On the robustness to corrosion in the life cycle assessment of an existing reinforced concrete bridge

Management of existing structures has traditionally been based on condition assessment, based on visual inspections, disregarding the susceptibility of different structural types to aging and deterioration. Robustness, as a measure of the effects of unpredictable damage to structural safety can be a complementary information to the results of inspection. Although robustness has mostly been used to evaluate the consequences of extreme events, a similar framework can be used to investigate the result of aging, allowing a better understanding of the potential effects of deterioration and allowing a better allocation of available maintenance funding. In this work, a probabilistic structural robustness indicator is used to quantify the susceptibility of structures to corrosion. The methodology is exemplified through a case study comprising an existing reinforced concrete bridge deck, heavily damaged due to reinforcement corrosion, and finally demolished due to safety concerns. Robustness measures the bridge deck safety tolerance to reinforcement corrosion. The principal effects of corrosion, including loss of area and bond between concrete and steel are modelled using a non-linear finite-element model, coupled with a Response Surface Method to compute the bridge reliability as a function of the corrosion level, and finally used to assess robustness. Results show that the redundancy of the bridge allows significant redistribution of loads between elements with different corrosion levels. As a result, the bridge presents significant robustness and tolerance to reinforcement corrosion.     

Variance‐based global sensitivity analysis for fuzzy random structural systems

There have been increasing advances in the sophisticated approaches like fuzzy randomness to handle different uncertainties in civil engineering; however, less attention has been paid to the formulation of a sensitivity analysis for fuzzy random structural systems. In this study, the main objective is to present the formulation of fuzzy Sobol sensitivity indices to quantify the influence of fuzzy random structural parameters. Meanwhile, uncertainty in derivation of limit states and acceptance criteria in collapse analysis is addressed briefly and treated using fuzzy model parameters. To show the application of the established sensitivity test, the collapse behavior of a steel moment frame subjected to sudden column removal is evaluated thoroughly. The proposed fuzzy sensitivity indices are determined for the problem and the overall influence of fuzzy acceptance criteria on the collapse assessment is shown using fragility analysis. The results show that the presented fuzzy sensitivity analysis can give detailed insight into the characteristics of fuzzy random systems, and the epistemic uncertainty in derivation of limit states can have significant effects on the reliability‐based collapse analysis. It is worth mentioning that to alleviate high computational demands in fuzzy probabilistic collapse analysis, a neural network metamodel is applied in conjunction with the genetic algorithm which is also of practical value to engineers and researchers.     

Life-cycle prediction of steel bridges using reliability-based fatigue deterioration profile: Case study of neka bridge

Fatigue deterioration profiles of critical elements in a railway truss bridge are determined using a probabilistic approach. A performance function including fatigue strength, R, and fatigue action, D, is used, where R is a material property with lognormal distribution. The random variable D depends on AASHTO category, stress spectrum and traffic features. By applying Monte-Carlo simulations on the performance function of each year, reliability index profile is calculated. The reliability profile decreases with life, and whenever reaches to a critical value, an MR&R action should be implemented. A numerical approach is presented to specify the effects of MR&R actions on the deterioration profile. These actions include re-welding, attaching CFRP and combination of them. The structural model is calibrated by results of a loading test. In addition, the uncertainties arisen from future traffic volume and the relevant S-N curve are considered by a statistical analysis. For a target reliability of 2.0, the retrofit time for deck and truss are estimated. Finally, the outputs of the research are used to recommend a plan for maintenance of Neka Bridge.     

Sensitivity analysis for failure assessment of concrete pipes subjected to sulphide corrosion

Sulphide corrosion in concrete sewers is the most common form of deterioration and should be investigated in failure assessment of sewage systems. Corrosion parameters are considered as random variables because of data scarcity and uncertainties involved in the corrosion affected concrete sewers. Sensitivity analysis is widely accepted as a necessary part of failure assessment of structures and infrastructure, in which the effect of random variables on the failure can be analysed.

