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.     

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.     

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.     

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。     

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.     

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.     

Probabilistic deterioration model of high-strength steel wires and its application to bridge cables

Bridge inspections reveal that severe corrosion and fatigue are the main failure mechanisms of bridge stay cables. This paper presents an empirical modelling of the long-term deterioration process of steel wires in cables with consideration of the simultaneous occurrence of uniform corrosion, pitting corrosion and fatigue induced by a combined action of environmental aggression and cyclic loading. Accelerated corrosion experiments are conducted to determine the different corrosion levels of high-strength steel wires, and time-dependent statistical models are developed to quantify uniform and pitting corrosion depth. Corrosion-fatigue process of steel wires is subsequently simulated using the corrosion models and cyclic stress obtained through cable force monitoring data. The mechanical properties of corroded steel wires, including yield stress, ultimate stress, ultimate strain and modulus of elasticity, are experimentally characterised, and the statistical models are established through regression analysis. Finally, the deterioration models of high-strength steel wires (including crack depth, ratio of broken wires, and remaining strength, among others) is extended to probabilistically assess the time-variant conditions of bridge cables (sectional area loss and remaining capacity). The presented study on the long-term deterioration of bridge cables would provide guidance to future decision-making regarding the maintenance and replacement of bridge cables.     

Computational platform for the integrated life-cycle management of highway bridges

Throughout their service life, highway bridges are subject to progressive deterioration in performance; an issue that may render the use of these facilities unsafe at some point in time. Over the last few decades, there has been successful research towards developing procedures for establishing the various vital elements required in the life-cycle management of civil infrastructure. It is noted, however, that frameworks for integrating these elements together are lacking. The objective of this paper is to present an integrated framework for the life-cycle management of highway bridges in the form of a detailed computational platform. The elements integrated into the framework include the advanced assessment of life-cycle performance, analysis of system and component performance interaction, advanced maintenance optimization, and updating the life-cycle performance by information obtained from structural health monitoring and controlled testing.     

Decision analysis for elevating bridge decks with steel pedestals

Steel pedestals have been proposed to elevate bridge decks to reduce the likelihood of collisions of overheight vehicles. However, the use of steel pedestals might also increase the bridge vulnerability to seismic events. This paper develops a formulation for decision analysis for elevating bridges with steel pedestals. The formulation accounts for the expected life-cycle costs (LCCs) associated with vehicular impacts to bridge decks and seismic events. The optimum height of the steel pedestals is then obtained by minimising the total expected costs. The expected LCC associated with a bridge retrofitted with the optimum pedestal height is compared with that of the same bridge before the installation of the steel pedestals to determine whether elevating the bridge with steel pedestals is justifiable. The proposed framework is applied on a typical two-span slab-on-girder bridge at different locations in the USA.     

Bridge life-cycle performance and cost: analysis,prediction, optimisation and decision-making

The development of a generalised framework for assessing bridge life-cycle performance and cost, with emphasis on analysis, prediction, optimisation and decision-making under uncertainty, is briefly addressed. The central issue underlying the importance of the life-cycle approach to bridge engineering is the need for a rational basis for making informed decisions regarding design, construction, inspection, monitoring, maintenance, repair, rehabilitation, replacement and management of bridges under uncertainty which is carried out by using multi-objective optimisation procedures that balance conflicting criteria such as performance and cost. A number of significant developments are summarised, including time-variant reliability, risk, resilience, and sustainability of bridges, bridge transportation networks and interdependent infrastructure systems. Furthermore, the effects of climate change on the probabilistic life-cycle performance assessment of highway bridges are addressed. Moreover, integration of SHM and updating in bridge management and probabilistic life-cycle optimisation considering multi-attribute utility and risk attitudes are presented.     

Time-dependent seismic fragility curves on optimal retrofitting of neutralised reinforced concrete bridges

The neutralisation (carbonation) of concrete usually results in material deterioration of a reinforced concrete (RC) bridge, so that the seismic capacity of the structure tends to degrade over time. This paper determined the deteriorated plastic hinge properties of the neutralised RC bridge column and performed the pushover analysis to obtain the decayed seismic capacity curves. As a result, the time-dependent fragility curves with respect to some representative damage levels can be established and the possible seismic loss can be expressed as a function of service time.

