Research ArticleDetermination of the Transport Properties of StructuralConcrete Using AC Impedance Spectroscopy Techniques
Lipeng Wu Peng Dai and Yong Li
School of Civil Engineering Shijiazhuang Tiedao University Shijiazhuang 050043 China
Correspondence should be addressed to Lipeng Wu lipengwuoutlookcom
Received 11 July 2016 Accepted 5 October 2016
Academic Editor Song Han
Copyright copy 2016 Lipeng Wu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
All over the world particularly in severe environmental conditions there are reinforced concrete structures that developnonnegligible phenomena of durability problems Most of the durability problems are related to hazardous substances invasionBoth engineering practice and scientific studies have revealed that the transport property of near-surface concrete is a main factorin the durability of concrete structures Among many transport parameters the chloride ion diffusion coefficient is the mostimportant one which provides important information on material design and service life prediction In this paper AC impedancespectroscopy technology was employed in the measurement of chloride ion diffusion coefficient The relationship betweenmesostructure parameters and chloride ion diffusion coefficient was deduced by introducing a reasonable equivalent circuit modelTaking into account the conductivity difference caused by various cementitious material systems the diffusion coefficient can becorrected and a diffusion coefficient determination method based on AC impedance spectroscopy technique was established Forthe convenience of application a relationship between the newly proposed method and a widely recognized standard method wasobtained The proposed method can be applied to laboratory testing and establishes the theoretical basis for field tests
1 Introduction
Durability of concrete structures is one of the unsolvedproblems in the field of civil engineering and is an interna-tional research concern [1] Durability problems are largelycaused by the intrusion of external hazardous substanceswhich means that the transport property of near-surfaceconcrete is an important aspect that affects durability [2] Agenerally accepted fact is that transport property is essentiallydetermined by the mesostructure
Concrete is a typical porous material Its pore systemincludes C-S-H gel pores capillary pores microcracks andmicropores Many ions such as Ca2+ Na+ K+ OHminus Clminusand SO4
2minus exist which constitute a complex dynamicelectrochemical system Under AC excitation the systemexhibits a characteristic of a resistor-capacitor combinationand themesostructure can be studied by usingAC impedancespectroscopy
To separate the desired mesostructure parameters frommeasured impedance data researchers have proposed anumber of equivalent circuit models [3ndash8] Some model
parameters can be obtained through numerical fitting byusing measured data and a preset equivalent circuit modelThese parameters can be used as quantitative characterizationof the mesostructure and hydration degree of cement-basedmaterial
2 Concrete Mesostructure and EquivalentCircuit Model
The selected scale should not be small when consideringthe role of pores in ion diffusion The C-S-H gel pore doesnot contribute to permeability Therefore only the capillarypores and the pores between C-S-H gels were consideredBasically three conduction pathways exist for alternatingcurrent in concrete that is continuous conduction dis-continuous conduction and the so-called ldquoinsulatingrdquo con-duction paths The continuous conduction path is a seriesof connected capillary pores or connected microcracks Ifthe pore connectivity is cut off by cementitious material orits hydration products the discontinuous conduction path
Hindawi Publishing CorporationJournal of EngineeringVolume 2016 Article ID 2630186 8 pageshttpdxdoiorg10115520162630186
2 Journal of Engineering
Discontinuous conduction path
Discontinuous point
ldquoInsulatingrdquo conduction path
Continuous conduction path
CDP RCP
Cmat
RCCP
Figure 1 Concrete mesostructure for AC conducting
C1 C2
R1 R2
Figure 2 Converted equivalent circuit
is formed In addition to continuous and discontinuousconduction paths isolated cementitious material particlesand their hydration products or even the entire solid concreteblock can also be conductive for alternating current Based onthe above considerations the concrete mesostructure for ACconducting can be described in Figure 1
The equivalent circuit model that corresponds to Figure 1can be expressed as
1119885 =11198851 +11198852 +11198853 (1)
where 1198851 is the impedance of the ldquoinsulatingrdquo conductionpath1198851 = 1(119895120596119862mat) and 119862mat is the capacitance of the testblock 1198852 is the impedance of the discontinuous conductionpath that is the sum of the capacitance of the discontinuouspoint and the resistance of the cut-off continuous conductionpath 1198852 = 119877CP + 1(119895120596119862DP) 119877CP is the resistance of the cut-off continuous conduction path and 119862DP is the capacitanceof discontinuous point and1198853 is the resistance of continuousconduction path 1198853 = 119877CCP
According to basic circuit theory the equivalent circuitdescribed in (1) can be converted to a circuit shown inFigure 2
The conversion relationship of the two equivalent circuitsis shown in
Figure 3 Nyquist plot of the equivalent circuit model shown inFigure 2
A parallel combination of a capacitor and a resistor pro-duces a semicircle in theNyquist plotTherefore two semicir-cles should appear on the plot of the equivalent circuit shownin Figure 2 Figure 3 shows the relationship between the resis-tance parameters and the location and size of the semicircles
Taking into account the second equation in (2) the resis-tance of the continuous conduction path is the intersectionpoint of the right semicircle with the real axis Howeverthe Nyquist plot of the measured impedance of cement-basedmaterials does not have two semicircles but often onlya semicircle appears Figure 4 is a typical Nyquist plot ofconcrete the concrete composition was 233 Kg silica fume4427 Kg normal Portland cement 750Kg sand 1125 Kggravel 1864 Kg water so 119908119887 = 04 the test age is 28 d
The left arc does not occur which indicates that 1198620 ismuch less than 1198621 Thus the diameter of the left arc is verysmall with respect to the right arc and therefore the left arcis not visible Cabeza et al [3 7] proved this point Thusthe equivalent circuit can be further simplified as shown inFigure 5 which also shows the corresponding Nyquist plot
The above discussion indicates that 119877CCP which is theparameter that characterizes the interconnecting porositythat is most relevant to permeability can be linked withmeasured impedance spectroscopy
Journal of Engineering 3
10MHz
1MHz
40Hz
0
100
200
300
400
500
600
minusZ
998400998400(o
hm)
100 200 300 400 500 600 700 8000
Z998400 (ohm)
Figure 4 High-frequency range Nyquist plot of typical concrete
C1
R1
R0
(a) Further simplified equivalent circuit
0
100
200
300
400
500
minusZ
998400998400(o
hm)
200 400 600100 500300 700
Z (ohm)
(b) Corresponding Nyquist plot of the simplified equivalent circuit
Figure 5 Further simplified equivalent circuit and its Nyquist plot
3 Relationship between AC ImpedanceParameters and Permeability
The relationship between AC impedance parameters andpermeability can be established in two ways An empir-ical relationship between the two can be mathematicallyregressed by conducting a large number of experimentsHowever the disadvantage of this approach is the lack ofreliable theoretical basis Another way to derive some kindof quantitative relationship between the two is through theo-retical derivation This paper adopted the latter approach
Einstein and Smoluchowski presented an equation onthe diffusion of charged particles in solution in 1905 and1906 respectively this equation is known as the EinsteinndashSmoluchowski equation [9] which is shown as follows
where 120583119902 is the ion mobility (m2(Vsdots)) 119896119861 is the Boltzmannconstant (138 sdot 10minus23 JK) q is the charge carried by ions(C) and 119879 is the absolute temperature (K) Through therelationship among the Boltzmann constant the Avogadroconstant (119873119860) the Faraday constant (119865) the elementaryelectric charge (119890) and the universal gas constant (119877) thatis 119896119861 = 119877119873119860 119865 = 119890119873119860 and 119902 = 119911119894119890 where 119911119894 is the absolutevalue of valence (4) was obtained
As for the most significant chloride ion diffusion coef-ficient 119863Clminus which is directly relevant to the durability ofreinforced concrete structures (4) can be specifically writtenas [9]
