Stochastic Modeling And Simulation Of Near Fault Ground Motions For Performance Based Earthquake Engineering

A comprehensive parameterized stochastic model of near-fault ground motions in two orthogonal horizontal directions is developed. The proposed model uniquely combines several existing and new sub-models to represent major characteristics of recorded near-fault ground motions. These characteristics include near-fault effects of directivity and fling step; temporal and spectral non-stationarity; intensity, duration and frequency content characteristics; directionality of components, as well as the natural variability of motions for a given earthquake and site scenario. By fitting the model to a database of recorded near-fault ground motions with known earthquake source and site characteristics, empirical "observations" of the model parameters are obtained. These observations are used to develop predictive equations for the model parameters in terms of a small number of earthquake source and site characteristics. Functional forms for the predictive equations that are consistent with seismological theory are employed. A site-based simulation procedure that employs the proposed stochastic model and predictive equations is developed to generate synthetic near-fault ground motions at a site. The procedure is formulated in terms of information about the earthquake design scenario that is normally available to a design engineer. Not all near-fault ground motions contain a forward directivity pulse, even when the conditions for such a pulse are favorable. The proposed procedure produces pulselike and non-pulselike motions in the same proportions as they naturally occur among recorded near-fault ground motions for a given design scenario. The proposed models and simulation procedure are validated by several means. Synthetic ground motion time series with fitted parameter values are compared with the corresponding recorded motions. The proposed empirical predictive relations are compared to similar relations available in the literature. The overall simulation procedure is validated by comparing suites of synthetic ground motions generated for given earthquake source and site characteristics to the ground motion prediction equations (GMPEs) developed as part of phase 2 of the Next Generation Attenuation (NGA) program, (NGA-West2, see, e.g., Campbell and Bozorgnia, 2014). Comparison is made in terms of the estimated median level and variability of elastic ground motion response spectra. The use of synthetic motions in addition to or in place of recorded motions is desirable in performance-based earthquake engineering (PBEE) applications, particularly when recorded motions are scarce or when they are unavailable for a specified design scenario. As a demonstrative application, synthetic motions from the proposed simulation procedure are used to perform probabilistic seismic hazard analysis (PSHA) for a near-fault site. The analysis shows that the hazard at a near-fault site is underestimated when the ground motion model used does not properly account for the possibility of pulselike motions due to the directivity effect.

For performance-based design, nonlinear dynamic structural analysis for various types of input ground motions is required. Stochastic (simulated) ground motions are sometimes useful as input motions, because unlike recorded motions they are not limited in number and because their properties can be varied systematically to study the impact of ground motion properties on structural response. This dissertation describes an approach by which the wavelet packet transform can be used to characterize complex time-varying earthquake ground motions, and it illustrates the potential benefits of such an approach in a variety of earthquake engineering applications. The proposed model is based on Thr´ainsson and Kiremidjian (2002), which use Fourier amplitudes and phase differences to simulate ground motions and attenuation models to their model parameters. We extend their model using wavelet packet transform since it can control the time and frequency characteristic of time series. The time- and frequency-varying properties of real ground motions can be captured using wavelet packets, so a model is developed that requires only 13 parameters to describe a given ground motion. These 13 parameters are then related to seismological variables such as earthquake magnitude, distance, and site condition, through regression analysis that captures trends in mean values, standard deviations and correlations of these parameters observed in a large database of recorded strong ground motions. The resulting regression equations then form a model that can be used to predict ground motions for a future earthquake scenario; this model is analogous to widely used empirical ground motion prediction models (formerly called "attenuation models") except that this model predicts entire time series rather than only response spectra. The ground motions produced using this predictive model are explored in detail, and are shown to have elastic response spectra, inelastic response spectra, durations, mean periods, etc., that are consistent in both mean and variability to existing published predictive models for those properties. That consistency allows the proposed model to be used in place of existing models for probabilistic seismic hazard analysis (PSHA) calculations. This new way to calculate PSHA is termed "simulation-based probabilistic seismic hazard analysis" and it allows a deeper understanding of ground motion hazard and hazard deaggregation than is possible with traditional PSHA because it produces a suite of potential ground motion time histories rather than simply a distribution of response spectra. The potential benefits of this approach are demonstrated and explored in detail. Taking this analysis even further, this suite of time histories can be used as input for nonlinear dynamic analysis of structures, to perform a risk analysis (i.e., "probabilistic seismic demand analysis") that allows computation of the probability of the structure exceeding some level of response in a future earthquake. These risk calculations are often performed today using small sets of scaled recorded ground motions, but that approach requires a variety of assumptions regarding important properties of ground motions, the impacts of ground motion scaling, etc. The approach proposed here facilitates examination of those assumptions, and provides a variety of other relevant information not obtainable by that traditional approach.

