MODELLING EFFECT OF COARSE AGGREGATES ON OXYGEN …

MODELLING EFFECT OF COARSE AGGREGATES ON OXYGEN TRANSPORT AND CORROSION PRODUCTS PRECIPITATION IN REINFORCED CONCRETE

Zhidong Zhang (1) and Ueli M. Angst (1)

(1) ETH Zurich, Institute for Building Materials, 8093 Zurich, Switzerland

Abstract The structure of concrete, in particular the microstructure of the steel-concrete interface

(SCI), can significantly affect corrosion of rebars. To support corrosion, oxygen needs to diffuse from the ambient environment to the steel surface. Meanwhile, corrosion products transport through the SCI and precipitate in concrete. Transport properties of concrete play an important role in these two processes. However, the effect of the heterogeneous structure of concrete especially coarse aggregates on oxygen transport and corrosion products precipitation in reinforced concrete is rarely studied in the literature. This study employed a numerical model to investigate such effect. Simulation domains in 2D were created with different aggregate contents and sizes. The model included oxygen diffusion, ions diffusion and migration, corrosion products oxidation and precipitation. The simulation results showed that the presence of aggregates significantly reduces oxygen diffusion. It becomes more pronounced for high aggregate contents which lead to more corrosion products formed at the interface. Furthermore, results showed that the interfacial transition zone (ITZ) around aggregates can enhance oxygen diffusion. Keywords: aggregates, oxygen diffusion, corrosion products, reinforced concrete, kinetic reaction

1. INTRODUCTIONCorrosion of reinforced concrete structures subjected to the natural environment is one of

the major concerns about the durability issues. When pH in concrete decreases caused by carbonation, or when chloride penetrates into concrete with liquid water, corrosion is apt to occur at the steel-concrete interface (SCI) (1). To evaluate the degradation of reinforced concrete, the effect of concrete structure, especially the SCI, must be well understood (2).

To construct the concrete structure for numerical modelling, concrete is generally viewed as a composite material with three components, including coarse aggregates, interfacial transition zone (ITZ), and mortar matrix (cement paste with fine aggregates). The mortar matrix is treated as a homogeneous medium. This approach works well for the macroscopic scale, but for the

4th International RILEM conference on Microstructure Related Durability of Cementitious Composites (Microdurability2020)

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mesoscopic and microscopic scales, we suggested to obtain the simulation domain from SEM-BSE images of the SCI (3).

In a composite material, coarse aggregates are commonly considered as impermeable and excluded in the simulations. It has been well known that the aggregate content and shape can significantly affect water and ions transport in concrete. Abyaneh et al., (4) used a 3D model to study the effect of the shape and orientation of aggregates on water transport and reported that the transport decreased when spherical aggregate particles were replaced with ellipsoidal particles due to the consequent increase in tortuosity of the cement paste. Liu et al., (5) employed a 2D model to simulate transport of multi-ions in concrete with different aggregate shapes and contents. They concluded that factors such as distribution, shape and content of aggregates have significant impacts on ion transport. Conclusions of these and more studies inspired us to investigate effects of these factors on corrosion of steel in concrete.

The measured thickness of ITZ, mainly based on the measured porosity in an SEM image, varies in different studies. Scrivener and Nemati (6) prepared concrete specimens which were impregnated with a fusible alloy liquid (Wood’s metal) and reported that the apparent width of ITZ is 30 – 100 µm, which is wider than the value of 10 – 20 µm by mercury intrusion porosimetry (7). Our recent study determined the thickness of ITZ based on the porosity map converted from SEM-BSE images (8). The thickness is about 5 µm at the upper side of an aggregate and at the underside, the thickness is much wider, more than 70 µm. In the numerical simulations, the ITZ is generally viewed as a uniform thin layer around each aggregate and its thickness depends on the size of the simulation domain. In the study of Du et al. (9), the thickness was assigned as 500 µm because the domain size is above 10 cm so a wider ITZ can be meshed. Abyaneh et al., (4) set an exponential function for the porosity distribution in the ITZ which is about 40 µm wide. The domain size is 7.5 mm so a narrow ITZ can be meshed. Liu et al., (5) set the ITZ thickness as 40 µm as well and the minimum mesh size is about 6.25 µm but their simulation domain is 5 cm, so they reported that the computation was very heavy.