To use (5) a certain concentration of chloride solutionmust be introduced and chloride ion mobility must be con-sidered InAC impedance spectroscopy testing themeasuredresistance (or resistivity conductivity) is a result of the jointaction of various ions in a pore solution To obtain thechloride ion diffusion coefficient the contribution of chlorideions to the conductance needs to be separated from the totalconductance To achieve this a 1molL NaCl solution wasused to saturate a concrete test block to weaken the influenceof other existing ions Thus the conductivity expression 120590 =119865sum119911119894120583119894119862119894 where119862119894 is the concentration and 119911119894 is the activitycoefficient (119911119894 = 1) can be written as
To further differentiate the contribution of chlorideions and sodium ions to the conductance the contributionpercentage of chloride ions is 61 which is close to thatof an infinitely diluted sodium chloride solution (604)under the conditions of 25∘C and 1molL concentrationthis information was verified by consulting a chemistryhandbook Combining (5) and (6) obtains
Taking into account the relationship between resistance(120588) conductivity (120590) and cell constant (119886 = 119897119860 where 119897 isthe thickness of the test block and119860 is the contact area of theelectrode and the test block) (8) is obtained
120590 = 1120588 =119886119877CCP (8)
4 Journal of Engineering
Table 1 Chemical compositions of cement and mineral admixtures ( by weight)
In (9) the influences of other ions on chloride ion dif-fusion coefficient determination have been largely removedTo further eliminate these effects some pastes (water-binderratio = 10) were prepared and the cementitious material thatwas used is as follows fly ash + Portland cement (cementreplacement level is 20 40 and 60 resp) slag +Portland cement (cement replacement level is 25 50 and75 resp) and silicon fume + Portland cement (cementreplacement level is 5 10 and 15 resp) The chemicalcompositions of cement and mineral admixtures are listed inTable 1
A conductivity cell with a length of 692 cm and anelectrode area of 962 cm2 was also made This experimentaims to investigate the influence of different pore solu-tions caused by different cementitious materials used onconductance Strictly speaking to carry out pore solutionconductivity tests the pore solution should be squeezed outof the concrete block However given the complexity of therequired equipment and the limited amount of the extractedpore solution this research adopted the simulation approachbymeasuring highwater-binder ratio paste that was preparedby using various cementitiousmaterials Before the age of 7 dthe paste will not solidify by shaking the container severaltimes every day The paste solution was shaken for 5 minutesthe day before the test and then left undisturbed for 24 hThen the upper solution was taken and injected into theconductivity testing cell The frequency of the alternatingcurrent is 2000Hz and the test ages are 28 and 90 d Figure 6shows the test results
Figure 6 shows that the addition of mineral admixturesreduces the concrete pore solution conductivity As gen-erally accepted the most important factor that influencespermeability is connected porosity rather than pore solutionconductivity To further eliminate the influence of other ionsonAC impedance testing for chloride iondiffusion coefficientdetermination a correction factor can be introduced Toperform this step the correction factor of ordinary Portlandcement concrete can be set as a benchmark For concrete thatuses other cementitious materials the correction factor maybe determined by interpolation in accordance with Table 2
000012
000010
000008
000006
000004
000002
000000
Con
duct
ivity
(Sm
minus1 )
28 90
Age (day)
100 cem25 sg50 sg75 sg20 fa
40 fa60 fa5 sf10 sf15 sf
Figure 6 Conductivity value of different paste solutions
Table 3 shows the concrete mix that was used in the experi-ment
First Φ100mm times 300mm cylinder test blocks wereprepared for the experiment Steel mold was removed oneday after pouring and then concrete cylinders were curedfor 28 or 90 d before being cut into Φ100mm times 50mmblocks for vacuum saturation (using 1molL NaCl solutionthe saturating regime is the same as that of ASTM C1202)
Then a 100mm times 100mm stainless steel plate wasadopted as the electrode To ensure close contact betweenthe electrodes and the concrete surface soaked filter papers(using 1molL NaOH solution) were introduced Prepressurewas applied to the electrodes by using screw caps Agilent4294A precision impedance analyzer was employed (seeFigure 10) and the test frequency is 40Hz to 40MHz Five
Journal of Engineering 5
Table 3 Concrete mix
Specimen number Materials used (unit kgm3)Cement Fly ash Slag Silicon fume Water Fine aggr Coarse aggr
test points were measured for each order of magnitude Thetest block electrode electrode installation and impedanceanalyzer are shown in Figures 7ndash9 respectively
Figure 11 shows the AC impedance spectroscopy testresult of the C0 test block (90 d)
To verify the validity of the measured impedance dataa validation check by using linear KramersndashKronig test [10]
In Figure 12 the abscissa axis represents the frequencyand the ordinate axis on both sides represents the residuals
6 Journal of Engineering
10MHz
1MHz
40Hz
200 400 600 800 1000 1200 14000
Z998400 (ohm)
0
200
400
600
800
1000
minusZ
998400998400(o
hm)
Figure 11 Nyquist plot of spectroscopy test results of specimen number C0
Z998400
Z998400998400
minus2
minus1
0
1
2
3
Resid
uals
()
10 20 30 405 15 25 35Data point
(a) Specimen number C0 90 dZ
998400Z
998400998400
minus2
minus1
0
1
2
Resid
uals
()
10 20 30 40Data point
(b) Specimen number FA2 90 d
Z998400
Z998400998400
10 20 30 40 50Data point
minus08
minus06
minus04
minus02
00
02
04
06
08
Resid
uals
()
(c) Specimen number GS2 90 dZ
998400Z
998400998400
10 20 30 40 50Data point
minus15
minus10
minus05
00
05
10
Resid
uals
()
(d) Specimen number SF2 90 d
Figure 12 Validation results
Journal of Engineering 7
of Voigt model fitting Equation (10) is used to calculate theresiduals
Residuals (Re119885) = (119885Re minus 119885Re-cal)2
1198852Re
Residuals (Im119885) = (119885Im minus 119885Im-cal)21198852Im
(10)
where 119885Re and 119885Im are real part and the imaginary part ofthe measured impedance respectively and119885Re-cal and119885Im-calare the fitted values obtained by using the Voigt model Smallresiduals correspond to better validity
Only measured data that passed the KramersndashKronig testcan be used for further numerical fitting Figure 12 showsthat the obtained impedance data shows good validity whichcan be attributed to the measures employed in this sectionMoreover the repeatability of the test data is good becauseof reliable close contact between the test block and theelectrodes
Parameters 1198770 1198771 and 1198621 can be obtained throughnumerical fitting of the measured impedance data and thepreset equivalent circuit shown in Figure 5 The chloride iondiffusion coefficient can be calculated by using119877CCP = 1198770+1198771and (9)
The method of determining chloride ion diffusion coeffi-cient based on the AC impedance technique is performed asfollows
(1) Prepare Φ100mm times 50mm specimens and conductvacuum Clminus saturating using 1molL NaCl solution(the saturating regime is the same as that of ASTMC1202)
(2) Carry out AC impedance testing to obtain impedancespectroscopy data
(3) Perform data validation(4) Obtain 119877CCP from equivalent circuit fitting(5) Calculate chloride ion diffusion coefficient using (9)(6) Modify the diffusion coefficient according to the
cementitious material that was used
The rapid chloride permeability test ASTM C1202 hasbeen adopted as national standard by many countriesincluding China the United States and Canada The ASTMC1202 method specifies the rating of chloride permeability ofconcrete based on the charge passed through the specimenduring 6 h of testing period ASTM C1202 tests that use thesame concrete blocks were conducted to perform a compar-ison Figure 13 shows the relationship between chloride iondiffusion coefficients obtained from impedance-based tech-nology and 6 h electric flux A linear correlation (119876C1202 =930 times 119863Clminus ) between the rapid chloride permeability testand the proposed method was obtained with a correlationcoefficient of 09 see Figure 13 for details
As can be seen from Figure 13 some data points devi-ate from the straight line As reported by Shi [11] theASTMC1202 method is virtually a measurement of electricalconductivity of concrete which depends on both the pore
