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.     

Probabilistic Seismic Demand Models and Fragility Estimates for Reinforced Concrete Bridges with Two-Column Bents

Probabilistic models are developed to predict the deformation and shear demands due to seismic excitation on reinforced concrete (RC) columns in bridges with two-column bents. A Bayesian methodology is used to develop the models. The models are unbiased and properly account for the predominant uncertainties, including model errors, arising from a potentially inaccurate model form or missing variables, measurement errors, and statistical uncertainty. The probabilistic models developed are akin to deterministic demand models and procedures commonly used in practice, but they have additional correction terms that explicitly describe the inherent systematic and random errors. Through the use of a set of “explanatory” functions, terms that correct the bias in the existing deterministic demand models are identified. These explanatory functions provide insight into the underlying behavioral phenomena and provide a means to select ground motion parameters that are most relevant to the seismic demands. The approach takes into account information gained from scientific/engineering laws, observational data from laboratory experiments, and simulated data from numerical dynamic responses. The demand models are combined with previously developed probabilistic capacity models for RC bridge columns to objectively estimate the seismic vulnerability of bridge components and systems. The vulnerability is expressed in terms of the conditional probability (or fragility) that a demand quantity (deformation or shear) will be greater than or equal to the corresponding capacity. Fragility estimates are developed for an example RC bridge with two-column bents, designed based on the current specifications for California. Fragility estimates are computed at the individual column, bent, and bridge system levels, as a function of the spectral acceleration and the ratio between the peak ground velocity and the peak ground acceleration.     

Probabilistic Performance-Based Procedure to Evaluate Pile Foundations at Sites with Liquefaction-Induced Lateral Displacement

Liquefaction-induced ground deformation has caused major damage to bridge and wharf structures in past earthquakes. Large lateral ground displacements may induce significant forces in the foundation and superstructure, which may lead to severe damage or even collapse. A performance-based earthquake engineering (PBEE) approach can provide an objective assessment of the likely seismic performance, so that agencies can evaluate bridge or wharf structures, compare retrofit strategies, and rank them within their overall system. In this paper, a probabilistic PBEE design procedure that incorporates findings from recent research on this problem is presented. The proposed approach can provide answers in terms that are meaningful to owners, such as expected repair costs and downtimes. The methodology is validated through its application to a well-documented case history. Results show that the proposed approach provides a good estimate of the seismic performance of pile-supported structures at sites with liquefaction-induced lateral displacement.     

Wave Passage and Ground Motion Incoherency Effects on Seismic Response of an Extended Bridge

This paper investigates the implications of ground motion spatial variability on the seismic response of an extended highway bridge. An existing 59-span, 2,164-meter bridge with several bearing types and irregularity features was selected as a reference structure. The bridge is located in the New Madrid Seismic Zone and supported on thick layers of soil deposits. Site-specific bedrock input ground motions were selected based on a refined probabilistic seismic hazard analysis of the bridge site. Wave passage and ground motion incoherency effects were accounted for after propagating the bedrock records to the ground surface. The results obtained from inelastic response-history analyses confirm the significant impact of wave passage and ground motion incoherency on the seismic behavior of the bridge. The amplification in seismic demands exceeds 150%, whereas the maximum suppression of these demands is less than 50%. The irregular and unpredictable changes in structural response owing to asynchronous earthquake records necessitate in-depth seismic assessment of major highway bridges with advanced modeling techniques to realistically capture their complex seismic response.     

Performance Evaluation of Deteriorating Highway Bridges Located in High Seismic Areas

This paper studies the life-cycle performance and cost of reinforced concrete highway bridges subjected to earthquake ground motions while they are continuously exposed to the attack of chloride ions. The penetration of chloride ions into the concrete is simulated through a finite difference approach that takes into account all the parameters that can affect the corrosion process. From simulation results, the corrosion initiation time is predicted, and the extent of structural degradation is calculated over the entire life of the bridge. A group of detailed bridge models with various structural attributes are developed to evaluate the changes in the structural capacity and seismic response of corroded bridges. For the purpose of the probabilistic seismic risk assessment of bridges, the seismic fragility curves are generated and updated at regular time intervals. The time-dependent fragility parameters are employed to investigate the life-cycle cost of bridges by introducing a performance index that combines the effects of probable seismic events and chloride-induced corrosion. The proposed approach provides a multihazard framework that leads to more realistic performance and cost estimates.     

