Advances in Materials Science and Engineering

Volume 2017, Article ID 2076986, 10 pages

https://doi.org/10.1155/2017/2076986

## Concentration Distribution of Chloride Ion under the Influence of the Convection-Diffusion Coupling

Department of Civil Engineering, Harbin Institute of Technology, Weihai 264209, China

Correspondence should be addressed to Y. Z. Zhang; nc.ude.tih@zyhz

Received 31 March 2017; Accepted 24 May 2017; Published 22 June 2017

Academic Editor: Xiao-Yong Wang

Copyright © 2017 Q. L. Zhao and Y. Z. Zhang. 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 transfer process of chloride ion under the action of the convection-diffusion coupling was analyzed in order to predict the corrosion of reinforcement and the durability of structure more accurately. Considering the time-varying properties of diffusion coefficient and the space-time effect of the convection velocity, the differential equation for chloride ion transfer under the action of the convection-diffusion coupling was constructed. And then the chloride ion transfer model was validated by the existing experimental datum and the actual project datum. The results showed that when only diffusion was considered, the chlorine ion concentration increased with the time and decreased with the decay index of time. Under the action of the convection-diffusion coupling, at each point of coupling region, the chloride ion concentration first increased and then decreased and tended to stabilize, and the maximum appeared at the moment of convection velocity being 0; in the diffusion zone, the chloride ion concentration increased over time, and the chloride ion concentration of the same location increased with the depth of convection (in the later period), the velocity of convection (in the early period), and the chloride ion concentration of the surface.

#### 1. Introduction

Chloride ion is the main factor affecting the durability of RC structures in subsea environment [1–6]. It can cause the corrosion of steel bars, diminish the bearing capacity of structures, and even influence the service life that cannot meet the design requirement [7, 8]. In the salt fog environment and splash zone, where the concrete structure is in an unsaturated state between water saturated and completely dry, the ion on the surface of concrete migrates into concrete by the diffusion of concentration and capillary absorption [9–11]. In the environment of pressure water, chloride ion transfers to internal parts mainly through convective motion caused by concentration diffusion and pressure infiltration [12]. It can be seen that the convection-diffusion coupling is the main approach of the transfer of chloride ion in concrete. Therefore, in order to improve the durability of concrete structure, studying the concentration distribution of chloride ion under the coupled action is of great significance.

Traditional research of the transmission of chloride ions in concrete considers only the diffusion effect, induces the analytical solution of chloride concentration based on the partial differential equation of the Fick’s second law [13–17], and modifies the equations according to the service environment [18–20]. Since the transmission mechanism of chloride ion is complex and the parameters for the partial differential equation are a lot, there is no accepted and precise analytical formula for chloride concentration. The methods adopted include empirical method, finite element method, difference method, and analytic method. DuraCrete [21] proposed an experience method which considers that within ( is the total convection depth) the chloride ion convection is mainly caused by pore fluid flow while that outside this region is mainly caused by concentration diffusion. Jin et al. [9] adopted the method of finite difference to calculate the chloride ion concentration in the region of the convection-diffusion coupling. Based on the law of conservation of matter, Pan and Chen [22] deduced convection-diffusion equation of chlorine ion in unsaturated concrete, and the preliminary analysis for stability of the parameters in the model and finite element calculation has been carried out. Li [23] analyzed the migration of moisture in concrete under the action of the pressure and established a theoretical model for chloride ion concentration in the unsaturated concrete, under the action of water flow rate, depth of penetration, and the convection-diffusion coupling. Xiang [24] distinguished the region of the convection-diffusion coupling and diffusion area and solved the equation of the convection-diffusion coupling by using the finite difference method. By assuming the initial boundary conditions and using traditional solutions, the questions of diffusion zone were answered. On this basis, Yue et al. [25] adopted the method of separation and substitution of variables, respectively, to solve the transfer of the chloride ion in the coupling and diffusion area. It is supposed that the speed of convection is constant and irrelevant to the position or time. The transfer of chloride ion in the concrete under the conditions of convection was obtained. Jia et al. [26] studied the transmission law of chloride ion in unsaturated concrete and steel structures by numerical simulation. Feng et al. [27] considered the difference of water transport between dry and wet cycles; a convection-diffusion equation for chloride ion transport in unsaturated concrete was derived. For the research above, the differential equations of the coupling of diffusion-convection are mostly the same, but the convection velocity is different. To simplify the calculation, the time-varying nature of diffusion coefficient was not considered in those researches.

