Probabilistic lifetime assessment of RC structures under coupled corrosion–fatigue deterioration processes
Introduction
Long-term performance of infrastructures is governed by structural deterioration, which is defined as the loss of capacity due to physical, chemical, mechanical or biological actions. Since corrosive environments and cyclic loading are among the main causes of reinforced concrete (RC) deterioration, a significant amount of research has been devoted to these two specific damage mechanisms [1], [2], [3]. Corrosion is the most common form of steel deterioration and consists in material disintegration as a result of chemical or electrochemical actions. Most metals corrode on contact with water (or moisture in the air), acids, bases, salts, and other solid and liquid chemicals. Metals will also corrode when exposed to gaseous materials like acid vapors, formaldehyde gas, ammonia gas, and sulfur containing gases [3]. Depending on the case, corrosion can be concentrated locally to form a pit, or it can extend across a wide area to produce general wastage. On the other hand, fatigue is the damage of a material resulting from repeated stress applications (e.g., cyclic loading). Fatigue is conditioned by many factors such as high temperature, i.e., creep–fatigue, and presence of aggressive environments, i.e., corrosion–fatigue [1], [2].
The damage to RC structures resulting from the corrosion of reinforcement is exhibited in the form of steel cross-section reduction, loss of bond between concrete and steel, cracking, and spalling of concrete cover [4], [5]. The corrosion of steel reinforcement has been usually associated with chloride ingress and carbonation [4]; however, recent studies have shown that other deterioration processes like biodeterioration might contribute significantly to this process [6]. In RC structures, the coupled effect of corrosion and fatigue has not been studied in as much detail as their separated effects. Coupled corrosion–fatigue deterioration results from the combined action of cycling stresses in corrosive environments. Localized corrosion leading to pitting may provide sites for fatigue crack initiation. Several experimental studies have shown that pitting corrosion has been responsible for the nucleation of fatigue cracks in a wide range of steels and aluminum alloys [7], [8], [9]. In such studies, pits are usually found at the origin of the fracture surface. Corrosive agents (e.g., seawater) increase the fatigue crack growth rate [10], whereas the morphology of metals/alloys at micro-level governs the pit nucleation sites [11]. Under these conditions, the formation and growth of pits is influenced by both a corrosive environment and cyclic loads and become a coupled damage mechanism.
Examples of structures that experience this type of damage are offshore platforms, bridges, chimneys and towers situated close to the sea or exposed to the application of de-icing salts. The effects of gradually accumulated corrosion on the low cycle fatigue of reinforcing steel have been recorded experimentally by Apostolopoulos et al. [12] showing that corrosion implies an appreciable reduction in the ductility, the strength and the number of cycles to failure.
Large research efforts have been made to predict the corrosion–fatigue life of structural members constituted by aluminum, titanium and steel alloys. Goswami and Hoeppner [13] proposed a seven-stage conceptual model in which the electrochemical effects in pit formation and the role of pitting in fatigue crack nucleation were considered. Other research studies focused on particular stages of the process. For instance, a transition model from pit to crack based on two criteria: stress intensity factor and competition between pit growth and crack growth, was proposed by Kondo [7], and further discussed by Chen et al. [14]. In order to take into consideration the entire progressive damage process and the uncertainties in each stage, Shi and Mahadevan [15] proposed a mechanics-based probabilistic model for pitting corrosion–fatigue life prediction of aluminum alloys.
The objective of this paper is to combine previous works on corrosion and fatigue to develop a probabilistic lifetime prediction model for RC structures under the coupled effect of corrosion and fatigue. The model assesses the total corrosion–fatigue life as the sum of three critical stages: (1) corrosion initiation and pit nucleation; (2) pit-to-crack transition, and (3) crack growth. The first considers the time from the end of construction until the generation of a pit. The length of this stage is estimated by considering Fick’s diffusion law and electrochemical principles. The second stage includes the pit growth until crack nucleation. In this stage the interaction between electrochemical and mechanical processes is taken into account. The latter stage covers the time of crack growth until reaching a critical crack size, which is defined as the crack size at which the RC member reaches a limit state of resistance.
The proposed model is described in Section 2. Section 3 presents a discussion about the probabilistic lifetime assessment and the reliability analysis. Finally, an application to bridge girders is given in Section 4.
Section snippets
Coupled corrosion–fatigue model
The corrosion–fatigue damage process in RC structures is conceptually depicted in Fig. 1. The process takes into account the interaction between (1) chloride ingress, (2) RC cracking and (3) cyclic loading. Chloride ingress leads to steel depassivation, and takes part in the kinematics of the corrosion process. Besides, the corrosion resulting from chloride ingress induces high localized corrosion (i.e., pitting corrosion), leading to reinforcing steel crack nucleation [7], [8], [9]. Concrete
Probabilistic lifetime assessment and time-dependent reliability analysis
An efficient probabilistic lifetime assessment depends on the integration of the mechanical model presented in Section 2 into a suitable probabilistic framework. Thus, the cumulative distribution function (CDF) of the total corrosion–fatigue life, , is defined as [26]where x is the vector of the random variables to be taken into account and f(x) is the joint probability density function of x. If structural failure is achieved when the crack or pit
RC girder and basic considerations
This section presents an example describing the coupled effect of corrosion–fatigue of a simply supported RC bridge girder subject to cyclic loading. The span of the girder is 10 m with the geometrical characteristics of the cross-section and the steel reinforcement given in Fig. 4b. The girder has been designed according to the EUROCODE 2 [28]. In addition to the dead load, a truck wheel load is applied on the girder. The design load, Pk, corresponds to a wheel load located in the middle of the
Conclusions
The combined action of corrosion and fatigue strongly influences the performance of RC structures and reduces substantially their lifetime. In this paper, a model that couples these two phenomena is developed and the consequences on the life-cycle of RC structures are assessed. The model takes into account the interaction between the following processes: (1) corrosion induced by chloride ingress, (2) concrete cracking resulting from the accumulation of corrosion products and (3) reinforcement
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