Cracking e ects on chloride di usion and corrosion initiation in RC …scientiairanica.sharif.edu/article_21140_4c3fc70704e38ce... · 2021. 1. 28. · Cracking e ects on chloride

Scientia Iranica A (2020) 27(5), 2301{2315

Sharif University of TechnologyScientia Iranica

Transactions A: Civil Engineeringhttp://scientiairanica.sharif.edu

Cracking e�ects on chloride di�usion and corrosioninitiation in RC structures via �nite element simulation

M. Ghanooni-Baghaa;�, M.A. Shayanfarb, and S.M.H. Farniac

a. Department of Civil Engineering, East Tehran Branch, Islamic Azad University, Tehran, P.O. Box 18735-136, Iran.b. The Centre of Excellence for Fundamental Studies in Structural Engineering, Iran University of Science and Technology, Tehran,

P.O. Box 16765-163, Iran.c. School of Civil Engineering, Iran University of Science and Technology, Tehran, P.O. Box 16765-163, Iran.

Received 1 April 2018; received in revised form 2 November 2018; accepted 13 November 2018

KEYWORDSReinforced concrete;Crack width;Crack depth;Chloride ingress;COMSOLmultiphysics.

Abstract. Chloride ion ingress into concrete causes steel corrosion over time, therebyending the service life of structures. Sometimes, it severely reduces the loading capacityof reinforced concrete and may even cause the sudden destruction of concrete structures.Concrete cracking stems from di�erent factors, such as shrinkage and tensile stress due tothermal loading and under loading. Modeling and estimating chloride ion ingress intocracked concrete over di�erent periods can facilitate the appropriate determination ofstructural lifetime and maintenance of reinforced concrete structures. Accordingly, thisresearch investigated the e�ects of the width and depth of concrete cracks on the rateof chloride ion di�usion and rebar corrosion. To this end, di�erent concrete specimenscharacterized by various cracking conditions were modeled in COMSOL multiphysics.Analytical results showed that the critical crack that reected the highest extent of chlorideingress into a speci�c region at di�erent times was not necessarily the defect with the largestthickness and depth. This �nding highlights the importance of investigating crack behaviorin the appropriate estimation of structural service life. Nevertheless, over time, considerablywide and deep cracks may ultimately be a reection of the substantial rate of ingress.© 2020 Sharif University of Technology. All rights reserved.

1. Introduction

Rebar corrosion is the most important factor in thedamage and destruction of reinforced concrete struc-tures [1]. Ignoring its possibility and progress maylead to the obsolescence of these structures and theconsiderable wastage of investments in constructionand maintenance [2,3]. Corrosion can threaten theperformance of reinforced concrete, even in the earlylife of the material [4,5]. Over time, chloride ion

*. Corresponding author.E-mail addresses: [email protected] (M.Ghanooni-Bagha); [email protected] (M.A. Shayanfar);[email protected] (S.M.H. Farnia)

doi: 10.24200/sci.2018.50496.1725

ingress or carbonation increases; in conjunction withhigh humidity, these processes enable reactions to occurbetween oxygen and moisture, thereby causing rustingin rebars and increasing the volume of steel [6,7]. Theresultant corrosion reduces and increases the area andvolume of steel, respectively; it destroys concrete coverand creates cracking, which reduces the strength of RCmembers and ends the service life of structures [8,9].Cracks create many paths for the ingress of destructiveelements into concrete and, thus, threaten the durabil-ity of concrete [10,11]. Given the complexity of chloridedi�usion into cracked concrete, appropriate estimationof the occurrence of this process in reinforced concreteis a critical issue [12].

Many researchers have studied the e�ects ofcorrosion and chloride di�usion on intact concreteblocks [13{15]. In an experimental research, Aldea et

2302 M. Ghanooni-Bagha et al./Scientia Iranica, Transactions A: Civil Engineering 27 (2020) 2301{2315

al. tested rapid chloride di�usion into concrete discssubjected to loading and tensile cracks with a thicknessof 0.05 to 0.4 mm [16]. The authors found thatchloride ingress is less sensitive to cracks in concretespecimens with typical resistance to such ingress thanthat in concrete specimens with high resistance [16].Conciatori et al. proposed a numerical model calledTransChlor on the basis of Fick's second law of di�usionand a �nite di�erence method to simulate chlorideion displacement in concrete [17]. Djerbi et al. usedcracked samples to test cracking (splitting tests) andinvestigate the e�ects of single cracks on chloride ionpenetration [18]. Their experimental results showedthat the permeability ratio of cracked segments (Dcr)reected the lack of concrete materials in the samples.The authors also discovered that permeability merelywas dependent on crack size; as crack size increased,permeability rose. For cracks with a width greater than80 �m, however, permeability remained constant [18].Jang et al. examined di�erent types of concrete withcracks that were up to 80 �m wide and identi�eda linear relationship between crack width and crackpermeability ratio in concrete characterized by cracksthat have a small width. The authors reported thatfor cracks of small widths, permeability ratio decreasedas concrete resistance increased [19]. Wang and Uedaexperimented on concrete samples with cracks thatwere 20 to 600 �m wide. The researchers indicated thatfor a crack width that exceeded the critical level (i.e.,60 �m), the amount of Dcr was no longer dependenton crack width [20]. Marsavina et al. tested specimenssimilar to concrete samples with arti�cial cracks cre-ated through the repeated placement and removal ofthin copper sheets in the samples (especially in long-term tests). The authors found that di�usion depthincreased with increasing crack depth (thicknesses ofthe arti�cial cracks in the experiments were set to 0.2,0.3, and 0.5 mm) [21]. The e�ects of crack widthremained undetermined{an issue that the researchersacknowledged as requiring further research [21]. Katoet al. proposed a mathematical model for chlorideion ingress into cracked concrete that could simulateingress under wet conditions and cyclic wet{dry condi-tions [22]. The researchers stated that in cracked seg-ments, the width of a crack dominantly inuenced therate of chloride ingress into concrete when the supply ofchloride was greater than its consumption [22]. Otherresearchers such as Otieno et al. (2016) [23,24], Wanget al. (2016) [25], and Leung and Hou (2014) [26] drewvaluable conclusions by modeling chloride ion di�usioninto cracked concrete.

