazard maps, the peak spectral acceleration for the site and the spectral acceleration corresponding to a period of 0.5 s. Empirical expressions are developed to represent the design response spectra. It is shown that by using inelastic spectral accelerations rather than the elastic spectral values in association with a reduction factor, the new method provides a more reliable estimate of the design forces. Key words: uniform hazard spectra; inelastic spectra, seismic design forces, force modification factor, foundation factor, seismic hazard for Canada.