Mathematical Problems in Engineering

Volume 2017, Article ID 5760512, 13 pages

https://doi.org/10.1155/2017/5760512

## Developing a Model for Chloride Ions Transport in Cement Concrete under Dynamic Flexural Loading and Dry-Wet Cycles

^{1}School of Materials Science & Engineering, Chang’an University, Xi’an, Shaanxi 710061, China^{2}School of Transportation, Southeast University, Nanjing, Jiangsu 210096, China^{3}Qinghai Research Institute of Transportation, Qinghai 810008, China

Correspondence should be addressed to Hua-xin Chen; nc.ude.dhc@nehcxh

Received 23 August 2017; Revised 5 November 2017; Accepted 28 November 2017; Published 24 December 2017

Academic Editor: Alessandro Arsie

Copyright © 2017 Bo-wen Guan 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

Chloride ions attack is the main factor leading to the degradation of concrete durability, while the diffusion process would be significantly aggravated under the dynamic flexural loading and dry-wet cycles. In this paper, the influence coefficients of dynamic flexural loading on chloride/water diffusion coefficients were established, based on the relationship between the dynamic flexural loading and the chloride ions diffusion coefficient of concrete. Based on the model of chloride ions transporting in dry-wet cycle environment, the transport model of chloride ions in concrete under the dynamic flexural loading and dry-wet cycles was established. The effects of different factors on the chloride ions transport law in concrete were analyzed through laboratory test. The results showed that the model was in good agreement with the experimental results. The theory and assumptions proposed applied in the model of chloride ions transport in concrete under the dynamic flexural loading and dry-wet cycles had certain rationality and scientificity.

#### 1. Introduction

Chloride ions could greatly harm the durability of reinforced concrete structures. In the area rich in chloride salt, concrete structures are not only exposed to chloride environment, but also subjected to the fatigue failure caused by repeated traffic loads. Under the dynamic flexural loading, the microcracks of concrete could easily sprout and expand. These microcracks not only constitute the transport channel of chloride ions, but also contribute to the water diffusion in concrete which increases the driving force of diffusion and convection. As for the concrete structure in tidal region, or areas where splash and water level change is prevailing, the concrete also suffers from dry-wet cycle of chloride solution. When concrete is in unsaturated state, the transmission of chloride ions in concrete is faster [1]. Due to the defect of design standard, the durability of concrete is insufficient. The cost of maintenance is increasing continuously which causes huge economic loss [2, 3]. Therefore, studying the effect of dynamic flexural loading and dry-wet cycles on chloride ions diffusion in concrete is of great significance for ensuring the safe operation of concrete works in the chloride enrichment area, and accurately predicting and improving the service life of the project. Chloride ions diffusion process in concrete has been studied by several researchers. Many of them [4–7] study the chloride diffusion characteristic in concrete based on Fick’s second law. The influences of different fatigue stress levels and temperature coupling on the chloride diffusion coefficient of concrete were investigated by Wang et al. [8, 9]. Ren et al. [10] had found that the chloride ions permeability coefficient and the fatigue stress level have an exponential relationship under the combined effect of fatigue load and chloride solution immersion. The combined action of loads with a chloride dry-wet cycle and freeze-thaw cycle on the flexural performance of reinforced concrete (RC) beams strengthened with textile reinforced concrete was studied by Yin et al. [11]. It had been found that the coupling of load and chloride ions caused sustained damage to the textile reinforced concrete (TRC) and reduced the durability of the TRC. The chloride penetration process in concrete with two different replacement ratios by supplementary cementitious materials, three different levels of flexural loading, and three different types of drying-wetting-carbonation exposure conditions was experimentally characterized by Ye et al. [12]. The result showed that the incorporation of supplementary cementitious materials makes concrete more vulnerable to chloride attack under a combined deterioration of cyclic drying-wetting and carbonation, since the deficiency of portlandite dominates the positive effects such as pore refinement. At present, the transmission model of chloride ions in concrete under different environmental factors or mechanical properties has been addressed by many researchers [13–16]. But little information is available about the experimental and theoretical analysis of chloride ions transport in concrete under the combined action of dynamic flexural loading and dry-wet cycle.