Nonlinear Soil–Abutment–Bridge Structure Interaction for Seismic Performance-Based Design

Current seismic design of bridges is based on a displacement performance philosophy using nonlinear static pushover analysis. This type of bridge design necessitates that the geotechnical engineer predict the resistance of the abutment backfill soils, which is inherently nonlinear with respect to the displacement between soil backfill and the bridge structure. This paper employs limit-equilibrium methods using mobilized logarithmic-spiral failure surfaces coupled with a modified hyperbolic soil stress–strain behavior (LSH model) to estimate abutment nonlinear force-displacement capacity as a function of wall displacement and soil backfill properties. The calculated force-displacement capacity is validated against the results from eight field experiments conducted on various typical structure backfills. Using LSH and experimental data, a simple hyperbolic force-displacement (HFD) equation is developed that can provide the same results using only the backfill soil stiffness and ultimate soil capacity. HFD is compatible with current CALTRANS practice in regard to the seismic design of bridge abutments. The LSH and HFD models are powerful and effective tools for practicing engineers to produce realistic bridge response for performance-based bridge design.     

Bridge Seismic Retrofitting Practices in the Central and Southeastern United States

This paper conducts a detailed review of the seismic hazard, inventory, bridge vulnerability, and bridge retrofit practices in the Central and Southeastern United States (CSUS). Based on the analysis of the bridge inventory in the CSUS, it was found that over 12,927 bridges (12.6%) are exposed to 7% probability of exceedance (PE) in 75-year peak ground acceleration (PGA) of greater than 0.20 g, and nearly 3.5% of bridges in the CSUS have a 7% PE in 75-year PGA of greater than 0.50 g. Since many of the bridges in this region were not designed with explicit consideration of the seismic hazard, many of them are in need of seismic retrofitting to reduce their seismic vulnerability. While several of the states in the CSUS have retrofitted some of their bridges, systematic retrofit programs do not currently exist. The review of retrofit practices in the region indicates that the most common retrofit approaches in the CSUS include the use of restrainer cables, isolation bearings, column jacketing, shear keys, and seat extenders. The paper presents an overview of the common approaches and details used for the aforementioned retrofit measures. This paper serves as a useful tool for bridge engineers in the CSUS as they begin to perform systematic retrofit of vulnerable bridges in the region.     

Seismic Fragility of Continuous Steel Highway Bridges in New York State

This paper presents the results of an analytical seismic fragility analysis of a typical steel highway bridge in New York State. The structural type and topological layout of this multispan I-girder bridge have been identified to be most typical of continuous bridges in New York State. The structural details of the bridge are designed as per New York State bridge design guidelines. Uncertainties associated with the estimation of material strength, bridge mass, friction coefficient of expansion bearings, and expansion-joint gap size are considered. To account for the uncertainties related to the bridge structural properties and earthquake characteristics, ten statistical bridge samples are established using the Latin Hypercube sampling and restricted pairing approach, and 100 ground motions are simulated numerically. The uncertainties of capacity and demand are estimated simultaneously by using the ratios of demands to capacities at different limit states to construct seismic fragility curves as a function of peak ground acceleration and fragility surfaces as a function of moment magnitude and epicentral distance for individual components using nonlinear and multivariate regressions. It has been observed that nonlinear and multivariate regressions show better fit to bridge response data than linear regression conventionally used. To account for seismic risk from multiple failure modes, second-order reliability yields narrower bounds than the commonly used first-order reliability method. The fragility curves and surfaces obtained from this analysis demonstrate that bridges in New York State have reasonably low likelihood of collapse during expected earthquakes.     

