Development of Static-Response-Based Objective Functions for Finite-Element Modeling of Bridges

The basic mechanisms and procedures of finite-element (FE) modeling and calibration are briefly presented in the context of bridge condition assessment. Different physical parameters of FE models are adjusted to simulate experimental measurements. To quantify the calibration process, static-response-based objective functions are carefully developed based on two powerful condition indices: bridge girder condition indicators and unit influence lines. Critical issues related to the indices are discussed in detail. Using an existing calibration strategy, a nominal FE bridge model is optimized by minimizing this global static-response-based objective function. The value of the objective function is reduced from 12.98 to 4.45%, which indicates convergence of the calibration process. It is shown that the automated calibration becomes practical due to the formulation of the static-response-based objective function.     

Development of Dynamic-Response-Based Objective Functions for Finite-Element Modeling of Bridges

The basic mechanism and procedures of finite-element (FE) bridge modeling and calibration are briefly presented. Different physical parameters of FE models are adjusted during the calibration process. Dynamic-response-based objective functions are carefully developed based on two powerful indices: the modal assurance criterion and frequency correlation trend line. The nominal bridge models are calibrated by minimizing the quantified difference between analytical results and experimental measurements. Using an existing calibration strategy, a nominal FE bridge model is optimized by minimizing this global dynamic-response-based objective function. The value of the objective function is reduced from 10.70 to 4.61%. The minimization of the objective function indicates the convergence of calibration and it is shown that the automated calibration becomes practical due to the formulation of the dynamic-response-based objective function.     

Modal Contribution Coefficients in Bridge Condition Evaluation

Impact modal testing combined with finite element (FE) analyses is currently being used to evaluate the condition of steel bridges in the state of Ohio. Using modal testing techniques, it is relatively easy to measure the dynamic response of bridges, including mode shapes, frequencies, and modal scaling factors. These responses are compared to the results of the FE analyses and the model is iteratively updated until a good agreement is obtained. After a good agreement between experimental and analytical results has been achieved, the FE model is used to obtain stresses that are used to load rate the bridge. During the iterative calibration process, several quantities, including the fundamental mode shapes and frequencies, are used to evaluate the accuracy of the FE model. Since each mode shape plays a different role in the dynamic behavior of the structure, a more efficient calibration routine can be achieved if more emphasis is placed on obtaining good matches for the modes that are most influential. The aim of this paper is to develop a quantitative measure of the contribution of different modes to the overall dynamic response of a structure. The proposed measure, a series of contribution coefficients, is used to identify which modes are most critical in the process of modal testing and FE model calibration. Several applications of the contribution coefficients are identified.     

Fuzzy Logic Based Condition Rating of Existing Reinforced Concrete Bridges

Fuzzy logic is a means for modeling the uncertainty involved in describing an event/result using natural language. The fuzzy logic approach would be particularly useful for remedying the uncertainties and imprecision in bridge inspectors’ observations. This study explores the possibilities of using fuzzy mathematics for condition assessment and rating of bridges, developing a systematic procedure and formulations for rating existing bridges using fuzzy mathematics. Computer programs developed from formulations presented in this paper are used for evaluating the rating of existing bridges, and the details are presented in the paper. In this approach, the entire bridge has been divided into three major components—deck, superstructure, and substructure—each of which is further subdivided into a number of elements. Using fuzzy mathematics in combination with an eigenvector-based priority setting approach, the resultant rating set for the bridge has been evaluated based on the specified ratings and importance factors for all the elements of the bridge. Then the defuzzified value of the resultant rating fuzzy set becomes the rating value for the bridge as a whole. It is argued that the methodology presented in this paper would help the decision makers/bridge inspectors immensely.     

