Probability Density Evolution of Chloride Ion Diffusion Process in Concrete

Abstract:

The diffusion of chloride ions in concrete is a stochastic process. In this paper， the Fick’s second law with random diffusion coefficient is adopted to describe the process. The analytical solution of the probability density function （PDF） of the chloride ion concentration under given boundary conditions is presented by solving the generalized probability density evolution equation （GDEE） about the chloride ion diffusion process. Taking the chloride ion diffusion coefficient obeying a lognormal distribution as an example， the correctness of the analytical solution is confirmed by numerically solving GDEE. It is shown that： the chloride ion diffusion process is a non-stationary spatio-temporal random field； the probability density and variability of the chloride ion concentration distribution not only depend on the stochasticity of the diffusion coefficient， but also are related to the developmental stage of the diffusion process.