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.     

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.     

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.     

Seismic Testing of a Two-Span Reinforced Concrete Bridge

A quarter-scale, two-span reinforced concrete bridge was tested using the shake-table system at the University of Nevada, Reno. The shake-table tests were part of a multiuniversity, multidisciplinary project utilizing the network for earthquake engineering simulation, with the objective of investigating the effects of soil-foundation-structure interaction on bridges. This paper discusses the development and testing of the bridge model, and selected experimental results, including those that demonstrate the effects of incoherent motions and stiffness irregularities on the distribution of forces and deformations within the bridge system. Motion incoherency affected the asymmetric bridge response (planar torsion of the superstructure), but had little effect on the symmetric bridge response (center-of-mass displacement of the superstructure). These experimental findings are consistent with conclusions from numerical analyses conducted by other researchers. During a 2.0?g PGA earthquake excitation, numerous longitudinal bars buckled and fractured at a drift ratio between 5.5 and 7.9%. Despite the level of damage, detailing of the column transverse reinforcement according to NCHRP 12-49 guidelines provided sufficient column ductility to prevent collapse during a subsequent 1.4?g PGA earthquake excitation.     

Seismic Behavior of Flexural Dominated Reinforced Concrete Bridge Columns at Low Temperatures

This paper presents the results from Phase II of an experimental study on the behavior of reinforced concrete bridge columns in cold seismicly active regions. Six half-scale circular reinforced concrete columns, designed to be flexural dominated, were tested under reversed cyclic loading while subjected to temperatures ranging from ?36°C (?33°F) to 22°C (72°F). Four of the units tested were reinforced concrete filled steel tube (RCFST) columns and the other two were ordinary reinforced concrete columns. Results obtained reiterated the observations made in Phase I, which is that low temperatures cause an increase in the flexural strength and initial stiffness as well as a reduction in the spread of plasticity and displacement capacity of the column. Another important observation made was that the plastic hinge length is drastically reduced in the RCFST units compromising the displacement capacity of this type of column even at room temperature conditions. Current predictive models were revised and modified to account for the low-temperature effect.     

Seismic Behavior of Concrete Columns Reinforced by Steel-FRP Composite Bars

Steel-fiber-reinforced polymer (FRP) composite bars (SFCBs) are a novel reinforcement for concrete structures. Because of the FRP’s linear elastic characteristic and high ultimate strength, they can achieve a stable postyield stiffness even after the inner steel bar has yielded, which subsequently enables a performance-based seismic design to easily be implemented. In this study, lateral cyclic loading tests of concrete columns reinforced either by SFCBs or by ordinary steel bars were conducted with axial compression ratios of 0.12. The main variable parameters were the FRP type (basalt or carbon FRP) and the steel/FRP ratio of the SFCBs. The test results showed the following: (1)?compared with ordinary RC columns, SFCB-reinforced concrete columns had a stable postyield stiffness after the SFCB’s inner steel bar yielded; (2)?because of the postyield stiffness of the SFCB, the SFCB-reinforced concrete columns exhibited less column-base curvature demand than ordinary RC columns for a given column cap lateral deformation. Thus, reduced unloading residual deformation (i.e., higher postearthquake reparability) of SFCB columns could be achieved; (3)?the outer FRP type of SFCB had a direct influence on the performance of SFCB-reinforced concrete columns, and concrete columns reinforced with steel-basalt FRP (BFRP) composite bars exhibited better ductility (i.e., a longer effective length of postyield stiffness) and a smaller unloading residual deformation under the same unloading displacement when compared with steel-carbon FRP (CFRP) composite bar columns; (4)?the degradation of the unloading stiffness by an ordinary RC column based on the Takeda (TK) model was only suitable at a certain lateral displacement. In evaluating the reparability of important structures at the small plastic deformation stage, the TK model estimated a much smaller residual displacement, which is unsafe for important structures.     

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.     

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.     

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.     

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.     

Experimental Study of Seismic Behaviors of As-Built and Carbon Fiber Reinforced Plastics Repaired Reinforced Concrete Bridge Columns

In order to reliably obtain seismic responses of as-built and repaired reinforced concrete bridge columns under near-fault ground motions, pseudodynamic testing of two bridge columns with a reduced scale of 2/5 was performed. Pseudodynamic test results reveal that a ductile member may have no chance to entirely develop its ductile behavior to dissipate seismic energy, because it may suddenly be destroyed by a significant pulse-like wave. The seismic performance of the two damaged bridge columns can be recovered after repair with carbon fiber reinforced plastics composite sheets. It is also experimentally confirmed that the flexural failure moment obtained from the pseudodynamic test is in good agreement with the plastic moment predicted by the ACI 318 code. As pseudodynamic test results are believed to be more accurate than numerical solutions, they can be considered as reference solutions in developing a finite-element model. An identical specimen was tested under cyclic loading to estimate basic properties of these columns, such as shear strength, flexural strength, and ductility, so that the seismic responses obtained from pseudodynamic tests can be thoroughly discussed. Furthermore, its hysteretic response may also be used to match a mathematical model to simulate the very complicated load-displacement relation for analysis.     

Probabilistic Models for Modulus of Elasticity of Self-Consolidated Concrete: Bayesian Approach

Current models of the modulus of elasticity, E, of concrete recommended by the American Concrete Institute and the American Association of State Highway and Transportation Officials are derived for normally vibrated concrete (NVC). Because self-consolidated concrete (SCC) mixtures differ from NVC in the quantities and types of constituent materials, supplementary cementing materials, and chemical admixtures, the current models, may not take into consideration the complexity of SCC, and thus they may predict the E of SCC inaccurately. Although some authors recommend specific models to predict E of SCC, they include only a single variable of assumed importance, namely, the design compressive strength of concrete, fc′. However, there are other parameters that may need to be accounted for while developing a prediction model for E of SCC. In this paper, a Bayesian variable selection method is used to identify the significant parameters in predicting the E of SCC, and more accurate models for E are generated using these variables. The models have a parsimonious parametrization for ease of use in practice and properly account for the prevailing uncertainties.     

Quick Seismic Response Estimation of Prestressed Concrete Bridges Using Artificial Neural Networks

Seismic early warning has been very important and has become feasible in Taiwan. Perhaps because of the lack of quick and reliable estimations of the induced structural response, however, the triggering criteria of almost all of the existing earthquake protection or early warning systems in the world are merely based on the collected or estimated data of the ground motion, without any information regarding the structural response. This paper presents a methodology of generating quick seismic response estimations of a prestressed concrete (PC) bridge using artificial neural networks (ANNs), which may be incorporated in a seismic early warning system for the bridge. In the methodology ANNs were applied to model the critical structural response of a PC bridge subjected to earthquake excitation of various magnitudes along various directions. The objective was to implement a well-trained network that is capable of providing a quick prediction for the critical response of the target bridge. The well-known multilayer perception (MLP) networks with back propagation algorithm were employed. A simple augmented form of MLP that can be quantitatively determined was proposed. These networks were trained and tested based on the analytical data obtained from the nonlinear dynamic finite fiber element analyses of the target PC bridge. The augmented MLPs were found to be much more efficient than the MLPs in modeling the critical bending moments of the piers and girder of the PC 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.     

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.     

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.