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.     

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.     

Life cycle cost management of concrete structures relative to chloride-induced reinforcement corrosion

Chloride-induced reinforcement corrosion is one of the major causes for the deterioration of concrete structures. This article has developed a performance-based life cycle cost management (LCCM) model for reinforced concrete structures relative to corrosion deterioration. This model is characterised by three features: (1) a chloride-induced probabilistic corrosion deterioration mechanism is used to predict the service life of concrete structures; (2) the performance of a concrete structure is measured by serviceability limit states and structural capacity limit states; and (3) a dual management methodology is adopted, in which management actions are optimised to maximise the life cycle performance of a concrete structure under limited budget constraints and minimum required serviceability constraints. Case studies of bridge decks and piers are provided to demonstrate the application of the proposed performance-based LCCM model.     

Modeling of Chloride Concentration Effect on Reinforcement Corrosion

Abstract:   The corrosion of reinforcement is one of the major causes of deterioration of reinforced concrete (RC) structures, considerably affecting their durability and reliability. The rate of reinforcement corrosion is governed by, among other factors, the presence of chlorides on the surface of the steel. The assessment of such deteriorating effects necessitates the development of relevant models and the utilization of advanced simulation techniques to enable the probabilistic analysis of concrete structures. In this article an approach for the assessment of the durability and reliability of RC structures under attack from chlorides is introduced. The field of chloride concentration at different locations in the structure (represented in 2D space by chosen longitudinal or cross sections) is modeled as a function of time by a cellular automata (CA) technique. The results of this simulation are then utilized for the assessment of a steel corrosion prognosis using a probabilistic 1D model at chosen points, although the rate of corrosion is based on experimental results. The concentrations of chlorides and pH levels are reflected in this way. The described approach is applied to an illustrative example showing the feasibility of capturing the effect of chloride concentration on the steel corrosion rate and consequently on the assessment of the service life and/or reliability of the structure.     

Some considerations on the performance cycle analysis of concrete girders in France

A performance assessment of corroded reinforced concrete (RC) structures requires an acute understanding of both material deterioration and its impact on structural behaviour, in order to evaluate its durability, safety, serviceability and remaining service life. The corrosion phenomenon is usually due to carbon dioxide and chloride ions. More generally, the environmental conditions may determine what kind of deterioration mechanism can produce structural degradation depending on relative humidity, temperature, severity of the surrounding environment, materials properties, etc. Consequently, the performance cycle prediction of reinforced concrete structures involves many factors, which introduce uncertainties. A probabilistic approach as opposed to a deterministic one is therefore more appropriate to generate reliable cycle predictions. This paper focuses on the application of the principles of such a probabilistic approach to calculate for a typical set of RC bridges in France, the critical times corresponding to every performance cycle, considering both chloride-induced corrosion and carbonation, but also concrete cracking and spalling. For this purpose, the impact of the environment on the RC structures and the principal material properties are taken into account in this analysis. A methodology is also provided for roughly assessing serviceability cycles from visual inspections.     

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。     

氯离子侵蚀环境下混凝土结构耐久性寿命评估方法研究

根据氯离子侵蚀环境下混凝土结构中钢筋锈蚀的发生和发展,分析了结构性能的衰退过程,得到了氯离子侵蚀环境下结构耐久性寿命评估模型.考虑到寿命评估模型中主要参数的不确定性影响,基于Monte Carlo原理,采用CrvstalBall软件对混凝土构件进行了随机模拟.随机模拟结果显示,保护层厚度及氯离子浓度是影响氯离子侵蚀环境下混凝土结构耐久性寿命的重要参数.     

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.     

Maintenance decision model for steel bridges: a case in the Netherlands

A probabilistic model is developed to investigate the crack growth development in welded details of orthotropic bridge decks. Bridge decks may contain many of these vulnerable details and bridge reliability cannot always be guaranteed upon the attainment of a critical crack. Therefore, insight into the crack growth development is crucial in guaranteeing bridge reliability and scheduling efficient maintenance schemes. The probabilistic nature of the crack growth development model and the dependence of this model on many interdependent random variables result in significant uncertainties regarding model outcome. To reduce some of these uncertainties, the probabilistic model is combined with a monitoring system installed on a part of the bridge. In addition, a Bayesian network is used to determine the dependence structure between the different details (monitored and non-monitored) of the bridge. This dependence structure enables us to make more accurate crack growth predictions for all details of the bridge while monitoring only a limited number of those details and updating the remaining uncertainties.     