Despite the insights provided by the studiesdiscussed above, they did not delve into the e�ectsof di�erent crack depths and thicknesses and theextent of concrete cover exposed to chloride di�usion.Addressing these issues can facilitate the appropriate

determination of structural lifetime and maintenanceof reinforced concrete structures. To address thede�ciency in existing research, the present study in-vestigated the simultaneous e�ects of crack width anddepth on the rate of chloride ion ingress into concreteand rebar corrosion in di�erent periods. Such e�ectswere also compared.

2. Formulating chloride di�usion

Di�usion refers to the displacement of mass, whichleads to the spread of chemical components until theyreach a uniform mode as they are displaced over time.These chemical components are combined solutionsin a solvent or components in gases such as oxygenin the air. The density of chemical components in

uid di�ers at initial stages and with the passing oftime as well as with the displacement of components.Ultimately, however, a uniform balance in the densityof uid is observed. The simplest de�nition of di�usionwas proposed through Fick's equations, which wereformulated by Adolph Fick in 1855. This de�nitionis expressed as follows [27,28]:

1. Molar ux is based on di�usion that depends on theconcentration gradient;

2. The rate of concentration changes in one pointof space, depending on the second derivation ofconcentration rather than space.

On the basis of the de�nition above, the �rst andsecond rules of di�usion were de�ned.

2.1. First law of Fickean di�usionThe �rst law of Fick in the mathematical form iswritten as follows:

Ni = �Dirci: (1)For species of i, N is the symbol of molar ux(mol.m2/s), D is the di�usion coe�cient (m2/s), and cis the amount of concentration (mol/m3).

Based on the mass continuity equation, we have:

@ci@t

+r �Ni = 0: (2)The second Fick's law directly translates into thefollowing relation:

@ci@t

= Dir2ci: (3)It is assumed here that coe�cientD is constant which iscorrect for dilute solutions; this assumption is usuallyused for di�usion inside the solids (such as chlorideion di�usion inside concrete), di�usion of chemicalmaterials into dilute solutions like water or othersimilar liquid solvents, and di�usion of dilute speciesinside gas (like di�using carbon dioxide in the air).

M. Ghanooni-Bagha et al./Scientia Iranica, Transactions A: Civil Engineering 27 (2020) 2301{2315 2303

2.2. Second law of Fickean di�usionSecond law of Fick di�usion is a linear equation ordependent variable of chemical species' concentration.Di�usion of each chemical species occurs alone. Thesetwo characteristics facilitate the proposed mass dis-placement systems by the second law of Fick fornumerical simulation. When di�usion is modeled,modeling mainly begins with this assumption that allcoe�cients of di�usion are equal and not dependent ontemperature, pressure or similar cases. These simpli�-cations lead to assuring linearity of mass displacementequations in the model area and also facilitate con-necting known analytic limits. Dimensional analysisof second Fick's law shows that in di�usion processes,the fundamental relationship between passed time andlongitudinal square is where di�usion forms in it.Perceiving this relationship is required for performingexact numerical simulations of the di�usion process.The laws of Fick di�usion have only one parameter fordetermining the speed of di�usion process and that isdi�usion coe�cient.

3. Modeling cracked concrete

3.1. Sample dimensionsThe dimensions of the 13 concrete specimens subjectedto two-dimensional modeling in this work were 300 �300 mm. As indicated in the investigation conducted inthe present research and various dimensional modelingexperiments, 300 � 300 mm ensures a good balancebetween the accuracy of results and the time devotedto analysis.

3.2. Physical and mechanical characteristicsof samples

All of the concrete specimens were modeled with aconcrete density of 2300 kg/m3, Young's modulus of25�10�9 Pa, and Poisson's ratio of 0.33. A 3% chloridesodium solution was used as the di�usion material (sur-face chloride load or Cs). The concrete characteristicsassumed for modeling are listed in Table 1. The valuesused for each crack mode were based on the fact thatthe most important parameter for the rate of sodiumchloride ingress included the characteristics of di�usionrate and that di�erent values were assigned to this

parameter in various conditions. The parameter valuesare also shown in Table 1.

3.3. Geometric characteristics of modelsThe modeling in this work was conducted by usingCOMSOL Multiphysics software [30]. Among the con-crete specimens modeled, one served as the referencespecimen with no cracking. The rest of the specimenshad crack widths of 30, 60, 100 (equivalent to a tenthof a millimeter), and 500 �m (equivalent to half amillimeter). All the cracks were modeled in the middleof the specimens. The depths of crack in specimenswere 50, 100, and 150 mm equivalent to 1/6, 1/3, and1/2 heights of the concrete specimens, respectively. Inall the models, certain rebar locations (represented bylines) were considered to obtain the desired outputsby using the software and examine and compare theresults. Each model included three vertical lines (ag,bh, and ci in Figure 1(a)) and three horizontal lines (ad,be, and cf in Figure 1(a)), which denote the possiblelocations of rebars within concrete.

3.4. Modeling softwareCOMSOL multiphysics software is a comprehensive setfor modeling. It is able to solve di�erential equationsof nonlinear systems by partial derivations throughFinite Element Method (FEM) in the spaces of 1,2, or 3 dimensional. Compared to other softwarepackages including �nite elements, the most importantadvantage of this software is the simplicity of applyingseveral di�erent physics to models. This software wasinvented by the students of Royal Institute of SwedenTechnology.

