2.3.2. Vacuum-Saturated Treatment

According to a national standard [30], the vacuum-saturated treatment must be performed before the accelerated chloride penetration experiment in order to ensure chloride ions could penetrate into concrete steadily. Also, it is necessary before testing electrochemical properties of rebar to guarantee RC samples were conductive. The vacuum-saturated procedure consisted of conditioning RC samples into a vacuum desiccator and applying a vacuum pressure of 5 kPa for 3 h. Subsequently, the desiccator was filled with deionized water until all samples were immersed, and the pressure was maintained for another one hour. Finally, samples were continuously immersed for 18 h without vacuum pressure.

#### 2.3.3. Accelerated Chloride Penetration Experiment

In general, it will take a long time to observe the corrosion of rebar due to the slow corrosion process of chloride ions by immersing RC samples into chloride solution. However, the accelerated chloride penetration experiment used in this study showed a more effective way to accelerate the corrosion process of rebar affected by chloride ions, which could simulate the natural aggressive environment well. The experimental setup is displayed in Figure 3. Each specimen was placed between two acrylic cells defined as cathode cell and anode cell. The volume of each cell is 270 cm3. Cathode cell was filled with 3.5 wt % NaCl solution, and anode cell was filled with 0.3 mol/L NaOH solution. Two stainless steel-based plates as cathode electrode and anode electrode were placed into these two cells. The cracked surface of specimen was placed into the cathode cell, and the other side was placed into the anode cell. Then, these two cells were connected to a DC regulated power supply, and the applied voltage was 20.0 V. This designed accelerated chloride penetration system was electrified for 96 h.

**Figure 3.** Experimental setup for accelerated chloride penetration.

2.3.4. Corrosion Density Test for Bar Based on Electrochemical Measurements

Nowadays, electrochemical measurements including TPP, LP and EIS measurements are popularly used in the studies of steel corrosion under different conditions. These three measurements were employed in this study to evaluate the electrochemical properties of rebar under an accelerated chloride penetration. Corrosion current density (*icorr*) is used as the index to evaluate the corrosion behavior of rebar.

The electrochemical measurements were carried out by CS350H electrochemical workstation in this study based on the three-electrode system shown in Figure 4. In this system, the rebar embedded in concrete was treated as the working electrode (WE) with a polarization area of 21.98 cm2, a saturated calomel electrode (SCE) with potassium chloride salt bridge placed in a Luggin capillary was used as the referenced electrode (RE) and a stainless steel-based plate with 2 mm × 100 mm × 150 mm was used as the counter electrode (CE).

Corrosion density is used to evaluate the corrosion behavior of rebar, and it can be obtained from TPP measurement directly or calculated by Stern-Geary equation

$$i\_{corr} = \frac{B}{R\_p} \tag{1}$$

where *icorr* is the corrosion density (μA/cm2); *B* is the Stern-Geary coefficient (mV/Decade); *Rp* is polarization resistance (Ω·cm2). The value of *B* can be calculated from TPP measurement or estimated to fall within the range from 25 mV to 52 mV. Song [33] demonstrated the estimated range value of *B* is applicable only in a uniform corrosion system at its corrosion potential, whereas the RC structure may be subjected to a non-uniform corrosion. The typical value (25 mV~52 mV) of *B* is not acceptable in a RC corrosion system. Therefore, the value of *B* should be calculated from TPP curves more accurately. Meanwhile, *Rp* can be obtained from LP and EIS measurements. The details of these three measurements are as follows.

TPP measurement is an electrochemical test method to characterize corrosion properties of metal materials based on the three-electrode system. TPP curves can be obtained by monitoring the potential used steady fixed levels of current at specific potential. In TPP curves, the current density *I* (A/cm2) and polarization potential *E* (V) under potentiodynamic polarization of rebar always conform to the Butler–Volmer equation:

$$I = i\_{corr} \left\{ \exp\left[\frac{2.303(E - E\_{corr})}{b\_d}\right] - \exp\left[\frac{2.303(E\_{corr} - E)}{b\_c}\right] \right\} \tag{2}$$

where *Ecorr* is the corrosion potential (V vs. SCE), respectively. *ba* and *bc* are the anodic Tafel slope and cathodic Tafel slope, respectively (mV/Decade). Values of these electrochemical parameters can be obtained by a curve-fitting approach named Tafel extrapolation method. Schematic illustration parameters in TPP curve are shown in Figure 5.

