Experimental Study on Chloride-Induced Corrosion of Soil Nail with Engineered Cementitious Composites (ECC) Grout

: Conventionally, a soil nail is a piece of steel reinforcement installed inside a hole drilled into the slope and ﬁlled with cement paste (CP) grout. Chloride penetration is a major deterioration mechanism of conventional soil nails as the CP grout is easy to crack with an uncontrollable crack opening when the soil nail is subject to loading or ground movements. Engineered Cementitious Composites (ECC) are a class of ﬁber-reinforced material exhibiting excellent crack control even when loaded to several percent of strain, and therefore, ECCs have great potential to replace traditional CP grout in soil nails for achieving a long service life. In this study, the chloride ion transport characteristics and electrically accelerated corrosion process of steel rebar in ECC and CP grouts are systematically studied. The rapid chloride ion penetration test results showed a reduction of 76% and 58% passing charges in ECC with 0.15% and 0.3% pre-loading strain, respectively, as compared to that in un-cracked CP. Furthermore, the accelerated corrosion experimental data showed that ECC under pre-loading strain still exhibited a coefﬁcient of chloride ion diffusion that is 20–50% lower than CP grout due to the ability to control crack width. Service life calculations based on experimentally measured parameters showed that the predicted corrosion rate and corrosion depth of soil nails in ECC grout were much lower than those in CP grout. The ﬁndings can facilitate the design of soil nails with excellent durability and long service life.


Introduction
Rainfall-triggered landslides in mountainous regions around the world have produced a large number of casualties and serious damages [1][2][3][4]. It is, therefore, necessary to provide a rational and reliable strategy to improve slope stability. One possible and economical way to stabilize geotechnical structures, such as soil slopes, excavations and retaining walls, is through the use of a soil-nailing technique [5,6]. The soil nails are placed in the active zone to offer sliding resistance along the identified potential failure surface. Soil nails usually consist of steel reinforcing bars placed in a drilled hole filled with cement paste (CP) grout. The steel bar is installed at an inclination of 10 to 20 degrees with the horizontal to resist tension, shear and bending loads. The various merits of soil nails compared to concrete retaining walls, such as quicker construction, lower cost and less environmentally destructive, have led to its widespread use in Hong Kong [7,8].
In a conventional soil nail system, the steel bar is protected against direct exposure to soil masses by the CP grout. Water and chemicals, however, can pass through the grout and reach the steel bar surface. The situation is particularly harmful if there is Table 1 lists the blending proportions of conventional CP grout and ECC (by weight of binder). The matrix components included CEM I Portland cement (Grade 52.5N, BS EN 197-1 [22]), fly ash, tap water, and polycarboxylate-ether superplasticizers (SP). Table 2 provides the chemical compositions of cement and fly ash. The polyvinyl alcohol fibers produced by Kuraray Co., Ltd. (Tokyo, Japan) were used to reinforce the matrix in the ECC. A mass ratio of 0.8% GCP TM ADVA 189 SP was utilized to tailor the fresh property of the mixtures. The polyvinyl alcohol fiber is around 39 µm and 8 mm in diameter and length, respectively. The ultimate tensile strength is 1600 MPa, and Young's modulus is 42.8 GPa. SP provided by Grace™ was used to control the workability of the ECC mixes and ensure the good dispersion of fibers. The SP content (0.8%), FA/PC ratio (2.0) and fiber content (1.25%) were all fixed in this investigation based on the CP's equivalent flowability with a min-slump flow test [13]. A truncated cone with a dimension of 60 mm height, 100 mm bottom diameter and 70 mm top diameter was filled with fresh mixtures and lifted upward immediately. The min-slump flow test was repeated twice to get an average value. The average diameters of the fresh CP and ECC mixtures were 23.87 and 23.14 cm, respectively.

Specimens Preparation and Test Methods
Rectangular panel specimens were prepared in the field ( Figure 1a) using site equipment for pumping and grouting. The dimension of specimens was 1000 mm length, 120 mm width and 120 mm height, as shown in Figure 1b. The diameter of the rebar was 16 mm. The fresh CP and ECC grouts were first mixed by a concrete mixer at 150 rpm, and then pumped into rectangular molds (in the form of a box) through a hose and nozzle. The pump rate was set at approximately~1.5 cubic meters per hour. The grout pipe was placed in the middle of the rectangular mold. After hardening, testing specimens were obtained from the two sides of the pipe. The CP and ECC grouts were cured at the casting site for 28 days and then moved to the laboratory for the chloride ion penetration and chloride ion corrosion tests.

