Dynamic effect of water penetration on steel corrosion in carbonated mortar: A neutron imaging, electrochemical, and modeling study

Carbonation may potentially lead to corrosion of steel bars in reinforced concrete. This concern presents a major barrier against the implementation of sustainable low-clinker cementitious materials in the design of reinforced concrete structures. Various studies have documented the relationship between different equilibrium moisture states in carbonated concrete and the corrosion rate of the embedded steel. However, limited attempts were focused on visually observing the dynamic (time-dependent) behavior of moisture penetration into concrete and the related corrosion state and rate. Moreover, there is a lack of data on the local moisture state in the cementitious matrix in the steel-concrete interfacial zone. In this study, liquid water uptake in carbonated mortar was in-situ and over time monitored by neutron imaging. The corrosion state of embedded steel was monitored by means of electrochemical measurements. This combined experiment revealed that the arrival of the waterfront at the steel surface led to a sharp decrease of the steel potential. The corrosion rate increased from negligibly low values ( < 1 µ m/year) to about 31 µ m/year within a couple of minutes. Based on the neutron images, it is concluded that the moisture ingress through the concrete cover is locally affected by the heterogeneity of projected (depth-averaged) porosity distribution, and that large obstacles such as entrapped air have an effect. These observations were further confirmed by numerical simulation results of water transport, which also showed that liquid water permeability of the studied carbonated mortar determined by the inverse analysis is much higher than reported values in the literature. Overall, this study highlights the importance of considering the dynamic and coupled corrosion and moisture transport behavior during the periods which active corrosion can occur in carbonated concrete exposed to cyclic wetting/drying conditions.


Introduction
Considering that the massive production and global use of cement is an important source for greenhouse gas emissions, modifying the composition of cementitious materials offers great opportunities in reducing the environmental footprint of the construction sector.By reducing the portion of clinker in the cement, the carbon footprint of concrete structures will be significantly decreased [1].In this regard, the grand challenge is to maximize the reduction in clinker, while still ensuring the durability of the material once it is exposed to actual service conditions.Generally, low-emission and low-clinker cementitious materials carbonate faster when exposed to environment containing carbon dioxide, which is a common concern with respect to the corrosion protection of embedded reinforcing steel [2].
A recent review of practical experience and scientific literature concluded that corrosion-related damage in carbonated concrete generally only occurs in situations where moisture can reach the reinforcing steel in both significant amounts and over pronounced time [3].The main factors controlling the extent to which moisture can reach the embedded steel are the concrete cover depth, the microstructure of the carbonated concrete (and thus the moisture transport and retention properties), and the moisture exposure conditions.A review of literature studies, reporting experimentally determined corrosion rates for steel in carbonated concrete, concluded that there is a general agreement: in low relative humidity (RH), the steel corrosion rate is negligibly low, while much higher corrosion rates (up to 10 μm/year, in extreme cases 100 μm/year) are reported for conditions where the concrete is in contact with liquid water [4].Experimental results in different exposure regimesshowed that corrosion rate significantly decreases by about 2 orders of magnitudes when changing partial immersion or 100% RH to 50% RH [5,6].
Nevertheless, studies on the relationship between the moisture condition and the steel corrosion rate in carbonated cementitious systems, such as the 20+ studies reviewed in Stefanoni et al. [4] and Angst et al. [3], generally reported corrosion rates after specimens had been exposed to a certain condition for a long period, which allowed for the moisture state inside the cementitious matrix to equilibrate with the external environment.The effect of water transport on steel corrosion was postulated to happen spontaneously, but no direct experimental results in the literature were able to visually verify it.In actual conditions of structures where concrete carbonation and subsequent steel corrosion can occur and potentially lead to damage, the exposure conditions are cyclic wetting and drying rather than a constant moisture state.Thus, there is a clear need for scientific studies on the effect of the time-variable moisture transport processes in the zone close to the embedded steel upon wetting (or drying) on steel corrosion.
However, there is a lack of knowledge on the moisture distribution at the microscopic scale, especially in the steel-concrete interfacial (SCI) zone.This is important because the moisture state and the microstructure of the cementitious matrix at the SCI directly control the corrosion state [7].Nevertheless, most studies measured the moisture state on the macroscopic scale (e.g., the entire specimen).The SCI is known to have different microstructure and chemical composition to the bulk concrete [8][9][10].Therefore, it is difficult to relate the moisture state determined on the macroscopic scale (bulk) to the moisture condition at the SCI.Directly observing water transport at the SCI becomes important and necessary.Traditional techniques for measuring moisture distribution, such as embedded relative humidity sensors [11,12] and gamma-ray attenuation [13], cannot be used for the SCI.Modern techniques, including micro-X-ray computed tomography (μXRCT) [14][15][16][17] and neutron radiography [18,19], are able to achieve a resolution in micro meter range, which have been commonly used to monitor the rapid water absorption in cement-based materials.As X-rays are not sensitive to water, contaminated water with highly sensitive ions was used (e.g., Cs [17,20]) or techniques that can enhance the measured signal (e.g., X-ray dark-field imaging [15]) are needed.Contrarily, neutrons are ideal for detecting water because of their high water attenuation coefficient, resulting in a high sensitivity to water.
This work grasps the opportunity of utilizing the neutron imaging technique to directly observe water transport in carbonated mortar and at the steel-mortar interface, thanks to the high resolution of this technique, while simultaneously performing electrochemical monitoring of embedded carbon steel electrodes to quantify changes in the corrosion state.This combined approach allows studying the dynamic behavior of the system during water absorption, namely the capillary water ingress and the coupled corrosion behavior of the steel.

