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.     

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.     

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.     

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.     

Estimating Liquefaction-Induced Lateral Displacements Using the Standard Penetration Test or Cone Penetration Test

A semiempirical approach to estimate liquefaction-induced lateral displacements using standard penetration test (SPT) or cone penetration test (CPT) data is presented. The approach combines available SPT- and CPT-based methods to evaluate liquefaction potential with laboratory test results for clean sands to estimate the potential maximum cyclic shear strains for saturated sandy soils under seismic loading. A lateral displacement index is then introduced, which is obtained by integrating the maximum cyclic shear strains with depth. Empirical correlations from case history data are proposed between actual lateral displacement, the lateral displacement index, and geometric parameters characterizing ground geometry for gently sloping ground without a free face, level ground with a free face, and gently sloping ground with a free face. The proposed approach can be applied to obtain preliminary estimates of the magnitude of lateral displacements associated with a liquefaction-induced lateral spread.     

Bidirectional Pseudodynamic Tests of Bridge Piers Designed to Different Standards

Circular reinforced concrete highway bridge piers, designed in accordance with the requirements of the California Department of Transportation (Caltrans) in the U.S., New Zealand, and Japanese specifications, are experimentally investigated to assess their seismic performance. Pseudodynamic test procedures are developed to perform experiments on 30% scaled models of the three prototype bridge piers. Each specimen is subjected to a sequence of three different earthquake ground motions scaled appropriately to represent: (1) the design basis earthquake (DBE) with a 90% nonexceedance probability; (2) the maximum considered earthquake (MCE) with a 50% nonexceedance probability; and (3) the MCE with a 90% nonexceedance probability. Damage states after the earthquakes are assessed and mapped for seismic risk assessment. The damage outcomes and the corresponding seismic risks validate the objectives of the performance-based design codes of the three countries. The results show that when bridge piers are designed to the specifications of each of the three countries, satisfactory performance with only slight to moderate damage can be expected for DBE. For the MCE, severe damage without collapse is likely for the Caltrans and Japanese piers. However, the NZ pier may not be able to survive MCE motions with sufficient reliability to ensure the preservation of life-safety.     

Seismic Effect on Highway Bridges in Chi Chi Earthquake

This paper reports the bridge damage in the Chi Chi earthquake. Damage to bridge structures may occur in the superstructure, the substructure, or the approaches. Typical types of damage are discussed and illustrated in this paper. A review of the design specifications in Taiwan is also presented to give the background on the seismic design of highway bridges in Taiwan.     

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.     

Vulnerability Assessment of Cable-Stayed Bridges in Probabilistic Domain

Vulnerability of a structure under terrorist attack can be regarded as the study of its behavior against blast-induced loads. A structure is vulnerable if a small damage can trigger a disproportionately large consequence and lead to a cascade of failure events or even collapse. The performance of structural vulnerability depends upon factors such as external loading condition and structural properties. As many of these factors are random in nature, it is necessary to develop a vulnerability assessment technique in the probabilistic domain. In this study, one such assessment framework is proposed for cable-stayed bridges. The framework consists of two stages of analysis: determining the probability of direct damage due to blast loads and assessing the subsequent probability of collapse due to component damage. In the first stage assessment, damage of the bridge component is defined as the exceedance of a predefined limit state such as displacement or yielding. The damage probability is obtained through a stochastic finite-element analysis and the first-order second-moment reliability method. The second stage assessment further calculates the probability of collapse due to direct damage of some component via an event tree approach. The proposed assessment methods are illustrated on a hypothetical single-tower cable-stayed bridge. It is seen that the proposed methods provide a quantitative tool for analyzing the vulnerability performance of cable-stayed bridges under terrorist attack.     

Implications of Design Assumptions on Capacity Estimates and Demand Predictions of Multispan Curved Bridges

The paper presents a detailed seismic performance assessment of a complex bridge designed as a reference application of modern codes for the Federal Highway Administration. The assessment utilizes state-of-the-art assessment tools and response metrics. The impact of design assumptions on the capacity estimates and demand predictions of the multispan curved bridge is investigated. The level of attention to detail is significantly higher than can be achieved in a mass parametric study of a population of bridges. The objective of in-depth assessment is achieved through investigation of the bridge using two models. The first represents the bridge as designed (including features assumed in the design process) while the second represents the bridge as built (actual expected characteristics). Three-dimensional detailed dynamic response simulations of the investigated bridge, including soil-structure interaction, are undertaken. The behavior of the as-designed bridge is investigated using two different analytical platforms for elastic and inelastic analysis, for the purposes of verification. A third idealization is adopted to investigate the as-built bridge’s behavior by realistically modeling bridge bearings, structural gaps, and materials. A comprehensive list of local and global, action and deformation performance indicators, including bearing slippage and inter-segment collision, are selected to monitor the response to earthquake ground motion. The comparative study has indicated that the lateral capacity and dynamic characteristics of the as-designed bridge are significantly different from the as-built bridge’s behavior. The potential of pushover analysis in identifying structural deficiencies, estimating capacities, and providing insight into the pertinent limit state criteria is demonstrated. Comparison of seismic demand with available capacity shows that seemingly conservative design assumptions, such as ignoring friction at the bearings, may lead to an erroneous and potentially nonconservative response expectation. The recommendations assist be given to design engineers seeking to achieve realistic predictions of seismic behavior and thus contribute to uncertainty reduction in the ensuing design.     

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.     

