A semi-closed-form solution for chloride diffusion in concrete with time-varying parameters

Reinforcement corrosion in concrete is a worldwide problem and billons of dollars are spent each year on repair and replacement of reinforced concrete structures because of corrosion damage of reinforcement. Chloride induced corrosion is the major type of corrosion encountered in reinforced concrete. The corrosion is initiated in reinforcement when chloride diffuses through the concrete cover and the chloride concentration at the reinforcement reaches a critical threshold level. Pick's second law of diffusion is commonly used for one-dimensional chloride diffusion. A closed-form solution based on error function is commonly used to predict the chloride concentrations, if the diffusion coefficient (D) and surface chloride concentration (Cs) remain constant. This solution is not applicable when D and Cs vary with time, which is the case in real-life situations. The finite difference or finite element methods with specialised software are generally used to solve such problems. This paper reviews existing methods and presents an alternative method based on a general closed-form solution with varying D but constant Cs. To incorporate the effect of varying Cs, an adaptation of the closed-form solution is presented. This solution can be used without the use of finite difference method or special computer software to predict the chloride concentrations.