Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence

By Tasnim Fatima, Adrian Muntean. 2010

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Abstract We explore the homogenization limit and rigorously derive upscaled equations for a microscopic reaction–diffusion system modeling sulfate corrosion in sewer pipes made of concrete. The system, defined in a periodically-perforated domain, is semi-linear, partially dissipative and weakly coupled via a non-linear ordinary differential equation posed on the solid–water interface at the pore level. First, we show the well-posedness of the microscopic model. We then apply homogenization techniques based on two-scale convergence for a uniformly periodic domain and derive upscaled equations together with explicit formulas for the effective diffusion coefficients and reaction constants. We use a boundary unfolding method to pass to the homogenization limit in the non-linear ordinary differential equation. Finally, we give the strong formulation of the upscaled system.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/10ff78b12f490570c58074cab40000fe3ab1f2cc