Advances in Materials Science and Engineering

Volume 2016, Article ID 1085934, 10 pages

http://dx.doi.org/10.1155/2016/1085934

## Chloride Transport in Undersea Concrete Tunnel

^{1}Department of Civil Engineering, Zhejiang University City College, Hangzhou, Zhejiang 310015, China^{2}Architecture Engineering College, Jinhua Polytechnic, Jinhua, Zhejiang 321017, China

Received 25 November 2015; Accepted 5 May 2016

Academic Editor: Seung-Jun Kwon

Copyright © 2016 Yuanzhu Zhang 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

Based on water penetration in unsaturated concrete of underwater tunnel, a diffusion-advection theoretical model of chloride in undersea concrete tunnel was proposed. The basic parameters including porosity, saturated hydraulic conductivity, chloride diffusion coefficient, initial water saturation, and moisture retention function of concrete specimens with two water-binder ratios were determined through lab-scale experiments. The variation of chloride concentration with pressuring time, location, solution concentration, initial saturation, hydraulic pressure, and water-binder ratio was investigated through chloride transport tests under external water pressure. In addition, the change and distribution of chloride concentration of isothermal horizontal flow were numerically analyzed using TOUGH2 software. The results show that chloride transport in unsaturated concrete under external water pressure is a combined effect of diffusion and advection instead of diffusion. Chloride concentration increased with increasing solution concentration for diffusion and increased with an increase in water pressure and a decrease in initial saturation for advection. The dominant driving force converted with time and saturation. When predicting the service life of undersea concrete tunnel, it is suggested that advection is taken into consideration; otherwise the durability tends to be unsafe.

#### 1. Introduction

With the urgent need for water transportation, subsea concrete tunnels gradually became the priority mode of crossing sea during the past few years in China. Xiamen Xiang’an tunnel is the first undersea tunnel in Chinese mainland in 2011; after that Qingdao Jiaozhou bay subsea tunnel and Hong Kong-Zhuhai-Macao subsea tunnel are successively constructed. However, booming developments of subsea tunnels have to face the challenge to meet the requirement of service life over 100 years because of the erosion of pressure seawater on tunnels.

For a long time, underwater concrete structures withstanding high hydrostatic pressure are usually viewed as fully saturated concrete [1]. Based on the hypothesis, most researchers only considered diffusion of chloride ions and used Fick’s diffusion laws to predict the service life of undersea tunnels [2–4]. However cement-based materials difficultly reach full saturation in fact. Powers and Brownyand [5] first proposed that cementitious materials were unsaturated through 220 d immersion tests of plain cement prisms. Afterwards, further studies on the relative humidity in concrete successively verified the unsaturated characteristics of concrete through laboratory experiments [6–8]. Recently, concrete coring tests of underwater projects in Denmark and Sweden also showed that most regions of concrete core samples were still unsaturated except near-surface zone; even the structures have served for decades [9]. Thus, chloride transport in undersea concrete structures especially for the low permeability structures made of high performance concrete should be treated as flow in unsaturated porous materials; that is, advection of chloride due to the motion of pore solution in unsaturated concrete should also be taken into account besides diffusion.

Most of existing studies about chloride diffusion-advection in concrete were focused on superstructures, in which governing equations of diffusion-advection models under drying, wetting, or repeated drying-wetting environments were established by taking relative humidity or saturation as basic variable and the influences of different factors such as time and solution concentration were discussed without considering hydraulic pressure [10–13]. However, underwater tunnels withstand a large pressure difference between inside wall and outside wall. Jin et al. [14] found that external water pressure had a significant influence on chloride transport through laboratory experiments and Chen’s experiments also proved the effect of water pressure on chloride motion in concrete [15], while they still took the fully saturated concrete assumptions to analyze the transport process. Zhang et al. confirmed the combined affection of capillary suction and water pressure on the motion of pore solution of unsaturated concrete based on laboratory experiments and numerical simulations [16]. As a result, we think that the advection of chloride ions with the movement of pore solution in undersea tunnel is correspondingly driven by both the effects.

Based on water penetration research in concrete of underwater tunnel [16], a diffusion-advection theoretical model of chloride in undersea concrete tunnel was proposed, and the variation of chloride concentration with pressuring time, location, solution concentration, initial saturation, hydraulic pressure, and water-binder ratio was investigated through laboratory tests under external water pressure. In addition, the distribution and change of chloride concentration of isothermal horizontal flow were numerically analyzed using TOUGH2 (Transport of Unsaturated Groundwater and Heat) software and different transport models were compared. The research is helpful to improvement of the service life prediction model of undersea concrete tunnel.

