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

TL;DR

This paper rigorously derives a homogenized reaction-diffusion model for sulfate-induced concrete corrosion in sewer pipes, providing explicit formulas for effective parameters using two-scale convergence.

Contribution

It introduces a novel homogenization approach for a semi-linear, coupled reaction-diffusion system in a perforated domain, including explicit effective coefficients.

Findings

Derived upscaled equations with explicit effective parameters.

Proved well-posedness and uniqueness of the homogenized model.

Applied boundary unfolding method for nonlinear interface conditions.

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. Firstly, we show the well-posedness of the microscopic model. We then apply homogenization techniques based on two-scale convergence for an uniformly periodic domain and derive upscaled equations together with explicit formulae 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, besides giving its strong formulation, we also prove that the upscaled two-scale model admits a unique solution.