Seismic Retrofit of Hollow Rectangular Bridge Columns

The seismic performance of rectangular hollow bridge columns is a significant issue of the high-speed rail project in Taiwan. The flexural ductility and shear capacity of such columns with the configuration of lateral reinforcement used in Taiwan have been studied recently. This paper reports that hollow rectangular bridge columns retrofitted with fiber-reinforced polymer (FRP) sheets were tested under a constant axial load and a cyclically reversed horizontal load to investigate their seismic behavior, including flexural ductility, dissipated energy, and shear capacity. An analytical model was also developed to predict the moment-curvature curve of sections and the load-displacement relationship of columns. Based on the test results, the seismic behavior of such columns will be presented. The test results were also compared to the proposed analytical model. It was found that the ductility factors of the tested piers are in the range from 3.4 to 6.3, and the proposed analytical model can predict the load-displacement relationship of such columns with acceptable accuracy. All in all, FRP sheets can effectively improve both the ductility factor and shear capacity of hollow rectangular bridge columns.     

Seismic Repair and Strengthening of Lap Splices in RC Columns: Carbon Fiber–Reinforced Polymer versus Steel Confinement

A design approach, developed specifically for seismic bond strengthening of the critical splice region of reinforced concrete columns or bridge piers, is presented and discussed. The approach is based on providing adequate concrete confinement within the splice zone for allowing the spliced bars to theoretically develop enough postelastic tension strains demanded by large earthquakes before experiencing splitting bond failure. The accuracy of the approach was validated experimentally by evaluating the seismic behavior of full-scale gravity load-designed (as-built) rectangular columns that were strengthened or repaired in accordance with the proposed approach. Three types of confinement were used and compared, namely, internal steel ties, external fiber polymer reinforced jackets, and a combination of both. The repaired/strengthened columns developed sizable postyield strains of the spliced bars, considerable increases in the lateral load and drift capacities, and much less concrete damage within the splice zone when compared with the as-built columns. As a further support of the adequacy of the design strengthening approach, the backbone lateral load-drift response of the strengthened columns showed a good agreement with the envelope response generated using nonlinear flexural analysis assuming perfect bond between the column reinforcement and concrete.     

Frequency-Domain Analysis of Long-Span Bridges Subjected to Nonuniform Seismic Motions

Nonuniform seismic motion affects the seismic behavior of long-span bridges. Three main reasons for this nonuniformity have been identified. They are local soil conditions, wave passage, and incoherency effects. Other effects, such as extended source and attenuation, are relatively small. The importance of nonuniform seismic motions, especially for sensitive and important structures, has led to the development of several methods of analysis. These methods can be subdivided into two general categories, deterministic and stochastic. Because of the inherent uncertainty of the nonuniform seismic motions, deterministic methods, mainly time integration methods, can be computationally inefficient. Stochastic methods have been based mainly on modal analysis methods. The input/output are described in terms of either power spectral density or response spectra. This paper presents a direct frequency-domain method that is based on formulating the whole soil-structure problem. The use of this direct frequency-domain method for solving nonuniform seismic support motions is shown. The application of the proposed method to a simple 2D bridge and a long-span suspension bridge is presented. Several observations were made. It is observed that nonuniform support motions may result in a large shifting of resonant frequencies of the structure. Also, large redistribution of bridge responses and internal forces were observed when using nonuniform seismic motions when compared with the uniform seismic motions case.     

Elastic-Plastic Seismic Behavior of Long Span Cable-Stayed Bridges

This paper investigates the elastic-plastic seismic behavior of long span cable-stayed steel bridges through the plane finite-element model. Both geometric and material nonlinearities are involved in the analysis. The geometric nonlinearities come from the stay cable sag effect, axial force-bending moment interaction, and large displacements. Material nonlinearity arises when the stiffening steel girder yields. The example bridge is a cable-stayed bridge with a central span length of 605 m. The seismic response analyses have been conducted from the deformed equilibrium configuration due to dead loads. Three strong earthquake records of the Great Hanshin earthquake of 1995 in Japan are used in the analysis. These earthquake records are input in the bridge longitudinal direction, vertical direction, and combined longitudinal and vertical directions. To evaluate the residual elastic-plastic seismic response, a new kind of seismic damage index called the maximum equivalent plastic strain ratio is proposed. The results show that the elastic-plastic effect tends to reduce the seismic response of long span cable-stayed steel bridges. The elastic and elastic-plastic seismic response behavior depends highly on the characteristics of input earthquake records. The earthquake record with the largest peak ground acceleration value does not necessarily induce the greatest elastic-plastic seismic damage.     

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.     

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.     

基于耐震时程法的连续刚构桥地震损伤分析

探讨了在真实成桥内力状态下,耐震时程法(Endurance time method,ETM)评估连续刚构桥地震反应与损伤的准确性和有效性. 以一座典型非规则连续刚构桥为背景,采用MIDAS/Civil模拟实际施工过程,经施工阶段分析得到10 a收缩徐变下的成桥内力状态,再借助等效荷载法建立考虑成桥内力状态的OpenSees动力分析模型;通过与天然地震动下的增量动力分析(Incremental dynamic analysis,IDA)结果相对比,验证了采用ETM可快速准确地得到地震反应的适用性;通过该方法分析了墩顶位移、梁端位移及碰撞力等地震反应,并采用位移延性系数和Park?Ang损伤指数对桥墩损伤进行了量化分析与评估. 结果表明:ETM可以有效地预测真实成桥内力状态下连续刚构桥达到某一损伤程度的时间;耐震时间较短时主桥桥墩较引桥桥墩的损伤要小,耐震时间较长时则反之.      

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.