Materials
Cement mortar was prepared with CEM II/B-M (T-LL) 42.5 N cement, a blended cement containing burnt oil shale and limestone.The waterto-cement ratio (w/c) was 0.6 and the sand-to-cement ratio was 2. The sand had a grain diameter of max. 1 mm.Steel wires (0.5 mm diameter) were placed horizontally with a 10 mm interval.Initially, a mortar slab with a dimension of 80 mm × 80 mm × 6 mm (thickness) was prepared (see the detail about sample preparation can be found in Ref. [6]).An Ag/AgCl sensor was embedded as a reference electrode in the top part of the mortar sample.To ensure a stable reference potential, the mortar in the top part was prepared by adding 0.1 M NaCl to the mixing water.After curing at 95% RH for 7 days, specimens were carbonated in a chamber at 20 • C, 57% relative humidity, and 4% CO 2 concentration for 7 days and then stored in the lab condition (~ 50% RH).The carbonation depth was checked by spraying phenolphthalein solution on the split cross section and the colorless surface indicated that the specimens were fully carbonated.For the water penetration measurement, a small specimen with two embedded steel wires was cut from the original specimen and polished to reduce the thickness (Fig. 1).The thickness was 3 mm to allow sufficient neutrons to pass through.The specimen was stored in a 53% RH desiccator before any experiments described in the following sections.

Water penetration, neutron imaging and electrochemical measurements
To prevent water evaporation during water penetration, the front and back surfaces of the specimen were covered by aluminum adhesive sheets and the bottom and top surfaces were open (see illustration in Fig. 1).The side surfaces were painted with epoxy to ensure insulation of the steel wires against water.A water reservoir was prepared with an inner dimension of 12 mm × 8 mm × 15 mm (width × thickness × depth) and the bottom part of the specimen was stuck to the inner reservoir wall (see setup in Fig. 2).The transparent reservoir was used so that the water level could be visually checked.During measurement, the reservoir was filled with distilled water and the top water surface was covered with a small piece of plastic film to minimize water evaporation.The reservoir was fixed on a steel base which was mounted on a magnet rod linked to a rotation stage.By using this system, we were able to minimize the change of relative position of the specimen to the scintillator during specimen handling.
The neutron imaging measurements were performed at NEUTRA, a thermal neutron imaging beamline [21], at the Paul Scherrer Institute, Switzerland.The experiments were performed at the measuring position No.2.The scintillator-camera box (MIDI) has been equipped with the fiber optics taper (FOT) [22].The FOT has been fitted with 30-µm thick gadolinium oxysulfide scintillator screen.The images of 2048 × 2048 pixels in size were acquired using a CCD camera (Andor, iKon-L).The pixel size was equal to 6.63 µm.The effective field of view (FOV) resulting from the shape and size of the FOT was of circular shape of approximately 10 mm in diameter A black body was installed upstream the specimen (see Fig. 2) and was supposed to compensate for background scattering and systematic biases in quantitative neutron imaging.However, the relatively small FOV of the imaging set-up contained only four black bodies (see Fig. 3b).Such a low number unfortunately would not reliably estimate of the scattering corrections [23].
The two steel wires and the Ag/AgCl reference electrode were connected to a Keithley Model 2100 multimeter to record potentials, E corr , of the steel wires vs. the embedded reference electrode in time interval of 30 seconds.Potentials recording started first and the neutron beam was then opened to obtain images of the original state of the specimen (specimen equilibrated at 53% RH).The projected 2D neutron images were acquired every second but only the density averaged image of 30 acquisitions was saved.After the recorded steel potentials stabilized, neutron imaging was stopped.Afterwards, water was added into the reservoir and neutron imaging restarted immediately.During the course of the liquid water uptake experiment, the recorded steel potentials and neutron images were regularly checked.Once the waterfront moved out the FOV, neutron imaging was stopped.This happened approximately at 36 min after adding water to the reservoir.
The complete setup (specimen, reservoir and steel base) was then kept immersed in a desiccator with water under vacuum for one day.After vacuum saturation, the specimen was brought back to the neutron stage and imaged again to obtain the images of the saturated specimen.
A possible concern about the corrosion potential measurement is the effect of neutrons.When neutrons hit steel, a small electrical current may be generated, whose intensity depends on the neutron flux and the size of steel.The potential measured during acquiring the initial state of the specimen was used to evaluate this effect.It was found that when the neutron beam started, the measured E corr increased by about 5 mV, which is roughly about 1% of the total change of E corr during liquid water uptake.Therefore, for the experimental setup in this study, the effect of neutrons on measured potential is considered negligible.

