Nonlinear Static Procedure for Fragility Curve Development

This study examines the fragility curves of a bridge by two different analytical approaches; one utilizes the time-history analysis and the other uses the capacity spectrum method. The latter approach is one of the simplified nonlinear static procedures recently developed for buildings. In this respect, a sample of 10 nominally identical but statistically different bridges and 80 ground-motion time histories are considered to account for the uncertainties related to the structural capacity and ground motion, respectively. The comparison of fragility curves by the nonlinear static procedure with those by time-history analysis indicates that the agreement is excellent for the state of at least minor damage, but not as good for the state of major damage where nonlinear effects clearly play a crucial role. Overall, however, the agreement is adequate even in the state of major damage considering the large number of typical assumptions under which the analyses of fragility characteristics are performed.     

Deterioration Rates of Typical Bridge Elements in New York

The New York State Department of Transportation (NYSDOT) maintains an inventory of over 17,000 highway bridges across the state. These bridges are inspected biennially or more often as necessary. Bridge inspectors are required to assign a condition rating for up to 47 structural elements of each bridge, including 25 components of each span of a bridge, in addition to the general components common to all bridges. The bridge condition rating scale ranges from 7 to 1; 7 being new and 1 being in failed condition. These condition ratings may be used to calculate the deterioration rates for each bridge element, while considering the effects of key factors, such as the bridge material type, on the deterioration rates. This paper describes an approach based on the Weibull distribution to calculate the deterioration rates of typical bridge elements in New York State using historical bridge inspection data and compares the results with those using the traditionally used Markov chains approach. It is observed that the Weibull-based approach performs better in terms of the observed conditions than the traditionally used Markov chains approach for developing deterioration curves for different bridge elements. Both Markov chains and Weibull-based approaches have been incorporated into a computer program that generates the deterioration curves for specific bridge elements based on historical NYSDOT bridge inspection data dating back to 1981. Case studies on the deterioration rates of various bridge elements in New York State are presented to demonstrate the two approaches. The case studies show that the element deterioration rate information can be used to determine the expected service life of different bridge elements under a variety of external factors. This information is extremely valuable for making bridge management decisions. Based on the Weibull-based approach, the deterioration rates for typical bridge elements in New York State have been presented.     

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.     

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.     

Efficient Longitudinal Seismic Fragility Assessment of a Multispan Continuous Steel Bridge on Liquefiable Soils

The increased failure potential of aging U.S. highway bridges and their susceptibility to damage during extreme events necessitates the development of efficient reliability assessment tools to prioritize maintenance and rehabilitation interventions. Reliability communication tools become even more important when considering complex phenomena such as soil liquefaction under seismic hazards. Currently, two approaches are widely used for bridge reliability estimation under soil failure conditions via fragility curves: liquefaction multipliers and full-scale two- or three-dimensional bridge-soil-foundation models. This paper offers a computationally economical yet adequate approach that links nonlinear finite-element models of a three-dimensional bridge system with a two-dimensional soil domain and a one-dimensional set of p-y springs into a coupled bridge-soil-foundation (CBSF) system. A multispan continuous steel girder bridge typical of the central and eastern United States along with heterogeneous liquefiable soil profiles is used within a statistical sampling scheme to illustrate the effects of soil failure and uncertainty propagation on the fragility of CBSF system components. In general, the fragility of rocker bearings, piles, embankment soil, and the probability of unseating increases with liquefaction, while that of commonly monitored components, such as columns, depends on the type of soil overlying the liquefiable sands. This component response dependence on soil failure supports the use of reliability assessment frameworks that are efficient for regional applications by relying on simplified but accepted geotechnical methods to capture complex soil liquefaction effects.     

