## 3 Research Results and Discussion
### Modeling of Chemical Radiation-Induced Corrosion Processes Using the COMSOL Software Package
- _Period of substantial carbonization:_ this period is characterized by micro-cracking, as the pores filled with calcium carbonate can no longer compensate for deformations in concrete (induced by loading or temperature, including radiation heating). Consequently, the infeed of oxygen and other gases contained in the air increases near the interface between the reinforcement and concrete. The corrosion current in the reinforcement goes up significantly; the total electrical resistance of concrete also increases, and the passivation layer deteriorates. In the course of further carbonization, the number of cracks increases, the number of free pores decreases, the resistance of concrete increases, and radiolytic processes move deeper into the structure due to the absence of water. This period is characterized by permeability mainly due to micro-cracking of concrete, enhanced by radiogenic heating, which leads to the accelerated corrosion of the reinforcement and carbonization. The authors employed the COMSOL software to simulate half of a reinforced concrete wall using the principle of symmetry. The arrangement of reinforcement whose diameter is 25 mm is shown in Figure 2a. The interaction between the wall faces and the external environment is shown in Figure 2b. Oxygen enters the structure and diffuses through the concrete, reacting with the reinforcement. In the steady state, the governing equation describing oxygen transport states that the divergence of the space-dependent effective oxygen diffusion (D\({}_{\text{O2}}\)) multiplied by the oxygen concentration gradient (\(\
abla\)C\({}_{\text{O2}}\)) must be equal to zero for all points in concrete [87]:  
\[\
abla\cdot\text{D}_{\text{O2}}(\
abla\text{C}_{\text{O2}})=0 \tag{1}\]  
Figure 2: Scheme of a wall segment modeled in the COMSOL software package, where (**a**) is the geometry of a modeled segment of a reinforced concrete wall (dimensions are shown in mm), and (**b**) shows boundaries of a concrete wall segment interacting with the surrounding atmosphere. Oxygen transport through concrete depends on many factors, including pore tortuosity and size distribution, wall adsorption capacity, capillary effects, and the moisture content in concrete. Experimental values of the effective oxygen diffusion in concrete as a function of the moisture content (or pore saturation) are presented in Table 3.  
Table 3 shows that as a consequence, D\({}_{\text{O2}}\) values vary with pore saturation. In all cases, the local equilibrium between the aqueous phase and the pore phase oxygen is assumed, and the C\({}_{\text{O2}}\) symbol denotes the concentration of oxygen in the pore phase. The charge transport in concrete is also important because the corrosion process is electrochemical. Ions dissolved in the concrete pore solution act as charge carriers in the presence of an electric field. The electric field is due to the electric potential difference (\(\varphi\)) in concrete. In the steady state, the charge transport equation means that the divergence of the reciprocal of space-dependent resistivity (1/\(\rho\)) multiplied by the gradient of the electric potential is zero for all points in concrete [87]:  
\[\
abla.\frac{1}{\rho}(\
abla\varphi)=0 \tag{2}\]  
The electrical resistance of concrete (\(\rho\)) is used to reduce the complex phenomenon of ion transport to a single parameter. The value of \(\rho\) is a function of pore saturation and is determined experimentally [166]. Table 3 shows values of \(\rho\) as a function of pore saturation [87]. Since the solution in the pores facilitates the travel of ions, specific resistance varies in inverse relation to the pore saturation. All system boundaries that are not steel reinforcement require natural (isolating) boundary conditions [87]:  
\[\overset{\rightarrow}{\text{n}}\cdot\
abla\text{C}_{\text{O2}}=0 \tag{3}\]  
\[\overset{\rightarrow}{\text{n}}\cdot\
abla\varphi=0 \tag{4}\]  
where \(\overset{\rightarrow}{\text{n}}\) is the unitary normal vector to the surface.