Stochastic service-life modeling of chloride-induced corrosion in recycled-aggregate concrete

The development and implementation of a stochastic service-life model for chloride-induced corrosion in reinforced recycled-aggregate concrete is presented in this work. The 1D model accounts for recycled aggregates that have been initially contaminated with chlorides from previous in-service exposure. Using a probabilistic approach, the model is employed to predict the service life of normal- and recycled-aggregate reinforced concrete with and without aggregate pre-contamination. Specifically, the effect of (a) type and replacement ratio of reclaimed aggregate, (b) chloride boundary conditions, (c) initial aggregate chloride concentration, and (d) thickness of contaminated aggregate shells on time to corrosion cracking was investigated herein. Results suggest that certain levels of contamination may be permissible in the design of reclaimed-aggregate reinforced concrete structures. Furthermore, quality control standards that limit thresholds of recycled aggregate replacement ratios and aggregate purity should be based on anticipated exposure conditions and old mortar thicknesses rather than initial degrees of aggregate contamination.     

Probabilistic capacity models and seismic fragility estimates for RC columns subject to corrosion

In this paper, probabilistic drift and shear force capacity models are developed for corroding reinforced concrete (RC) columns. The developments represent a merger between a probabilistic model for chloride-induced corrosion, a time-dependent corrosion rate, and previously developed probabilistic models for drift and shear force capacity of pristine (undamaged) RC columns. Fragility estimates are obtained for an example corroding column by applying the developed models at given shear and drift demands. Model uncertainties in both the capacity and corrosion models are considered in the fragility estimation, in addition to uncertainties in environmental conditions, material properties, and structural geometry. Sensitivity analyses of the corroding RC column are carried out to identify the parameters to which the reliability of the example column is most sensitive. The developed models consider different combinations of chloride exposure condition, environmental oxygen availability, water-to-cement ratios, and curing conditions. They are applicable to both existing and new RC columns and may be employed for the prediction of service-life and life-cycle cost analysis of RC structures.     

Probabilistic modeling of chloride-induced corrosion in concrete structures using first- and second-order reliability methods

Concrete structures are subjected to chloride-induced corrosion that can lead to shortened service life. Reliable predictions of life cycle performance of concrete structures are critical to the optimization of their life cycle design and maintenance to minimize their life cycle costs. This paper presents two simplified semi-analytical probabilistic models based on the first- and second-order reliability methods to model the uncertainty of the key parameters including surface chloride concentration, chloride threshold, cover depth and diffusion coefficient, which govern the chloride ingress into concrete and corrosion of reinforcing steel. A case study of a reinforced concrete highway bridge deck is used to illustrate the capability and efficiency of these simplified probabilistic models in modeling the uncertainty and predicting the time-dependent probability of corrosion. The models enable to quantify the impact of the different governing parameters on probability of corrosion and service life, which can be used to develop cost-effective management strategies.     

Influence of chloride threshold value in service life prediction of reinforced concrete structures

Extensive studies have been reported on the development of service-life prediction of reinforced concrete structures in the last two decades. Service life of a reinforced concrete structure is dependent on the corrosion process, specifically chloride threshold value. Chloride threshold value is a distinctive property and is dependent on several factors such as the supplementary cementitious material used, presence of surface cracks, water to binder ratio, type of steel reinforcement, exposure conditions, measurement methods, etc. Although chloride threshold value is an influential parameter in service-life prediction, a definitive chloride threshold value considering these factors is not reported in the existing literature and standards. Moreover, values adopted in many analytical tools for service life predictions based on the type of steel reinforcement alone are not appropriate and leads to inaccurate calculations. There is a gap in the available literature in understanding the selection of suitable chloride threshold values to be adopted for a specific system. Therefore, it is imperative to study the variation of chloride threshold value with exposure conditions as well as other influencing parameters, to achieve proper service life prediction. In the paper, several influencing parameters on chloride threshold value and its significance on prediction method are comprehensively reviewed. Moreover, suitable recommendations are highlighted for Indian and international standards at the later part of the study.     

