Simulating Chloride Penetration in Fly Ash Concrete by a Fractal Derivative Model

Abstract

In the real engineering field, the chloride ions behave abnormal diffusion phenomena in concrete caused by different compositions of the concrete which lead to the complex physical and chemical properties. This paper utilizes a fractal derivative model and a fractional derivative model to describe the diffusion phenomena. Furthermore, according to actual experimental data in the field, the fractional and fractal model can simulate the diffusion behavior of chloride ions in concrete. In comparison to the fractional derivative model, the fractal derivative model gives a simpler mathematical expression and lower calculation costs. In addition, the linear regression analysis method is used to establish an effective relationship between the internal composition of concrete and the parameters of fractal model such as fractal order; a, and diffusion coefficient, D. As a result, the fractal model with the parameters estimated by previous relationship can predict the diffusion behavior of chloride ions.