Modeling of Corrosion Rate and Resistivity of Steel Reinforcement of Calcium Aluminate Cement Mortar

Civil Engineering School, Polytechnic University of Madrid, C/ Profesor Aranguren, s/n, Ciudad Universitaria, 28040 Madrid, Spain Spanish Institute of Cement and Its Applications (IECA), C/ José Abascal 53, 28003 Madrid, Spain Centro de Investigación y de Estudios Avanzados del IPN, Unidad Mérida, km 6 Antigua Carretera a Progreso, 97310 Mérida, YUC, Mexico I.E.S. “Enrique Tierno Galván”, C/ Camino de los Frailes, s/n, Leganés, 28911 Madrid, Spain


Introduction
Steel reinforcement corrosion is one of the major problems for a reinforced concrete structure exposed to a chloride environment.
e passivation layer is removed locally by the chloride ions when the critical chloride threshold level is achieved.Corrosion process imposes rebar cross-sectional area reduction and internal expansion promoted by the corrosion products which results in the cover concrete cracking.Particularly, corrosion of steel-reinforced concrete made of calcium aluminate cement (CAC) has been reported in Europe [1,2].For instance, in Spain, a block of flats collapsed in November 1978, resulting in several persons injured.It is estimated that about 200,000 dwellings were built in Spain between 1950 and 1970 using calcium aluminate cement (CAC) concrete.
It has been reported [3] that the lower the level of C 3 A in Portland cements, the lower the chloride ion binding capacity is.Also, the binding capacity depends on the type of the calcium aluminate hydration products such as C 3 A, C 4 AF, and C 12 A 7 [4].is binding capacity also reduces the chloride diffusion through the pore system [5].erefore, calcium aluminate cement (CAC) might provide a high binding capacity due to the high Al 2 O 3 content and reduce the corrosion rate [6].Moreover, the chloride binding capacity increases by the curing time [7].e high efficiency of CAC regarding chloride binding is also found in other ion immobilization [8].
en, a chemical process in which hexagonal phases of the cement, CAH 10 and C 2 AH 8 , turn into cubic phases, C 3 AH 6 , leads to an increase of porosity [5], and the corrosion initiation increases together with the porosity.
e above-mentioned hydrates in CAC could be converted into stable hydrates by means of a carbonation curing process without the instance of increased porosity; then, the volumetric instability of CAC is avoided [9].
As it is well known, the presence of chloride ions in the environment (sea water, salty fog, deicing salts, salty solutions, etc.) is the main promoting factor of corrosion initiation [5][6][7].Although aluminous hydrates can react with chloride ions forming chloroaluminates, the amount of remaining chloride ions in the pore solution in equilibrium could be enough to initiate signi cant reinforcement corrosion along the time [10].Currently, new corrosion protection coatings based on chloride immobilization are being studied [11].Also, bound chlorides may be released by changes in the pore solution such as pH lowering or freechloride reduction [6].It is remarkable that the corrosion rate level was found to be directly in uenced by the degree of conversion from hexagonal to cubic phases which was achieved by increasing the curing temperature [10,12].
Corrosion intensity measurements have been used over time as an accurate electrochemical parameter related to the corrosion state of the steel reinforcement in concrete.It was established that corrosion rates over a band ranged between 0.1 and 0.2 µA/cm 2 should be considered of signi cance in concrete reinforcement made of portland cement [13] and 0.1 µA/cm 2 for concrete reinforcement made of CAC cement [14].
Characteristic values of corrosion intensity (I corr ) and resistivity serve to establish the corrosion state.erefore, the knowledge of the corrosion level will be very helpful when corrosion assessment is made.e conversion process was induced by the increase of the curing temperature.e characteristic values of corrosion intensity and resistivity (expressed as ohmic drop data) of calcium aluminate cement (CAC) mortars exposed to chloride-containing environments are presented.
e scope of the present work is to set such limiting values in steel-reinforced calcium aluminate cement-based materials exposed to a wet chloride contaminated environment.e nal scope of this study is to obtain a mathematical model which lead to know the relationship between the corrosion intensity and the ohmic drop of the steel reinforcement with the water-cement ratio, curing temperature, and the environmental chloride content.