Even though the effect of concrete structure on mass transport have been well studied in the literature, studies on the effect of coarse aggregates on O2 transport and corrosion products precipitation are rarely found. In this paper, a coupling model with iron oxidation, ions diffusion and migration (see the previous study (10)) was used to simulate transport and precipitation of corrosion products. The 2D simulation domains were created with circular aggregates and different aggregate contents.

2. THE MODEL

2.1 Conceptual model for corrosion products transport and oxidation Either for the chloride-induced corrosion (11) or the carbonation-induced corrosion (12),

corrosion of steel in concrete means the dissolution of iron atoms which is the transition from metallic state to a bivalent oxidation state.

Fe → Fe2+ + 2e− (1)

However, in studies characterizing the composition of corrosion products, they always found compounds with ferric iron. This is because there is an intermediate step of oxidation of Fe2+ ions, which involves oxygen and hydroxide ion and leads to the final formation of Fe3+ (13).

Fe2+ → Fe3+ + e− (2)


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Fe3+ oxides and hydroxides are highly insoluble (14,15), but Fe2+ hydroxide (Fe(OH)2) can be relatively more soluble (10-2 to 10-4 M, depending on pH). This means that for corrosion products to precipitate, the Fe2+ ions released at the steel surface are either oxidized to Fe3+ or to form Fe(OH)2 after the saturation level of Fe2+ is reached. Meanwhile, the transport of Fe2+ away from the steel surface continues. These processes constantly dilute the Fe2+ concentration.

Figure 1: Schematic representation of the reaction path from Fe2+ release to formation of solid corrosion products in the water-saturated concrete (adapted from (10)). In the figure, A=Fe2+ release, B=Fe(OH)2 precipitation, C=oxidation, D=FeOOH precipitation, E=Fe2+ diffusion.

Therefore, a model to describe the fate of Fe2+ ions released into a water-saturated concrete during the corrosion process is illustrated in Figure 1. For the uniform corrosion (i.e., carbonation induced) at the macroscopic scale, we assume that the anodic and cathodic reactions occur on the same steel surface. Two half-cell reactions is merged to provide the complete corrosion reaction.

2Fe + O2 + 2H2O → 2Fe2+ + 4OH− (3)

As aforementioned, the direct precipitation of Fe2+ only occurs when the saturation level of Fe2+ is above a certain level (i.e., 10-3 M).

Fe2+ + 2OH− → Fe(OH)2(4)

The oxidation of Fe2+ to Fe3+ (to form FeOOH) can be viewed as a kinetic process as the oxidation rate is in competition with the rate of the Fe(OH)2 formation. The Fe2+ oxidation by O2 can be well described by controlling parameters, such as pH and Fe2+ (16,17). Some studies showed that if pH is higher than a certain level the oxidation kinetics are not pH dependent (18). Thus, the oxidation rate is only dependent on [Fe2+] and dissolved oxygen [O2]aq.

−d[Fe2+]dt

= 𝑘𝑘[Fe2+][O2]aq (5)

where 𝑘𝑘 is a kinetic constant. Precipitation of FeOOH is here assumed to occur immediately.

2.2 Ion transport Ion transport in the porous media by diffusion under the concentration gradient and

migration under the electrical field is described by the extended Nernst-Planck equation (e.g., (19,20)). The advection is not considered in saturated concrete.

𝜕𝜕𝑐𝑐𝑖𝑖

𝜕𝜕𝜕𝜕= ∇ �𝐷𝐷𝑖𝑖𝛻𝛻𝑐𝑐𝑖𝑖 + 𝑧𝑧𝑖𝑖𝐹𝐹𝑐𝑐𝑖𝑖

𝐷𝐷𝑖𝑖

𝑅𝑅𝑅𝑅𝛻𝛻𝜓𝜓� + 𝑅𝑅𝑖𝑖 (6)

where 𝑧𝑧𝑖𝑖 (-) is the charge number, and 𝑖𝑖 represents the 𝑖𝑖 th ion/molecule (see Table 1). 𝑐𝑐𝑖𝑖 (mol/m3) is the concentration. 𝐹𝐹 is the Faraday constant (9.64846E-4 C/mol). 𝜓𝜓 (V) is the local


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electrical potential. 𝑅𝑅𝑖𝑖 is the source/sink term which can take into account oxidation/reactions. The effective diffusion coefficient 𝐷𝐷𝑖𝑖 (m2/s) depends on the pore network so it is described as a function of the tortuosity 𝜏𝜏 (-) and constructivity 𝛿𝛿𝑖𝑖 (-) of the pore structure (21).

