Tsuyoshi Takada

A Bayesian Framework for Prediction of Seismic Ground Motion

Abstract Current needs of the site-specific hazard and risk analysis for critical facilities and accumulation of the observed records make the development of site-specific ground-motion attenuation relationship feasible. The use of the site-specific attenuation relationship has two advantages: lack of bias and representation of the specific site. This study develops the site-specific attenuation relationship within the Bayesian updating framework. Rather than developing new attenuation relationships, we develop a correction term to the existing past attenuation equation within the Bayesian framework. The correction term is described as a linear function of source magnitude and distance. New data are those observed at the specific site in recent years. Although the use of a prior distribution is one of the most controversial issues of the Bayes’ theorem, both the noninformative prior and the informative prior in terms of the gamma-normal prior are used to develop the posterior distribution for the prediction of ground motion. We feel that the reader should focus on the development of the site-specific attenuation relationship and quantification of the uncertainty of ground-motion prediction. Statistical uncertainty has been ignored in the existing attenuation relationships, while it is not ignorable in the site-specific attenuation relationship due to the limited number of data available at the specific site. This is particularly notable for the ground-motion prediction of large-magnitude-near-source earthquakes where seismic hazard is sensitive. Because the unknown parameters are treated as random variables in the Bayesian approach, the statistical uncertainty associated with them can be quantified in terms of the posterior distribution. The Bayesian methodology will be an effective approach to updating the attenuation relationship on a site basis when new data from observations become available.

Wavelet-Based Generation of Energy- and Spectrum-Compatible Earthquake Time Histories

A method of modifying earthquake ground motion based on the wavelet transform is proposed, to take into account the effects of linear/nonlinear response spectra, frequency content, and ground motion energy. A wavelet-based procedure has been used to decompose recorded ground motion into finite wavelet coefficients, and then, with matrix processing, the coefficients have been suitably substituted and scaled to match the re- sponse spectra and total energy of earthquake ground motions. The proposed method has been verified by modifying five recorded accelerograms such that they are compatible with the same linear/nonlinear and energy spectra.

Galerkin Method to Analyze Systems with Stochastic Flexural Rigidity

A new stochastic analysis method based on the Bubnov-Galerkin approximation is proposed herein for estimating the response variability of systems with spatially varying flexural rigidity. Such a flexural rigidity is idealized as a multi-dimensional, statistically homogeneous, continuous Gaussian stochastic field. Two kinds of techniques for evaluating the response statistics are utilized: a first-order perturbation technique and the Monte Carlo simulation technique. Numerical examples are presented in this paper.

Load combination of aftershocks and tsunami for tsunami-resistant design

Occurrence of huge tsunami and numerous aftershocks are expected after a gigantic subduction earthquake occurs. Therefore, the important coastal structures (tsunami refuge buildings, seawalls and nuclear power plants etc.) must be designed against tsunami as well as ground shaking. In tsunami-resistant design, it is needed to consider that tsunami may arrive at the structure in a short time after the mainshock from the experience of 2011 Tohoku earthquake. When the action effects both from aftershocks and tsunami to the structure occur simultaneously, practically reasonable assessment of load combination from aftershocks and tsunami is needed. In order to treat the load combination problem reasonably, stochastic load combination technique can be used, which requires stochastic modeling of action effects from aftershocks and tsunami. Once the combined action effect is estimated reasonably, the reliability analysis follows, where load and resistance factors can be obtained under the condition that the conditional target reliability for a limit state function is given. Load combination method of aftershocks and tsunami on the tsunami-resistant design is demonstrated at some sites in Japan. Finally, load and resistance factor design format for the tsunami-resistant design is proposed.

Risk Assessment, Management and Monitoring of Infrastructure Systems

Urban infrastructure constitutes physical facilities such as road and highway networks, buildings, railways, dams, bridges, underground areas, water supplies and so on, all of which provide essential services to support and sustain civilian life in an urban area. It is a public asset that is accessible to everybody and serves as a basis for their economic and social activities. Therefore the economy of one nation is heavily dependent upon the satisfactory performance of its infrastructures. In this paper the concept of risk assessment and management of urban infrastructures are discussed. Focus of discussion is put on the risk due to natural disaster and infrastructure deterioration, and on the sustainability of infrastructure. The concept of risk assessment is herein presented first, followed by examples of risk assessment and management due to natural disasters. The last part introduces infrastructure monitoring as an essential tool for risk reduction. Current practices in monitoring of infrastructure system, such as bridges and railways, are demonstrated.

Target structural reliability in life cycle consideration

The concept of minimising life cycle cost can be rationally applied to determine a target reliability of structures. However, there has been a recent legal requirement to reduce CO2 emissions, therefore, the minimisation of life cycle CO2 emission could be an alternative approach in structural design. This paper explains the general formulae for deciding the optimum reliability by minimising the total life cycle cost and the amount of CO2 emission in the structures lifetime, and also shows that these formulae can be applied to decision making for the cost-benefit problem related to seismic strengthening of structures. Additionally, the role of the engineer is discussed, reflecting the current situation in Japan.

Development of a New Mathematical Framework for Seismic Probabilistic Risk Assessment for Nuclear Power Plants – Plan and Current Status –

After the severe accident in Fukushima Daiichi Nuclear Power Station, safety improvement and enhancement have been installed. In midterm and long term, continuous efforts to improve and enhance safety are required, and technical basis and fundamentals are needed to achieve them.

Stochastic Prediction of Seismic Ground Motions Using Macro-Spatial Correlation Model

Estimating a macro-spatial correlation of seismic ground motions is very important for earthquake damage predictions, building portfolio analyses, etc. in which simultaneous damages in different locations have to be taken into consideration. In this study, the residual value between an observed and a ground motion predicted by an empirical mean attenuation equation is focused on. The residual value is now modelled assuming that it constitutes a homogeneous two-dimensional stochastic field in such a way that the joint probability density function (PDF) of seismic ground can be characterized by the spatial correlation model as well as by an empirical mean attenuation equation. Once it can be given in terms of the correlation model with the PDF, stochastic prediction of the ground motion at the locations unobserved can be effectively done with using the data observed at the near-by stations.