The estimation of MDOF nonlinear structural response given an earth-quake of magnitude M at distance R is studied with respect to issues such as the benefits and harms of (1) first scaling the records, (2) selecting records from the “wrong” magnitude, (3) alternative choices for how to scale the records, and (4) scaling records to a significantly higher or lower intensity, etc. We find that properly chosen scaling can reduce the necessity of the number of nonlinear analyses by a factor of about four, and that proper scaling does not introduce any bias. Several global and local nonlinear damage measures are considered. A five-DOF model of a steel structure is used; other cases are under study. The paper finishes with a demonstration of the use of such results in the estimation of the annual probability of exceeding a specified interstory ductility (drift) or other damage measures.

Limitations of the existing earthquake ground motion database lead to scaling of records to obtain seismograms consistent with a ground motion target for structural design and evaluation. In the engineering seismology community, acceptable limits for 'legitimate' scaling vary from one (no scaling allowed) to 10 or more. The concerns expressed by detractors of scaling are mostly based on the knowledge of, for example, differences in ground motion characteristics for different earthquake magnitude-distance (M w -R close ) scenarios, and much less on their effects on structures. At the other end of the spectrum, proponents have demonstrated that scaling is not only legitimate but also useful for assessing structural response statistics for M w -R close scenarios. Their studies, however, have not investigated more recent purposes of scaling and have not always drawn conclusions for a wide spectrum of structural vibration periods and strengths. This article investigates whether scaling of records randomly selected from an M w -R close bin (or range) to a target fundamental-mode spectral acceleration (S a ) level introduces bias in the expected nonlinear structural drift response of both single-degree-of-freedom oscillators and one multi-degree-of-freedom building. The bias is quantified relative to unscaled records from the target M w -R close bin that are 'naturally' at the target S a level. We consider scaling of records from the target M w -R close bin and from other M w -R close bins. The results demonstrate that scaling can indeed introduce a bias that, for the most part, can be explained by differences between the elastic response spectra of the scaled versus unscaled records.(7) Regress (in log-log space) the resulting ratios of scaled over unscaled nonlinear structural responses on the corresponding scale factors. AMPLITUDE SCALING OF GROUND MOTION RECORDS 1825Depending on the vibration period (T ) and strength (R) of the SDOF structure, these results demonstrate that intra-bin scaling records up can result in nonlinear structural responses (here S I d ) that are biased high, whereas the converse is true for scaling down. The magnitude of the bias for a given scale factor is smaller for longer-period structures and for stronger (closer to elastic) structures; it also depends on the characteristics (e.g. M w and R close ) of the records that are scaled. These results are summarized further in the conclusions section. SDOF structures-inter-bin scalingAlternatively, one could either 'correct' for a scaling-induced bias by using results like those presented in this paper, or select records with spectra that are, once scaled, similar to that of the target S a , M w , and R close . Such a selection of the records to be scaled has been demonstrated to significantly reduce the potential for biased responses.

Summary 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.

In Europe, the design of new structures according to modern regulations requires a uniform hazard spectrum for a given return period (e.g., 475 years). The assumption is that the resulting collapse probability is equally uniform for all structures, regardless of their structural properties or location. However, the uncertainty in the collapse capacity and hazard curves at different sites lead to an unequal level of risk. This discrepancy is undesirable given that some inhabitants will live in dwellings with a lower seismic safety than others living in structures designed according to the same regulation. The estimation of risk-targeted hazard maps allows for the definition of a design ground motion leading to a uniform level of risk. Using hundreds of fragility models developed for European buildings and hazard results from the SHARE project, we calculate risk-targeted hazard maps for a pre-established annual collapse probability.

