## 3 Results and Discussion
### Influence of Diffusion Coefficient  
It was found that the chloride deposition curve in Figure 2 generally followed [PERSON]'s second law (Equation (2)) [42,43]. Based on the data in Figure 2, Figure 4 plots the regression curves of the chloride  
Figure 3: Qualitative expression of the chloride penetration curves [24].  
coefficient using the Origin software. The chloride ion diffusion coefficient D and surface concentration of chloride C for each group can be determined by Equation (2), as shown in Table 3.  
\[C(x,t)=C_{0}+(C_{s}-C_{0})[1-erf(\frac{x}{2\sqrt{Dt}})], \tag{2}\]  
where \(C(x,t)\) is the chloride percentage in concrete depth \(x\) at exposure time \(t\) (%), \(C_{s}\) is the chloride percentage at the concrete surface (%), \(C_{0}\) is the initial percentage of chloride in concrete, and \(erf(z)\) is the error function, \(erf(z)=\frac{2}{\sqrt{1t}}\int_{0}^{z}\exp(-z^{2})dz\).  
Figure 4 shows the regression curves of the chloride diffusion coefficient for PCFA0, PCFA15, and PCFA30 using [PERSON]'s second law. The chloride diffusion coefficient significantly decreased with the 15% and 30% replacements of cement by mass, with reduction ratios of about 26.1% and 37.9%, respectively, compared to normal concrete. The related coefficient reductions were 3.1984 \(\times\) 10\({}^{-12}\) and 4.6441 \(\times\) 10\({}^{-12}\) m\({}^{2}\)/s. This indicated that the chloride diffusion coefficient reduced more as the fly ash dosage rose. However, the reduction rate was slower as more fly ash was added. This was clear from the fact that the chloride diffusion coefficient of the PCFA30 sample was not proportionally reduced, which was less than half of that (1.4457 \(\times\) 10\({}^{-12}\) m\({}^{2}\)/s) for the PCFA15 sample. Two main reasons for the reduction of the chloride diffusion coefficient were the (1) pozzolanic effect formed tobermorite and calcium aluminate hydrate product [44], which could have increased the chloride binding resistance, and (2) Al\({}_{2}\)O\({}_{3}\) in the fly ash was the essential ingredient to generate [PERSON]'s salt. The chloride ions in concrete are mainly in the form of [PERSON]'s salt. Al\({}_{2}\)O\({}_{3}\) reacts with Ca(OH)\({}_{2}\) and may lower the C/A (calcium/aluminum) product and accelerate AFM (monosulphate) to form [PERSON]'s salt, as explained in Equation (3). This process physically and chemically benefits the chloride binding capacity. Nevertheless, differentiating between the chemical and physical absorption process with  
Figure 4: Regression curves of chloride coefficient using [PERSON]’s second law (by mass%).  
\begin{table}
\begin{tabular}{c c c c c} \hline
**ID** & **D/(\(\times\)10\({}^{-12}\) m\({}^{2}\)/s)** & **C\({}_{s}\)/\%** & **R\({}^{2}\)** & \(\sigma^{2}\) \\ \hline PCFA0 & 12.2617 & 0.8210 & 0.9988 & 0.0006 \\ PCFA15 & 9.0633 & 0.7614 & 0.9970 & 0.0014 \\ PCFA30 & 7.6176 & 0.7187 & 0.9966 & 0.0014 \\ \hline \end{tabular}
\end{table}
Table 3: Regression results of chloride diffusion coefficient. D: chloride ion diffusion coefficient; C\({}_{\text{S}}\): chloride percentage at the concrete surface; and \(\sigma^{2}\): the mercury surface tension force.  
the chosen test setup was difficult in this study since chloride penetration have extensive transport mechanisms in concrete. Consequently, the decrease of free chloride content leads to reduce the chloride diffusion coefficient [45]. However, differentiating between the chemical and physical adsorption process needs further study.