Modeling of Chloride Distribution in Cement‐Based Materials with Neumann Boundary Condition

Abstract

e nonstable transport of chloride in cement-based materials, including diffusion, convection, and chloride binding, is described as a general form of Fick's law. Inspired by the heat transport of concrete, the second boundary condition called the Neumann boundary condition is considered in the chloride transport of concrete. e theoretical deduction of one-dimensional chloride distribution with the Neumann boundary condition is performed, while a virtual boundary is introduced to carry out the approximate treatment. Finally, the comparison between the general Dirichlet boundary condition and the present Neumann boundary condition and the influence of the thickness of the virtual boundary as well as the influence of the water-cement ratio (w/c) are discussed.

Diffusion coefficient and tortuosity: Brownian Motion

“…It is the total amount of chlorides in the sample (ANDRADE, 1993) and is called the apparent diffusion coefficient (Da) (ANDRADE and KROPP, 2002;LIZARAZO and CLAISSE, 2008;AGUAYO et al, 2014). Varying with time, in the non-steady regime (Dns) the diffusion flux and the concentration gradient will be given by Equation ( 6) (Fick's second law) (CALLISTER and RETHWICH, 2012;ÁVILA, 2019;MENG et al, 2018). The definition of the apparent diffusion coefficient (Da) for the non-steady state is in the form (ANDRADE, 1993) Equation (6):…”

Modeling of Chloride Binding Capacity in Cementitious Matrices Including Supplementary Cementitious Materials

“…Chloride migration through concrete has been explained by multiple literary sources [11][12][13] as the process in which chloride travels under a concentration differential from higher concentration at the surface of the concrete towards lower concentrations deeper below the surface. This diffusion process is assumed to follow Fick's laws of diffusion [14,15]. When the concentration of chloride ions reaches a certain threshold [11,16], the iron atoms in the reinforcement are activated and react with the chloride ions to form ferrous chloride, which then reacts with water to form ferrous hydroxide, thus regenerating the chloride ions, which become available and are able to react with more iron, leading to further corrosion.…”