Chloride diffusion-induced corrosion is a major factor that affects the durability of concrete structures. Thus, the study of chloride diffusion in concrete is important. In this study, a mesoscopic structure model is proposed and used to investigate chloride diffusion in concrete. The concrete is assumed to be a heterogeneous material composed of two phases of aggregate and mortar matrix. The aggregates are randomly distributed convex polygons. The chloride diffusion is assumed to occur only in the mortar matrix phase. The modified chloride diffusion coefficient in the mesoscale model is proposed. The effect of a single aggregate in chloride diffusion in concrete is analyzed. The present numerical model is validated on the basis of the experimental data. The influence of aggregate in the presented model, including aggregate random distribution form, aggregate content, and the validity of polygonal aggregate based on circle, is explored further. The simulation results indicate that the polygonal aggregate random distribution has a negligible influence on chloride diffusion in concrete, the polygonal aggregate content has a certain effect, and the presented mesoscale numerical model is an effect method for predicting the chloride diffusion in concrete.

Chloride-induced reinforcement corrosion is a major cause of deterioration in reinforced concrete structures. This corrosion may result in serious damage to concrete structures and increased cost of repair and inspection [

Considerable efforts have been made by using different methods to investigate various models to explain the diffusion behavior of chloride in heterogeneous concrete materials. Many researchers have explored the chloride diffusion in concrete by using experimental methods [

In recent years, with the development of computers, an increasing number of mesoscopic methods have been used to simulate chlorine diffusion in concrete numerically. A lattice modeling for chloride ingress in concrete is adopted in [

In the mesoscopic model, chloride diffusion in concrete is assumed to obey Fick’s law without other heterogeneity on the influence of diffusion. The mesoscale mechanics of concrete has been discussed in recent decades with the development of multiscale mechanical theories. Roelfstra et al. [

Notably, the mesoscopic model includes the two-phase aggregate and mortar matrix in concrete regardless of the kind of mesoscale models. ITZ is a thin layer between the aggregate and mortar matrix. Many researchers have investigated the microstructures of ITZ in concrete by using various methods. Determining the diffusivity of ITZ through experiments is complicated and difficult. Thus, this factor is usually neglected when calculating the uniform thickness. The ITZ thickness is usually 20, 40, and 50

The diffusion coefficient of ITZ (

Although numerical simulations have made some progress on chloride diffusion, relevant research, such as the influence of particle shape, is still incomplete. Thus, further work needs to be conducted. The present study focuses on the influences of mesostructure parameters on chloride diffusivity in concrete, including aggregate distribution, shape, and content.

Taking all these into account, to reveal the particulars of chloride diffusion in a heterostructural concrete, a simple two-phased structure model was constructed and used in this present article. The aggregate shape is a convex polygonal based on a circle. Therefore, the aggregate shape is much closer to the actual situation. The influences of aggregate distribution and content are discussed.

In this article, the chloride diffusion in concrete on mesoscopic scale is discussed. Section

In the present work, the mesoscale concrete material constituents are the mortar matrix and aggregates. The mortar matrix is assumed to be homogeneous, no cracks are considered, and it is strongly dependent on the type of cement, number of pores, water-to-cement ratio, and other additives present used. Random spatial distribution and the popular take-place method [

The distribution of aggregate with different sizes used in the concrete specimen was determined by using a sieve analysis for a given aggregate volume fraction. The aggregate fraction refers to the volume fraction of coarse aggregate in unit volume concrete, and it is approximately 30%–70% in concrete [

We can calculate the percentage of different diameter aggregate volume fractions according to equation (

The mesoscale model of concrete.

The most commonly used equation for chloride diffusion in concrete is Fick’s law. The chloride diffusion coefficient in aggregate is zero. Thus, the chloride diffusion in the mesoscale model of concrete is similar to the diffusion in porous material. When applying Fick’s law to a porous material, such as concrete, the equation can be expressed as follows:

In the method, the aggregate is assumed to have a spherical shape. In the study, the aggregate is assumed to be polygonal, and the calibration of the chloride diffusion is proposed.