The S-surfaces representing retrofitting cost versus service time for a neutralised RC bridge subjected to different earthquake levels were determined quantitatively in a case study. Throughout the whole life-cycle of a bridge, critical service times corresponding to dramatically increased slopes in the S-surface associated with cost elevations can be identified to assist in the development of a financially optimised strategy for timely seismic retrofitting.     

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.     

Life-cycle cost-oriented multiobjective optimization of composite frames considering the slab effect

The life-cycle cost-oriented design philosophy is a promising tool for building resilient cities as it helps in gaining insights into the impact of hazard-induced damage and repair of civil and infrastructure systems. In this study, a socioeconomic parameter-independent practical formulation was introduced for life-cycle cost analysis by combining the economic loss rate associated with different damage limit states and cloud analysis-based probabilistic seismic demand model. A framework for life-cycle cost analysis-based seismic design optimization was proposed using an emerging nature-inspired algorithm, namely, the multiobjective cuckoo search. By considering an eight-story prototype composite frame, the framework was used to determine the trade-off design alternatives between competing optimization objectives. Conventional and improved fiber models were developed to comparatively evaluate the influence of the slab spatial composite effect on Pareto optimal designs. The key drivers of change in three cost indicators were identified using generalized linear models. The result indicates that the overstrength factor is the critical design parameter affecting the initial construction, seismic damage, and life-cycle costs, with statistical significance at the 0.001 level.     

Stochastic life-cycle analysis: renewal-theory life-cycle analysis with state-dependent deterioration stochastic models

For the life-cycle analysis (LCA) of deteriorating engineering systems, it is critical to model and incorporate the various deterioration processes and associated uncertainties. This paper proposes a renewal-theory life-cycle analysis (RTLCA) with state-dependent stochastic models (SDSMs) that describe the deterioration processes. The SDSMs capture the multiple deterioration processes and their interactions through modelling the changes in the system state variables due to different deterioration processes. Then proper capacity and demand models that take the time-variant state variables as input are adopted to fully capture the impact of deterioration processes on the capacity, demand, and other time-variant performance indicators of the engineering system. The SDSMs are then integrated into RTLCA to efficiently evaluate various life-cycle performance quantities such as availability, operation cost and benefits of the engineering system. To implement the proposed formulation, a sampling-based approach is adopted to simulate samples from the relevant probability density functions (PDFs) to estimate the life-cycle performance quantities, while stochastic simulation-based approach is adopted to estimate the time-variant performance indicators needed to inform intervention activities. As an illustration, the proposed formulation is used to analyse the life-cycle performances of an example reinforced concrete bridge subject to deterioration due to corrosion and seismic loading.     

非一致氯离子侵蚀下近海桥梁时变地震易损性研究

近海桥梁往往处于氯离子空间分布不均匀的复杂环境,在服役过程中往往会遭受非一致氯离子侵蚀,导致材料及结构性能不断退化,降低桥梁抵御地震的能力。为研究非一致氯离子侵蚀下桥梁地震损伤风险变化规律,文章以氯离子扩散规律及钢筋锈蚀机理为基础,基于Duracrete模型及以往试验结果,确定不同环境参数及锈蚀参数的概率分布类型及统计特征,建立钢筋及混凝土材料退化规律。结合地震易损性分析理论,建立非一致氯离子侵蚀环境下桥梁时变地震易损性评估流程。随后,以一座多跨连续梁桥为例,分析退化桥梁抗震能力变化特征,研究不同构件的地震损伤时变规律。研究结果表明,氯离子侵蚀下的桥墩截面抗弯承载力和曲率延性均表现出明显的退化,并且曲率延性退化程度高于抗弯承载力。非一致氯离子侵蚀会导致桥墩损伤分布发生演变,桥墩易损位置可能从墩顶、墩底转移至低水位处。随着服役时间增加,桥墩损伤概率明显增大,而支座、挡块及桥台的损伤概率略有降低。     

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。     

Seismic analysis incorporating detailed structure–abutment–foundation interaction for quasi-isolated highway bridges

