Effect of Asynchronous Earthquake Motion on Complex Bridges. I: Methodology and Input Motion

Based on observed damage patterns from previous earthquakes and a rich history of analytical studies, asynchronous input motion has been identified as a major source of unfavorable response for long-span structures, such as bridges. This study is aimed at quantifying the effect of geometric incoherence and wave arrival delay on complex straight and curved bridges using state-of-the-art methodologies and tools. Using fully parametrized computer codes combining expert geotechnical and earthquake structural engineering knowledge, suites of asynchronous accelerograms are produced for use in inelastic dynamic analysis of the bridge model. Two multi-degree-of-freedom analytical models are analyzed using 2,000 unique synthetic accelerograms with results showing significant response amplification due to asynchronous input motion, demonstrating the importance of considering asynchronous seismic input in complex, irregular bridge design. The paper, Part 1 of a two-paper investigation, presents the development of the input motion sets and the modeling and analysis approach employed, concluding with sample results. Detailed results and implications on seismic assessment are presented in the companion paper: Effect of Asynchronous Motion on Complex Bridges. Part II: Results and Implications on Assessment.     

Temporal aN and aT in Earthquake Ground Motion at a Single Point

This paper describes a continued study on three-dimensional temporal characteristics of earthquake ground motions at a single point. Based on an instantaneous tangential and normal acceleration decomposition of ground acceleration trajectory, a ground motion can be partitioned into a finite sequence of staggered time intervals of acceleration and deceleration. A formulation is developed to estimate speed and angular changes over a partitioned interval in terms of rates of positive and negative tangential and normal acceleration. Based on these concepts, general ground motion properties, peak ground acceleration, peak ground velocity, and peak ground displacement are examined. Several Northridge earthquake records are studied in detail. It is found that the highest peak of ground acceleration in these records corresponds to a high peak of deceleration, and a velocity maximum often precedes the peak of acceleration.     

Light-Based Motion Tracking of Equipment Subjected to Earthquake Motions

Traditional sensors, such as accelerometers and displacement transducers, are widely used in laboratory and field experiments in earthquake engineering to measure the motions of both structural and nonstructural components. Such sensors, however, must be physically attached to the structure and require cumbersome cabling and configurations and substantial time for setup. For reduced-scale experiments, these conventional sensors may substantially alter the dynamic properties of the system by changing the mass, stiffness, and damping properties of the specimen. Moreover, it is very difficult with traditional sensors to capture the three-dimensional motions of light or oddly shaped components such as microscopes, computers,?or other building contents. In this paper, the methodology of light-based motion tracking is applied to the measurement of the three-dimensional motions of various types of equipment and building contents commonly found in biological and chemical science laboratories. The system is comprised of six high-speed, high-resolution charge-coupled-device (CCD) cameras outfitted with a cluster of red-light emitting diodes (LEDs). Retroreflective (passive) spherical markers discretely located in a scene are tracked in time and used to describe the behavior of various types of equipment and contents subjected to a range of earthquake motions. Results from this study show that the nonintrusive, light-based approach is extremely promising in terms of its ability to capture relative displacements in three orthogonal directions and complementary rotations.     

Effect of Asynchronous Earthquake Motion on Complex Bridges. II: Results and Implications on Assessment

Nonuniform seismic excitation has been shown through previous analytical studies to adversely affect the response of long-span bridge structures. To further understand this phenomenon, this study investigates the response of complex straight and curved long-span bridges under the effect of parametrically varying asynchronous motion. The generation process and modeling procedures are presented in a companion paper. A wide-ranging parametric study is performed aimed at isolating the effect of both bridge curvature and the two main sources of asynchronous strong motion: geometric incoherence and the wave-passage effect. Results from this study indicate that response for the 344?m study structure is amplified significantly by nonsynchronous excitation, with displacement amplification factors between 1.6 and 3.4 for all levels of incoherence. This amplification was not constant or easily predicable, demonstrating the importance of inelastic dynamic analysis using asynchronous motion for assessment and design of this class of structure. Additionally, deck stiffness is shown to significantly affect response amplification, through response comparison between the curved and an equivalent straight bridge. Study results are used to suggest an appropriate domain for consideration of asynchronous excitation, as well as an efficient methodology for analysis.     