Rapid Chloride Ion Penetration Test
After 28 days of curing, the rapid chloride ion penetration test (RCPT), according to ASTM C1202-12 [23], was adopted for all mixes in this study. Diskshape cement paste grout and ECC samples with a dimension of 100 mm in

Rapid Chloride Ion Penetration Test
After 28 days of curing, the rapid chloride ion penetration test (RCPT), according to ASTM C1202-12 [23], was adopted for all mixes in this study. Disk-shape cement paste grout and ECC samples with a dimension of 100 mm in diameter were obtained by coring from the grouted panel. All disk-shaped samples were further polished by a water-cooled diamond saw until the height of the specimen became 50 mm. To study the effect of cracking on chloride ion penetration, the disk-shaped samples were fractured by splitting tension under vertical loading in an MTS machine ( Figure 2). The loading rate was kept constant at 0.02 mm/s. The horizontal displacement was continuously monitored using two LVDTs, which were positioned at opposite sides of the specimen (Figure 2). Various samples were pre-loaded to tensile strains of 0%, 0.15%, and 0.3% along the centerline of the specimens. The pre-loaded samples were denoted as PC-0%, ECC-0%, ECC-0.15% and ECC-0.3%, respectively. Four replicates were prepared for each pre-loaded group. After fracturing, the specimens were placed in a vacuum saturation apparatus for 3 h and then immersed in water for 18 h under natural ambient pressure. Then, the cylindrical surface of the specimens was covered with epoxy coating before each specimen was sandwiched into the RCPT set up, as shown in Figure 3. One side of the cells was filled with 3.0% (wt.%) NaCl solution and the other with 1.2% (wt.%) NaOH solution. A DC voltage of 60 V was applied between the specimen's two sides to determine the electrical conductance in coulombs. The passed charge was recorded per 30 min over a 6-h period to provide a rapid indication of chloride ion penetrability. After fracturing, the specimens were placed in a vacuum saturation apparatus for 3 h and then immersed in water for 18 h under natural ambient pressure. Then, the cylindrical surface of the specimens was covered with epoxy coating before each specimen was sandwiched into the RCPT set up, as shown in Figure 3. One side of the cells was filled with 3.0% (wt.%) NaCl solution and the other with 1.2% (wt.%) NaOH solution. A DC voltage of 60 V was applied between the specimen's two sides to determine the electrical conductance in coulombs. The passed charge was recorded per 30 min over a 6-h period to provide a rapid indication of chloride ion penetrability. After fracturing, the specimens were placed in a vacuum saturation apparatus for 3 h and then immersed in water for 18 h under natural ambient pressure. Then, the cylindrical surface of the specimens was covered with epoxy coating before each specimen was sandwiched into the RCPT set up, as shown in Figure 3. One side of the cells was filled with 3.0% (wt.%) NaCl solution and the other with 1.2% (wt.%) NaOH solution. A DC voltage of 60 V was applied between the specimen's two sides to determine the electrical conductance in coulombs. The passed charge was recorded per 30 min over a 6-h period to provide a rapid indication of chloride ion penetrability. After the rapid chloride penetrability test, the specimens were split to measure the penetration of chlorides by using the colorimetric method. A silver nitrate aqueous solution (0.1 mol/L AgNO3) was sprayed on one split surface of the specimens to reveal the depth of chloride penetration (Xd). The chloride diffusion After the rapid chloride penetrability test, the specimens were split to measure the penetration of chlorides by using the colorimetric method. A silver nitrate aqueous solution (0.1 mol/L AgNO 3 ) was sprayed on one split surface of the specimens to reveal the depth of chloride penetration (X d ). The chloride diffusion coefficient (D) under non-steady-state migration was calculated from X d according to the Bassuoni et al. [24] and Edvardsen et al. [25] via Equation (1): where D is the non-steady-state diffusion coefficient (×10 −12 m 2 /s), V is applied voltage (V), T is the average value of initial and final temperatures in the solution ( • C), L is the thickness of the specimen (mm), X d is the average value of penetration depth (mm) and t is the time (h).

