Because of the limited number of strong-motion records that have measured ground response at large strains, any statistical analyses of seismic site-response models subject to strong ground motions are severely limited by a small number of observations. Recent earthquakes in Japan, including the M w 9.0 Tohoku earthquake of March 2011, have substantially increased the observations of strong-motion records that can be used to compare alternative site-response models at large strains and can subsequently provide insight into the accuracy and precision of site-response models. Using the Kiban-Kyoshin network (KiK-net) downhole array data in Japan, we analyze the accuracy (bias) and variability (precision) resulting from common siteresponse modeling assumptions, and we identify critical parameters that significantly contribute to the uncertainty in site-response analyses. We perform linear and equivalent-linear site-response analyses at 100 KiK-net sites using 3720 ground motions ranging in amplitude from weak to strong; 204 of these records have peak ground accelerations greater than 0:3g at the ground surface. We find that the maximum shear strain in the soil profile, the observed peak ground acceleration at the ground surface, and the predominant spectral period of the surface ground motion are the best predictors of where the evaluated models become inaccurate and/or imprecise. The peak shear strains beyond which linear analyses become inaccurate in predicting surface pseudospectral accelerations (PSA; presumably as a result of nonlinear soil behavior) are a function of vibration period and are between 0.01% and 0.1% for periods < 0:5 s. Equivalent-linear analyses become inaccurate at peak strains of ∼0:4% over this range of periods. We find that, for the sites and ground motions considered, site-response residuals at spectral periods > 0:5 s do not display noticeable effects of nonlinear soil behavior.
The ground-motion prediction equations (GMPEs) developed as part of the Next Generation Attenuation of Ground Motions (NGA-West) project in 2008 are becoming widely used in seismic hazard analyses. However, these new models are considerably more complicated than previous GMPEs, and they require several more input parameters. When employing the NGA models, users routinely face situations in which some of the required input parameters are unknown. In this paper, we present a framework for estimating the unknown source, path, and site parameters when implementing the NGA models in engineering practice, and we derive geometrically-based equations relating the three distance measures found in the NGA models. Our intent is for the content of this paper not only to make the NGA models more accessible, but also to help with the implementation of other present or future GMPEs.
Nonlinear soil behavior often exhibits a strong influence on surficial ground motions, and seismic site response models attempt to quantify these effects. However, site response models exhibit large uncertainties and can on occasion poorly replicate observed ground motions. In this study, nonlinear total-stress site response model predictions for 5626 ground motions at 114 KiKnet vertical seismometer arrays are calculated and compared to observed ground motions and predictions from linear and equivalent-linear analyses. Using this large database of onedimensional (1D) site response model predictions, a variety of statistical analyses are performed to quantify model bias and precision, and these statistical analyses are paired with physical insights into site and ground-motion behavior. As expected, there are deviations between the linear, equivalent-linear, and nonlinear site response constitutive models at large shear strains. When using cumulative Arias Intensity to assess the temporal evolution of model uncertainty, the equivalent-linear model is shown to have excessive bias early in the ground motion record, but this bias is obscured when the entire record is considered. Another less intuitive result is that on average, across the entire dataset, all models-linear, equivalent-linear, and nonlinear-tend to underpredict high-frequency ground motions in the aggregate. A number of physical hypotheses are explored to provide insights into these persistent biases. The use of a depth-dependent shear-wave velocity gradient, in particular, has a significant impact on the model bias, even more so than changing the constitutive model for dynamic soil behavior. Using an unprecedented number of sites and ground motions, the results of this study provide insights for the present limitations of, and potential improvements to, 1D site response model predictions.
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