Theoretical Studies of the XY-FP Seismic Isolation Bearing for Bridges

The XY-friction pendulum (XY-FP) bearing is a modified friction pendulum that consists of two perpendicular steel rails with opposing concave surfaces and a connector. The connector resists tensile forces, allows independent sliding in the two orthogonal directions and enables small relative rotation of the rails about a vertical axis. Theoretical analyses were undertaken to study applications of XY-FP bearings to bridges. Two of the key features of the XY-FP bearing for the seismic isolation of bridges are: (1) resistance to tensile axial loads and (2) opportunity to provide a different period of isolation in each principal direction of the isolated structure. Numerical analyses on an XY-FP isolated bridge with different isolation periods in the principal directions subjected to near-field ground motions demonstrated the effectiveness of XY-FP bearings. Furthermore, numerical analyses that investigated the sensitivity of XY-FP isolation system response to differences in the coefficients of friction of the bearings demonstrated that bounding analysis using upper and lower estimates of the coefficients of friction will generally provide conservative estimates of displacements and shear forces for isolation systems with nonuniform isolator properties.     

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.     

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.     

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.     

Effects of Pier and Deck Flexibility on the Seismic Response of Isolated Bridges

The seismic response of bridges isolated by elastomeric bearings and the sliding system is investigated under two horizontal components of real earthquake ground motions. The selected bridges consist of multispan continuous deck supported on the piers and abutments. Three different mathematical models of the isolated bridge are considered for the analytical seismic response by considering and ignoring the flexibility of the deck and piers. The mathematical formulation for seismic response analysis of various mathematical models of the bridges isolated by different isolation systems is presented. The accuracy and computational efficiency of various mathematical models of isolated bridges is investigated by comparing their responses under different system parameters and earthquake ground motions. The important parameters selected are the flexibility of deck, piers, and isolation systems. There was significant difference in the computational time required for different models, but it was observed that the seismic response of the bridges obtained from different equivalent mathematical models is quite comparable even for an unsymmetrical bridge. Thus, the earthquake response of a seismically isolated bridge can be effectively obtained by modeling it as a single-degree-of-freedom system (i.e., considering the piers and deck as rigid) supported on an isolation system in two horizontal directions.     

Seismic Response of Isolated Bridges

The seismic response of bridges seismically isolated by lead-rubber bearings (L-RB) to bidirectional earthquake excitation (i.e., two horizontal components) is presented in this paper. The force-deformation behavior of L-RB is considered as bilinear, and the interaction between the restoring forces in two orthogonal horizontal directions is duly considered in the response analysis. The specific purpose of the study is to assess the effects of seismic isolation on the peak response of the bridges, and to investigate the effects of the bidirectional interaction of restoring forces of isolation bearings. The seismic response of the lumped mass model of continuous span isolated bridges is obtained by solving the governing equations of motion in the incremental form using an iterative step-by-step method. To study the effectiveness of L-RB, the seismic response of isolated bridges is compared with the response of corresponding nonisolated bridges (i.e., bridges without isolation devices). A comparison of the response of the isolated bridges obtained by considering and ignoring the bidirectional interaction of bearing forces is made under important parametric variation. The important parameters included are the flexibility of the bridge piers and the stiffness and yield strength of the L-RB. The results show that the bidirectional interaction of the restoring forces of the L-RB has considerable effects on the seismic response of the isolated bridges. If these interaction effects are ignored, then the peak bearing displacements are underestimated, which can be crucial from the design point of view.     

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.     

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.     

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.     

Seismic Vulnerability and Mitigation during Construction of Cable-Stayed Bridges

The implications of earthquake loading during balanced cantilever construction of a cable-stayed bridge are examined. Finite-element models of a cable-stayed bridge were developed and multiple ground motion time history records were used to study the seismic response at the base of the towers for six stages of balanced cantilever construction. Probabilistic seismic hazard relationships were used to relate ground motions to bridge responses. The results show that there can be a high probability of having seismic responses (forces/moments) in a partially completed bridge that exceed, often by a substantial margin, the 10%/50-year design level (0.21% per annum) for the full bridge. The maximum probability of exceedance per annum was found to be 20%. This occurs because during balanced-cantilever construction the structure is in a particularly precarious and vulnerable state. The efficacy of a seismic mitigation strategy based on the use of tie-down cables intended for aerodynamic stability during construction was investigated. This strategy was successful in reducing some of the seismic vulnerabilities so that probabilities of exceedance during construction dropped to below 1% per annum. Although applied to only one cable-stayed bridge, the same approach can be used for construction-stage vulnerability analysis of other long-span bridges.     

