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 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.     

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.     

Closed-Form Fragility Estimates, Parameter Sensitivity, and Bayesian Updating for RC Columns

Reinforced concrete (RC) columns are the most critical components in bridges under seismic excitation. In this paper, a simple closed-form formulation to estimate the fragility of RC columns is developed. The formulation is used to estimate the conditional probability of failure of an example column for given shear and deformation demands. The estimated fragilities are as accurate as more sophisticated estimates (i.e., predictive fragilities) and do not require any reliability software. A sensitivity analysis is carried out to identify to which parameter(s) the reliability of the example column is most sensitive. The closed-form formulation uses probabilistic capacity models. A Bayesian procedure is presented to update existing probabilistic models with new data. The model updating process can incorporate different types of information, including laboratory test data, field observations, and subjective engineering judgment, as they become available.     

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.     

Seismic Retrofit of State Street Bridge on Interstate 80

The State Street Bridge, in Salt Lake City, was designed and built in 1965 according to the 1961 AASHO specifications; the design did not include earthquake-induced forces or displacements since only wind loads were considered. The bridge consists of four reinforced concrete (RC) bents supporting composite welded steel girders; the bents are supported on cast-in-place concrete piles and pile caps. A vulnerability analysis of the bridge was conducted that determined deficiencies in (1) confinement of column lap splice regions, (2) anchorage of longitudinal column bars in the bent cap, (3) confinement of column plastic hinge zones, and (4) shear capacity of columns and bent cap–column joints. Seismic retrofit designs using carbon-fiber-reinforced-polymer (CFRP) composites and steel jackets were performed and compared for three design spectra, including the 10% probability of exceedance in 250 years earthquake. The CFRP composite design was selected for implementation and application of the composite was carried out in the summer of 2000 and 2001, while the bridge was in service. The paper describes the CFRP composite design, which, in addition to column jackets, implemented an “ankle wrap” for improving joint shear strength and a “U-strap” for improving anchorage of column bars in the bent cap; other retrofit measures were implemented, such as bumper brackets and a deck slab retrofit. A capacity versus demand evaluation of the as-built and retrofitted bents is presented.     

Probabilistic Capacity Models and Fragility Estimates for Reinforced Concrete Columns based on Experimental Observations

A methodology to construct probabilistic capacity models of structural components is developed. Bayesian updating is used to assess the unknown model parameters based on observational data. The approach properly accounts for both aleatory and epistemic uncertainties. The methodology is used to construct univariate and bivariate probabilistic models for deformation and shear capacities of circular reinforced concrete columns subjected to cyclic loads based on a large body of existing experimental observations. The probabilistic capacity models are used to estimate the fragility of structural components. Point and interval estimates of the fragility are formulated that implicitly or explicitly reflect the influence of epistemic uncertainties. As an example, the fragilities of a typical bridge column in terms of maximum deformation and shear demands are estimated.     

Analytical Evaluation of Seismic Performance of RC Frames Rehabilitated Using FRP for Increased Ductility of Members

Many reinforced concrete (RC) frame structures designed according to pre1970 strength-based codes are susceptible to abrupt strength deterioration once the shear capacity of the columns is reached. Fiber composites are used to increase the shear strength of existing RC columns and beams by wrapping or partially wrapping the members. Increasing the shear strength can alter the failure mode to be more ductile with higher energy dissipation and interstorey drift ratio capacities. The objective of this study was to analytically evaluate the effect of varying distributions of fiber-reinforced polymer (FRP) rehabilitation on the seismic performance of three existing RC frames with different heights when subjected to three types of scaled ground motion records. The FRP wrapping is designed to increase the displacement ductility of frame members to reach certain values representing moderate ductility and high ductility levels. These values were assumed based on previous experimental work conducted on members wrapped using FRP. The study also investigates the effect of the selected element’s force–displacement backbone curve on the capacities of the structures with respect to maximum interstory drift ratio, maximum peak ground acceleration, or peak ground velocity resisted by the frames, maximum storey shear-to-weight ratio and maximum energy dissipation. It was found that for low-rise buildings, the FRP rehabilitation of columns only was effective in enhancing the seismic performance; while for high-rise ones, rehabilitation of columns only was not as effective as rehabilitation of both columns and beams. Ignoring representing the postpeak strength degradation in the hysteretic nonlinear model of FRP-rehabilitated RC members was found to lead to erroneous overestimation of the seismic performance of the structure.     

