Accelerated Laboratory Assessment of Discrete Sacrificial Anodes for Rehabilitation of Salt-Contaminated Reinforced Concrete

Three types of commercial DSAs were investigated, denoted S, B, and X, respectively, and each contained a sacrificial anode encased in a repair patch. The size and chemical composition of the three types of DSAs are given in Fig. 2 and Table 1. No. 3 rebar (diameter 9.525 mm), steel wire, fast-curing epoxy, and acrylic pipe were purchased from Home Depot (Lewiston, Idaho). Due to the good chemical stability, graphite bar (from Fanty_store, Shenzhen, Guangdong, China) was selected as the reference electrode. An ASTM specification C150 (ASTM 2016) Type $\mathrm{I}/\mathrm{II}$ portland cement was used in this study as received. The chemical composition of cement was reported by Du et al. (2017). Analytical grade NaCl was purchased from Sigma-Aldrich (St. Louis, Missouri) and used without further purification. The fine aggregate used was multipurpose siliceous sand; before proportioning and admixing, the fine aggregate was prewetted and taken to a saturated surface dry (SSD) condition. A high-range water-reducing admixture (7920) from BASF (San Diego, California) was used to achieve a reasonable workability of the mortar mixture, at a dosage of 0.4% by mass of cement.

The top rebar was cut into three parts to the length of 12.2 cm (4.8 in.), 12.2 cm (4.8 in.), and 36.6 cm (14.4 in.) for Sections 1, 2, and 3, respectively. Steel wires were soldered to one end of the three parts, and then the three parts were glued with epoxy and fixed in a short length of acrylic pipe (Fig. 1). After the preparation, the top rebar was mechanically connected but electrically disconnected. The top rebar was placed in the middle of the width of the specimen, and the distance between the center of the top rebar and the top surface of the specimen was $9\mathrm{cm}$. The bottom rebar also was placed in the middle of the width of the specimen, and the distance between the center of the bottom rebar and the bottom surface of the specimen was $3\mathrm{cm}$. The graphite electrode was placed close to the top rebar (approximately $0.5\mathrm{cm}$).

To simulate aged concrete of bridge decks, the specimens consisted of two layers: a chloride-contaminated layer and a chloride-free layer. Two typical levels of chloride contamination, 1.0% and 2.0% by mass of cement, were simulated. The water-to-cement mass ratio was 0.45 and the sand-to-cement mass ratio was 3.0. Triplicate specimens were prepared for each type of DSA with each level of chloride contamination. The specimens were named with a letter and two numbers, denoting type of DSA, chloride contamination level (e.g., 1 denotes 1% chloride contamination), and specimen number, respectively (Table 2).

The SSD sand first was mixed with cement in a $25\text{-}\mathrm{L}$ mixer for 60 s, then water was added and mixed for 120 s. Afterward, the water-reducing admixture was added into the mortar mixture and mixed continuously for about 5 min. The fresh chloride free mixture then was cast into the mold, which already had the rebars, graphite electrode, and DSA embedded, and was carefully compacted to minimize the amount of entrapped air. The 8-cm-thick chloride-free layer was cured for 1 h, and then the fresh chloride contaminated mixture was prepared by following the same steps (except using water with a given amount of dissolved NaCl) and cast into the mold and carefully compacted. All the specimens were demolded after being cured at room temperature (RT) and relative humidity (RH) of $20\%\pm 2\%$ for $24\mathrm{h}$. After demolding, all the mortar specimens were cured under the same conditions for another 27 days before measurement. To enable ponding of aqueous solutions on the top surface, silicone was sprayed along the four sides of the top surface.

All specimens were tested under the same conditions. The period of a wet–dry cycle was 2 weeks (1 week for the wet cycle and 1 week for the dry cycle). About $100\mathrm{mL}$ tap water was added on the top surface of the specimens every weekday during the wet cycle of the first 12 weeks. After that, to accelerate the initiation of corrosion of the rebar, $100\mathrm{mL}$ 23% by weight NaCl solution was used instead of tap water every Monday of the wet cycle. The $24\text{-}\mathrm{h}$ freeze–thaw exposure of specimens was conducted in accordance with ASTM C666 (ASTM 2015b) after every six wet–dry cycles. The EIS measurement was carried out before each freeze–thaw exposure.

For morphology and elemental analysis, cross-sectional samples were cut from the representative DSAs after service and from the corresponding new DSAs before service. Three strips of cross-sectional samples representing the changes in microstructural properties were cut from the cement mortar specimens incorporating three different representative DSAs. After being coated with carbon powder and vacuumed, the sliced samples were subjected to scanning electron microscopy (SEM) to examine the morphology at the microscopic level. The beam conditions used were as follows: $15\mathrm{kV}$ accelerating voltage, 50 nA beam current, and focused beam diameter. Energy-dispersive X-ray spectroscopy (EDX) semiquantified the percentages of different elements of specific sections by picking up different spots on the samples.