Rating and Reliability of Existing Bridges in a Network

Currently, the load rating is the method used by State DOTs for evaluating the safety and serviceability of existing bridges in the United States. In general, load rating of a bridge is evaluated when a maintenance, improvement work, change in strength of members, or addition of dead load alters the condition or capacity of the structure. The AASHTO LRFD specifications provide code provisions for prescribing an acceptable and uniform safety level for the design of bridge components. Once a bridge is designed and placed in service, the AASHTO Manual for Condition Evaluation of Bridges provides provisions for determination of the safety and serviceability of existing bridge components. Rating for the bridge system is taken as the minimum of the component ratings. If viewed from a broad perspective, methods used in the state-of-the-practice condition evaluation of bridges at discrete time intervals and in the state-of-the-art probability-based life prediction share common goals and principles. This paper briefly describes a study conducted on the rating and system reliability-based lifetime evaluation of a number of existing bridges within a bridge network, including prestressed concrete, reinforced concrete, steel rolled beam, and steel plate girder bridges. The approach is explained using a representative prestressed concrete girder bridge. Emphasis is placed on the interaction between rating and reliability results in order to relate the developed approach to current practice in bridge rating and evaluation. The results presented provide a sound basis for further improvement of bridge management systems based on system performance requirements.     

Reliability-Based Load and Resistance Factor Rating Using In-Service Data

Traditional bridge evaluation techniques are based on design-based deterministic equations that use limited site-specific data. They do not necessarily conform to a quantifiable standard of safety and are often quite conservative. The newly emerging load and resistance factor rating (LRFR) method addresses some of these shortcomings and allows bridge rating in a manner consistent with load and resistance factor design (LRFD) but is not based on site-specific information. This paper presents a probability-based methodology for load-rating bridges by using site-specific in-service structural response data in an LRFR format. The use of a site-specific structural response allows the elimination of a substantial portion of modeling uncertainty in live load characterization (involving dynamic impact and girder distribution), which leads to more accurate bridge ratings. Rating at two different limit states, yield and plastic collapse, is proposed for specified service lives and target reliabilities. We consider a conditional Poisson occurrence of identically distributed and statistically independent (i.i.d.) loads, uncertainties in field measurement, modeling uncertainties, and Bayesian updating of the empirical distribution function to obtain an extreme-value distribution of the time-dependent maximum live load. An illustrative example uses in-service peak-strain data from ambient traffic collected on a high-volume bridge. Serial independence of the collected peak strains and of the counting process, as well as the asymptotic behavior of the extreme peak-strain values, are investigated. A set of in-service load and resistance factor rating (ISLRFR) equations optimized for a suite of bridges is developed. Results from the proposed methodology are compared with ratings derived from more traditional methods.     

Long-Term Structural Health Monitoring of the San Ysidro Bridge

As part of the Lifecycle Innovative Financing Evaluation initiative, the San Ysidro Bridge along U.S. Route 550 will be monitored throughout a 10?year warranty period to determine changes in deflection, stiffness, and load-carrying capacity. This paper discusses an initial live-load test on the San Ysidro Bridge as well as a subsequent load test on a full-scale single lane test bridge. The two load tests in conjunction with finite element modeling were used to determine the load rating for both shear and moment of the San Ysidro Bridge. This load rating was then compared with the load rating using the distribution factors from the American Association of State Highway and Transportation Officials (AASHTO) Standard and Load and Resistance Factor Design Specifications. According to both AASHTO specifications, the interior girder shear controlled the load rating of the San Ysidro Bridge. Using the finite element modeling scheme of frame and shell elements the interior girder moment was found to control the design. This load rating will be used as a baseline for comparison with future load ratings throughout the warranty period.     

Quantifying Field-Test Behavior for Rating Steel Girder Bridges

Field testing is valuable for evaluating existing bridges. It allows the owner to reduce the conservatism of analytical rating methods and safely rate the bridge for higher loads. Many factors not considered in design contribute to the response of a tested bridge. Several of these, like actual load distribution and additional stiffness from curbs and railings, are welcome benefits that can be used to increase load ratings. However, there are also contributions from bearing restraint forces and unintended composite action that may not be reliable during the bridge's service life. These factors tending to increase the load capacity need to be separated and quantified so that the bridge owner can: (1) confirm the origin of the useable benefit; and (2) remove the unwanted contributions. Presented are procedures for load rating steel girder bridges through field testing. A systematic approach is presented to separate and quantify the contributions from various effects. Therefore, the responsible engineer can remove the unwanted contributions and justify an experimental load rating. The procedures are demonstrated for a three-span steel girder bridge.     

