Time-variant reliability profiles for steel girder bridges

Evaluation of existing steel bridges becomes more important due to natural aging, increasing load spectra, deterioration caused by corrosion, and other problems. In the result, bridge structures exposed to aggressive environmental conditions are subjected to time-variant changes of resistance. Therefore, there is a need for evaluation procedures for an accurate prediction of the load carrying capacity and reliability of bridge structures, in order to make rational decisions about repair, rehabilitation, and expected life-cycle costs. The objective of this paper is to develop time-variant reliability models for steel girder bridges. Traditional methods based on deterministic analysis do not reveal the actual load carrying capacity of the structure. The proposed approach is based on reliability analysis of components and structural systems. The study involves the selection of representative structures, formulation of limit state functions, development of load models, development of resistance models for corroded steel girders, development of the reliability analysis method, reliability analysis of selected bridges, and development of the time-dependant reliability profiles including deterioration due to corrosion. The results of the study can be used for a better prediction of the service life of deteriorating steel girder bridges, and development of optimal reliability-based maintenance strategies.     

Life-cycle reliability assessment of reinforced concrete bridges under multiple hazards

This paper proposes a novel probabilistic methodology for estimating the life-cycle reliability of existing reinforced concrete (RC) bridges under multiple hazards. The life-cycle reliability of an RC bridge pier under seismic and airborne chloride hazards is compared to that of a bridge girder under traffic and airborne chloride hazards. When conducting a life-cycle reliability assessment of existing RC bridges, observational data from inspections can provide the corrosion level in reinforcement steel. Random variables related with the prediction of time-variant steel weight loss can be updated based on the inspection results using Sequential Monte Carlo Simulation (SMCS). This paper presents a novel procedure for identifying the hazards that most threaten the structural safety of existing RC bridges, as well as the structural components with the lowest reliability when these bridges are exposed to multiple hazards. The proposed approach, using inspection results associated with steel weight loss, provides a rational reliability assessment framework that allows comparison between the life-cycle reliabilities of bridge components under multiple hazards, helping the prioritisation of maintenance actions. The effect of the number of inspection locations on the updated reliability is considered by incorporating the spatial steel corrosion distribution. An illustrative example is provided of applying the proposed life-cyle reliability assessment to a hypothetical RC bridge under multiple hazards.     

Life-Cycle Performance of RC Bridges: Probabilistic Approach

This article addresses the problem of reliability assessment of reinforced concrete (RC) bridges during their service life. First, a probabilistic model for assessment of time-dependent reliability of RC bridges is presented, with particular emphasis placed on deterioration of bridges due to corrosion of reinforcing steel. The model takes into account uncertainties associated with materials properties, bridge dimensions, loads, and corrosion initiation and propagation. Time-dependent reliabilities are considered for ultimate and serviceability limit states. Examples illustrate the application of the model. Second, updating of predictive probabilistic models using site-specific data is considered. Bayesian statistical theory that provides a mathematical basis for such updating is outlined briefly, and its implementation for the updating of information about bridge properties using inspection data is described in more detail. An example illustrates the effect of this updating on bridge reliability.     

Capacity loss evaluation of reinforced concrete bridges located in extreme chloride-laden environments

This article provides a comprehensive procedure for the structural performance evaluation and life-cycle cost (LCC) analysis of reinforced concrete highway bridges located in extreme chloride-laden environments. An integrated computational methodology is developed to simulate the chloride intrusion and to estimate the corrosion initiation time. The effects of various influential parameters on the chloride diffusion process are examined and the changes in geometry and material properties of structural members are calculated over the entire life of the bridge. In order to evaluate the global structural degradation due to the corrosion mechanisms, an inventory of bridges with different structural attributes are investigated. The extent of capacity loss is calculated using the moment-curvature and nonlinear static (pushover) analysis. Results of this study are then utilised to find the LCC of bridges. Different inspection and maintenance strategies are considered to minimise the total LCC, which includes the initial construction cost, inspection and maintenance costs and service failure costs. The proposed approach indicates the inspection and maintenance intervals in a way that the inspection and maintenance costs are optimised while the safety of the bridge is ensured.     