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.     

Analytical Models and Guidelines for the Ductility Enhancement of Circular Reinforced Concrete Single-Column Bents Using Fiber-Reinforced Polymers

The target displacement ductility requirements for circular RC single-column bridge bents are considered using a proposed multifailure mode algorithm to determine the required thickness of fiber-reinforced polymer wraps (FRPs). The procedure is developed using two in-house computer algorithms, PACCC (plastic analysis of circular concrete columns) and PACCC-FRP, to generate a moment-curvature analysis using circular segment slices and subsequent failure mode predictions in single-column bents for both FRP-wrapped and unwrapped circular RC sections. The results of the study showed good comparison to published experimental tests at the ultimate force-deflection states of RC sections and against three commercial “software test beds.” The study uses PACCC-FRP to show that single columns experiencing a brittle failure may be retrofitted with FRP wraps in order to increase the displacement ductility and satisfy target ductility values within the ductility wrap envelope, or wrap-saturation level, as established herein.     

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.     

Active Confinement of Reinforced Concrete Bridge Columns Using Shape Memory Alloys

This paper presents experimental and analytical work conducted to explore the feasibility of using an innovative technique for seismic retrofitting of RC bridge columns using shape memory alloys (SMAs) spirals. The high recovery stress associated with the shape recovery of SMAs is being sought in this study as an easy and reliable method to apply external active confining pressure on RC bridge columns to improve their ductility. Uniaxial compression tests of concrete cylinders confined with SMA spirals show a significant improvement in the concrete strength and ductility even under small confining pressure. The experimental results are used to calibrate the concrete constitutive model used in the analytical study. Analytical models of bridge columns retrofitted with SMA spirals and carbon fiber-reinforced polymer (CFRP) sheets are studied under displacement-controlled cyclic loading and a suite of strong earthquake records. The analytical results proves the superiority of the proposed technique using SMA spirals to CFRP sheets in terms of enhancing the strength and effective stiffness and reducing the concrete damage and residual drifts of retrofitted columns.     

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.     

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.     

Empirical Predictive Models for Earthquake-Induced Sliding Displacements of Slopes

Earthquake-induced sliding displacement is the parameter most often used to assess the seismic stability of slopes. The expected displacement can be predicted as a function of the characteristics of the slope (yield acceleration) and the ground motion (e.g., peak ground acceleration), yet there is significant aleatory variability associated with the displacement prediction. Using multiple ground motion parameters to characterize the earthquake shaking can significantly reduce the variability in the prediction. Empirical predictive models for rigid block sliding displacements are developed using displacements calculated from over 2,000 acceleration–time histories and four values of yield acceleration. These empirical models consider various single ground motion parameters and vectors of ground motion parameters to predict the sliding displacement, with the goal of minimizing the standard deviation of the displacement prediction. The combination of peak ground acceleration and peak ground velocity is the two parameter vector that results in the smallest standard deviation in the displacement prediction, whereas the three parameter combination of peak ground acceleration, peak ground velocity, and Arias intensity further reduces the standard deviation. The developed displacement predictive models can be used in probabilistic seismic hazard analysis for sliding displacement or used as predictive tools for deterministic earthquake scenarios.     