In the current study, the results of sensitivity analysis of a corrosion affected concrete sewer in the UK showed that among eight random variables, alkalinity of concrete and relative depth of the flow have the most effect on the probability of sewer failure. The analysis showed less significant contribution of some variables in failure functions. Therefore, it would not be necessary to consider those parameters as random variables and they can be treated as deterministic constant values for further studies.     

Structural integrity of corrosion-affected cast iron water pipes using a reliability-based stochastic analysis method

A significant proportion of current water networks are composed of cast iron pipes. The occurrence of failures of this type of pipe is increasing due to ageing and progressive deterioration (i.e. corrosion). This necessitates the completion of structural integrity assessment and reliability analysis of in-service cast iron water pipes. The failure of a cast iron pipe can be characterised by fracture, when the stress intensity factor exceeds the toughness of the pipe material. In this research, a stochastic model for the stress intensity factor is developed and a time-dependent analysis method is employed to quantify the failure probability so that the time for the pipe to be failed and, hence, requiring repairs or replacement is determined with confidence. For a comprehensive structural assessment, two types of stresses (hoop and axial) are considered for two cases of corrosion (external and internal). A case study is provided to illustrate the application of the proposed method. In the system failure analysis, it is found that hoop stress is the dominant stress, since it can result in external corrosion, the effects of which are known to be of greater significance than those caused by internal corrosion.     

Coupled reliability model of biodeterioration, chloride ingress and cracking for reinforced concrete structures

Maintaining and operating civil infrastructure systems has been recognized as a critical issue worldwide. Among all possible causes of safety reduction during the structural lifetime, deterioration is particularly important. Structural deterioration is usually a slow time-dependent process controlled by safety and operation threshold specifications. This paper presents a model of RC deterioration by coupling biodeterioration (i.e., chemical, physical and mechanical action of live organisms), steel corrosion, and concrete cracking. The final purpose of the model is to compute the reduction of the concrete section and the area of steel reinforcement in order to assess the change of structural capacity with time. Given the uncertainties in both the parameters and the model, the probabilistic nature of loads, the material properties and the diffusion process are taken into account to evaluate structural reliability. The model is illustrated with an example where the inelastic behavior of a pile subject to random loading is considered. The results of the analysis have shown that the effect of biodeterioration on the structural performance is significant and can cause an important reduction of its lifetime. On the whole, the paper states that modeling the effects of biodeterioration in RC structures should be included as part of infrastructure planning and design, especially, when they are located in aggressive environments.     

Inspection and maintenance planning of underground pipelines under the combined effect of active corrosion and residual stress

In this paper, a maintenance policy is proposed for pipelines subjected to active corrosion and residual stress, by taking into account imperfect inspection results. The degradation of the pipeline is induced by uniform corrosion, leading to losses of the pipe wall thickness. Localized corrosion is not considered herein, as neither pitting nor crevice corrosion are strongly influenced by external loading conditions and, hence, are not critical in structural strength considerations. When the corroded layers are removed, strain relaxation occurs, causing a redistribution of residual stresses. In parallel, the inspection is applied to detect the corrosion defects, namely the thickness of the corroded layer, and it has a detection threshold under which no corrosion rate can be measured. Due to uncertainties, each inspection is affected by the probability of detecting small defects and the probability of wrong assessment in terms of defect existence and size. The present work aims at integrating imperfect inspection results in the cost model for corroded pipelines, where the failure probabilities are computed by reliability methods. A numerical application on a gas pipe shows the influence of corrosion rates and residual stresses on the optimal maintenance planning.     

Reliability evaluation of reinforced concrete beams

The purpose of this paper is to evaluate the time-invariant reliability of reinforced concrete beams designed under the provisions of the ACI Building Code. A wide range of practical design situations is considered. The beams are subjected to bending, shear, and torsion. The interaction between shear and torsion is considered via an elliptical failure surface defined in the shear-torsion stress space. No interaction is assumed between flexural resistance and resistance in both shear and torsion. Representative statistics and appropriate probability distributions of the basic resistance and load variables are selected from previous related work. The reliability analysis is performed using modern reliability methods, in which the formulation of the limit-state functions is consistent with the underlying design criteria. Reliability indices for various failure modes are compared and a system reliability analysis is performed to include all failure modes. It is found that the reliability indices are most sensitive to live load, model uncertainties, and material strengths. For the failure modes considered, the reliability indices are found to be rather insensitive to design parameter values, indicating that the ACI Building Code achieves its desired objective of uniform reliability across a wide range of design situations.     

