Advances in Materials Science and Engineering

Volume 2018 (2018), Article ID 7591576, 10 pages

https://doi.org/10.1155/2018/7591576

## Numerical Prediction of Chloride Penetration in Concrete Exposed to a Marine Environment at Tide

Department of Civil and Environmental Engineering, Hanyang University, Ansan 15588, Republic of Korea

Correspondence should be addressed to Ki Yong Ann; rk.ca.gnaynah@nnak

Received 21 December 2017; Accepted 29 March 2018; Published 24 April 2018

Academic Editor: Robert Cerný

Copyright © 2018 Sung In Hong and Ki Yong Ann. 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

Reinforced concrete structures under cyclic exposure to the corrosive environment such as the tidal zone as a part of marine structure entail the higher risk of steel corrosion. In this paper, chloride penetration in concrete exposed to the tidal zone was predicted using a combined moisture and chloride transport model. For the analysis of moisture transport, pore size distribution in concrete was determined from the experimental observation and used to determine the moisture permeability and degree of saturation. Then, the chloride profile through nonsaturated concrete cover was calculated by applying the moisture distribution along the penetration depth to the chloride convection and diffusion model. To assess sensitivity of the service life to the environment and concrete mix conditions, this study used three types of tide levels and water to cement ratios in the simulation. Under 10 years of tidal exposure condition, the minimum required cover depth at which the threshold chloride concentration reaches on the steel embedment increases only about 1.13 times as the tide level increases from the minimum to the highest while that for the ratio increases about 1.69 times.

#### 1. Introduction

The chloride-induced corrosion in RC structures especially exposed to marine environment has been regarded as a major problem in the aspect of structural safety. When a sufficient amount of chloride reaches on the steel surface in concrete, the passive film, maintained by high alkalinity of concrete pore solution, starts to dissolve and steel corrosion easily occurs [1]. After that, serial expansions of the corrosion products can cause concrete cracking from the location of steel embedment, thereby resulting in delineation of the concrete cover [2]. Thus, to assess the risk of chloride-induced corrosion and prevent the deterioration process during the life cycle of RC structures, a proper prediction model able to reflect the effects of material and environment actions on chloride ingress would be required.

Under the marine environment, the rate of chloride penetration in concrete largely depends on the exposure condition that changes with daily variation of the tide level [3]. Nevertheless, a number of studies for assessing the chloride ingress at the tidal zone with a single diffusion model have been carried out based on the assumption that the concrete pore network is fully saturated [3–6]. However, most of the concrete structures exposed to the tidal environment are in nonsaturated state, and the chloride transport is driven by both diffusion via concentration gradient through continuous pore water channel and convection via moisture movement through nonsaturated pores. In fact, as the exposure area becomes higher from the lowest tide level, chloride distribution in concrete becomes hard to be described with a single diffusion analysis since the moisture gradient in concrete simultaneously occurs during the repeated wet/dry cycles [7].

In the consideration of the transport mechanism in nonsaturated concrete, several prediction models have been developed [8–11]. Saetta et al. first suggested the S-shaped curve equation relating the chloride diffusivity with the moisture level to predict the chloride penetration under nonsaturated environment [8]. Based on this semiempirical expression of chloride diffusivity, the two-dimensional numerical model for predicting temperature, relative humidity, and chloride transport in concrete was developed by Martin-Pérez et al. [9]. Nielsen and Geiker proposed the moisture dependent chloride diffusivity with a composite theory of the cement matrix to assess the chloride diffusion in nonsaturated state [10]. Recently, Sleiman et al. used the S-shaped curve relation of chloride diffusivity and moisture level to assess the effect of types of moisture adsorption isotherms on the ionic penetration in concrete [11]. However, moisture level at given humidity level largely changes with the concrete pore size distribution which also determines the moisture diffusivity as functions of humidity level and mix condition [12] and thus could affect the rate of chloride penetration in nonsaturated concrete.

The main topic in this study is to evaluate the dependences of tide level and the water to cement ratio on the chloride penetration using the combined moisture and chloride transport model. To implement the numerical calculation of the nonlinear transport behavior in the tidal zone, the finite element method (FEM) was adopted in solving the partial derivative equations with time-dependent boundary conditions. Moisture transport under the wet/dry cycles was modelled based on the statistical permeability theory to relate the pore size distribution in concrete to the moisture permeability. Then, chloride penetration in nonsaturated concrete can be predicted by applying the calculated spatial values of moisture transport to the chloride transport model.