The Illinois Department of Transportation has adopted an economical and pragmatic methodology for designing earthquake-resistant highway bridges in the Midwestern United States. These so-called quasi-isolated bridges employ low-cost non-seismically designed bearing components as sacrificial structural fuses. During seismic events, fusing actions of these components and subsequent sliding of superstructures on substructures are intended to achieve response characteristics similar to those of conventionally isolated bridges that employ specially designed isolators. This study explores seismic structure-abutment-foundation interaction for quasi-isolated bridges in Illinois, employing a detailed yet efficient non-linear finite-element model for seat-type bridge abutments. The abutment model incorporates many structural components and geotechnical mechanisms that are critical to seismic response of the structure-abutment-foundation (SAF) system. Through non-linear static analyses performed on a complete bridge model, the force-transfer mechanisms, component fusing performance, and potential failure modes of the SAF system were explored. Using earthquake ground motions, non-linear dynamic analyses were conducted to evaluate seismic characteristics of the quasi-isolated bridge, sequences of critical limit state occurrences, and effects of abutment attributes on bridge seismic performance. The influence of abutment model sophistication on simulated bridge response was also highlighted by direct comparison of simulation results obtained from different models.     

Life-cycle cost analysis of reinforced concrete structures in marine environments

Chloride-induced corrosion of carbon steel reinforcement is the main cause of deterioration of reinforced concrete (RC) structures in marine environments. One of the ways to protect RC structures from corrosion is to use corrosion-resistant stainless steel reinforcing bars. However, stainless steel is between six and nine times more expensive than carbon steel. Thus, its use can only be justified on a life-cycle cost basis. In the paper a time-variant probabilistic model was presented to predict expected costs of repair and replacement which was then used to calculate life-cycle costs for RC structures in marine environments under different exposure conditions. Results of the life-cycle cost analysis can be applied to select optimal strategies improving durability of RC structures in marine environments, including the use of stainless steel reinforcement.     

Zerstörungsfreier elektrochemischer Chloridentzug an der Donaubrücke Pfaffenstein: Langzeiterfahrungen über eine bauwerksschonende und verkehrserhaltende Technologie

Non‐Destructive Electrochemical Chloride Extraction on the Danube Bridge Pfaffenstein: Long‐Term Experiences about a Structure‐ and Traffic‐keeping Technology Between 2003 and 2007 in total 200 m² of corrosion active hollow box girder floor slabs were rehabilitated by a non‐destructive, electrochemical chloride extraction (ECE) within the Danube bridge Pfaffenstein that is situated in Regensburg along the highway A93. These concrete areas were chloride contaminated by a leaking drainage system from the carriageway above – up to 4% by cement mass. Hence, the reinforcement was corrosion active, but did not show considerable loss of cross‐section or concrete deterioration. After completing the ECE, where more than 28 kg of chloride could be removed, multiple potential surveys have been made about a time span of up to three years. These measurements have shown that chloride induced corrosion activity could be eliminated safely, also with some residual chloride. Both highway and a heavy traffic bearing main street, which crosses under the bridge, haven't been affected by the repair. The principle of ECE, its side effects and the experiences collected by the author since 2001 shall be discussed here.     

Seismic risk assessment of reinforced concrete bridges in flood-prone regions

This article presents a conditional seismic risk evaluation framework of bridges located in seismically active flood-prone regions. Flood-induced bridge scour causes loss of lateral support at bridge foundations and thus the effect of seismic hazard on bridge performance gets amplified. Two example reinforced concrete bridges located in Sacramento County in California are considered. The regional multihazard scenario is characterised by combining scour resulted from regional flood events of different intensities with a suite of earthquake ground motions that represents regional seismicity. Uncertainties in the hazard models are discussed and their influences on bridge performance are investigated. A separate set of analysis is performed to evaluate the bridge performance only under earthquake ground motions. Seismic fragility curves and risk curves for the example bridges are generated. Result shows higher seismic risk of bridges when the impact of regional flood hazard on bridges is considered in the analysis framework. This suggests the use of a combined seismic and flood hazard model for reliable seismic risk evaluation of bridges located in flood-prone regions.