Roebling Suspension Bridge. II: Ambient Testing and Live-Load Response

This is the second part of a two-part paper on the evaluation of the historic Roebling suspension bridge using dynamic-analysis techniques. Dynamic properties are determined using ambient field testing under natural excitation. The finite-element (FE) model described in the first part of this two-part paper is modified to more accurately represent current bridge properties. Modifications of the model are based on correlating the FE model frequencies with ambient test frequencies by adjusting the FE model stiffness parameters. The updated 3D FE model is subsequently subjected to an extreme live-load condition to evaluate static safety margins. In addition, cable areas are reduced by 10 to 40% to simulate further deterioration and corrosion. The safety margin of the main cables is demonstrated to be good even when assuming a very conservative 40% cable area reduction, and truss member forces remain within the maximum load-carrying capacity even when the cable areas are reduced by 40%.     

Parameter Estimation for Multiple-Input Multiple-Output Modal Analysis of Large Structures

Experimental modal analysis (EMA) has been explored as a technology for condition assessment and damage identification of constructed structures. However, successful EMA applications such as damage detection to constructed systems pose certain difficulties. The properties of constructed systems are influenced by temperature changes as well as other natural influences such as movements in addition to any deterioration and damage. Writers were challenged in their attempts to measure the dynamic properties of an aged bridge by EMA due to inconsistencies within the data set due to short-term variations in ambient conditions. A complex interaction was observed between the dynamic properties of the bridge, hour-to-hour changes in temperature, and controlled damages applied to the bridge. Inconsistencies in the data set made curve fitting difficult for some common parameter estimation algorithms that have been designed to handle consistent data sets. Although the quality of measurements within the entire data set was affected by time variance and nonlinearity, increasing the number of reference measurements significantly improved the reliability of the information which could be extracted. In conjunction with the multiple-input multiple-output technique, a parameter estimation method using complex mode indicator function (CMIF) was developed and implemented in this study to determine the modal properties with proper scaling to obtain modal flexibility. This method proved to be very successful among many others with the data acquired from the aged and deteriorated highway bridge. In this paper, challenges in reliable identification of modal parameters from large structures are reviewed and the new CMIF based algorithm is documented. The method is evaluated on actual bridge data sets from a damage detection research study.     

Nonlinear Finite Element Analysis of a FRP-Strengthened Reinforced Concrete Bridge

Three-dimensional nonlinear finite element (FE) models are developed to examine the structural behavior of the Horsetail Creek Bridge strengthened by fiber-reinforced polymers (FRPs). A sensitivity study is performed varying bridge geometry, precracking load, strength of concrete, and stiffness of the soil foundation to establish a FE model that best represents the actual bridge. Truck loadings are applied to the FE bridge model at different locations, as in an actual bridge test. Comparisons between FE model predictions and field data are made in terms of strains in the beams for various truck load locations. It is found that all the parameters examined can potentially influence the bridge response and are needed for selection of the optimal model which predicts the magnitudes and trends in the strains accurately. Then, using the optimal model, performance evaluation of the bridge based on scaled truck and mass-proportional loadings is conducted. Each loading type is gradually increased until failure occurs. Structural responses are compared for strengthened and unstrengthened bridge models to evaluate the FRP retrofit. The models predict a significant improvement in structural performance due to the FRP retrofit.     