Electrochemical Measurements.
Steel rebars embedded in CAC mortars (Figure 1) were electrochemically monitored after 5 years of exposure to either a 0.5 mol/l or 1.5 mol/l NaCl solution.
ereby, corrosion intensity and ohmic drop values were measured according to [13].
2.3.XRD.Solid-phase analysis was performed by XRD by means of a Philips PW 1730 di ractometer equipped with a graphite monochromator, and Cu K α1 radiation was used over a 2θ angular range of 5-65 °, with a step size of 0.04 °at 2 s per step.

Results and Discussions
3.1.XRD Analysis.X-ray di ractograms shown in Figure 2 demonstrate that, after ve years, all the specimens su ered the complete conversion from hexagonal phases to cubic phases which are the most stable forms, and then, it is not expected any signi cant change along the time.erefore, the electrochemical parameters recorded during this period could be considered as the characteristics values of such material, which are only dependant on the mix proportions (watercement and cement-aggregate ratios) and the environmental conditions (e.g., chloride content and temperature).
e semiquantitative determination of the crystalline compounds, calculated from the intensity of re ections at 11 12 ) and gibbsite c-Al(OH) 3 re ections was detected.e intensity of the cubic phase re ections increases with time, while that corresponding to hexagonal CAH 10 decrease [6,10].e chloride binding capacity is increased not only by the curing time for calcium aluminate cements [7] but also by the curing temperature and compactness of the mortar as shown in Figure 2.  Advances in Civil Engineering found for CAC mortars for di erent mix proportions and conservation conditions.As expected, higher water-cement ratios lead to higher porosities in the cases of 40 °C and 60 °C and, therefore, lead to a higher characteristic corrosion intensities.Also, it was found that the higher the chloride content, the higher the corrosion intensity is.Corrosion intensity measurements are the most accurate electrochemical measurements related to the corrosion state of the steel reinforcement [13].erefore, a characteristic value of corrosion intensity, I corr , can be quite helpful when service life estimations are required.

Characteristic Value of Corrosion Intensity. Figure 3 presents the characteristic values of corrosion intensity
is parameter is presented as the most appropriate one because it provides very useful estimations for designing in order to establish a safe service life calculation.By using this technique, some authors have observed an inhibition e ect on the steel corrosion in CAC mortars subjected to a chloride environment [14].Also, a higher corrosion resistance in marine environments as compared to Portland cement has been found [15].

Characteristic Value of Corrosion Potential.
Corrosion potential is an electrochemical parameter related to the corrosion state of the steel (Figure 4).However, regarding the steel reinforcement of the reinforced concrete, this parameter is only useful when the real history of the Advances in Civil Engineering reinforced concrete structure is well known.If not, the measurements could be misinterpreted due to the in uence of the conditions of the surrounding mortar or concrete.e negative values of corrosion potential show that the steel rebars are corroding (Figure 4) [16].Nevertheless, this parameter cannot be used to di erentiate the relative performance of the steel in the environmental conditions considered in the present study.

Characteristic Value of Ohmic Drop.
Ohmic drop data, which are related to the resistivity of the mortar or concrete embedding the steel rebar, are in uenced by the microstructural and humidity changes in the mortar.erefore, rst of all, this parameter is a ected by the conversion reaction and the subsequent increase of porosity [5] and then by the increase of humidity in the pores and the possible penetration of some ions from the exterior.After the conversion process, resistivity or ohmic drop values tend to reach a more stable level if the environmental conditions remain constant [17], such value is the characteristic resistivity which is presented in Figure 5 as ohmic drop value, expressed as ohm•cm.
In mortars made with a water/cement ratio of 0.5, it is evident that the increase of NaCl in the solution leads to a decrease of the ohmic drop.On the contrary, the increase of temperature for every NaCl solution seems to result in a decrease of the ohmic drop.With regard to mortars made with a water/cement ratio of 0.35 and cured at 20 °C or 40 °C, these two conclusions are not clear.is fact seems to be a consequence of the more dense structure obtained in mortars made with a lower water/cement ratio.Only when these mortars (water/cement ratio of 0.35) are cured at 60 °C, the general trend observed in mortars made with water/cement ratio of 0.5 is found again.

