Journal of Engineering Mathematics

, Volume 91, Issue 1, pp 143–163

# Macroscopic models for a mushy region in concrete corrosion

• Christos V. Nikolopoulos
Article

## Abstract

Macroscopic models for the corrosion of concrete due to sulphation, describing the formation of a mushy region, are derived and studied by further expanding previous related studies. These models are derived from averaging using the multiple-scales method applied on microscopic Stefan-type problems to capture the effects of the microscopic transformation of calcite into gypsum. The resulting macroscopic model for the diffusion and production of the sulphate inside the concrete is coupled with a time-dependent Eikonal equation describing the evolution of the reaction at each point of the concrete wall. In certain cases and for specific geometries of the microstructure, the Eikonal equation admits analytical solutions, and the model takes the form of a macroscopic non-local problem. The models derived are solved numerically with the use of a finite-element method, and the results for various microstructure geometries on the microscale are presented.

## Keywords

Concrete corrosion Eikonal equation Moving-boundary problems Perturbation methods  Sulphide corrosion

## Notes

### Acknowledgments

The author wants to thank Professor A. A. Lacey for having a very useful discussion regarding this work.

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