𝐷𝐷𝑖𝑖 = 𝐷𝐷𝑖𝑖0 𝜙𝜙𝛿𝛿𝑖𝑖

𝜏𝜏2(7)

where 𝐷𝐷𝑖𝑖0 (m2/s) is the free diffusion coefficient of species 𝑖𝑖 in pure water. 𝛿𝛿𝑖𝑖 is species

dependent and related to the interaction between species and pore structure. Poisson's equation is coupled with Eq. (6) to take into account the effect of the electrical

potential on the ion transport.

∇𝜓𝜓 =𝐹𝐹

𝜀𝜀𝑟𝑟𝜀𝜀0� 𝑐𝑐𝑖𝑖𝑧𝑧𝑖𝑖 (8)

where 𝜀𝜀𝑟𝑟 and 𝜀𝜀0 are the relative and vacuum dielectric permittivity of the pore solution. Ion species in concrete are also considered in the model (see Table 1). Therefore, the

presence of these ions can change the potential field and thus affects the transport of Fe2+.

Table 1: Ions/molecules included in modelling

Cations Ca2+ K+ Na+ H+ Fe2+ Initial concentration (M) 0.0223 0.0089 0.0039 2e-9 0

𝐷𝐷𝑖𝑖0 (×10-9 m2/s) 0.793 1.957 1.33 9.3 0.719

Anions Cl- HCO3- SO42- S2- OH- Initial concentration (M) 0.013 0.0028 0.0197 0.0011 5E-5

𝐷𝐷𝑖𝑖0 (×10-9 m2/s) 2.03 1.1 1.07 0.731 5.3 Molecules O2 FeOOH Fe(OH)2

Initial concentration (M) 0.00028 0 0 𝐷𝐷𝑖𝑖

0 (×10-9 m2/s) 1.97 0 0

2.3 Modelling The 2D simulation domains in this study consist of three phases, namely, mortar matrix,

coarse aggregates and ITZ. This paper only considered the circular shape of aggregates. Other shapes (e.g., oval) were also investigated which showed higher tortuous effect than the circular aggregates but results are not shown due to the length limit of the paper. Three aggregate/domain ratios (0.45, 0.3 and 0.15) were compared as displayed in Figure 2.

Figure 2: Aggregate content and mesh for three aggregate/domain ratios: a) 0.45, b) 0.3 and c) 0.15.


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A simulation domain was set as 2 cm × 2 cm and the maximum diameter of aggregates was about 10 times smaller than the domain size (22). Three aggregate sizes (2, 1.5 and 1 mm) were considered according to the Fuller aggregate gradation. The ITZ for each aggregate was considered as a thin layer around the aggregate with a thickness about 100 µm which is close to the upper limit of measured ITZ thickness (6). The porosity of ITZ is not uniform and decreases from a high value at the aggregate surface to the same as the mortar matrix (see Figure 3). We consider this assumption more realistic than the generally used approach of setting a constant porosity for the ITZ. The finite element method was used to solve the partial differential equations. The minimum size of element is 6 µm so that the ITZ can be well meshed.

3. RESUTLS AND DISCUSSIONAs shown in Figure 2, the left boundary of the domain is the surface of the steel. The release

of Fe2+ is constant with a corrosion rate of 10 µm/year which is in the range of natural corrosion. According to Eq. (3), with 1 M Fe2+ being released, 2 M OH- is released as well and 0.5 M O2 is consumed at the steel surface. On the right boundary, the constant oxygen concentration of 0.28 M was applied, meaning that O2 from air can be quickly dissolved into the pore solution with the consumption of O2 in the concrete due to corrosion.

Figure 3: Porosity distribution at ITZ: a) An example in 2D and b) A porosity profile decreasing with the distance from an aggregate.