Improved Bayesian network configurations for probabilistic identification of degradation mechanisms: application to chloride ingress

Probabilistic modelling of deterioration processes is an important task to plan and quantify maintenance operations of structures. Relevant material and environmental model parameters could be determined from inspection data; but in practice, the number of measures required for uncertainty quantification is conditioned by time-consuming and expensive tests. The main objective of this study was to propose a method based on Bayesian networks for improving the identification of uncertainties related to material and environmental parameters of deterioration models when there is limited available information. The outputs of the study are inspection configurations (in space and time) that could provide an optimal balance between accuracy and cost. The proposed methodology was applied to the identification of random variables for a chloride ingress model. It was found that there is an optimal discretisation for identifying each model parameter and that the combination of these configurations minimises identification errors. An illustration to the assessment of the probability of corrosion initiation showed that the approach is useful even if inspection data are limited.     

Seismic fragility increment functions for deteriorating reinforced concrete bridges

Fragility increment functions are developed to estimate the seismic fragility of reinforced concrete (RC) bridges subject to deterioration due to the onset and progression of corrosion of the reinforcement. For each mode of failure considered, the fragility at time t of a deteriorating bridge is obtained by multiplying the initial fragility of the undeteriorated bridge by a corresponding increment function expressed in terms of the environmental conditions, the original material properties, time, a measure of the seismic demand, and a set of unknown model parameters. The developed increment functions account for the effects on the fragility estimates of the loss of the reinforcement and of the increasing uncertainty over time. As an application, the developed increment functions are used to estimate the seismic fragility of an example RC bridge. The proposed fragility increment functions are useful to estimate the fragility of deteriorating bridges without any extra reliability analysis once the fragility of the undeteriorated bridge is known. In particular, the proposed fragility increment functions can be used to assess the time-variant fragility of bridges for applications such as reliability-based design, life-cycle cost analysis, and risk analysis.     

Prediction of Onset of Corrosion in Concrete Bridge Decks Using Neural Networks and Case-Based Reasoning

Abstract:   This article proposes a methodology for predicting the time to onset of corrosion of reinforcing steel in concrete bridge decks while incorporating parameter uncertainty. It is based on the integration of artificial neural network (ANN), case-based reasoning (CBR), mechanistic model, and Monte Carlo simulation (MCS). A probabilistic mechanistic model is used to generate the distribution of the time to corrosion initiation based on statistical models of the governing parameters obtained from field data. The proposed ANN and CBR models act as universal functional mapping tools to approximate the relationship between the input and output of the mechanistic model. These tools are integrated with the MCS technique to generate the distribution of the corrosion initiation time using the distributions of the governing parameters. The proposed methodology is applied to predict the time to corrosion initiation of the top reinforcing steel in the concrete deck of the Dickson Bridge in Montreal. This study demonstrates the feasibility, adequate reliability, and computational efficiency of the proposed integrated ANN-MCS and CBR-MCS approaches for preliminary project-level and also network-level analyses.     

Probabilistic service life of reinforced concrete structures with randomly distributed corrosion-induced cracks

This paper proposed a probabilistic service life prediction method for reinforced concrete (RC) structures with randomly distributed chloride corrosion-induced cracking. In the proposed method, spatial randomness of environmental, geometric and physical factors was considered that influence corrosion process and crack propagation of RC structures at the material level. Karhunen–Loéve (KL) expansion method was utilised for modelling the spatial random fields. Four limit state functions were proposed based on four deterioration events (corrosion initiation, surface crack initiation, modulus degradation and exceedance of repair limit). Then, time-dependent reliability analyses of an RC bridge slab were conducted using the proposed method. Finally, sensitivity analysis of the statistical parameters including mean, variance, correlation length as well as the truncation number for KL expansion method were conducted to determine the effects of those parameters to the service life.     