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.     

Estimation of Collapse Load of Single-Cell Concrete Box-Girder Bridges

The simplified equations available at present to predict the collapse loads of single-cell concrete box-girder bridges with simply supported ends are based on either space truss analogy or collapse mechanisms. Experimental studies carried out by various researchers revealed that, of the two formulations available to predict the collapse load, the one based on collapse mechanisms is found to be more versatile and better suited to box sections. Under a pure bending collapse mechanism, the existing formulation is found to predict collapse load with high accuracy. However, in the presence of cross-sectional distortion, there are significant errors in the existing theoretical formulation. This paper attempts to resolve this problem, by proposing a modification to the existing theory, incorporating an empirical expression to assess the extent of corner plastic hinge formation, under distortion–bending collapse mechanism. The modified theoretical formulations are compared with the experimental results available in the literature. New sets of experiments are also conducted to validate the proposed modified theory to estimate the collapse load. In all cases, it is seen that the modified theory to predict the collapse load match very closely with the experimental results.     

Experimental Study of the XY-Friction Pendulum Bearing for Bridge Applications

The XY-friction pendulum (XY-FP) bearing is a modified Friction Pendulum (Earthquake Protection Systems, Inc., Vallejo, Calif.) bearing that consists of two perpendicular steel rails with opposing concave surfaces and a connector. The connector resists tensile forces, provides for independent sliding in the two principal directions of the isolators, and ideally, permits unhindered rotation about its vertical axis. Experimental studies on an XY-FP seismically isolated truss-bridge model were undertaken to study response under tridirectional excitations and to evaluate the use of XY-FP bearings for bridges. A truss bridge model was tested on a pair of earthquake simulators using acceleration orbits and near-field earthquake histories. The experimental results demonstrated the effectiveness of the XY-FP bearings as an uplift-prevention isolation system: the XY-FP bearings simultaneously resisted significant tensile loads and functioned as seismic isolators. The bidirectional horizontal response of the small-scale XY-FP isolation system was coupled due to the internal construction of the small-scale connectors that joined the two rails of each XY-FP bearing and the limited free-to-rotate capacity of the XY-FP bearings due to misalignment of the isolators during installation.     

Modeling of Jointed Connections in Segmental Bridges

Precast segmental construction of bridges can accelerate construction and minimize the cost of medium span bridges in environmentally sensitive and difficult to access locations. Despite these benefits, the use of precast segmental bridges in seismic regions of the United States remains limited. A main obstacle to their use is concern regarding the seismic response of segment joints. Recent experimental research programs studied the seismic performance of segmental superstructures. However, an estimate of the seismic response of full-scale segmental bridges to real earthquake records remains unknown. This paper presents a segment joint modeling approach and is an important first step toward accurately estimating the seismic response of superstructure segment joints to input ground motions. The approach is a compromise between the detailed and computationally intensive continuum mechanics based finite element approach and a simple approach that models the joints with rotational springs. The approach considers the nonlinear tendon-grout slip response and was validated with data from large-scale experiments. Numerous modeling sensitivity studies were performed and recommendations for implementation in full-scale models are presented.     

Impact Factors for Curved Continuous Composite Multiple-Box Girder Bridges

The results from a parametric study on the impact factors for 180 curved continuous composite multiple-box girder bridges are presented. Expressions for the impact factors for tangential flexural stresses, deflection, shear forces and reactions are deduced for AASHTO truck loading. The finite-element method was utilized to model the bridges as three-dimensional structures. The vehicle axle used in the analysis was simulated as a pair of concentrated forces moving along the concrete deck in a circumferential path with a constant speed. The effects of bridge configurations, loading positions, and vehicle speed on the impact factors were examined. Bridge configurations included span length, span-to-radius of curvature ratio, number of lanes, and number of boxes. The effect of the mass of the vehicle on the dynamic response of the bridges is also investigated. The data generated from the parametric study and the deduced expressions for the impact factors would enable bridge engineers to design curved continuous composite multiple-box girder bridges more reliably and economically.     