Roundness of aggregate diagram.

The adopted number of polygon edges is 5 to 20 in the study. Due to the random inscribed polygons in a circle, we will use the concept of average roundness of the coarse aggregate particles as follows:

The permeability of ordinary aggregate is usually assumed to be zero in the process of diffusion. Chloride cannot diffuse through the aggregates, which is bound to bypass the aggregate particles to make the diffusion path extension. The effect of aggregate shape on chloride diffusion coefficient is different and similar to [

Partial differential equation (

For example, when the side length is 0.5 m square concrete specimen, it is assumed that the left border of the critical concentration ^{2}/a. Generate a circle and a polygonal aggregate whose areas are 40% of the concrete’s area, while generate a smaller circle and a polygonal aggregate, whose areas are 20% of the total area as in Figure

The distribution of chloride concentration in concrete (

The chloride diffusion in concrete was simulated based on the previous methods. Experimental data was from Mangat and Molloy [_{s} = 1.5%, Vagg = 0.5 were adopted. The other parameters used were the same as those in [

The mesostructure of concrete is shown in Figure

Comparison of the experimental data and simulated results.

Distribution of chloride concentration (

In this section, some numerical cases are designed to examine the effect of aggregate distribution mode and shape (Table

Numerical design for aggregate analysis.

Test case | ^{2}/s) | Aggregate shape | Aggregate fraction (%) | |
---|---|---|---|---|

1 | 1.5 | 5 × 10^{−12} | Polygonal | 50 |

2 | 1.5 | 5 × 10^{−12} | Polygonal | 35, 50, 70 |

3 | 1.5 | 5 × 10^{−12} | Circular, polygonal | 70 |

In this mesoscale model, the polygonal aggregate is a random generation based on Monte Carlo. Thus, the distribution of aggregate particles is different each time. For case 1, the specimen is 0.1 m

The distribution of chloride concentration at

For case 2, the effect of the volume fraction of aggregate was analyzed. The specimens are shown in Figure

Distribution of chloride concentration at

The chloride concentration is 0.03641%, 0.008154%, and 0.0000405% at the right side; the depth is 0.5 m when

As for case 3, the effect of the present two-dimensional numerical method for polygonal aggregate can be proven again. When polygonal aggregate is adopted,

Distribution of chloride concentration in concrete. (a) Polygonal aggregate. (b) Circular aggregate.

Distribution profile of chloride concentration from the mesoscopic model. (a) Polygonal aggregate. (b) Circular aggregate.

In this work, a mesoscopic numerical model was presented on the basis of the polygonal aggregate, and the chloride diffusion in concrete was investigated. The proposed simulation method on mesoscopic level was verified by experimental values and simulated results. The method that adopted polygonal aggregate was realistic. The modified effective diffusion coefficient was presented, and the effect of polygonal aggregate was discussed. The following conclusions can be drawn on the basis of the obtained results:

The mesoscale numerical model based on polygonal random aggregate that generates the tortuosity of diffusion path can provide the effective chloride diffusion coefficient, which includes the aggregate factor with a simple formula that can be expressed as

The mesoscale numerical result based on polygonal random aggregate shows a good correlation with the experimental data. It further validated the mesoscopic model of the polygonal aggregate to predict the precision of chloride concentration.

The random distribution of polygonal aggregate has a negligible influence on chloride diffusion in concrete.

An increment in the polygonal aggregate content increases the tortuosity of the chloride diffusion path and decreases the global chloride diffusion speed.

Finally, the presented model can be used successfully in simulating chloride penetration. The presence of polygonal coarse aggregates in concrete can be included in the model and provide more insights into the transport behavior. In all the analyses presented in this work, concrete was assumed to be fully saturated. Consequently, capillary suction and the effects of chloride binding were not considered. The next step can carry out relevant simulated calculation.

The data used to support the findings of this study were supplied by Ling Yao under license and so cannot be made freely available. Requests for access to these data should be made to the corresponding author.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The research was financially supported by the Institute Foundation ZB2018009, by the Fund for Shanxi “1331 Project” Key Subjects Construction.