Determination of degree of water saturation
The attenuation of neutrons depends on material properties and the thickness of the specimen.The number of neutrons that pass through the specimen at a given location can be calculated by the Beer-Lambert law.
where μ i is the attenuation coefficient of components in the material, z i is the thickness of each component that neutrons pass through, and I 0 is the neutron flux in the absence of a specimen.
During liquid water uptake, the change of measured neutron flux is caused by water, so the Beer-Lambert law can be applied to specimen in original state and during water absorption [18,19], given (2) where μ w the effective attenuation coefficient of water, z w = z w (x, y) is the water occupied path length at the given location, I 1 and I m are measured neutron fluxes in original state and during water movement, so z w can be determined by solving the above two equations.
The volumetric water content w c (m 3 /m 3 ) is the ratio of z w to the thickness of the specimen z m .
Note that this volumetric water content depends on the location (x, y) within the specimen, and is an average over the thickness of the mortar.The effective attenuation coefficient of water (=3.635451/cm) was measured in the previous study [24] on the same facility at NEUTRA.
After vacuum saturation with water, the above calculated w c can be considered to be approx.the porosity ϕ of the material in the path of neutrons, which is hereafter referred to as "projected porosity".At each location, this projected porosity ϕ corresponds to an average porosity over the thickness of the specimen (3 mm), and it represents the difference between the original (equilibration at 53% RH) and saturated states.
The degree of saturation, S, is then estimated by ) ln where I s is the measured neutron flux at vacuum saturation and S 1 represents the initial degree of saturation after the specimen was equilibrated at 53% RH.Again, the approach used here allowed determining the degree of saturation as a function of the position (x,y) in the specimen, averaged over the thickness of the mortar as the present of steel has been excluded in Eq. (4).

Corrosion rate determination
The instantaneous corrosion current density of the upper steel wire in both the dry (equilibrated at 53% RH) and the wet (~36 min after contact with liquid water) states was quantified by means of the linear polarization resistance method [25].The upper steel wire was polarized ± 15 mV from the open circuit potential by taking the lower steel wire as the counter electrode.The sweep rate was 0.5 mV/s.IR correction was made on the basis of ohmic resistances determined by means of electrochemical impedance spectroscopy (EIS) in both the dry and wet state.The obtained polarization resistance, R p , was converted to instantaneous corrosion current density with the help of the following equation: The conversion constant, B, was assumed B = 26 mV for corroding steel [25].The corrosion current density, i corr (μA/cm 2 ), was converted to corrosion rate with a unit of μm/year by 11.6 × i corr .

Measurements of sorption isotherm
The sorption isotherm is used to determine the initial water content of the specimen and as input data for numerical simulations (see Section 4).The present study employed a Dynamic Vapor Sorption analyzer (DVS Advantage ET85, Surface Measurement Systems Ltd.) to measure the sorption isotherm.A small piece of cement paste prepared with the same cement and w/c as the mortar in this study was kept in a constant RH environment until the measured mass reached equilibrium.As reported in the previous study [26], the equilibrium water content in a cementitious material is mainly controlled by the amount of dry hardened cement paste so that cement paste and mortar prepared with the same cement and w/c have a very similar sorption isotherm (the S -RH curve).Therefore, this study determined sorption isotherm for the mortar specimen based on the measured curve for cement paste.The paste sample was initially vacuum saturated with water.The controlled RH in the DVS started at 97% and then decreased stepwise to 11%.The equilibrium criteria was defined when a mass change (dm/dt) is less than 0.0005%/min over 10 min or a maximal time of 1000 min per each step was reached.Finally, the sample was dried in a nitrogen gas environment at 40 • C, which represents the condition of RH = 0%.More information about the DVS measurements can be found elsewhere [27].

