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.     

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.     

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     

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.     

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.     

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.     

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.     

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.     

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.

     

A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures

A three-dimensional meshfree method for modeling arbitrary crack initiation and crack growth in reinforced concrete structure is presented. This meshfree method is based on a partition of unity concept and formulated for geometrically non-linear problems. The crack kinematics are obtained by enriching the solution space in order to capture the correct crack kinematics. A cohesive zone model is used after crack initiation. The reinforcement modeled by truss or beam elements is connected by a bond model to the concrete. We applied the method to model the fracture of several reinforced concrete structures and compared the results to experimental data.     

Reliability assessment and design load factors for reinforced concrete containment structures

The current ASME code for reinforced concrete containment structures is not based on probability concepts. This paper develops reliability assessment and probability-based design load factors for reinforced concrete containment structures. The purpose of constructing reinforced concrete containment structures is to protect against radioactive release, and so the use of a serviceability limit state related to cracking that can cause the emission of radioactive materials is suggested as a critical limit state for reinforced concrete containment structures. Load factors for the design of reinforced concrete containment structures are proposed. The proposed load factors are also examined in terms of a set of code performance objectives and consistency in limit state probability.     

Doubling the service life of concrete structures. II: Performance of nanoscale viscosity modifiers in mortars

A new approach for increasing the service life of concrete structures is evaluated in a series of mortar specimens. The new approach consists of employing nanoscale viscosity modifiers to increase the viscosity of the concrete pore solution and concurrently and proportionally decrease the diffusion rates of deleterious ions such as chlorides and sulfates. In part I of this series, viscosities of bulk solutions of the admixtures in water and electrical conductivities of admixture solutions also containing potassium chloride were examined to verify the viability of this new technology. In the current paper, these studies are extended to quantifying the performance of one of these admixtures in mortars by measuring the penetration depth of chloride ions in cylindrical specimens exposed to a 1 mol/L chloride ion solution for up to 1 year. While significant reductions in the 1 year penetration depth are produced when the viscosity modifier is utilized via conventional addition to the mixing water, the best performance is achieved when a solution of the viscosity modifier is utilized to pre-wet fine lightweight aggregates that are then added to the mortar mixture. A scaling function appropriate for radial diffusion was used to estimate the relative effective diffusion coefficients. Compared to a reference mortar, the best mixture reduced the effective diffusion coefficient by a factor of 2.7, consistent with the overall objective of doubling concrete service life.     

Constitutive modeling of reinforced concrete and prestressed concrete structures strengthened by fiber-reinforced plastics

A batch of constitutive models for steel reinforcing bar, prestressing tendon, concrete and fiber-reinforced plastic are proposed for the nonlinear finite element analysis of reinforced concrete structures, prestressed concrete structures, reinforced concrete structures strengthened by fiber-reinforced plastics and prestressed concrete structures strengthened by fiber-reinforced plastics. These material models have been tested against series of experimental data and good agreements have been obtained, which justifies the validity and the usefulness of the proposed nonlinear constitutive models.     

Reliability of testing procedures for reinforced concrete structures experimentally checked on bending-stressed beams

The investigation, carried out to check the reliability of testing procedures for reinforced concrete structures reported in Eurocode 2 (1988), has revealed situations in which bending-stressed beams, even when seriously defective, could be judged correctly built because residual deflections after the first or second short-term loading may remain within the limit set by EC2 for passing the test. Even an eventual check on elastic deformability, at least as usually carried out, does not substantially improve the reliability, which definitely improves only if the theoretical deflections are calculated with particular care (among other things, by experimentally measuring the concrete elastic modulus and by introducing the real value for the homogenization coefficient for steel areas instead of the conventional one); but, though it appears capable of revealing anomalies in the stress level in concrete, it fails to reveal a lack of concrete strength. It can be concluded that these procedures need improvement.

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Resume Les études menées pour vérifier la fiabilité des modes opératoires d’essai des structures de béton armé, décrites par l’Eurocode 2 (1988), ont mis en évidence des cas où des poutres contraintes en flexion, même lorsqu’elles étaient très défectueuses, ont pu être jugées correctes, du fait que, après le premier ou le deuxième chargement de courte durée, des courbures résiduelles peuvent subsister dans la limite admissible de l’Eurocode 2. Même une vérification éventuelle de la déformabilité, du moins telle qu’elle est effectuée en général, n’améliore pas notablement la fiabilité, qui ne progresse nettement qui si les flèches théoriques sont calculées avec un soin particulier, notamment en mesurant expérimentalement le module élastique du béton et en introduisant la valeur réelle du coefficient d’homogénéisation pour les zones d’armature au lieu du coefficient conventionnel; cependant, si on peut ainsi détecter des anomalies dans le niveau de contrainte du béton, on ne peut déceler un défaut de résistance du béton. En conclusion, ces méthodes demandent à être améliorées.