To further confirm the phase composition of corrosion products of DSAs and find the difference between the DSAs before and after service, X-ray diffraction analysis (XRD) was conducted on the slice samples of DSAs. The XRD test was performed on a Siemens (Munich, Germany) D5000 diffractometer using Cu $\mathrm{K}\alpha$ radiation in the $2\theta$ region between 2° and 90° with a scanning rate of $0.05°/\min$.

As a reference electrode, the graphite embedded in the mortar specimen should have a stable electrode potential, which was partially validated in this work. $\mathrm{Ag}/\mathrm{AgCl}$ saturated KCl aqueous electrode ($\mathrm{Ag}/\mathrm{AgCl}$) and saturated calomel electrode (SCE) are two commonly used reference electrodes in concrete (Duffó et al. 2009), which have a potential of $+197$ and $+241\mathrm{mV}$ with respect to a standard hydrogen electrode, respectively. However, because their long-term stability could be significantly compromised by extreme service conditions, and their costs are high, an alternative reference electrode should be developed for concrete (or mortar). Muralidharan et al. (2006) investigated the feasibility of using graphite as a reference electrode in cement mortar with a chloride contamination level of 0% and 3% by weight of cement. All the mortar specimens were placed in a yard for testing. They found that the potential evolution of embedded graphite electrode versus SCE was about $75\mathrm{mV}$ for 12 months, which was limited and acceptable. Similarly, the present study also investigated the potential of embedded graphite electrode against $\mathrm{Ag}/\mathrm{AgCl}$.

The potential evolution of most of the graphite electrodes embedded in mortar specimens was about $100\mathrm{mV}$, which was acceptable and consistent with the results of Muralidharan et al. (2006) (Fig. 3). However, the potential evolution of Graphite electrode S1-1 had two abnormal values (about $-700\mathrm{mV}$) around the 250th day, and the fluctuation of the potential evolution of Graphite electrodes B2-3 and X2-1 reached almost $200\mathrm{mV}$. Moreover, the potential evolution of Graphite electrodes $\mathrm{B}2-2,\mathrm{X}1-3$, and X2-2 suddenly became unstable after about 400 days, 200 days, and 250 days, respectively. Then the difference of the potentials of corresponding graphite reference electrodes between wet–dry cycles could be as large as $250\mathrm{mV}$. The possible factor that contributed to this phenomenon is that a graphite electrode is sensitive to the environmental changes in concrete, such as the fluctuations of moisture level (Muralidharan et al. 2006). Therefore, it is viable to use a graphite electrode as an embedded reference electrode to monitor the half-cell potential of reinforcements in concrete. However, periodical calibration using an external reference electrode (e.g., $\mathrm{Ag}/\mathrm{AgCl}$) is necessary.

All the electrical parameters were measured versus the embedded graphite electrode. However, to make the results more comprehensible, all the parameters were reported against $\mathrm{Ag}/\mathrm{AgCl}$.

Half-cell potential is one of the key parameters that provides information regarding the state of reinforcement corrosion (Ahmad 2003). It is used as a thermodynamic parameter for assessing whether or not the corrosion of reinforcement is likely to occur. According to ASTM C876 (ASTM 2015a), the probability of active corrosion of reinforcement exceeds 90% when the half-cell potential of the rebar against $\mathrm{Ag}/\mathrm{AgCl}$ drops below $-233\mathrm{mV}$.

The half-cell potential of Section 1 of the top rebars in all specimens decreased to an extremum value of about $-300\mathrm{mV}$ in the first 50 days, and then increased to a level above $-233\mathrm{mV}$ and kept fluctuating, and after a certain amount of time ($212–419\mathrm{days}$) dropped below $-233\mathrm{mV}$ again (Fig. 4). Due to the chloride contamination in the top portion, the top rebar suffered from severe corrosion during the first 50 days, and the effect of passivation seemed to be counteracted, which corresponds to the decreasing process of half-cell potential of the top rebar. Then the passivation of the top rebar dominated, which protected the top rebar from corrosion and hence increased the half-cell potential. Afterward, the half-cell potentials decreased during the wet cycle and increased during the dry cycle. This finding was consistent with that of Angst et al. (2011), because the wet–dry cycle was necessary for depassivation and the rebar had a tendency to repassivate without further chloride ingress.