基于氯盐最不利侵蚀下锈蚀RC框架结构时变地震易损性研究

基于一维Fick第二定律,采用DuraCrete规范中钢筋锈蚀初始时刻的概率预测模型,并基于概率统计的钢筋直径预测模型,计算不同龄期下RC结构中钢筋的锈蚀深度。基于修正斜压场理论并以锈蚀深度为单变量,对不同龄期下受压区锈胀开裂混凝土峰值应力进行计算;根据锈蚀深度对钢筋本构和Mander约束混凝土本构模型中相关参数进行了修正。于地震易损性模型中引入时间参数,建立含时间参数的RC结构地震易损性模型。最后,基于上述材料力学性能退化模型,采用基于力的纤维塑性铰模型,建立三层RC平面框架结构数值模型,并结合本文所提出的时变地震易损性模型,给出了三层平面RC框架0、5、10和15年龄期的易损性曲线和曲面。所提研究方法可用于既有RC框架结构生命周期内的抗震性能及损失预测分析。     

Probabilistic design and management of environmentally sustainable repair and rehabilitation of reinforced concrete structures

This paper presents a probabilistic sustainability design framework for the design of concrete repairs and rehabilitations intended to achieve targeted improvements in quantitative sustainability indicators. The framework consists of service life prediction models combining deterioration mechanisms with limit states and life cycle assessment models for measuring the impact of a repair or rehabilitation. Both types of models (service life or LCA) are formulated stochastically so that the time to repair and the accumulated sustainability impact are described by probability density functions. This leads to a probabilistic calculation of cumulative impacts throughout the structure’s service life, from initial repair to functional obsolescence (end of life). The methods discussed are in accordance with sustainability design requirements within the 2010 fib Model Code. A case study is presented which computes the probability that reinforced concrete repair strategies using thicker concrete cover will meet future greenhouse gas emission reduction targets proposed by the UN Intergovernmental Panel on Climate Change.     

Evaluation of service life design models on concrete structures exposed to marine environment

Durability of reinforced concrete is primarily influenced by the penetration of aggressive substances into concrete, which are degrading concrete and reinforcement. For structures in marine environment chlorides are the most critical environmental load, which are causing serious corrosion damages. Data collected during the survey of the Krk Bridge, a large reinforced concrete arch bridge structure located on the Adriatic coast, is used as documented reference in this research. The structure has been exposed to the marine environment for over 25 years. Based on collected materials data and the exposure conditions, the service life of this structure is estimated using three currently available prediction models, two deterministic models, the North American Life-365 model and the Croatian CHLODIF model, and the DuraCrete probabilistic method. All these models are based on the chloride diffusion process, but with different detailing of the model parameters. The conclusion is an evaluation of the service life predictive ability of each of these three service life models.     

Concrete cover cracking due to uniform reinforcement corrosion

Service life design (SLD) is an important tool for civil engineers to ensure that the structural integrity and functionality of the structure is not compromised within a given time frame, i.e. the service life. In SLD of reinforced concrete structures, reinforcement corrosion is of major concern and reinforcement de-passivation is a frequently used limit state. The present paper investigates an alternative limit state: corrosion-induced cover cracking. Results from numerical simulations of concrete cover cracking due to reinforcement corrosion are presented. The potential additional service life is calculated using literature data on corrosion rate and Faraday’s law. The parameters varied comprise reinforcement diameter, concrete cover thickness and concrete material properties, viz. concrete tensile strength and ductility (plain concrete and fibre reinforced concrete). Results obtained from the numerical simulations reveal that, depending on the serviceability limit state applied, the service life of a reinforced concrete structure can be increased significantly by allowing minor damage of the cover.     

碳化环境下混凝土结构耐久性模型的更新方法

碳化环境下的混凝土结构耐久性模型,是基于扩散理论、快速试验、自然暴露试验以及工程经验建立的。由于结构固有的不确定性和服役环境的复杂性,理论模型的预测结果与实际结构检测的耐久状况存在较大偏差。该文利用工程耐久性检测获得的碳化深度、检测钢筋锈蚀比例、检测混凝土开裂比例,综合先验知识,基于贝叶斯理论,提出碳化环境下的耐久性模型更新方法。结合结构实际的检测结果,经过更新的耐久性预测模型与待评估结构实际耐久状况更相符。依此模型进行相应剩余耐久寿命的概率预测和耐久性评级,为既有结构耐久性评估提供参考。     

锈蚀钢筋混凝土柱的修正压-剪-弯分析模型研究

随着服役时间的增加,混凝土结构中钢筋易发生锈蚀,引起混凝土结构承载性能下降,严重影响工程结构的继续使用。该文在分析纵筋锈蚀后的屈曲效应、箍筋锈蚀后的约束效应、混凝土和钢筋材料性能劣化的基础上,建议了考虑锈蚀影响的钢筋、混凝土及锈蚀钢筋与混凝土界面粘结性能的本构模型,以锈蚀钢筋混凝土柱为研究对象,对反复荷载作用下钢筋混凝土柱的分析模型进行修正,建立了锈蚀钢筋混凝土柱压-剪-弯交互作用下极限承载力计算模型,并通过21根锈蚀混凝土柱的试验结果对建议分析模型进行了验证。研究结果表明:锈蚀钢筋混凝土柱极限承载力试验值与计算值之比的平均值为1.021,方差为0.014,建议模型极限承载力预测值与试验结果吻合较好,可用于低周反复荷载作用下锈蚀钢筋混凝土柱的承载力分析。     

