Nirmal Jayaram

Correlation of Spectral Acceleration Values from NGA Ground Motion Models

Ground motion models (or “attenuation relationships”) describe the probability distribution of spectral acceleration at an individual period, given a set of predictor variables such as magnitude and distance, but they do not address the correlations between spectral acceleration values at multiple periods or orientations. Those correlations are needed for several calculations related to seismic hazard analysis and ground motion selection. Four NGA models and the NGA ground motion database are used here to measure these correlations, and predictive equations are fit to the results. The equations are valid for periods from 0.01 seconds to 10 seconds, versus similar previous equations that were valid only between 0.05 and 5 seconds and produced unreasonable results if extrapolated. Use of the new NGA ground motion database also facilitates a first study of correlations from intra- and inter-event residuals. Observed correlations are not sensitive to the choice of accompanying ground motion model, and intra-event, inter-event, and total residuals all exhibit similar correlation structure. A single equation is thus applicable for a variety of correlation predictions. A simple example illustrates the use of the proposed equations for one hazard analysis application.

A Computationally Efficient Ground-Motion Selection Algorithm for Matching a Target Response Spectrum Mean and Variance

Dynamic structural analysis often requires the selection of input ground motions with a target mean response spectrum. The variance of the target response spectrum is usually ignored or accounted for in an ad hoc manner, which can bias the structural response estimates. This manuscript proposes a computationally efficient and theoretically consistent algorithm to select ground motions that match the target response spectrum mean and variance. The selection algorithm probabilistically generates multiple response spectra from a target distribution, and then selects recorded ground motions whose response spectra individually match the simulated response spectra. A greedy optimization technique further improves the match between the target and the sample means and variances. The proposed algorithm is used to select ground motions for the analysis of sample structures in order to assess the impact of considering ground-motion variance on the structural response estimates. The implications for code-based design and performance-based earthquake engineering are discussed.

Statistical Tests of the Joint Distribution of Spectral Acceleration Values

Assessment of seismic hazard using conventional probabilistic seismic hazard analysis (PSHA) typically involves the assumption that the logarithmic spectral acceleration values follow a normal distribution marginally. There are, however, a variety of cases in which a vector of ground-motion intensity measures are considered for seismic hazard analysis. In such cases, assumptions regarding the joint distribution of the ground-motion intensity measures are required for analysis. In this article, statistical tests are used to examine the assumption of univariate normality of logarithmic spectral acceleration values and to verify that vectors of logarithmic spectral acceleration values computed at different sites and/or different periods follow a multivariate normal distribution. Multivariate normality of logarithmic spectral accelerations are verified by testing the multivariate normality of interevent and intraevent residuals obtained from ground-motion models. The univariate normality tests indicate that both interevent and intraevent residuals can be well represented by normal distributions marginally. No evidence is found to support truncation of the normal distribution, as is sometimes done in PSHA. The tests for multivariate normality show that interevent and intraevent residuals at a site, computed at different periods, follow multivariate normal distributions. It is also seen that spatially distributed intraevent residuals can be well represented by the multivariate normal distribution. This study provides a sound statistical basis for assumptions regarding the marginal and joint distribution of ground-motion parameters that must be made for a variety of seismic hazard calculations.

Considering Spatial Correlation in Mixed-Effects Regression and the Impact on Ground-Motion Models

Abstract Ground-motion models are commonly used in earthquake engineering to predict the probability distribution of the ground-motion intensity at a given site due to a particular earthquake event. These models are often built using regression on observed ground-motion intensities and are fitted using either the one-stage mixed-effects regression algorithm proposed by Abrahamson and Youngs (1992) or the two-stage algorithm of Joyner and Boore (1993). In their current forms, these algorithms ignore the spatial correlation between intraevent residuals. This paper emphasizes the theoretical importance of considering spatial correlation while fitting ground-motion models and proposes an extension to the Abrahamson and Youngs (1992) algorithm that allows the consideration of spatial correlation. By refitting the Campbell and Bozorgnia (2008) ground-motion model using the mixed-effects regression algorithm considering spatial correlation, it is apparent that the variance of the total residuals and the ground-motion model coefficients used for predicting the median ground-motion intensity are not significantly different from the published values even after the incorporation of spatial correlation. However, there is an increase in the variance of the intraevent residual and a significant decrease in the variance of the interevent residual. These changes have implications for risk assessments of spatially-distributed systems because a smaller interevent residual variance implies lesser likelihood of observing large ground-motion intensities at all sites in a region.

Loss Estimation of Tall Buildings Designed for the PEER Tall Building Initiative Project

As part of the PEER Centers Tall Building Initiative (TBI) project, practicing engineers designed three structural systems, each based on commonly used codes and guidelines, in addition to the guidelines developed by PEER. The designs were analyzed by three research teams, using a set of 75 ground-motion pairs, to predict response parameters for evaluating the performance of tall buildings. This study focuses on analytically estimating the seismic losses to these buildings to assess their relative seismic performance. The loss assessment process follows a comprehensive simulation approach that takes into account several random variables, such as building response, repair costs, etc. Throughout this study, epistemic and aleatory uncertainties in the random variables are accounted for in order to quantify those in loss estimates. Based on the dollar-loss results, the performance of the dual-system building is compared and contrasted with that of the other building systems considered in the PEER study.

Deaggregation of Lifeline Risk: Insights for Choosing Deterministic Scenario Earthquakes

Probabilistic seismic risk assessment for lifelines is less straightforward than for individual structures. Analytical risk assessment techniques such as the “PEER framework” are insufficient for a probabilistic study of lifeline performance, due in large part to difficulties in describing ground-motion hazard over a region. As a result, Monte Carlo simulation and its variants appear to be the best approach for characterizing ground motions for lifelines. A challenge with Monte Carlo simulation is its large computational expense, and in situations where computing lifeline losses is extremely computationally demanding, assessments may consider only a single “interesting” ground-motion scenario and a single associated map of resulting ground motion intensities. In this paper, a probabilistic simulation-based risk assessment procedure is coupled with a deaggregation calculation to identify the ground-motion scenarios most likely to produce exceedance of a given loss threshold. The deaggregation calculations show that this “most-likely scenario” depends on the loss level of interest, and is influenced by factors such as the seismicity of the region, the location of the lifeline with respect to the faults and the current performance state of the various components of the lifeline. It is seen that large losses are typically caused by moderately large magnitude events with large average values of inter-event and intra-event residuals, implying that the scenario ground motions should be obtained in a manner that accounts for ground-motion uncertainties. Explicit loss analysis calculations that exclude residuals will demonstrate that the resulting loss estimates are highly biased.