Extra-�ne mode from the defaults of software wasselected for meshing due to its high accuracy in investi-gating the results. The accuracy of this meshing (dou-ble zooming) for a speci�c sample is given in Figure 1.

3.5. Modeling validation and veri�cationIn order to validate the results of software and modelingoutput, three types of modeling were conducted usingCOMSOL Multiphysics software and the results werecompared with those of MATLAB modeling. Also,for veri�cation, the results were compared with the�ndings of Jin et al. [31] and Wang and Ueda [20].First, a sample with no crack was modeled in MATLAB

Table 1. Values of the parameters employed in modeling [29].

Parameter Calibrated value

Coe�cient of chloride di�usion into concrete 6 � 10�11 (m2/s)Di�usion coe�cient of chloride-damaged areas (between crack and concrete) 1:2� 10�9 (m2/s)Di�usion coe�cient of chloride in small cracks (width lower than 100 �m) 2� 10�9 (m2/s)Di�usion coe�cient of chloride in large cracks (width larger than 100 �m) 4� 10�9 (m2/s)Chloride concentration (3% solution of sodium chloride) 523.4 (mol/m3) pore solutionSize of damaged zone for small cracks (crack width less than 100 �m) 1 (mm)


Figure 1. (a) Reference lines and (b) Meshing of one specimen (2 � magni�cation).

Figure 2. The rate of chloride ion ingress in speci�c width sections (20, 60, 100, 140, 180, 220, and 260 mm) at the end of10 years.

and COMSOL and the di�usion rate of chloride ionwas compared in speci�c horizontal sections (20, 60,100, 140, 180, 220, and 260 mm) which showed goodagreement with each other (Figure 2). In the researchof Jin et al., �ve square concrete samples characterizedby 100 mm in height, crack widths of 10, 30, 60, 90,and 120 microns in size, and crack depth of 30 mmwere modeled. A relationship between crack di�usionrate (Dcr) and crack width was proposed, based onwhich a speci�c di�usion rate for each crack wasconsidered. Concrete samples were held under chloridepressure and a diagram was drawn for showing therate of di�usion in 10 days. Similar modeling withthe assumptions above was also done in COMSOLsoftware. Based on Figure 3, it is clear that diagramshave good consistency with each other.

In another research, considering di�usion time of

10 hours and a crack width of 60 mm, Wang andUeda [20] calculated the value of chloride density byincreasing the depth of crack based on the experimentaldata in Meso scale model of Ismail et al. [11]. Inthe simulation process, the di�usion rate of normaland cracked concretes was set to 1:1 � 10�10 m2/sand 2:76 � 10�6 m2/s, respectively. In addition,the value of surface chloride concentration equal to7:68 � 10�3 g/cm3 was considered. Through thementioned assumptions, modeling was done by usingCOMSOL software and the obtained results showedgood agreement with those of Wang and Ueda.

4. Modeling results

The e�ects of crack thickness and depth on variousparts of the concrete specimens were illuminated on


Figure 3. The rate of chloride ion ingress due to crack at the end of 10 days.

the basis of the modeling and analysis results. Inthese diagrams, the horizontal axis represents time(measured in days), and the vertical axis denotes therate of chloride di�usion (measured in mol/m3). Somepoints about all of the �gures in the following are worthdiscussing. The reference points and lines indicated inthe �gures are shown in Figure 1(a). In the analysisprocess, cracking was examined every day for the �rst50 days. From the 51st day to the �rst year, crackingwas examined every 10 days. After the �rst year up tothe 10th year, cracking was examined every 50 days.In the presentation of results, two-day �ndings overthe �rst 50 days are shown. From the 51st day to the�rst year, 20-day �ndings are presented. After the �rstyear up to the end of the 10th year, 100-day �ndings areshown. This type of presentation was adopted to ensurethe conciseness and easy interpretation of the data.In the diagrams drawn on the basis of the referencelines, the length of each line corresponds to the rate ofchloride ion ingress all around the area covered by theline. Each vertical line in a diagram represents the rateof chloride ion ingress or a speci�c width on a referenceline.

4.1. General view of chloride ion di�usion inthe modeled samples

Chloride di�usion proceeding only from the upperborders of the concrete specimens was modeled. In themodeling of di�usion into cracks, di�usion initiatingfrom crack borders was not represented and di�erentdi�usion rates were applied. As shown in Table 1, eachcracked concrete specimen was assigned three di�usionrates: the �rst related to the healthy section of thespecimen, the second associated with a crack, andthe third related to the broken segment between acrack and the healthy section of the specimen. The�nal di�usion rate normally corresponds to the largest

crack in a concrete structure; a fragile section that issmaller than a crack but larger than the healthy sectionof concrete exhibits the lowest di�usion rate. Aftermeshing and applying the parameters listed in Table 1,the analyses were carried out over 3650 days (10 years)as the period in which di�usion was examined. Theresults are shown in Figure 4(a).

The chloride concentration at the end of the3650th day is illustrated in Figure 4(a). As ex-pected, increasing crack thickness and depth elevatedthe di�usion rate. A comparison of the specimensindicated that crack thickness exerted greater e�ect onchloride di�usion than crack depth. The comparisonof chloride ingress in di�erent periods into the un-cracked specimen and the cracked specimen with acrack thickness of 500 �m and a crack depth of 150 mmis shown in Figure 4(b).

Figure 4(b) shows that during the �rst few days,the concentration of chloride from a distance aroundthe crack of the cracked specimen is less than that inthe non-cracked sample. This �nding indicated thatin the �rst few days, chloride tended to penetratemore e�ectively into a crack. In cracked segments,therefore, more chloride will penetrate into the partsclose to a crack up to a certain radius. The di�erencein the chloride penetration of cracked and un-crackedconcretes will decrease with increasing distance from acrack.

