Advances in Materials Science and Engineering

Volume 2017 (2017), Article ID 1901459, 10 pages

https://doi.org/10.1155/2017/1901459

## Prediction of Time-Dependent Chloride Diffusion Coefficients for Slag-Blended Concrete

^{1}College of Engineering, Department of Architectural Engineering, Kangwon National University, Chuncheon-Si 200-701, Republic of Korea^{2}Department of Architectural Engineering, Hanyang University, Ansan-Si 426-791, Republic of Korea

Correspondence should be addressed to Xiao-Yong Wang

Received 25 August 2016; Accepted 10 November 2016; Published 1 January 2017

Academic Editor: Kazunori Fujikake

Copyright © 2017 Ki-Bong Park et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The chloride diffusion coefficient is considered to be a key factor for evaluating the service life of ground-granulated blast-furnace slag (GGBS) blended concrete. The chloride diffusion coefficient relates to both the concrete mixing proportions and curing ages. Due to the continuous hydration of the binders, the capillary porosity of the concrete decreases and the chloride diffusion coefficient also decreases over time. To date, the dependence of chloride diffusivity on the binder hydration and curing ages of slag-blended concrete has not been considered in detail. To fill this gap, this study presents a numerical procedure to predict time-dependent chloride diffusion coefficients for slag-blended concrete. First, by using a blended cement hydration model, the degree of the binder reaction for hardening concrete can be calculated. The effects of the water to binder ratios and slag replacement ratios on the degree of the binder reaction are considered. Second, by using the degree of the binder reaction, the capillary porosity of the binder paste at different curing ages can be determined. Third, by using the capillary porosity and aggregate volume, the chloride diffusion coefficients of concrete can be calculated. The proposed numerical procedure has been verified using the experimental results of concrete with different water to binder ratios, slag replacement ratios, and curing ages.

#### 1. Introduction

Chloride ingress is considered to be one of the major factors in the deterioration mechanisms of reinforced concrete in marine environments. The resulting corrosion of steel reinforcements causes serious detrimental effects, such as concrete cover cracking, reduced reinforcement in cross sections, decreased bonding between the steel rebar and concrete, and reduced yield strength and ductility of the steel rebar in reinforced concrete structures. However, to improve the resistance of concrete against chloride ingress, slag is widely used as a mineral admixture. Generally, incorporating GGBS into blended binders can increase the total porosity but will refine the pore size. Slag-blended concrete presents a lower chloride diffusivity and higher chloride binding capacity than control concrete [1].

The chloride diffusion coefficient is a key factor in the service life evaluation of slag-blended concrete. As for the chloride diffusivity in ordinary Portland cement (OPC) concrete or slag-blended concrete, Papadakis [2] and Demis et al. [3] evaluated the chloride diffusivity of fully hardened concrete as a function of the ultimate porosity. Alexander and Thomas [4] evaluated the chloride diffusivity of concrete after 28 days of curing as a function of the water to binder ratios. The Life-365 program [5] also uses the Alexander and Thomas equation [4] to determine concrete diffusivity. However, the Papadakis [2], Demis et al. [3], and Alexander and Thomas [4] models are not perfect. The Papadakis [2] and Demis et al. [3] models assume that cement is completely hydrated (i.e., the hydration degree is 100%) regardless of the water to cement ratio. Wang and Lee [6] reported that concretes with lower water to cement ratios had slower rates of hydration and lower ultimate degrees of hydration. The chloride diffusivity calculated according to the Alexander and Thomas model [4] does not consider other factors, such as the binder content, binder reactivity, and curing methods.

The composition of hydration products, capillary porosity, and chloride diffusivity relate closely to the degree of hydration in hardening or hardened concrete. Han [7] and Fan and Wang [8] proposed hydration-based chloride ingress models. Time-dependent chloride diffusivity was calculated by using the development of the capillary porosity of concrete over time. However, the Han [7] and Fan and Wang [8] models do not consider the reaction of mineral admixtures and are only valid for Portland cement concrete. In the literature, some models have been proposed that evaluate the chloride diffusivity of concrete containing mineral admixtures. Song et al. [9, 10] calculated the final degrees of reaction of cement and silica fume in silica fume-blended concrete. The capillary porosity, chloride diffusivity, and water permeability were determined by considering the final degrees of the binder reaction and the concrete mixing proportions. Oh and Jang [11] evaluated the chloride diffusivity of fly ash and slag-blended concrete by considering the final degrees of the binder reaction and the concrete porosity. However, Song et al. [9, 10] and Oh and Jang [11] studies are only valid for fully hardened concrete; they do not consider the dependence of chloride diffusivity on curing ages because their models do not account for the kinetic reaction processes of mineral admixtures.

