## 3 Research Results and Discussion
### Modeling of Chemical Radiation-Induced Corrosion Processes Using the COMSOL Software Package
These boundary conditions state that gradient vectors must always be perpendicular to the normal vector at the insulating boundaries; that is why no transport occurs across the surface. It is assumed that the oxygen concentration at the concrete-anode interface is equal to the atmospheric oxygen concentration (i.e., the anode itself does resist the oxygen transport) [87]:  
\[\text{C}_{\text{O2}}(0,y)=\text{C}_{\text{O2}}^{*} \tag{5}\]  
where \(\text{C}_{\text{O2}}(0,y)\) is the concentration of oxygen at the concrete-reinforcement interface, and \(\text{C}_{\text{O2}}^{*}\) is the concentration of oxygen in the atmosphere, which is a constant value. An interpolation relationship containing a multiplier (a coefficient of proportionality) was additionally formulated to take into account changes in the electrical conductivity of concrete over the time interval of 100 years. Subsequently, the value of the initial function \begin{table}
\begin{tabular}{c c c} \hline \hline
**PS (\%)** & **Concrete Resistivity \(\rho\) (\(\Omega\cdot\text{m}\))** &
\begin{tabular}{c} **Effective Diffusivity of Oxygen** \\ **D\({}_{\text{O2}}\cdot\)10\({}^{\text{th}}\) (m\({}^{2}\)/s)** \\ \end{tabular} \\ \hline
20 & 5.727 & 152 \\
30 & 1.227 & 115 \\
40 & 500 & 83 \\
50 & 205 & 49 \\
55 & 170 & 39 \\
60 & 142 & 28 \\
65 & 125 & 20 \\
70 & 102 & 15 \\
75 & 80 & 10 \\
80 & 64 & 8.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Specific resistivity of concrete \(\rho\) and effective oxygen diffusion D\({}_{\text{O2}}\) as a function of pore saturation PS% [87]. of electrical conductivity will be multiplied by the appropriate coefficient depending on the time of oxidation (over the initial period of time--(1/10^7)); 9 years--(1/45); 50 years--(1/14); and 100 years--(1/2.8)). Determining the relationship between the moisture content and temperature/humidity in concrete is of great importance for an accurate prediction of the durability of reinforced concrete structures [167]. The results show that the water saturation of pores, considered as a characteristic of the moisture content, changes nonlinearly depending on the relative humidity of concrete. Its change pattern is greatly affected by the water-cement ratio and temperature [166]. [PERSON] and [PERSON] developed a model conveying the relationship between pore water saturation, temperature, and relative humidity in concrete. In addition, they experimentally verified it by an independent test [166]. Hence, dependencies specified in [166] were used to link temperature, water-cement ratio of concrete, humidity, and water saturation in further computations. In this case, the temperature range was 10 to 45 \({}^{\circ}\)C.  
Computation parameters entered into the COMSOL software package are shown in Table 4.  
Three of many possible chemical reactions that can occur at the interface between the reinforcement and concrete (actively corroding reinforcement) are considered: oxygen reduction, oxidation of the steel reinforcement (here represented as iron oxidation), and hydrogen evolution due to water reduction. When atmospheric oxygen diffuses and reaches the surface of the reinforcement, it can be reduced to hydroxide ion in the aqueous solution [87,168]:  
\[\text{O}_{2}+2\text{H}_{2}\text{O}+4\text{e}^{-}\to 4\text{OH}^{-} \tag{6}\]  
Corrosion occurs when iron in the steel reinforcement undergoes oxidation. The corrosion reaction is described by the model [87,168]:  
\[\text{Fe}\rightarrow\text{Fe}^{2+}+2\text{e}^{-} \tag{7}\]  
Finally, pore water adjacent to the reinforcement can be reduced to form hydrogen gas [87]:  
\[2\text{H}_{2}\text{O}+2\text{e}^{-}\rightarrow\text{H}_{2}+2\text{OH}^{-} \tag{8}\]