Testing resultLinear fit
0
1000
2000
3000
4000
Char
ge p
asse
d (C
oulo
mb)
1 2 3 4 50
DClminus (10minus12 m2sminus1)
Figure 13 Relationship between chloride ion diffusion coefficientusing ACIS and 6 h electric flux from ASTM C1202 tests
structure characteristics and pore solution chemistry ofconcrete Supplementary cementing materials such as silicafume fly ash and ground blast furnace slag may have asignificant effect on the chemistry or electrical conductivityof pore solution depending on the alkali content of the sup-plementary cementing material replacement level and agewhich has little to do with the chloride permeability ASTMC1202 method is susceptible to pore solution conductanceHowever the proposed method eliminates the effect of poresolution conductivity on permeability by using a carefullydesigned technique This effect may be an important reasonfor the moderate correlation between the two methods
5 Conclusions
(1) High-frequency AC impedance spectroscopy can reflectthe mesostructural properties of materials which enables usto indirectly study the permeability of concrete An equiva-lent circuit model with a clear physical meaning was adoptedthrough an investigation of AC conduction paths in concreteThrough numerical fitting of theNyquist plot of themeasuredimpedance spectroscopy and a preset model a parameterthat characterizes diffusion resistance that depends on theinterconnected porosity and pore solution conductivity wasobtained Based on the EinsteinndashSmoluchowski equationthe chloride ion diffusion coefficient was derived and theproposed formula was modified to eliminate the influenceof pore solution conductivity on diffusion coefficient mea-surementThen an accurate formula that reflects chloride iondiffusion resistance was obtained(2) With test block size specimen pretreatment im-
pedance test parameters equivalent circuit selection anddiffusion coefficient formula modification taken into consid-eration a method of determining the chloride ion diffusioncoefficient based on AC impedance spectroscopy was estab-lished In addition the test procedure was summarized forpractical purposes
8 Journal of Engineering
(3)The relationship between the proposed method andthe traditional ASTMC1202 method was established Resultsshowed that a certain but not very high degree of linear cor-relation exists which can be attributed to the fact that ASTMC1202 method is essentially a conductance method influ-enced by pore solution conductivity whereas pore solutionconductivity has little effect compared with interconnectedporosity on chloride ion diffusion behavior in concrete
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors acknowledge the support from National NaturalScience Foundation of China (Grant nos 51408379 and51508350) and Natural Science Foundation of Hebei China(Grant no E2013210125)
References
[1] L Kong and Y Du ldquoEffect of lightweight aggregate and theinterfacial transition zone on the durability of concrete basedon grey correlationrdquo Indian Journal of Engineering andMaterialsSciences vol 22 no 1 pp 111ndash119 2015
[2] A E Long G D Henderson and F R Montgomery ldquoWhyassess the properties of near-surface concreterdquo Constructionand Building Materials vol 15 no 2-3 pp 65ndash79 2001
[3] M Cabeza M Keddam X R Novoa I Sanchez and HTakenouti ldquoImpedance spectroscopy to characterize the porestructure during the hardening process of Portland cementpasterdquo Electrochimica Acta vol 51 no 8-9 pp 1831ndash1841 2006
[4] G Dotelli and C M Mari ldquoThe evolution of cement pastehydration process by impedance spectroscopyrdquo Materials Sci-ence and Engineering A vol 303 no 1-2 pp 54ndash59 2001
[5] M Cabeza P Merino X R Novoa and I Sanchez ldquoElectricaleffects generated by mechanical loading of hardened Portlandcement pasterdquo Cement and Concrete Composites vol 25 no 3pp 351ndash356 2003
[6] P Gu P Xie J J Beaudoin and R Brousseau ldquoAC impedancespectroscopy (I) a new equivalent circuit model for hydratedportland cement pasterdquo Cement and Concrete Research vol 22no 5 pp 833ndash840 1992
[7] G Song ldquoEquivalent circuit model for AC electrochemicalimpedance spectroscopy of concreterdquo Cement and ConcreteResearch vol 30 no 11 pp 1723ndash1730 2000
[8] M Shi Z Chen and J Sun ldquoDetermination of chloridediffusivity in concrete by AC impedance spectroscopyrdquo Cementand Concrete Research vol 29 no 7 pp 1111ndash1115 1999
[9] C Andrade ldquoCalculation of chloride diffusion coefficients inconcrete from ionic migration measurementsrdquo Cement andConcrete Research vol 23 no 3 pp 724ndash742 1993
[10] J M Esteban and M E Orazem ldquoOn the application ofthe Kramers-Kronig relations to evaluate the consistency ofelectrochemical impedance datardquo Journal of the ElectrochemicalSociety vol 138 no 1 pp 67ndash76 1991
[11] C Shi ldquoEffect of mixing proportions of concrete on its elec-trical conductivity and the rapid chloride permeability test
(ASTMC1202 or ASSHTOT277) resultsrdquoCement and ConcreteResearch vol 34 no 3 pp 537ndash545 2004
is formed In addition to continuous and discontinuousconduction paths isolated cementitious material particlesand their hydration products or even the entire solid concreteblock can also be conductive for alternating current Based onthe above considerations the concrete mesostructure for ACconducting can be described in Figure 1
The equivalent circuit model that corresponds to Figure 1can be expressed as
1119885 =11198851 +11198852 +11198853 (1)
where 1198851 is the impedance of the ldquoinsulatingrdquo conductionpath1198851 = 1(119895120596119862mat) and 119862mat is the capacitance of the testblock 1198852 is the impedance of the discontinuous conductionpath that is the sum of the capacitance of the discontinuouspoint and the resistance of the cut-off continuous conductionpath 1198852 = 119877CP + 1(119895120596119862DP) 119877CP is the resistance of the cut-off continuous conduction path and 119862DP is the capacitanceof discontinuous point and1198853 is the resistance of continuousconduction path 1198853 = 119877CCP
According to basic circuit theory the equivalent circuitdescribed in (1) can be converted to a circuit shown inFigure 2
The conversion relationship of the two equivalent circuitsis shown in
Figure 3 Nyquist plot of the equivalent circuit model shown inFigure 2
A parallel combination of a capacitor and a resistor pro-duces a semicircle in theNyquist plotTherefore two semicir-cles should appear on the plot of the equivalent circuit shownin Figure 2 Figure 3 shows the relationship between the resis-tance parameters and the location and size of the semicircles
Taking into account the second equation in (2) the resis-tance of the continuous conduction path is the intersectionpoint of the right semicircle with the real axis Howeverthe Nyquist plot of the measured impedance of cement-basedmaterials does not have two semicircles but often onlya semicircle appears Figure 4 is a typical Nyquist plot ofconcrete the concrete composition was 233 Kg silica fume4427 Kg normal Portland cement 750Kg sand 1125 Kggravel 1864 Kg water so 119908119887 = 04 the test age is 28 d
The left arc does not occur which indicates that 1198620 ismuch less than 1198621 Thus the diameter of the left arc is verysmall with respect to the right arc and therefore the left arcis not visible Cabeza et al [3 7] proved this point Thusthe equivalent circuit can be further simplified as shown inFigure 5 which also shows the corresponding Nyquist plot
The above discussion indicates that 119877CCP which is theparameter that characterizes the interconnecting porositythat is most relevant to permeability can be linked withmeasured impedance spectroscopy
Journal of Engineering 3
10MHz
1MHz
40Hz
0
100
200
300
400
500
600
minusZ
998400998400(o
hm)
100 200 300 400 500 600 700 8000
Z998400 (ohm)
Figure 4 High-frequency range Nyquist plot of typical concrete
C1
R1
R0
(a) Further simplified equivalent circuit
0
100
200
300
400
500
minusZ
998400998400(o
hm)
200 400 600100 500300 700
Z (ohm)
(b) Corresponding Nyquist plot of the simplified equivalent circuit
Figure 5 Further simplified equivalent circuit and its Nyquist plot
3 Relationship between AC ImpedanceParameters and Permeability
The relationship between AC impedance parameters andpermeability can be established in two ways An empir-ical relationship between the two can be mathematicallyregressed by conducting a large number of experimentsHowever the disadvantage of this approach is the lack ofreliable theoretical basis Another way to derive some kindof quantitative relationship between the two is through theo-retical derivation This paper adopted the latter approach
