Reactive transport modelling of concurrent chloride ingress and carbonation in concrete

Abstract

The carbonation is a fundamental durability process for concrete structures exposed to nearly all environments. In air-borne chloride environments, the chloride ingress occurs simultaneously with the carbonation, constituting a multi-phase and multi-species transport-reaction problem. This paper regards concrete as a reactive porous medium partially saturated by pore solution and addresses this problem through a comprehensive transport-reaction model taking into account the dissociation and dissolution–precipitation equilibria in pore solution, transport of gas and aqueous phases and local electrical field. Especially the incongruent dissolution of C–S–H is addressed, a coating-reaction kinetics is assumed for the CH carbonation and new chloride adsorption laws are used upon carbonation of C–S–H. The established model is solved through finite volume method and validated by laboratory experiments of chloride ingress in carbonated OPC concretes. The parametric analysis for concurrent carbonation and chloride ingress under constant relative humidity shows that: (1) the concurrent carbonation will globally promote the chloride ingress and the involved corrosion risk for embedded steel; (2) the significant RH range for this carbonation impact will be on medium levels around 75%; (3) the concretes incorporating SCMs, especially in large quantities, will behave differently to the influence of carbonation. Accordingly, the concurrent carbonation should be considered in appropriate way in durability design against chloride ingress.

Appendices

Appendix A: CH carbonation kinetics

Fig. 11

The crystal of portlandite (in the centre) is coated by a precipitated calcite layer of variable thickness through which ions must diffuse to maintain the calcite precipitation

Based on the mechanism described in Fig. 11, the dissolution kinetics of portlandite was derived in [43] as,

$$ \frac{{\text{d}}}{{{\text{d}}t}}\left( {n_{{{\text{CH}}}} } \right) = \frac{{n_{{{\text{CH}}}}^{0} }}{{\tau_{{{\text{CH}}}} }}f_{{{\text{coating}}}} \ln \left( {\beta_{{{\text{CH}}}} } \right){\text{ with }}f_{{{\text{coating}}}} = \frac{{r_{{\text{p}}}^{2} }}{{1 + c\frac{{r_{{\text{p}}} }}{{r_{{\text{c}}} }}\left( {r_{{\text{c}}} - r_{{\text{p}}} } \right)}} $$

(23)

where the characteristic time $\tau_{{{\text{CH}}}}$ is approximated to 720 s for spherical crystals of portlandite with radius of R₀ = 40 μm. The geometry factors, r_p and r_c, are the relative radii of internal and external spheres, i.e. R_p/R₀ and R_c/R₀, and can be related to the molar quantities as,

$$ r_{p} = \left( {\frac{{n_{{{\text{CH}}}} }}{{n_{{{\text{CH}}}}^{0} }}} \right)^{\frac{1}{3}} , \, r_{c} = \left( {\frac{{n_{{{\text{CH}}}} }}{{n_{{{\text{CH}}}}^{0} }} + \frac{{V_{{{\text{C}}\overline{{\text{C}}} }} }}{{V_{{{\text{CH}}}} }}\left( {1 - \frac{{n_{{{\text{CH}}}} }}{{n_{{{\text{CH}}}}^{0} }}} \right)} \right)^{\frac{1}{3}} $$

(24)

The parameter $c$ was calibrated, as 0.32 × 10⁶, by accelerated carbonation experiment (50% CO₂) on hardened cement pastes (HCP) with OPC CEM I as binder and w/c ratio of 0.45. The CH content at the surface of HCP specimens (cylindrical specimens with 4 cm in length and 3.2 cm in diameter) was measured by TGA after 14d of accelerated carbonation.

