Reinforced concrete is a widely used construction material. It is not only cheap but, in contrast to other materials such as timber or steel, very durable. However, in the last decades it has become clear that the durability of reinforced concrete is strongly affected by the corrosion of the steel bars in its interior. Usually, the steel bars are protected by a thin oxide layer at their surface which is formed because of the highly alkaline environment. The high pH in concrete (about 13) is mostly due to the calcium hydroxide produced during the curing period. Since concrete is a porous material, gaseous CO2 diffuses into its interior under natural environmental conditions where it reacts with available Ca(OH)2 to produce CaCO3 (and H2O). While the carbonation does not present any immediate danger for the set cement (the strength can even increase), it lowers the pH in the concrete and therefore allows the corrosion of the reinforcing steel bars. This phenomenon is considered as one of the major processes inducing corrosion in concrete and leads to an enormous loss in the range of the upper hundreds of millions Euro in Germany annually. It is therefore of great importance to have simple (i.e. easily computable) models which predict the carbonation penetration accurately.

To predict the advancement of carbonation fronts in concrete, systems of partial and ordinary differential equations involving the exchange of constituents across pore-water and pore-air as well as pore-water and solid-matrix interfaces as well as chemical reactions in the water-filled part of the pores are employed. We are considering the carbonation reaction in the form We focus on the following aspects:

(a) Moving-Reaction-Interface-Modelling

A particular phenomenological feature of carbonation is the formation of reaction surfaces and / or layers that progress into the concrete-based materials (see figure 2). The deeper cause for the formation of these patterns is not quite clear, although the major chemical and physical reasons seem to be known. We formulate the carbonation process as a whole, first as a one-dimensional, then as a two-dimensional mechanism. The result of this is likely to be a coupled system of non-linear partial differential equations in fixed or moving domains. The most important processes we are dealing with are the carbonation kinetics, the changes in the pore configurations induced by reaction and the transfer of humidity. Monitoring of such processes enables conclusions about moving reaction-front behaviour and can lead to a better prediction of penetration depths and of the corrosion initiation time. The mathematical techniques used in this study particularly include fixed-domain transformations, maximum estimates and fixed-point methods for coupled systems of parabolic partial differential equations.

(b) General isoline models and their comparison with Moving-Reaction-Interface-Modelling (see (a))

(c) Intermediate models (a mix of the results of (a) and (b))