Numerical modeling for predicting service life of reinforced concrete structures exposed to chloride environments

Degradation of reinforced concrete (RC) structures due to chloride penetration followed by reinforcement corrosion has been a serious problem in civil engineering for many years. In the present paper, a systematic and robust model for predicting service life of RC structures is developed which takes environmental humidity and temperature fluctuations, chloride binding, diffusion and convection, as well as the decay of structural performance into account. The interactions between the decay of structural performance, heat and moisture transfer are considered in a coupled thermal-hygro-mechanical model. The governing equations of heat, moisture and chloride transport into nonsaturated concrete are described particularly and solved numerically by finite element analysis in space and time domains. Comparisons of numerical results with analytical solutions and experimental observations are conducted to establish the validity of the proposed numerical model. Applications of the numerical model are demonstrated by predicting service life of a RC slab exposed to a chloride environment.     

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.     

Water repellent surface impregnation for extension of service life of reinforced concrete structures in marine environments: The role of cracks

The enhancement of long-term durability of marine structures is a matter of interest to many researchers. The study presented in this paper examines the effectiveness of a water reducer and chloride barrier surface impregnation of the concrete cover of reinforced concrete (RC) structures, exposed to a marine environment. Specific focuses is on how surface cracks created (1) before impregnation and (2) after impregnation, affect the effectiveness of the surface treatment. The experiments are conducted in an environment which is as close as possible to the real humid subtropical marine environment.A series of reinforced concrete (RC) prisms and concrete cylinders, each treated with various commercial surface impregnation agents, were exposed to cyclic sea water shower under an outdoor environment to accelerate the dry/wet cycles for 1 year. Six types of surface impregnation agents, including four types of silane-based water repellent agents and two types of sodium silicate-based pore blockers (water–glass) were applied. Three types of RC prisms were prepared to simulate the different cracking possibilities, which may occur in surface impregnated concrete structures, during their service life. No cracks were introduced in the first prism group, while cracks were introduced before and after surface impregnation, in the second and third groups, respectively. The time-dependent water absorption of all specimens was monitored during exposure to the dry/wet cycles. Finally the specimens were split open to measure the penetration depths of the surface impregnation agents and the chloride penetration profiles. The areas with corrosion evident in the steel reinforcement in the RC prisms were also measured.Sodium silicate-based pore blockers were found to be inefficient in preventing chloride penetration of concrete under simulated marine exposures. The long-term efficiency of water repellent agents used for surface impregnation was found to be highly dependent on the type of agent and whether impregnation was carried out before or after crack formation.     

Methodology of calculating required chloride diffusion coefficient for intended service life as function of concrete cover in reinforced marine structures

For marine reinforced concrete (RC) structures, chloride initiated corrosion of reinforcement is generally accepted as the service life limiting degradation mechanism. A methodology is described for how the maximum required chloride diffusion coefficient (D) of a concrete for achieving an intended service life (t) can simply be calculated as a function of concrete cover thickness (x) over the reinforcement by D = constant·x²/t.The principle is based on the usual mathematical solution to Fick's 2nd law of diffusion. The constant is broken down into 3 factors; chloride concentration factor, aging factor and temperature factor, in which input parameters have to be selected. These factors are calculated for a range of selected input parameters illustrating their sensitivity. The largest uncertainty lays in proper selection of the aging factor of the diffusion coefficient. Some concrete recipes satisfying estimated chloride diffusion coefficients are proposed as part of the methodology.     

钢筋混凝土结构的温度场

火灾会导致钢筋混凝土性能退化,该文基于元胞自动机(Cellular Automata,CA)与纤维模型提出了一种用于火灾下钢筋混凝土梁非线性分析的方法。建立CA模型模拟了火灾中梁截面温度扩散演化过程,得到不同升温时间下截面各处的温度;引入损伤模型得到钢筋损伤因子-升温时间变化关系;将元胞自动机模型与纤维模型结合,对火灾下钢筋混凝土连续梁进行时变非线性分析。结果表明：CA模型能够有效模拟钢筋混凝土梁截面的温度扩散过程;引入的损伤模型可有效将钢筋损伤进行量化;编制的MATLAB计算程序可有效用于高温损伤后钢筋混凝土梁的非线性分析;CA模型与纤维模型的有效结合可分析钢筋混凝土梁的变形与承载力时变演化过程,并对其耐火寿命进行评估。该方法可为火灾下钢筋混凝土结构的耐火寿命预测与评估提供理论工具。     

