A space fractal derivative temperature model in characterization of chloride ions superdiffusion in concrete in a marine environment

In the past decades, more research and experiments have shown that the chloride diffusion in the concrete is no longer following Fickian law and the diffusion process can be significantly affected by the exposure temperatures. In this paper, we propose a space fractal derivative temperature model to describe chloride fast diffusion in concrete. An explicit solution is derived in terms of the complementary error function. The proposed model is verified by using the experimental data of chloride ions in Type I, polypropylene fibers plus metakaolin 10 (PPFs + MK10), and PPFs + MK15 at four different temperatures. Compared with the two Sodani models, the proposed space fractal derivative temperature model is much better in fitting the experimental data, which provides an efficient tool to characterize the chloride ions superdiffusion in concrete at different temperatures. The relationships between the temperature, the diffusion coefficient and the space derivative order are also quantified in this work, which shows the way to determine physical parameters and allows us to predict the long range of future realizations of reinforced concrete structures in marine hot environments.