For performance-based design, nonlinear dynamic structural analysis for various types of input ground motions is required. Stochastic (simulated) ground motions are sometimes useful as input motions, because unlike recorded motions they are not limited in number and because their properties can be varied systematically to study the impact of ground motion properties on structural response. This dissertation describes an approach by which the wavelet packet transform can be used to characterize complex time-varying earthquake ground motions, and it illustrates the potential benefits of such an approach in a variety of earthquake engineering applications. The proposed model is based on Thráinsson and Kiremidjian (2002), which use Fourier amplitudes and phase differences to simulate ground motions and attenuation models to their model parameters. We extend their model using wavelet packet transform since it can control the time and frequency characteristic of time series. The time- and frequency-varying properties of real ground motions can be captured using wavelet packets, so a model is developed that requires only 13 parameters to describe a given ground motion. These 13 parameters are then related to seismological variables such as earthquake magnitude, distance, and site condition, through regression analysis that captures trends in mean values, standard deviations and correlations of these parameters observed in a large database of recorded strong ground motions. The resulting regression equations then form a model that can be used to predict ground motions for a future earthquake scenario; this model is analogous to widely used empirical ground motion prediction models (formerly called "attenuation models") except that this model predicts entire time series rather than only response spectra. The ground motions produced using this predictive model are explored in detail, and are shown to have elastic response spectra, inelastic response spectra, durations, mean periods, etc., that are consistent in both mean and variability to existing published predictive models for those properties. That consistency allows the proposed model to be used in place of existing models for probabilistic seismic hazard analysis (PSHA) calculations. This new way to calculate PSHA is termed "simulation-based probabilistic seismic hazard analysis" and it allows a deeper understanding of ground motion hazard and hazard deaggregation than is possible with traditional PSHA because it produces a suite of potential ground motion time histories rather than simply a distribution of response spectra. The potential benefits of this approach are demonstrated and explored in detail. Taking this analysis even further, this suite of time histories can be used as input for nonlinear dynamic analysis of structures, to perform a risk analysis (i.e., "probabilistic seismic demand analysis") that allows computation of the probability of the structure exceeding some level of response in a future earthquake. These risk calculations are often performed today using small sets of scaled recorded ground motions, but that approach requires a variety of assumptions regarding important properties of ground motions, the impacts of ground motion scaling, etc. The approach proposed here facilitates examination of those assumptions, and provides a variety of other relevant information not obtainable by that traditional approach.

This book introduces new research topics in earthquake engineering through the application of computational mechanics and computer science. The topics covered discuss the evaluation of earthquake hazards such as strong ground motion and faulting through applying advanced numerical analysis methods, useful for estimating earthquake disasters. These methods, based on recent progress in solid continuum mechanics and computational mechanics, are summarized comprehensively for graduate students and researchers in earthquake engineering. The coverage includes stochastic modeling as well as several advanced computational earthquake engineering topics. Contents: Preliminaries: Solid Continuum Mechanics; Finite Element Method; Stochastic Modeling; Strong Ground Motion: The Wave Equation for Solids; Analysis of Strong Ground Motion; Simulation of Strong Ground Motion; Faulting: Elasto-Plasticity and Fracture Mechanics; Analysis of Faulting; Simulation of Faulting; BEM Simulation of Faulting; Advanced Topics: Integrated Earthquake Simulation; Unified Visualization of Earthquake Simulation; Standardization of Earthquake Resistant Design; Appendices: Earthquake Mechanisms; Analytical Mechanics; Numerical Techniques of Solving Wave Equation; Unified Modeling Language. Key Features Includes a detailed treatment of modeling of uncertain ground structures, such as stochastic modeling Explains several key numerical algorithms and techniques for solving large-scale, non-linear and dynamic problems Presents applications of methods for simulating actual strong ground motion and faulting Readership: Graduate students and researchers in earthquake engineering; researchers in computational mechanics and computer science.

Introduction to Computational Earthquake Engineering covers solid continuum mechanics, finite element method and stochastic modeling comprehensively, with the second and third chapters explaining the numerical simulation of strong ground motion and faulting, respectively. Stochastic modeling is used for uncertain underground structures, and advanced analytical methods for linear and non-linear stochastic models are presented. The verification of these methods by comparing the simulation results with observed data is then presented, and examples of numerical simulations which apply these methods to practical problems are generously provided. Furthermore three advanced topics of computational earthquake engineering are covered, detailing examples of applying computational science technology to earthquake engineering problems.

