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 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.     

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 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.     

Seismic Performance of Concrete-Filled FRP Tube Columns for Bridge Substructure

A set of column-footing subassemblies were prepared to investigate construction feasibility and seismic performance of structural joints for concrete-filled fiber reinforced polymer (FRP) tubes (CFFT) as bridge substructure. Based on the common practices of the precast industry and previous research on CFFT, the test matrix included a control reinforced concrete (RC) column and three CFFT columns, all with similar RC footings. The three CFFT columns included a cast-in-place CFFT column with starter bars, a precast CFFT column with grouted starter bars, and a precast CFFT column with unbonded posttensioned rods. The columns were subjected to a constant axial load and a pseudostatic lateral load. All proposed joints proved feasible in construction and robust under extreme load conditions. FRP tube, when secured properly in the footing, showed great influence on the seismic performance of the column by providing both longitudinal reinforcement and hoop confinement to the core concrete. The CFFT columns exhibited significant improvement over traditional RC columns in both ultimate strength and ductility. The study also showed that practices of the precast concrete industry can be easily and effectively implemented for the CFFT column construction.     

Vulnerability Screening and Capacity Assessment of Reinforced Concrete Columns Subjected to Blast

In this study, a nonlinear model is developed to study the response of blast-loaded reinforced concrete (RC) columns. The strain rate dependency and the axial load and P?Δ effects on the flexural rigidity variation along the column heights were implemented in the model. Strain rate and axial load effects on a typical RC column cross section were investigated by developing strain-rate-dependent moment-curvature relationships and force-moment interaction diagrams. Analysis results showed that the column cross section strength and deformation capacity are highly dependent on the level of strain rates. Pressure-impulse diagrams were developed for two different column heights with two different end connection details (ductile and nonductile) and the effects of the axial load on the column midheight deflection and end rotation at failure were evaluated for both connection types. Based on the results of this study, a pressure-impulse band (PIB) technique is proposed. The PIB technique presents a useful tool that covers practical uncertainties associated with RC column reinforcement details as well as possible increase of column axial loads resulting from different blast-induced progressive collapse scenarios. Finally, the uses of the PIB technique for vulnerability screening of critical infrastructure or postblast capacity assessment of RC columns of target structures are presented.     

Effects of Corrosion of Steel Reinforcement on RC Columns Wrapped with FRP Sheets

This study investigated the effectiveness of carbon fiber-reinforced polymer (CFRP) sheets in protecting reinforced concrete (RC) columns from corrosion of steel reinforcement. Thirty small-scale RC columns and four midscale RC columns were used in this study. The small-scale columns were used for a comprehensive parametric study, whereas the midscale columns were used to evaluate design guidelines proposed based on the results of the small-scale column tests. The test columns were conditioned under an accelerated corrosion process and then tested under uniaxial compression up to failure. The test results showed that although CFRP sheet wrapping decreased the corrosion rate, the corrosion of steel reinforcement could continue to occur, eventually showing a decrease in ultimate axial compression capacity. Design guidelines were proposed based on the small-scale RC column tests and evaluated through a comparison with the test results of midscale RC columns. The proposed design guidelines introduced a concept of effective area to account for the corrosion damage, such as internal cracking and cross-sectional loss of steel reinforcement.     

Prestressed CFRP for Strengthening of Reinforced Concrete Structures: Recent Developments at Empa, Switzerland

In civil engineering today, only 20 to 30% of the strength of carbon-fiber-reinforced polymer (CFRP) strips is used when they are applied as externally bonded strips for flexural and shear strengthening or in confinement of reinforced concrete (RC) structural elements. The strips are better used when the CFRP material is prestressed. This offers several advantages, including reduced crack widths, reduced deflections, reduced stress in the internal steel, and possibly increased fatigue resistance. In this paper, recent developments in the field of RC strengthening using prestressed CFRP are presented. The paper focuses on developments in flexural and shear strengthening and column confinement made at the Swiss Federal Laboratory for Materials Testing and Research (Empa). Several innovative ideas have been successfully realized in the laboratory. For example, a gradient prestressing technique without end anchorage plates was developed and successfully applied to a 17?m RC bridge girder. A confinement technique using nonlaminated thermoplastic CFRP straps was also investigated and applied to 2?m high RC columns. These results are encouraging, although practical and theoretical problems remain to be solved before these techniques can be fully applied.     

Fiber-Reinforced Plastic Jackets for Ductility Enhancement of Reinforced Concrete Bridge Columns with Poor Lap-Splice Detailing

This paper presents an inclusive testing program conducted on scaled models of reinforced concrete (RC) bridge columns with insufficient lap-splice length. Thirteen half-scale circular and square column samples were tested in flexure under lateral cyclic loading. Three columns were tested in the as-built configuration whereas ten samples were tested after being retrofitted with different composite-jacket systems. A brittle failure was observed in the as-built samples due to bond deterioration of the lap-spliced longitudinal reinforcement. The jacketed circular columns demonstrated a significant improvement in their cyclic performance. Yet, tests conducted on square jacketed columns showed a limited improvement in clamping on the lap-splice region and for enhancing the ductility of the column.     