Time-dependent performance indicators of damaged bridge superstructures

The ability of a structure to survive an extreme event without collapse reduces in time due to deterioration processes. Therefore, in the lifetime management of structures and infrastructures, the resistance to sudden local damage has to be considered together with the effect of progressive deterioration. The aim of this paper is to present a framework for computation of time-dependent performance indicators of civil structures and infrastructures, with emphasis on bridges, including reliability, vulnerability, robustness and redundancy. A brief theoretical background and selected structural performance indicators regarding vulnerability, redundancy and robustness are presented. The approach is based on probabilistic performance assessment supported by finite element analysis and applied to an existing bridge. Time-variation of vulnerability, redundancy and robustness associated with various damage scenarios under uncertainty and the effects of several loading conditions on performance are investigated.     

Event oriented analysis of series structural systems

The event oriented analysis of technical objects is in general accomplished by representing them as complete or incomplete systems and subsystems of events. It is argued in the article how the compound engineering systems of events can be partitioned by inclusion-exclusion expansion into individual and common cause modes. The event analysis is based on the random variable model and employs the results of operational modes and effect analysis, of the reliability analysis and of the uncertainty analysis. The system redundancy and robustness are considered as uncertainties, due to the fact that really a number of events are possible, expressed by the entropy concept in probability theory, conditioned by operational and failure modes, respectively. Relative and average uncertainty measures are introduced to facilitate uncertainty interpretations in engineering problems. It is investigated how the sensitivity analysis of reliability measures can be applied to the assessments of system uncertainties. Numerical examples presented in the article illustrate the application of event oriented system analysis to series structural systems with common cause failures. Additionally, system performance presentation and optimization with constraints, as well as potential improvements in system analysis, design and maintenance are investigated.     

氯盐侵蚀下修正混凝土桥梁的结构可靠性退化模型

结构退化可靠性(概率论)模型已经被用于计算结构的失效性。考虑钢筋混凝土腐蚀初始点、腐蚀速度以及时变荷载提出相应的修正模型。耐久性设计规范中已考虑混凝土桥梁的全寿命周期的可靠性分析以及时变荷载,但对于耐久性设计考虑不周,没有考虑到除冰盐的运用将引起长期退化和结构安全度的降低。另外,保护层厚度不足或水灰比过高也会增加结构失效的可能性。     

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.     

Condition assessment for bridges: a hierarchical evidential reasoning (HER) framework

Infrastructure risk management practices enable decision-makers to effectively monitor and assess structural condition for repairing/replacing elements before major damage or collapse state is reached. Improved techniques have enhanced inspection and monitoring of infrastructure, but assessment and interpretation of the collected data remains a challenge. In this article, a hierarchical evidential reasoning (HER) framework is proposed for the condition assessment of bridges. The approach involves using a HER framework for classifying bridge data into primary, secondary, tertiary and life safety-critical elements. The proposed HER framework combines different distress indicators (bodies of evidence) at different hierarchical levels. The information is aggregated using Dempster–Shafer (D–S) and Yager rule of combination to propagate both aleatory and epistemic uncertainties throughout the model. Furthermore, importance and reliability factors (collectively termed ‘‘credibility factor’) are introduced for discounting evidence based on importance of bridge element and reliability of the collected data. The data are systematically combined to obtain primary/secondary/tertiary/life safety-critical condition indices. Finally, an overall bridge condition index is obtained. The indices are based on information from multiple sources thereby providing a more reliable assessment of bridge condition. The HER framework is applied to data from an existing bridge in order to demonstrate application of the proposed approach.     