Einstein and Smoluchowski presented an equation onthe diffusion of charged particles in solution in 1905 and1906 respectively this equation is known as the EinsteinndashSmoluchowski equation [9] which is shown as follows
where 120583119902 is the ion mobility (m2(Vsdots)) 119896119861 is the Boltzmannconstant (138 sdot 10minus23 JK) q is the charge carried by ions(C) and 119879 is the absolute temperature (K) Through therelationship among the Boltzmann constant the Avogadroconstant (119873119860) the Faraday constant (119865) the elementaryelectric charge (119890) and the universal gas constant (119877) thatis 119896119861 = 119877119873119860 119865 = 119890119873119860 and 119902 = 119911119894119890 where 119911119894 is the absolutevalue of valence (4) was obtained
As for the most significant chloride ion diffusion coef-ficient 119863Clminus which is directly relevant to the durability ofreinforced concrete structures (4) can be specifically writtenas [9]
To use (5) a certain concentration of chloride solutionmust be introduced and chloride ion mobility must be con-sidered InAC impedance spectroscopy testing themeasuredresistance (or resistivity conductivity) is a result of the jointaction of various ions in a pore solution To obtain thechloride ion diffusion coefficient the contribution of chlorideions to the conductance needs to be separated from the totalconductance To achieve this a 1molL NaCl solution wasused to saturate a concrete test block to weaken the influenceof other existing ions Thus the conductivity expression 120590 =119865sum119911119894120583119894119862119894 where119862119894 is the concentration and 119911119894 is the activitycoefficient (119911119894 = 1) can be written as
To further differentiate the contribution of chlorideions and sodium ions to the conductance the contributionpercentage of chloride ions is 61 which is close to thatof an infinitely diluted sodium chloride solution (604)under the conditions of 25∘C and 1molL concentrationthis information was verified by consulting a chemistryhandbook Combining (5) and (6) obtains
Taking into account the relationship between resistance(120588) conductivity (120590) and cell constant (119886 = 119897119860 where 119897 isthe thickness of the test block and119860 is the contact area of theelectrode and the test block) (8) is obtained
120590 = 1120588 =119886119877CCP (8)
4 Journal of Engineering
Table 1 Chemical compositions of cement and mineral admixtures ( by weight)
In (9) the influences of other ions on chloride ion dif-fusion coefficient determination have been largely removedTo further eliminate these effects some pastes (water-binderratio = 10) were prepared and the cementitious material thatwas used is as follows fly ash + Portland cement (cementreplacement level is 20 40 and 60 resp) slag +Portland cement (cement replacement level is 25 50 and75 resp) and silicon fume + Portland cement (cementreplacement level is 5 10 and 15 resp) The chemicalcompositions of cement and mineral admixtures are listed inTable 1
A conductivity cell with a length of 692 cm and anelectrode area of 962 cm2 was also made This experimentaims to investigate the influence of different pore solu-tions caused by different cementitious materials used onconductance Strictly speaking to carry out pore solutionconductivity tests the pore solution should be squeezed outof the concrete block However given the complexity of therequired equipment and the limited amount of the extractedpore solution this research adopted the simulation approachbymeasuring highwater-binder ratio paste that was preparedby using various cementitiousmaterials Before the age of 7 dthe paste will not solidify by shaking the container severaltimes every day The paste solution was shaken for 5 minutesthe day before the test and then left undisturbed for 24 hThen the upper solution was taken and injected into theconductivity testing cell The frequency of the alternatingcurrent is 2000Hz and the test ages are 28 and 90 d Figure 6shows the test results
Figure 6 shows that the addition of mineral admixturesreduces the concrete pore solution conductivity As gen-erally accepted the most important factor that influencespermeability is connected porosity rather than pore solutionconductivity To further eliminate the influence of other ionsonAC impedance testing for chloride iondiffusion coefficientdetermination a correction factor can be introduced Toperform this step the correction factor of ordinary Portlandcement concrete can be set as a benchmark For concrete thatuses other cementitious materials the correction factor maybe determined by interpolation in accordance with Table 2
000012
000010
000008
000006
000004
000002
000000
Con
duct
ivity
(Sm
minus1 )
28 90
Age (day)
100 cem25 sg50 sg75 sg20 fa
40 fa60 fa5 sf10 sf15 sf
Figure 6 Conductivity value of different paste solutions
Table 3 shows the concrete mix that was used in the experi-ment
First Φ100mm times 300mm cylinder test blocks wereprepared for the experiment Steel mold was removed oneday after pouring and then concrete cylinders were curedfor 28 or 90 d before being cut into Φ100mm times 50mmblocks for vacuum saturation (using 1molL NaCl solutionthe saturating regime is the same as that of ASTM C1202)
Then a 100mm times 100mm stainless steel plate wasadopted as the electrode To ensure close contact betweenthe electrodes and the concrete surface soaked filter papers(using 1molL NaOH solution) were introduced Prepressurewas applied to the electrodes by using screw caps Agilent4294A precision impedance analyzer was employed (seeFigure 10) and the test frequency is 40Hz to 40MHz Five
Journal of Engineering 5
Table 3 Concrete mix
Specimen number Materials used (unit kgm3)Cement Fly ash Slag Silicon fume Water Fine aggr Coarse aggr
test points were measured for each order of magnitude Thetest block electrode electrode installation and impedanceanalyzer are shown in Figures 7ndash9 respectively
Figure 11 shows the AC impedance spectroscopy testresult of the C0 test block (90 d)
To verify the validity of the measured impedance dataa validation check by using linear KramersndashKronig test [10]
In Figure 12 the abscissa axis represents the frequencyand the ordinate axis on both sides represents the residuals
6 Journal of Engineering
10MHz
1MHz
40Hz
200 400 600 800 1000 1200 14000
Z998400 (ohm)
0
200
400
600
800
1000
minusZ
998400998400(o
hm)
Figure 11 Nyquist plot of spectroscopy test results of specimen number C0
Z998400
Z998400998400
minus2
minus1
0
1
2
3
Resid
uals
()
10 20 30 405 15 25 35Data point
(a) Specimen number C0 90 dZ
998400Z
998400998400
minus2
minus1
0
1
2
Resid
uals
()
10 20 30 40Data point
(b) Specimen number FA2 90 d
Z998400
Z998400998400
10 20 30 40 50Data point
minus08
minus06
minus04
minus02
00
02
04
06
08
Resid
uals
()
(c) Specimen number GS2 90 dZ
998400Z
998400998400
10 20 30 40 50Data point
minus15
minus10
minus05
00
05
10
Resid
uals
()
(d) Specimen number SF2 90 d
Figure 12 Validation results
Journal of Engineering 7
of Voigt model fitting Equation (10) is used to calculate theresiduals
Residuals (Re119885) = (119885Re minus 119885Re-cal)2
1198852Re
Residuals (Im119885) = (119885Im minus 119885Im-cal)21198852Im
(10)
where 119885Re and 119885Im are real part and the imaginary part ofthe measured impedance respectively and119885Re-cal and119885Im-calare the fitted values obtained by using the Voigt model Smallresiduals correspond to better validity
Only measured data that passed the KramersndashKronig testcan be used for further numerical fitting Figure 12 showsthat the obtained impedance data shows good validity whichcan be attributed to the measures employed in this sectionMoreover the repeatability of the test data is good becauseof reliable close contact between the test block and theelectrodes
Parameters 1198770 1198771 and 1198621 can be obtained throughnumerical fitting of the measured impedance data and thepreset equivalent circuit shown in Figure 5 The chloride iondiffusion coefficient can be calculated by using119877CCP = 1198770+1198771and (9)
The method of determining chloride ion diffusion coeffi-cient based on the AC impedance technique is performed asfollows
(1) Prepare Φ100mm times 50mm specimens and conductvacuum Clminus saturating using 1molL NaCl solution(the saturating regime is the same as that of ASTMC1202)
(2) Carry out AC impedance testing to obtain impedancespectroscopy data
(3) Perform data validation(4) Obtain 119877CCP from equivalent circuit fitting(5) Calculate chloride ion diffusion coefficient using (9)(6) Modify the diffusion coefficient according to the