Improved Seismic Response of Multisimple-Span Skewed Bridges Retrofitted with Link Slabs

Results of a recent bridge inventory evaluation indicated that about 50% of Turkish highway bridges have more than 30° of skew angle and can be classified as irregular bridges. During the recent major earthquake in Turkey, multisimple-span bridges with continuous decks and link slabs performed well even though these bridges were in the vicinity of the fault line. This study aims to evaluate the improvements in seismic response of skew bridges in terms of forces and displacements when link slabs are added as a retrofit tool. A series of elastic dynamic analyses and nonlinear time history analyses were conducted to investigate the seismic response of various standard highway bridges with different span lengths and skew angles. A new reinforcement design for edge zones of link slabs is proposed for bridges located in high seismic zones. In practice, link slabs can be implemented easily during a regular redecking of a bridge.     

Seismic Performance of Multisimple-Span Bridges Retrofitted with Link Slabs

During earthquakes multisimple-span bridges are vulnerable to span separation at their expansion joints. A common way of preventing unseating of spans is to have cable or rod restrainers that provide connections between adjacent spans. Alternatively, dislocation of the girders can be controlled with a link slab that is the continuous portion of the bridge deck between simple spans. Seismic retrofit with link slab should be more cost-effective than the existing methods when it is performed during redecking or removal of expansion joints. Maintenance cost associated with expansion joints could also be reduced. This paper discusses the use of link slabs for retrofit of seismically deficient multisimple-span bridges with precast, prestressed concrete girders. The concept is equally applicable to bridges with steel girders. Analytical studies for typical overpasses were performed to investigate the effectiveness of the proposed link slab application. A simple preliminary design procedure was also developed.     

Effects of Seismically Induced Pounding at Expansion Joints of Concrete Bridges

This paper presents the result of a study on the effect of pounding at expansion joints on concrete bridge response to earthquake ground motions. An engineering approach, rather than continuum mechanics approach, is emphasized. First, the dynamic behavior of a damped multidegree-of-freedom bridge system separated by an expansion joint involving an impact is examined by means of the finite element method. Second, the sensitivity analysis of the stiffness in gap elements is performed. Third, usefulness of the analysis method for simulation of pounding phenomena is demonstrated and the effect of pounding on the ductility demands measured in terms of the rotation of column ends is investigated. Two-dimensional finite element analysis using a bilinear hysterestic model for bridge substructure joints and a nonlinear gap element for the expansion joint is performed on a realistic bridge with an expansion joint. The effects of the primary factors on the ductility demand such as gap sizes and characteristics of earthquake ground motion are investigated through a parametric study. The major conclusions are (1) the effect of impact most directly depends on the size of momentum (or pounding magnitude); and (2) the pounding effect is generally found to be negligible on the ductility demand for wide practical ranges of gap size and peak ground acceleration, but is potentially significant at the locations of impact.     

Live-Load Distribution Factors for Concrete Box-Girder Bridges

The current American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) Specifications impose fairly strict limits on the use of its live-load distribution factor for design of highway bridges. These limits include requirements for a prismatic cross section, a large span-length-to-width ratio, and a small plan curvature. Refined analyses using 3D models are required for bridges outside of these limits. These limits place severe restrictions on the routine design of bridges in California, as box-girder bridges outside of these limits are frequently constructed. This paper presents the results of a study investigating the live-load distribution characteristics of box-girder bridges and the limits imposed by the LRFD specifications. Distribution factors determined from a set of bridges with parameters outside of the LRFD limits are compared with the distribution factors suggested by the LRFD specifications. For the range of parameters investigated, results indicated that the current LRFD distribution factor formulas generally provide a conservative estimate of the design bending moment and shear force.