Seasonally Frozen Soil Effects on the Seismic Site Response

Several large-magnitude earthquakes, including the Prince William Sound earthquake of March 1964 and the Denali earthquake of November 2002, occurred in the state of Alaska and caused considerable damages to its transportation system, including damage to several highway bridges and related infrastructure. Some of these damages are related to frozen soil effects. However, only limited research has been carried out to investigate the effects of frozen soils on seismic site responses. A systematic investigation of seasonally frozen soil effects on the seismic site response has been conducted and is presented in this paper. One bridge site in Anchorage, Alaska, was selected to represent typical sites with seasonally frozen soils. A set of input ground motions was selected from available strong-motion databases and scaled to generate an ensemble of hazard-consistent input motions. One-dimensional equivalent linear analysis was adopted to analyze the seismic site response for three seismic hazard levels, i.e., maximum considered earthquake (MCE), AASHTO design, and service design level hazards. Parametric studies were conducted to assess the sensitivity of the results to uncertainties associated with the thickness and shear-wave velocity of seasonally frozen soils. The results show that the spectral response of ground motions decreases as the thickness of seasonally frozen soil increases, and the results are insensitive to the shear-wave velocity of seasonally frozen soils. In conclusion, it is generally conservative to ignore the effects of seasonally frozen soils on seismic site response in the design of highway bridges.     

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.     

Reliability-Based Assessment of Suspension Bridges: Application to the Innoshima Bridge

Many suspension and cable-stayed bridges were designed and constructed between Honshu Island and Shikoku Island in Japan. All these bridges were designed according to the allowable stress design method. In the allowable stress design method, it is not possible to quantify the reliabilities of both bridge components and the entire bridge system. Therefore, in light of current reliability-based design philosophy, there is an urgent need to assess the safety of suspension bridges from a probabilistic viewpoint. To develop cost-effective design and maintenance strategies, it is necessary to assess the condition of suspension bridges using a reliability-based approach. This is accomplished by a probabilistic finite-element geometrically nonlinear analysis. This study describes an investigation into the reliability assessment of suspension bridges. The combination of reliability analysis and geometrically nonlinear elastic analysis allows the determination of reliabilities of suspension bridges. A probabilistic finite-element geometrically nonlinear elastic code, created by interfacing a system reliability analysis program with a finite-element program, is used for reliability assessment of suspension bridges. An existing suspension bridge in Japan, the Innoshima Bridge, is assessed using the proposed code. The assessment is based on static load effects. Reliabilities of the bridge are obtained by using 2D and 3D geometrically nonlinear models. Furthermore, damage scenarios are considered to assess the effects of failure of various elements on the reliability of undamaged components and on the reliability of the bridge. Finally, sensitivity information is obtained to evaluate the dominant effects on bridge reliability.     

Simplified AASHTO Load and Resistance Factor Design Girder Live Load Distribution in Illinois

Illinois began full transition to the American Association of State Highway and Transportation Officials load and resistance factor design (LRFD) bridge design specifications from the traditional load factor design code or standard specifications in 2002. To facilitate implementation of the new specification, engineers from the Illinois Department of Transportation undertook a series of investigations. The studies focused on interpretation of LRFD for the design of typical bridges in Illinois and the simplification of its procedures for determination of live load lane distributions to primary superstructure girders. Some important presented results from the conducted investigations are believed not only relevant to bridge design in Illinois, but to other states and jurisdictions which employ or will employ LRFD in the near future. The initial simplifications and interpretations focused on concrete deck-on-steel girder bridges and were subsequently expanded to include concrete deck-on-prestressed concrete girder structures. These types of structures comprise a large portion of Illinois’ inventory. Illinois Department of Transportation engineers continue to build on the studies described in the paper such that policies and procedures for other types of typical bridges can be formulated.     

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.     

Performance-Based Design Approach in Seismic Analysis of Bridges

The seismic design requirements used in the United States are based on the recommendations of the American Association of State Highway and Transportation Officials. These requirements are primarily based on the importance of the structure, the level of deformation imposed on the structure, soil conditions, and the ductility of structural members, especially piers and supports. In the performance-based design approach, the design is primarily focused on meeting a performance objective, which is in line with a desired level of service. Currently, the effort toward implementing the performance-based design approach in buildings is under way in the United States. The seismic performance criteria for buildings have been established and reported by various organizations. It seems that at least three levels of performance, ranging from “fully operational” to “near collapse” can be used to meet the postearthquake conditions, safety, usage, and occupancy for the varous levels of service expected from all types of structures. In this paper a critical evaluation of these performance criteria and their relevance to highway bridge design, in conjunction with the current design practice, is discussed. Various types of designs such as those based on strength, deformation, nonlinear behavior, and energy, which can be used to meet the specified performance levels in seismic design of highway bridges, are also discussed in the paper. Examples of real applications of the method in highway bridges are reviewed. Furthermore, the procedure by which the performance-based method has been implemented in these example cases is described and discussed in the paper.     