As for the time dependence of chloride diffusivity, Nokken et al. [12] and Yu and Ye [13] found that chloride diffusion into concrete decreased over time. Concrete containing mineral admixtures has shown reduced chloride diffusivity compared to reference concrete. An empirical time parameter [14–16] has frequently been used to describe the age dependence of the chloride diffusion coefficient. However, this empirical time parameter cannot fully describe the evolution of the hardening concrete microstructure. The influence of various factors, such as the cement type, water to binder ratio, and slag replacement ratio, on this empirical time parameter requires further investigation [17].

To address the shortcomings of these current models, this paper presents a numerical procedure that analyzes the time dependence of the chloride diffusion coefficient. By using a blended cement hydration model, the degree of the reaction of binders and the capillary porosity of binder paste were calculated. Furthermore, the chloride diffusion coefficients at different curing ages were determined, considering the capillary porosity and aggregate volume.

#### 2. Cement Hydration Model and Chloride Diffusion Coefficient Model

##### 2.1. Cement Hydration Model

Wang and Lee [6, 18] proposed a hydration model for concrete containing supplementary cementitious materials, such as silica fume, fly ash, and slag. Hydration equations were proposed for cement and mineral admixtures, respectively, and the mutual interactions between cement hydration and mineral admixture reactions are considered with the capillary water content and calcium hydroxide content. The hydration model is valid for concrete with different water to binder ratios, mineral admixture replacement ratios, and curing temperatures [6, 18].

The reaction degrees of cement and mineral admixtures are used as fundamental indicators to evaluate the development of concrete properties. The degree of cement hydration () is defined as the ratio of the mass of hydrated cement to the mass of cement in the mixing proportion. The value of the degree of cement hydration () ranges between 0 and 1. A degree of cement hydration of means the absence of any hydration, and a degree of cement hydration of means that cement has fully hydrated.

By using an integration method, the degree of cement hydration can be determined as follows: where is time and is rate of cement hydration. The detailed equations for are available in our former research [6, 18].

Similarly, the reaction degree of a mineral admixture () is defined as the ratio of the mass of reacted mineral admixture to the mass of the mineral admixture in the mixing proportion. The value of the degree of the mineral admixture reaction () ranges between 0 and 1. means the absence of any mineral admixture reaction, and indicates that the mineral admixture has reacted completely. The reaction degree of the mineral admixture reaction can also be determined using an integration method in the time domain as follows:where is the rate of the mineral admixture reaction. The detailed equations for are available in our former research [6, 18].

In cement-mineral admixture blends, the production of chemically bound water relates to both cement hydration and mineral admixture reactions. The chemically bound water content can be determined as follows: where is the chemically bound water content, is the mass of cement in the mixing proportion, and is the mass of the mineral admixture in the mixing proportions. The expression is the mass of the chemically bound water from cement hydration, and the expression is the mass of the chemically bound water from the slag reactions [6, 18].

In the cement-mineral admixture blends, both cement hydration and mineral admixture reactions contribute to the formation of gel water. The content of gel water can be calculated as follows:where is the mass of gel water, is the mass of gel water produced from cement hydration, and is the mass of gel water produced from slag reaction.

The mass of combined water equals the sum of chemically bound water and gel water. The mass of combined water can be determined as follows:where is the mass of combined water.

In cement-mineral admixture blends, capillary water is consumed by both cement hydration and mineral admixture reactions. The capillary water content can be calculated as follows:where is the mass of capillary water in the hardening concrete and is the mass of water in the mixing proportion. The expression is the mass of capillary water consumed by cement hydration and the expression is the mass of the consumed capillary water from the slag reactions.

For hardened concrete, the capillary porosity equals the sum of capillary water and chemical shrinkage. The capillary porosity can be determined as follows:where is the capillary porosity of hardening concrete, is the chemical shrinkage from cement hydration, and is the chemical shrinkage from slag reactions.

##### 2.2. Chloride Diffusion Coefficient Model

Concrete is a three-phase material consisting of a cement paste matrix, aggregate, and interfacial transition zones (ITZs) between the cement paste matrix and aggregate. The interfacial transition zone has a higher capillary porosity and contains higher calcium hydroxide volume fractions compared to the bulk matrix. Interfacial zones are formed due to the particle-packing effect and the one-sided growth effect [19]. The particle-packing effect arises because the cement particles cannot pack together as well near a flat edge as in a free space. The one-sided growth effect is reactive growth from the cement side, but not from the aggregate side. The cement paste matrix is interconnected through interfacial transition zones. Garboczi [19] found that when the aggregate volume fractions are greater than 50%, the interfacial transition zone will be fully percolated. This observation agrees with the experimental results from Princigallo et al. [20]. Because most concretes have aggregate volume fractions above 50%, the interfacial transition zones in the usual concrete are percolated.