The half-cell potentials of most specimens decreased one or two wet–dry cycles after every freeze–thaw action. The freeze–thaw actions generated a network of well distributed and uniform cracks, which could increase both the initial sorptivity and total water absorption and promote the transport of chloride ions (Yang et al. 2006). Therefore, the depassivation of the top rebars was facilitated and the half-cell potentials decreased. In addition, the amplitudes of the fluctuations of the half-cell potentials of specimens with a chloride contamination level of 2% by weight were larger than those of specimens with a chloride contamination level of 1% by weight. This was due mainly to the bound chloride ions, because the wet–dry cycles resulted in the lowest value of diffusion coefficient and surface chloride content (Song et al. 2008). The higher chloride contamination level resulted in a larger amount of bound chloride (Yuan et al. 2009), which increased the reservoir of chloride ions that were locally available at the steel–concrete interface (Glass and Buenfeld 1997, 2000).

Compared with previous studies (Angst et al. 2011; Bouteiller et al. 2012), the trends of half-cell potential of the embedded rebars before the initiation of corrosion were similar, increasing during the first $50–100\mathrm{days}$ and then becoming stable until the initiation of corrosion. However, Bouteiller et al. (2012) found that the half-cell potential of the rebars embedded in the concrete specimens with a water-to-cement ratio of 0.45 kept fluctuating between $-100$ and $-300\mathrm{mV}$ (against SCE) for over 600 days, whereas Angst et al. (2011) found that some rebars embedded in the concrete specimens with a water-to-cement ratio of 0.40 repassivated after a sudden decrease of half-cell potential on the 126th day. The reasons for these phenomena were that the specimens were chloride free, which made the pH value well sustained and facilitated the spontaneous repassivation (Glass and Buenfeld 2000), and that the chloride concentration of the solution used during the wet cycle was too low, which made the available chloride content at the interface between the rebar and concrete matrix much lower than the critical chloride threshold (Alonso et al. 2000; Glass and Buenfeld 1997).

When the half-cell potential of top rebar dropped below $-233\mathrm{mV}$ again, it implies that the passive film was compromised and localized corrosion reinitiated. However, half-cell potential alone is not sufficient to confirm the corrosion state of rebar because it can be influenced by a number of factors, including polarization by limited diffusion of oxygen, concrete porosity, and the presence of highly resistive layers (Song and Saraswathy 2007).

To confirm the state of reinforcement corrosion, the value of corrosion current density ($i_{\mathrm{corr}}$) is a better indicator. It is a kinetic parameter that represents an overall estimate of the rate of corrosion attack of reinforcement (Ahmad 2003). The rebar is considered in a passive state when $i_{\mathrm{corr}}$ is smaller than $0.1\mathrm{\mu A}/{\mathrm{cm}}^2$, whereas the rebar is in an active state when $i_{\mathrm{corr}}$ is larger than $1\mathrm{\mu A}/{\mathrm{cm}}^2$ (Ahmad 2003). The rebar is in metastable state if $i_{\mathrm{corr}}$ is between 0.1 and $1\mathrm{\mu A}/{\mathrm{cm}}^2$. The corrosion current densities obtained from electrochemical measurements are listed in Table 3. The values of corrosion current density were used to confirm that the top rebars were in a metastable state, and the sacrificial anodes were subsequently connected to the top rebar to provide cathodic protection. Based on the half-cell potential evolution and the change of corrosion current density, the time-to-corrosion ($T_i$) was estimated (Table 4).

Section 1 of the top rebar of each specimen reached the metastable state ($0.1\mathrm{\mu A}/{\mathrm{cm}}^2<i_{\mathrm{corr}}<1\mathrm{\mu A}/{\mathrm{cm}}^2$) after different numbers of wet–dry cycles based on the aforementioned criterion. Section 1 of B1-1 reached the metastable state after only 12 wet–dry cycles, and 10 other specimens reached the metastable state after 18 wet–dry cycles, including 4 specimens that had already initiated corrosion. Section 1 of the top rebar of S2-3 reached the metastable state after 24 wet–dry cycles, whereas Section 1 of the top rebars of B1-3, B2-1, B2-3, and X2-2 reached the metastable state after 30 wet–dry cycles. Moreover, the results of X2-1 and X2-3 showed that Section 1 of their top rebars was still in passive state.

Before the top rebars reached the metastable state, the corrosion current density of most top rebars fluctuated below $0.1\mathrm{\mu A}/{\mathrm{cm}}^2$, which was consistent with the half-cell potential evolution. The top rebars of all specimens with the chloride contamination level of 1% by weight reached the metastable state ($0.1\mathrm{\mu A}/{\mathrm{cm}}^2<i_{\mathrm{corr}}<1\mathrm{\mu A}/{\mathrm{cm}}^2$) between 212 and 283 days, except B1-1 and B1-3. Conversely, the differences between the time-to-corrosion of specimens with the chloride contamination level of 2% by weight were much larger. This indicates that the type of embedded sacrificial anode had limited influence on the time-to-corrosion of rebar. This is consistent with the results of half-cell potential evolution. However, the total chloride content still played an important role. When the top rebar was in a metastable state, the corresponding corrosion current densities of the top rebars of most specimens with higher chloride contamination levels were higher than those of specimens with lower chloride contamination levels. This is consistent with the results of Alonso et al. (2000).