Kinematic Soil-Structure Interaction from Strong Motion Recordings

Earthquake strong motion recordings from 29 sites with instrumented structures and free-field accelerographs are used to evaluate variations between foundation-level and free-field ground motions. The focus of the paper is on buildings with surface and shallowly embedded foundations. The foundation/free-field ground motion variations are quantified in terms of frequency-dependent transmissibility function amplitude ∣H∣. Procedures are developed to fit to ∣H∣ analytical models for base slab averaging for the assumed conditions of a rigid base slab and a vertically propagating, incoherent incident wave field characterized by ground motion incoherence parameter κ. The limiting assumptions of the model are not strictly satisfied for actual structures, and the results of the identification are apparent κ values (denoted κa) that reflect not only incoherence effects, but also possible foundation flexibility and wave inclination effects. Nonetheless, a good correlation is found between κa values and soil shear wave velocity for sites with stiff foundation systems. Based on these results, recommendations are made for modifying free-field ground motions to estimate base slab motions for use in response analyses of buildings.     

Probabilistic Critical Excitation Method for Earthquake Energy Input Rate

Since earthquake ground motions and their input effects on structures are very uncertain even with the present state of knowledge, it is desirable to develop a “robust” structural design method taking into account these uncertainties. Approaches based on critical excitation methods have been proven to be promising for such robust structural design. A new critical excitation method is developed here in which the mean earthquake energy input rate is chosen as a measure of criticality. The earthquake energy input rate is closely correlated with the story deformation and this supports the suitability of the energy input rate as a criticality measure in the case where the deformation is crucial in the design. The ground motion is described as a uniformly modulated nonstationary random process. The power [area of power spectral density (PSD) function] and the intensity (magnitude of PSD function) are fixed and the critical excitation is found under these restrictions. The key for finding the new random critical excitation is the interchange of the order of the double maximization procedures with respect to time and to the PSD function. Examples for a specific envelope function of the ground motion are presented for demonstrating the validity of the proposed method. Extension of the proposed method will be discussed for a more general ground motion model, i.e., nonuniformly modulated nonstationary models, and for a more general problem for variable envelope functions and variable frequency contents.     

Response Spectrum Analysis of Suspension Bridges for Random Ground Motion

The response spectrum method of analysis for suspension bridges subjected to multicomponent, partially correlated stationary ground motion is presented. The analysis is based on the relationship between the power spectral density function and the response spectrum of the input ground motion and fundamentals of the frequency domain spectral analysis. The analysis duly takes into account the spatial correlation of ground motions between the supports, the quasi-static component of the response, and the modal correlation between different modes of vibration. A suspension bridge is analyzed under a set of important parametric variations in order to (1) compare between the responses obtained by the response spectrum method of analysis and the frequency domain spectral analysis; and (2) investigate the behavior of suspension bridges under seismic excitation. The parameters include the spatial correlation of ground motion, the angle of incidence of the earthquake, the ratio between the three components of ground motion, the number and nature of modes considered in the analysis, and the nature of the power spectral density function of ground motion. It is shown that the response spectrum method of analysis provides a fair estimate of responses under parametric variations considered in the study.     

