Carbonation caused by atmospheric carbon dioxide is one of the major physicochemical processes which can compromise the service life of reinforced concrete structures. While the bulk of the carbonation reaction is that of calcium hydroxide, other constituents of the porous matrix can also carbonate and compete with calcium hydroxide for carbon dioxide. Particularly the carbonation of calcium-silicate hydrates and unhydrated constituents are neglected by most authors in carbonation prediction models. In this paper, a mathematical model of carbonation is extended to include additional carbonation and hydration reactions. The competition of the several reactions and their effect on the carbonation depth is investigated by dimensional analysis and numerical simulations. A parameter study emphasises that multiple internal reaction layers appear. Their position and speed essentially depend on the strength of the different reactions. It is also observed that, for a wide range of parameters, the effect of some of the additional reactions on the carbonation depth is small. In particular, a comparison with data from laboratory experiments justifies the neglect of the carbonation of the unhydrated constituents in prediction models. (M. A. Peter), a.muntean@tue.nl (A. Muntean), sebam@math.uni-bremen.de (S. A. Meier), mbohm@math.unibremen.de (M. Böhm).

Carbonation is the reaction of environmental carbon dioxide with alkaline species in concrete. It is one of the major degradation mechanisms affecting the durability of reinforced concrete structures. In this paper, a mathematical model of the carbonation process is formulated and simulated using the finite-element method. Nonlinear reaction rates, Robin boundary conditions and a decrease of the concrete porosity in time are taken into account. A dimensional analysis based on a nondimensionalisation of the entire model is introduced to identify the key parameters and the different characteristic time and length scales of the whole process. Numerical simulations show the occurrence of an internal reaction layer travelling through the material. The speed and the width of the layer are rigorously defined via dimensionless quantities. A parameter study shows that the speed and the width are strongly related to the size of the Thiele modulus which is typically large. The relevance of other parameters is also investigated. The model is validated for accelerated and natural carbonation settings.

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A model reference adaptive control law is de ned for nonlinear distributed parameter systems. The reference model is assumed to be governed by a strongly coercive linear operator de ned with respect to a Gelfand triple of re exive Banach and Hilbert spaces. The resulting nonlinear closed loop system is shown to be well posed. The tracking error is shown to converge to zero, and regularity results for the control input and the output are established. With an additional richness, or persistence of excitation assumption, the parameter error is shown to converge to zero as well. A nite dimensional approximation theory is developed. Examples involving both rst (parabolic) and second (hyperbolic) order systems and linear and nonlinear systems are discussed, and numerical simulation results are presented.

SUMMARYSeveral choices of scaling are investigated for a coupled system of parabolic partial differential equations in a two-phase medium at the microscopic scale. This system may be regarded as modelling a reactiondiffusion problem, the Stokes problem of single-phase flow of a slightly compressible fluid or as a heat conduction problem (with or without interfacial resistance), for example. It is shown that, starting with the same problem on the microscopic scale, different choices of scaling of the diffusion coefficients (resp. permeability or conductivity) and the interfacial-exchange coefficient lead to different types of macroscopic systems of equations. The characterization of the limit problems in terms of the scaling parameters constitutes a modelling tool because it allows to determine the right type of limit problem. New macroscopic models, not previously dealt with, arise and, for some scalings, classical macroscopic models are recovered. Using the method of two-scale convergence, a unified approach yielding rigorous proofs is given covering a very broad class of different scalings.