Due to the cement particle-packing effect, the ITZ shows a higher water to cement ratio. Therefore, the effective water to cement ratio in the bulk cement paste will be reduced. Nadeau [20, 21] proposed a model to consider water to cement gradients between the aggregate and bulk cement paste. The model is a function of the overall water-cement ratio, volume fraction and radius of the aggregate, specific gravity of cement, and thickness of the ITZ. The equations for determining the effective water to binder ratio of bulk cement paste in concrete are given as follows [21, 22]:where is the binder volume fraction in the bulk binder paste, is the volume of the aggregate, is the overall water to binder ratio of concrete, is the specific gravity of the binder, is a constant equal to approximately , and is the thickness ratio of ITZ. is the effective water to binder ratio in the bulk binder paste, whereas indicates the water volume fraction in the bulk binder paste.

The diffusivity of the cement paste phase is mainly dependent on the capillary pores in the cement paste, which can be determined as follows [8]:where and are the relation coefficients between the capillary porosity and chloride diffusivity, respectively; is the capillary porosity in the binder paste; and is volume of binder paste calculated from the effective water to binder ratio . In (9), the intrinsic diffusion coefficient relates to the type of binder, such as cement or slag. Exponent () relates to the pore size distribution or the complexity of the microstructure of the reaction products. As shown in (9) and (10), with the progress of binder hydration, the capillary porosity of concrete decreases and the chloride diffusion coefficient decreases correspondingly.

When the diffusivity of the aggregate particle inclusions is assumed to be zero, according to the composite sphere assemblage (CSA) model [11], the chloride diffusion coefficient of concrete can be determined as follows:where is the diffusivity of concrete and is the diffusivity in the interfacial transition zone.

By using a hard core/soft shell model, Garboczi [19] evaluated the connectivity of the interfacial zones for different choices of interfacial zone thicknesses. Furthermore, by comparison with cement mortar mercury intrusion data [23], a choice of 20 *μ*m for the interfacial zone thickness was found to give the best agreement with the mercury data. The mean radius of coarse aggregate is approximately 10 mm. Hence, in this study, a thickness ratio of ITZ of approximately is used.

Bentz and Garboczi [24] studied the effects of mineral admixtures on the interfacial transition zone. They found that smaller admixtures allow better packing nearer to the aggregate edge, and the reactivity of the mineral admixture controls the consumption of the calcium hydroxide. For fly ash blended mortar, the fraction ratio of CSH between ITZ and the bulk matrix is similar to plain cement mortar [22]. Similarly, based on an analysis of the chloride diffusivity of concrete with various fly ash and slag additions, Oh and Jang [11] proposed that, for Portland cement concrete, fly ash blended concrete, and slag-blended concrete, the ratios between and are almost the same ().

The effects of slag addition on the chloride diffusion coefficients of concrete are summarized as follows: first, incorporating GGBS into blended binders can increase the total porosity because the reactivity of slag is lower than the reactivity of cement. This point is considered using slag-blended cement hydration models ((1) and (7)). Second, calcium silicate hydrate (CSH) gel produced from slag reactions has finer gel pores than the gel from cement hydration. This effect is considered using an intrinsic diffusion coefficient in (9). Third, the formation of slag reaction products can fill large capillary voids and reduce the average pore size. This effect is considered using a chloride diffusion exponent in (9). In our study, the evolution of the chloride diffusion coefficient over time is directly related to the time-dependent development of capillary porosity. We do not use the empirical time parameter [14–16] to describe the age dependence of the chloride diffusion coefficient. Compared with the empirical time parameter method [14–16], the physical meaning of the model proposed in this study is much clearer.

However, the proposed model in this study for the chloride diffusion coefficient of concrete shows some limits. First, the chloride diffusivity in the ITZ is dependent on the distance from the aggregate surface [25, 26]. The chloride diffusivity in the ITZ is not analyzed in detail in this study. Second, for hardening concrete, the moisture transport from the water-rich ITZ to the drying bulk paste is not considered [25]. Water transport plays a prominent role in the hardened ITZ microstructure [27]. Therefore, the present version of the proposed model is not perfect and needs to be improved.

#### 3. Verification of the Proposed Model

The experimental results from Song and Kwon [15] were used to verify the proposed model. Song and Kwon [15] performed a systematic experimental study of the chloride diffusivity of slag-blended concrete. They measured a chloride diffusion coefficient for slag-blended concrete with various mixing proportions at different curing ages. Table 1 shows the chemical and physical properties of the cement and slag. Table 2 shows the mixing proportions of the concrete specimens. Concrete specimens with three different water to binder ratios of 0.47, 0.42, and 0.37 and two different slag contents of 30% and 50% were prepared. Concrete cylinder specimens were cured under moist conditions. At curing periods of 28 days (four weeks), 90 days (three months), 180 days (six months), and 270 days (nine months), the chloride diffusion coefficients were measured through an electrical accelerated method. After the electrical accelerated test, a silver nitrate solution (AgNO_{3} with a concentration of 0.1 mol/L) was used as an indicator to measure the chloride penetration depth that was achieved, and the chloride diffusion coefficient was calculated according to the penetration depth [15]. The diffusion coefficient determined by this test is a migration coefficient, which does not include binding, among other effects.