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

作者：Chen Wen^*; Zhang Jianjun; Zhang Jinyang

来源：Journal of Fractional Calculus and Applied Analysis, 2013, 16(1): 76-92.

DOI：10.2478/s13540-013-0006-y

• variable-order fractional derivative
• sub-diffusion
• time dependence
• concrete
• chloride ions
• chloride binding
• concentration dependence

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.

• 出版日期2013-3
• 单位河海大学