In this paper, transport behavior of chloride ions under the combined action of dynamic flexural loading and dry-wet cycles is considered as the effect of dynamic flexural loading on the chloride ions diffusion coefficient and water diffusion coefficient. The influence coefficients of dynamic flexural loading on chloride ions diffusion coefficient and water diffusion coefficient were established, respectively. And then according to the equation of chloride ions transport in concrete under the action of dry-wet cycle and the equation of chloride ions transport in concrete under the action of dynamic flexural loading, the equation of chloride ions transport in concrete under the combined action of dynamic flexural loading and dry-wet cycles was established. The rationality of the model was verified by comparing the experimental results and model results. The research results provide a reference for the design and life prediction of road concrete engineering under the interaction of dynamic flexural loading and dry-wet cycle in a salt rich environment.

#### 2. Model for Chloride Ions Transport in Cement Concrete under Dynamic Flexural Loading

##### 2.1. Characterization of Chloride Ions Diffusion Coefficient Based on Crack Area

In concrete, there are native microcracks and connected micropores. When concrete is subjected to chloride attack, the chloride ions will pass through the pores and defects into the concrete and spread to the depth. The dynamic flexural loading intensifies the initiation and propagation of microcracks in concrete. And the chloride ions diffusion channel and diffusion rate increase consequently. When dynamic flexural loading is applied to concrete, the microcracks in concrete would open, and the tip of the crack could generate a partial vacuum, resulting in the chloride solution entering the crack rapidly by pumping. When the load is unloaded, the closed crack would force salt solution spraying. In such a cycle, the chloride solution forms turbulent diffusion near the microcracks, which greatly improves the diffusion capacity of chloride ions.

Here, the concrete is divided into two parts: the matrix and the microcrack. The chloride ions diffuse into the concrete through the pores and microcracks of the matrix. The total diffusion flux of chloride ions into the concrete includes the matrix diffusion flux and microcrack diffusion flux, as shown below:where is the total chloride ions diffusion flux into the concrete; is the chloride ions diffusion flux into concrete through the matrix; is the chloride ions diffusion flux into the concrete through the crack; is the area of the concrete matrix; is the area of concrete cracks.

According to the diffusion theory, diffusion flux is the product of the diffusion coefficient of ions by the ion concentration gradient, as follows:where is the mass concentration of chloride ions; is the diffusion direction of chloride ions; is the total diffusion coefficient of chloride ions in concrete; is diffusion coefficient of chloride ions through concrete matrix; is diffusion coefficients of chloride ions through cracks.

Then (2) are taken into (1) and deformed:

Equation (3) is the diffusion coefficient of chloride ions characterized by the crack area. The chloride diffusion coefficient is the result of the integration of chloride ions diffusing through the connected pore and crack. It is an equivalent diffusion coefficient and it can be tested according to the Nordic standard NT BUILD 443-The immersion test.

For ordinary concrete, the crack area is very small and the matrix area is much larger than the crack area, so (3) can be simplified as

If the dynamic flexural loading is applied to the concrete, the dynamic flexural loading will cause the fatigue cumulative damage to the concrete. The crack area will increase and the chloride ions diffusion coefficient will also increase. The chloride ions diffusion coefficient can be expressed as below after the damage:where is the chloride diffusion coefficient after fatigue damage of concrete; is the crack area of concrete after fatigue damage.

The crack area consists of two parts, the initial crack area and the extended crack area:where is the change of crack area of the concrete after fatigue damage.

Then (6) is taken into (5), obtainingwhere is the equivalent chloride ions diffusion coefficient tested according to the Nordic standard NT BUILD 443-The immersion test or other methods; is the maximum diffusion coefficient of chloride ions in concrete cracks.

Equation (7) is the characterization of chloride ions diffusion coefficient based on crack area and initial diffusion coefficient after the fatigue damage.

##### 2.2. Effects of Fatigue Damage on Crack Area

The bottom of middle part of concrete beam and pavement slab is under the maximum flexural tensile stress. Under the combined action of cyclic bending stress and chloride diffusion, the bending deformation of this part is the largest and the structure is the weakest. It will lead to the fastest rate of chloride ions penetration. A unit is selected from this part as shown in Figure 1. Three hypotheses are made as follows:(1)The concrete is homogeneous and the chloride ions diffuse in the concrete unit in one dimension;(2)The initial microcracks are evenly distributed in the concrete;(3)The damage of concrete is only the expansion of microcracks during fatigue damage.