Because rebar corrosion in concrete is complicated and stochastic, statistically speaking, there could be a few uncommonly large or small values of corrosion current density and time-to-corrosion. Alonso et al. (2000) found that, based on the corrosion current density, rebars of specimens with the total chloride content of 0.48% by weight were in an active state at the beginning and entered a passive state after 36 days. Yu et al. (2010) found that the rebar in one self-compacting concrete specimen with a water-to-cement ratio of 0.5 was not corroded after 600 days, and Angst et al. (2011) found that rebars in concrete specimens with a water-to-cement ratio of 0.4 had stable pitting only during wet cycles and immediately stopped corroding during dry cycles.

Depolarized potential (also known as potential decay) of the rebar in concrete often is considered to be a significant parameter that verifies the effectiveness of the cathodic protection applied by sacrificial anodes (Bertolini et al. 2002). When the depolarized potential is lower than $-100\mathrm{mV}$ (i.e., potential decay is higher than $100\mathrm{mV}$), the cathodic protection is effective and a near-passive state has been induced in the protected rebar (Bertolini et al. 2002). The depolarized potentials of Sections 2 and 3 of the top rebars of representative specimens were about 0 mV (Fig. 5). This indicates that the discrete sacrificial anodes could not effectively protect Sections 2 and 3 of the top rebars because they were not electrically connected to Sections 2 and 3 of the top rebar, which means that the throwing power of discrete sacrificial anodes was limited and negligible. However, the results of the depolarized potential of Section 1 of the top rebars of all specimens, except uncorroded rebars, were lower than $-100\mathrm{mV}$ (Fig. 6). This indicates that discrete sacrificial anodes could guarantee a sufficient cathodic polarization and effectively protect the connected rebar section (Bertolini et al. 2002). Because each section of the top rebar was electrically disconnected, the onset of macrocouples caused by different conditions of polarization of each section was avoided and the results of depolarized potential were reliable (Bertolini et al. 2002).

The depolarized potentials of Section 1 of the top rebars of specimens incorporating S-type DSAs were between $-50$ and $-200\mathrm{mV}$ at the beginning of cathodic protection [Fig. 6(a)]. Section 1 of the top rebars of all specimens with the chloride contamination level of 1% by weight tended to decrease over time, whereas only that of S2-3 had a suppress trend. The rebar trend of depolarized potential indicated that the anodes needed to suppress the rebar potential to continuously and effectively provide electrons to the protected section of the top rebars. This is consistent with the decreasing trend of corrosion current density ($i_{\mathrm{corr}}$) of Section 1 of the top rebars after the connection of anodes. When the rebar was protected or repassivated, the resistance of the rebar would be kept in a range of high values or increased. In other words, the depolarized potential of DSAs would be kept in a range of low values or decreased, so as to maintain a sufficient level of current density of cathodic protection. Conversely, the depolarized potentials of S2-1 and S2-2 kept fluctuating between $-100$ and $-200\mathrm{mV}$ after the connection and tended to be stable over time. Such results were consistent with the corresponding results of $i_{\mathrm{corr}}$, which reveals that the anode of S2-1 could not effectively protect the rebar and the anode of S2-2 could only imperfectly repassivate the rebar. Bertolini et al. (2002) found that sacrificial anodes had poor effectiveness in protecting rebars, and initiated pitting corrosion when placed a few meters above sea level. Because the testing condition was similar to sea level and Section 1 of the top rebar of S2-1 and S2-2 were actively corroded when the anodes were connected, the S-type sacrificial anode could probably prevent only new pitting from being initiated, but could not prevent existing pitting from propagating. The amplitudes of the fluctuation of depolarized potential of S2-1, S2-2, and S2-3 were on average 120% larger than those of S1-1, S1-2, and S1-3. The effect of chloride contamination level on the depolarized potential of DSAs probably could be enhanced by wet–dry cycles because the moisture at the interface between anode and concrete matrix was vital to anode performance (Liu and Shi 2009).

