Corrosion of steel rebars in reinforced concrete structures represents the most common and dangerous deterioration mechanism affecting their structural integrity. To investigate the environmental degradation mechanisms affecting reinforced concrete elements, the present work presents a multi-physics numerical model analysing the carbonation corrosion deterioration phenomena. Concrete carbonation is described via a system of transport-diffusion-reaction coupled equations evaluating the environmental carbon dioxide penetration, moisture transport and the chemical processes that characterize the carbonation phenomena. Changes in the concrete chemical composition and mechanical properties are observed. Additionally, the carbonation chemical reactions lower the pH value of the pore water causing the progressive depassivation of the steel rebar. As its protective layer dissolves, the rebar corrosion process starts due to presence of moisture and oxygen on the metal surface. Using the electrochemical kinetic equations the amount of rust produced by the corrosion process is numerically evaluated on the depassivated portion of the rebar. Eventually, as rust deposits increase in volume, cracking and spalling of the concrete cover is observed and modelled using the phase field model for fracture.