cementitious material that was used
The rapid chloride permeability test ASTM C1202 hasbeen adopted as national standard by many countriesincluding China the United States and Canada The ASTMC1202 method specifies the rating of chloride permeability ofconcrete based on the charge passed through the specimenduring 6 h of testing period ASTM C1202 tests that use thesame concrete blocks were conducted to perform a compar-ison Figure 13 shows the relationship between chloride iondiffusion coefficients obtained from impedance-based tech-nology and 6 h electric flux A linear correlation (119876C1202 =930 times 119863Clminus ) between the rapid chloride permeability testand the proposed method was obtained with a correlationcoefficient of 09 see Figure 13 for details
As can be seen from Figure 13 some data points devi-ate from the straight line As reported by Shi [11] theASTMC1202 method is virtually a measurement of electricalconductivity of concrete which depends on both the pore
Testing resultLinear fit
0
1000
2000
3000
4000
Char
ge p
asse
d (C
oulo
mb)
1 2 3 4 50
DClminus (10minus12 m2sminus1)
Figure 13 Relationship between chloride ion diffusion coefficientusing ACIS and 6 h electric flux from ASTM C1202 tests
structure characteristics and pore solution chemistry ofconcrete Supplementary cementing materials such as silicafume fly ash and ground blast furnace slag may have asignificant effect on the chemistry or electrical conductivityof pore solution depending on the alkali content of the sup-plementary cementing material replacement level and agewhich has little to do with the chloride permeability ASTMC1202 method is susceptible to pore solution conductanceHowever the proposed method eliminates the effect of poresolution conductivity on permeability by using a carefullydesigned technique This effect may be an important reasonfor the moderate correlation between the two methods
5 Conclusions
(1) High-frequency AC impedance spectroscopy can reflectthe mesostructural properties of materials which enables usto indirectly study the permeability of concrete An equiva-lent circuit model with a clear physical meaning was adoptedthrough an investigation of AC conduction paths in concreteThrough numerical fitting of theNyquist plot of themeasuredimpedance spectroscopy and a preset model a parameterthat characterizes diffusion resistance that depends on theinterconnected porosity and pore solution conductivity wasobtained Based on the EinsteinndashSmoluchowski equationthe chloride ion diffusion coefficient was derived and theproposed formula was modified to eliminate the influenceof pore solution conductivity on diffusion coefficient mea-surementThen an accurate formula that reflects chloride iondiffusion resistance was obtained(2) With test block size specimen pretreatment im-
pedance test parameters equivalent circuit selection anddiffusion coefficient formula modification taken into consid-eration a method of determining the chloride ion diffusioncoefficient based on AC impedance spectroscopy was estab-lished In addition the test procedure was summarized forpractical purposes
8 Journal of Engineering
(3)The relationship between the proposed method andthe traditional ASTMC1202 method was established Resultsshowed that a certain but not very high degree of linear cor-relation exists which can be attributed to the fact that ASTMC1202 method is essentially a conductance method influ-enced by pore solution conductivity whereas pore solutionconductivity has little effect compared with interconnectedporosity on chloride ion diffusion behavior in concrete
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors acknowledge the support from National NaturalScience Foundation of China (Grant nos 51408379 and51508350) and Natural Science Foundation of Hebei China(Grant no E2013210125)
References
[1] L Kong and Y Du ldquoEffect of lightweight aggregate and theinterfacial transition zone on the durability of concrete basedon grey correlationrdquo Indian Journal of Engineering andMaterialsSciences vol 22 no 1 pp 111ndash119 2015
[2] A E Long G D Henderson and F R Montgomery ldquoWhyassess the properties of near-surface concreterdquo Constructionand Building Materials vol 15 no 2-3 pp 65ndash79 2001
[3] M Cabeza M Keddam X R Novoa I Sanchez and HTakenouti ldquoImpedance spectroscopy to characterize the porestructure during the hardening process of Portland cementpasterdquo Electrochimica Acta vol 51 no 8-9 pp 1831ndash1841 2006
[4] G Dotelli and C M Mari ldquoThe evolution of cement pastehydration process by impedance spectroscopyrdquo Materials Sci-ence and Engineering A vol 303 no 1-2 pp 54ndash59 2001
[5] M Cabeza P Merino X R Novoa and I Sanchez ldquoElectricaleffects generated by mechanical loading of hardened Portlandcement pasterdquo Cement and Concrete Composites vol 25 no 3pp 351ndash356 2003
[6] P Gu P Xie J J Beaudoin and R Brousseau ldquoAC impedancespectroscopy (I) a new equivalent circuit model for hydratedportland cement pasterdquo Cement and Concrete Research vol 22no 5 pp 833ndash840 1992
[7] G Song ldquoEquivalent circuit model for AC electrochemicalimpedance spectroscopy of concreterdquo Cement and ConcreteResearch vol 30 no 11 pp 1723ndash1730 2000
[8] M Shi Z Chen and J Sun ldquoDetermination of chloridediffusivity in concrete by AC impedance spectroscopyrdquo Cementand Concrete Research vol 29 no 7 pp 1111ndash1115 1999
[9] C Andrade ldquoCalculation of chloride diffusion coefficients inconcrete from ionic migration measurementsrdquo Cement andConcrete Research vol 23 no 3 pp 724ndash742 1993
[10] J M Esteban and M E Orazem ldquoOn the application ofthe Kramers-Kronig relations to evaluate the consistency ofelectrochemical impedance datardquo Journal of the ElectrochemicalSociety vol 138 no 1 pp 67ndash76 1991
[11] C Shi ldquoEffect of mixing proportions of concrete on its elec-trical conductivity and the rapid chloride permeability test
(ASTMC1202 or ASSHTOT277) resultsrdquoCement and ConcreteResearch vol 34 no 3 pp 537ndash545 2004
Figure 4 High-frequency range Nyquist plot of typical concrete
C1
R1
R0
(a) Further simplified equivalent circuit
0
100
200
300
400
500
minusZ
998400998400(o
hm)
200 400 600100 500300 700
Z (ohm)
(b) Corresponding Nyquist plot of the simplified equivalent circuit
Figure 5 Further simplified equivalent circuit and its Nyquist plot
3 Relationship between AC ImpedanceParameters and Permeability
The relationship between AC impedance parameters andpermeability can be established in two ways An empir-ical relationship between the two can be mathematicallyregressed by conducting a large number of experimentsHowever the disadvantage of this approach is the lack ofreliable theoretical basis Another way to derive some kindof quantitative relationship between the two is through theo-retical derivation This paper adopted the latter approach
Einstein and Smoluchowski presented an equation onthe diffusion of charged particles in solution in 1905 and1906 respectively this equation is known as the EinsteinndashSmoluchowski equation [9] which is shown as follows
where 120583119902 is the ion mobility (m2(Vsdots)) 119896119861 is the Boltzmannconstant (138 sdot 10minus23 JK) q is the charge carried by ions(C) and 119879 is the absolute temperature (K) Through therelationship among the Boltzmann constant the Avogadroconstant (119873119860) the Faraday constant (119865) the elementaryelectric charge (119890) and the universal gas constant (119877) thatis 119896119861 = 119877119873119860 119865 = 119890119873119860 and 119902 = 119911119894119890 where 119911119894 is the absolutevalue of valence (4) was obtained
As for the most significant chloride ion diffusion coef-ficient 119863Clminus which is directly relevant to the durability ofreinforced concrete structures (4) can be specifically writtenas [9]
To use (5) a certain concentration of chloride solutionmust be introduced and chloride ion mobility must be con-sidered InAC impedance spectroscopy testing themeasuredresistance (or resistivity conductivity) is a result of the jointaction of various ions in a pore solution To obtain thechloride ion diffusion coefficient the contribution of chlorideions to the conductance needs to be separated from the totalconductance To achieve this a 1molL NaCl solution wasused to saturate a concrete test block to weaken the influenceof other existing ions Thus the conductivity expression 120590 =119865sum119911119894120583119894119862119894 where119862119894 is the concentration and 119911119894 is the activitycoefficient (119911119894 = 1) can be written as