Material model for the analysis of reinforced concrete surface structures

A material model for the analysis of reinforced concrete surface structures is developed. The constitutive model employs the smeared crack concept, i.e. only average stresses are considered at an integration point. While uncracked concrete is modelled with a plasticity approach, the paper focuses on the numerical treatment of cracked reinforced concrete in a state of plane stress. Special attention is given to the modelling of the tension stiffening effect, the re-orientation of the principal tensile strain direction and the compressive strength of cracked concrete. The material model has been implemented in the finite element program SEGNID and tested extensively. Here the comparisons of calculated and experimentally measured results on reinforced concrete surface structures-several panels, a plate subjected to torsion and a free-formed shell-are presented.List of symbols d bar diameter - D stiffness matrix - D _c stiffness matrix of concrete - D _s stiffness matrix of reinforcement - D rotational stiffness matrix - f stress - f _c stresses in concrete - f _c1 tensile stress in concrete - f _c2 compressive stress in concrete - f _c2,min concrete compressive strength - f _c cylinder crushing strength - f _s stresses in reinforcement - f _t concrete tensile strength - f _y yield strength of reinforcement - f ₁ applied principal tensile stress - f ₂ applied principal compressive stress - F tension force - F _y yield force - l length - M moment - Q dowel resistance - r _xy vector of unbalanced stresses - s applied load - s applied stress vector - T ₁, T ₂ transformation matrices - w crack width - x, y reference coordinate system - 1, 2 crack oriented coordinate system - curvature - _xy incremental strain in the reference coordinate system Extended version of the contribution Two-dimensional FE-analysis of reinforced concrete membrane elements to the International Conference on Computational Engineering Science, Atlanta, April 10–14, 1988, presented by the second named author     

A finite element for the analysis of reinforced concrete structures

Formulation of a four-node isoparametric element suitable for modelling cracks in reinforced concrete structures is presented. The standard isoparametric element is known to give spurious shear stresses. The conventional remedy of selective integration breaks down in a ‘cracked’ element. It is shown that the proposed formulation gives superior results as compared to both the standard isoparametric element and the conventional selectively integrated element.     

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.     

Reliability of reinforced concrete structures under fatigue

This paper focuses on time-variant reliability assessment of deteriorating reinforced concrete structures under fatigue conditions. A strategy combining two time scales, namely the micro-scale of instantaneous structural dynamics (or statics) and the macro-scale of structural lifetime, is proposed. Non-linear response of reinforced concrete structures is simulated by means of the finite element method with adequate material model. A phenomenological fatigue damage model of reinforced concrete is developed and calibrated against experimental results available in the literature. Reliability estimates are obtained within the response surface method using the importance/adaptive sampling techniques and the time-integrated approach. The proposed assessment strategy is illustrated by an example of a concrete arch under fatigue loading. The obtained results show a general inapplicability of local and linear fatigue models to system level of structures.     

High performance repairing of reinforced concrete structures

Steel fibered high strength concrete (SFHSC) is an effective material that can be used for repairing concrete elements. Design of normal strength concrete (NSC) elements that should be repaired using SFHSC can be based on general concepts for design of two-layer beams, consisting of SFHSC in the compressed zone and NSC without fibers in the tensile zone. It was previously reported that such elements are effective when their section carries rather large bending moments. Steel fibers, added to high strength concrete, increase its ultimate deformations due to the additional energy dissipation potential contributed by fibers. When changing the fibers’ content, a required ductility level of the repaired element can be achieved. Providing proper ductility is important for design of structures to dynamic loadings. The current study discusses experimental results that form a basis for finding optimal fiber content, yielding the highest Poisson coefficient and ductility of the repaired elements’ sections. Some technological issues as well as distribution of fibers in the cross section of two-layer bending elements are investigated. The experimental results, obtained in the frame of this study, form a basis for general technological provisions, related to repairing of NSC beams and slabs, using SFHSC.     