Modeling.
A relationship between the electrochemical parameters (corrosion intensity and ohmic drop), the mix proportions (w/c ratio), and temperature and the storage conditions (0.5 M or 1.5 M NaCl solution) is obtained in the present research program.is relationship was achieved by using a factorial design of experiments, which provides an approach to the study of a process with a large number of variables involved such as reinforcement corrosion in reinforced concrete mortar or concrete.Also, it allows determining the variables having signi cant e ects on the corrosion process.e traditional experimental method changes a variable which remains constant the rest of the time, and then, data variation is attributed to the shift in that variable.erefore, this method is very time consuming, and it does not measure the interaction between several variables at a time [18][19][20].

Factorial Design of Experiments.
e variables chosen for studying the characteristic values of the corrosion intensity and ohmic drop formed eight combinations with water-cement ratios of 0.35 and 0.50, chloride contents of 0.5 M and 1.5 M, and curing temperature of 20 °C and 60 °C.
is choice was made taking into account the actual values which can be found in real cases.
en, the modi ed Box-Hunter statistical method was applied in order to have a relationship between the corrosion intensity and the ohmic drop of the steel reinforcement with the curing temperature, water-cement ratio, and the environmental chloride content.us, the designed experiment includes three variables: curing temperature, water-cement ratio, and chloride content. is kind of design includes eight experiences on the cube presented in Figure 6 (numbered spheres at the corners).en, it is formed by 8 experimental combinations corresponding to a 2 3 factorial design.
e variables were coded in order to obtain the three levels of −1, 0, and +1.e levels or values of the coded variables X 1 , X 2 , and X 3 were obtained from (1), where X 1 is the curing temperature, X 2 is the water-cement ratio, and X 3 is the chloride content:   Advances in Civil Engineering where X i is the value or level to code, X′ i is the uncoded variable, X 0 is the central value (mean value of the matrix composition), and δ is the distance between the central value and the +1 and −1 levels.e scope is to sample a reasonable range of the values of interest.If a variable is signi cant and the results show that extreme values are desirable, subsequent experiments can explore this new range.
e corresponding values of the three variables were calculated considering chloride concentrations from 0.5 M to 1.5 M, curing temperatures from 20 °C to 60 °C, and water/cement ratios from 0.35 to 0.50.ese values represent the working range proposed to study the e ect of these variables on the corrosion intensity and ohmic drop.Table 1 shows the variables used in this study, where X 1 is the curing temperature, X 2 is the water-cement ratio, and X 3 is the chloride content.erefore, the 2 3 factorial design of experiments has been de ned.(2)

In uence
However, the interactions between each of the two factors have been calculated according to the following equations: ( Finally, the interaction between all the three parameters considered is given by the following equation: e con dence interval (CI) is calculated by using ( 5) and considering a standard deviation, s, equal to 2.5 for the corrosion rate study and 150 for the ohmic drop study when an active corrosion process is onset, whereas these values are much higher if the corrosion process is not produced.e student coe cient, t, is 2.306 for 8 experiments, n, considering a con dence level of 95%: CI t s n √ . ( Main e ects and interactions between variables are shown in Table 2, where the curing temperature and the combined factor (T) (w/c) are higher than the experimental error, while the chloride content is slightly lower.is means that these two parameters (curing temperature and T × w/c) are the most important with regard to the corrosion rate of the reinforcement.In relation to the ohmic drop study, it is observed the great in uence on this parameter of the curing  Advances in Civil Engineering temperature and the water-cement ratio, considered isolated and also combined.e e ect of the chloride content is of less important when compared with the other two variables.e curvature e ect, C, is the di erence of the average of the data at the central points and the average of the factorial design experiment data, which was calculated according the following equation: e con dence interval of the curvature e ect (CICE) was calculated taking into account the total number of experiments, N, according to the following equation: e values considered in this case were s 2.5 for the I corr study and s 150 for the ohmic drop study, t 2.306, N 4, and n 8. e curvature value is lower than the interval of condence of the curvature e ect.
us, a linear model to determine the in uence between variables can be chosen; this means that it is not necessary to take into account such curvature e ect.