Use of Exact Solutions of Wave Propagation Problems to Guide Implementation of Nonlinear Seismic Ground Response Analysis Procedures

One-dimensional nonlinear ground response analyses provide a more accurate characterization of the true nonlinear soil behavior than equivalent-linear procedures, but the application of nonlinear codes in practice has been limited, which results in part from poorly documented and unclear parameter selection and code usage protocols. In this article, exact (linear frequency-domain) solutions for body wave propagation through an elastic medium are used to establish guidelines for two issues that have long been a source of confusion for users of nonlinear codes. The first issue concerns the specification of input motion as “outcropping” (i.e., equivalent free-surface motions) versus “within” (i.e., motions occurring at depth within a site profile). When the input motion is recorded at the ground surface (e.g., at a rock site), the full outcropping (rock) motion should be used along with an elastic base having a stiffness appropriate for the underlying rock. The second issue concerns the specification of viscous damping (used in most nonlinear codes) or small-strain hysteretic damping (used by one code considered herein), either of which is needed for a stable solution at small strains. For a viscous damping formulation, critical issues include the target value of the viscous damping ratio and the frequencies for which the viscous damping produced by the model matches the target. For codes that allow the use of “full” Rayleigh damping (which has two target frequencies), the target damping ratio should be the small-strain material damping, and the target frequencies should be established through a process by which linear time domain and frequency domain solutions are matched. As a first approximation, the first-mode site frequency and five times that frequency can be used. For codes with different damping models, alternative recommendations are developed.     

Dynamic Analysis of Nonlinear Frames by Prandtl Neural Networks

A new type of activation function, based on the use of the Prandtl–Ishlinskii operator, has been developed and used in the feed forward neural networks in order to improve their capabilities in learning to identify and analyze nonlinear structures subject to dynamic loading. The genetic algorithm has been used in its training. The neural network, which is referred to as the Prandtl neural network here, has been trained and used in the analysis of two shear frames, a single degree of freedom (SDOF) and a 3DOF, both subjected to earthquake excitations. To assess the capabilities of the Prandtl neural network under ideal situations, the data on the response of the frames have been obtained through the integration of their governing nonlinear equations of motion. The training has been based on the white noise while the strong earthquakes of 200% El Centro in 1940 and Gilroy have been used for testing. Results have shown the high precision of the Prandtl neural network in solving highly hysteretic problems. The issue is important for two main applications in structural dynamics and control: (1) analysis of highly nonlinear structures where it is desired to train a neural network to directly learn the behavior of a structure from experimental data; and (2) intelligent active control of structures where neural network emulators are designed to provide as precise predictions about the future response of the structures as possible, in order to be used in the determination of the required control forces.     

Ground Motion Induced by Train Passage

Two methods are illustrated to effectively calculate the ground motion induced by constant speed moving loads. On the one hand, the dynamic Betti–Rayleigh reciprocity theorem allows one to take full advantage of the availability of Green’s functions for a homogeneous or a horizontally layered half-space. On the other hand, the spectral element method allows one to deal with complicated configurations, including dynamic soil-structure interaction, with an accuracy that is significantly higher than classical finite element or finite difference methods. Both the Betti–Rayleigh and spectral element methods are considered in three dimensions. After validating both methods, the decay of peak ground motion with distance is analyzed as a function of load speed and frequency. For speeds lower than the Rayleigh wave velocity in the soil, the decay turns out to be much faster than for a stationary point load. This effect is studied in detail by an analytical approach and interpreted in terms of destructive interference. Finally, the previous analytical and numerical results are checked against the records obtained at Ath, Belgium, during a field experiment to study ground motion induced by high-speed trains in soft soil conditions.     

Dynamic and Seismic Analysis of Foundations based on Free Field B-Spline Characteristic Response Histories

A direct time domain formulation for the analysis of unbounded media and foundations is developed that treats dynamic excitations and ground motion in a uniform manner. The method uses the boundary element method with higher order B-Spline fundamental solutions to compute the characteristic responses of the surface of the elastodynamic domain. Subsequently, time histories of the system response to general excitations are computed by a mere superposition scheme that accommodates in a uniform manner arbitrary time histories of external loads and/or ground motion. The characteristic responses are computed in the form of time dependent flexibility matrices of the medium that are sparse due to the finite duration of the B-Spline excitation signal and the characteristics of the wave propagation. The duration of the B-Spline impulse response is limited to only a few time steps. Consequently, significant savings in computing time and storage requirements are achieved. Furthermore, the characteristic responses do not depend on the type or wave form of the actual external excitations and the presence of rigid foundations. This is a significant advantage when the response of a system to excitations of long duration is to be computed. In addition, the proposed approach significantly reduces the size of the problems under consideration and yet fully considers the effects of the free field. The significance of nonrelaxed boundary conditions and correct representation of the free field is established. The method is demonstrated and validated through applications pertaining to the analysis of foundations and inclusions subjected to transient loads and seismic excitations.     