4.2. Rate of chloride di�usion on the basis oftiming with respect to reference lines andpoints

The set of diagrams displaying the rate of chloridedi�usion into each reference line or point was intendedto investigate and compare the rate of chloride concen-tration at each distance and point from the di�usionsurface and crack in various specimens. The reference


Figure 4. (a) Chloride concentration in di�erent samples on the 3650th day (end of 10 years). (b) Chloride ingress in 5and 50 days and 1, 5, and 10 years at the top of the un-cracked concrete specimen and bottom of the concrete sample witha 500 �m wide and 150 mm deep crack.

lines represent hypothetical rebars with concrete coverincluding the distance covered, and the reference pointsrepresent the locations of the hypothetical rebars.

Each vertical line in Figure 5 shows the rateof chloride ion ingress into the reference line ad (seereference lines in Figure 1(a)) from the beginning tothe end (located at the center of a specimen) of theline. The �gure indicates that di�usion over time wasnonlinear and that the di�erence among the modelscould sometimes be large or small. The 30 and 50 �mcracks generally behave in a similar manner; the sameis true for the 100 and 500 �m cracks. A considerabledi�erence in behavior occurred between the 50 and100 �m cracks primarily because of the increasingcracking zone in the specimens. Another interesting�nding is that the 50 mm distance of reference linead from the di�usion surface showed that the mostextensive di�usion occurred in the un-cracked specimenup to about the 250th day. This �nding is attributedto the tendency of chloride ions to pass through a crack

Figure 5. Comparison of the rate of chloride ion ingressinto the specimen with a 50 mm crack and the un-crackedconcrete sample (vertical reference line ad located 50 mmfrom the side of the sample).

instead of un-cracked parts. Thus, at a distance fartherfrom a cracked specimen's center (where a crack islocated), the concentration of chloride ions was initiallylower than that in the un-cracked concrete, whereingress occurred uniformly all around the surface.


Figure 6. Magni�ed version of Figure 5 (reference line ad) on the 2865th day.

Figure 6 shows a magni�ed image of chloridedi�usion on the 2865th day; the 30 and 50 �m crackswere eliminated from the �gure. The top and bottomparts of the �gure show that on the 2865th day, thehighest chloride ion concentration was observed in the500 �m crack. The chloride di�usion rates of the500 and 100 �m crack were 413 and 412 mol/m3,respectively. In the un-cracked specimen, the chloridedi�usion rate was 405 mol/m3. The lowest ratesof di�usion on the 2865th day were 216, 215, and206 mol/m3.

Figures 5 and 7 indicate that up to the �rst50 days, corrosion due to chloride ion concentrationwas the most prevalent in the un-cracked concretesample. This trend continued up to the 80th dayand declined thereafter. As previously stated, fromabout the 250th day, the cracked concrete samplesgradually showed more chloride concentration thanthe un-cracked sample. Up to the 500th day, all thecracked samples exhibited more chloride concentrationin the reference line ad than the un-cracked samplein the same reference line. On the 3600th day, atthe highest point of reference line ad, the rate ofchloride di�usion into the un-cracked concrete samplewas 418.46 mol/m3; the rate of chloride di�usion into

Figure 7. Magni�ed version of Figure 5 (specimens with30 and 100 �m cracks eliminated) for the �rst 50 days.

Figure 8a. Comparison of the rate of chloride ion ingressinto the concrete sample with a 50 mm crack andun-cracked concrete sample (reference line ag located50 mm from the top of the sample).

the concrete sample with a 500 �m wide and 50 mmdeep crack was 425.68 mol/m3.

The reference lines in Figure 8a are horizontal(line ag) and span 3 mm (from the sample center,beside the crack) to 50 mm of its edge. As illustrated inthe �gure, from the very �rst days of the observation,the samples with 100 and 500 �m cracks showed moreconcentration of chloride ions than the un-crackedsample. In the third and fourth days, all the crackedsamples showed a higher chloride concentration inreference line ag than the sample without cracks. Thisresult is ascribed to the closeness of the right side ofreference line ag to the cracks; at the time of di�usion,more chloride ions penetrated into the cracks. InFigures 8a and 8b, the black portions, which representchloride ion di�usion into the un-cracked sample, arealso represented with dotted lines because chloride ioningress from the top to the bottom of the sample wasuniform. Thus, the horizontal reference line showsonly one concentration level for this sample in di�erentperiods.

The magni�ed image of chloride di�usion on the3600th day (Figure 8a) is provided in Figure 8b.


Figure 8b. Magni�ed image of the 3600th day inFigure 8a.

The highest chloride concentration was observed inthe concrete specimen with a 500 �m crack, and thedi�usion rate was 473 mol/m3. As expected, thelowest chloride concentration was observed in the un-cracked concrete, with chloride di�using at a rate of418 mol/m3.

Each vertical line in Figure 9 represents thechloride ion ingress rate in line cf from the beginningto the end (center of a sample) of the line. Despite theincrease in crack depth, the concentration of chlorineions is generally three times less than that shown inFigure 5. This di�erence is due to increase in coverdistance of the closest probable rebar to 20 mm. Notethat despite the reference line nearing the center ofthe concrete samples (i.e., the location of cracks), thechloride di�usion rate minimally increased; however,such di�usion was lower than ever because the concretecover of the rebar was farther from the di�usion surface

Figure 9. Comparison of the rate of chloride ion ingressin the concrete sample with a 150 mm crack andun-cracked concrete sample (reference line cf located70 mm from the edge of the sample).

