Katsu Goda

Spatial Correlation of Peak Ground Motions and Response Spectra

The intensities of ground motions and structural responses at two sites are correlated. The magnitude of the correlation depends on the distance between the sites and the natural vibration periods of the structures. This study investigates the spatial correlation of the peak ground motions and the pseudospectral acceleration (PSA) responses using the California records and the Chi-Chi records. Because the correlation arises from interevent and intraevent variability, the correlations for individual variability alone and for the combined variability are assessed. The analysis results indicate that the spatial intraevent correlation decreases as the separation distance increases and that the magnitude of the correlation of the PSA responses depends on the considered natural vibration periods. The results also indicate that the spatial intraevent correlation of the PSA responses for the California records decays more rapidly than that for the Chi-Chi records. Based on the analysis results, a simple empirical equation to predict the spatially varying correlation coefficient of the PSA responses, which can be employed in seismic-hazard and seismic-risk assessments, is proposed.

Orientation-dependent ground motion measure for seismic hazard assessment

Attenuation relations of the pseudo-spectral acceleration (psa) response are used to assess seismic hazard and uniform hazard spectra (uhs). The relations are based on a scalar measure although earthquake excitations are inherently vector quantities. For a single-degree-of-freedom system, this may or may not be important depending on whether the estimated uhs accurately reflect the estimated seismic hazard. For buildings that are sensitive to two orthogonal horizontal components of excitations, a vector or orientation-dependent ground-motion measure could be valuable. These encourage us to assess the orientation effect on the probability of the psa along a random orientation exceeding the geometric mean and quadratic mean and to propose an orientation-dependent ground-motion measure that is based on the maximum resultant psa and a response ratio, defined as the ratio of the psa in an arbitrary orientation to the maximum resultant psa. Numerical results show that the probability that the psa along a random orientation exceeds the geometric mean or the quadratic mean is about 50%. The results also show that the response ratio plotted in the polar coordinate almost always falls among three circles. Attenuation relations are developed based on the developed measure for a set of records selected from the peer Next Generation Attenuation database. Use of the relations for assessing seismic hazard is illustrated. Also, for comparative purposes, attenuation relations based on the geometric and quadratic means are developed and used to assess the seismic hazard. Online material: Adopted record selection criteria and analysis results of the developed attenuation relations.

Probabilistic Characteristics of Seismic Ductility Demand of SDOF Systems with Bouc-Wen Hysteretic Behavior

This study investigates probabilistic characteristics of the peak ductility demand of inelastic single-degree-of-freedom systems. The hysteretic behavior of structural systems is represented by the Bouc-Wen model, which takes various hysteretic curves with degradation and pinching behavior into account, and a prediction equation of the peak ductility demand is developed. The application of the developed equation in reliability analysis of structures subject to earthquake loading is illustrated. The results indicate that the effects due to degradation and pinching behavior on the peak ductility demand as well as the reliability of structures can be significant, especially for stiff structures.

Effect of Spatial Correlation on Estimated Ground-Motion Prediction Equations

The consideration of spatially correlated seismic hazard could be of importance for seismic risk assessment. The estimation of this correlation for the peak ground acceleration and the pseudospectral acceleration has been reported in the literature, although it is not presented as a necessary ingredient for developing ground-motion prediction equations (GMPEs). In the present study, we show that spatial correlation can be incorporated in the existing regression algorithms given by Joyner and Boore for assessing a GMPE. The modified algorithms can be used to estimate both GMPE coefficients and spatial correlation model parameters simultaneously. In particular, they are used to investigate the influence of spatial correlation on GMPEs and to assess parameters of an empirical spatial correlation model by considering a set of 592 California records. Analysis results indicate that the effects of incorporating spatial correlation on the estimated GMPEs are insignificant, and that spatial correlation parameters obtained using the modified algorithm are similar to those estimated based on statistical analysis of regression residuals.