Modeling.
e data obtained in the corrosion intensity and ohmic drop of mortar were tted to a polynomial function (( 8) and ( 9), resp.), which allows a prediction of the experimental data as Figures 7 and 8 show: e R 2 coe cient was calculated according to (10) to evaluate the reliability of the proposed models.Such coe cient gave a reliability of about 20% for the corrosion intensity estimation and 70% for the ohmic drop one.e simulation results were compared with the experimental data, and correlation was found to be good for ohmic drop.On the contrary, a worse prediction has been found for corrosion intensity:   Advances in Civil Engineering where z i is the experimental data, z * i is the calculated data using the model, and z i is the average value, whereas n is the number of data.

Response Surfaces.
e mathematical model allows the simulation of the corrosion intensity (Figure 9) and ohmic drop (Figure 10) response in function of the variables studied.Once the system has been described with the model equation, the computer and the software facilitate the solving the model and plot the results.For example, Figure 9 shows the surfaces of response for three cases considered: (a) constant curing temperature of 20 °C, 30 °C, and 40 °C, (b) constant water-cement ratios of 0.40, 0.50, and 0.60, and (c) constant chloride content of 1 M, 1.5 M, and 2 M.
Corrosion intensity and ohmic drop data are used to assess the corrosion state of steel reinforcement in concrete.Both of them give an idea about the development of the corrosion process of the steel.is fact justi es that the same factors in uence both of them.However, the magnitude of such in uence is di erent for each property.at is, the ohmic drop is mainly a ected by the e ect of the curing temperature and the water-cement ratio, separately.Also, the combined e ect of these factors is of importance.
However, for the corrosion intensity study, it has been determined that such combined e ect is the most relevant, and the e ect of the curing temperature is also signi cant but not the isolated e ect of the water-cement ratio. is result is due to the e ect of the water-cement ratio on the capillary porosity of the material and the liquid phase contained in the pores [21], which a ect greatly the measurements of the mortar, and then is re ected in the ohmic drop measurements.
On the contrary, once the corrosion process has been initiated, the higher or lesser porosity is of less importance to the corrosion intensity.is only could be a ected in some cases by the access of oxygen from the exterior to the reinforcement.
With regard to the chloride content, it has a minor importance when the corrosion process is initiated.Only it has a signi cant in uence on the ohmic drop as a result of a decrease in the resistivity of the material due to a hygroscopic e ect and the presence of ions.e interaction of the water-cement ratio and the environmental chloride content is appreciable.

Conclusions
Based on the presented analysis, the following conclusions can be drawn: (i) e values of corrosion rate, and corrosion potential and which show a steady-state plateau in corrosion data for CAC-reinforced mortars exposed to chloride environments, have been stated.(ii) Very negative values of corrosion potential from −400 mV to −600 mV were recorded showing an active corrosion process of the steel reinforcement.However, this parameter did not allow distinguishing the magnitude of the process.By contrary, the characteristic corrosion rate of the steel depends on the combined e ect of the curing temperature and the water-cement ratio showed the main e ect interaction study and then by the isolated e ect of the curing temperature and chloride content.(iii) Factorial design methods are a useful tool to model the relation between characteristic values of I corr and ohmic drop with curing temperature, water-cement ratio, and chloride content with a quite important saving in time.However, result utilisation is limited to the experimental range considered because of the high heterogeneity of the material.(iv) High curing temperature, water-cement ratio, and chloride content ratios o er the maximum I corr .Its interactions can play in a di erent way, which justify the statistical study.erefore, further studies must be addressed to evaluate other variables or ranges.
(v) e obtained equation can predict characteristic values of I corr and ohmic drop in reinforced mortars.
From the interaction, a study can be deduced that the parameters a ecting mostly I corr are the combined e ect of the curing temperature and the water-cement ratio and then the isolated e ect of the curing temperature and the water-cement ratio.However, for the ohmic drop, the isolated e ects of the curing temperature and the water-cement ratio are the most important and a little lesser the combined e ect.Also, the chloride content has a significant relevance but of lesser in uence.

Table 2 :
Main e ects and interactions.