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.     

On-site detection of corrosion in reinforced concrete structures

The availability of on-site methods of diagnosis of the deterioration rate in reinforced concrete structures is a pressing technical need all over the world. Two new methods are proposed in this paper which are derived from the polarization resistance method, but which, differing from this method, are applicable to full-size structures, in spite of the non-uniform distribution of the electric signals in them. The two proposed procedures are of a simplicity and reliability comparable with those offered by direct measurement of polarization resistance.     

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 effect of steel fibres on the earthquake-resistant design of reinforced concrete structures

The results of an experimental investigation are presented, studying the effect of fibres on the behaviour of reinforced-concrete (RC) structures designed in accordance with Eurocode 8. Twelve two-span continuous RC columns, eight with and four without steel fibres, were tested to failure, under constant axial force and monotonic or cyclic lateral displacement. Specimens without fibres suffered in some cases premature brittle failure, reflecting the incompatibility between post-peak concrete behaviour and the theoretical model underlying RC design. It was shown that it is possible to correct for this incompatibility through the use of steel fibres, resulting in a behaviour that satisfied current performance requirements for strength and ductility.     

Performance of glass fiber reinforced plastic bars as a reinforcing material for concrete structures

The increasing use of fiber reinforced plastic (FRP) bars to reinforce concrete structures necessitates the need for either developing a new design code or adopt the current one to account for the engineering characteristics of FRP materials. This paper suggests some modifications to the currently used ACI model for computing flexural strength, service load deflection, and the minimum reinforcement needed to avoid rupturing of the tensile reinforcement. Two series of tests were conducted to check the validity of the suggested modifications. The first series was used to check the validity of the modifications made into the flexural and service load deflection models. The test results of the first series were also analyzed to develop two simple models for computing the service load deflection for beams reinforced with glass FRP (GFRP) bars. The second series was used to check the accuracy of the modification suggested into minimum reinforcement model.Test results of the first series indicate that the flexural capacity of the beams reinforced by GFRP bars can be accurately predicted using the ultimate design theory. They also show that the current ACI model for computing the service load deflection underestimates the actual deflection of these beams. The two suggested models for predicting service load deflection accurately estimated the measured deflection under service load, and the simpler of the two pertains better predictions than those of the models available in the literature. Test results of the second series reveal that there is an excellent agreement between the predicted and recorded behavior of the test specimens, which suggests the validity of the proposed model for calculating the required minimum reinforcement for beams reinforced by GFRP bars.     

A contribution to the gamma radiography of reinforced concrete structures

A systematic presentation of arrangements and materials for detection of reinforced concrete by means of gamma-radiography is the first aim of this paper. New proposals concerning auxiliary techniques in gamma-radiography have been investigated:

1. Photometric measurements on simple gamma-radiographies have been applied, in order to estimate the diameter of an embedded bar, on the basis of the difference in film density, between the image of the bar and its surrounding area.
2. Ordinary photogrammetric apparatuses have been used on twin stereo-radiographies for direct discrimination of complicated bars of concrete reinforcements. The same method has been applied for a direct reading of the position and diameter of every bar simultaneously, instead of repetitive application of two-equations systems for each bar in conventional stereo-radiography.

     

Multiprobe chloride sensor for in situ monitoring of reinforced concrete structures

In situ monitoring of the chloride content is one of the most important procedures in preventing and controlling chloride-induced corrosion in reinforced concrete structures. Thus, the development of chloride sensors is of paramount importance for the continuous monitoring of concrete structures. The sensors must present long lifetime and reliability and operate in a wide range of chloride concentrations.The present work aims at developing and testing a sensor based on Ag/AgCl electrodes for in situ monitoring of chloride ions in reinforced concrete structures. Although these electrodes are widely used in analytical experiments due to their sensitivity to the chloride ion, little is known on their behaviour during exposure to alkaline environments, such as those existing in concrete.The multiprobe sensor presented in this work was tested in mortar and concrete specimens, revealing good stability. The results reveal that the Ag/AgCl sensor presents good sensitivity in a wide range of chloride concentrations.