退化钢筋混凝土桥梁概率耐久性评估方法

提出了考虑时间、空间变异特性的退化钢筋混凝土桥梁耐久性概率评估的随机有限元方法.首先,通过考虑钢筋与混凝土之间时变的粘结滑移关系及腐蚀钢筋的应力应变关系,采用弥散裂纹方法对退化钢筋混凝土桥梁进行有限元分析.然后,提出了退化钢筋混凝土桥梁耐久性概率评估的随机有限元分析方法,基于文献及现场调查的数据,采用蒙特卡罗仿真方法对钢筋均匀及点锈蚀、混凝土保护层厚度、表面氯离子含量、氯离子扩散系数及腐蚀率等进行随机抽样,考虑这些时变及空间变异的因素对钢筋混凝土桥梁可靠度的影响.最后,以天津滨海新区的一座钢筋混凝土梁桥为例分析了所提方法的应用.     

Reliability-Based Optimization of Design Code for Tension Piles

A reliability-based calibration of a design code for offshore tension pile foundations in clay is presented by an example. The design against pullout in ultimate loading is considered. The calibration is performed by means of a numerical optimization technique in conjunction with probabilistic and deterministic models for load and capacity. The probabilistic models allow for predictions of the reliability against pullout. The deterministic models express design load and design capacity in terms of characteristic values and partial safety factors. The code calibration consists of determination of the partial safety factors such that—over a specified scope of code—designs with reliabilities with minimum deviations from some prescribed target reliability result when applying the deterministic models with this particular set of partial safety factors. For tutorial purposes, the scope of code is represented by a limited number of design cases, and emphasis is placed on the demonstration of the code calibration principles and a proper formulation of the code format.     

CFRP-Based Strengthening Technique to Increase the Flexural and Energy Dissipation Capacities of RC Columns

A strengthening technique, combining carbon fiber-reinforced polymer (CFRP) laminates and strips of wet layup CFRP sheet, is used to increase both the flexural and the energy dissipation capacities of reinforced concrete (RC) columns of square cross section of low to moderate concrete strength class, subjected to constant axial compressive load and increasing lateral cyclic loading. The laminates were applied according to the near surface mounted technique to increase the flexural resistance of the columns, while the strips of CFRP sheet were installed according to the externally bonded reinforcement technique to enhance the concrete confinement, particularly in the plastic hinge zone where they also offer resistance to the buckling and debonding of the laminates and longitudinal steel bars. The performance of this strengthening technique is assessed in undamaged RC columns and in columns that were subjected to intense damage. The influence of the concrete strength and percentage of longitudinal steel bars on the strengthening effectiveness is assessed. In the groups of RC columns of 8 MPa concrete compressive strength, this technique provided an increase of about 67% and 46% in terms of column’s load carrying capacity, when applied to undamaged and damaged columns, respectively. In terms of energy dissipation capacity, the increase ranged from 40%–87% in the undamaged columns, while a significant increase of about 39% was only observed in one of the damaged columns. In the column of moderate concrete compressive strength (29 MPa), the technique was even much more effective, since, when compared to the maximum load and energy dissipation capacity of the corresponding strengthened column of 8 MPa of average compressive strength, it provided an increase of 39% and 109%, respectively, showing its appropriateness for RC columns of buildings requiring upgrading against seismic events.     

Single-Parameter Methodology for the Prediction of the Stress-Strain Behavior of FRP-Confined RC Square Columns

The study presented in this paper proposes a new theoretical framework to interpret and capture the mechanics of the fiber-reinforced polymer (FRP) confinement of square reinforced concrete (RC) columns subjected to pure compressive loads. The geometrical and mechanical parameters governing the problem are analyzed and discussed. A single-parameter methodology for predicting the axial stress–axial strain curve for FRP-confined square RC columns is described. Fundamentals, basic assumptions, and limitations are discussed. A simple design example is also presented.     

Bond Strength of Lap-Spliced Bars in Concrete Confined with Composite Jackets

The effectiveness of fiber-reinforced polymer (FRP) and textile-reinforced mortar (TRM) jackets was investigated experimentally and analytically in this study to confine old-type reinforced concrete (RC) columns with limited capacity because of bond failure at lap-splice regions. The local bond strength between lap-spliced bars and concrete was measured experimentally along the lap-splice region of six full-scale RC columns subjected to cyclic uniaxial flexure under constant axial load. The bond strength of the two column specimens tested without retrofitting was found to be in good agreement with the predictions given by two existing bond models. These models were modified to account for the contribution of composite material jacketing to the bond resistance between lap-spliced bars and concrete. The effectiveness of FRP and TRM jackets against splitting at lap splices was quantified as a function of jacket properties and geometry as well as in terms of the jacket effective strain, which was found to depend on the ratio of lap-splice length to bar diameter. Consequently, simple equations for calculating the bond strength of lap splices in members confined with composite materials (FRP or TRM) are proposed.     