Impressed Voltage Accelerated Corrosion Test
To study the ECC grout soil nails under various cracking conditions, rectangular specimens with the rebar in the middle were pre-loaded under uniaxial tension with prescribed tensile strains of 0%, 0.15% and 0.30%. Three replicates were prepared for each prescribed group. During the testing, a controlled displacement rate of 0.2 mm/min was adopted, and two linear variable displacement transducers (LVDTs) were attached on opposite sides of each specimen to quantify the tensile deformation, as shown in Figure 4. After the loaded specimen was removed from the testing machine, it was placed in contact with 5% NaCl solution in a container and an external direct current source with 20 V constant voltage was applied to the rebar to accelerate the steel corrosion process. In this test, the steel rebar contacted the anode, and the NaCl solution served as the cathode. During the accelerated corrosion process, the impressed current was measured and recorded every 2 h. This test would be ended when the impressed current reaches a steady condition.
where D is the non-steady-state diffusion coefficient (×10 −12 m 2 /s), V is applied voltage (V), T is the average value of initial and final temperatures in the solution (°C), L is the thickness of the specimen (mm), Xd is the average value of penetration depth (mm) and t is the time (h).

Impressed Voltage Accelerated Corrosion Test
To study the ECC grout soil nails under various cracking conditions, rectangular specimens with the rebar in the middle were pre-loaded under uniaxial tension with prescribed tensile strains of 0%, 0.15% and 0.30%. Three replicates were prepared for each prescribed group. During the testing, a controlled displacement rate of 0.2 mm/min was adopted, and two linear variable displacement transducers (LVDTs) were attached on opposite sides of each specimen to quantify the tensile deformation, as shown in Figure 4. After the loaded specimen was removed from the testing machine, it was placed in contact with 5% NaCl solution in a container and an external direct current source with 20 V constant voltage was applied to the rebar to accelerate the steel corrosion process. In this test, the steel rebar contacted the anode, and the NaCl solution served as the cathode. During the accelerated corrosion process, the impressed current was measured and recorded every 2 h. This test would be ended when the impressed current reaches a steady condition.

Passing Charges
The results of the rapid chloride ion penetrability test on day 28 are given in Figure 5. It could be seen that the passing charge increased with increasing prescribed strains of the specimens due to the larger cracks. The total passing charges through the ECC specimens were 2850, 4180 and 7540 coulombs under prescribed strains of 0%, 0.15% and 0.3%, respectively. Namely, the passing charge

Passing Charges
The results of the rapid chloride ion penetrability test on day 28 are given in Figure 5. It could be seen that the passing charge increased with increasing prescribed strains of the specimens due to the larger cracks. The total passing charges through the ECC specimens were 2850, 4180 and 7540 coulombs under prescribed strains of 0%, 0.15% and 0.3%, respectively. Namely, the passing charge increased 1.47-2.65 times as the prescribed strains increased from 0% to 0.3%. It was noticed that the ECC-0% performed better than virgin CP grout in the resistance to chloride ion penetration. This is attributed to the lower average pores in ECC, which inhibit the transportation of chloride [26]. Moreover, the incorporation of fly ash in ECC may enhance the resistance of chloride penetration in cementitious materials, as the pozzolanic reaction results in fewer capillary pores and reduces the transport of chloride ions [27]. In comparison to CP-0%, the increase of the passing charges in ECC-0.15% and ECC-0.3% are 24% and 42%, respectively. The qualitative indications of the chloride ion penetrability based on the measured values from this test method are provided in Table 3. The results indicated that the chloride permeability level for virgin CP, ECC-0% and ECC-0.15% grouts were high, but that for the ECC-0% was a moderate level.
Infrastructures 2021, 6, x FOR PEER REVIEW 7 of 16 chloride ion penetration. This is attributed to the lower average pores in ECC, which inhibit the transportation of chloride [26]. Moreover, the incorporation of fly ash in ECC may enhance the resistance of chloride penetration in cementitious materials, as the pozzolanic reaction results in fewer capillary pores and reduces the transport of chloride ions [27]. In comparison to CP-0%, the increase of the passing charges in ECC-0.15% and ECC-0.3% are 24% and 42%, respectively. The qualitative indications of the chloride ion penetrability based on the measured values from this test method are provided in Table 3. The results indicated that the chloride permeability level for virgin CP, ECC-0% and ECC-0.15% grouts were high, but that for the ECC-0% was a moderate level.