Spatial time-dependent reliability analysis of corroding pretensioned prestressed concrete bridge girders

Accelerated pitting corrosion tests have been performed to obtain spatial and temporal maximum pit-depth data for prestressing wires. This data is then used to develop probabilistic models of pitting corrosion and strength capacity of 7-wire strands. The probabilistic model of pitting corrosion for strands is then combined with a non-linear Finite Element Analysis and probabilistic models of corrosion initiation and propagation to study the spatial and temporal effects of pitting corrosion on a typical pretensioned prestressed concrete bridge girder. The limit states considered are flexural strength and serviceability. The spatial time-dependent reliability analysis takes into account the uncertainties and variabilities related to material properties, dimensions, loads and corrosion parameters as well as the spatial variability of pitting corrosion of prestressing strands. Including the spatial variability of pitting corrosion in the reliability analysis increased both the probability of strength and serviceability failure when compared with a mid-span sectional analysis.     

A Bayesian Probabilistic Approach for Acoustic Emission‐Based Rail Condition Assessment

The investigation described in this article aims at developing a Bayesian‐based approach for probabilistic assessment of rail health condition using acoustic emission monitoring data. It comprises the following three phases: (i) formulation of a frequency‐domain structural health index (SHI), via a linear transformation method, tailored to damage‐sensitive frequency bandwidth; (ii) establishment of data‐driven reference models, using Bayesian regression about the real and imaginary parts of the SHI derived with monitoring data from the intact rail; and (iii) quantitative evaluation of discrimination between the new observations representative of current rail health condition and the baseline model predictions in terms of Bayes factor. If the deviation of the new observations from the predictions is within an acceptable tolerance, no damage is flagged, and the new data are further used to update and refine the reference models. If the observations deviate substantially from the model predictions in a probabilistic sense, damage is signaled, damage severity is quantified, and damage location determined. The proposed approach is examined by using field monitoring data acquired from an instrumented railway turnout, and the coincidence between the assessment results and the actual health conditions demonstrates its effectiveness in damage detection, localization, and quantification.     

混凝土矮箱梁桥疲劳性能监测与评估

采用动态称重(WIM)技术对陕西省省道S305线崾岘中桥进行交通荷载监测,分析得出了适合陕西省混凝土桥梁的标准疲劳车模型。采用动应变监测技术对混凝土矮箱梁关键部位进行长期动应变监测,获得了运营状态下混凝土矮箱梁的实测应力谱;运用Miner线性准则和应力幅 循环次数曲线对结构进行疲劳寿命评估;对超载情况下混凝土矮箱梁的疲劳寿命进行了分析。结果表明:在目前交通荷载作用下,混凝土矮箱梁的疲劳寿命为5 120年,考虑腐蚀疲劳的因素后疲劳寿命降至254年;当超载车辆比例低于1%时,超载对桥梁结构的疲劳寿命影响很小;当超载车辆比例达到10%时,结构的疲劳寿命随着超载率的提高而显著降低;该研究成果可为崾岘中桥未来维护管理提供技术支撑,同时为同类型其他桥梁的疲劳寿命评估提供参考。     

A Refined Methodology for Durability‐Based Service Life Estimation of Reinforced Concrete Structural Elements Considering Fuzzy and Random Uncertainties

Abstract: A reliable method for service life estimation of the structural element is a prerequisite for service life design. A new methodology for durability‐based service life estimation of reinforced concrete flexural elements with respect to chloride‐induced corrosion of reinforcement is proposed. The methodology takes into consideration the fuzzy and random uncertainties associated with the variables involved in service life estimation by using a hybrid method combining the vertex method of fuzzy set theory with Monte Carlo simulation technique. It is also shown how to determine the bounds for characteristic value of failure probability from the resulting fuzzy set for failure probability with minimal computational effort. Using the methodology, the bounds for the characteristic value of failure probability for a reinforced concrete T‐beam bridge girder has been determined. The service life of the structural element is determined by comparing the upper bound of characteristic value of failure probability with the target failure probability. The methodology will be useful for durability‐based service life design and also for making decisions regarding in‐service inspections.     