Nonlinear Earthquake Response Modeling of a Large-Scale Two-Span Concrete Bridge

A quarter scale model of a two-span RC bridge was tested using the Network for Earthquake Engineering Simulation (NEES) multiple shake table system at the University of Nevada, Reno, Nev. The project was funded through a National Science Foundation-NEES demonstration grant. The bridge system was tested from a preyield state until column failure. In depth analytical modeling was conducted to determine the effectiveness of current structural analysis software and methodology in predicting the bridge model response. Both SAP2000 v.9 and Drain-3DX were used for this purpose. Both models produced reasonable results up to column failure, however, the Drain-3DX model was determined to be most effective to predict the nonlinear bridge model response. Parametric studies were conducted to investigate optimal element discretization and integration parameters. Existing equations for pre and postyield column shear stiffness showed good correlation when compared with the measured data.     

Seismic Behavior of RC Columns with Bond-Critical Regions: Criteria for Bond Strengthening Using External FRP Jackets

In 2003, an experimental research program was initiated at the American University of Beirut with the objectives of (1) evaluating the effectiveness of external fiber-reinforced polymer (FRP) confinement in improving the bond strength of spliced reinforcement in reinforced-concrete (RC) columns and its implications on the lateral load capacity and ductility of the columns under seismic loading; and (2) establishing rational design criteria for bond strengthening of spliced reinforcement using external FRP jackets. This paper presents a discussion of recent experimental results dealing with rectangular columns and the results of a pilot study conducted on circular columns with particular emphasis on aspects related to the bond strength of the spliced column reinforcement. A nonlinear analysis model is developed for predicting the envelope load–drift response, taking into account the effect of FRP confinement on the stress–strain behavior of concrete in compression. Results predicted by the model showed excellent agreement with the test results. Design expressions of the bond strength of spliced bars in FRP-confined concrete were assessed against the current experimental data, and a criterion for seismic FRP strengthening of bond-critical regions in RC members is proposed.     

Closed-Form Sensitivity of Earthquake Input Energy to Soil-Structure Interaction System

The input energy to a soil-structure interaction (SSI) system during earthquake shaking is taken as a structural performance measure and is formulated in the frequency domain. The purpose of this paper is to derive the closed-form expression of the sensitivity of the input energy to the SSI system with respect to uncertain parameters representing soil stiffness and damping. It is demonstrated first that the input energy expression can be of a compact form consisting of the product between the input motion component (Fourier amplitude spectrum of acceleration) and the structural model component (so-called energy transfer function). With the help of this compact form, it is shown that the formulation of earthquake input energy in the frequency domain is essential for deriving the closed-form expressions of the sensitivity of the input energy to the SSI system with respect to uncertain parameters in contrast to the time-domain formulation including inevitable numerical error and instability. This formulation is then extended to a multidegree-of-freedom superstructure model. Numerical examples support the fact that the closed-form expressions enable one to find in a reliable and efficient way the most critical combination of the uncertain parameters that leads to the maximum energy input.     

Seismic Fragility Analysis of Structural Systems

A method is presented for the evaluation of the seismic fragility function of realistic structural systems. The method is based on a preliminary, limited, simulation involving nonlinear dynamic analyses performed to establish the probabilistic characterization of the demands on the structure, followed by the solution of a general system reliability problem with correlated demands and capacities. The results compare favorably with the fragility obtained by plain Monte Carlo simulation, while the associated computational effort is orders of magnitude lower. The method is demonstrated with two applications, a steel-concrete box girder viaduct with RC piers subjected to both uniform and nonuniform excitations, and a three-dimensional RC building structure subjected to bidirectional excitation.     

R-Factor Parameterized Bridge Damage Fragility Curves

Damage fragilities describe the probability that a bridge will incur certain (discrete) damage states conditioned on the intensity of the earthquake it may experience. Reinforced concrete box girder highway overpass bridges are prevalent among the total inventory of bridges in California. For this class of bridges, a method for computing damage fragilities for three damage states (concrete cover spalling, longitudinal bar buckling, and column failure) based on the bridge force reduction factors (R-factors) is derived in this paper. Bridge damage fragilities are described by equations relating the median intensity and uncertainty of ground motion to discrete damage states of column concrete cover spalling, column bar buckling, and column failure using the bridge R-factor as the principal parameter describing the bridge structure. Such damage fragility equations are furnished for earthquake intensities measured using pseudospectral acceleration (Sa) and cumulative absolute displacement (CAD) in both the bridge longitudinal and transverse directions.