Passing charges (Coulomb) Δ = 42% Figure 5. Total charges passed through CP and ECC grouts at 28-days curing. ECC specimens were significantly lower than CP specimens for the total passed charges.

Chloride Diffusion Coefficient
The chloride penetration depth was measured from the visible white silver chloride precipitation, as shown in Figure 6. The average depths of chloride migrating into CP-0% was 33 mm, while the values for ECC were 17, 20 and 25 mm under prescribed strains of 0%, 0.15% and 0.3%, respectively. Total charges passed through CP and ECC grouts at 28-days curing. ECC specimens were significantly lower than CP specimens for the total passed charges.

Chloride Diffusion Coefficient
The chloride penetration depth was measured from the visible white silver chloride precipitation, as shown in Figure 6. The average depths of chloride migrating into CP-0% was 33 mm, while the values for ECC were 17, 20 and 25 mm under prescribed strains of 0%, 0.15% and 0.3%, respectively. The diffusion coefficient results obtained from the aforementioned Equation (2) are summarized in Figure 7. The diffusion coefficient was 1.86 × 10 −11 m 2 /s in CP-0% grout. For the ECC specimens, while a higher diffusion coefficient is induced by increased prescribed strains, the measured values up to 0.3% were all lower than that for CP-0% grout. The diffusion coefficients of ECC under prescribed strains of 0%, 0.15% and 0.3% were 50%, 41% and 25% lower than those of CP grout, respectively. Previous research showed that the incorporation of fly ash in cement materials could reduce the diffusivity of chloride ions due to the densification of the pore size structure in the hydration products [28]. In addition, the fly ash in ECC formed more C3A than CP grout, which could facilitate the adsorption of more chloride ions to form the Friedel's salt (C3A·CaCl2·10H2O) [29]. From the results of the current study, it is apparent that the ECC grout is more robust than conventional CP grout against chloride ion penetration.  Figure 8 illustrates the impressed current versus exposure time for the steel bar in ECC and CP grouts under the fixed potential. Each line in Figure 8 represents the average of three specimens. A two-stage procedure of current-time can be observed. The impressed current of all specimens first increased with the testing time (Phase I) and then reached a steady stage (Phase II). Because the specimens were soaked in tap water and saturated before the accelerated corrosion test, the same value of the initial current was recorded for the ECC and CP specimens. During the corrosion The diffusion coefficient results obtained from the aforementioned Equation (2) are summarized in Figure 7. The diffusion coefficient was 1.86 × 10 −11 m 2 /s in CP-0% grout. For the ECC specimens, while a higher diffusion coefficient is induced by increased prescribed strains, the measured values up to 0.3% were all lower than that for CP-0% grout. The diffusion coefficients of ECC under prescribed strains of 0%, 0.15% and 0.3% were 50%, 41% and 25% lower than those of CP grout, respectively. Previous research showed that the incorporation of fly ash in cement materials could reduce the diffusivity of chloride ions due to the densification of the pore size structure in the hydration products [28]. In addition, the fly ash in ECC formed more C 3 A than CP grout, which could facilitate the adsorption of more chloride ions to form the Friedel's salt (C 3 A·CaCl 2 ·10H 2 O) [29]. From the results of the current study, it is apparent that the ECC grout is more robust than conventional CP grout against chloride ion penetration. The diffusion coefficient results obtained from the aforementioned Equation (2) are summarized in Figure 7. The diffusion coefficient was 1.86 × 10 −11 m 2 /s in CP-0% grout. For the ECC specimens, while a higher diffusion coefficient is induced by increased prescribed strains, the measured values up to 0.3% were all lower than that for CP-0% grout. The diffusion coefficients of ECC under prescribed strains of 0%, 0.15% and 0.3% were 50%, 41% and 25% lower than those of CP grout, respectively. Previous research showed that the incorporation of fly ash in cement materials could reduce the diffusivity of chloride ions due to the densification of the pore size structure in the hydration products [28]. In addition, the fly ash in ECC formed more C3A than CP grout, which could facilitate the adsorption of more chloride ions to form the Friedel's salt (C3A·CaCl2·10H2O) [29]. From the results of the current study, it is apparent that the ECC grout is more robust than conventional CP grout against chloride ion penetration.  