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.     

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.     

Nonlinear Analysis of Ordinary Bridges Crossing Fault-Rupture Zones

Rooted in structural dynamics theory, three approximate procedures for estimating seismic demands for bridges crossing fault-rupture zones and deforming into their inelastic range are presented: modal pushover analysis (MPA), linear dynamic analysis, and linear static analysis. These procedures estimate the total seismic demand by superposing peak values of quasi-static and dynamic parts. The peak quasi-static demand in all three procedures is computed by nonlinear static analysis of the bridge subjected to peak values of all support displacements applied simultaneously. In the MPA and the linear dynamic analysis procedures, the peak dynamic demand is estimated by nonlinear static (or pushover) analysis and linear static analysis, respectively, for forces corresponding to the most-dominant mode. In the linear static analysis procedure, the peak dynamic demand is estimated by linear static analysis of the bridge due to lateral forces appropriate for bridges crossing fault-rupture zones. The three approximate procedures are shown to provide estimates of seismic demands that are accurate enough to be useful for practical applications. The linear static analysis procedure, which is much simpler than the other two approximate procedures, is recommended for practical analysis of “ordinary” bridges because it eliminates the need for mode shapes and vibration periods of the bridge.     

Effect of Near-Fault Vertical Ground Motions on Seismic Response of Highway Overcrossings

Results of comprehensive nonlinear response history analyses on a range of configurations representing typical highway overcrossings subjected to combined effects of vertical and horizontal components of near-fault ground motions are reported. Current seismic design guidelines in California neglect the vertical components of ground motions for peak ground accelerations less than 0.6?g and provide rather simplistic measures to account for vertical effects when they need to be incorporated in the design. Results from the numerical simulations show that the vertical components of ground motions cause significant amplification in the axial force demand in the columns and moment demands in the girder at both the midspan and at the face of the bent cap. Axial capacity of the columns and moment capacity of the girder at the face of the bent cap were generally found to be sufficient to resist the amplification in the respective demands due to vertical effects. However, midspan moments in negative bending due to vertical motions are found to exceed the capacity of the girder. The amplified midspan moments lead to yielding of the top reinforcement resulting in average peak strains on the order of 1%. It is concluded that seismic demand analysis of ordinary highway bridges in general and overcrossings in particular should incorporate provisions for considering the adverse vertical effects of near-fault ground motions.     

Effect of Side Retainers on Seismic Response of Bridges with Elastomeric Bearings

Often, to restrain the lateral displacement of elastomeric bearings in slab-girder bridges, two retainers in the form of angles or welded plates are placed on each side of the bearings, with a slight clearance to allow for longitudinal movement of the elastomer. The existence of the gap introduces nonlinearity into the seismic analysis of the structure, which is commonly ignored. In addition, by considering the gap, the elastomer’s stiffness in the transverse direction contributes to the overall stiffness of the system. This paper investigates the behavior of these retainers under earthquake forces. The retainers’ stiffness, the gap distance, and the period of the bridge are used as variable parameters. It is shown that the seismic demand on retainers is nonlinear in nature and depends on the frequency content of the input motion. It is also proved that ignoring the gap in the seismic analysis model can lead to lower seismic demands on the retainers and substructure. Design recommendations are given for bridges with such retainers.     

Hilbert-Huang Transform Analysis of Dynamic and Earthquake Motion Recordings

This study examines the rationale of Hilbert-Huang transform (HHT) for analyzing dynamic and earthquake motion recordings in studies of seismology and engineering. In particular, this paper first provides the fundamentals of the HHT method, which consist of the empirical mode decomposition (EMD) and the Hilbert spectral analysis. It then uses the HHT to analyze recordings of hypothetical and real wave motion, the results of which are compared with the results obtained by the Fourier data processing technique. The analysis of the two recordings indicates that the HHT method is able to extract some motion characteristics useful in studies of seismology and engineering, which might not be exposed effectively and efficiently by Fourier data processing technique. Specifically, the study indicates that the decomposed components in EMD of HHT, namely, the intrinsic mode function (IMF) components, contain observable, physical information inherent to the original data. It also shows that the grouped IMF components, namely, the EMD-based low- and high-frequency components, can faithfully capture low-frequency pulse-like as well as high-frequency wave signals. Finally, the study illustrates that the HHT-based Hilbert spectra are able to reveal the temporal-frequency energy distribution for motion recordings precisely and clearly.     

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.     

Damage Analysis of Hanshin Expressway Viaducts during 1995 Kobe Earthquake. III: Three-Span Continuous Girder Bridges

Almost all the single reinforced concrete (RC) piers from P35 to P350 received consistently severe damage, considering the large residual inclination of piers included in earthquake-induced severe damage. However, some of the piers in the section from P35 to P350 remained lightly damaged, and this phenomenon is observed especially in many piers under fixed bearings in continuous girder bridges. In this study, using experimentally based models for metal bearings and installing them to an existing FEM code, a nonlinear dynamic response analysis of a continuous girder bridge system is conducted. It is shown that the results depend on the ground motion, but the fuse effect of the breaking of the bearings could have been a reason for the phenomenon.     

Performance Evaluation of Short Span Reinforced Concrete Arch Bridges

In this paper, the static and seismic performance of some short span reinforced concrete arch bridges, before and after strengthening interventions, are evaluated. To verify whether retrofit strategies for the considered arch bridges, which were designed for resisting under permanent and service actions, were adequate for earthquake resistance, seismic analyses of the as-built model of the structures have been undertaken. To account for multiple input effects on arches, induced by out-of-phase motions at foundation levels as well as different boundary conditions at structural supports, the seismic response of the structures under correlated horizontal and vertical multiple excitations is calculated. The effects on arch bridges of conventionally used uniform input and partially correlated multiple inputs with phase shifts are compared. In all cases, the results are discussed with particular reference to the influence of structural configuration, secondary systems, cross-section thickness of the arch, and retrofit interventions.     

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.     

Seismic Modeling of Skewed Bridges with Elastomeric Bearings and Side Retainers

Elastomeric expansion bearings are often restrained laterally by retainers on each side. The retainers are in the form of a concrete shear block, rolled steel angles, or welded plates. To allow for longitudinal temperature movements, the retainers are placed with a slight clearance (gap) from the elastomer. The gap introduces nonlinearity in the seismic analysis of the bridge and, therefore, is often ignored by designers for the sake of simplicity. This paper compares the seismic response of straight and skewed slab-girder single-span bridges under the conditions of zero gap and standard gap for the retainers. Nonlinear time-history analysis is employed to measure the seismic demand on retainers, elastomers, and pinned bearings in each case. The stiffness of end-diaphragms and elastomeric bearings is included in the analysis. It is shown that these relationships are nonlinear in nature and depend on the frequency content of the input motion. It is also proved that ignoring the nonlinearity in the seismic bridge model can lead to erroneous results that are unsafe to use.     

Orthogonal Effects in Seismic Analysis of Skewed Bridges

In seismic analysis of bridges, the designer chooses the direction of the applied earthquake forces arbitrarily. This paper investigates the effects of seismic force direction on the responses of slab-girder skewed bridges in response spectrum and time history linear dynamic analyses. The combination rules for orthogonal earthquake effects, such as the 100/30, 100/40?percentage rules and the SRSS method are also examined. It is concluded that either the SRSS or the 100/40?percentage rule in the skew direction should be used in the response spectrum analysis of skewed bridges. For time history analysis none of the combination rules provide conservative results. In this case, the application of paired acceleration time histories in several angular directions is recommended.     

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.     

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.     

Seismic Effect on Highway Bridges in Chi Chi Earthquake

This paper reports the bridge damage in the Chi Chi earthquake. Damage to bridge structures may occur in the superstructure, the substructure, or the approaches. Typical types of damage are discussed and illustrated in this paper. A review of the design specifications in Taiwan is also presented to give the background on the seismic design of highway bridges in Taiwan.     

Seismic Response of Multiple Span Steel Bridges in Central and Southeastern United States. I: As Built

The seismic response of typical multispan simply supported (MSSS) and multispan continuous steel girder bridges in the central and southeastern United States is evaluated. Nonlinear time history analyses are conducted using synthetic ground motion for three cities for 475 and 2,475-year return period earthquakes (10 and 2% probability of exceedance in 50 years). The results indicate that the seismic response for the 475-year return period earthquake would lead to an essentially linear response in typical bridges. However, the seismic response for a 2,475-year return period earthquake resulted in significant demands on nonductile columns, fixed and expansion bearings, and abutments. In particular, pounding between decks in the MSSS bridge would result in significant damage to steel bearings and would lead to the toppling of rocker bearings, which may result in unseating of the bridge deck.     

Nonlinear Earthquake Response Modeling of a Large-Scale Two-Span Concrete Bridge

A quarter scale model of a two-span RC bridge was tested using the Network for Earthquake Engineering Simulation (NEES) multiple shake table system at the University of Nevada, Reno, Nev. The project was funded through a National Science Foundation-NEES demonstration grant. The bridge system was tested from a preyield state until column failure. In depth analytical modeling was conducted to determine the effectiveness of current structural analysis software and methodology in predicting the bridge model response. Both SAP2000 v.9 and Drain-3DX were used for this purpose. Both models produced reasonable results up to column failure, however, the Drain-3DX model was determined to be most effective to predict the nonlinear bridge model response. Parametric studies were conducted to investigate optimal element discretization and integration parameters. Existing equations for pre and postyield column shear stiffness showed good correlation when compared with the measured data.     

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.