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.     

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.     

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.     

钢筋混凝土斜拉桥寿命期内整体极限承载力分析

提出基于定期检测和健康监测技术的斜拉桥结构服役期内主梁整体失效模式及其极限承载力演化规律的分析方法,为结构的全寿命设计以及结构安全预警的分级提供理论依据。首先,利用结构的检测/监测数据,建立与实际结构状态相符的有限元模型,并分析构件的耐久性损伤,在此基础上计算考虑抗力退化的构件的极限承载力;然后,在有限元模型上施加逐级渐进的车辆荷载,分析各构件的内力状态;最后,将荷载效应超过抗力的主梁截面设置为塑性铰,改变结构体系,继续施加车辆荷载,直至结构承受的车辆荷载达到最大值,对应的变结构体系和车辆荷载分别为最终主梁整体失效模式和极限承载力。利用上述方法对我国北方某座干线斜拉桥在运营期内的4个典型状态进行计算分析,研究该桥在运营期内的失效模式及其极限承载力的演化规律。结果表明,所提出的方法可以获得在车辆荷载作用下斜拉桥主梁整体失效模式和相应的极限承载力;斜拉桥在服役过程中主梁开裂、钢筋锈蚀、边界条件变化等导致桥梁结构损伤、甚至结构体系及其相应的力学模型发生较大的变化,使结构失效模式及其极限承载力发生较大的变化。     

Model for cover cracking of RC beams due to partial surface steel corrosion

Cracking of the cover concrete due to steel corrosion is considered by many researchers to indicate the end-of-service life of corrosion-affected reinforced concrete (RC) structures. Numerous models have been developed to predict the time from corrosion initiation to cracking of the cover concrete. In the previous models, concrete with corroding steel bars was assumed to behave like a thick-walled cylinder under uniform internal pressure. Recent research publications have however, shown that steel corrosion is often concentrated on the surface of the steel that faces the direction of ingress of corrosion agents. This paper presents a model that relates the level of partial surface steel corrosion with the transverse and vertical strains measured on the exterior faces of corrosion-affected RC beams. The model assumes that the remaining section of the steel after corrosion is elliptical shaped. Finally, the model is calibrated with experimental data in the literature and it is shown that assuming uniform steel corrosion underestimates the internal pressure applied by the expansive corrosion products.     

Fatigue performance assessment and service life prediction of high-speed ship structures based on probabilistic lifetime sea loads

This article focuses on estimating probabilistic lifetime sea loads for high-speed ship structures with the aim of assessing fatigue performance and predicting service life from available data. Performance assessment and service life prediction for naval ship structures are extremely important issues. In particular, understanding the effect of sea loading on naval high-speed vessels is still a challenge. Potential lifetime load effects including low frequency wave-induced and high frequency slam-induced whipping loadings are investigated in this article by using a probabilistic approach. Clearly, integration of probabilistic sea loads into structural reliability assessment and service life prediction will provide a more reliable estimation of the long-term structural performance. Accordingly, this article presents an approach for fatigue reliability evaluation of ship structures based on the estimated lifetime sea loads. Loading information associated with sea states, ship speeds and relative wave headings is obtained from a joint high-speed sealift ship monohull structural seakeeping trials, while the S–N curves are established based on the British Standards.     

温福铁路CX-SUN混凝土外加剂作用机理研究

温福铁路处于东南沿海地区,台湾海峡西岸,许多桥梁位于海水和地下水侵蚀环境,为了确保设计使用年限达到100年以上,针对东南沿海环境温福线铁路桥梁混凝土抗腐蚀,提高耐久性,应用了CX-SUN抗侵蚀外加剂。CX-SUN海工高性能混凝土抗侵蚀外加剂产品,可解决钢筋混凝土因长期遭受地表海水和地下水中各种化学物质的侵蚀破坏而过早丧失服役现象,使混凝土使用年限提高20~30年。