Figure 8 illustrates the impressed current versus exposure time for the steel bar in ECC and CP grouts under the fixed potential. Each line in Figure 8 represents the average of three specimens. A two-stage procedure of current-time can be observed. The impressed current of all specimens first increased with the testing time (Phase I) and then reached a steady stage (Phase II). Because the specimens were soaked in tap water and saturated before the accelerated corrosion test, the same value of the initial current was recorded for the ECC and CP specimens. During the corrosion  Figure 8 illustrates the impressed current versus exposure time for the steel bar in ECC and CP grouts under the fixed potential. Each line in Figure 8 represents the average of three specimens. A two-stage procedure of current-time can be observed. The impressed current of all specimens first increased with the testing time (Phase I) and then reached a steady stage (Phase II). Because the specimens were soaked in tap water and saturated before the accelerated corrosion test, the same value of the initial current was recorded for the ECC and CP specimens. During the corrosion progress, the negatively charged chloride ions from the solution were attracted toward the positively charged steel bar as the electrical potential was applied to the soil nails. Eventually, the steel bar surface began to corrode as the chloride ions reached a critical concentration at the soil nail surface. As the increased corrosion products diffused along the cracks and gradually filled the pores of CP grout or ECC surrounding the rebar, the impressed current increased (Phase I). As seen from Figure 8, the current recorded for all ECC and CP specimens achieved approximately 170-180 mA at 180 h. After 100 h, a lower current was recorded in the cracked ECC (ECC-0.15% and ECC-0.3%) compared with the undamaged ECC. However, at around 180 h, all specimens reached the steady-state in Phase II, and the recorded current was about the same ( Figure 8). This might be attributed to the continuous oxygen reaction occurring at a steady speed. In this study, the presence of a steady-state (Phase II) reflected that the corrosion rate had reached the maximum value.

Impressed Current and Ohmic Resistance
Infrastructures 2021, 6, x FOR PEER REVIEW 9 of 16 progress, the negatively charged chloride ions from the solution were attracted toward the positively charged steel bar as the electrical potential was applied to the soil nails. Eventually, the steel bar surface began to corrode as the chloride ions reached a critical concentration at the soil nail surface. As the increased corrosion products diffused along the cracks and gradually filled the pores of CP grout or ECC surrounding the rebar, the impressed current increased (Phase I). As seen from Figure 8, the current recorded for all ECC and CP specimens achieved approximately 170-180 mA at 180 h. After 100 h, a lower current was recorded in the cracked ECC (ECC-0.15% and ECC-0.3%) compared with the undamaged ECC. However, at around 180 h, all specimens reached the steady-state in Phase II, and the recorded current was about the same ( Figure 8). This might be attributed to the continuous oxygen reaction occurring at a steady speed. In this study, the presence of a steady-state (Phase II) reflected that the corrosion rate had reached the maximum value. During the early stage of corrosion, the oxides that formed the passive film on the steel rebar were thermodynamically stable in the alkaline environment around the soil nail. As the chloride ions built up around the steel rebar, the corrosion tended to be localized, and the chloride-induced corrosion initiation followed the model of pitting corrosion. However, it is generally known that pit nucleation is typically accompanied by passivation. The chloride ions bound in the steel rebar may induce corrosion, whereas the hydroxyl ions bound in the solid phase prevent corrosion [30,31]. In the corrosion progress, the anodic reaction was the oxidation process that leads to a dissolution or loss of metal, while the cathode reaction was the process of reduction that leads to the formation of a hydroxyl ion from dissolved oxygen. For steel rebar embedded in CP and ECC grouts, the anodic reactions depended on the pH of the interstitial electrolyte, the presence of aggressive anions and the existence of an appropriate electrochemical potential at the steel surface [32,33]. As illustrated in Figure  9, evident corrosion products are detected on the surface of metallic rebar regardless of CP or ECC. During the early stage of corrosion, the oxides that formed the passive film on the steel rebar were thermodynamically stable in the alkaline environment around the soil nail. As the chloride ions built up around the steel rebar, the corrosion tended to be localized, and the chloride-induced corrosion initiation followed the model of pitting corrosion. However, it is generally known that pit nucleation is typically accompanied by passivation. The chloride ions bound in the steel rebar may induce corrosion, whereas the hydroxyl ions bound in the solid phase prevent corrosion [30,31]. In the corrosion progress, the anodic reaction was the oxidation process that leads to a dissolution or loss of metal, while the cathode reaction was the process of reduction that leads to the formation of a hydroxyl ion from dissolved oxygen. For steel rebar embedded in CP and ECC grouts, the anodic reactions depended on the pH of the interstitial electrolyte, the presence of aggressive anions and the existence of an appropriate electrochemical potential at the steel surface [32,33]. As illustrated in Figure 9, evident corrosion products are detected on the surface of metallic rebar regardless of CP or ECC.   The ohmic resistance (R s ) for all specimens during the corrosion progress can be calculated from Equation (2).