Ultimate strength reliability analysis of corroded steel-box girder bridges

Structural reliability theory is a useful tool for estimating the risks associated with deteriorating structures. The aim of this study is to develop and demonstrate a procedure for the assessment of box girder bridge ultimate strength reliability with the degradation of plate members due to general corrosion taken into account. A probabilistic model for ultimate steel-box girder strength is established on the basis of an analytic formula that considers corrosion-related, time-dependent strength degradation. The study involves the selection of representative structures, formulation of limit state functions, development of resistance models for corroded steel-box girders, development of load models, development of a reliability analysis method, reliability analysis of the selected bridges and development of the time-dependant reliability profiles, including deterioration due to corrosion. The results of this study can be used for the better prediction of the service life of deteriorating steel-box girder bridges and the development of optimal reliability-based maintenance strategies.     

沿海桥梁混凝土结构腐蚀调查及分析

针对日照沿海桥梁的耐久性现状进行调研,通过对桥梁墩身、边梁和栏杆混凝土的保护层厚度、碳化深度以及桥梁不同部位的游离氯离子浓度的检测表明:桥梁混凝土结构保护层厚度偏小、车辆超载、结构设计不合理、施工管理不当、缺乏维护管理是导致沿海桥梁混凝土结构损伤劣化的主要原因。此外,海洋环境中的氯离子和空气中的二氧化碳将导致桥梁混凝土中钢筋腐蚀,海水中的盐在混凝土中结晶将导致桥梁墩身腐蚀破坏。     

Multi-objective and probabilistic decision-making approaches to sustainable design and management of highway bridge decks

The aging and deterioration of highway bridges and the new requirements for sustainable infrastructures and communities require innovative approaches for their management that can achieve an adequate balance between social, economic and environmental sustainability. This paper presents a multi-objective decision-making approach for the sustainable design and management of highway bridge decks, which can consider several and conflicting objectives, such as the minimisation of owner's costs, users costs, and environmental impacts and uses goal setting and compromise programming to determine the satisficing and compromise solutions that yield the best trade-off between all competing objectives. The proposed approach is based on robust reliability-based mechanistic models of the deterioration and service life of reinforced concrete bridge decks, which include diffusion models for the prediction of chloride ingress into concrete and steel corrosion and thick-walled cylinder models for the prediction of stresses induced by the accumulating corrosion products in the concrete cover. The proposed approach is illustrated on the life cycle design and management of highway bridge decks using normal and high performance concrete. It is shown that the high performance concrete deck alternative is a Pareto optimum, while the normal concrete deck is found to be a dominated solution in terms of life cycle costs and environmental impacts.     

Predicting the probability of failure of timber bridges using fault tree analysis

The resilience of a community in an extreme event depends mainly on the robustness of the critical infrastructures. Road bridges are a critical link of the road network, which plays a focal role in Australia’s economy, prosperity, social well-being and quality of life. Timber bridges are a weaker link of the Australian road network and they often provide critical access to the rural communities. This research uses a number of bridge inspection reports to develop a method to predict the probability of failure of a timber bridge. The inspected condition states of the elements in the timber bridge are used to develop a Markov chain based model and Gamma process model to predict the deterioration of each element. The probability of condition state movement for each element thus calculated were used in fault tree analysis to estimate likelihood of failure of a bridge in a given time period. Although the developed method is based on limited data and it has several limitations, model can be further refined with the availability of more inspection reports. The method developed is demonstrated using an inspection report for a timber bridge, which was not used in the development of the models.     

基于可靠度的组合桥梁设计及维护策略(英文)

Currently,the design practice of highway bridges around the world are moving towards limit states design,a reliability-based design procedure.Canadian Highway Bridge Design Code(CHBDC)is the first design code entirely developed based on limit states design philosophy,including foundations and FRP components.However,reliability of a structure decreases in service due to environmental attacks and material deterioration such as fatigue,corrosion and many other reasons.Therefore,the structure should be inspected periodically,and the reliability of the structure should be evaluated according to its age and field data.If its reliability is reduced to a certain level,a repair should be scheduled as well as some preventive maintenance measures should be implemented to prevent further deterioration.Recently,many research works have been conducted to investigate reliability-deterioration mechanisms for each type of infrastructure and its components,optimize the inspection and maintenance strategy,predict remaining service life,estimate its life cycle cost.This paper is focused on the study of reliability-deterioration mechanisms of slab on steel girder bridges due to fatigue and corrosion of steel girders as well as corrosion of reinforcement in the deck slab.Examples will also be given to illustrate the proposed life cycle management strategy for composite slab on steel girder bridges.     