Similarly, the depolarized potential of B1-3, B2-1, and B2-2 was about $-50\mathrm{mV}$ at the beginning of cathodic protection and tended to decrease over time, whereas the depolarized potential of B1-1 and B1-2 was about $-200\mathrm{mV}$ at the beginning of cathodic protection, and then kept fluctuating, tended to be stable, and slightly increased over time, respectively [Fig. 6(b)]. The corrosion current density ($i_{\mathrm{corr}}$) of B1-1 and B2-2 effectively decreased, whereas that of B1-2 increased after the connection of the anodes, which was consistent with the corresponding results of depolarized potential. The amplitude of fluctuation B1-2 ($200\mathrm{mV}$) was larger than that of B1-1 and B1-3 (30–50 mV). A similar phenomenon was found in specimens incorporating S-type and B-type anodes, which means that cathodic protection by sacrificial anodes may not be able to effectively protect the actively corroded rebars. The chloride contamination level seemed to have a limited effect on the stability of depolarized potential of Type B DSAs; however, the effect of wet–dry and freeze–thaw cycles on the amplitude of fluctuation of depolarized potential increased from 50 to $100\mathrm{mV}$ after 150 days, which is attributable to the increased number of cracks in the cement matrix.

For specimens incorporating with X-type anodes, the depolarized potential of Section 1 of the top rebar of X1-1, X1-2, and X1-3 initially was between $-10$ and $-60\mathrm{mV}$, and that of X2-2 was about $-200\mathrm{mV}$ [Fig. 6(c)]. All tended to decrease over time except that of X1-1. The tendency of corrosion current density of X1-3 was consistent with the results of depolarized potential. Oddly, based on the aforementioned criterion, the depolarized potential of X1-1 demonstrated a useless anode but the corrosion current density of X1-1 significantly decreased, which indicated that the corrosion current density was a more reliable parameter to confirm the effectiveness of a DSA. Comparing the amplitude of the fluctuation of depolarized potential of specimens with different chloride contamination levels (1% by weight ${\mathrm{Cl}}^{-}$, $60\mathrm{mV}$ versus 2% by weight ${\mathrm{Cl}}^{-}$, $250\mathrm{mV}$) showed that the stability of the Type X DSA was greater at a lower chloride contamination level.

In addition to depolarized potential, on potential can be regarded as a driving power that guarantees the transport of electrons from DSA to rebar. It also determines the polarized potential of the rebar, which indicates whether or not the rebar is completely protected (Rajani and Kleiner 2003). There is a polarized potential shift between the on potential and polarized potential, which is dependent on how long the rebar is connected to the DSA. It often takes weeks or even months to achieve full polarization, in which rebars are polarized to $-733\mathrm{mV}$ against $\mathrm{Ag}/\mathrm{AgCl}$ (Rajani and Kleiner 2003). In this study, because the polarization period was only 20 or $68\mathrm{h}$, some of the rebars might not have been completely polarized.

Fig. 7 depicts the on potential of Section 1 of the top rebars of specimens over time. The on potential of Section 1 of the top rebars of all specimens incorporating a Type S anode was about $-500\mathrm{mV}$ over time, except S1-1 [Fig. 7(a)]. The on potential of S1-1 decreased from $-500$ to $-800\mathrm{mV}$ and then increased to $-600\mathrm{mV}$ over time. If the on potential of the top rebar was only $-500\mathrm{mV}$, the corresponding polarized potential could hardly be lower than $-733\mathrm{mV}$ because the polarization period was only 20 or $68\mathrm{h}$ and the typical polarized potential shift is about $-160\mathrm{mV}$ (Rajani and Kleiner 2003). This indicates that the S-type anode could not completely polarize the top rebar and perfectly protect it, which means that new pitting would not initiate but existing pitting would propagate (Bertolini et al. 1998). This was consistent with the results of corrosion current density after the connection of anodes. For S1-1, after the connection, the anode needed to provide more electrons to the top rebar than the amount of consumed electrons, which corresponded to the decreasing trend of the on potential. Because further corrosion of top rebar was prevented, the anode needed only to provide a lesser number of electrons to offset the consumed electrons, which corresponded to the increasing trend of the on potential. In addition, the amplitude of the fluctuation of the on potential was kept stable at about $100\mathrm{mV}$, and the wet–dry cycles, freeze–thaw actions, and different chloride contamination levels seemed to have limited influence on the on potential.

The on potential of Section 1 of the top rebars of all specimens incorporating Type B anode also was about $-500\mathrm{mV}$ over time, except B2-1 and B1-2 [Fig. 7(b)]. However, the amplitude of the fluctuation of the on potential of specimens incorporating B type anodes was $100\mathrm{mV}$, which was greater than that of specimens incorporating S-type anodes. This indicates that the influences of wet–dry cycles and freeze–thaw actions on the performance of Type B anodes were almost twice those on Type S anodes. For B1-2, the on potential was about $-600\mathrm{mV}$ and then tended to increase over time, which indicates that this anode was losing its effectiveness of protecting the top rebar. This was consistent with the results of depolarized potential and corrosion current density.