where R s is the ohmic resistance of CP and ECC grouts during the corrosion progress (ohm), U is the constant DC voltage (20 V) and I is the recorded current in Figure 8. R 0 is the ohmic resistance of an extra resistor for each specimen to avoid a large current in the circuit, and the value is shown in Table 4.  Figure 10 shows the calculated R s development for the CP and ECC grouts during various corrosion periods. It could be seen that the R s gradually decreased with increasing exposure time. As pre-loaded strain increased from 0% to 0.15% and 0.3%, the R s for ECC specimens were quite close to each other irrespective of their pre-loading strain. Whereas the R s for CP-0% was higher than both the uncracked and cracked ECC over most of the corrosion period. The ohmic resistance (Rs) for all specimens during the corrosion progress can be calculated from Equation (2).
where Rs is the ohmic resistance of CP and ECC grouts during the corrosion progress (ohm), U is the constant DC voltage (20 V) and I is the recorded current in Figure 8. R0 is the ohmic resistance of an extra resistor for each specimen to avoid a large current in the circuit, and the value is shown in Table 4.  Figure 10 shows the calculated Rs development for the CP and ECC grouts during various corrosion periods. It could be seen that the Rs gradually decreased with increasing exposure time. As pre-loaded strain increased from 0% to 0.15% and 0.3%, the Rs for ECC specimens were quite close to each other irrespective of their pre-loading strain. Whereas the Rs for CP-0% was higher than both the uncracked and cracked ECC over most of the corrosion period.

Prediction of Chloride Concentration on Steel Surface and Corrosion Rate
To analyze the effects of grout materials and pre-loading strain on the service life of soil nails as exposed to the extreme chloride condition, the schematic of a soil nail under the chloride exposure is illustrated in Figure 11. The diameter of the rebar and grout cylinder is 16 and 89 mm, respectively. The chloride ion penetration occurs either through the capillary pores or cracks by permeation, capillary suction and diffusion. This transport process has been extensively explored, and several models have been developed to predict the chloride penetration profiles [10,28,32]. Most of these models are based upon Fick's second law and has been widely applied in the engineering and research aspect. In this study, three assumptions are made to simplify the problem: (i) diffusion is taken to be the major process, (ii) the cracks are not explicitly considered, but their presence will lead to an effective increase in diffusion coefficient as measured in the tests described in Section 3.2 and (iii) axisymmetric diffusion in the real situation is simplified into unidirectional diffusion (from outer grout surface into rebar surface) in a semi-infinite domain. and diffusion. This transport process has been extensively explored, and several models have been developed to predict the chloride penetration profiles [10,28,32]. Most of these models are based upon Fick's second law and has been widely applied in the engineering and research aspect. In this study, three assumptions are made to simplify the problem: (i) diffusion is taken to be the major process, (ii) the cracks are not explicitly considered, but their presence will lead to an effective increase in diffusion coefficient as measured in the tests described in Section 3.2 and (iii) axisymmetric diffusion in the real situation is simplified into unidirectional diffusion (from outer grout surface into rebar surface) in a semi-infinite domain. The diffusion of chloride ions into concrete can then be described by Crank's solution to Fick's second law [34][35][36][37]. This law for a one-dimensional case is: where C is the concentration, D is the diffusion coefficient, t is the diffusion duration and x is the diffusion distance. For unidirectional flow, the solution of this equation is as follows: where C(x,t) is the chloride concentration at a distance x (mm) from the outside surface at corrosion time t (s), C0 is the chloride concentration (30 mg/L) on the outside surface of the grout and erf is the error function. Equation (3) assumed that the grout is homogenous, and the diffusion coefficient D is independent of chloride concentration and temperature (T). In fact, for a certain interval period, this second law of Fick's has been found to be a fair estimate for the depth of chloride in a homogenous structure either exposed to the ambient state of The diffusion of chloride ions into concrete can then be described by Crank's solution to Fick's second law [34][35][36][37]. This law for a one-dimensional case is: where C is the concentration, D is the diffusion coefficient, t is the diffusion duration and x is the diffusion distance. For unidirectional flow, the solution of this equation is as follows: where C(x, t) is the chloride concentration at a distance x (mm) from the outside surface at