Investigation of effect of near-fault motions on substandard bridge structures

The objective of this study was to investigate the effects of near-fault ground motions on substandard bridge columns and piers. To accomplish these goals, several large scale reinforced concrete models were constructed and tested on a shake table using near- and far-field ground motion records. Because the input earthquakes for the test models had different characteristics, three different measures were used to evaluate the effect of the input earthquake. These measures are peak shake table acceleration, spectral acceleration at the fundamental period of the test specimens, and the specimen drift ratios.For each measure, force-displacement relationships, strains, curvatures, drift ratios, and visual damage were evaluated.Results showed that regardless of the measure of input or response, the near-fault record generally led to larger strains,curvatures, and drift ratios. Furthermore, residual displacements were small compared to those for columns meeting current seismic code requirements.     

Development of damage probability matrices based on Greek earthquake damage data

A comprehensive study is presented for empirical seismic vulnerability assessment of typical structural types,representative of the building stock of Southern Europe, based on a large set of damage statistics. The observational database was obtained from post-earthquake surveys carried out in the area struck by the September 7, 1999 Athens earthquake. After analysis of the collected observational data, a unified damage database has been created which comprises 180,945 damaged buildings from/after the near-field area of the earthquake. The damaged buildings are classified in specific structural types,according to the materials, seismic codes and construction techniques in Southern Europe. The seismic demand is described in terms of both the regional macroseismic intensity and the ratio ag/ao, where ag is the maximum peak ground acceleration (PGA) of the earthquake event and ao is the unique value PGA that characterizes each municipality shown on the Greek hazard map. The relative and cumulative frequencies of the different damage states for each structural type and each intensity level are computed in terms of damage ratio. Damage probability matrices (DPMs) and vulnerability curves are obtained for specific structural types. A comparison analysis is fulfilled between the produced and the existing vulnerability models.     

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.     

Development of a Specification for Bridge Seismic Retrofit with Carbon Fiber Reinforced Polymer Composites

The U.S. Interstate 80 bridge over State Street in Salt Lake City is very near the Wasatch fault, which is active and capable of producing large earthquakes. The bridge was designed and built in 1965 according to the 1961 American Association of State Highway Officials specifications, which did not consider earthquake-induced forces or displacements. The bridge consists of reinforced concrete bents supporting steel plate welded girders. The bents are supported on cast-in-place concrete piles and pile caps. A seismic retrofit design was developed using carbon fiber reinforced polymer (CFRP) composites, which was implemented in the summer of 2000 and the summer of 2001, to improve the displacement ductility of the bridge. The seismic retrofit included column jacketing, as well as wrapping of the bent cap and bent cap-column joints for confinement, flexural, and shear strength increase. This paper describes the specifications developed for the CFRP composite column jackets and composite bent wrap. The specifications included provisions for materials, constructed thickness based on strength capacity, and an environmental durability reduction factor. Surface preparation, finish coat requirements, quality assurance provisions, which included sampling and testing, and constructability issues regarding the application of fiber composite materials in the retrofit of concrete bridges are also described.     

Seismic Performance Assessment of Damage-Controlled FRP-Retrofitted RC Bridge Columns Using Residual Deformations

Despite the improved performance of fiber-reinforced plastic (FRP)-retrofitted bridges, residual deformations in the event of an earthquake are inevitable. Little consideration is currently given to these deformations when assessing seismic performance. Moreover, important structures are currently required not only to have high strength and high ductility but also to be usable and repairable after high intensity earthquakes. This paper presents a definition of an FRP-RC damage-controllable structure. An intensive study of 109 bridge columns, extracted from recent research literature on the inelastic performance of FRP retrofitted columns with lap-splice deficiencies, flexural deficiencies, or shear deficiencies, is used to evaluate the recoverability of such retrofitted columns. The residual deformation, as a seismic performance measure, is used to evaluate the performance of 39 FRP-retrofitted RC columns from the available database. Based on this evaluation, a requirement for the recoverable and irrecoverable states of FRP-RC bridges is specified. Finally, the Seismic Design Specifications of Highway Bridges for RC piers is adapted to predict the residual deformations of FRP-RC columns.