Fragility Increment Functions for Deteriorating Reinforced Concrete Bridge Columns

The increased deformation and shear fragilities of corroding RC bridge columns subject to seismic excitations are modeled as functions of time using fragility increment functions. These functions can be applied to various environmental and material conditions by means of controlling parameters that correspond to the specific condition. For each mode of failure, the fragility of a deteriorated column at any given time is obtained by simply multiplying the initial fragility of the pristine/nondeteriorated column by the corresponding function developed in this paper. The developed increment functions account for the effects of the time-dependent uncertainties that are present in the corrosion model as well as in the structural capacity models. The proposed formulation is a useful tool for engineering practice because the fragility of deteriorated columns is obtained without any extra reliability analysis once the fragility of the pristine column is known. The fragility increment functions are expressed as functions of time t and a given deformation or shear demand. Unknown parameters involved in the models are estimated using a Bayesian updating framework. A model selection is conducted during the assessment of the unknown parameters using the Akaike information criterion and the Bayesian information criterion. For the estimation of the parameters, a set of data are obtained by first-order reliability method analysis using existing probabilistic capacity models for corroding RC bridge columns. Example fragilities of a deteriorated bridge column typical of current California’s practice are presented to demonstrate the developed methodology. The increment functions suggested in this paper can be used to assess the time-variant fragility for application to life cycle cost analysis and risk analysis.     

Probabilistic Seismic Demand Model for California Highway Bridges

A performance-based seismic design method enables designers to evaluate a graduated suite of performance levels for a structure in a given hazard environment. The Pacific Earthquake Engineering Research Center is developing a framework for performance-based seismic design. One component of this framework is a probabilistic seismic demand model for a class of structures in an urban region with a well-defined seismic hazard exposure. A probabilistic seismic demand model relates ground motion intensity measures to structural demand measures. It is formulated by statistically analyzing the results of a suite of nonlinear time-history analyses of typical structures under expected earthquakes in the urban region. An example of a probabilistic seismic demand model for typical highway bridges in California is presented. It was formulated using a portfolio of 80 recorded ground motions and a portfolio of 108 bridges generated by varying bridge design parameters. The sensitivity of the demand models to variation of bridge design parameters is also discussed. Trends derived from this sensitivity study provide designers with a unique tool to assess the effect of seismicity and design parameters on bridge performance.     

Evaluation of Seismic Damage to Memphis Bridges and Highway Systems

This paper presents a procedure for the evaluation of the expected seismic damage to bridges and highway systems in Memphis and Shelby County, Tenn. Data pertinent to 452 bridges and major arterial routes were collected and implemented as a geographic information system database. The bridges were classified into several bridge types using a bridge classification system modified from the NBIS∕Federal Highway Administration coding guidelines. The bridge damage states considered are no∕minor damage, repairable damage, and significant damage. The fragility curves corresponding to these damage states were established for various bridge types. Given an earthquake with a moment magnitude of 7.0 occurring at Marked Tree, Ark., the intensity of ground shaking and liquefaction-induced permanent ground deformation in Memphis and Shelby County were estimated, and then the expected damage to bridges and highway systems was determined. The results can be used to prioritize bridges for retrofitting, to prepare a pre-earthquake preparedness plan, to develop a postearthquake emergency response plan, and to assess the regional economic impact from the damage to highway transportation systems.     

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.     

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.     

Inelastic Damage Analysis of Reinforced Concrete Bridge Columns Based on Degraded Monotonic Energy

This paper summarizes the prediction of seismic damage of two existing bridges. The objective is to apply a damage index definition for reinforced concrete bridge columns under cyclic loading to existing bridge columns that might experience real seismic loading in the future, and to evaluate the ability of the damage index in describing the damage progression of the bridge columns during real seismic loading. Two existing bridges were selected from the Greater Vancouver Area in Canada. The first bridge, the Garneau Flyover, was designed in 1985 to ATC-6-1981 and is expected to have sufficient resistance to lateral earthquake loading. The second bridge, the Clydesdale Street Underpass, was designed long before ATC-6-1981 and is expected to show little or no lateral earthquake resistance. The damage index is applied to each of these structures, with columns modeled using the CANNY nonlinear structural analysis program. Shear and bond slip deformations were considered by making a simple modification to the column flexural properties. A series of nonlinear dynamic analyses were performed using records from the 1971 San Fernando, 1978 Miyaki-Oki (Japan), 1989 Loma Prieta, and 1999 Taiwan earthquakes fitted to the Vancouver firm ground spectrum. The calculated damage index provides a simple numerical indicator of the damage during an earthquake, easily computed from the results of a nonlinear dynamic analysis.     

