Numerical simulation of chloride ion transport in concrete based on a random aggregate model

2.1. Materials and concrete mix proportion

The cement used is ordinary Portland cement with a grade of 42.5. The water-to-cement ratio is set at 0.4. The fine aggregate is river sand. The maximum particle size of the coarse aggregate is 26.5 mm, with continuous grading. The specific mix proportions of the concrete specimen are shown in Table 1.

2.2. Calculated methods

A three-dimensional spherical random aggregate model of concrete is created using the Monte Carlo method to obtain coarse aggregates that meet the grading requirements. These aggregates are randomly distributed within the concrete specimens, accounting for 60 % of the total volume. The Interfacial Transition Zone (ITZ) between the cement paste and the aggregate is designated to be 0.1 mm thick. Notably, the chloride ion diffusion coefficient within the ITZ is significantly higher compared to that of the cement mortar. In this paper, it is designed as three times greater than the diffusion coefficient in the cement mortar. Additionally, the diffusion coefficient for the aggregate is fixed at a value of 0. The activation energy was 11.92 kJ/mol. The aggregate information is imported into the COMSOL software to establish the geometric model of the concrete specimen, as shown in Fig. 1 and Fig. 2.

Fig. 1Randomly distributed aggregate

Fig. 2Mesh subdivision

The aggregate particle size distribution follows a randomized Fuller gradation, calculated using the following equation:

where $D_i$ is the aggregate size (mm); $V_{agg}$ is the aggregate volume fraction (%), $D_{min}$ is the minimum particle size (mm), $D_{max}$ is the maximum particle size (mm), and $s$ is the normalization parameter. Using the generated aggregate size $D_i$ and the local coordinate system origin as reference, the spatial distribution of aggregate vertices can be stochastically determined through spherical coordinates as follows:

where $\left(x_i,y_i,z_i\right)$ is the Cartesian coordinate of the aggregate vertex, $\left(r_i,\theta ,\phi \right)$ is spherical coordinates.

To clarify the influence of water-binder ratio, mineral admixtures and other factors on ion transport performance, this work takes chloride ion transport in saturated state as an example. According to the law of conservation of mass, the diffusion equation can be expressed as:

where $J$ represents the flow rate of chloride ion (mol·m^-2·s^-1), $D$ denotes the diffusion coefficient of chloride ion (m²·s^-1), $C$ indicates the concentration of chloride ion (mol·m^-3), and $t$ corresponds to the diffusion time (s). $x$, $y$ and $z$ are the three reference directions of three-dimensional space.

The study focuses on analyzing the variation of chloride ion concentration along the depth of concrete under different influencing factors. In normal circumstances, physical model experiments use powder grinding to test the average chloride ion concentration of the same concrete at different depths. To provide more realistic results, COMSOL displays the concentration distribution of chloride ions in two-dimensional and three-dimensional contour plots. Graphing software can be used to obtain distribution of chloride ion concentration along the concrete depth at different ages.

2.3. Model validation

To verify the accuracy and reliability of the model proposed in this study, concrete specimens with aggregate volume fraction of 60 % were selected. The aggregate size was controlled in the range of 5-26.5 mm, and the concrete specimen size was 100 mm × 50 mm. The mix ratio is shown in Table 3. According to GBT50082-2024 “Standard Test Method for Long-term Performance and Durability of Concrete”, the content of free chloride ions at different depths of concrete under different erosion time was determined.

In this study, a concrete model with the same test parameters was established. The chloride diffusion coefficients obtained from the model calculations were compared with those measured during experiments, as illustrated in Fig. 3. It was observed that as the temperature increased, both the apparent chloride ion diffusion coefficient calculated by the model and that measured through tests exhibited a gradual rise. A comparison of the simulation results with the experimental data reveals a strong correlation, with the overall error remaining below 5 %. This indicates that the model developed in this study can effectively predict the transport behavior of chloride ions in concrete. To further investigate the influence of temperature and mix ratios on the chloride ion transport properties in concrete at the meso-scale, this work will use this model to carry out parametric studies on the characteristics of different temperatures and mineral admixture contents.