The on potential of Section 1 of the top rebars of all specimens incorporating Type X anodes was about $-600\mathrm{mV}$ over time, except X1-1 [Fig. 7(c)]. This indicates that Type X anodes could effectively transport electrons to the top rebars and fully protect them, which was consistent with the corresponding results of depolarized potential and corrosion current density. Similarly, the influences of wet–dry cycles and freeze–thaw actions on the amplitude of the fluctuation of on potential of Type X anodes were about $200\mathrm{mV}$, which was almost 4 times that of Type S anodes.

Because the internal cracks of concrete may increase with the number of wet–dry cycles and freeze–thaw actions and the corrosion product of the rebar also may change with time and condition, using only one equivalent circuit could not accurately explain the complexity. Therefore, based on the simplified Randles cell, five equivalent electrical circuit models [Figs. 8(a–e)] were employed to interpret the impedance spectra of different conditions (Ribeiro and Abrantes 2016). In Fig. 8, $R_o$ represents the offset resistance, the value of which was minor and negligible and which had no physical meaning; $R_c$ and $Q_c$ represent the resistance and constant phase element (CPE) of the concrete that covered the rebar, respectively; and $R_{\mathrm{ct}}$ and $Q_{\mathrm{dl}}$ represent the charge transfer resistance and the CPE of the double layer at the rebar–concrete interface, which were composed of passive film and corrosion product, respectively. The CPE often is used instead of a perfect capacitor when the semicircle of a Nyquist plot is displaced or depressed (Ribeiro and Abrantes 2016), which is caused by the roughness of the corrosion product at the surface of rebar or the heterogeneity of the specimen (Nazari et al. 2017b). The impedance of CPE is expressed as follows (Nazari et al. 2017b):where $Y_o$ = magnitude of CPE; and generally $0.9\le n\le 1$. The existence of Warburg impedance ($W$) in the low frequency indicated that the corrosion of the top rebar was controlled by a diffusive process (Nazari et al. 2017a). The main differences between the equivalent circuits were how the parallel connection of $Q_c$ and $R_c$ was added to the simplified Randles cell and to which cell the Warburg impedance should be added.

Because the corrosion process of rebars in concrete was stochastic and complex, results of representative specimens incorporating each type of DSA and with each level of chloride contamination were selected. The impedance Nyquist plots and the corresponding Bode diagrams of Section 1 of the top rebars of representative specimens after different numbers of wet–dry cycles are shown in Figs. 9 and 10, respectively. The measured data of the impedance (real, imagined, and absolute) or the phase angle were plotted in scatters and the fitting curves were calculated from the equivalent circuit models. For S1-1 and S2-1, because there were two semicircles in the Nyquist plots and the slope of the Bode magnitude plots in low frequency increased after 12 wet–dry cycles, Equivalent circuits Figs. 8(a and d) were used to interpret the Nyquist plots of S1-1 and S2-1 before and after 12 wet–dry cycles, respectively. According to the findings of Montemor et al. (2000), the increase of the slope indicates the decrease of charge transfer resistance, which is consistent with the values in Table 5. The change of the concrete–steel interface, which was due to the growth of the rust layer at the interface, led to the use of different equivalent circuits. For B1-1, because the low-frequency part of the Nyquist plot was a line and the slope of the Bode magnitude plots in low frequency after 30 wet–dry cycles was greater than that of preceding plots, Equivalent circuits Figs. 8(a and b) were needed to interpret the Nyquist plots of B1-1 before and after 30 wet–dry cycles, respectively. Because the amount of microcracks increased with wet–dry and freeze–thaw cycles, which facilitated the diffusion of ${\mathrm{O}}_2$ and ${\mathrm{Cl}}^{-}$ in the cement matrix, the values of Warburg impedance decreased. When the top rebar was directly in contact with the external substances, the Warburg impedance element in the equivalent circuit was eliminated. Similarly, according to the change of the slope of the Bode magnitude plots, Equivalent circuits Figs. 8(c and e) were used to interpret the Nyquist plots of B2-2 after 6 and 12 wet–dry cycles, respectively. Then Equivalent circuit Fig. 8(d) was used to interpret the condition of B2-2 after 18 wet–dry cycles due to the increase of microcracks. Equivalent circuit Fig. 8(b) finally was used to interpret the Nyquist plot of B2-2 after 30 wet–dry cycles. Moreover, for X1-3, Equivalent circuit Fig. 8(b) was used during the first 6 wet–dry cycles and Equivalent circuit Fig. 8(d) was used after that to investigate the corresponding Nyquist plots. For X2-2, Equivalent circuit Fig. 8(d) was used during the first 12 wet–dry cycles, whereas Equivalent circuits Figs. 8(c and e), respectively, were used from 18 to 24 wet–dry cycles and after 30 wet–dry cycles to interpret the corresponding Nyquist plots.

