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.     

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.     

Seismic Performance Assessment of Simply Supported and Continuous Multispan Concrete Girder Highway Bridges

Seismic evaluations of typical concrete girder bridges are conducted for both a multispan simply supported and a multispan continuous girder bridge common to the Central and Southeastern United States. These evaluations are performed for an approximate hazard level of 2% in 50?years by performing nonlinear time history analyses on three-dimensional analytical models. The results show significant vulnerabilities in the reinforced concrete columns, the abutments, and also in unseating of the girders. In general, the longitudinal loading of the bridges results in larger demands than the transverse loading. However, the simply supported bridge sustains bearing deformations in the transverse direction which are on the same order as their longitudinal response. These results suggest that both longitudinal and transverse loading are significant and should be considered when performing seismic hazard analyses of these bridges.     

Innovative Bridge Condition Assessment from Dynamic Response of a Passing Vehicle

An innovative approach for damage assessment of a bridge deck is proposed with the measured dynamic response of a vehicle moving on top of a structure. The simply supported bridge deck is modeled as a Euler–Bernoulli beam. The moving vehicle serves as a smart sensor and force transducer in the structural system. The damage is defined as the flexural stiffness reduction in the beam finite element. The identification algorithm is based on dynamic response sensitivity analysis, and it is realized with a regularization technique from the measured vehicle acceleration measurement. Measurement noise, road surface roughness, and model errors are included in the simulations, and the results indicate that the proposed algorithm is computationally stable and efficient, and the identified results are acceptable and not sensitive to the different parameters studied.     

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.     

Dynamic Monitoring of Steel Girder Highway Bridge

Currently there are different monitoring techniques that have been considered for use in the structural evaluation of bridges. These include approaches based on both static and dynamic behavior. The use of dynamic properties has advantages over static properties, since components of the dynamic properties are only marginally influenced by variations in the loading. When dynamic properties are used, field studies have shown that it is not always sufficient to use only natural frequencies and modal displacements. Some research for structural evaluation of bridges indicates that techniques based on use of derivatives of the natural frequencies and the modal displacements may be more effectively used to generate effective diagnostic parameters for structural identification. This paper presents the results of applying one of these methods, the modal flexibility approach, to a field study of a bridge in which the bearings were partially restrained in colder weather. While others have used impact methods with the modal flexibility method, in this study the approach is modified so that excitation is provided by vehicular traffic. The results show that the modified modal flexibility method provides a clear indication that there have been changes in the bridge’s structural behavior.     

Seismic Behavior of Steel Girder Bridge Superstructures

Recent earthquakes exposed the vulnerabilities of steel plate girder bridges when subjected to ground shaking. This paper discusses the behavior of steel plate girder bridges during recent earthquakes such as Petrolia, Northridge, and Kobe. The paper also discusses the recent experimental and analytical investigations that were conducted on steel plate girder bridges and their components. Results of these investigations showed the importance of shear connectors in distributing and transferring the lateral forces to the end and intermediate cross frames. Also, these investigations showed the potential of using end cross frames as ductile elements that can be used to dissipate the earthquake input energy. The paper also gives an update on specifications and guidelines for the seismic design of steel plate girder bridges in the United States.     

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.     

Influence of Inelastic Tower Links on Cable-Supported Bridge Response

A new concept for bridge tower designs in seismic zones incorporates sacrificial link schemes that enable the tower shafts to remain elastic under large seismic excitation. In order to study the influence of inelastic tower links on the seismic response of cable-supported bridges, global seismic time history analyses were performed on models of the new San Francisco-Oakland Bay Bridge East Span self-anchored suspension bridge (SASB) and a cable-stayed bridge (CSB) alternative. The addition of inelastic links to the signature tower improved the behavior of both structures. The tower and overall bridge demands were reduced, including the tower drift and moments as well as the suspension cable, cable stay, and superstructure drifts and axial loads. The inelastic tower links protected the SASB and CSB tower shafts from nonlinear behavior under the 1,500-year Safety Evaluation Earthquake (SEE) event as well as a 2,500-year event. When the inelastic tower links were removed, the SASB tower shafts yielded under the SEE. It was shown that the inelastic tower links could be used to tune the dynamic response of bridge towers in regions of high seismicity.     

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.     

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.     

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.     

Refined Stick Model for Dynamic Analysis of Skew Highway Bridges

Stick models are widely employed in the dynamic analysis of bridges when only approximate results are desired or when detailed models are difficult or time-consuming to construct. Although the use of stick models for regular bridges has been validated by various researchers, the application of such models to skew highway bridges continues to present challenges. The conventional single-beam stick model used to represent the bridge deck often fails to capture certain predominant vibration modes that are important in obtaining the true dynamic response of the bridge. In this paper, a refined stick model is proposed for the preliminary dynamic analysis of skew bridges. The model utilizes a dual-beam stick representation of the bridge deck. The validity of the model is established by comparing results obtained from the proposed model with numerical solutions obtained for skew plates and a skew bridge. It is shown that this dual-beam stick model is superior to the conventional single-beam model in estimating the natural vibration frequencies and in predicting the predominant vibration modes of the bridge. Because of its simplicity and relative accuracy, this model is recommended for the preliminary dynamic analysis of skew highway bridges.     

