Advances in Materials Science and Engineering

Volume 2015, Article ID 616980, 8 pages

http://dx.doi.org/10.1155/2015/616980

## Prediction of Chloride Penetration into Hardening Concrete

Department of Architectural Engineering, Kangwon National University, Chuncheon-si 200 701, Republic of Korea

Received 30 April 2015; Revised 29 June 2015; Accepted 1 July 2015

Academic Editor: Antônio G. B. de Lima

Copyright © 2015 Wei-Jie Fan and Xiao-Yong Wang. 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

In marine and coastal environments, penetration of chloride ions is one of the main mechanisms causing concrete reinforcement corrosion. Currently, most of experimental investigations about submerged penetration of chloride ions are started after the four-week standard curing of concrete. The further hydration of cement and reduction of chloride diffusivity during submerged penetration period are ignored. To overcome this weak point, this paper presents a numerical procedure to analyze simultaneously cement hydration reaction and chloride ion penetration process. First, using a cement hydration model, degree of hydration and phase volume fractions of hardening concrete are determined. Second, the dependences of chloride diffusivity and chloride binding capacity on age of concrete are clarified. Third, chloride profiles in hardening concrete are calculated. The proposed numerical procedure is verified by using chloride submerged penetration test results of concrete with different mixing proportions.

#### 1. Introduction

The ingress of chloride ions constitutes a major source of durability problems affecting reinforced concrete structures which are exposed to marine environments. Once a sufficient quantity of chloride ions has accumulated around the embedded steel, pitting corrosion of the metal is liable to occur unless the environmental conditions are strongly anaerobic. In the design of concrete structures, the influence of chloride ingress on service life must be considered [1].

The literature is rich in papers dealing with modeling of chloride attack of concrete. Papadakis [2, 3] proposes chemical reaction equations for silica fume, low calcium fly ash, and high calcium fly ash blended concrete. Using the volumetric relations calculated chemical reaction equations, porosity and chloride diffusivity of hardened concrete are determined. Han [4] proposes a modified diffusion coefficient that considers the effect of chloride binding and evaporable water on the diffusion coefficient. Based on the modified diffusion coefficient, numerical methods are used to estimate chloride concentration according to concrete depth and external and internal conditions. Spiesz [5, 6] analyzed chloride penetration profiles during rapid chloride migration tests. The diffusion flux during migration tests is shown to be insignificant compared to the electrical migration flux. However, it should be noticed that current models [2–6] focus on chloride penetration into fully hardened concrete.

Currently, most of experimental investigations about submerged penetration of chloride ions are started after the four-week standard curing of concrete [7–9]. After concrete with four-week initial curing, cement hydration reaction will proceed continuously [10, 11]. Hence four-week initial cured concrete is not fully hardened concrete, but slowly hardening concrete. After four-week initial curing of concrete, chloride diffusivity continuously decreases with the prolongation of curing period [7–9]. For chloride penetration into hardening concrete, cement hydration and chloride ingress will occur simultaneously, and current chloride penetration models [2–6] are not valid for hardening concrete.

To overcome the weak points of current models [2–6], this paper presents a numerical procedure to analyze simultaneously cement hydration reaction and chloride ion penetration process. By combining hydration model with chloride ingress model, the dependences of chloride diffusivity and chloride binding capacity on age of concrete are clarified. Furthermore, chloride profiles in hardening concrete are determined.

The original contributions of this paper are shown as follows: first, evaluate the phase volume fractions of hardening concrete by using a kinetic hydration model; second, predict the evolution of chloride diffusivity by using capillary porosity in cement paste; third, consider interactions between cement hydration and chloride penetration. The influences of curing ages on chloride attack durability are clarified.

#### 2. Cement Hydration Model

Tomosawa [12] proposed a shrinking-core model to model the hydration of Portland cement. However, Tomosawa’s original model does not consider the effects of capillary water on cement hydration and is only valid for low strength or ordinary strength concrete with higher water to binder ratios. Recently, to overcome weak points of Tomosawa’s model, Wang [10, 11] revised Tomosawa’s model to consider effects of water to binder ratio, mineral compositions, and capillary water concentrations on cement hydration process. The revised model is valid for concrete with different strengths, different cement mineral compositions, and different curing methods.

The proposed blended cement hydration model by Wang [10, 11] is valid for not only blended cement but also Portland cement. Using the hydration model, hydration degree of cement and reaction degree of mineral admixtures are determined. Furthermore, the age dependent properties of hardening concrete are evaluated using reaction degrees of binders.

The proposed blended cement hydration model by Wang [10, 11] consists of two parts, that is, cement hydration model and mineral admixtures reaction model. Because this paper mainly focuses on hydration related properties of Portland cement concrete, only cement hydration model is shown. Mineral admixtures reaction model is not shown in this paper.

This revised Portland cement hydration model by Wang [10, 11] is expressed as a single equation consisting of three coefficients: the reaction coefficient in the induction period; the effective diffusion coefficient of water through the C–S–H gel; and a coefficient of the reaction rate of mineral compound of cement as shown in the following equations:where (, and 4) represents reaction degree of mineral compounds of cement C_{3}S, C_{2}S, C_{3}A, and C_{4}AF, respectively; is the degree of cement hydration and can be calculated from the weight fraction of mineral compound and reaction degree of mineral compound ; is the stoichiometric ratio by mass of water to cement (= 0.25); is the physically bound water in C–S–H gel (= 0.15); is the density of water; is the density of the cement; is the amount of water at the exterior of the C–S–H gel; is the radius of unhydrated cement particles; is the effective surface area of the cement particles in contact with water; and is the total surface area if the surface area develops unconstrained.

The reaction coefficient is assumed to be a function of the degree of hydration as shown in (2), where and are the coefficients determining this factor; controls the rate of the initial shell formation and controls the rate of the initial shell decay:

The effective diffusion coefficient of water is affected by the tortuosity of the gel pores as well as the radii of the gel pores in the hydrate. This phenomenon can be described as a function of the degree of hydration and is expressed as follows:

In addition, free water in the capillary pores is depleted as hydration of cement minerals progresses. Some water is bound in the gel pores, and this water is not available for further hydration, an effect that must be taken into consideration in every step of the progress of the hydration. Therefore, the amount of water in the capillary pores is expressed as a function of the degree of hydration in the previous step as shown in the following:where and are the mass fractions of cement and water in the mix proportion.

The effect of temperature on these reaction coefficients is assumed to follow Arrhenius’s law as shown inwhere , , , and are temperature sensitivity coefficients and , , , and are the values of , , , and at 20°C.

Using reaction degree of cement, the phase volume fractions of hardening cement paste (sealed curing) can be determined as follows:where , , , , , , and are the volume of anhydrous cement, capillary water, gel water, evaporable water (the sum of capillary water and gel water), chemical shrinkage, capillary porosity (the sum of capillary water and chemical shrinkage), and total porosity (the sum of capillary porosity and gel water), respectively.

On the basis of degree of reactions of mineral compounds of cement, the parameters of hydration model are calibrated and shown in Table 1. Using this Portland cement hydration model, Wang [10, 11] evaluated the heat evolution rate, adiabatic temperature rise, compressive strength development, and thermal stress development in both ordinary strength concrete and high strength concrete.