With the consideration of a time-varying characteristic of diffusion coefficient, the differential equation for the transfer of chloride ion under the action of the convection-diffusion coupling was set up. The coupling zone and the diffusion zone were distinguished by the convection velocity. The numerical analysis with MATLAB was adopted to predict the concentration of chloride ion, and the influences of the parameters were analyzed.

#### 2. The Differential Equation of Transfer of Chloride Ion under the Action of the Coupling of Chloride Ion

Because the depth of capillary absorption and penetration is limited, the convective region exists only within a certain depth beneath the surface of the concrete. DuraCrete [21] thought that the depth of influenced convection was 14 mm. Lei [28] concluded that the depth of a convection zone in an underground structure was approximately 5 mm to 10 mm. Within this depth, the chloride ion transferred into internal layer of the concrete under the action of the convection-diffusion coupling. If the depth was greater than this value, the transfer of the chloride ion was mainly under the influence of diffusion.

The one-dimensional equation of the transfer of chloride ion under the action of convection-diffusion is shown below [9, 25]:In the expression, value refers to the concentration of chlorine; is the diffusion coefficient of chloride ion; is the calculating depth of chloride ion. and refer to flow velocity of pore fluid under the action of pressure permeability and capillary, respectively.

An initial condition is Boundary conditions are In the expression, is the concentration of free chlorine ion on the surface of the concrete; is the initial concentration of free chloride ion for the concrete.

##### 2.1. The Diffusion Coefficient of Chloride Ion

In the transfer process of chloride ion, diffusion coefficient is very important [29, 30]. In the current research, diffusion coefficient is mainly considered in three situations.

*(**1) Constant*. The diffusion coefficient is invariant during the whole service period; the expression isIn the expression, is water-binder ratio.

*(**2) Time-Varying*. The diffusion coefficient of chloride ion changes over time. It is generally believed that the law of change can be expressed by an exponential function [31, 32]:In the expression, is the diffusion coefficient of time ; is the test age of diffusion coefficient of the concrete, which is usually evaluated as 28 d. is the diffusion coefficient of time , according to type (4); is the attenuation index of time.

*(**3) Tend to Be Stable after Some Years*. After some years, the hydration of concrete is basically completed, and the change of the internal microstructure probably does not occur any longer. At this point, the diffusion coefficient of chloride ion tends to a stable value [32].In the expression, is the time when diffusion coefficient tends to be stable.

##### 2.2. Convection Velocity

Under the condition of convection, permeation rate of pore fluid caused by pressure or capillary action decreases gradually with increasing depth and reaches 0 when it gets to the depth of the convection. In order to simplify the calculation, it is assumed that the permeation rate of the pore fluid linearly decreases over time. refers to the maximum rate, and the time spent before convection speed reaches zero is . In the expression, is the total depth of convection.

The depth of convection at time :

The convection velocity under the effect of space and time:where is the convection velocity of the* x* point at the* t* time.

In conclusion, (1) becomes

#### 3. Model Verification

##### 3.1. Verification with Existing Experimental Datum

Wang and Zhou [33] studied the transmission of chloride ion in concrete specimen in the seaside environment simulated by salt frog box. The size of the concrete specimen is 100 mm × 100 mm × 400 mm, and the load level was set to be 0, 0.3, and 0.5 of its strength. The transmission time was 35 d, 70 d, 120 d, and 180 d and the water cement ratio is set to be 0.38. was 0.20. For , with the consideration of its change over time, stood at 0.25% at the time of 35 d and 70 d and reached 0.32% at 120 d and 240 d. The paper of Park et al. [34] took mm/s. was 10 mm; was 0. When only diffusion and the convection-diffusion coupling were taken into account, the calculated results and experimental results are shown by Figure 1.