To correctly analyze the Nyquist plots, the semicircles should be isolated and should related to different phenomena, and a localized analysis should be performed (Ribeiro and Abrantes 2016). The diameters of the semicircles in the Nyquist plots and the slope of the Bode magnitude plots in low frequency of all the representative specimens decreased with the increase in number of wet–dry cycles before the connection of DSAs (Figs. 9 and 10). This indicates that the charge transfer resistance, $R_{\mathrm{ct}}$, decreased with the numbers of wet–dry cycles and freeze–thaw actions, which was consistent with the data in Table 5 and the results of Ribeiro and Abrantes (2016). According to the well-known Stern–Geary equation (Feliu et al. 1998), the corrosion current density increased with the decrease of charge transfer resistance before the connection of DSAs, which suggests that the top rebars of all the representative specimens were about to corrode or had been suffering from corrosion already after a certain number of wet–dry cycles and freeze–thaw actions. The decrease of charge transfer resistance consequently resulted in the decrease of the phase angle in the Bode phase plots (Montemor et al. 2000). After the connection of DSAs, the charge transfer resistance of all the representative specimens except S2-1 increased. This was consistent with the trend of the corrosion current density, indicating that all the representative DSAs except S2-1 could more or less provide some protection to the top rebars of all the representative specimens.

The values of the electrochemical parameters of each specimen are listed in Table 5. The values of $R_o$ were mostly very small and negligible, which coincides with the definition of the corresponding part of the equivalent circuit. The $p$-values of $R_o$ for each representative specimen were between 0.18 and 0.76, which are larger than 0.05 and suggest that the values of $R_o$ of each representative specimen were not significantly different. Most of the values of $R_c$ were on the order of ${10}^0-{10}^3\mathrm{\Omega }{\mathrm{cm}}^{-2}$ and the $p$-values of $R_c$ for each representative specimen were around 0.37, also larger than 0.05, indicating that the influences of wet–dry cycles and freeze–thaw actions on the resistance of $\mathrm{concrete}/\mathrm{mortar}$ with different chloride contamination levels were not significantly different. Compared with $R_c$, the range of the $p-$ values of $Q_c(Y_o)$ and $Q_c(n)$ was from 0.07 to 0.94 and from 0.02 to 0.92, respectively, which suggests that the porosities of the representative specimens were slightly different, likely influenced by wet–dry cycles and freeze–thaw actions. All the values of $R_{\mathrm{ct}}$ had a decreasing trend before the connection of DSAs, whereas all the values of $R_{\mathrm{ct}}$ except that of S2-1 were increased after the connection of DSAs, which was consistent with the results of depolarized potential and on potential. The $p$-values of $R_{\mathrm{ct}}$ were between 0.18 and 0.99, which statistically validates the effectiveness of all representative anodes except S2-1 and the different performance of cathodic protection of each type of anode. The values of $C_{dl}$ were calculated as follows (Nazari et al. 2017b):

The value of capacitance depends on the size of the plates, the distance between the plates, and the properties of the dielectric, and the relationship can be expressed as (Nazari et al. 2017b)where $\epsilon$ = dielectric constant; ${\epsilon }_o$ = vacuum permittivity; $A$ = area of plate surface; and $\delta$ = distance between two plates. For S1-1, B1-1, and B2-2, the values of $C_{dl}$ decreased with the increase of the values of $R_{\mathrm{ct}}$ after the connection of DSA, which was consistent with the findings of Nazari et al. (2017b). The decrease of $C_{dl}$ corresponds to the decrease of the area of plate surface ($A$) or the increase of the distance between two plates ($\delta$) caused by the repassivation of the rebar. However, there seemed to be a time lag between the connection of DSA and the decrease of $C_{dl}$, which was mainly the result of the competition between the corrosion of the rebar and the protection or repassivation by the DSAs. For S2-2, the values of $C_{dl}$ increased with the decrease of the values of $R_{\mathrm{ct}}$ after the connection of DSA, which was consistent with the results of depolarized potential and on potential. The increase of $C_{dl}$ suggests that the area of the plate surface ($A$) increased with the process of corrosion due to the absence of effective protection of DSA. The values of $C_{dl}$ of X1-3 and X2-2 increased with the increase of the values of $R_{\mathrm{ct}}$. A possible explanation for the increasing trend of $C_{dl}$ of X1-3 and X2-2 is that the time lag of this type of anode is longer than that of the other two types and the value of $C_{dl}$ decreases when the rebar is completely repassivated or perfectly protected. Further investigations are necessary to validate the hypothesis.

