A mixture theory-based concrete corrosion model coupling chemical reactions, diffusion and mechanics

Abstract

A 3-D continuum mixture model describing the corrosion of concrete with sulfuric acid is built. Essentially, the chemical reaction transforms slaked lime (calcium hydroxide) and sulfuric acid into gypsum releasing water. The model incorporates the evolution of chemical reaction, diffusion of species within the porous material and mechanical deformations. This model is applied to a 1-D problem of a plate-layer between concrete and sewer air. The influx of slaked lime from the concrete and sulfuric acid from the sewer air sustains a gypsum creating chemical reaction (sulfatation or sulfate attack). The combination of the influx of matter and the chemical reaction causes a net growth in the thickness of the gypsum layer on top of the concrete base. The model allows for the determination of the plate layer thickness h = h(t) as function of time, which indicates both the amount of gypsum being created due to concrete corrosion and the amount of slaked lime and sulfuric acid in the material. The existence of a parameter regime for which the model yields a non-decreasing plate layer thickness h(t) is identified numerically. The robustness of the model with respect to changes in the model parameters is also investigated.

Homogenization of degenerate coupled transport processes in porous media with memory terms

“…Homogenization of a coupled system of diffusion-convection equations in a domain with periodic microstructure, modeling the flow of isothermal immiscible compressible fluids through porous media, was theoretically studied, eg, by Amaziane et al 27,28 In Krehel et al, 29 the authors applied two-scale convergence techniques to obtain the macro model of thermal-diffusion reaction problems (including the Dufour ad Soret effects) modeling behavior of concrete at high temperatures. In Fatima et al, 30 the authors derived upscaled system and formulae for the effective transport coefficients and reaction parameters of a reaction-diffusion system modeling sulfate corrosion of concrete in locally periodic perforated domains, see also Fatima and Muntean 31 and Vromans et al 32 In the present paper, our aim is to extend our previous result, 33 where we established a homogenization result for a fully nonlinear degenerate parabolic system (with mixed homogeneous Dirichlet-Neumann boundary conditions) arising from the heat and moisture flow through partially saturated porous media ignoring the memory phenomena and assuming a in (12) independent of p . In particular, in our preceding work, 33 the degeneracy in the elliptic part of the mass balance equation (liquid water) has been transferred to the parabolic term using the so-called Kirchhoff transformation…”

Homogenization of a pseudo-parabolic system via a spatial-temporal decoupling: Upscaling and corrector estimates for perforated domains

“…According to [33], there are several options for γ αβ , but all these options lead to non-invertible G. Suppose we take γ 11 = γ 22 = γ 1 < 0 and γ 12 = γ 21 = γ 2 < 0 with γ 1 > γ 2 . Then G is invertible and positive definite for φ 3 > 0, since the determinant of G equals (γ 2 1 − γ 2 2 )φ 3 .…”

“…The microscopic equations of our concrete corrosion model are conservation laws for mass and momentum for an incompressible mixture, see [33] and [36] for details. The existence of weak solutions of this model was shown in [34] and Chapter 2 of [36].…”

“…The existence of weak solutions of this model was shown in [34] and Chapter 2 of [36]. The parameter space dependence of the existence region for this model was explored in [33]. The two-scale convergence for a subsystem of these microscopic equations, a pseudo-parabolic system, was shown in [35].This paper handles the same pseudo-parabolic system as in [35]but on a perforated microscale domain.…”

“…In[33] a concrete corrosion model has been derived from first principles. This model combines mixture theory with balance laws, while incorporating chemical reaction effects, mechanical deformations, incompressible flow, diffusion, and moving boundary effects.…”