Figure 10. Comparison of the rate of chloride ion ingressin the concrete sample with a 70 mm crack and un-crackedconcrete sample (horizontal reference line ci located70 mm from the top of the sample).

by 20 mm. This feature exerted greater e�ect on therate of chloride ion ingress than the increase in crackdepth to 100 mm, thus resulting in rebar corrosion.An increase in rebar cover causes corrosion. Thistrend naturally depends on the distance from cracks, asdemonstrated in Figure 10, wherein the reference line,instead of vertical line cf, is represented as horizontalline ci. Each vertical line in the �gure shows the rateof chloride ion ingress into line ci.

As indicated in Figure 10, cover distance was �xedat 70 mm, but chloride ion concentration increased.This �nding reects closeness to the cracks; referenceline ci begins from the distances near the cracks.

As presented in the calculations in Figure 11, upto the 210th day, the highest concentration of chlorideions was observed in the un-cracked concrete becauseof the tendency of chloride ions to pass through cracksinstead of un-cracked segments. From about the 560thday up to the 2170th day, chloride ion concentration in

Figure 11. Comparison of the rate of chloride ion ingressin the concrete samples with a crack 100 �m wide and 50,100, and 150 mm deep and un-cracked concrete (referenceline ad located in 500 mm of the sample's left edge, itstarts from 500 mm of the sample's upper surface andcontinues to the middle of sample).


Figure 12. Comparison of the rate of chloride ion ingress in the concrete samples with di�erent crack.

the reference line ag in the specimen with a crack depthof 100 mm was higher than that in the specimen witha crack depth of 150 mm. Before and after these depthranges, chloride ion concentration was higher in deepcracks, thus con�rming the uncertainty and relativityof physical crack characteristics (depth, thickness, andcracking zone stemming from a crack) as factors indetermining the corrosion rate. For each speci�c rebarin concrete, a crack characterized by speci�c conditionsappears to be more harmful than other cracks indi�erent periods. For a more accurate comparison ofthe data discussed above, two cracking modes, namely30 and 500 �m cracks, were incorporated into themodeling.

Figure 12 shows a barely noticeable di�erence inchloride ion di�usion at various depths (50, 100, and150 mm) for the specimen with a 30 �m crack; chlorideion concentration all around the �gure indicated thatsuch concentration was higher in 100 mm cracks thanthat in 150 mm cracks (until the end of the 10thyear). This �nding demonstrates that a critical crackof speci�c length and width occurs for each type ofrebar installed in concrete; increasing each parameteris the only measure for preventing critical conditionsin such rebars. Dotted lines were incorporated intothe �gures to simultaneously investigate all the modelswith di�erent widths and depths. This approachwas necessary because the results obtained from theconnecting points of chloride concentration in eachperiod were derived from one reference point and wereall represented as curves (in the analyses, the referencepoint shown in Figure 1 is the point at which corrosionrate is calculated and represented; such a point canserve as the hypothetical location of rebars consideringcover distance).

Because the extent of corrosion in Figure 13 andother similar diagrams is very high, these diagrams canbe better analyzed through magni�ed versions of theimages.

Figure 14 suggests that based on the initial

days of observation, the reference point in the un-cracked specimen exhibited the highest chloride ionconcentration. The concentration that di�ered mostconsiderably from all the other concentrations was thatfound in the specimen with a 100 �m wide and 150 mmdeep crack. Chloride concentration was the highest inthe specimen with a 500 �m wide and 100 mm deepcrack, whereas such concentration was the lowest in thespecimen with a 30 �m wide and 150 mm deep crack(days before the 18th, Figure 14). The concentrationsshould, in practice, be very low and close to zero, butthe same cannot be said for the samples up to the 10thday. This problem stems from the inadequate accuracy

Figure 13. Chloride ion ingress into the reference point a.

Figure 14. Magni�ed version of Figure 13, zoomed imageof the �rst 100 days.


Figure 15. Magni�ed version of Figure 8b for the intervalof around 201 to 280 days.

of the daily analysis; however, because our analysisspans a long-term horizon (10 years), the aforemen-tioned inadequacy can be disregarded. As presentedin Figure 15, the un-cracked sample gradually lost thelargest proportion of chloride concentration, and somedisplacements of the cracks occurred with the highestconcentrations of chloride ions. These displacementsbegan on the 250th day and lasted until the 600thday. Beyond this period, the positions of the cracksremained �xed, and the concentration of chloride ionsin each crack steadily increased. The magni�ed versionof Figure 13, showing the scenario at the end of the 10thyear, is provided in Figure 16.

Figure 16 reveals that at the end of the 10th year,the rate of chloride ion di�usion in the reference pointwas highest at a distance of 50 mm from the top andleft sides of the modeled specimen with a 500 �m wideand 150 mm deep crack. The next highest rate ofdi�usion was observed in the specimen with a 500 �mwide and 100 mm deep crack, followed by the specimenwith the 100 �m wide and 150 mm deep crack. Onthe basis of these �ndings, a zone wherein the di�usionlevel is relatively close (meeting the distance of concretecover), the width of cracks is a more important factor incorrosion than the depth of cracks. This conclusion canbe con�rmed by a comparison of the images of referencepoint c, which is located 700 mm away from the top and

Figure 16. Chloride ion concentration in the referencepoint a.

Figure 17. Chloride ion concentration in the referencepoint c, zoomed image of the interval of 20 to 75 days.

left sides of the modeled specimens. The sample witha 30 �m wide and 50 mm deep crack di�ered slightlyfrom the specimen with a 50 �m wide and 50 mm deepcrack, with the former exhibiting the lowest chloridedi�usion. The un-cracked sample had the least chlorideion di�usion.

Magni�cation was repeated for the referencepoint c (Figure 17).

