On the mathematics of time-dependent apparent chloride diffusion coefficient in concrete

This paper provides an improved mathematical analysis of chloride penetration into concrete employing a time-dependent diffusion coefficient for the solution of Fick's second law of diffusion. In the paper the possible errors caused by the application of oversimplified mathematical expressions used in some models for the evaluation of service life of reinforced concrete structures are discussed. The results from this mathematical analysis demonstrate that some models based on the oversimplified error function complement (ERFC) solutions may easily overestimate the service life by orders of magnitude, especially when the age factor is high. Some chloride profiles after up to 10 years' field exposure were used to compare the oversimplified with the improved models. The results show that both the oversimplified and the improved models fairly well predict the 10 years' chloride ingress in Portland cement concrete, but the oversimplified ERFC model significantly underestimates the chloride ingress in concrete with fly ash.