Kirchhoff transformation analysis for determining time/depth dependent chloride diffusion coefficient in concrete

This article uses the Kirchhoff transformation method to solve a non-steady one-dimensional diffusion equation when the apparent diffusion coefficient is expressed as a function of time, depth, and concentration of chloride for concrete exposed to chloride environment. The analytical results obtained by the proposed method, which are coincided with those calculated from the Boltzmann–Matano methodology under specific condition, can be used to conveniently predict the chloride diffusion process physically and chemically so that the traditional natural diffusion test to obtain time/depth dependent apparent diffusion coefficient may be greatly simplified. Two new simplified methods to effectively process the experimental results from the natural diffusion test are proposed: one is called the long-specimen-at-one-specific-time method using fewer specimens at one time and the other the short-specimen-at-long-elapsed-time method using more specimens at various service times. Two numerical examples are provided to illustrate the application of these two proposed methods.