Life-cycle modelling of concrete cracking and reinforcement corrosion in concrete bridges: A case study
Introduction
As one of the fundamental transport infrastructures, bridges continuously support social and economic development of the world. The consistently operational performance of bridges plays a critical role for both public and private sectors. Bridge inspection, maintenance and repair become daily routines for maintaining the health of bridges [1]. However, the service life of many bridges in the world is expected to be less than their design life due to the continuous deterioration of bridges induced by daily traffic loading and environmental conditions [2], [3]. Therefore, it becomes increasingly important to maintain and repair the deteriorated bridges in a timely and cost-effective manner.
Concrete is one of the commonly used construction materials for bridges. Concrete cracking is generally used as one of the primary indicators for assessing the severity of reinforced concrete (RC) bridge deterioration [4]. Cracks in RC bridges can be classified into two main types, i.e. loading cracks and non-loading cracks [5]. While the non-loading cracks are mainly caused by environmental factors (e.g. cyclic changes in temperature and moisture), the loading cracks are caused by external loading imposed on the bridges (e.g. traffic loading, earthquake, etc.) [6], [7]. The crack development in RC bridges over time could result in the corrosion of reinforcements in concrete, delamination, which affects the mechanical properties of concrete material, and ultimately reduce the service life of a bridge [8]. Most importantly, corrosion of steel bars in concrete induced by cracking may lead to the failure of the bridges. Concrete cracking and corrosion of reinforcing steel bars have a bilateral influence on each other [9]. During the corrosion process of steel bars, the hydrated ferric oxide (i.e. rust), which is a larger substance than the original ferrous hydroxide, causes the expansion of the internal space between concrete and reinforcing steel bars. This produces a higher inner pressure in concrete which results in the formation of cracks around the interface between concrete and steel bars [10]. As the corrosion proceeds, cracks can propagate from the inner surface to the external surface, i.e. so-called corrosion-induced cracking. Although a high alkaline environment in concrete can hinder the corrosion of steel bars through the formation of a passive layer, cracks in concrete could provide a pathway for chloride ions, acidic ions, carbon dioxide and other substances to corrode the steel bars in concrete [11]. In addition, under sulfate attack, formation of ettringite could happen in concrete [12], ultimately lead to concrete cracking due to expansion of ettringite within the concrete [13]. Previous experimental studies have shown that the steel bar corrosion in concrete depends on crack characteristics [14], such as width, types and frequency, particularly at the initial stage of corrosion.
Several theoretical studies have been carried out to investigate the relationship between corrosion of steel bars and crack development in RC structure members [15], [16], [17], [18], [19]. Based on the relationship between residual load capacity, surface crack width and corrosion of steel bars of a RC structure, an empirical model is proposed to predict the structural performance of corroded RC structures [20]. In addition, a theoretical model for crack widths has been developed to assess the serviceability of the RC structures based on the concept of fracture energy under combined reinforcement corrosion and applied loading effects [21]. Further, a mathematical model was proposed to predict the service life of the RC bridge structures exposed to chloride environment based on Fick’s second law [22]. Moreover, to account for the uncertainties of structural deterioration induced by the combined effects of progressive loading (corrosion and cracking) and extreme loading (earthquake and impact), a stochastic model was used to predict the time-dependent performance of infrastructures using structural reliability analysis with the aim of improving decision-making for maintenance and replacement of infrastructures [2]. Furthermore, because of the importance of failure probability assessment for structural systems which have different uncertain inputs [23], a probabilistic model regarding structural deterioration subject to corrosion was developed to predict the probability of failure (PoF) of reinforcing steels in a RC bridge deck in a marine environment throughout its 75 years’ service life [24].
Although much research work has been done in last decades to develop the reliability-based life-cycle performance model for bridges [25], [26], [27], the accuracy of the realistic model forecasting of future bridge performance is much dependent on the accurate determination of the model parameters. This is rather challenging due to a range of uncertainties surrounding these parameters resulting from the limited measurement data as well as the correlation between these parameters, e.g. the corrosion rate of reinforcing steel bars is closely correlated to the crack propagation of concrete. Although autoregressive processes have been implemented to predict the long-term deterioration of concrete structures [28], the determination of the model coefficients depends on the collection of a large amount of historical data. In addition, even if several reliability-based mathematical model have been established to simulate the reinforcement corrosion of highway bridges [29], the chloride diffusion coefficient and corrosive rate of reinforcements are significantly affected by the crack propagation of concrete cover over time. Without historical crack measurement data, the long-term reinforcement corrosion behavior cannot be correctly modelled. Using the historical data collected from bridge inspection, the purpose of this study is to develop an engineering reliability analysis (ERA)-based framework to assess the life-cycle performance of RC bridges subject to reinforcement corrosion by concrete cracking. The current research represents the first step towards fundamental understanding of the concrete cracking induced reinforcement corrosion, which could potentially contribute to the development of effective bridge maintenance strategies.
Section snippets
ERA-based framework for life-cycle condition assessment of bridges
Fig. 1 shows the details of developed ERA-based framework for assessing the life-cycle performance of the RC bridges which are gradually deteriorating resulting from steel bar corrosion due to the development of concrete cracking. First, the initial crack characteristics (e.g. crack width) at time t0 are quantified through data collection via bridge inspection. Then, the development of crack characteristics over time is captured from next bridge inspection at time t0 + Δt (Δt: bridge inspection
Problem description
The developed ERA-based framework was implemented to conduct life-cycle condition assessment of a RC highway bridge (Long Feng Xi Bridge, Chongqing, China) based on the historical inspection data of concrete surface crack width (Fig. 5a). The present study mainly focuses on the No. 4 span of the bridge as shown in Fig. 5 b-c. The developments of the 3 cracks have been regularly monitored, and the image of the cracks are shown in Fig. 5 d and e. The historical crack width data collected from
Results and discussions
As shown in Fig. 6 (a), the long-term crack width is predicted using an autoregression approach based on the available eight-year crack width measurements of 3 different cracks obtained from routine bridge inspection. The model coefficients were determined based on the measurement data using a well-established methodology proposed by Hagan et al (1987) [31]. The linear crack width evolution trend results from the limited historical measurement data. With more crack data available over the time,
Conclusion
The present study investigated the concrete crack induced corrosion of steel bars by developing ERA-based model using the eight-year inspection data from 3 different cracks of an operating bridge. The following are some major conclusions:
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The residual service life of a RC bridge based on the allowable crack width (W0) is dependent on the maintenance intervention cycle period (Tcycle). To make sure the PoF of surface crack width is less than 5%, the Tcycle should be reduced by 65% (i.e. change T
Limitations
It should be mentioned that the relationship between the diffusion coefficient, corrosion rate of reinforcement and crack width was established based on previous literatures which ignores the variation of real environment condition. In addition, the traffic load induced concrete cracking was not considered in this study. Our future research will address these limitations and focus on model validation by collecting more bridge inspection data.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors wish to thank the Australian Research Council (ARC IH150100006), CRC Bushfire & Natural Hazards, and The University of Melbourne for their support.
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