Macroscopic models for a mushy region in concrete corrosion
- 114 Downloads
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.
KeywordsConcrete corrosion Eikonal equation Moving-boundary problems Perturbation methods Sulphide corrosion
The author wants to thank Professor A. A. Lacey for having a very useful discussion regarding this work.
- 2.Fasano A, Natalini R (2006) Lost beauties of the Acropolis: what mathematics can say, SIAM News, 39, July/August 2006Google Scholar
- 3.Bohm M, Devinny JS, Jahani F, Mansfeld FB, Rosen IG, Wang C (1999) A moving boundary diffusion model for the corrosion of concrete wastewater systems: simulation and experimental validation. In: Proceedings of the American control conference, San Diego, California, June 1999, pp 1739–1743Google Scholar
- 4.Böhm M, Rosen IG (1997) Global weak solutions and uniqueness for a moving boundary problem for a coupled system of quasilinear diffusion-reaction equations arising as a model of chemical corrosion of concrete surfaces. Institut fur Mathematik Humboldt-Universitat, BerlinGoogle Scholar
- 6.Fatima T, Muntean A (2014) Sulfate attack in sewer pipes: derivation of a concrete corrosion model via two-scale convergence. Nonlinear Anal 15(1):326–344Google Scholar
- 11.Jaklic A, Leonardis A, Solina F (2000) Segmentation and recovery of superquadrics, Computational Imaging and Vision, vol 20. Kluwer, DordrechtGoogle Scholar
- 14.Ockendon J, Howison S, Lacey A, Movchan A (2003) Applied partial differential equations. Oxford University Press, OxfordGoogle Scholar