Projected porosity distribution calculated from neutron images
The neutron imaging measurements only provide 2D images, which do not include the variation of a property (i.e., phases, water, and porosity) along with the depth as much as 3D tomography, while instead, the property is depth-averaged, so this is a definite improvement compared with only taking 2D images at the specimen surface (such as the use of SEM images to create simulation domains [28]).The neutron beam was focused on a small part of the specimen where the upper steel wire is located.The neutron attenuation coefficient of steel is similar to dry cementitious materials, so that it is difficult to locate the steel wire within the mortar in a neutron image.To locate the steel wire, the selected FOV includes the epoxy covered surface.Because of the pronounced difference in neutron attenuation of epoxy and steel, the exact location can be identified (see Fig. 3a and b).
As shown in Fig. 3b, there are regions of epoxy, black dots from the black body (indicated by white arrows), and regions out of FOV, which are not useful for further image analysis.To simplify the image analysis, a small part of image with the steel wire was cropped out, as indicated in Fig. 3c.
The ϕ distribution as estimated from w c according to Eq. ( 5) and based on the difference of neutron images between the initial (equilibration at 53% RH) and saturated states is shown in Fig. 3b with the gray level in the image corresponding to the porosity level.Two air voids with bright color are clearly seen at the location overlaid with the steel wire.These air voids were trapped during sample casting, presumably due to the presence of the steel wire.Fig. 3c shows that porosity at the locations of air voids is about 0.3.Considering the thickness of the specimen (3 mm) and low measured porosity at the other regions, a rough estimation indicates that the thickness of air voids (along with the depth) is a bit over 1 mm, which agrees well with the size of air voids shown in Fig. 3c (further confirming the spherical shape of the air voids).
From this location to the right, there are two bright lines indicating the lower and upper boundaries of the steel wire.However, the distance between these two lines is wider than the diameter of steel wire, so that the bright regions are mortar with high ϕ.The low line seems wider and brighter than the upper line, which might be caused by settlement of fresh mortar during casting [10].From the air voids to the left, there are no bright regions, indicating that the steel wire had a good contact with the surrounding mortar, that is, without a gap.Apart from these features, the ϕ distribution clearly shows the highly heterogeneous structure of cement-based materials in the 2D projected image at the microscopic level.It is expected that the microstructure (in 3D) of cement-based materials is more heterogeneous.
Z. Zhang et al.

Degree of saturation and water content
The spatiotemporal distribution of the degree of saturation was calculated by Eq. ( 6), in which S 1 at each pixel depends on its porosity (S 1 = f(ϕ(x, y))).By using the calculation method presented in Section 3.4, sorption isotherms for pixels with different porosities can be determined.Examples for three sorption isotherms are shown in Fig. 4, together with the experimentally determined sorption isotherm of the cement paste (DVS, black squares).As shown in Fig. 3c, the heterogeneous microstructure of the mortar results in a spatially variable ϕ distribution.Based on this distribution, the initial degree of saturation at each pixel (after equilibration at 53% RH) can be calculated.This leads to values of S 1 in the range of 0.15-0.35.
Some examples of degree of saturation at selected times are shown in Fig. 5.We can see that the initial water distribution is very non-uniform because of the highly heterogeneous microstructure.Even though mortar is generally viewed as a homogeneous material on the macroscopic scale, the microstructural heterogeneity is able to significantly affect water transport and distribution.The initial S at some locations seems very high (see t = 4.17 min in Fig. 5).Comparing to the ϕ distribution in Fig. 3c, we observe that the high S locations generally have low ϕ so they can be filled with water at low RHs.If plotting S and ϕ in  With liquid water uptake, S in these low ϕ regions gradually increases.Contrarily, some regions always have very low S although S of their neighboring regions increases, especially two macroscopic air voids and the high ϕ region around the steel wire.Fig. 6 clearly shows that S in high ϕ regions increases much more slowly than in low ϕ regions.This slow increase might be caused by the fact that the large pores or voids in these regions cannot be fully filled up with water during imbibition.
With water moving up, the waterfront reaches the bottom of the steel wire at around 15 min after adding water into the reservoir.Water movement then seems to be slowed down by the presence of the steel wire.This may be explained because the cross area for water transport becomes narrower.The presence of air voids is also able to change the path of liquid water uptake as water cannot directly pass through air voids.As can be seen, the region between the air void on the left-hand side and the specimen edge is narrow, water transport in this region becomes much slower than the other regions (see t = 17.22 to 20.87 min in Fig. 5).After water passing through the narrow region, S in the left part of the wire is much higher than the right part because there is no high porosity region around the steel wire.Finally at t = 36 min, S in most regions reaches a high level, while S of two air voids and other high ϕ regions remain still low.
Saturation profiles along the direction of liquid water uptake (y-direction in Fig. 5) were calculated by averaging saturation at each point in x-direction between 3 and 7 mm (thereby, the two air voids were excluded from the profile calculations).Calculated results of saturation profiles in Fig. 7 clearly show a sharp waterfront in the early water absorption, which is then disturbed by the steel wire with the process of water uptake.From the profiles determined at t > 20 min, it can be observed that in the zones directly around the steel, the degree of saturation is significantly lower than locations further away from the steel.This was observed in Fig. 5 as well.For instance, at t = 36 min, S is about 0.47 in the steel-mortar interfacial zone, while elsewhere in the sample (both in front of and behind the steel) S is above 0.6.This can be explained by the higher ϕ and more large pores (probably beyond capillarity) at the steel-mortar interfacial zone than the bulk matrix.Large pores can not be filled by capillary transport and high ϕ is able to reduce the degree of saturation.Considering that profiles in Fig. 7 are depth-averaged S, the actual S at the steel-mortar interface can be estimated by assuming high S in mortar close to interface; therefore, the actual S at the interface would be much lower than that shown in Fig. 7.
Another observation in Fig. 7 is that S at a given location (e.g., y=0.5 mm) increases sharply with the arrival of the waterfront, while the increase rate becomes very low after waterfront passes.The later stage may take much longer time to observe a significant change in S and the slow water absorption in the later stage will be discussed in Section 4.2.
The volumetric water content w c distributions calculated by Eq. ( 5) at different water absorption times are provided in Fig. 8.They show very similar trends to S distributions in Fig. 5.In regions close to the steel wire and two air voids, water contents are lower, presumably because more large pores in these regions are not filled with water.Different from Fig. 5, regions with low porosity also have low water content due to their low ability to retain water.Another difference is that more water accumulates in the area below two air voids.Comparing with the Fig. 6.Degree of saturation vs. projected porosity (from Fig. 3c) at different water penetration times: (a) t = 4.17 min (the initial stage of water uptake), (b) t = 15.13 min (when the waterfront reaches the steel surface, and (c) t = 36 min (the end of experiment).Fig. 7. Saturation profiles (averaged over the x-direction in Fig. 3, see text for explanations) along the water uptake direction y, for different times (min).The location of the steel wire is indicated by two vertical black solid lines.measured ϕ distribution in Fig. 3, we see that this area shows a slightly higher ϕ than the region to its right and thus water transport is hindered in the low ϕ region.