Appendix B: Supplementary relations for transport properties

2.1 Diffusion coefficients for CO₂ and water vapour

The diffusion coefficients $D_{{{\text{CO}}_{{2}} (G)}}^{e}$ and $D_{{{\text{va}}(G)}}^{e}$ in (18) and (19) take into account the porosity and tortuosity of pore structure [69],

$$ D_{{{\text{CO}}_{{2}} ,{\text{va}}({\text{G}})}}^{e} = D_{{{\text{CO}}_{{2}} ,{\text{va}}({\text{G}})}}^{0} \phi^{2.7} \left( {1 - s_{{\text{L}}} } \right)^{4.2} $$

(25)

The term D⁰_CO2,va refer to the specific diffusion coefficients of CO₂ and water vapour in air, taking 1.6 × 10⁻⁵ m²/s for CO₂ and 2.82 × 10⁻⁵ m²/s for water vapour under T = 293 K and p_atm = 101.325 kPa.

For cement-based materials with higher w/c ratios, between 0.5 and 0.8, Papadakis et al. [70] proposed an empirical relation for the effective diffusivity of CO₂,

$$ D_{{{\text{CO}}_{{2}} (G)}}^{e} = 1.64 \times 10^{{{ - }6}} \phi_{{\text{p}}}^{1.8} \left( {1 - h} \right)^{2.2} $$

(26)

with ϕ_p standing for the porosity of cement paste in concretes. Both models in (25) and (26) are used in the simulations for CO₂ diffusivity respectively for w/c lower and higher than 0.5.

2.2 Permeability

Carbonation will also decrease the intrinsic permeability in (20) by pore precipitation. The intrinsic permeability considers the porosity change through the following relation [71],

$$ k_{{\text{int}}} = k_{{\text{int}}}^{0} \left( {\frac{\phi }{{\phi_{0} }}} \right)^{3} \left( {\frac{{1 - \phi_{0} }}{1 - \phi }} \right)^{2} $$

(27)

with k⁰_int and ϕ₀ referring to the initial values for intrinsic permeability and porosity. The relative permeability coefficient of liquid $k_{rl}$ is also derived from van Genuchten’s model [54], taking the following form,

$$ k_{{{\text{rl}}}} = \sqrt {s_{{\text{L}}} } \left[ {1 - \left( {1 - s_{{\text{L}}}^{b} } \right)^{1/b} } \right]^{2} $$

(28)

with the parameter b taking the same value as in (6). The dynamic viscosity of liquid water is retained for the pore solution, taking η_l = 0.1 Pas for T = 293 K.

2.3 Ionic diffusion coefficient

The ionic diffusivity model from Yokozeki et al. [72] is retained in the simulations, taking the following form,

$$ D_{i}^{e} = \frac{{1 - cv_{{{\text{ca}}}} }}{{1 - dv_{{{\text{fa}}}} }}v_{{\text{p}}} f\left( {\phi_{{\text{p}}} } \right)s_{{\text{L}}}^{\lambda } D_{i}^{0} $$

(29)

From the right side to left side, D⁰_i represents the diffusivity of ion i in pure water (dilute solution), e.g. 2.032 × 10^–9 m²/s for Cl⁻ in water under 25 °C. The function s_L^λ scales the pore saturation effect on the diffusivity, and the exponent λ takes 6.0 following Nguyen [45] for cement-based materials. The function f(ϕ_p) represents the effect of pore structure on the diffusivity, taking the following expression based on percolation theory [73],

$$ f\left( {\phi_{p} } \right) = 0.001 + 0.07\phi_{p}^{2} + 1.8\left( {\phi_{p} - 0.18} \right)^{2} \cdot {\text{H}}\left( {\phi_{p} - 0.18} \right) $$

(30)

with ϕ_p for capillary porosity of cement paste in concrete. So far, the diffusivity is scaled from pore solution to cement pastes. Then, the term v_p refers to the volumetric fraction of cement paste in concrete, and the last term describes the tortuosity effect provided by the fine and coarse aggregates: v_fa and v_ca refer to the volumetric fractions of fine and coarse aggregates, and c = 2.1, d = 0.65 for two tortuosity parameters.