Fractal derivative model with time dependent diffusion coefficient for chloride diffusion in concrete

More research and experiments have indicated that under different water cement ratios, the binding effect of concrete on chloride ions and the blocking effect of hydration on chloride ions are clearly dominant. During this time period, the diffusion rate of chloride ions will increase or decrease with time, resulting in the classical Fickian diffusion law no longer being applicable. This study establishes an improved fractal model with a time-dependent diffusion coefficient for chloride diffusion in concrete. An explicit solution is derived in terms of the complementary error function. The proposed model is verified by fitting the chloride ion concentration data from different concrete immersion tests. The results show that the fractal model can fit the data in different spatial scales, and the corresponding prediction accuracy is rather high when compared to the three integer order models with constant, variable diffusion coefficient, and curing age. Therefore, the fractal derivative model is feasible in describing the anomalous diffusion of chloride ions in concrete.