Ultrasonic C-Scan Imaging of Post-Tensioned Concrete Bridge Structures for Detection of Corrosion and Voids

Abstract:   Corrosion of the nation's transportation infrastructure is a widespread and costly problem. Efficiency, durability, safety, and environmental concerns have made the inspection and structural assessment of these structures a vital issue. The current state of the art in concrete bridge condition evaluation relies on visual inspection. However, deterioration in pre-stressing/post-tensioned strand or tendon condition is not always reflected by distress visible on the concrete surface. Further, the effect of deterioration of pre-stressing/post-tensioned steel is more disruptive than that of mild reinforcement. Strand, due to its high mechanical strength and metallurgical characteristics, is smaller in cross section than conventional reinforcing steel and is proportionally more impaired by loss of section. Methodology for pre-stressed concrete bridge condition evaluation, therefore, could be revolutionized through the development of accurate, quantitative nondestructive test methods for strand in pre-tensioned and post-tensioned structures. This article presents a new sensing method using ultrasound C-scan imaging for structural health monitoring of post-tensioned bridges. Preliminary results from tests are presented that show promising potential for the detection of corrosion and voids in concrete post-tensioned bridges.     

Proof load testing for bridge assessment and upgrading

Bridge deterioration with time and ever increasing traffic loads raise concerns about reliability of aging bridges. One of the ways to check reliability of aging bridges is proof load testing. A successful proof load test demonstrates immediately that the resistance of a bridge is greater than the proof load. This reduces uncertainty in the bridge resistance and so increases the bridge reliability. The paper considers a reliability-based calibration of intensities of proof loads for aging bridges to verify either an existing or increased load rating taking into account possible bridge deterioration. Intensities of proof loads are calibrated based on a consistent target reliability index. The influence of test risk, dead to live load ratio, and uncertainties associated with dead and live loads and bridge resistance is considered. The results presented in the paper relate to short and medium span bridges.     

A simplified management procedure for bridge network maintenance

Structural problems due to corrosion, ageing, durability, aggressive environments, materials defects, lack of ductility and unforeseen behaviour under seismic loads may significantly compromise the resistance and safety of bridges. Scheduled maintenance of bridges becomes important to ensure complete serviceability of the road network. Among existing bridge management systems (BMSs), this work is a contribution to the evaluation criteria of bridge condition by means of visual inspection, prediction of future structural condition and planning of maintenance intervention. After a brief review of some existing BMSs, a simple new procedure for evaluation of bridge condition by means of visual inspection, aimed at general planning of maintenance in a BMS framework, is presented in this paper. This procedure is applied to stock, including about 200 bridges and viaducts, of the Veneto region road network in the north-eastern part of Italy, and is then discussed.     

A performance‐based bridge LCCA model using visual inspection inventory data

Since most bridge life cycle cost analysis (LCCA) depends heavily on the analyst's experience to determine the times and costs of remedial actions over a bridge's lifetime, the results are often subject to question because of their subjectivity. While some work has been done over the years to develop reliable deterioration models for determining such times and costs, the proposed models often require sophisticated inspection data, which is costly to obtain, and/or complex mathematical calculations. A simple linear deterioration model based on visual inspection inventory data concerning bridge components is introduced and integrated into the LCC analysis. The proposed model provides an alternative approach to bridge LCC analysis that can improve the objectivity of analysis and does not require input of sophisticated inspection, and thus facilitates application of bridge life cycle cost analysis. The LCCA method developed in this study is applied to a case study of alternative PCI (Pre‐stressed Concrete I‐girder) and a PCB (Pre‐stressed Concrete Box‐girder) bridges for the purpose of model validation.     