Figure 17 shows that at the interval between the20th and 75th days, many displacements occurred inthe samples that registered the highest concentrations,and many irregularities were observed in the curvesthat reect the highest chloride concentrations. Inthis instance, the un-cracked sample did not have thehighest chloride ion concentration from the very �rstdays of the observation. This �nding is ascribed to thereference point being close to the cracks. Ultimately,because more chloride ions penetrate along the cracks,the un-cracked specimen exhibited the highest chlorideion concentration in the reference point c for a short du-ration at the interval between the 70th and 120th days.After this period, however, concentration soon de-creased. Chloride ion concentration in the un-crackedspecimen ultimately reached its lowest level aroundthe 320th day. Since then, the displacement trendstabilized up to the 10th year, as shown in Figure 18.

Figures 17 and 18 di�er in that chloride ion

Figure 18. Chloride ion concentration in the referencepoint c at the end of the 10th year.


Figure 19. Chloride ion ingress into the reference point f .

concentration in the former is generally lower than thatin the latter; they are similar (only partially di�erent)in terms of the location of cracks toward one another.The concentration in the reference point c was lowerthan that in the reference point a, indicating thatdi�usion occurred only from the upper surface of thesample and that despite the 20 mm closeness of thereference point c to the cracks, it was located far fromthe di�usion level (upper surface) by about 20 mm.As mentioned earlier, cover corrosion (at a distancefrom the di�usion surface and edge) is one of the mostimportant factors in preventing rebar corrosion.

Reference point f (distances of 70 and 150 mmfrom the left and upper surfaces of the specimens,respectively) is illustrated in Figure 19. Unlike theother �gures, this one does not reect numerous irreg-ularities among the cracks' curves. When a referencepoint is located at an adequate distance from bothdi�usion surfaces and cracks, the irregularities of thetwo previous modes will occur less frequently; whena reference point is close to both di�usion surfacesand cracks, more displacements will occur. Thesephenomena con�rm that only one or some criticalcracks exist for each rebar in a speci�c period (crackwith the highest chloride concentration); such cracksdo not necessarily have the largest width or depth.

Figure 19 shows that the specimen with a 100 �mwide and 150 mm deep crack had less chloride concen-tration than that found in the specimen with a 500 �umwide and 150 mm deep crack. This result contrastswith that derived for the two previous modes and showsthat when a reference point is far from a speci�c zonebut near a di�usion surface and crack (in contrast tothe situation in the two previous modes), crack depthis a more important factor than crack width.

Figures 20 and 21 compare three reference points(a, b, c) in the un-cracked concrete specimen, thespecimen with a 500 �m wide and 150 mm deep crack(Figure 20), and the specimen with a 500 �m wide and50 mm deep crack (Figure 21).

Figures 20 and 21 show that the un-crackedsample, in which the reference point was 70 mm away

Figure 20. Comparison of chloride ion ingress into thereference points a, b, and c in the un-cracked sample andthe sample with a 500 �m wide and 50 mm deep crack.

Figure 21. Comparison of chloride ion ingress into thereference points a, b, and c in the un-cracked sample andthe sample with a 500 �m wide and 150 mm deep crack.

from the top and left sides of the sample (concretecover of 70 mm or reference point c), exhibited thelowest concentration of chloride ions. These �guresalso indicate that the reference point a had the highestchloride concentration, highlighting the importance ofconcrete cover in preventing chloride ion ingress.

Figures 22 and 23 show noteworthy points re-garding the cracks; these points were nearer to thecracks than the points illustrated in the previousdiagrams. As can be seen from Figure 22(a), at aroundthe time intervals, no speci�c displacement occurredamong the lines{a �nding that contrasts with thosepresented in the previous diagrams. This is becausethe reference point was very close to the crack andthe di�usion surface and because reference point g wasclose enough to the cracks with less depth (unlike,for example, reference point i, which was somehowfar from the cracks with a depth of 50 mm). Thus,everything was advanced as expected, and a crack wasmore critical from the beginning of the observationto the 10th year, during which the cracks exhibitedthe greatest thickness and depth near point g (crackswith a depth of 50 mm). In the entire analysis,the lowest chloride ingress rate occurred in the un-cracked sample; the other specimens were cracked in


Figure 22. Comparison of chloride ion ingress into the reference point g in the (a) initial days of observation (zoomed)and (b) in all analysis periods.

Figure 23. Comparison of chloride ion ingress into the reference point i: (a) in all analysis periods, (b) initial days ofobservation (zoomed), and (c) �nal days of observation (zoomed).

accordance with the importance of thickness and depthfactors. The accuracy of this problem can be clari�edwhen the reference point examined was changed fromg to i. As seen in Figure 23(c), despite the referencepoint being located at a horizontal distance from thecracks, some irregularities and displacements occurred,similar to the situation seen within the initial days ofobservation. This �nding is attributed to the fact that

the reference point was located far from the di�usionpoint. However, because point i was still close to thecracks, the trend of irregularities somehow ended atthe end of the �rst year. Figure 23(a) shows that thecracked concrete sample with the greatest thicknessand the crack depth nearer to reference point i (i.e.,100 mm) was the specimen that exhibited the criticalcrack, as expected.