Fig. 3Comparison between calculated results and test results

3.1. Effect of age on concrete chloride diffusion

The internal chloride ion concentration in reinforced concrete can be influenced to some extent by the duration of the external chloride ion attack. As time progresses, the concentration of chloride ions within the cement mortar increases. The longer the time, the more pathways are available for chloride ions to transport and the weaker the resistance to chloride ion movement within the concrete. For analysis, the chloride ion concentration is set at 100 mol/m³, and the critical concentration of chloride ions is 0.13 %. The termination time is 28 days, with a time step of 1 day. Changing the time factor analyses the migration of chloride ions under different time conditions.

Fig. 4Chloride ion distribution in concrete at varying temperatures

a) ADM20

b) ADM25

c) ADM30

The temperature is set at 20 ℃, 25 ℃, and 30 ℃, respectively, and the chloride ion concentration maps and contour plots at 3, 7, 14, and 28 days are generated. The distribution of chloride ion concentration along the depth of eroded concrete is shown in Fig. 3. The chloride ion penetration depths in the concrete are provided in Table 4.

As shown in Fig. 4 and Table 3, the chloride ion penetration depth in concrete increases by 10.9 % at 25 °C and 27.9 % at 30 °C compared to 20 °C at 3 days. This increase continues to 13.4 % (25 °C) and 28.5 % (30 °C) after 7 days, further rising to 13.7 % (25 °C) and 29.8 % (30 °C) after 14 days. By 28 days, the penetration depth increases by 17.3 % at 25 °C and 34.9 % at 30 °C. Notably, at 30 °C, the chloride penetration reaches 11.06 mm. The 28-day chloride penetration depth reaches 8.20 mm at 20 °C, with chloride concentration remaining below 5 mol/m³ at 20 mm depth. This represents a 2.86 mm increase in penetration depth and a 15 mol/m³ concentration difference at 20 mm depth compared to earlier measurements. The data clearly demonstrate that elevated temperatures accelerate both chloride penetration depth and erosion rate in concrete. Notably, temperature exerts a substantially greater influence on concrete durability.

Fig. 5Three-dimensional cloud maps of chloride ion concentration distribution (20 ℃)

a) 3 d

b) 7 d

c) 14 d

d) 28 d

Figs. 5-7 illustrate the three-dimensional distribution of chloride ion concentration in concrete at 20 °C, 25 °C, and 30 °C, respectively, while Figs. 8-10 present the corresponding two-dimensional distributions. The chloride ion erosion process at 20°C is simulated in Figs. 5(a-d) and 8(a-d) for curing periods of 3, 7, 14, and 28 days. With increasing concrete age, the expansion of red regions in these figures demonstrates progressive chloride ion penetration. Notably, the temperature effect becomes more evident at higher temperatures (25 °C and 30 °C) in Figs. 6-7 compared to Fig. 5 (20 °C), clearly visualizing how elevated temperatures accelerate chloride ion erosion in concrete.

Fig. 6Three-dimensional cloud maps of chloride ion concentration distribution (25 ℃)

a) 3 d

b) 7 d

c) 14 d

d) 28 d

Fig. 7Three-dimensional cloud maps of chloride ion concentration distribution (30 ℃)

a) 3 d

b) 7 d

c) 14 d

d) 28 d

Fig. 8Two-dimensional cloud maps of chloride ion concentration distribution (20 ℃)

a) 3 d

b) 7 d

c) 14 d

d) 28 d

Fig. 9Two-dimensional cloud maps of chloride ion concentration distribution (25 ℃)

a) 3 d

b) 7 d

c) 14 d

d) 28 d

Fig. 10Two-dimensional cloud maps of chloride ion concentration distribution (30 ℃)

a) 3 d

b) 7 d

c) 14 d

d) 28 d

3.2. Effect of temperature on chloride ion transport rate in concrete

Fig. 11 illustrates the chloride ion concentration and its distribution along the depth at temperatures of 20 ℃, 25 ℃, and 30 ℃. The initial diffusion coefficient of chloride ions in concrete changes with temperature variations: it is 2×10^–11 m²/s at 20 ℃; it increases to 2.62×10^–11 m²/s at 25 ℃; and it further rises to 3.41×10^–11 m²/s at 30 ℃. Compared with the results at 20 ℃, which increase by 31 % and 70.5 % at 25 ℃ and 30 ℃, respectively, Fig. 10 indicates a positive correlation between the initial diffusion coefficient and temperature.