Influence of the exposure scenario and spatial correlation on the probabilistic life-cycle seismic performance of deteriorating RC frames

The probabilistic life-cycle seismic performance of reinforced concrete (RC) frames under chloride-induced corrosion is investigated considering the influence of the environmental aggressiveness and exposure scenario and the role of spatial correlation of the random variables. Chloride ingress and corrosion damage are described at cross-sectional level by two-dimensional concentration maps and damage indices. At the structural level, the seismic performance is evaluated in terms of lateral load response of the deteriorating structural system by means of time-variant non-linear analysis over the structural lifetime. The uncertainties involved in the problem are taken into account in probabilistic terms by Monte Carlo simulation. The procedure is applied to life-cycle assessment of a three-storey RC frame under different exposure scenarios, defined by varying both the concentration level and the spatial distribution of chlorides on the external surface of the columns, as well as different correlation levels of the random variables involved in the probabilistic analysis.     

Corrosion and capacity prediction of marine steel infrastructure under a changing environment

The deterioration of marine steel infrastructure caused by corrosion may be influenced by a changing climate and/or pollution level which may lead to its serviceability and structural failure. However, almost all corrosion research until recently assumed time-invariant environmental conditions. A structural reliability analysis is applied here to simulate steel sheet piles in sea water conditions under a changing environment. Corrosion of marine steel infrastructure is modelled as a spatial time-dependent process including sea water temperature and sea level rise due to global warming and dissolved inorganic nitrogen concentration increase caused by pollution. The steel sheet piles are divided vertically into 70 elements to consider the spatial variability of different corrosion zones and sea level rise effects. Two limit states are considered: (i) stress of steel sheet piles reaches their yield stress and (ii) pitting corrosion perforation to provide an alert to repair or maintenance. The results show that ignoring the effects of a changing environment can underestimate structural capacity failure risks, and pollution will have a more significant effect on capacity of steel sheet piles than sea water temperature and sea level rise caused by global warming.     

Probabilistic analysis of underground pipelines subject to combined stresses and corrosion

This paper presents a nonlinear limit state model for the analysis of underground pipelines, stressed both in the circumferential and the longitudinal directions. The effects of internal fluid pressure, external soil and traffic loads, temperature and longitudinal pipe bending etc., are considered. A nonlinear corrosion model is used to represent the loss of pipe wall thickness with time. To allow for the uncertainties of the design variables, a reliability analysis technique has been adopted; this also allows calculation of the relative contribution of the random variables and the sensitivity of the reliability index or failure probability. Results obtained for typical pipelines are presented.     

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.     

Effects of climate variations and global warming on the durability of RC structures subjected to carbonation

Carbonation affects the performance, serviceability and safety of reinforced concrete (RC) structures when they are placed in environments with important CO ₂ concentrations. Since the kinetics of carbonation depends on parameters that could be affected by climate change (temperature, atmospheric CO ₂ pressure and relative humidity (RH)), this study aims at quantifying the effect of climate change on the durability of RC structures subjected to carbonation risks. This work couples a carbonation finite element model with a comprehensive reliability approach to consider the uncertainties inherent to the deterioration process. The proposed methodology is applied to the probabilistic assessment of carbonation effects for several cities in France under various climate change scenarios. It was found that climate change and local RH have a significant impact on corrosion initiation risks.     

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.     

Structural reliability of concrete bridges including improved chloride-induced corrosion models

A structural deterioration reliability (probabilistic) model has been used herein to calculate probabilities of structural failure. New reinforced concrete corrosion initiation, corrosion rate and time-variant load models are proposed. Three durability design specifications are considered in a lifetime reliability analysis of a RC slab bridge. Time-variant increases in loads are considered also. It was found that the application of de-icing salts causes significant long-term deterioration and reduction in structural safety for poor durability design specifications. A reduced cover or increased water-cement ratio increases failure probabilities. When compared to the case of “no deterioration”, it was observed also that the probability of failure only marginally increased for good durability design specifications. The approaches described herein are relevant to other physical infrastructure also.