5. Conclusions

A numerical simulation study was conducted to evalu-ate e�ects of cracks on chloride di�usion and corrosioninitiation in RC structures, and the following result wasobtained:

All the �gures show that the most important factorin chloride ion ingress into the concrete samples wasthe distance from the di�usion surface. Given thatsuch ingress causes rebar corrosion in the reinforcedconcrete, concrete cover is a critical factor in theanalysis of chloride ingress and rebar corrosion;

Over time, critical cracks do not always occur inspeci�c parts of the concrete samples. In a speci�clocation and di�erent times, critical cracks werenot necessarily those with the greatest thicknessand depth. Nevertheless, over time, considerablywide and deep cracks may ultimately reect thesubstantial ingress rate;

Generally, crack thickness exerted more e�ects thancrack depth on the rate of chloride ion di�usion andon relatively far points from the cracks. When thereference points were relatively close to the cracks,however, crack depth was the more important fac-tor. Depending on the closeness of rebars, rebarcorrosion can increasingly accelerate under a crackdepth and rebar location that is conducive to suchcorrosion. The insight derived from the �ndings isthat depending on rebar location in the reinforcedconcrete, the critical depth of a crack is not basedon the greatest depth, but on the correspondencebetween crack depth and rebar location;

Crack thickness exerted more e�ects than crackdepth in most of the modes (time or location). This�nding is attributed not only to crack thickness,for which the importance of a cracked zone wasdemonstrated, but also to the increase in crackthickness. Under this situation, the thickness ofa cracked zone also increased, thereby leading toincreased chloride ion ingress into concrete;

In the points relatively far from the cracks, the un-cracked sample, up to a noticeable period, registeredthe highest chloride ion concentration. This phe-nomenon is due to the fact that when concrete isun-cracked, chloride ion ingress into concrete andits entire surface is almost the same. Crackingtypically penetrates concrete from the weak sideof the material, thus ensuring the relative safetyof points farther from cracks against chloride ioningress as time passes;

To determine the initiation of corrosion, criticalchloride concentration should be used as a factorof analysis. This issue was not covered in thisresearch. To compare concrete zones on the basis

of distance from a di�usion surface and a crack,the time at which the approximate concentrationin the studied zones is reached can be comparedwith half of the surface chloride loading rate. Inthe reference point a, which represents the pointsrelatively near the di�usion level (or meeting thethickness of concrete cover), the time at which halfof the surface chloride loading rate is reached forall the cracks is around the 500th day, with littledi�erence occurring among the cracks. In pointf , which represents the points relatively far fromthe cracks and di�usion surface, this phenomenonoccurred for the specimens with a 100 �m wide and100 mm deep crack exactly at the end of the 10thyear. For the 100 and 500 �m cracks with a depthof 150 mm, the chloride ion concentration was littlemore than half of the surface chloride loading rate;for the other cracks, the chloride concentration wasslightly less than the chloride loading rate. Forthe point g, which represents the points close tothe di�usion surface and cracks, the specimens withthe 100 and 500 �m cracks at a depth of 50 mm,half of the surface chloride loading rate was reachedaround the 50th day. For the un-cracked sample,this rate was reached around the 500th day. Forthe rest of the specimens, this rate was reached inthe days between the 50th and 500th days. Finally,the surface chloride loading was reached for point i,which was near the cracks and far from the di�usionsurface, around the 400th day in the sample with a500 �m wide and 100 mm deep crack; for the un-cracked sample, this rate was reached on the 1000thday; for the rest of the specimens, the rate wasreached in the days between the 400th and 100thdays.

References

1. Neville, A.M., Properties of Concrete, Fourth andFinal Edition Standards, Prentice-Hall, Incorporated,Englewood Cli�s, NJ USA (1996).

2. MacGregor, J.G., Reinforced Concrete: Mechanics andDesign, Prentice-Hall, Incorporated, Englewood Cli�s,NJ USA (1992).

3. Dhinakaran, G. and Sreekanth, B. \Physical, mechan-ical, and durability properties of ternary blend con-crete", Scientia Iranica, 25(5), pp. 2440{2450 (2018).

4. Tuutti, K. \Service life of structures with regard tocorrosion of embedded steel", Special Publication, 65,pp. 223{236 (1980).

5. Priyanka, C., Vijayalakshmi, B., Nagavalli, M., andDhinakaran, G. \Strength and durability studies onhigh volume readymade ultra�ne slag based highstrength concrete", Scientia Iranica, 26(5), pp. 2624{2632 (2019).


6. Shayanfar, M.A., Barkhordari, M.A., and Ghanooni-Bagha, M. \E�ect of longitudinal rebar corrosionon the compressive strength reduction of concrete inreinforced concrete structure", Advances in StructuralEngineering, 19(6), pp. 897{907 (2016).

7. Shayanfar, M.A., Barkhordari, M.A., and Ghanooni-Bagha, M. \Probability calculation of rebars corrosionin reinforced concrete using css algorithms", Journal ofCentral South University, 22(8), pp. 3141{3150 (2015).

8. Ghanooni-Bagha, M., Shayanfar, M.A., Shirzadi-Javid, A.A., and Ziaadiny, H. \Corrosion-inducedreduction in compressive strength of self-compactingconcretes containing mineral admixtures", Construc-tion and Building Materials, 113(1), pp. 221{228(2016).

9. Ghanooni-Bagha, M., Shayanfar, M.A., Reza-zadeh,O., and Zabihi-Samani, M. \The e�ect of materials onthe reliability of reinforced concrete beams in normaland intense corrosions", Journal of Eksploatacja INiezawodnosc, 19(3), pp. 393{402 (2017).

10. Rahmani, K., Ghaemian, M., and Hosseini, A. \Ex-perimental study of the e�ect of water to cement ratioon mechanical and durability properties of nano-silicaconcretes with polypropylene �bers", Scientia Iranica,26(5), pp. 2712{2722 (2018).

11. Ismail, M., Toumi, A., Fran�cois, R., and Gagn�e,R. \E�ect of crack opening on the local di�usionof chloride in cracked mortar samples", Cement andConcrete Research, 38(8), pp. 1106{1111 (2008).

12. Ismail, M., Toumi, A., Francois, R., and Gagn�e, R.\E�ect of crack opening on the local di�usion ofchloride in inert materials", Cement and ConcreteResearch, 34(4), pp. 711{716 (2004).