#### 2. Theoretical Basis

##### 2.1. Chloride Transport by Diffusion in Concrete

Diffusion results in chloride ions transport from the regions of high ions concentration to the regions of lower ions concentration.

Under steady-state condition, diffusion flux of free chloride ions is usually described by Fick’s 1st diffusion law as follows:where is the diffusion flux of free chloride ions, kg/(m^{2}s); is the chloride diffusion coefficient of concrete, m^{2}/s; is the nabla operator; is the volume concentration of free chloride dissolved in pore solution, kg/m^{3}; the negative sign in (1) indicates that diffusion occurs with the concentration reduction.

If chloride concentration changes with time (i.e., nonsteady diffusion condition), chloride movement can be described by Fick’s 2nd diffusion law as where is the diffusion time, s.

However concrete is not a homogeneous isotropic material to satisfy the hypothesis of Fick’s diffusion laws; hence the effective diffusion coefficient is used to replace in (1). Many researchers have devoted their efforts to studying of concrete. The studies generally believed that depended not only on the test method, but also on the factors such as service time, saturated degree, and temperature of concrete. Atkinson and Nickerson [17] proposed a model as follows:where is the chloride diffusion coefficient in saturated concrete, m^{2}/s; is the porosity; is a pore structure parameter which can be obtained from Millington-Quirk model [18]:where is the saturated degree.

##### 2.2. Chloride Transport by Advection in Concrete

Advection means ions transport due to the carrier fluid’s bulk motion. The advection flux can be expressed aswhere is the advection flux of free chloride ions, kg/(m^{2}s); is the fluid velocity, m/s.

The fluid movement in capillary pores of saturated concrete is driven by hydraulic head difference (i.e., water pressure difference), which can be described by Darcy’s law as follows:where is the saturated hydraulic conductivity, m/s; is the hydraulic head, m; is the water density, kg/m^{3}; is the acceleration of gravity, m/s^{2}; is the hydraulic pressure of the flow path, Pa.

Based on Darcy’s law, Richards proposed motion equation of water in unsaturated soils in 1931, namely, Richards’ equation:where is the water content; is the unsaturated hydraulic conductivity, m/s; is the total driving potential, Pa; is the relative hydraulic conductivity, and it ranges between 0 (dry state) and 1 (saturated state), which is commonly represented by Van Genuchten-Mualem model [19–21]:where is the residual water content; is the saturated water content; and is an empirical material parameter which can be fitted by experimental data.

Because the temperature of underwater is generally constant, isothermal transport is considered for the advection model; thus the total driving potential includes matric potential , pressure potential , and gravity potential .

Matric potential can be viewed as capillary suction of porous materials. It is negative and generally described by Van Genuchten-Mualem model [19–21] as follows:where is an empirical factor fitted by experimental data.

Pressure potential is caused by the difference of pressure in pressure field. For undersea concrete tunnel, the outer surface contacts hydraulic water while the inner surface contacts atmosphere. Considering the connectivity of capillary pores, it is assumed that the air in unsaturated pores directly connects with external atmosphere; thus the pore solution in unsaturated zone is subjected to atmospheric pressure without additional hydrostatic pressure. However, the pore solution in saturated zone directly connects with external hydraulic water, so it is subjected to the additional hydrostatic pressure which depends on the surface pressure and location [22]. Therefore, pressure potential can be calculated by where is the external water pressure on the surface, Pa; erfc is the complementary error function; is the distance from the exposed surface, m; is the bulk modulus, Pa.

Gravity potential is equal to the work that per unit volume of water is moved from its location to a fixed reference location, which can be described aswhere is the distance from the fixed reference location, m.

##### 2.3. Chloride Transport by Diffusion-Advection in Concrete of Undersea Tunnel

With continuous seawater ingress into undersea tunnel, initial unsaturated zone near the inlet surface gradually reaches full saturation. In saturated zone, , water motion is mostly controlled by pressure potential, while in unsaturated zone, , water motion is mostly controlled by matric potential. So chloride transport in undersea tunnel is combined driven by diffusion and advection, which are driven by the difference of concentration and driving potentials converted with saturation, respectively. As a matter of fact, a part of chloride ions will combine to binding chloride by chemical reaction and physical bond. After the ion-combination reaction, residual free chloride ions transport in concrete by diffusion and advection which can be expressed as follows: where is the total flux of free chloride ions, kg/(m^{2}s).

Ogata and Banks [23] have proposed an analytic solution for the diffusion-advection function under saturated state, but under unsaturated state the complicated partial differential equation (13) has to be solved by finite difference method or finite element method.

#### 3. Experiment Research

Concrete specimens with two different water-binder ratios () of 0.36 and 0.4 were prepared in our experiments (Table 1).