To further differentiate the contribution of chlorideions and sodium ions to the conductance the contributionpercentage of chloride ions is 61 which is close to thatof an infinitely diluted sodium chloride solution (604)under the conditions of 25∘C and 1molL concentrationthis information was verified by consulting a chemistryhandbook Combining (5) and (6) obtains
Taking into account the relationship between resistance(120588) conductivity (120590) and cell constant (119886 = 119897119860 where 119897 isthe thickness of the test block and119860 is the contact area of theelectrode and the test block) (8) is obtained
120590 = 1120588 =119886119877CCP (8)
4 Journal of Engineering
Table 1 Chemical compositions of cement and mineral admixtures ( by weight)
In (9) the influences of other ions on chloride ion dif-fusion coefficient determination have been largely removedTo further eliminate these effects some pastes (water-binderratio = 10) were prepared and the cementitious material thatwas used is as follows fly ash + Portland cement (cementreplacement level is 20 40 and 60 resp) slag +Portland cement (cement replacement level is 25 50 and75 resp) and silicon fume + Portland cement (cementreplacement level is 5 10 and 15 resp) The chemicalcompositions of cement and mineral admixtures are listed inTable 1
A conductivity cell with a length of 692 cm and anelectrode area of 962 cm2 was also made This experimentaims to investigate the influence of different pore solu-tions caused by different cementitious materials used onconductance Strictly speaking to carry out pore solutionconductivity tests the pore solution should be squeezed outof the concrete block However given the complexity of therequired equipment and the limited amount of the extractedpore solution this research adopted the simulation approachbymeasuring highwater-binder ratio paste that was preparedby using various cementitiousmaterials Before the age of 7 dthe paste will not solidify by shaking the container severaltimes every day The paste solution was shaken for 5 minutesthe day before the test and then left undisturbed for 24 hThen the upper solution was taken and injected into theconductivity testing cell The frequency of the alternatingcurrent is 2000Hz and the test ages are 28 and 90 d Figure 6shows the test results
Figure 6 shows that the addition of mineral admixturesreduces the concrete pore solution conductivity As gen-erally accepted the most important factor that influencespermeability is connected porosity rather than pore solutionconductivity To further eliminate the influence of other ionsonAC impedance testing for chloride iondiffusion coefficientdetermination a correction factor can be introduced Toperform this step the correction factor of ordinary Portlandcement concrete can be set as a benchmark For concrete thatuses other cementitious materials the correction factor maybe determined by interpolation in accordance with Table 2
000012
000010
000008
000006
000004
000002
000000
Con
duct
ivity
(Sm
minus1 )
28 90
Age (day)
100 cem25 sg50 sg75 sg20 fa
40 fa60 fa5 sf10 sf15 sf
Figure 6 Conductivity value of different paste solutions
Table 3 shows the concrete mix that was used in the experi-ment
First Φ100mm times 300mm cylinder test blocks wereprepared for the experiment Steel mold was removed oneday after pouring and then concrete cylinders were curedfor 28 or 90 d before being cut into Φ100mm times 50mmblocks for vacuum saturation (using 1molL NaCl solutionthe saturating regime is the same as that of ASTM C1202)
Then a 100mm times 100mm stainless steel plate wasadopted as the electrode To ensure close contact betweenthe electrodes and the concrete surface soaked filter papers(using 1molL NaOH solution) were introduced Prepressurewas applied to the electrodes by using screw caps Agilent4294A precision impedance analyzer was employed (seeFigure 10) and the test frequency is 40Hz to 40MHz Five
Journal of Engineering 5
Table 3 Concrete mix
Specimen number Materials used (unit kgm3)Cement Fly ash Slag Silicon fume Water Fine aggr Coarse aggr
test points were measured for each order of magnitude Thetest block electrode electrode installation and impedanceanalyzer are shown in Figures 7ndash9 respectively
Figure 11 shows the AC impedance spectroscopy testresult of the C0 test block (90 d)
To verify the validity of the measured impedance dataa validation check by using linear KramersndashKronig test [10]
In Figure 12 the abscissa axis represents the frequencyand the ordinate axis on both sides represents the residuals
6 Journal of Engineering
10MHz
1MHz
40Hz
200 400 600 800 1000 1200 14000
Z998400 (ohm)
0
200
400
600
800
1000
minusZ
998400998400(o
hm)
Figure 11 Nyquist plot of spectroscopy test results of specimen number C0
Z998400
Z998400998400
minus2
minus1
0
1
2
3
Resid
uals
()
10 20 30 405 15 25 35Data point
(a) Specimen number C0 90 dZ
998400Z
998400998400
minus2
minus1
0
1
2
Resid
uals
()
10 20 30 40Data point
(b) Specimen number FA2 90 d
Z998400
Z998400998400
10 20 30 40 50Data point
minus08
minus06
minus04
minus02
00
02
04
06
08
Resid
uals
()
(c) Specimen number GS2 90 dZ
998400Z
998400998400
10 20 30 40 50Data point
minus15
minus10
minus05
00
05
10
Resid
uals
()
(d) Specimen number SF2 90 d
Figure 12 Validation results
Journal of Engineering 7
of Voigt model fitting Equation (10) is used to calculate theresiduals
Residuals (Re119885) = (119885Re minus 119885Re-cal)2
1198852Re
Residuals (Im119885) = (119885Im minus 119885Im-cal)21198852Im
(10)
where 119885Re and 119885Im are real part and the imaginary part ofthe measured impedance respectively and119885Re-cal and119885Im-calare the fitted values obtained by using the Voigt model Smallresiduals correspond to better validity
Only measured data that passed the KramersndashKronig testcan be used for further numerical fitting Figure 12 showsthat the obtained impedance data shows good validity whichcan be attributed to the measures employed in this sectionMoreover the repeatability of the test data is good becauseof reliable close contact between the test block and theelectrodes
Parameters 1198770 1198771 and 1198621 can be obtained throughnumerical fitting of the measured impedance data and thepreset equivalent circuit shown in Figure 5 The chloride iondiffusion coefficient can be calculated by using119877CCP = 1198770+1198771and (9)
The method of determining chloride ion diffusion coeffi-cient based on the AC impedance technique is performed asfollows
(1) Prepare Φ100mm times 50mm specimens and conductvacuum Clminus saturating using 1molL NaCl solution(the saturating regime is the same as that of ASTMC1202)
(2) Carry out AC impedance testing to obtain impedancespectroscopy data
(3) Perform data validation(4) Obtain 119877CCP from equivalent circuit fitting(5) Calculate chloride ion diffusion coefficient using (9)(6) Modify the diffusion coefficient according to the
cementitious material that was used
The rapid chloride permeability test ASTM C1202 hasbeen adopted as national standard by many countriesincluding China the United States and Canada The ASTMC1202 method specifies the rating of chloride permeability ofconcrete based on the charge passed through the specimenduring 6 h of testing period ASTM C1202 tests that use thesame concrete blocks were conducted to perform a compar-ison Figure 13 shows the relationship between chloride iondiffusion coefficients obtained from impedance-based tech-nology and 6 h electric flux A linear correlation (119876C1202 =930 times 119863Clminus ) between the rapid chloride permeability testand the proposed method was obtained with a correlationcoefficient of 09 see Figure 13 for details
As can be seen from Figure 13 some data points devi-ate from the straight line As reported by Shi [11] theASTMC1202 method is virtually a measurement of electricalconductivity of concrete which depends on both the pore
Testing resultLinear fit
0
1000
2000
3000
4000
Char
ge p
asse
d (C
oulo
mb)
1 2 3 4 50
DClminus (10minus12 m2sminus1)
Figure 13 Relationship between chloride ion diffusion coefficientusing ACIS and 6 h electric flux from ASTM C1202 tests
structure characteristics and pore solution chemistry ofconcrete Supplementary cementing materials such as silicafume fly ash and ground blast furnace slag may have asignificant effect on the chemistry or electrical conductivityof pore solution depending on the alkali content of the sup-plementary cementing material replacement level and agewhich has little to do with the chloride permeability ASTMC1202 method is susceptible to pore solution conductanceHowever the proposed method eliminates the effect of poresolution conductivity on permeability by using a carefullydesigned technique This effect may be an important reasonfor the moderate correlation between the two methods