The Stern–Geary coefficient *B* related to *ba* and *bc* can be calculated by

$$B = \frac{b\_d \times b\_c}{2.303 \times (b\_d + b\_c)}\tag{3}$$

After obtaining a stable open circuit potential (OCP), TPP measurement could be carried out from −250 mV to 250 mV vs. OCP, the scanning rate of which is 1 mV/s.

Besides, LP measurement is another electrochemical method to obtain resistances of metal materials accurately. Polarization curves in LP measurement can be obtained as the same method in TPP measurement. As shown in Figure 6, the value of *Rp* is defined as the slope of potential to current density, can be obtained as follows:

$$R\_p = \left. \frac{\Delta E}{\Delta I} \right|\_{I \to 0}^{E \to E\_{\text{cvr}}} \tag{4}$$

**Figure 4.** Experimental setup for electrochemical measurements (a three-electrode system).

**Figure 5.** Schematic illustration of the Tafel potentiodynamic polarization (TPP) curve with Tafel electrode slopes.

**Figure 6.** Schematic illustration of polarization resistance.

In this study, LP measurements were carried out from −10 mV to 10 mV vs. OCP with the scanning rate of 0.167 mV/s.

In addition, EIS measurement based on alternating currents (AC) used to analyze corrosion mechanisms of steel has been well documented for many years [34]. Applied AC amplitude signal was equal to 10 mV over the frequency range from 0.01 Hz to 100,000 Hz. To better understand the electrochemical phenomena, an equivalent circuit was used to simulate the electrochemical behavior of rebar. The equivalent circuit is illustrated in Figure 7, which shows the solution resistance (*Rp*1), concrete resistance (*Rp*2), polarization resistance of rebar (*Rp*3), external concrete capacitance (*CPE*1) and double layer capacitance on the surface of rebar (*CPE*2).

**Figure 7.** Equivalent circuit for reinforced concrete (RC) samples.

The immittance *Z* (Ω·cm2) of this equivalent circuit is given by

$$Z = R\_{p1} + \frac{1}{T\_1(j\omega)^{p\_1} + \frac{1}{R\_{p2} + \frac{1}{T\_2(j\omega)^{P\_2} + \frac{1}{R\_{p3}}}}} \tag{5}$$

in which,

$$T\_n(j\omega)^{p\_n} = T\_n \omega^{p\_n} \left[ \cos(\frac{p\_n \pi}{2}) + j \sin(\frac{p\_n \pi}{2}) \right] (n = 1, 2) \tag{6}$$

where *Tn* and *pn* are parameters of CPE (μF·cm2); ω is the frequency of applied AC (Hz); *j* = √ −1. The obtained impedance data could be analyzed by *Z* view program to fit with the immittance equation of this equivalent circuit.

The voltage applied in EIS measurements is much smaller than those of LP and TPP measurements, which means EIS measurements display a smaller disturbance and better reproducibility of electrochemical systems than the others [35]. Therefore, EIS measurements can be performed continuously, while the others cannot because the error in a continuous test procedure can be very large. The disturbances of these three measurements are ranked from small to large: EIS measurements, LP measurements, TPP measurements. Therefore, the test sequence should be the same as the disturbance. Besides, EIS, LP and TPP measurements should be conducted only once on each specimen before an accelerated chloride penetration experiment. Because the electrochemical property of each rebar in concrete is very stable after 28-day curing, and the test results are treated as unique initial values to evaluate the differences of corrosion behavior of rebar. Furthermore, EIS, LP and TPP measurements should be conducted three times, one time and one time, respectively, after accelerated chloride penetration experiments in order to obtain more statistical random sampling test results and quantitatively analyze the effects of crack on electrochemical properties of rebar.

## *2.4. Statistical Analysis Methods*

After obtaining *icorr* of rebar, One-way analysis of variance (ANOVA) combined with Turkey's honest significant difference (Turkey's HSD) test was performed to analyze the effect of crack on rebar corrosion and determine the most significant factor that influences durability of RC material. One-way ANOVA was used in this study to determine whether crack width, number or spacing is the most significant factor, and Turkey's HSD test was performed for further judging the accuracy of the One-way ANOVA results. The details of these two methods are as follows:
