Time-dependent concrete chloride diffusion coupled with nonlinear chloride binding: An analytical study

Both the temporal dependence of chloride diffusion coefficient and the effect of nonlinear chloride binding substantially affect the behavior of concrete chloride diffusion. This study develops an exact chloride diffusion solution that accommodates the above two factors by introducing a simplified but reasonably realistic nonlinear chloride binding isotherm. The introduction of this isotherm makes it possible to achieve an analytical solution to a highly nonlinear chloride diffusion equation that involves a free chloride concentration dependent dimensionless factor which reflects the effect of chloride binding. First, a time-dependent chloride diffusion model incorporating the introduced isotherm is established with the corresponding exact solution derived. The proposed solution is successfully validated against two existing analytical solutions and a numerical solution. Parametric study is conducted using the proposed solution to investigate how the parameters regarding chloride ingress influence the corrosion initiation time, and results show that the increase of the initial effective chloride diffusivity or the before-ingress age decreases the corrosion initiation time bringing an acceleration of a different level to chloride diffusion while the increase of the age factor prolongs the corrosion initiation time decelerating chloride diffusion to some extent, and as each of the three nonlinear chloride binding associated parameters (i.e., the deflection-point concentration, the former slope and the latter slope) increases, the corrosion initiation time rises and the retardation effect on chloride diffusion is enhanced to a various extent. Lastly, to demonstrate the practical validity of the proposed solution, the solution is applied to reproducing a reported chloride diffusion test, and it turns out that our solution reproduces the diffusion test reasonably well, justifying its practical validity.