General Approach for Training Back-Propagation Neural Networks in Vibration Control of Multidegree-of-Freedom Structures

A general approach is proposed for back-propagation training of multilayer feed-forward (MLFF) neural networks for active control of earthquake-induced vibrations in multidegree-of-freedom structures. The training functions for adjustment of connection weights of the neural network controller are formulated in the proposed approach by minimizing a general cost function using the steepest gradient descent scheme. The proposed method can be applied for training an MLFF neural network controller in vibration control of building structures both in the pattern (online) and batch (off-line) mode. The method can be implemented in structural control systems with more than one control action. Case studies are presented to demonstrate the feasibility of implementing the training approach for effective vibration control of structures subjected to earthquake ground motions.     

Protecting Base-Isolated Structures from Near-Field Ground Motion by Tuned Interaction Damper

This paper deals with the combined use of a low-damping base-isolation system and a semiactive control system referred to as a tuned interaction damper (TI damper). The TI damper generates friction-type forces (rigid-plastic behavior) through interactions between the primary isolated structure and an auxiliary structure. Because of its energy-dissipation nature, a base-isolated structure controlled by a TI damper is inherently stable, and as a semiactive control device, its operation requires only minimal external power. The efficacy of the proposed hybrid system is examined through a numerical simulation for a five-story scaled building subjected to near-field ground motions. A sensitivity analysis on the parameter dependence of the structural response on control force limit, stiffness ratio, and frequency ratio is presented. By tuning these parameters to optimal values, the performance of the base-isolated structure equipped with a TI damper can be enhanced. Based on the numerical simulation results, it is concluded that a TI damper is capable of suppressing the base drift of base-isolated structures subjected to near-field earthquake ground motions while maintaining the superstructure interstory drift and accelerations at small levels.     

Influence of Input Motion and Site Property Variabilities on Seismic Site Response Analysis

Seismic site response analysis evaluates the influence of local soil conditions on earthquake ground shaking. There are multiple sources of potential uncertainty in this analysis; the most significant pertaining to the specification of the input motions and to the characterization of the soil properties. The influence of the selection of input ground motions on equivalent-linear site response analysis is evaluated through analyses performed with multiple suites of input motions selected to fit the same target acceleration response spectrum. The results indicate that a stable median surface response spectrum (i.e., within ±20% of any other suite) can be obtained with as few as five motions, if the motions fit the input target spectrum well. The stability of the median is improved to ±5 to 10% when 10 or 20 input motions are used. If the standard deviation of the surface response spectra is required, at least 10 motions (and preferably 20) are required to adequately model the standard deviation. The influence of soil characterization uncertainty is assessed through Monte Carlo simulations, where variations in the shear-wave velocity profile and nonlinear soil properties are considered. Modeling shear-wave velocity variability generally reduces the predicted median surface motions and amplification factors, most significantly at periods less than the site period. Modeling the variability in nonlinear properties has a similar, although slightly smaller, effect. Finally, including the variability in soil properties significantly increases the standard deviation of the amplification factors but has a lesser effect on the standard deviation of the surface motions.     

Identification of the Soil–Structure Interaction System Using Earthquake Response Data

This paper demonstrates how system identification techniques can be successfully applied to a soil–structure interaction system using the earthquake response data. The parameters identified are the shear moduli of several near-field soil regions and Young’s moduli of the shell sections of the structure. The soil–structure interaction system is modeled by the finite element method combined with the infinite element formulation for the unbounded layered soil medium. The simulated earthquake responses using the identified parameters are shown to be in excellent agreement with the observed response data. Prediction of the responses is also carried out for a larger earthquake event using the identified parameters as the initial properties in the equivalent linearization procedure. It has been found that the predicted responses are also compared very well with the measured responses.     