Electrochemical measurements vs. degree of saturation
Fig. 9 shows the time evolution of the average degree of saturation, S, at the surface of the upper steel wire (black squares) and the steel potentials of the two steel wires embedded in the specimen (red lines).The solid red line represents the upper steel electrode (the corresponding cover depth of approx.12 mm), and the dashed line stands for the lower steel electrode (cover depth of 2 mm).The degree of saturation S at the surface of the upper steel electrode starts to dramatically rise at t = 15 min.The sharp increase lasts for about 8 min, until it starts leveling out at approx.t = 23 min.In the same time period, the potential, E corr , of the upper steel shows a sharp decrease, from initially approx.-100 mV to approx.-500 mV vs. Ag/AgCl.For the lower steel wire that has a very short distance for water penetration, a similar sharp change in E corr happened almost immediately after contact of the specimen with liquid water.
The results of the electrochemical corrosion rate measurements performed in the dry and wet stages are also indicated in Fig. 9.These  data show that the instantaneous corrosion rate is negligibly low in the dry state (specimen here equilibrated at 53% RH), approx.0.16 μm/ year.Once the waterfront reached the steel and E corr decreased to approx.-500 mV vs. Ag/AgCl, the instantaneous corrosion rate increased significantly to 31 μm/year.As above-mentioned, measured S in Fig. 7 (squares) is depth-averaged and the actual S is lower than these shown in the figure.Therefore, a certain amount of air still exists at the steel-mortar interface while water contacts the steel.Under such condition, with effects of both oxygen in air and water (more precisely, water with ions and low pH), the high corrosion was observed.