To investigate the effect of aggregates, simulations were firstly done for a domain without any aggregates. By adjusting 𝛿𝛿O2 for O2, we can make sure that there is always a small amount of O2 on the steel surface for corrosion (0.00005 M in this study). This means that corrosion can continue almost with infinite time. Then, the same value of 𝛿𝛿O2 was used for simulations with aggregates. The simulations stopped if oxygen at any location on the steel surface is zero. Therefore, by comparing the time of O2 depletion at the steel surface, one can tell how the presence of aggregates affects O2 diffusion and corrosion products precipitation.

Figure 4 shows an example of O2 reduction when the presence of aggregates is considered. It is clear that aggregates can significantly reduce O2 diffusion as O2 concentration at the steel surface decreases very quick and reduces to zero after just two days (comparing with the infinite time for the domain without aggregates).

a) b)

Aggregate


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Figure 4: Example of oxygen reduction for the case of aggregate/domain ratio 0.15.

Figure 5 compares O2 concentration and corrosion products at 0.5 d for three aggregate/domain ratios. It shows that more aggregates has the more pronounced reduction of O2 diffusion. The amount of Fe(OH)2 is very low but its concentration at the steel surface is slightly higher than 1E-3 M. This means that this concentration difference is not high enough to form a large amount of Fe(OH)2 as the most Fe2+ is oxidized to form FeOOH. This agrees with the conclusion of the previous study (10). The concentration of Fe2+ at the steel surface decreases slightly with the decreases of the aggregate/domain ratio. This is due to the fact that the high aggregate content reduces the Fe2+ diffusion, leading to the accumulation of Fe2+ ions at the steel surface. As a result, the concentration of FeOOH at the steel surface increases with the decreases of the aggregate/domain ratio.

Figure 5: Averaged profiles of oxygen concentration and corrosion productions at 0.5 d for aggregate ratios: a) 0.45, b) 0.3 and c) 0.15.

The cases without ITZ were also simulated in this study. The oxygen depletion time is compared for two cases (with and without ITZ) in Figure 6, which shows that O2 diffusion is even more reduced if there is no ITZ. The time when O2 depletion is about 25% lower than the cases with ITZ for all three aggregate/domain ratios, but the effect of ITZ seems less significant than the presence of aggregates, which is in agreement with conclusion in the literature (23).


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Figure 6: Effect of ITZ on oxygen reduction.

4. CONCLUSIONSThis paper studies the effect of coarse aggregates on O2 diffusion and precipitation of

corrosion products in the reinforced concrete. Numerical simulation results show that - The presence of aggregates significantly reduce O2 diffusion. This becomes more

pronounced with the increase of aggregate content (up to 0.45 aggregate ratio).- The high aggregate contents lead to more Fe2+ ions accumulating at the steel surface.

Consequently, a higher amount of FeOOH is formed but it rapidly drops with the distancefrom the steel surface.

- The presence of porous ITZ can enhance the diffusion oxygen from the ambientenvironment to the steel surface.

This paper reports the preliminary simulation results of the effect of coarse aggregates on corrosion in reinforced concrete. More simulations will be performed, including the effects of different aggregate shapes, corrosion rates, etc.

ACKNOWLEDGEMENTS The authors would thank the Swiss National Science Foundation (SNSF) for the financial

support through the ENDURE project (grant number PP00P2-163675).

REFERENCES 1. Angst UM, Geiker MR, Michel A, Gehlen C, Wong H, Isgor OB, et al. The steel--

concrete interface. Mater Struct. 2017;50(2):143.2. Zhang Z, Angst U. A discussion of the paper “Effect of design parameters on

microstructure of steel-concrete interface in reinforced concrete.” Vol. 128, Cement andConcrete Research. 2020. p. 105949.

3. Zhang Z, Angst U, Michel A, Jensen M. An image-based local homogenization methodto model mass transport at the steel-concrete interface. In: P.A.M.Basheer, editor. SixthInternational Conference on the Durability of Concrete Structures. Leeds, UK: WhittlesPublishing; 2018. p. 807–14.