No abstract

This study presents effective probabilistic procedures for evaluating ground-motion hazard at the free-field surface of a nonlinear soil deposit located at a specific site. Ground motion at the surface, or at any depth of interest within the soil formation (e.g., at the structure foundation level), is defined here in terms either of a suite of oscillator-frequency-dependent hazard curves for spectral acceleration, , or of one or more spectral acceleration uniform-hazard spectra, each associated s S (f) a with a given mean return period. It is presumed that similar information is available for the rock-outcrop input. The effects of uncertainty in soil properties are directly included. This methodology incorporates the amplification of the local soil deposit into the framework of probabilistic seismic hazard analysis (PSHA). The soil amplification is characterized by a frequency-dependent amplification function, AF(f), where f is a generic oscillator frequency. AF(f) is defined as the ratio of to the spectral s S (f) a acceleration at the bedrock level,. The estimates of the statistics of the ampli-s S (f) a fication function are obtained by a limited number of nonlinear dynamic analyses of the soil column with uncertain properties, as discussed in a companion article in this issue (Bazzurro and Cornell, 2004). The hazard at the soil surface (or at any desired depth) is computed by convolving the site-specific hazard curve at the bedrock level with the probability distribution of the amplification function. The approach presented here provides more precise surface ground-motion-hazard estimates than those found by means of standard attenuation laws for generic soil conditions. The use of generic ground-motion predictive equations may in fact lead to inaccurate results especially for soft-clay-soil sites, where considerable amplification is expected at long periods, and for saturated sandy sites, where high-intensity ground shaking may cause loss of shear strength owing to liquefaction or to cyclic mobility. Both such cases are considered in this article. In addition to the proposed procedure, two alternative, easier-to-implement but approximate techniques for obtaining hazard estimates at the soil surface are also briefly discussed. One is based on running a conventional PSHA with a rockattenuation relationship modified to include the soil response, whereas the other consists of using a simple, analytical, closed-form solution that appropriately modifies the hazard results at the rock level.

Ground-motion prediction equations (GMPEs) have recently been developed in the Next Generation Attenuation (NGA) project for application to shallow crustal earthquakes in tectonically active regions. We investigate the compatibility of those models with respect to magnitude scaling, distance scaling, and site scaling implied by Italian strong motion data. This is of interest because (1) the Italian data are principally from earthquakes in extensional regions that are poorly represented in the NGA dataset, and (2) past practice in Italy has been to use local GMPEs based on limited datasets that cannot resolve many significant source, path, and site effects. We find that the magnitude scaling implied by the Italian data is compatible with four NGA relations. However, the Italian data attenuate faster than implied by the four NGA GMPEs at short periods; the differences are statistically significant. Comparison with the fifth one was not possible because it was developed for rock conditions only. Three regression coefficients are reevaluated for the four NGA GMPEs to reflect the faster attenuation: a constant term, a term controlling the slope of distance attenuation, and a source fictitious depth term. The scaling of ground motion with respect to site shear wave velocity is consistent between the NGA models and Italian data. Moreover, the data are found to contain a nonlinear site effect that is generally compatible with NGA site terms. The intraevent scatter of Italian data is higher than in the NGA models, although interevent scatter is comparable to NGA recommendations when the faster distance attenuation is considered. On the basis of these findings, we recommend using the NGA relations, with the aforementioned minor modifications, to evaluate ground motions for seismic hazard analysis in Italy.

The advantages and disadvantages of using scalar and vector ground motion intensity measures (IMs) are discussed for the local, story-level seismic response assessment of three-dimensional (3-D) buildings. Candidate IMs are spectral accelerations, at a single period ( Sa) or averaged over a period range ( Sa avg). Consistent scalar and vector probabilistic seismic hazard analysis results were derived for each IM, as described in the companion paper in this issue ( Kohrangi et al. 2016 ). The response hazard curves were computed for three buildings with reinforced concrete infilled frames using the different IMs as predictors. Among the scalar IMs, Sa avg tends to be the best predictor of both floor accelerations and inter story drift ratios at practically any floor. However, there is an improvement in response estimation efficiency when employing vector IMs, specifically for 3-D buildings subjected to both horizontal components of ground motion. This improvement is shown to be most significant for a tall plan-asymmetric building.