13. Shayanfar, M.A., Barkhordari, M.A., and Ghanooni-Bagha, M. \Estimation of corrosion occurrence in RCstructure using reliability based PSO optimization",Periodica Polytechnica, Civil Engineering, 59(4), pp.531{543 (2015).

14. Andrade, C., Alonso, C., and Molina, F.J. \Covercracking as a function of bar corrosion: Part I-Experimental test", Materials and structures, 26(8),pp. 453{464 (1993).

15. Suryavanshi, A.K., Swamy, R.N., and Cardew, G.E.\Estimation of di�usion coe�cients for chloride ionpenetration into structural concrete", Materials Jour-nal, 99(5), pp. 441{449 (2002).

16. Aldea, C.M., Shah, S.P., and Karr, A. \E�ect of crack-ing on water and chloride permeability of concrete",Journal of Materials in Civil Engineering, 11(3), pp.181{187 (1999).

17. Conciatori, D., Sadouki, H., and Bruhwiler, E.\Capillary suction and di�usion model for chlorideingress into concrete", Cement and Concrete Research,38(12), pp. 1401{1408 (2008).

18. Djerbi, A., Bonnet, S., Khelidj, A., and Baroghel-Bouny, V. \Inuence of traversing crack on chloridedi�usion into concrete", Cement and Concrete Re-search, 38(6), pp. 877{883 (2008).

19. Jang, S.Y., Kim, B.S., and Oh, B.H. \E�ect of crackwidth on chloride di�usion coe�cients of concrete bysteady-state migration tests", Cement and ConcreteResearch, 41(1), pp. 9{19 (2011).

20. Wang, L. and Ueda, T. \Mesoscale modelling of thechloride di�usion in cracks and cracked concrete",Journal of Advanced Concrete Technology, 9(3), pp.241{249 (2011).

21. Marsavina, L., Audenaert, K., De Schutter, G.,Faur, N., and Marsavina, D. \Experimental and nu-merical determination of the chloride penetration incracked concrete", Construction and Building Materi-als, 23(1), pp. 264{274 (2009).

22. Kato, E., Kato, Y., and Uomoto, T. \Developmentof simulation model of chloride ion transportationin cracked concrete", Journal of Advanced ConcreteTechnology, 3(1), pp. 85{94 (2005).

23. Otieno, M., Beushausen, H., and Alexander, M.\Chloride-induced corrosion of steel in crackedconcrete-Part I: Experimental studies under acceler-ated and natural marine environments", Cement andConcrete Research, 79, pp. 373{385 (2016).

24. Otieno, M., Beushausen, H., and Alexander, M.\Chloride-induced corrosion of steel in crackedconcrete-Part II: Corrosion rate prediction models",Cement and Concrete Research, 79, pp. 386{394(2016).

25. Wang, J., Basheer, P.M., Nanukuttan, S.V., Long,A.E., and Bai, Y. \Inuence of service loading andthe resulting micro-cracks on chloride resistance ofconcrete", Construction and Building Materials, 108,pp. 56{66 (2016).

26. Leung, C.K. and Hou, D. \Numerical simulation ofchloride-induced corrosion initiation in reinforced con-crete structures with cracks", Journal of Materials inCivil Engineering, 27(3), p. 04014122 (2014).

27. Crank, J., The Mathematics of Di�usion, OxfordUniversity Press, Oxford, England (1979).

28. Poulsen, E. and Mejlbro, L., Di�usion of Chloride inConcrete: Theory and Application, CRC Press, BocaRaton, FL, USA (2010).

29. Bentz, D.P., Garboczi, E.J., Lu, Y., Martys, N.,Sakulich, A.R., and Weiss, W.J. \Modeling of theinuence of transverse cracking on chloride penetrationinto concrete", Cement and Concrete Composites, 38,pp. 65{74 (2013).

30. Comsol Multiphysics. See Wikipedia, Bluebook,https://en.wikipedia.org/wiki/COMSOL Multiphysics(History), \Navier-Stokes equations", Cyclopedia(2016).

31. Jin, W.L., Yan, Y.D., and Wang, H.L. \Chloridedi�usion in the cracked concrete", Fracture Mechan-ics of Concrete and Concrete Structures-Assessment,Durability, Monitoring and Retro�tting of ConcreteStructures, pp. 880{886 (2010).


Biographies

Mohammad Ghanooni-Bagha received PhD degreein Structural Engineering at Iran University of Scienceand Technology in 2015. Now, he is an AssistantProfessor in East Tehran Branch, Islamic Azad Uni-versity, Tehran, Iran. His research interests includedurability prediction of concrete structure, reliabilityanalysis, seismic rehabilitation, optimal structural con-trol, wavelet analysis and health monitoring, active andsemi-active dampers, and meta-heuristic.

Mohsen Ali Shayanfar received PhD degree atMcGill University in 1995. Now, he is an AssociateProfessor at Iran University of Science and Technology,

Tehran, Iran. His research interests include nonlinear�nite element Method, reliability analysis, durabil-ity prediction of concrete structure, seismic rehabil-itation, optimal structural control, wavelet analysisand health monitoring, construction management, andmeta-heuristic.

Seyed Mohammad Hossein Farnia received MScdegree at Iran University of Science and Technology,in 2016. Now, he is a Research Assistant at therehabilitation research center in Iran University ofScience and Technology, Tehran, Iran. His researchinterests include durability design of concrete struc-ture, reliability analysis, seismic rehabilitation, waveletanalysis, and health monitoring.

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Cracking e ects on chloride di usion and corrosion initiation in RC …scientiairanica.sharif.edu/article_21140_4c3fc70704e38ce... · 2021. 1. 28. · Cracking e ects on chloride