Based on water penetration in unsaturated concrete of underwater tunnel, a diffusionadvection 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 waterbinder ratios were determined through labscale experiments. The variation of chloride concentration with pressuring time, location, solution concentration, initial saturation, hydraulic pressure, and waterbinder 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.
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 KongZhuhaiMacao 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 [
Most of existing studies about chloride diffusionadvection in concrete were focused on superstructures, in which governing equations of diffusionadvection models under drying, wetting, or repeated dryingwetting environments were established by taking relative humidity
Based on water penetration research in concrete of underwater tunnel [
Diffusion results in chloride ions transport from the regions of high ions concentration to the regions of lower ions concentration.
Under steadystate condition, diffusion flux of free chloride ions is usually described by Fick’s 1st diffusion law as follows:
If chloride concentration changes with time (i.e., nonsteady diffusion condition), chloride movement can be described by Fick’s 2nd diffusion law as
However concrete is not a homogeneous isotropic material to satisfy the hypothesis of Fick’s diffusion laws; hence the effective diffusion coefficient
Advection means ions transport due to the carrier fluid’s bulk motion. The advection flux can be expressed as
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:
Based on Darcy’s law, Richards proposed motion equation of water in unsaturated soils in 1931, namely, Richards’ equation:
Because the temperature of underwater is generally constant, isothermal transport is considered for the advection model; thus the total driving potential includes matric potential
Matric potential
Pressure potential
Gravity potential
With continuous seawater ingress into undersea tunnel, initial unsaturated zone near the inlet surface gradually reaches full saturation. In saturated zone,
Ogata and Banks [
Concrete specimens with two different waterbinder ratios (
Mix proportion of concrete.
Specimens number 

Mix proportion/(kg/m^{3})  

Cement  Fly ash  Water  Sand  Gravel  
BI  0.36  419  46  168  532  1 241 
BII  0.40  379  42  168  542  1 266 
The cube compressive strength (
Strength, porosity, saturated hydraulic conductivity, and chloride diffusion coefficient of the specimens.
Number 





BI  45.3  8.6  1.8 × 10^{−11}  4.0 × 10^{−12} 
BII  44.7  9  2.2 × 10^{−11}  4.4 × 10^{−12} 
In order to analyze the effect of water saturation on chloride transport in concrete, three initial states were designed: natural state and being oven dried at 105°C for 1 h and 8 h. First, the mass of the concrete specimen (the specimen information will be introduced in Section
Initial saturation of the specimens.
Number 

Condition 


BI  0.36  Natural state  0.715 
BII1  0.40  Natural state  0.718 
BII2  0.40  Oven dried for 1 h  0.441 
BII3  0.40  Oven dried for 8 h  0.312 
From Table
Cubic specimens with length of 100 mm were cast from the concrete mixes of Table
Humidity control for isotherm adsorption test/%.
Condition  Saturated salt solutions  Water  

LiCl  MgCl_{2}  NaBr  NaCl  KCl  
Theoretic  11.3  33.1  59.1  75.5  85.1  100 
Measured  14.7  39.3  55.7  70.5  78.4  98 
Regression parameters (
Number 





BI  0.36  9.662  0.519  0.991 
BII  0.40  12.576  0.554  0.988 
Isothermal adsorption curves for the concrete mixtures.
Moisture characteristic curves for the concrete mixtures.
The device shown in Figure
Chloride penetration tester.
The working conditions are shown in Table
Place a 1 cm thickness silicone gasket with
Open the valve of nitrogen bottle and adjust pressure to the designated value.
When the pressure reading is stable, then open the valve of the tank to supply pressure water which penetrates into concrete through the preformed hole of specimens. Until the scheduled pressuring time is reached, turn off the valve of the tank.
Take the specimen out from the chamber and split it along the diameter using a Universal Testing Machine (Figure
Working conditions of chloride transport tests.
Working conditions  Specimens number  Pressure (MPa) 

Pressuring time (h) 

1  BII1  1.5  3%  72 
2  BII1  1.5  15%  168 
3  BII1  1.5  15%  72 
4  BII2  1.5  15%  72 
5  BII3  1.5  15%  72 
6  BI  1  15%  72 
7  BI  1.5  15%  72 
8  BI  2  15%  72 
Solution transport diagram.
From Figure
Chloride concentration profile under different pressuring time and solution concentration.
Chloride concentration profile under different initial saturation.
Chloride concentration profile under different hydraulic pressure.
From the chloride concentration profiles (Figures
Comparing curve
We take working conditions 6–8, for example, to discuss the process of chloride transport, which can be divided into three stages.
Thus, diffusionadvection theoretical model of chloride can explain the experimental results of chloride concentration increases with water pressure in Figure
As for specimens with different initial saturation
As for specimens with different solution concentration
The EOS9 module and EWASG module of TOUGH2 software were used to run the numerical simulation, which could simulate water and chloride ions transport, respectively [
The numerical simulation was carried out on 200 mm diameter, 150 mm height cylinder model with
Schematic diagram for half of the model.
It is noteworthy that the unit of chloride concentration is volume concentration of pore liquid (kg/m^{3}) in theoretical analysis and numerical simulation, while it is expressed as mass percent of concrete powder (%) in RCT test. Thus, we should change the unit of chloride concentration from volume concentration into mass percent concentration if quantitatively comparing the results of simulations with those of experiments. The unit conversion formula can be written as
From (
From Figure
Chloride concentration simulation under different solution concentration.
The effect of initial saturation on chloride transport was studied by running examples where the initial saturation varied with 0.312, 0.718, and 1 under
Chloride concentration simulation under different initial saturation.
If the capillary suction is neglected (set
To study the influence of water pressure on chloride penetration, only water pressure was varied while maintaining the initial saturation as 0.715 and initial surface chloride concentration as 15% with sample block BI. The results of numerical analysis are shown in Figure
Chloride concentration simulation under different hydraulic pressure.
If water pressure is neglected (set
Theoretical models of chloride diffusionadvection in unsaturated concrete of undersea tunnel were established. The variations of chloride concentration with pressuring time, location, solution concentration, initial saturation, hydraulic pressure, and waterbinder ratio were investigated through penetration tests under external water pressure. In addition, the change and distribution of chloride concentration were numerically analyzed using TOUGH2 software. The results show the following.
Chloride transport under external water pressure in unsaturated concrete is a combined effect of diffusion and advection, where diffusion is driven by the difference of concentration and advection is driven by capillary suction and hydraulic pressure. Hence, for the subsea concrete tunnels which withstand hydraulic pressure on outside wall and atmospheric pressure on inside wall, chloride transport is affected by diffusion, capillary suction, and external pressure instead of diffusion.
Chloride concentration in concrete declined with depth and increased with time. The higher the difference of chloride concentration is, the higher the chloride concentration is. Meanwhile it shows that the higher the hydraulic pressure and the lower the initial saturation of concrete, the higher the chloride concentration. The change of chloride concentration slowed down with time because the concentration difference declined for the concentration growth and the smaller driving potential of pressure replaced the larger driving potential of capillary suction with the saturation growth.
Service life of undersea concrete tunnel will be overpredicted if only chloride diffusion in tunnel based on the full saturated concrete hypothesis is considered. Because advection plays an important role in chloride transport of undersea tunnel, the effect of capillary suction and water pressure on the durability design of subsea tunnel should be taken into consideration; otherwise it tends to be unsafe.
The authors declare that they have no competing interests.
This work was supported by the National Natural Science Foundation of China (no. 51208463), Natural Science Foundation of Zhejiang Province of China (no. LY12E08012), and Jinhua Technology Bureau Research (20153050).