Durability design of reinforced concrete structures: a comparison of the use of durability indexes in the deemed-to-satisfy approach and the full-probabilistic approach

To show the application of the chloride conductivity index test in service life prediction (SLP) using both the deemed-to-satisfy and probabilistic approaches to performance-based durability design. It is desirable to adopt a performance-based approach with respect to durability design of reinforced concrete (RC) structures. This is based on the perception that the durability of RC is achieved when the limiting value from an established test method is met. In South Africa, the durability index (DI) approach has been developed, which permits performance-based specifications for durability of RC. This approach involves the application of a test method together with a SLP model. This integrated approach links material properties directly with the expected service life of RC structures and environmental conditions. Two DIs are relevant to degradation processes in RC: the chloride conductivity index which is related to chloride ingress, and the oxygen permeability index related to carbonation. The study presented here focuses on the application of the chloride conductivity index as the main input parameter of a SLP model concerned with chloride-induced reinforcement corrosion. The methodology and output of the SLP model as applied in the deemed-to-satisfy approach are compared with those of the probabilistic approach. Both approaches are exemplified using a concrete pier cast in situ in a marine environment. The performance-based durability specifications from the deemed-to-satisfy approach are found to be more conservative compared to those of the probabilistic approach.     

Probabilistic models applied to safety assessment of reinforced concrete structures subjected to chloride ingress

This paper addresses the analysis of probabilistic corrosion time initiation in reinforced concrete structures exposed to chloride penetration. Structural durability is an important criterion that must be evaluated for every type of structure. Considering reinforced concrete members, chloride diffusion process is widely used to evaluate durability, especially when these structures are constructed in aggressive atmospheres. The chloride ingress triggers the corrosion of reinforcements; therefore, by modelling this phenomenon, the corrosion process can be better evaluated as well as the structural durability. The corrosion begins when a threshold level of chloride concentration is reached at the steel bars of reinforcements. Despite the robustness of several models proposed in the literature, deterministic approaches fail to predict accurately the corrosion time initiation due the inherent randomness observed in this process. In this regard, structural durability can be more realistically represented using probabilistic approaches. A probabilistic model capable to model chloride ingress is presented in this paper. The chloride ingress is modelled using the Fick’s diffusion law. This law simulates the chloride diffusion process considering time-dependent effects. The probability of failure is calculated using Monte Carlo simulation and the first order reliability method with a direct coupling approach. Some examples are considered in order to study these phenomena. Moreover, a simplified method is proposed to determine optimal values for concrete cover.     

Computer-aided modeling of concrete service life

A significant step forward for a thorough durability design process of reinforced concrete structures is the development of software packages, based on predictive models, for the estimation of concrete strength and service life. Such an attempt, in full compliance with the European Standards for cement and concrete, is presented in this study. Upon defining the concrete mix design, the software calculates the main chemical and volumetric characteristics, as well as the compressive strength, of concrete. By taking into account the environmental conditions where the structure will be exposed, concrete service life is predicted, using fundamental mathematical models (based on reaction engineering principles) that simulate the reinforced concrete deterioration mechanisms leading to corrosion of the embedded reinforcement (caused by either carbonation or chloride ingress). A validation process of the yielded results is also presented, and the effectiveness of the simulation tool in designing for durability is illustrated. The goal of this study is to promote wider acceptance in achieving feasible and durable solutions to structural concrete design problems.     

钢筋混凝土腐蚀研究综述

综合探讨了混凝土中钢筋腐蚀的机理、影响因素及其检测方法,以及腐蚀结构的耐久性评定和使用寿命预测,通过分析提出了混凝土钢筋腐蚀研究的难点以及今后的重点研究方向。     

Modeling of chloride-induced corrosion in reinforced concrete structures

A numerical procedure is presented in this paper for the prediction of chloride induced steel corrosion in reinforced concrete structures. Finite element analysis is introduced for the mechanical analysis of crack initiation and propagation due to the accumulation of corrosion products around the reinforcement, while the alternating direction implicit method is used to solve the transport equations of temperature, humidity, chloride ions and oxygen in concrete. Based on the assumption of a uniform distribution of corrosion products, a self-adaptation process for the variation of boundary conditions is proposed through a series of diffusion analyses together with crack propagation in concrete. Therefore, the interaction between the corrosion rate and the propagation of cracks in concrete is taken into account. Furthermore, a numerical program is developed and a case study involving bridge deck exposed to a marine environment in Hong Kong is investigated. The results show that interactive behavior has a significant effect on the corrosion rate of the reinforcement, and the non-cracking model significantly overestimates the service life of structures.     