The specialty section Earthquake Engineering is one branch of Frontiers in Built Environment and welcomes critical and in-depth submissions on earthquake ground motions and their effects on buildings and infrastructures. Manuscripts should yield new insights and ultimately contribute to a safer and more reliable design of building structures and infrastructures. The scope includes the characterization of earthquake ground motions (e.g. near-fault, far-fault, short-period, long-period), their underlying properties, their intrinsic relationship with structural responses, and the true behaviors of building structures and infrastructures under risky and uncertain ground motions. More specific topics include recorded ground motions, generated ground motions, response spectra, stochastic modeling of ground motion, critical excitation, geotechnical aspects, soil mechanics, soil liquefaction, soil-structure interactions, pile foundations, earthquake input energy, structural control, passive control, active control, base-isolation, steel structures, reinforced concrete structures, wood structures, building retrofit, structural optimization, uncertainty analysis, robustness analysis, and redundancy analysis. This eBook includes four original research papers, in addition to the Specialty Grand Challenge article, on the critical earthquake response of elastic-plastic structures under near-fault or long-duration ground motions which were published in the specialty section Earthquake Engineering. In the early stage of dynamic nonlinear response analysis of structures around 1960s, a simple hysteretic structural model and a simple sinusoidal earthquake ground motion input were dealt with together with random inputs. The steady-state response was tackled by an equivalent linearization method developed by Caughey, Iwan and others. In fact, the resonance plays a key role in the earthquake-resistant design and it has a strong effect even in case of near-fault ground motions. In order to draw the steady-state response curve and investigate the resonant property, two kinds of repetition have to be introduced. One is a cycle, for one forced input frequency, of the initial guess of the steady-state response amplitude, the construction of the equivalent linear model, the analysis of the steady-state response amplitude using the equivalent linear model and the update of the equivalent linear model based on the computed steady-state response amplitude. The other is the sweeping over a range of forced input frequencies. This process is quite tedious. Four original research papers included in this eBook propose a new approach to overcome this difficulty. Kojima and Takewaki demonstrated that the elastic-plastic response as continuation of free-vibrations under impulse input can be derived in a closed form by a sophisticated energy approach without solving directly the equations of motion as differential equations. While, as pointed out above, the approach based on the equivalent linearization method requires the repetition of application of the linearized equations, the method by Kojima and Takewaki does not need any repetition. The double impulse, triple impulse and multiple impulses enable us to describe directly the critical timing of impulses (resonant frequency) which is not easy for the sinusoidal and other inputs without a repetitive procedure. It is important to note that, while most of the previous methods employ the equivalent linearization of the structural model with the input unchanged, the method treated in this eBook transforms the input into a series of impulses with the structural model unchanged. This characteristic guarantees high accuracy and reliability even in the large plastic deformation range. The approach presented in this eBook is an epoch-making accomplishment to open the door for simpler and deeper understanding of structural reliability of built environments in the elastic-plastic range

This book provides rigorous foundations of applying modern computational mechanics to earthquake engineering. The scope covers the numerical analysis of earthquake wave propagation processes and the faulting processes, and also presents the most advanced numerical simulations of earthquake hazards and disasters that can take place in an urban area.Two new chapters included are advanced topics on high performance computing and for constructing an analysis model.This is the first book in earthquake engineering that explains the application of modern numerical computation (which includes high performance computing) to various engineering seismology problems.

This book provides a new framework for analysis of slope nonlinear stochastic seismic dynamic response based on the new theoretical tool of stochastic dynamics. The coupling effects of uncertainty of geological parameters, strong dynamic nonlinearity, and randomness of ground motion are considered in the process of the seismic dynamic stability assessment of slope. In this book, an intensity frequency non-stationary stochastic ground motion model based on time-domain stochastic process description is preliminarily established to characterize the randomness of earthquakes. The spatial distribution random field model of geotechnical parameters is established to describe the time-space variability of geotechnical parameters. Based on the basic theory of stochastic dynamics, the seismic stability performance evaluation method of slope is established. The slope seismic dynamic model test based on large complex shaking table is performed to verify and modify the proposed framework and method. This book sheds new light on the development of nonlinear seismic stochastic dynamics and seismic design of slope engineering.