Advances in Civil Engineering

Volume 2018, Article ID 3789214, 6 pages

https://doi.org/10.1155/2018/3789214

## Modeling Chloride Diffusion Coefficient of Steel Fiber Reinforced Concrete under Bending Load

^{1}School of Materials Science & Engineering, Southeast University, Nanjing 211189, China^{2}Jiangsu Key Laboratory of Construction Materials, Nanjing 211189, China^{3}College of Civil Engineering and Architecture, Zhejiang University of Technology, Hangzhou 310014, China

Correspondence should be addressed to Qiannan Wang; moc.361@uesnqw

Received 13 August 2017; Accepted 20 December 2017; Published 4 April 2018

Academic Editor: Song Han

Copyright © 2018 Qiannan Wang 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 the most important parameter when predicting chloride ingress in concrete. This paper proposed a model for calculating the chloride diffusion coefficient of steel fiber reinforced concrete (SFRC). Considering the concrete structures in service are usually subjected to external loads, the effect of bending load was discussed and expressed with a stress factor in the model. The chloride diffusion coefficient of cement paste was calculated with capillary porosity and then used to predict the chloride diffusion coefficient of SFRC. Some factors in the model were determined with experimental results. Chloride bulk diffusion tests were performed on SFRC and plain concrete (without fiber) specimens under bending load. SFRC showed slightly better chloride resistance for unstressed specimens. The compressive stress decreased the chloride diffusion coefficient of SFRC, while it caused no change in plain concrete. For the tensile zone, the chloride resistance of concrete was improved significantly by adding steel fibers. Overall, SFRC performed better chloride resistance, especially under bending load. The proposed model provides a simple approach for calculating the chloride diffusion coefficient of SFRC under bending load.

#### 1. Introduction

Chloride-induced rebar corrosion is one of the major forms of environmental attack to reinforced concrete, which may lead to reduction in the strength, serviceability, and esthetics of the concrete structures [1, 2]. Moreover, cracks caused by mechanical loads reduce the chloride resistance of concrete and speed up the initiation of steel corrosion in concrete, which frequently occurs in field applications [3]. The addition of steel fibers significantly improves the resistance of concrete to crack initiation and propagation [4]. It is also generally accepted that steel fiber reinforced concrete (SFRC) has better durability than plain concrete [5]. However, the effect of steel fibers on chloride transport has not been fully understood yet.

Some work has been carried out over the past few decades to investigate the chloride transport property of SFRC [6, 7]. Mangat and Gurusamy [3] found that steel fibers had an insignificant effect on chloride transport. Roque et al. [5] observed that SFRC exhibited lower rates of chloride diffusion compared with plain concrete, although the reduction was generally small. On the contrary, El-Dieb [8] observed that an increasing fibers’ volume fraction leads to a slightly higher chloride diffusion coefficient. Considering the disagreements in the observed results, the chloride transport property of SFRC needs to be further studied and the effects of steel fibers need to be discussed. Besides, limited work has been performed on chloride transport property of SFRC under bending load. The study on prediction of chloride ingress in SFRC under load is also scarce.

The chloride diffusion coefficient is the most important parameter when predicting the chloride ingress in concrete. The intention of this paper is to present a model for predicting the chloride diffusion coefficient of SFRC under bending load. Besides, the effect of steel fibers on the chloride transport in concrete was investigated with bulk diffusion tests. The chloride diffusion coefficients of SFRC under compression and tension were determined and discussed.

#### 2. Chloride Diffusion Theory

##### 2.1. Fick’s Second Law

The mechanism of chloride transport into concrete structures is a rather complicated process [9]. For simplicity’s sake, all kinds of chloride transport mechanisms in concrete are generally regarded as “apparent diffusion.” By assuming that the chloride diffusion coefficient is constant, the well-known analytical solution of Fick’s second law of diffusion iswhere is chloride concentration at depth and immersion time , is chloride concentration at the surface, is depth, is immersion time, and is chloride diffusion coefficient.