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.     

Structural Reliability Estimation with Vibration-Based Identified Parameters

This paper presents a unique structural reliability estimation method incorporating structural parameter identification results based on the seismic response measurement. In the shaking table test, a three-bent concrete bridge model was shaken to different damage levels by a sequence of earthquake motions with increasing intensities. Structural parameters, stiffness and damping values of the bridge were identified under damaging seismic events based on the seismic response measurement. A methodology was developed to understand the importance of structural parameter identification in the reliability estimation. Along this line, a set of structural parameters were generated based on the Monte Carlo simulation. Each of them was assigned to the base bridge model. Then, every bridge model was analyzed using nonlinear time history analyses to obtain damage level at the specific locations. Last, reliability estimation was performed for bridges modeled with two sets of structural parameters. The first one was obtained by the nonlinear time history analysis with the Monte Carlo simulated parameters which is called nonupdated structural parameters. The second one was obtained by updating the first set in Bayesian sense based on the vibration-based identification results which is called updated structural parameters. In the scope of this paper, it was shown that residual reliability of the system estimated using the updated structural parameters is lower than the one estimated using the nonupdated structural parameters.     

Probabilistic Capacity Models and Fragility Estimates for Reinforced Concrete Columns Incorporating NDT Data

Knowing the ability of reinforced concrete (RC) bridges to withstand future seismic demands during their life-cycle can help bridge owners make rational decisions regarding optimal allocation of resources for maintenance, repair, and/or rehabilitation of bridge systems. The accuracy of a reliability assessment can be improved by incorporating information about the current aging and deterioration conditions of a bridge. Nondestructive testing (NDT) can be used to evaluate the actual conditions of a bridge, avoiding the use of deterioration models that bring additional uncertainties in the reliability assessment. This paper develops probabilistic deformation and shear capacity models for RC bridge columns that incorporate information obtained from NDT. The proposed models can be used when the flexural stiffness decays nonuniformly over a column height. The flexural stiffness of a column is estimated based on measured acceleration responses using a system identification method and the damage index method. As an application of the proposed models, a case study assesses the fragility (the conditional probability of attaining or exceeding a specified capacity level) of the column in the Lavic Road Overcrossing for a given deformation or shear demand. This two-span concrete box-girder bridge located in Southern California was subject to the Hector Mine Earthquake in 1999. Pre- and postearthquake estimates of the univariate shear and deformation fragilities and of the bivariate shear-deformation fragility are computed and compared. Both displacement and shear capacities are found to decrease after the earthquake event. Additionally, the results show that the damage due to the Hector Mine Earthquake has a larger impact on the shear capacity than the deformation capacity, leading to a more significant increment in the shear fragility than in the deformation fragility.     

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.     

Multidimensional Performance Limit State for Hazard Fragility Functions

This paper addresses an alternative methodology to calculate fragility functions that considers multiple limit states parameters, such as combinations of response variables of accelerations and interstory drifts. Limit states are defined using a generalized multidimensional limit states function that allows considering dependencies among limit thresholds modeled as random variables in the calculation of fragility curves that are evaluated as function of the return period. A California hospital is used as example to illustrate the proposed approach for developing fragility curves. The study investigates the sensitivity of the proposed approach for evaluating fragility curves when uncertainties in limit states are considered. Influence of structural and response parameters, such as stiffness, damping, acceleration and displacement thresholds, ground motion input, and uncertainties in structural modeling, are also investigated. The proposed approach can be considered as an alternative approach for describing the vulnerable behavior of nonstructural components that are sensitive to multiple parameters such as displacements and accelerations (e.g., partition walls, piping systems, etc.).     

Use of Isolation for Seismic Retrofitting Bridges

The increasing acceptance of seismic isolation for bridges is being demonstrated by the number of bridges now being designed or retrofitted using this technology. This technology is now being used for bridges across the United States. Seismic isolation in California, Tennessee-Arkansas, and New York are but a few examples of how this technology is producing cost-effective solutions for bridge owners. This paper discusses the application at these locations and the application of the American Association of State Highway and Transportation Officials Guide Specification for Seismic Isolation Design.     

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.