The rate of corrosion of concrete reinforcement and possibilities of its mathematical modelling

The paper describes a method for the mathematical modelling of steel reinforcement corrosion rate. This method is based exclusively on experimental results and expression of the influence of significant corrosion factors in the form of functional relations. The method takes into account the reality of the effects of corrosion factors, their contigency and complexity, and various circumstances occurring in practice. It represents one way towards the development of methods for the prediction of service life of reinforced concrete and structures.     

Some questions on the corrosion of steel in concrete. Part II: Corrosion mechanism and monitoring,service life prediction and protection methods

This second part addresses some important issues that remain controversial despite the vast amounts of work devoted to investigating corrosion in concrete-embedded steel. Specifically, these refer to: 1) the relative significance of galvanic macrocouples and corrosion microcells in reinforced concrete structures; 2) the mechanism by which reinforcements corrode in an active state; 3) the best protective methods for preventing or stopping reinforcement corrosion; 4) the possiblity of a reliable prediction of the service life of a reinforced concrete structure; and 5) the best corrosion measurement and control methods. The responses provided are supported by experimental results, most of which were obtained by the authors themselves.     

锈蚀钢筋混凝土结构可靠度评估

钢筋锈蚀是混凝土结构破坏最主要的原因之一,目前钢筋混凝土结构可靠度研究大多数没有考虑锈蚀的影响。提出了锈蚀钢筋混凝土结构可靠度评估方法。首先分析大气环境下和氯离子环境下钢筋锈蚀的模型,然后考虑钢筋面积和粘结强度的降低,建立锈蚀钢筋混凝土结构抗力的随机模型,最后采用一次二阶矩实用分析法计算可靠度指标,以评估大气环境下和氯离子环境下混凝土结构可靠度。两个算例表明,该方法可用于锈蚀钢筋混凝土结构可靠度评估。     

Possibility of improvement of potentiodynamic method for monitoring corrosion rate of steel reinforcement in concrete

Quantitative data on corroding steel reinforcement in reinforced concrete structures are undoubtedly very useful for evaluation of their service life and timely repairs. The method of electrode potential measurement is a convenient and simple test for this purpose, but it provides no quantitative data on corrosion rate and only information regarding active or passive state of steel reinforcement can be obtained. We show here the possibility of obtaining quantitative data on degree of corrosion of steel reinforcement by a potentiodynamic method. The developed method is based on experimentally estimated mathematical relation between the results of potentiodynamic method and degree of corrosion of steel reinforcement. It is possible to calculate the degree of corrosion of steel reinforcement using this mathematical relation and the measured values of current density by the potentiodynamic method.     

Reinforced concrete bridge deck reliability model incorporating temporal and spatial variations of probabilistic corrosion rate sensor data

The reliability of reinforced concrete (RC) bridge decks depends significantly on the rate of corrosion of the reinforcing steel. Structural health monitoring (SHM) techniques, including embedded corrosion rate sensors, can greatly improve the quantification of the steel corrosion rate, which can lead to improved estimates of structural safety and serviceability. Due to uncertainties in concrete properties, environmental conditions, and other factors, the rate of corrosion of reinforcing steel can be highly variable, both within a given structural component and over time. By placing multiple corrosion rate sensors throughout a structural component, such as a bridge deck, these spatial and temporal variabilities can be monitored and as such better predicted, for use in a reliability model. The objective of this investigation is to present a reliability model for a RC bridge deck incorporating both spatial and temporal variations of probabilistic corrosion rate sensor data. This objective is accomplished using a computational reliability model and Monte Carlo simulation. Corrosion rate sensor data is assumed for multiple critical sections throughout a RC bridge deck over time by applying empirical spatial and temporal relationships. This data is then used to improve an existing spatially invariant reliability model. The improved reliability model incorporates several sub-models to determine the changes in load effects on and resistance of a RC bridge deck slab over time, as well as spatial correlation of corrosion and a system approach to account for spatial variability. The improved reliability model incorporating both spatial and temporal variations in corrosion rate data provides a better estimate of the service life of a RC bridge deck slab.