##### 2.2. Time-Dependent Chloride Diffusion Coefficient

The chloride diffusion coefficient of concrete is not constant but decreases over time due to the continuous hydration [10–12]. Tang and Nilsson [13, 14] proposed the mathematical expression for a time-dependent chloride diffusion coefficient based on Crank’s mathematics of diffusion [14]:where is the time-dependent diffusion coefficient, is the concrete age, and and are constants, with normally being referred to as the age factor. With a pair of known diffusion coefficient and age, represented by and , (2) can be rewritten as

The analytical solution of Fick’s second law can only be derived under the assumption that the chloride diffusion coefficient is constant. Therefore, mathematical treatment needs to be done to the time-dependent chloride diffusion coefficient to get an average coefficient, which is defined as apparent chloride diffusion coefficient as given in the below equation:where and are the age when concrete starts to be exposed to chlorides and exposure duration, respectively.

Strictly speaking, the apparent diffusion coefficient instead of can be used in the analytical solution of Fick’s second law and (1) can be rewritten as

If the age factor is determined, the apparent chloride diffusion coefficient can be calculated with a pair of and . Consequently, the chloride distribution in concrete after certain immersion time can be predicted with (5).

##### 2.3. Modeling Chloride Diffusion Coefficient *D*_{0}

SFRC consists of cement paste, aggregate, and steel fibers. Compared with cement paste, the aggregate and steel fibers can be considered as impermeable. The chloride diffusion coefficient of SFRC at time can be expressed aswhere is the chloride diffusion coefficient of cement paste at time , and are the volume fractions of aggregate and steel fibers in SFRC, respectively. and can easily be obtained with the mix proportions of SFRC. is a correction factor reflecting the effects of aggregate and steel fibers on chloride transport in SFRC. is the stress factor ( is 1 for concrete under no stress).

The presence of aggregate and steel fibers leads to formation of interfacial transition zone (ITZ) between the paste and the aggregate/fibers in SFRC. Due to its higher porosity and bigger pore size, ITZ has much higher diffusivity than paste. As a result, the presence of ITZ increases the rate of chloride transport in concrete. On the other hand, the presence of aggregate increases the tortuosity of chloride’s transport path in concrete and consequently decreases the chloride diffusivity. Moreover, steel fibers can restrain the crack initiation and propagation, and the high relative surface area of fibers can adsorb some chlorides and retard the chloride ingress. It requires a lot of work to study these effects of aggregate and fibers on chloride transport in SFRC. For simplicity, in this study, the factor was introduced to describe the influences of aggregate and steel fibers on chloride transport in SFRC.

Cracks caused by mechanical loads create easy path for chloride transport and speed up the chloride ingress in concrete, which frequently occurs in field applications [15, 16]. Therefore, to consider the effects of stress on chloride diffusion coefficient of SFRC, a stress factor was introduced in (6). is dependent on the property of concrete and the stress conditions. The values of and were determined with the test results.

There are several models predicting the chloride diffusion coefficient of cement paste [17–20]. The model proposed by Garboczi and Bentz [17] is adopted in this study and shown in the below equation:where is the diffusion coefficient of chloride in bulk water ( is 2.03 × 10^{−9} m^{2}/s at 25°C), is the capillary porosity of cement paste at time ; is the Heaviside function such that for and for . The relationship is suitable for cement paste with a capillary porosity range of .

Sun [21] performed mercury intrusion porosimetry (MIP) test on the paste specimen with the same mix proportions and the same materials as the paste of concrete in this study. The MIP test was performed at the age of 60 days. The capillary porosity was 17.45%. Substituting the value of in (7), the chloride diffusion coefficient of cement paste at time ( = 60 d) was calculated to be 6.36 × 10^{−12} m^{2}/s. If the factors and are determined, the chloride diffusion coefficient at time can be predicted with (6), and the apparent chloride diffusion coefficient can be calculated with (4), consequently.

#### 3. Experimental Program

##### 3.1. Materials and Mixture Proportions

Mixture proportions of the concrete used in this study are given in Table 1. C50 was plain concrete without fiber. C50-1 and C50-1.5 were concrete with steel fibers of 1% and 1.5% in volume fraction, respectively. The materials used in this study were P.II52.5R Portland cement; Class I fly ash (FA); natural sand with a maximum grain size of 4.75 mm and a density of 2650 kg/m^{3}; gravel with size ranging from 5 to 20 mm and a density of 2700 kg/m^{3}; water; and hooked steel fibers with a diameter of 0.65 mm and a length of 35 mm.