Linear Analysis of Ordinary Bridges Crossing Fault-Rupture Zones

Rooted in structural dynamics theory, two approximate procedures for estimating peak responses of linearly elastic “ordinary” bridges crossing fault-rupture zones are presented: response spectrum analysis (RSA) procedure and a linear static analysis procedure. These procedures estimate the peak response by superposing peak values of quasi-static and dynamic responses. The peak quasi-static response in both procedures is computed by static analysis of the bridge with peak values of all support displacements applied simultaneously. In RSA, the peak dynamic response is estimated by dynamic analysis including all significant modes, which is simplified in the latter procedure to static analysis of the bridge for appropriately selected forces; usually only one mode—the most dominant mode—is sufficient in the RSA procedure. Appearing in these procedures is the “effective” influence vector that differs from the influence vector for spatially uniform excitation, and the response spectrum used in the RSA procedure differs from the standard California Department of Transportation (CALTRANS) spectrum. Both of these simplified procedures provide estimates of peak response that are close enough to results of the “exact” response history analysis to be useful for practical application.     

Saturation Effects of Soils on Ground Motion at Free Surface Due to Incident SV Waves

A study is presented of saturation effects of subsoil on seismic motions at the free surface of a half space due to an inclined (SV) wave. By treating the soil as a partially water-saturated porous medium that is characterized by its degree of saturation, porosity, permeability, viscosity, and compressibility, a theoretical formulation is developed for the computation of free-surface amplitudes in both the horizontal and vertical components, which are defined as a function of the degree of saturation, the angle of incidence, and the frequency. Numerical results are presented using typical sand properties. It is shown that even a slight decrease of full saturation may lead to a substantial influence on the free-surface amplitudes in both the components and the amplitude ratios between them, and this influence is dependent on the angle of incidence. Significant phase shift between the horizontal and vertical components may also occur due to this slight change in saturation. At small incident angles, partial saturation of subsoil generally may cause a greater vertical-to-horizontal ratio compared with a fully saturated model. It is suggested that one may need to carefully take into account the saturation condition in the interpretation of field observations on seismic ground motions.     

Cross-Modal Dynamic Capture: Congruency Effects in the Perception of Motion Across Sensory Modalities.

This study investigated multisensory interactions in the perception of auditory and visual motion. When auditory and visual apparent motion streams are presented concurrently in opposite directions, participants often fail to discriminate the direction of motion of the auditory stream, whereas perception of the visual stream is unaffected by the direction of auditory motion (Experiment 1). This asymmetry persists even when the perceived quality of apparent motion is equated for the 2 modalities (Experiment 2). Subsequently, it was found that this visual modulation of auditory motion is caused by an illusory reversal in the perceived direction of sounds (Experiment 3). This "dynamic capture" effect occurs over and above ventriloquism among static events (Experiments 4 and 5), and it generalizes to continuous motion displays (Experiment 6). These data are discussed in light of related multisensory phenomena and their support for a "modality appropriateness" interpretation of multisensory integration in motion perception. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Bayesian Learning Using Automatic Relevance Determination Prior with an Application to Earthquake Early Warning

A novel method of Bayesian learning with automatic relevance determination prior is presented that provides a powerful approach to problems of classification based on data features, for example, classifying soil liquefaction potential based on soil and seismic shaking parameters, automatically classifying the damage states of a structure after severe loading based on features of its dynamic response, and real-time classification of earthquakes based on seismic signals. After introduction of the theory, the method is illustrated by applying it to an earthquake record dataset from nine earthquakes to build an efficient real-time algorithm for near-source versus far-source classification of incoming seismic ground motion signals. This classification is needed in the development of early warning systems for large earthquakes. It is shown that the proposed methodology is promising since it provides a classifier with higher correct classification rates and better generalization performance than a previous Bayesian learning method with a fixed prior distribution that was applied to the same classification problem.