corrosion time t (s), C 0 is the chloride concentration (30 mg/L) on the outside surface of the grout and erf is the error function. Equation (3) assumed that the grout is homogenous, and the diffusion coefficient D is independent of chloride concentration and temperature (T). In fact, for a certain interval period, this second law of Fick's has been found to be a fair estimate for the depth of chloride in a homogenous structure either exposed to the ambient state of the atmosphere and/or submerged. The solution given by Equation (4) is valid only if the boundary and material properties are constant. The initial condition is C t (x, t) = 0 when x > 0 and t = 0, and C t (x, t) = C 0 for x = 0 and t = 0. In this study, we assumed that the chlorides in the grout are not present initially, and the chlorides in the system are totally from the exposure condition.
In this case, the service life of soil nails would be designed as 120 years. As shown in Figure 11, the chloride transportation distance to the rebar surface is 73 mm, C 0 is assumed to be 30 mg/L and the diffusion coefficient D of CP and ECC grouts are obtained from Figure 7. Based on calculations from Equation (4), the predicted results of chloride concentration on the rebar surface are shown in Figure 12. Specifically, the chloride concentration on the rebar surface for CP and ECC grouts with different pre-loading conditions after 120-years of exposure was illustrated. The results in Figure 12 demonstrated that larger pre-loading conditions in grout resulted in higher chloride concentration on the surface of the steel rebar. With good crack control, as well as lower diffusivity in the uncracked state, the ECC grouts loaded to 0.15% and 0.30% strain still exhibit chloride concentration on the steel rebar surface than the virgin CP grout.
shown in Figure 11, the chloride transportation distance to the rebar surface is 73 mm, C0 is assumed to be 30 mg/L and the diffusion coefficient D of CP and ECC grouts are obtained from Figure 7. Based on calculations from Equation (4), the predicted results of chloride concentration on the rebar surface are shown in Figure 12. Specifically, the chloride concentration on the rebar surface for CP and ECC grouts with different pre-loading conditions after 120-years of exposure was illustrated. The results in Figure 12 demonstrated that larger pre-loading conditions in grout resulted in higher chloride concentration on the surface of the steel rebar. With good crack control, as well as lower diffusivity in the uncracked state, the ECC grouts loaded to 0.15% and 0.30% strain still exhibit chloride concentration on the steel rebar surface than the virgin CP grout. Corrosion penetration in the steel rebar is calculated next. The rates of corrosion varied with changes in the temperature, the quantity of chloride in the surrounding grounds, the resistance to chloride of the grout materials and the duration for corrosion. Based on Liu and Weyers's [35] statistical analysis, the experimental corrosion rate is shown in Equation (5) with consideration of the concrete temperature, ohmic resistance, chloride content on the surface of steel bar and exposure time: where i is the steel corrosion current (μA/cm 2 ), Ccl is chloride content on the surface of steel at a given time (kg/m 3 ), T is the temperature at the steel surface (Kelvin), R is the ohmic resistance of the cover concrete (ohms) and t is corrosion time (years). It should be noted that the values of chloride content Ccl on the surface of steel at different times were obtained from Figure 12, which represent an extreme condition for soil nails exposed to a natural condition in Hong Kong (with C0 = 30 mg/L). T is kept at 296.45 Kelvin for the average temperature in Hong Kong. The ohmic resistance of CP Corrosion penetration in the steel rebar is calculated next. The rates of corrosion varied with changes in the temperature, the quantity of chloride in the surrounding grounds, the resistance to chloride of the grout materials and the duration for corrosion. Based on Liu and Weyers's [35] statistical analysis, the experimental corrosion rate is shown in Equation (5) with consideration of the concrete temperature, ohmic resistance, chloride content on the surface of steel bar and exposure time: where i is the steel corrosion current (µA/cm 2 ), C cl is chloride content on the surface of steel at a given time (kg/m 3 ), T is the temperature at the steel surface (Kelvin), R is the ohmic resistance of the cover concrete (ohms) and t is corrosion time (years). It should be noted that the values of chloride content C cl on the surface of steel at different times were obtained from Figure 12, which represent an extreme condition for soil nails exposed to a natural condition in Hong Kong (with C 0 = 30 mg/L). T is kept at 296.45 Kelvin for the average temperature in Hong Kong. The ohmic resistance of CP and ECC (cracked and loaded to 0.15% and 0.30%) were obtained from the steady value in Figure 10.