In Fig. 11, a series of SEM pictures demonstrates the morphology of the matrix of the representative cement mortar specimens after the embedded DSAs lost their effectiveness. There were a significant number of microcracks between the fine aggregates and along the surface of the fine aggregates. This suggests that the cement matrix had seriously deteriorated due to the wet–dry cycles and freeze–thaw cycles. With the increase of the microcracks in the cement matrix, the rebar could get access to more water, oxygen, and deleterious substances such as ${\mathrm{Cl}}^{-}$, which accelerated the corrosion rate. This confirms the hypotheses proposed to explain the change of equivalent circuits for interpreting the EIS results. It also explains why some of the DSAs lost their effectiveness in only 2 years. In addition, the microscopic morphology of the representative DSA samples before and after service are shown in Fig. 12. The DSA samples before service consisted of the matrix and the zinc core, whereas there was a dim layer with a thickness of $100\pm 50\mathrm{\mu m}$ between the matrix and the zinc core in the DSA samples after service. Unlike the matrix of DSA samples before service that were tightly attached to the zinc core, there was a crack between the layer and the matrix. This specific microcrack probably was caused by the formation of the dim layer, which was the oxidation product of zinc core.

To further investigate the chemical composition of the dim layer and validate the hypothesis, EDX mapping was conducted on the DSA samples after service. In Fig. 13, the hot spots (i.e., spots with more signals) in the second row represent the distribution of oxygen while the hot spots in the third row represent the distribution of zinc. Obviously, the hot spots of zinc element are intensive in the zinc core and dim layer, whereas the hot spots of oxygen element are intensive in the dim layer and mortar matrix. The overlapping area of hot spots of oxygen and zinc provides convincing evidence that the dim layer is mainly consisted of the oxidation products of zinc. Moreover, Fig. 14 illustrates the EDX spectrum of randomly selected spots in the dim layer, zinc core, and matrix. The major portions of the dim layers of the representative Type S, B, and X DSAs were 81.1%, 64.4%, and 72.9% by weight zinc and 15.7%, 23.2%, and 17.4% by weight oxygen, respectively. Conversely, the major portions of the zinc cores of the representative Type S, B and X DSAs are 94.7%, 96.4%, and 92.4% by weight zinc, and 1.1%, 0.5%, and 1.7% by weight oxygen, respectively. Interestingly, there was some zinc (15% by weight) diffused in the matrix. Generally, the zinc core is fully constrained in the matrix of DSAs, which leaves no space for the oxidation product of zinc core during the service life. This significantly limits the DSA’s potential to continuously protect the connected rebar. Because the resistance of zinc oxide is much greater than that of pure zinc, the potential that is necessary for pumping electrons from the zinc core to the connected rebar will become increasingly large with the growth of the zinc oxide layer, which finally leads to the failure of DSA. Based on the SEM observation, the thickness of the zinc oxide layer was only $100\pm 50\mathrm{\mu m}$, which means that over 90% of the zinc core was wasted. Therefore, to extend the service life and improve the utilization rate of DSAs, some soft and fluid material could be embedded between the zinc core and the matrix that provides flexible room for the oxidation products. In addition, an external electrical current could be connected to the DSA for some period to reduce and rejuvenate partial oxidized zinc and decrease the resistance of the zinc oxide layer. Further studies are needed to validate the feasibility of these methods.

The XRD spectra of representative samples of DSAs before and after service are depicted in Fig. 15. All types of DSAs have almost the same spectra in Fig. 15(a), indicating that the zinc core in all types of DSAs had high purity. This is consistent with the results of Table 1 and the results of previous studies (Boshkov et al. 2005; Salinas et al. 1999). The small peaks of ZnO of Type X DSAs mean that a tiny fraction of the zinc core of Type X DSAs may be oxidized during the cutting process. The peaks in the remaining figures [Figs. 15(b–d)] indicate the phase composition of DSAs after service, which was $\mathrm{Zn}(\mathrm{OH}{)}_2,{\mathrm{Zn}}_5(\mathrm{OH}{)}_8{\mathrm{Cl}}_2·{\mathrm{H}}_2\mathrm{O}$ (ZHC), and ZnO. This is consistent with the results of previous studies (Boshkov et al. 2005; Seré et al. 1998). Compared with the spectra of DSAs before service, all the peaks of Zn of the DSAs after service exhibited a lower intensity. This indicates the consumption of zinc and confirms the effectiveness of all the DSAs that protected the connected section of top rebar.