Life-cycle cost analysis of cracking in a reinforced concrete beam under uniform chloride corrosion

Corrosion of rebar is a complex process and one of the most important factors of failure of reinforced concrete structures which reduces the strength and serviceability of the structures. The crack width is an important parameter for designing and evaluating the performance of concrete structures. This paper presents an analytical model to calculate the crack width caused by corrosion. Crack propagation due to corrosion product expansion was investigated at different stages across the concrete cover starting from the reinforcing bar-concrete interface through to the surface. A merit of this model is that it is directly related to the factors that affect the corrosion induced cracking process. Then, the predicted crack width was chosen as a random variable in the calculation of structural failure probability using a stochastic gamma process, after which life cycle costs and the optimum repair period were determined using a renewal process. Furthermore, the effects of structural parameters, including rebar diameter and corrosion rate, on the probability of failure and maintenance costs were investigated, indicating that crack width and life cycle costs are most significantly affected by corrosion rate. That is, a 16-times increase in corrosion rate results in 32 percent reduction in repair time. Moreover, it is to be noted that increasing the allowable fracture limit by 10 percent resulted in the doubling of optimum repair time. In other words, the optimum repair period is significantly affected by the allowed fracture limit which indicates the threshold for structural repair.