5 Conclusions
(1) High-frequency AC impedance spectroscopy can reflectthe mesostructural properties of materials which enables usto indirectly study the permeability of concrete An equiva-lent circuit model with a clear physical meaning was adoptedthrough an investigation of AC conduction paths in concreteThrough numerical fitting of theNyquist plot of themeasuredimpedance spectroscopy and a preset model a parameterthat characterizes diffusion resistance that depends on theinterconnected porosity and pore solution conductivity wasobtained Based on the EinsteinndashSmoluchowski equationthe chloride ion diffusion coefficient was derived and theproposed formula was modified to eliminate the influenceof pore solution conductivity on diffusion coefficient mea-surementThen an accurate formula that reflects chloride iondiffusion resistance was obtained(2) With test block size specimen pretreatment im-
pedance test parameters equivalent circuit selection anddiffusion coefficient formula modification taken into consid-eration a method of determining the chloride ion diffusioncoefficient based on AC impedance spectroscopy was estab-lished In addition the test procedure was summarized forpractical purposes
8 Journal of Engineering
(3)The relationship between the proposed method andthe traditional ASTMC1202 method was established Resultsshowed that a certain but not very high degree of linear cor-relation exists which can be attributed to the fact that ASTMC1202 method is essentially a conductance method influ-enced by pore solution conductivity whereas pore solutionconductivity has little effect compared with interconnectedporosity on chloride ion diffusion behavior in concrete
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors acknowledge the support from National NaturalScience Foundation of China (Grant nos 51408379 and51508350) and Natural Science Foundation of Hebei China(Grant no E2013210125)
References
[1] L Kong and Y Du ldquoEffect of lightweight aggregate and theinterfacial transition zone on the durability of concrete basedon grey correlationrdquo Indian Journal of Engineering andMaterialsSciences vol 22 no 1 pp 111ndash119 2015
[2] A E Long G D Henderson and F R Montgomery ldquoWhyassess the properties of near-surface concreterdquo Constructionand Building Materials vol 15 no 2-3 pp 65ndash79 2001
[3] M Cabeza M Keddam X R Novoa I Sanchez and HTakenouti ldquoImpedance spectroscopy to characterize the porestructure during the hardening process of Portland cementpasterdquo Electrochimica Acta vol 51 no 8-9 pp 1831ndash1841 2006
[4] G Dotelli and C M Mari ldquoThe evolution of cement pastehydration process by impedance spectroscopyrdquo Materials Sci-ence and Engineering A vol 303 no 1-2 pp 54ndash59 2001
[5] M Cabeza P Merino X R Novoa and I Sanchez ldquoElectricaleffects generated by mechanical loading of hardened Portlandcement pasterdquo Cement and Concrete Composites vol 25 no 3pp 351ndash356 2003
[6] P Gu P Xie J J Beaudoin and R Brousseau ldquoAC impedancespectroscopy (I) a new equivalent circuit model for hydratedportland cement pasterdquo Cement and Concrete Research vol 22no 5 pp 833ndash840 1992
[7] G Song ldquoEquivalent circuit model for AC electrochemicalimpedance spectroscopy of concreterdquo Cement and ConcreteResearch vol 30 no 11 pp 1723ndash1730 2000
[8] M Shi Z Chen and J Sun ldquoDetermination of chloridediffusivity in concrete by AC impedance spectroscopyrdquo Cementand Concrete Research vol 29 no 7 pp 1111ndash1115 1999
[9] C Andrade ldquoCalculation of chloride diffusion coefficients inconcrete from ionic migration measurementsrdquo Cement andConcrete Research vol 23 no 3 pp 724ndash742 1993
[10] J M Esteban and M E Orazem ldquoOn the application ofthe Kramers-Kronig relations to evaluate the consistency ofelectrochemical impedance datardquo Journal of the ElectrochemicalSociety vol 138 no 1 pp 67ndash76 1991
[11] C Shi ldquoEffect of mixing proportions of concrete on its elec-trical conductivity and the rapid chloride permeability test
(ASTMC1202 or ASSHTOT277) resultsrdquoCement and ConcreteResearch vol 34 no 3 pp 537ndash545 2004
In (9) the influences of other ions on chloride ion dif-fusion coefficient determination have been largely removedTo further eliminate these effects some pastes (water-binderratio = 10) were prepared and the cementitious material thatwas used is as follows fly ash + Portland cement (cementreplacement level is 20 40 and 60 resp) slag +Portland cement (cement replacement level is 25 50 and75 resp) and silicon fume + Portland cement (cementreplacement level is 5 10 and 15 resp) The chemicalcompositions of cement and mineral admixtures are listed inTable 1
A conductivity cell with a length of 692 cm and anelectrode area of 962 cm2 was also made This experimentaims to investigate the influence of different pore solu-tions caused by different cementitious materials used onconductance Strictly speaking to carry out pore solutionconductivity tests the pore solution should be squeezed outof the concrete block However given the complexity of therequired equipment and the limited amount of the extractedpore solution this research adopted the simulation approachbymeasuring highwater-binder ratio paste that was preparedby using various cementitiousmaterials Before the age of 7 dthe paste will not solidify by shaking the container severaltimes every day The paste solution was shaken for 5 minutesthe day before the test and then left undisturbed for 24 hThen the upper solution was taken and injected into theconductivity testing cell The frequency of the alternatingcurrent is 2000Hz and the test ages are 28 and 90 d Figure 6shows the test results
Figure 6 shows that the addition of mineral admixturesreduces the concrete pore solution conductivity As gen-erally accepted the most important factor that influencespermeability is connected porosity rather than pore solutionconductivity To further eliminate the influence of other ionsonAC impedance testing for chloride iondiffusion coefficientdetermination a correction factor can be introduced Toperform this step the correction factor of ordinary Portlandcement concrete can be set as a benchmark For concrete thatuses other cementitious materials the correction factor maybe determined by interpolation in accordance with Table 2
000012
000010
000008
000006
000004
000002
000000
Con
duct
ivity
(Sm
minus1 )
28 90
Age (day)
100 cem25 sg50 sg75 sg20 fa
40 fa60 fa5 sf10 sf15 sf
Figure 6 Conductivity value of different paste solutions
Table 3 shows the concrete mix that was used in the experi-ment
First Φ100mm times 300mm cylinder test blocks wereprepared for the experiment Steel mold was removed oneday after pouring and then concrete cylinders were curedfor 28 or 90 d before being cut into Φ100mm times 50mmblocks for vacuum saturation (using 1molL NaCl solutionthe saturating regime is the same as that of ASTM C1202)
Then a 100mm times 100mm stainless steel plate wasadopted as the electrode To ensure close contact betweenthe electrodes and the concrete surface soaked filter papers(using 1molL NaOH solution) were introduced Prepressurewas applied to the electrodes by using screw caps Agilent4294A precision impedance analyzer was employed (seeFigure 10) and the test frequency is 40Hz to 40MHz Five
Journal of Engineering 5
Table 3 Concrete mix
Specimen number Materials used (unit kgm3)Cement Fly ash Slag Silicon fume Water Fine aggr Coarse aggr
test points were measured for each order of magnitude Thetest block electrode electrode installation and impedanceanalyzer are shown in Figures 7ndash9 respectively
Figure 11 shows the AC impedance spectroscopy testresult of the C0 test block (90 d)
To verify the validity of the measured impedance dataa validation check by using linear KramersndashKronig test [10]
In Figure 12 the abscissa axis represents the frequencyand the ordinate axis on both sides represents the residuals
6 Journal of Engineering
10MHz
1MHz
40Hz
200 400 600 800 1000 1200 14000
Z998400 (ohm)
0
200
400
600
800
1000
minusZ
998400998400(o
hm)
Figure 11 Nyquist plot of spectroscopy test results of specimen number C0
Z998400
Z998400998400
minus2
minus1
0
1
2
3
Resid
uals
()
10 20 30 405 15 25 35Data point
(a) Specimen number C0 90 dZ
998400Z
998400998400
minus2
minus1
0
1
2
Resid
uals
()
10 20 30 40Data point
(b) Specimen number FA2 90 d
Z998400
Z998400998400
10 20 30 40 50Data point
minus08
minus06
minus04
minus02
00
02
04
06
08
Resid
uals
()
(c) Specimen number GS2 90 dZ
998400Z
998400998400
10 20 30 40 50Data point