Seismic fragility estimates for corroding reinforced concrete bridges

Seismic fragility of reinforced concrete (RC) bridges is defined as the conditional probability that the seismic demand exceeds the corresponding capacity, specified for a certain performance level, for given seismic intensity measures. However, the structural properties of RC bridges change over time due to the onset of corrosion in the reinforcing steel. Therefore, seismic fragility of RC bridges changes during a bridge lifetime. This paper proposes a method to estimate the seismic fragility of corroding RC bridges. Structural capacities are defined using probabilistic models for deformation and shear capacities of RC columns. Probabilistic models are also used to estimate the corresponding demands for given seismic intensity measures. The capacity and demand models are then combined with probabilistic models for chloride-induced corrosion and time-dependent corrosion rate to model the dependency on time of the seismic fragility of RC bridges. In particular, the loss of reinforcing steel is modelled as a function of the thickness of the cover concrete for each reinforcing bar in the RC columns. The stiffness degradation in the cover concrete over time due to corrosion-induced cracking is also considered in the fragility estimates. Seismic fragility estimates are then formulated at the column, bent, and bridge levels. The fragility formulations properly incorporate the uncertainties in the capacity and demand models, and the inexactness (or model error) in modelling the material deterioration. The proposed method accounts for the variation of structural capacity and seismic demand over time due to the effects of corrosion in the reinforcing steel. As an application, seismic fragility estimates are developed for a corroding RC bridge with 11 two-column bents over a 100-year period.     

氯离子侵蚀效应对RC桥墩抗震性能的影响

为研究混凝土桥梁结构在服役期内由于环境氯离子侵蚀效应引起钢筋、混凝土锈蚀退化等导致结构抗震性能退化的规律,以某多跨钢筋混凝土连续梁桥为例,采用OpenSees软件建立非线性动力分析模型,根据已有研究成果并基于概率方法研究了墩柱截面主筋和箍筋锈蚀的开始时间和锈蚀率大小,进而建立了钢筋的直径及屈服强度退化模型;针对考虑纵筋锈蚀、考虑箍筋锈蚀、同时考虑纵筋和箍筋锈蚀3种情况,分别分析了材料退化对桥墩抗震性能的影响。结果表明:同等条件下箍筋锈蚀比纵筋锈蚀更早;随着时间的推移,氯离子侵蚀效应会导致桥墩抗震能力下降,结构的抗震需求明显增加;与以往只考虑纵筋锈蚀的情况相比,同时考虑箍筋和纵筋锈蚀时桥墩抗震性能退化更严重。     

Reliability analysis with nondestructive inspection

Nondestructive inspection tools are commonly used to inspect structures or structural components with resistance deterioration due to defect size growth. The quality of the tools is mainly defined by the rate of detecting a defect with defect size s, (s), and the accuracy in sizing a detected defect. The uncertainty of sizing a detected defect can be incorporated in limit state functions that include defect size, and a reliability evaluation can be carried out with the efficient first-order reliability method (FORM). The rate of detecting a defect can also be incorporated in the reliability evaluation of an inspected structure or structural component. This is done, in this paper, by introducing a standard normally distributed variate, Z, and defining a limit state function as a function of and (s). Advantages of using this limit state function, rather than using a limit state function based on the actual defect size and the critical defect size distributed according to the rate of detection curve, are discussed. It is shown that one only needs to use the mean rate of defect detection curve to consider the uncertainty in the rate of detection. The incorporation of the uncertainty in rate of detection for reliability updating analysis with inspection results, and for reliability-based selection of optimal inspection and maintenance schedule for resistance deteriorating structures are also presented. The proposed approach is illustrated by two examples in evaluating reliability with inspection information and in selecting an optimal inspection and maintenance schedule by minimizing the probability of time to failure before inspection and before the time at the end of remaining service life.