The corrosion rate of the steel rebar in soil nails is calculated from the predicted empirical Equation (6) [38] and shown in Figure 13. It can be found from the figure that the corrosion rate in ECC specimens is lower than that in CP. To find the corrosion depth (H) of the steel rebar, the corrosion rate in µA/cm 2 can be transformed into the corrosion rate in µm/year through Equation (6). Then, the corrosion depth (H) in the predicted 120 years can be calculated by Equation (7).
1 µA/cm 2 = 10 mA/m 2 = 11.6 µm/year where the H is the corrosion depth (µm) and I t is the corrosion current (µA/cm 2 ) at various corrosion times t (year).
corrosion rate in μm/year through Equation (6). Then, the corrosion depth (H) in the predicted 120 years can be calculated by Equation (7).
1 μA/cm 2 = 10 mA/m 2 = 11.6 μm/year (6) where the H is the corrosion depth (μm) and It is the corrosion current (μA/cm 2 ) at various corrosion times t (year). The results of the predicted corrosion depth of rebars in CP and ECC grouts are presented in Figure 14. It could be seen that the corrosion depth of CP-0% grout specimen was 3.05 mm. For the ECC specimens, the 120-year corrosion depth was 2.75, 2.84 and 2.94 mm under prescribed strains of 0%, 0.15% and 0.3%, respectively. The 120-year corrosion depths of ECC-0%, ECC-0.15% and ECC-0.3% were 9.8%, 6.9% and 3.6% lower than the values of CP-0%, respectively. It should be noted that the corrosion rate used to predict chloride concentration on the surface of rebar was obtained from the maximum value (phase II in Figure 8); therefore, the corrosion rates reported in Figure 14 is probably higher than those in real practice. However, for the purpose of comparison amongst different mixes and because all steel rebars went through the same preparation procedure, we could conclude that the rebar in ECC grout (even loaded to 0.30% strain) has lower corrosion depth than that in un-cracked CP grout under the same environmental conditions. The results of the predicted corrosion depth of rebars in CP and ECC grouts are presented in Figure 14. It could be seen that the corrosion depth of CP-0% grout specimen was 3.05 mm. For the ECC specimens, the 120-year corrosion depth was 2.75, 2.84 and 2.94 mm under prescribed strains of 0%, 0.15% and 0.3%, respectively. The 120-year corrosion depths of ECC-0%, ECC-0.15% and ECC-0.3% were 9.8%, 6.9% and 3.6% lower than the values of CP-0%, respectively. It should be noted that the corrosion rate used to predict chloride concentration on the surface of rebar was obtained from the maximum value (phase II in Figure 8); therefore, the corrosion rates reported in Figure 14 is probably higher than those in real practice. However, for the purpose of comparison amongst different mixes and because all steel rebars went through the same preparation procedure, we could conclude that the rebar in ECC grout (even loaded to 0.30% strain) has lower corrosion depth than that in un-cracked CP grout under the same environmental conditions. Corrosion time = 120 years Figure 14. Predicted corrosion depth of soil nails exposed to chloride solution for 120 years.

Conclusions
This paper reports the results of a systematic bench-scale study on the chloride ion transport characteristics and chloride-induced corrosion process of steel rebar Figure 14. Predicted corrosion depth of soil nails exposed to chloride solution for 120 years.