## 3 Research Results and Discussion
### Modeling of Chemical Radiation-Induced Corrosion Processes Using the COMSOL Software Package
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter**\({}^{\star}\) & **Expression** \\ \hline \(\text{A}_{\text{Fe}}\) & \(0.41\) [V] \\ \(\text{A}_{\text{H2}}\) & \(-0.15\) [V] \\ \(\text{A}_{\text{O2}}\) & \(-0.18\) [V] \\ \(\text{C}_{\text{O2\_ref}}\) & \(9.46\) [mol/m\({}^{3}\)] \\ \(\text{C}_{\text{O2\_ref}}\)\_9\_100 & \(8.6\) [mol/m\({}^{3}\)] \\ \(\text{E}_{\text{eq}}\)\_Fe & \(-0.76\) [V] \\ \(\text{E}_{\text{eq}}\)\_H2 & \(-1.03\) [V] \\ \(\text{E}_{\text{eq}}\)\_O2 & \(0.189\) [V] \\ \(\text{I}_{\text{O}}\)\_Fe & \(7.1\times 10^{-5}\) [A/m\({}^{2}\)] \\ \(\text{I}_{\text{O}}\)\_H2 & \(1.1\times 10^{-2}\) [A/m\({}^{2}\)] \\ \(\text{I}_{\text{O}}\)\_O2 & \(7.7\times 10^{-7}\) [A/m\({}^{2}\)] \\ \(\text{L}\) & \(3.175\times 10^{-2}\) [m] \\ \(\text{R}_{\text{reinforcement bar}}\) & \(0.635\times 10^{-2}\) [m] \\ S & \(2.54\times 10^{-2}\) [m] \\ W & \(6.35\times 10^{-2}\) [m] \\ PS & \(0.6\) \\ \hline \hline \end{tabular} \({}^{\star}\)letter designations are given in Appendix A.  
\end{table} 
Table 4: The list and standard values of parameters used in computations made by the COMSOL software package. Corresponding boundary conditions are added to COMSOL using the \"electrode reaction\" function. The value equal to \(-0.07\)\(\mu\)A/cm\({}^{2}\) is taken as the initial parameter of current density for the oxidative reaction of the reinforcement. It corresponds to the experimental values provided in [69]. The period of time needed for concrete carbonization to reach the boundary of the reinforcement is 9 years; it was calculated by the authors in accordance with Formula (1) [89]:  
\[\mathrm{C}=\mathrm{k}\cdot\alpha_{1}\cdot\alpha_{2}\cdot\alpha_{3}\cdot\beta_{ 1}\cdot\beta_{2}\cdot\beta_{3}\cdot\sqrt{t}; \tag{9}\]  
where C is carbonation depth (cm); t is time (years); K is the coefficient; \(\alpha_{1}\) is the coefficient depending on the type of concrete; \(\alpha_{2}\) is the coefficient depending on the type of cement; \(\alpha_{3}\) is the coefficient depending on the water-cement ratio; \(\beta_{1}\) is the coefficient depending on temperature; \(\beta_{2}\) is the coefficient depending on humidity; \(\beta_{3}\) is the coefficient depending on CO\({}_{2}\) concentration. [89]  
In the aftermath of 9 years of carbonization of a 50 mm thick protective layer of reinforcement, the initial coefficient of oxygen diffusion is recalculated by the authors (reduced by a factor of 1.1) in compliance with the experimental data provided in [88] for carbonized concrete. In turn, the current density of the oxidative reaction of the reinforcement is increased by a factor of 10 according to [86]. In addition, a logical Expression (10) is entered into the D\({}_{\mathrm{c}}\) settings responsible for oxygen diffusion in the COMSOL software package:  
\[if(\mathrm{t}<2.838\mathrm{e}+\frac{8,D_{02(PS)}}{1000,D_{02(PS)}}); \tag{10}\]  
where \(D_{02(PS)}\) is the dependence between the effective oxygen diffusion coefficient and pore saturation (see Table 3), and c is the name of the atmospheric oxygen concentration variable. Expression (10) sets the value of the oxygen diffusion coefficient in the concrete material for the first 9 years (i.e., 2.838e+8 s) as 1/1000 of the initial one at the pre-set moisture content in concrete pores. After 9 years, the value of the diffusion coefficient will be equal to the initial value determined by the D\({}_{\mathrm{O2}}\) function (Table 3). A change in the value of current density for the oxidative reaction of the reinforcement as a result of the accumulation of the gamma radiation dose is taken in proportion to experimental values for gamma-irradiated concrete specimens with steel reinforcement at relative humidity RH 50% in accordance with the data extracted from the study [69] (0.24 \(\mu\)A/cm\({}^{2}\), with the accumulated dose of 1.8 MGy for 6 months of irradiation). The dose value is 11.4 Gy/h, which corresponds to values of radioactive waste specified in [74]. A change in parameters of current was mainly achieved due to a change in concrete resistance.