Data analysis by means of numerical simulations of moisture transport
The neutron imaging results clearly show that the heterogeneous microstructure has a significant influence on water transport and local water content.In order to further explore how the non-homogeneous porosity distribution affects water distribution, a model was employed to simulate moisture transport.A numerical moisture transport model is also able to assess the moisture ingress beyond the experimental time.
The selected model in this study is a two-phase model, including liquid water and water vapor, which was developed based on Richards' equation (as the governing equation for mass conservation), van Genuchten equation (for sorption isotherms) [29] and Mualem model (for relative permeability) [30].Details about this model can be found elsewhere [31][32][33] and in the Appendix.
Since we want to simulate water passing around the steel wire, the cross section of the specimen was taken as the simulation domain, which   is in 2D and shown in Fig. 10.Two steel wires with distance 10 mm are embedded.As indicated by the neutron imaging results (see Fig. 3) and as known from other studies [8], a highly porous layer can be found around the steel wire, which is wider below the wire than that above the wire.Therefore, a porous layer (about 0.3 mm thick below and 0.2 mm above the steel wire) was created around the steel wire (see the enlarged figure in Fig. 10b).Porosity was assumed to exponentially increase from the bulk mortar towards the steel surface as commonly used to represent the ITZ thickness in concrete [34].Porosity at the underside of the steel surface was set as 0.7 and for the rest part of the domain porosity was assigned as ϕ m = 0.15, namely, the bulk porosity of the studied specimen.This way leads to the average porosity at the bottom of the steel wire, if drawing a horizontal line, is about 0.25, which is roughly in the same range with the measured porosity by neutron imaging (see Fig. 3).This study ran additional simulations with different assumptions for the porosity distribution around the steel wire.These different simulations did not significantly change the main observations from the model as presented in this section.
With the change of porosity, the moisture retention capacity of cement-based materials changes as well.This is generally considered in a sorption isotherm, which is the main input to the moisture transport model.The sorption isotherm is here mathematically described by the van Genuchten equation [29]: where P c (Pa) is capillary pressure which is calculated from RH by the Kelvin's law (the equation can be found elsewhere, e.g., [31]), and α (Pa) and m are two fitting parameters.Previous study has shown that, to consider the dependence of sorption isotherms on porosity, m can be viewed as a constant while taking α as a function of porosity ϕ [28].
where c is a constant and taken as 4.33 [28].By fitting measured adsorption isotherm provided in Fig. 4, α 0 and m are determined as 9 × 10 5 Pa and 0.26, respectively.The calculated water vapor adsorption isotherms for different porosities are compared in Fig. 4, which shows that the curve shifts down with the increase of porosity, leading to much sharper drop from the saturated condition.In other words, the high porosity regions need higher RH to reach the same level of S as the low porosity regions.When the specimen contacts liquid water, most pores at the boundary are filled with liquid water except pores over the capillary range and pores with trapped air, so it is generally found that the actual boundary RH is lower than 100%, because RH =100% can only be reached by vacuum saturation [35].In this study, the boundary RH was set at 99% for the simulations.
The KC coefficient C K is the only unknown in the selected moisture transport model (see the Appendix for the model).Therefore, it may be determined by fitting experimental data and then further to calculate the intrinsic permeability, so-called inverse analysis method [32].In this study, simulation results are fitted to the measured mean S on the surface of the upper steel wire.As compared in Fig. 9, the good agreement between the simulated curve (black solid line) and the measured results (black squares) suggests that the choice of the two-phase moisture transport model and the model setup are appropriate.
According to the calculated intrinsic permeability curve in Fig. A-1, as ϕ m = 0.15, the corresponding intrinsic permeability to liquid water is 3.8 × 10 − 16 m 2 , which is about 200 times -5 orders of magnitudes higher than the measured permeabilities for NC cement-based materials with the same w/c (mortars and cement pastes) [32,36,37], but is in the same level as the measured permeability to nitrogen gas [38].Such high permeability and fast water uptake imply that pores in the studied mortar have been coarsened by carbonation.This finding is in agreement with other studies [39,40] which reported that coarsening of pore structure and increasing gas diffusion were observed on all carbonated cement pastes.
Furthermore, the saturation profiles along y-direction were calculated by averaging the modelled S in z-direction and excluding steel wires.To compare with results from the neutron imaging in Figs.7 and 11 only shows simulated saturation profiles in the region of the upper steel wire.Clearly, the simulated results can well capture major observations of the measured profiles, such as the shape of the waterfront and the effect of steel wire on water transport.The drop of S in regions close to the steel surface is obvious in the simulated profiles, caused by the more porous layer around the steel wire.It is also clear that S above the wire is slightly higher than that below the wire, due to the fact that porosity below the wire is lower.These results match well the measured results in Fig. 7 and further proves that the heterogeneous microstructure of porous materials can directly affect moisture transport and water distribution.
The numerical simulation was run longer than the experiment, namely until the internal RH equilibrates with the boundary RH (99% RH for the boundary condition), which took about 100 min.The saturation profile at t = 100 min, shown as a black dashed line in Fig. 11, is clearly much higher than the curve at the end of experiment (t = 35.48min).However, the neutron imaging measurement did not run so long to obtain the final water content in the specimen.