#### 2. Methodology

##### 2.1. Moisture Transport

To predict the chloride transport in nonsaturated concrete, moisture distribution through the concrete depth was determined, considering the liquid and vapour transport which can be expressed aswhere is the moisture content (kg/m^{3}), is the time, is the permeability of the liquid water (kg/m·s·Pa), is the capillary pressure (Pa), is the permeability of water vapour (kg/m·s·Pa), and is the water vapour pressure (Pa). Assuming the thermodynamic equilibrium condition in concrete, it is possible to relate the pressure terms in (1) to the relative humidity () such thatwhere is the saturation vapour pressure (Pa), is the density of water (kg/m^{3}), is the gas constant (J/kg·K), is the temperature (K), and is the water molecular weight (kg/mol). Thus, combining (1) and (2), moisture distribution in concrete in terms of relative humidity can be expressed aswhere is the moisture storage capacity (kg/m^{3}), denoting the slope of water vapour isotherms for adsorption and desorption.

As the humidity level increases, the liquid permeability () increases due to the increase in the water content in concrete, while the vapour permeability () decreases due to the decrease in the nonsaturated porosity. was determined based on the statistical permeability model [13], considering the probabilistic effect of the variation of pore sizes on the moisture flow in the porous cement matrix such thatwhere is the porosity, is the tortuosity determined using a semiempirical model suggested by Nakarai et al. [14], is the viscosity of liquid water (Pa·s), is the normalized pore size distribution, is the parameter of the Rayleigh–Ritz (R-R) density function, and is the critical radius below which the pores are fully saturated (m), which can be expressed aswhere is the thickness of water molecules on the pore wall (m) and is the capillary condensation radius (m). can be determined according to the BET model [15] such that

In the assumption of the cylindrical pore shape, can be determined by using Kelvin’s law such thatwhere is the constant dependent on the curvature of liquid-vapour interface [12, 15] and is the surface tension of water (N/m). For the simplicity of the analysis, change in during the moisture adsorption and desorption was not considered and assumed to be unity.

Before capillary condensation, adsorption of water molecules occurs through the nonsaturated pores, and the rate depends on the vapour permeability that can be described with the Knudsen diffusion model such thatwhere is the degree of saturation, is the mean free path of the water molecule (m), is the mean of pore radii over unsaturated pores (m) which was assume to be 2.5 m equal to one-half of the maximum pore size, and is the diffusion coefficient of water vapour in air (m^{2}/s), which was determined by taking into account the water vapour pressure and temperature differences [16] such thatwhere is the water vapour diffusivity at reference values of pressure () and temperature () (). In this study, the moisture content resulting from the vapour adsorption in nonsaturated pores was excluded due to its marginal influence on the chloride transport. Thus, the degree of saturation at wetting () was determined based on the pore size distribution such that

When vapour desorption proceeds, partial water contents remain through ink-bottle pores. By taking into account a probability of interconnection between larger pores and smaller at the given humidity level [13], the degree of saturation at drying () can be determined as

When sea water contacts with the concrete surface, it was assumed that water vapour adsorption proceeds into the concrete cover, and the degree of saturation () was calculated with (12). When water vapour desorption proceeds from the inner concrete depth to the environment, the degree of saturation was calculated with (13).

##### 2.2. Chloride Transport

Under the nonsaturated condition, chloride transport in concrete is driven by both diffusion via concentration gradient and convection via moisture flux. Considering the chloride binding during the combined ionic penetration, the mass balance equation for the chloride transport can be expressed aswhere is the bound chloride concentration in concrete (kg/m^{3}), is the free chloride concentration in pore solution (kg/m^{3}), is the effective chloride diffusion coefficient (m^{2}/s), and is the moisture diffusion coefficient (m^{2}/s) which accounts for the rate of combined liquid and vapour transport and can be obtained from (3) such that

The Langmuir isotherm was used to describe a nonlinear relationship between free and bound chlorides. The derivative formula of the relation indicates the chloride binding capacity [9], which can be expressed aswhere and are the binding parameters for the Langmuir isotherm.

##### 2.3. Boundary Conditions

To mimic a typical tidal environment, three types of exposure conditions to the concrete surface were considered as low, medium, and high tide levels, corresponding to 0.3, 0.5, and 0.7 days of daily drying time, respectively. Accordingly, daily wetting time for the chloride ingress decreases from 0.7 to 0.3 days with increasing the tide levels. To do this, moisture and chloride fluxes into or out of the concrete surface were simulated using the following boundary conditions [8]:where is the outward unit normal at the boundary, and are the mass transfer coefficients, respectively, for the relative humidity and chloride (m/s), and are the relative humidity and free chloride concentration at concrete surface, and are the relative humidity and free chloride concentration at environment, and is the environment factor, accounting for 1 during wetting and 0 during drying. Other values for the boundary condition are given in Table 1.