Evaluation of Load Distribution Factor by Series Solution for Orthotropic Bridge Decks

In bridge engineering, the three-dimensional behavior of a bridge system is usually reduced to the analysis of a T-beam section, loaded by an equivalent fraction of the applied live load, which is called the live load distribution factor (LDF). The LDF is defined in the both the AASHTO Standard Specifications and the LRFD Specifications primarily for concrete slabs and has inherent applicable limitations. This paper provides explicit formulas using series solutions for LDF of orthotropic bridge decks, applicable to various materials but intended for fiber-reinforced polymer (FRP) decks. The present formulation considers important parameters that represent the response characteristics of the structure that are often omitted or limited in the AASHTO Specifications. A one-term series solution is proposed based on the macroflexibility approach, in which the bridge system is simplified into two major components, deck and stringers. The governing equations for the two components are obtained separately, and the deflections and interaction forces are solved by ensuring displacement compatibility at stringer lines. The LDF is calculated as the ratio of the single stringer interaction force to the summation of total stringer interaction forces. To verify this solution, a finite-element (FE) parametric study is conducted on 66 simply supported concrete slab-on-steel girder bridges. The results from the series solution correlates well with the FE results. It is also illustrated that the series solution can be applied to predict LDF for FRP deck-on-steel girder bridges, by favorable comparisons among the analytical, FE, and testing results for a one-third-scale bridge model. The scale test specimen consists of an FRP sandwich deck attached to steel stringers by a mechanical connector. The series solution is further used to obtain multiple regression functions for the LDF in terms of nondimensional variables, which can be used for simplified design purposes.     

Proposal of an Integrated Index for Prioritization of Bridge Maintenance

The bridge rating used in bridge management systems commonly uses only a structural condition. Factors such as seismic risk, hydraulic vulnerability, and strategic importance are commonly used in an isolated fashion. However, these factors are relevant when there is no possibility to calibrate deterioration models. This research uses the needs-based framework for developing an integrated bridge index (IBI) as an aid for prioritization and decisions made on maintenance and rehabilitation of bridges. The index weighs the structure distresses, hydraulic vulnerability, seismic risk, and strategic importance of the bridge. The index was calibrated using visual inspection, survey to experts, and regression analysis. After, the index was applied on six bridges placed on a primary road of Chile. To organize visual inspection, bridge inventory, and compute IBI and rank bridges, a software was developed. The calibration of the IBI index shows a correlation of 98% and all the parameters obtained were significant. Further research is needed to integrate cost with the proposed index and allocate maintenance activities.     

Reliability-Based Assessment of Suspension Bridges: Application to the Innoshima Bridge

Many suspension and cable-stayed bridges were designed and constructed between Honshu Island and Shikoku Island in Japan. All these bridges were designed according to the allowable stress design method. In the allowable stress design method, it is not possible to quantify the reliabilities of both bridge components and the entire bridge system. Therefore, in light of current reliability-based design philosophy, there is an urgent need to assess the safety of suspension bridges from a probabilistic viewpoint. To develop cost-effective design and maintenance strategies, it is necessary to assess the condition of suspension bridges using a reliability-based approach. This is accomplished by a probabilistic finite-element geometrically nonlinear analysis. This study describes an investigation into the reliability assessment of suspension bridges. The combination of reliability analysis and geometrically nonlinear elastic analysis allows the determination of reliabilities of suspension bridges. A probabilistic finite-element geometrically nonlinear elastic code, created by interfacing a system reliability analysis program with a finite-element program, is used for reliability assessment of suspension bridges. An existing suspension bridge in Japan, the Innoshima Bridge, is assessed using the proposed code. The assessment is based on static load effects. Reliabilities of the bridge are obtained by using 2D and 3D geometrically nonlinear models. Furthermore, damage scenarios are considered to assess the effects of failure of various elements on the reliability of undamaged components and on the reliability of the bridge. Finally, sensitivity information is obtained to evaluate the dominant effects on bridge reliability.     

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.     