Unbonded Posttensioned Concrete Bridge Piers. II: Seismic Analyses

The seismic response characteristics of a proposed unbonded posttensioned concrete bridge-pier system are evaluated. Time-history analyses are carried out on prototype designs of single-column piers and two-column bents using detailed nonlinear finite-element (FE) models and equivalent single-degree-of-freedom (SDOF) systems embedded with phenomenological constitutive models. The phenomenological models are based on the hysteretic behavior of the prototype designs from cyclic analyses using nonlinear FE models, which have been calibrated and verified against experiments. The two modeling techniques are compared and evaluated for simulating the response of unbonded posttensioned bridge piers. Extensive time-history analyses are carried out on the SDOF models to study the influence of unbonded posttensioning on seismic response. To assess the adequacy of the proposed bridge-pier system, the seismic demands on the prototype designs are compared to their capacities as established in a companion paper. The applicability of current bridge design specifications to designing the proposed bridge-pier system is discussed.     

Investigation on the Impact of Seasonally Frozen Soil on Seismic Response of Bridge Columns

This paper presents the development of numerical models that investigated the seismic response of a simple two span prototype bridge system during warm and frozen temperatures. Models from both temperature conditions were subjected to a range of seismic intensities to examine the effect of seasonal freezing on the response of the system. Stiffness characteristics were defined using cyclic models of a bridge pier that were previously developed and validated using results from an experimental program on identical full-scale column-foundation units, which were tested during the summer and winter months. Dynamic characteristics of the seismic models were defined using approaches found in the literature. Frozen conditions increased the maximum bending moment and shear force demands for all seismic intensities, with nonlinearity in the column/foundation reducing the difference between the peak responses at higher intensities. At the depth of maximum foundation shear for the frozen model, demand was three times higher than the unfrozen for the 500-year return period and twice during the 2,500-year event. This is significant as one will assume shear is not critical at this location if the effects of frozen conditions are ignored. Apart from the smallest intensity event, increased peak lateral displacements were developed by the warm model down the length of the column and foundation. However, the displacement demand to capacity ratio was higher at the column top for the frozen model, exceeding the capacity during the 2,500-year return period event.     

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.     

Dynamic Response of a Highway Bridge Subjected to Moving Vehicles

Several full-scale load tests were performed on a selected Florida highway bridge. The bridge was dynamically excited by two fully loaded trucks, and the strain, acceleration, and displacement at selected points were recorded for the investigation of the bridge’s dynamic response. Experimental data were compared with simplified vehicle and bridge finite-element models. The vehicle was represented as a three-dimensional mass–spring–damper system with 11?degrees of freedom, and the bridge was modeled as a combination of plate and beam elements that characterize the slab and girders, respectively. The equations of motion were formulated with physical components for the vehicle and modal components for the bridge. The coupled equations were solved using a central difference method. It was found that the numerical analysis matched well with the experimental data and was used to successfully explain critical dynamic phenomena observed during the testing. Impact factors for this tested bridge were thoroughly investigated by using these models.     

Effect of Vehicle Velocity on the Dynamic Amplification of Two Vehicles Crossing a Simply Supported Bridge

The effect of multiple vehicles on a bridge’s dynamic amplification is a complex problem. Previously writers have examined multiple vehicle presence by constructing elaborate finite element models or undertaking field tests. Although both these methods give valuable information regarding the magnitude of dynamic amplification, the results tend to be site specific and give limited insight into how large amplifications occur. This paper examines the dynamic amplification factor of a simply supported bridge being crossed by two loads traveling in both the same and opposing directions. Simple numerical point load models are used to determine the critical load velocities and load positions that result in high amplifications. An experimentally validated finite element model is used to examine the applicability of the conclusions to real bridge/vehicle systems.     

Probabilistic Seismic Demand Models and Fragility Estimates for Reinforced Concrete Highway Bridges with One Single-Column Bent

In performance-based seismic design, general and practical seismic demand models of structures are essential. This paper proposes a general methodology to construct probabilistic demand models for reinforced concrete (RC) highway bridges with one single-column bent. The developed probabilistic models consider the dependence of the seismic demands on the ground motion characteristics and the prevailing uncertainties, including uncertainties in the structural properties, statistical uncertainties, and model errors. Probabilistic models for seismic deformation, shear, and bivariate deformation-shear demands are developed by adding correction terms to deterministic demand models currently used in practice. The correction terms remove the bias and improve the accuracy of the deterministic models, complement the deterministic models with ground motion intensity measures that are critical for determining the seismic demands, and preserve the simplicity of the deterministic models to facilitate the practical application of the proposed probabilistic models. The demand data used for developing the models are obtained from 60 representative configurations of finite-element models of RC bridges with one single-column bent subjected to a large number of representative seismic ground motions. The ground motions include near-field and ordinary records, and the soil amplification due to different soil characteristics is considered. A Bayesian updating approach and an all possible subset model selection are used to assess the unknown model parameters and select the correction terms. Combined with previously developed capacity models, the proposed seismic demand models can be used to estimate the seismic fragility of RC bridges with one single-column bent. Seismic fragility is defined as the conditional probability that the demand quantity of interest attains or exceeds a specified capacity level for given values of the earthquake intensity measures. As an application, the univariate deformation and shear fragilities and the bivariate deformation-shear fragility are assessed for an example bridge.