تجزیه و تحلیل حساسیت مبتنی بر انتشار ساده مدل شروع خوردگی سازه های بتنی در معرض کلریدها

This paper presents the results of a sensitivity analysis of the diffusion-based corrosion initiation model for reinforced concrete structures built in chloride-laden environments. Analytical differentiation techniques are used to determine the sensitivity of the time to corrosion initiation to the four governing parameters of the model, which include chloride diffusivity in concrete, chloride threshold level of steel reinforcement, concrete cover depth, and surface chloride concentration. For conventional carbon steel, the time to corrosion initiation is found to be most sensitive to concrete cover depth, followed by chloride diffusion coefficient, with normalized sensitivity coefficients of about 2 and − 1. For corrosion resistant steels, the time to corrosion initiation is most sensitive to the surface chloride concentration and chloride threshold level followed by the concrete cover depth and chloride diffusion coefficient. The results of this sensitivity analysis are discussed in detail, including the variations in predicted time to corrosion initiation induced by variations of the four model parameters and their implications for the design and maintenance of concrete structures built in corrosive environments.

The chloride-induced corrosion of the steel reinforcement is identified as the main cause of deterioration of different types of concrete structures (e.g. bridges, parking garages, off-shore platforms, etc.). The sources of chlorides are the seawater and deicing salts used during winter. The corrosion of the steel reinforcement leads to concrete fracture through cracking, delamination and spalling of the concrete cover, reduction of concrete and reinforcement cross sections, loss of bond between the reinforcement and concrete, and reduction in strength and ductility. As a result, the safety and serviceability of concrete structures are reduced. One of the earliest studies on corrosion of reinforcing steel embedded in concrete structures was reported by Stratfull [22], in which chlorides and moisture were identified as the main causes for extensive corrosion in reinforced concrete bridge piers built in a marine environment after only seven years from initial construction. In the last three decades, the chloride-induced corrosion of reinforced concrete structures has been extensively studied [8], [19], [15] and [6], particularly, as a result of the high costs of highway bridge repair in North America and Europe from the effects of deicing salts used during winter or from seawater for coastal structures. A reliable prediction of the time to corrosion initiation of concrete structures exposed to chlorides is critical for the selection of a durable and cost-efficient design and for the optimization of the inspection and maintenance of built structures, which is essential to minimize the life cycle costs. Existing models are mostly based on the assumption of a Fickian process of diffusion for predicting the time and space variations of chloride content in concrete and on the concept of chloride threshold to define the corrosion resistance of reinforcing steel to chloride attack. Therefore, the governing parameters of this diffusion-based corrosion initiation time include the concrete cover depth, chloride diffusion coefficient in concrete, surface chloride concentration, and chloride threshold level assuming the presence of moisture and oxygen for the corrosion to proceed. In practice, the design of durable concrete structures is mainly based on specifying a minimum concrete cover depth (depending on the environmental exposure), a maximum water-to-cement ratio (to achieve low chloride diffusivity), and as well the use of more corrosion resistant reinforcing steels (e.g. stainless steel). However, a considerable level of uncertainty may be associated with one or more of the above identified parameters. This is due to: (i) heterogeneity and aging of concrete with temporal and spatial variability of its chloride diffusivity; (ii) variability of concrete cover depth, which depends on quality control, workmanship and size of structure; (iii) variability of surface chloride concentration, which depends on the severity of the environmental exposure; and (iv) uncertainty in chloride threshold level that depends on the type of reinforcing steel, type of cementing materials, test methods, etc. [1]. It is clear that the combination of these uncertainties leads to a considerable uncertainty in the model output, i.e. the time to corrosion initiation. This uncertainty in the model output could have serious consequences in terms of reduced service life, inadequate planning of inspection and maintenance and increased life cycle costs. Therefore, undertaking a sensitivity analysis becomes imperative to assess the impact of uncertainties from the input parameters on the uncertainty of the model output. In the literature, several methods and techniques have been used for the sensitivity analysis of different types of models in different fields of applications, including Monte Carlo simulations, response surface methods, differential analysis techniques, nominal range sensitivity analysis, etc. [21]. Fewer sensitivity studies are found in the literature that deal with the performance of concrete structures that incorporate or evaluate the impact of the uncertainties in the model parameters on the model output, such as service life [5], [11], [12], [13] and [14]. In this paper, a sensitivity analysis of the diffusion-based model for time to corrosion initiation using the differential analysis technique is undertaken to identify the most significant parameters and quantify their impacts on the time to corrosion initiation. This consists of evaluating the variations in the time to corrosion initiation caused by variations in the input data of the model, which include concrete cover depth, chloride diffusion coefficient, surface chloride concentration, and chloride threshold level. The results of a sensitivity analysis can provide valuable insights and a better understanding of the chloride diffusion-induced corrosion of reinforcing steel in concrete and its governing parameters. A sensitivity analysis can be used to identify the importance of uncertainties in the model input for the purpose of prioritizing additional data collection or research on the parameters that are found significant. Furthermore, the results of a sensitivity analysis can provide effective decision support in the design of durable new structures, as well as in the optimization of inspection and maintenance of existing structures.

The sensitivity of time to corrosion initiation of the reinforcing steel to the four governing parameters of the diffusion-based corrosion initiation model, namely the cover depth, chloride diffusivity, surface chloride concentration and chloride threshold level was investigated. The variations in time to onset of corrosion induced by realistic variations of the four governing parameters were determined. These results have important applications in both modeling and practice: 1. The sensitivities of the time to corrosion initiation to concrete cover and chloride diffusion coefficient are independent of the ratio of surface chloride content and chloride threshold of the steel. The concrete cover depth has a higher impact on time to onset of corrosion than does the diffusion coefficient. 2. Considering a feasible range of chloride diffusion coefficients that is relatively easy to achieve in practice for normal concrete, say from 10− 12 to 10− 11 m2/s, decreasing the chloride diffusion coefficient is considered as an effective measure of extending the time to onset of corrosion. A 50% decrease in the chloride diffusion coefficient increases the time to corrosion by 100%. Increasing the concrete cover is an even more effective parameter than chloride diffusion coefficient, since a 50% increase of concrete cover increases the time to onset of corrosion by 125%. 3. The sensitivity of the time to corrosion to the surface chloride content is a function of the ratio of surface chloride content and chloride threshold of the steel. A 50% decrease in surface chloride content would extend the time to onset of corrosion by 261%, 95%, 69%, and 51% in light, moderate, high, and severe conditions, respectively. 4. The sensitivity of the time to corrosion to the chloride threshold level is a function of the ratio of surface chloride content and chloride threshold of the steel. Considering only the “intrinsic” variations (± 40%) associated with conventional black carbon steel that are mainly caused by the heterogeneous nature of concrete materials, the variation in time to onset of corrosion will be − 40% to 60%, − 28% to 32%, − 26% to 24%, and − 24% to 19%, for light, moderate, high, and severe exposure conditions, respectively. Comparing different corrosion resistant steels, the sensitivity is higher for more corrosion resistant steels with higher chloride thresholds. In practice, increasing chloride threshold is an effective measure to increase the time to onset of corrosion, but the effectiveness of using a more corrosion resistant steel will be lowered with the increasing severity of the exposure, e.g. a 50% increase in chloride threshold will extend the time to onset of corrosion by 260%, 100%, 69%, and 36% for light, moderate, high, and severe conditions. In summary, a sensitivity analysis was presented in this paper to quantify the error in the predicted time to corrosion initiation by using the simplified deterministic diffusion model with parameters that can have high levels of uncertainty. The impact of each design parameter on the service life of concrete structures that is critical for a durable design was also evaluated. The results of this sensitivity analysis can be used as a guide for the design of durable concrete structures built in chloride-laden environments and for the optimization of inspections and priorities of data collections.