Effect of moisture penetration on corrosion rate
The results from electrochemical measurements on the corrosion state of the steel together with the penetration of moisture through the mortar, shown in Fig. 9, clearly reveal the dynamic behavior of the steelmortar system upon capillary water uptake and the dramatic increase of the instantaneous corrosion rate within the arrival of the water front at the steel surface (from 0.16 to 31 μm/year).The largest increase in corrosion state happened within only a few minutes, as evidenced by E corr in Fig. 7. Stefanoni et al. determined the instantaneous corrosion rate of steel electrodes in comparable samples (identical cement type, mix proportions, and carbonation procedure) and reported 10 μm/year for the saturated state, that is, after exposure to water for >2 weeks [7].
For samples equilibrated at 50% RH, a corrosion rate of 0.03 μm/year was reported [6].These literature data are thus in good agreement with the here determined values.
Note that S will continue increasing beyond the measurement period in this study (~36 min), although at a much slower pace than in the initial stages.Nevertheless, this further increase in water uptake duration may not significantly increase the instantaneous corrosion rate after the waterfront has reached the steel, depending on the microstructure of materials and wetting time, which was confirmed by previous studies, where the instantaneous corrosion rate was monitored over time during wetting in comparable specimens [5,41].The prolonged water uptake will increase water content but reduce the amount air at the steel-mortar interface so less oxygen will be available for corrosion.Based on this point, corrosion rate is not expected to rapidly increase in the prolonged water uptake.This continued, but decelerated increase in S at the steel-mortar interface can be explained by different reasons as discussed in Section 4.2.
It has been shown that the instantaneous corrosion rate of a metal embedded in carbonated cementitious media is governed by the pore structure and the moisture content [7].In this context, it is important to recognize that the pore structure of the cementitious matrix in the interfacial zone is primarily relevant for the corrosion kinetics.The present work has revealed differences in interfacial porosity as compared to the bulk matrix, with a generally higher porosity in the interfacial zone.This finding, based on neutron imaging, is in agreement with other studies utilizing microscopic techniques [8] or X-ray Z. Zhang et al. computed microtomography [10].Further studies are needed to characterize the interfacial pore structure of carbonated steel-concrete interfaces and to quantify its effect on the corrosion rate as a function of the spatiotemporal moisture changes in the concrete upon cyclic wetting/drying exposure conditions.

Two-stage water absorption
The measured S and w c distributions show a sharp waterfront penetrating the specimen.This means that most pores can be filled with water in a short time, governed by the capillary absorption, which is known as the primary water absorption [42].However, regions with high porosity are found to be difficult to fill with water during capillary uptake, because these regions contain pores of over-capillary dimensions.Another observation in reported neutron imaging results (see Figs. 5 and 8) is that the local S or w c vary significantly in both time and space.It is believed that temporal variations are caused by trapped air in these pores.As water can quickly fill pores in the capillary range, air in some pores, such as large pores surrounded by small capillary pores, is trapped and thus these pores are hardly saturated with water in the short time [43].With water uptake, the pressure from the liquid on trapped air increases, which leads to the redistribution of air during water uptake.With more water being absorbed, the trapped air in the interior of the material gradually dissolves in the liquid phase and slowly moves to the open specimen surfaces [42,44,45].Therefore, more water can enter the porous material.Nevertheless, this process takes much longer time than the primary stage, which is generally considered as the secondary water absorption [42].The neutron imaging measurements in this study captured the primary water absorption, but did not continue long enough to observe the second stage.Apart from the air dissolution theory, the microstructural alteration of hydration products observed in nuclear magnetic resonance (NMR) measurements [46][47][48] may also contribute to the secondary water absorption.
It is expected that the water content at the steel surface will continuously increase in the secondary water absorption.However, the moisture transport model employed in this study does not consider the secondary water uptake.Models, such as the dual-permeability model [49] and time-dependent permeability models [35,50,51], were proposed to predict water uptake for the long duration.Future studies may benefit from using these models, in particular in combination with neutron imaging and electrochemical corrosion state measurements, to study the effect of the long-term water absorption on steel corrosion in carbonated concrete.
Additionally, further research is needed to link the dynamic changes within carbonated concrete, both with regard to the spatiotemporal moisture distribution and related effects on steel corrosion, in the context of external exposure conditions, particularly cyclic wetting/ drying exposure (such as XC4 according to the European standards -EN 206), that may likely be dominated by relatively short-term wetting events.

Conclusions
Based on neutron imaging of the spatiotemporal moisture distribution in 2D projected images in carbonated mortar and simultaneous electrochemical monitoring of the corrosion state of embedded steel electrodes, as well as numerical moisture transport simulations, the following conclusions can be drawn: (1) When the waterfront during water uptake reached the embedded steel, the corrosion state of the steel was observed to change dramatically, that is, from a state of negligibly low instantaneous corrosion rates (<1 µm/year) to a state of pronounced corrosion activity (about 31 µm/year) within only a few minutes.(2) This finding highlights the importance of considering the dynamic and coupled corrosion and moisture transport behavior governing the periods during which active corrosion can occur in carbonated concrete exposed to cyclic wetting/drying conditions.(3) Future attempts towards ensuring the durability of carbonated concrete may benefit from a better understanding of these processes, and in particular the spatiotemporal moisture distribution at the steel-concrete interface in time-variable exposure conditions.
With respect to the heterogeneity of the concrete properties, the following additional conclusions are drawn from this work: (1) Based on measured water uptake by neutron imaging (up to 36 min), we can see that water transport is significantly affected by the local microstructure, which leads to considerable variability in the spatial distribution of water in the mortar.The measured spatiotemporal distributions of both degree of saturation and water content reveal that water tends to move slowly into the following regions: low porosity regions which have low water capacity and very high porosity regions (air voids and the steelmortar interface) where the sizes of some pores are over the capillary range so they cannot be filled with water by capillary absorption.(2) Air can be trapped in large pores that are surrounded by small capillary pores, because liquid water is easily absorbed by small capillary pores and thus blocks the paths for air movement.With the prolonged water contact, water will redistribute with the dissipation of trapped air and slowly move into finer pores, such as gel pores.(3) The numerical simulations of moisture transport confirmed that the presence of high porous regions around steel wire can significantly affect the path of water transport and cause lower degree of water saturation in these regions.Therefore, the heterogeneity of porosity distribution in the mortar and large obstacles such as entrapped air should be considered to predict water distribution.(4) Liquid water permeability of the studied carbonated mortar is several orders of magnitudes higher than the generally reported values for non-carbonated cementitious materials in the literature.
the use of the Dynamic Vapor Sorption analyzer.

