A variable-order time-fractional derivative model for chloride ions sub-diffusion in concrete structures

This study proposes a new variable-order fractional diffusion equation model to describe the coupled chloride diffusion-binding processes in reinforced concrete, in which the order of fractional derivative term is a variable function instead of a constant in the standard fractional model. The concentration influence coefficient k is introduced to capture the effect of concentration dependency on chloride transport due to the chloride binding behavior. The two parameters in the proposed model can be determined directly by a statistical analysis of measurement data. Four test cases illustrate that the proposed variable-order fractional derivative model agrees significantly better with experimental data than the most commonly used traditional model governed by the classical Fick's second law, especially when a large concentration coefficient k is involved. That proposed model is also verified by accurately predicting chloride concentration profiles in a period of 200 days.