4. Dehghanpoor Abyaneh S, Wong HS, Buenfeld NR. Modelling the diffusivity of mortarand concrete using a three-dimensional mesostructure with several aggregate shapes.Comput Mater Sci. 2013;78:63–73.

5. Liu Q, Feng G, Xia J, Yang J, Li L. Ionic transport features in concrete composites


662

containing various shaped aggregates: a numerical study. Compos Struct. 2017;183(1):371–80.

6. Scrivener KL, Nemati KM. The percolation of pore space in the cement paste/aggregateinterfacial zone of concrete. Cem Concr Res. 1996;26(1):35–40.

7. Snyder KA, Winslow DN, Bentz DP, Garboczi EJ. Effects of Interfacial ZonePercolation on Cement-Based Composite Transport Properties. MRS Proc. 1991;245.

8. Zhang Z, Angst UM, Michel A. A framework for modelling corrosion-relateddegradation in reinforced concrete. In: Caspeele R, Taerwe L, Frangopol DM, editors.IALCCE 2018. Ghent, Belgium: Taylor & Francis; 2019. p. 979–86.

9. Du X, Jin L, Ma G. A meso-scale numerical method for the simulation of chloridediffusivity in concrete. Finite Elem Anal Des. 2014;85:87–100.

10. Stefanoni M, Zhang Z, Angst U, Elsener B. The kinetic competition between transportand oxidation of ferrous ions governs precipitation of corrosion products in carbonatedconcrete. RILEM Tech Lett. 2018 Sep 14;3:8.

11. Wong HS, Zhao YX, Karimi AR, Buenfeld NR, Jin WL. On the penetration of corrosionproducts from reinforcing steel into concrete due to chloride-induced corrosion. CorrosSci. 2010;52(7):2469–80.

12. Angst U, Elsener B, Jamali A, Adey B. Concrete cover cracking owing to reinforcementcorrosion - Theoretical considerations and practical experience. Mater Corros.2012;63(12):1069–77.

13. Stratmann M. The Atmospheric Corrosion of Iron - A Discussion of the Physico-Chemical Fundamentals of this Omnipresent Corrosion Process. Berichte derBunsengesellschaft für Phys Chemie. 1990 Jun;94(6):626–39.

14. Cornell RM, Schwertmann U. The Iron Oxides, Structure, Properties, Reactions,Occurences and Uses. 2003. 1–121 p.

15. Fraser L, Stanger B, Griffin T, Jabri M, Sones G, Steelman M, et al. Seamless FluidsPrograms : A Key to Better Well Construction. Oilf Rev. 1996;8(2):42–56.

16. Stumm W, Lee GF. Oxygenation of Ferrous Iron. Ind Eng Chem. 1961;53(2):143–6.17. Pham AN, Waite TD. Oxygenation of Fe(II) in natural waters revisited: Kinetic modeling

approaches, rate constant estimation and the importance of various reaction pathways.Geochim Cosmochim Acta. 2008;72(15):3616–30.

18. Morgan B, Lahav O. The effect of pH on the kinetics of spontaneous Fe(II) oxidation byO2in aqueous solution - basic principles and a simple heuristic description. Chemosphere.2007;68(11):2080–4.

19. Baroghel-Bouny V, Thiéry M, Wang X. Modelling of isothermal coupled moisture-iontransport in cementitious materials. Cem Concr Res. 2011;41(8):828–41.

20. Jensen MM, Johannesson B, Geiker MR. A Numerical Comparison of Ionic Multi-Species Diffusion with and without Sorption Hysteresis for Cement-Based Materials.Transp Porous Media. 2015;107(1):27–47.

21. Atkinson A, Nickerson AK. The diffusion of ions through water-saturated cement. JMater Sci. 1984;19(9):3068–78.

22. Wu Z, Wong HS, Buenfeld NR. Influence of drying-induced microcracking and relatedsize effects on mass transport properties of concrete. Cem Concr Res. 2015;68:35–48.

23. Delagrave A, Bigas JP, Ollivier JP, Marchand J, Pigeon M. Influence of the interfacialzone on the chloride diffusivity of mortars. Adv Cem Based Mater. 1997;5(3–4):86–92.


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MODELLING EFFECT OF COARSE AGGREGATES ON OXYGEN …