Role of Shear Keys in Seismic Behavior of Bridges Crossing Fault-Rupture Zones

This paper examines the role of shear keys at bridge abutments in the seismic behavior of “ordinary” bridges. The seismic responses of bridges subjected to spatially uniform and spatially varying ground motions for three shear-key conditions—nonlinear shear keys that break off and cease to provide transverse restraint if deformed beyond a certain limit; elastic shear keys that do not break off and continue to provide transverse restraint throughout the ground shaking; and no shear keys—are examined. Results show that seismic demands for a bridge with nonlinear shear keys can generally be bounded by the demands of a bridge with elastic shear keys and a bridge with no shear keys for both types of ground motions. While ignoring shear keys provides conservative estimates of seismic demands in bridges subjected to spatially uniform ground motion, such a practice may lead to underestimation of some seismic demands in bridges in fault-rupture zones that are subjected to spatially varying ground motion. Therefore, estimating the upper bounds of seismic demands in bridges crossing fault-rupture zones requires analysis for two shear-key conditions: no shear keys and elastic shear keys.     

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.     

Seismic Performance of a River Dike Improved by Sand Compaction Piles

Sand compaction piling is one of the commonly used countermeasures for earthquake liquefaction hazard of river dikes. This paper presents a case study of the performance of an instrumented dike in northeast Japan that was improved by sand compaction piles and subjected to the 2003 Northern Miyagi Earthquake, with the aim to better understand the effectiveness of this ground improvement method. Simulation has been carried out by means of a fully coupled numerical procedure which employs a sophisticated cyclic elastoplastic constitutive model and the updated Lagrangian algorithm. Comparisons between the field measurements and the computed responses, including the time histories of accelerations and pore-water pressures at different locations, show reasonably good agreement. Numerical simulation has also been made of the same dike but without ground improvement to identify the effects of sand compaction piles in altering the performance of the dike. The study demonstrates that the comprehensive numerical procedure is a promising tool for development of seismic performance-based design of earth structures.     

Dynamic Performance Simulation of Long-Span Bridge under Combined Loads of Stochastic Traffic and Wind

Slender long-span bridges exhibit unique features which are not present in short and medium-span bridges such as higher traffic volume, simultaneous presence of multiple vehicles, and sensitivity to wind load. For typical buffeting studies of long-span bridges under wind turbulence, no traffic load was typically considered simultaneously with wind. Recent bridge/vehicle/wind interaction studies highlighted the importance of predicting the bridge dynamic behavior by considering the bridge, the actual traffic load, and wind as a whole coupled system. Existent studies of bridge/vehicle/wind interaction analysis, however, considered only one or several vehicles distributed in an assumed (usually uniform) pattern on the bridge. For long-span bridges which have a high probability of the presence of multiple vehicles including several heavy trucks at a time, such an assumption differs significantly from reality. A new “semideterministic” bridge dynamic analytical model is proposed which considers dynamic interactions between the bridge, wind, and stochastic “real” traffic by integrating the equivalent dynamic wheel load (EDWL) approach and the cellular automaton (CA) traffic flow simulation. As a result of adopting the new analytical model, the long-span bridge dynamic behavior can be statistically predicted with a more realistic and adaptive consideration of combined loads of traffic and wind. A prototype slender cable-stayed bridge is numerically studied with the proposed model. In addition to slender long-span bridges which are sensitive to wind, the proposed model also offers a general approach for other conventional long-span bridges as well as roadway pavements to achieve a more realistic understanding of the structural performance under probabilistic traffic and dynamic interactions.