Performance of a Tied-Arch Reinforced Concrete Railway Bridge: Rating, Safety Assessment, and Bond Length Evaluation

This study presents investigations regarding visual inspection, dynamic testing, and finite-element modeling of an approximately 80-year old reinforced concrete tied-arch railway bridge that is still in service in Turkey. Investigations were conducted as part of a systematic periodic inspection along Ankara-Zonguldak railway line. The bridge is subject to heavy freight trains with increasing axle loads. Field tests such as material tests and dynamic tests were used to calibrate the finite-element model of the bridge. Detailed information regarding testing and model updating procedure is given. Based on test results, computer model was refined. The calibrated model of the bridge structure was then used for structural assessment and evaluation. Despite sufficient overall safety, local details were found to be problematic. Due to insufficient bond length in hanger-to-arch connection, a strengthening scheme using steel channel sections was proposed.     

Analytical Load Rating of an Open-Spandrel Arch Bridge: Case Study

The live load structural capacity of open-spandrel arch bridge structures is difficult to quantify. In addition to live and dead loads, geometric nonlinear effects, temperature effects, and material behavior play key roles in the design and load rating of such a structure. This paper is a case study that illustrates the effect these variables have on load rating a two-span shallow concrete arch bridge. Presented are load ratings of the structure’s arch ribs using a three-dimensional finite-element model with American Association of State Highway and Transportation Officials publications. As a result of this study, a refined analysis is recommended for load rating arch bridges.     

Experimental Assessment of Dynamic Responses Induced in Concrete Bridges by Permit Vehicles

Results from experimental testing of three permit vehicles are presented in the paper. The selected heavy vehicles, which require permits from state DOTs, included two tractor-trailer systems and a midsize crane. The vehicles were experimentally tested on popular existing speed bumps and on a representative highway bridge. The selected bridge was a reinforced-concrete structure constructed in 1999, located on the U.S. 90 in Northwest Florida. The bridge approach depression, combined with a distinct joint gap between the asphalt pavement and the concrete deck, triggered significant dynamic responses of the vehicle-bridge system. Similar dynamic vibrations were observed and recorded when the permit vehicles were driven over the speed bumps. Time histories of relative displacements, accelerations, and strains for selected locations on the vehicle-bridge system were recorded. The analysis of experimental data allowed for assessment of actual dynamic interactions between the vehicles and the speed bumps as well as dynamic load allowance factors for the selected bridge.     

Structural Testing of Prestressed Concrete Girders from the Lake View Drive Bridge

On the evening of December 27, 2005, the fascia beam supporting the east-side parapet wall of the third span of the Lake View Drive Bridge failed under the action of dead load. This paper describes the structural testing and posttest forensic examination of two girders recovered from the partially collapsed Lake View Drive Bridge. The objective of this paper is to describe the tests conducted and report the observations. An interior and an exterior prestressed concrete adjacent box girder were tested to failure in flexure. Prior to testing, an extensive visual inspection was conducted to assess the extant condition of the 42-year-old girders. Following testing, the girders were sawcut near their failure regions to permit an extensive forensic investigation. Conclusions based on the pre- and posttest inspections and test results are presented. Recommendations intended to reinforce issues that need to be considered in the bridge inspection and rating process of similar structures are presented.     

Comparative Study of Fatigue Provisions for the AASHTO Fatigue Guide Specifications and LRFR Manual for Evaluation

The recently developed Manual for condition evaluation and load and resistance factor rating (LRFR) of highway bridges in 2003 provides an alternative procedure for practicing engineers to evaluate the fatigue life of steel bridge structures. Although the evaluation manual maintains several aspects used in the AASHTO fatigue guide specification in 1990, it also utilizes formulas and values specified in the AASHTO LRFD bridge design specifications in 1998. A comparative study of the fatigue lives provided by the procedures in the Evaluation manual and the Guide specifications was performed using a life prediction of 14 steel bridges with different structural configurations and various fatigue details. It has been shown that longer predicted fatigue lives are typically obtained when using the Evaluation manual. The ratio of the finite evaluation fatigue lives for the two procedures was found to be in a range of 0.99–2.14.