Appendix: Moisture transport model
In the simulation domain, we consider each element as a homogeneous porous medium that consists of solid and pores so that the porosity represents the available space for moisture transport.Therefore, a continuum moisture transport that is commonly used for the REV (representative elementary volume) level can be employed to simulate moisture transport at each element.Unsaturated moisture transport in a rigid porous material can be formulated by the Richards' equation.An S-based version is written as where η l is the dynamic viscosity of liquid water, k rl is relative permeability, K l is the intrinsic permeability, M v is the molar mass of water molecule, ρ l is liquid water density, x D is a resistant parameter to consider the microstructural effect on vapor diffusion (taking as 2.74 for cement-based materials based on the fitting of experimental data of CO 2 and oxygen diffusion [52]), and P vs is the saturated vapor pressure in air.

∂S ∂t
Relative permeability k rl is expressed as a function of S by using the van Genuchten -Mualem model [29,30].
where m is taken from van Genuchten equation (see Eq. ( 8)).
In terms of the intrinsic permeability K l , it is commonly inversely determined by fitting a measured mass change curve of a specimen subjecting to drying or wetting/absorption if consider cementitious materials as homogeneous porous media [31,53].In this study, we consider the heterogeneity of concrete microstructure, so K l as a function of porosity is resealable to assume.Following with previous studies [28,54], the Kozeny-Carman (KC) equation is used to calculate K l based on porosity.
where C K is the KC coefficient, ρ s the bulk density of dried material (~1750 kg/m 3 ), and τ the tortuosity which can be written as a function of porosity as well (τ = ϕ − 2.5 according to the Bruggeman relation [28]).Therefore, the only unknown is C K whose value depends on the material properties.This study takes C K as a fitting parameter so the simulation results were fitted to the measured mean degree of saturation under the upper steel wire to determine C K .The calculated intrinsic permeability as a function of porosity is displayed in Fig. A-1.

Fig. 1 .
Fig. 1.Illustration of the geometry and size of the specimen, (a) the front view and (b) the side view.

Fig. 2 .
Fig. 2. Schematic drawing of the in-situ neutron imaging water penetration test (a) photograph of the setup (b).

Fig. 3 .
Fig. 3. Illustration of imaging area and projected porosity.(a) the neutron imaging area (FOV) indicated by the red circle; (b) the difference between initial and saturated states of the FOV (the black area on the left-hand side in the circle is epoxy); and (c) cropped area (the red rectangle in b) with the steel wire (indicated by the white dashed lines) for image analysis.Two air voids are highlighted with red arrows.

Z
. Zhang et al. one figure, Fig. 6a clearly shows that the initially high S is only observed in the low ϕ regions.

Fig. 8 .
Fig. 8. Volumetric water content during water uptake.The black lines indicate the location of the steel wire and the black arrows show the locations of two air voids.

Fig. 9 .
Fig. 9. Comparison of measured and simulated mean degree of saturation on the surface of the upper steel wire with measured corrosion potentials for both steel wires in the sample.The measured instantaneous corrosion rates at initial condition and 36 min of water absorption are indicated in the figure.Note that the lower steel wire (dashed line) was located outside the FOV of the neutron imaging.

Fig. 10 .
Fig. 10.Porosity distribution of the simulation domain with two embedded steel wires.The enlarged figure shows the highly porous layer around the steel wire.

Fig. 11 .
Fig. 11.Simulated saturation profiles at different times.Profiles are calculated by averaging saturation in z-direction excluding the steel wire.The upper horizontal axis corresponds to y (in x-axis) in Fig. 7.

Fig. A- 1 .
Fig. A-1.Intrinsic permeability as a function of porosity calculated by KC equation.

= 2 D
∇[D a (S)∇S] (A-1)where D a (S) is diffusivity, which is a function of S.For a two-phase model, D a (S) has contributions from liquid water and water vapor,D a (S) = D l (S) + D v (S) v0 ϕ xD (1 − S) xD+2 P vs RH ϕ dP c dS (A-4)