Service life prediction of repaired concrete structures under chloride environment using finite difference method

Service life of concrete structures under chloride environment can be predicted by formulations based on the mechanism of chloride ion diffusion. This mechanism can be mathematically described using the partial differential equation (PDE) of the Fick’s second law. One-dimensional PDE can be solved analytically by assuming constant surface chloride ion concentration and constant diffusion coefficient. However, the solution becomes more complicated when two additional conditions are included, i.e., concrete cover repair or replacement and time dependent variation of the surface chloride ion concentration and diffusion coefficient. In this paper, a numerical finite difference based formulation is proposed to effectively accommodate these two additional conditions. By virtue of numerical computation, the nonlinear initial chloride ion concentration can be treated in point-wise manner and both the time dependent surface chloride ion concentration and diffusion coefficient can be iteratively updated. Based on a Crank–Nicolson scheme within the finite difference method, a proper formulation accounting for space-dependent diffusion coefficient was derived; chloride ion concentration profiles are obtained and the service life of repaired concrete structures under chloride environment is predicted. Numerical examples and observations are finally presented.