A Comparison of Seismic-Hazard and Risk Deaggregation

The deaggregation of seismic hazard is an effective way to identify scenario events that contribute to a selected seismic-hazard level. Depending on the use of the deaggregation results, the contribution may be defined as equal to or exceeding the selected hazard level. The deaggregation of seismic hazard should consider all uncertainty, aleatory uncertainty, and epistemic uncertainty. The identified scenario events can be used to check the responses of structures such as buildings. However, structures are constructed to provide service rather than just sustain environmental disturbances, and the seismic-risk assessment is at least as important and valuable as the seismic-hazard assessment for emergency preparedness planning and for the financial industry. Therefore, the notion of the deaggregation of seismic hazard is extended to that of seismic risk in the present study. Other issues investigated in this study are the impact of approximate treatment of epistemic uncertainty and the Cascadia subduction events on the deaggregation, and the differences in the identified scenario events from the deaggregation of seismic hazard and seismic risk. Numerical results suggest that the contribution of the uncertainty in attenuation relations to the deaggregation results can be very significant, and that the identified scenario events by deaggregating seismic hazard and seismic risk are somewhat different. Also, the elapsed time since the last major event for source zones whose earthquake occurrence is modeled as a renewal process can affect the deaggregation results significantly.

Interperiod Dependence of Ground-Motion Prediction Equations: A Copula Perspective

Abstract The conventional approach for developing empirical prediction equations of multivariate ground-motion parameters (e.g., response spectra at a set of vibration periods) is based on regression analysis of the individual parameters; their dependence is subsequently characterized by evaluating the linear correlation coefficient of the logarithm of the ground-motion parameters that are corrected by using a ground-motion prediction equation. A copula technique, which offers a flexible way of describing nonlinear dependence among multivariate data in isolation from their marginal distribution functions, can be used to validate this two-step approach. This new perspective on the multivariate aspects of the development of ground-motion prediction equations is explored through analysis of the strong ground-motion data associated with the Boore and Atkinson (2008) Pacific Earthquake Engineering Research–Next Generation Attenuation of Ground Motions (PEER-NGA) relation. The analysis results demonstrate that multivariate ground-motion parameters can be marginally modeled as a lognormal variate, and their interperiod dependence can be captured by using the normal copula. This finding validates the conventional two-step approach.

Implied preference for seismic design level and earthquake insurance

Seismic risk can be reduced by implementing newly developed seismic provisions in design codes. Furthermore, financial protection or enhanced utility and happiness for stakeholders could be gained through the purchase of earthquake insurance. If this is not so, there would be no market for such insurance. However, perceived benefit associated with insurance is not universally shared by stakeholders partly due to their diverse risk attitudes. This study investigates the implied seismic design preference with insurance options for decisionmakers of bounded rationality whose preferences could be adequately represented by the cumulative prospect theory (CPT). The investigation is focused on assessing the sensitivity of the implied seismic design preference with insurance options to model parameters of the CPT and to fair and unfair insurance arrangements. Numerical results suggest that human cognitive limitation and risk perception can affect the implied seismic design preference by the CPT significantly. The mandatory purchase of fair insurance will lead the implied seismic design preference to the optimum design level that is dictated by the minimum expected lifecycle cost rule. Unfair insurance decreases the expected gain as well as its associated variability, which is preferred by risk-averse decisionmakers. The obtained results of the implied preference for the combination of the seismic design level and insurance option suggest that property owners, financial institutions, and municipalities can take advantage of affordable insurance to establish successful seismic risk management strategies.

Effects of seabed surface rupture versus buried rupture on tsunami wave modeling

Abstract Parametric investigations of tsunami wave modeling are performed to discuss an important issue related to the sensitivity of tsunami simulation results to varied top‐edge depths of a shallowly dipping fault plane (seabed surface rupture versus buried fault rupture). Input boundary conditions (i.e., vertical seabed deformation) for tsunami simulation are calculated using so‐called Okada equations. The analysis results for the 2011 Tohoku, Japan, tsunami case study highlight the significant effects of varied top‐edge depth parameters on vertical seabed deformation and tsunami wave heights. In particular, the uplifted water outside of the fault plane for the buried rupture case, in comparison with the seabed surface‐rupture case, causes large tsunami waves. The results are applicable to other tsunamigenic earthquakes that occur on a gently dipping fault plane at a shallow depth (e.g., anticipated Nankai–Tonankai earthquake) and have important implications on how tsunami inversion should be carried out and how developed source models should be interpreted. Online Material: Figures of vertical deformation, maximum inundation height contours, and inundation height profiles.