Fig. 11Chloride ion diffusion coefficient of water binder ratio of 0.4

3.3. Impact of mineral admixtures on chloride ion transport in concrete

Ground granulated blast furnace slag shares a chemical composition similar to ordinary Portland cement. When incorporated into cement, its reactivity is fully utilized, optimizing the internal pore structure and significantly enhancing the concrete’s density and impermeability.

Fig. 12Effect of different mineral powder content on chloride ion penetration depth of concrete

a) ADM20

b) BSF50

c) BSF100

d) BSF130

The meso-scale results demonstrate that with slag contents of 10.4 %, 20.8 %, and 27.1 %, the chloride ion diffusion coefficient of concrete exhibits reductions of 0.2 %, 0.4 %, and 0.6 %, respectively at 3 days; 0.5 %, 0.9 %, and 1.3 % at 7 days; 0.8 %, 1.6 %, and 2.4 % at 14 days; and 1.4 %, 2.7 %, and 4.1 % at 28 days, respectively. The results at 3, 7, and 14 days indicate that the GGBFS content has a limited impact on concrete's early-stage chloride ion resistance. Fig. 12 displays the cloud map of chloride ion concentration distribution in concrete with varying slag contents at 28 days. Beyond 28 days, the effect of slag becomes more pronounced as the curing age increases. The resistance to chloride ion penetration improves progressively with higher slag content, as illustrated in Fig. 12.

3.4. Impact of fly ash on chloride ion migration in concrete

The chloride ion diffusion coefficients of concrete decreased with increasing fly ash content (8.3 %, 16.7 %, and 25 %), showing reductions of 0.3 %, 0.8 %, and 1.4 % at 3 days; 0.7 %, 1.8 %, and 3.1 % at 7 days; 1.2 %, 3.2 %, and 5.5 % at 14 days; and 2.1 %, 5.4 %, and 9.2 % at 28 days, respectively. These results suggest that fly ash has a relatively minor effect on chloride ion resistance during the early stages (3-14 days).

Fig. 13Effect of varying fly ash content on chloride ion penetration depth in concrete

a) FA40

b) FA80

c) FA120

As illustrated in Fig. 13, higher fly ash proportions led to a gradual reduction in chloride ion penetration depth at 28 days. This improvement is primarily due to the presence of glassy microspheres in fly ash, which decrease water demand, enhance workability, and refine the concrete’s pore structure and density. Furthermore, fly ash demonstrates superior effectiveness in improving chloride ion resistance compared to slag.

3.5. Impact of combined slag and fly ash on chloride ion transport in concrete

The incorporation of either slag (10.4 %, 20.8 %, 27.1 %) or fly ash (8.3 %, 16.7 %, 25 %) individually improved the chloride ion resistance of concrete. However, the combined use of 27.1 % slag and 25 % fly ash yielded the most substantial enhancement, reducing chloride ion diffusion coefficients by 3.1 %, 7.1 %, 12.4 %, and 20.2 % at 3, 7, 14, and 28 days, respectively. This synergistic effect also led to a significant decrease in chloride ion penetration depth, as demonstrated in Figs. 14 and 15. Further analysis revealed that a water-to-binder ratio of 0.4, when combined with 27.1 % slag and 25 % fly ash, optimally enhanced the concrete's resistance to chloride ion penetration.

Fig. 14Impact of mineral admixtures on concrete erosion resistance

a) Chloride ion concentration distribution

b) Chloride ion diffusion coefficient

Fig. 15Effect of combined fly ash and slag on chloride ion penetration depth in concrete