minus15
minus10
minus05
00
05
10
Resid
uals
()
(d) Specimen number SF2 90 d
Figure 12 Validation results
Journal of Engineering 7
of Voigt model fitting Equation (10) is used to calculate theresiduals
Residuals (Re119885) = (119885Re minus 119885Re-cal)2
1198852Re
Residuals (Im119885) = (119885Im minus 119885Im-cal)21198852Im
(10)
where 119885Re and 119885Im are real part and the imaginary part ofthe measured impedance respectively and119885Re-cal and119885Im-calare the fitted values obtained by using the Voigt model Smallresiduals correspond to better validity
Only measured data that passed the KramersndashKronig testcan be used for further numerical fitting Figure 12 showsthat the obtained impedance data shows good validity whichcan be attributed to the measures employed in this sectionMoreover the repeatability of the test data is good becauseof reliable close contact between the test block and theelectrodes
Parameters 1198770 1198771 and 1198621 can be obtained throughnumerical fitting of the measured impedance data and thepreset equivalent circuit shown in Figure 5 The chloride iondiffusion coefficient can be calculated by using119877CCP = 1198770+1198771and (9)
The method of determining chloride ion diffusion coeffi-cient based on the AC impedance technique is performed asfollows
(1) Prepare Φ100mm times 50mm specimens and conductvacuum Clminus saturating using 1molL NaCl solution(the saturating regime is the same as that of ASTMC1202)
(2) Carry out AC impedance testing to obtain impedancespectroscopy data
(3) Perform data validation(4) Obtain 119877CCP from equivalent circuit fitting(5) Calculate chloride ion diffusion coefficient using (9)(6) Modify the diffusion coefficient according to the
cementitious material that was used
The rapid chloride permeability test ASTM C1202 hasbeen adopted as national standard by many countriesincluding China the United States and Canada The ASTMC1202 method specifies the rating of chloride permeability ofconcrete based on the charge passed through the specimenduring 6 h of testing period ASTM C1202 tests that use thesame concrete blocks were conducted to perform a compar-ison Figure 13 shows the relationship between chloride iondiffusion coefficients obtained from impedance-based tech-nology and 6 h electric flux A linear correlation (119876C1202 =930 times 119863Clminus ) between the rapid chloride permeability testand the proposed method was obtained with a correlationcoefficient of 09 see Figure 13 for details
As can be seen from Figure 13 some data points devi-ate from the straight line As reported by Shi [11] theASTMC1202 method is virtually a measurement of electricalconductivity of concrete which depends on both the pore
Testing resultLinear fit
0
1000
2000
3000
4000
Char
ge p
asse
d (C
oulo
mb)
1 2 3 4 50
DClminus (10minus12 m2sminus1)
Figure 13 Relationship between chloride ion diffusion coefficientusing ACIS and 6 h electric flux from ASTM C1202 tests
structure characteristics and pore solution chemistry ofconcrete Supplementary cementing materials such as silicafume fly ash and ground blast furnace slag may have asignificant effect on the chemistry or electrical conductivityof pore solution depending on the alkali content of the sup-plementary cementing material replacement level and agewhich has little to do with the chloride permeability ASTMC1202 method is susceptible to pore solution conductanceHowever the proposed method eliminates the effect of poresolution conductivity on permeability by using a carefullydesigned technique This effect may be an important reasonfor the moderate correlation between the two methods
5 Conclusions
(1) High-frequency AC impedance spectroscopy can reflectthe mesostructural properties of materials which enables usto indirectly study the permeability of concrete An equiva-lent circuit model with a clear physical meaning was adoptedthrough an investigation of AC conduction paths in concreteThrough numerical fitting of theNyquist plot of themeasuredimpedance spectroscopy and a preset model a parameterthat characterizes diffusion resistance that depends on theinterconnected porosity and pore solution conductivity wasobtained Based on the EinsteinndashSmoluchowski equationthe chloride ion diffusion coefficient was derived and theproposed formula was modified to eliminate the influenceof pore solution conductivity on diffusion coefficient mea-surementThen an accurate formula that reflects chloride iondiffusion resistance was obtained(2) With test block size specimen pretreatment im-
pedance test parameters equivalent circuit selection anddiffusion coefficient formula modification taken into consid-eration a method of determining the chloride ion diffusioncoefficient based on AC impedance spectroscopy was estab-lished In addition the test procedure was summarized forpractical purposes
8 Journal of Engineering
(3)The relationship between the proposed method andthe traditional ASTMC1202 method was established Resultsshowed that a certain but not very high degree of linear cor-relation exists which can be attributed to the fact that ASTMC1202 method is essentially a conductance method influ-enced by pore solution conductivity whereas pore solutionconductivity has little effect compared with interconnectedporosity on chloride ion diffusion behavior in concrete
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors acknowledge the support from National NaturalScience Foundation of China (Grant nos 51408379 and51508350) and Natural Science Foundation of Hebei China(Grant no E2013210125)
References
[1] L Kong and Y Du ldquoEffect of lightweight aggregate and theinterfacial transition zone on the durability of concrete basedon grey correlationrdquo Indian Journal of Engineering andMaterialsSciences vol 22 no 1 pp 111ndash119 2015
[2] A E Long G D Henderson and F R Montgomery ldquoWhyassess the properties of near-surface concreterdquo Constructionand Building Materials vol 15 no 2-3 pp 65ndash79 2001
[3] M Cabeza M Keddam X R Novoa I Sanchez and HTakenouti ldquoImpedance spectroscopy to characterize the porestructure during the hardening process of Portland cementpasterdquo Electrochimica Acta vol 51 no 8-9 pp 1831ndash1841 2006
[4] G Dotelli and C M Mari ldquoThe evolution of cement pastehydration process by impedance spectroscopyrdquo Materials Sci-ence and Engineering A vol 303 no 1-2 pp 54ndash59 2001
[5] M Cabeza P Merino X R Novoa and I Sanchez ldquoElectricaleffects generated by mechanical loading of hardened Portlandcement pasterdquo Cement and Concrete Composites vol 25 no 3pp 351ndash356 2003
[6] P Gu P Xie J J Beaudoin and R Brousseau ldquoAC impedancespectroscopy (I) a new equivalent circuit model for hydratedportland cement pasterdquo Cement and Concrete Research vol 22no 5 pp 833ndash840 1992
[7] G Song ldquoEquivalent circuit model for AC electrochemicalimpedance spectroscopy of concreterdquo Cement and ConcreteResearch vol 30 no 11 pp 1723ndash1730 2000
[8] M Shi Z Chen and J Sun ldquoDetermination of chloridediffusivity in concrete by AC impedance spectroscopyrdquo Cementand Concrete Research vol 29 no 7 pp 1111ndash1115 1999
[9] C Andrade ldquoCalculation of chloride diffusion coefficients inconcrete from ionic migration measurementsrdquo Cement andConcrete Research vol 23 no 3 pp 724ndash742 1993
[10] J M Esteban and M E Orazem ldquoOn the application ofthe Kramers-Kronig relations to evaluate the consistency ofelectrochemical impedance datardquo Journal of the ElectrochemicalSociety vol 138 no 1 pp 67ndash76 1991
[11] C Shi ldquoEffect of mixing proportions of concrete on its elec-trical conductivity and the rapid chloride permeability test
(ASTMC1202 or ASSHTOT277) resultsrdquoCement and ConcreteResearch vol 34 no 3 pp 537ndash545 2004
test points were measured for each order of magnitude Thetest block electrode electrode installation and impedanceanalyzer are shown in Figures 7ndash9 respectively
Figure 11 shows the AC impedance spectroscopy testresult of the C0 test block (90 d)
To verify the validity of the measured impedance dataa validation check by using linear KramersndashKronig test [10]
In Figure 12 the abscissa axis represents the frequencyand the ordinate axis on both sides represents the residuals
6 Journal of Engineering
10MHz
1MHz
40Hz
200 400 600 800 1000 1200 14000
Z998400 (ohm)
0
200
400
600
800
1000
minusZ
998400998400(o
hm)
Figure 11 Nyquist plot of spectroscopy test results of specimen number C0
Z998400
Z998400998400
minus2
minus1
0
1
2
3
Resid
uals
()
10 20 30 405 15 25 35Data point
(a) Specimen number C0 90 dZ
998400Z
998400998400
minus2
minus1
0
1
2
Resid
uals
()
10 20 30 40Data point
(b) Specimen number FA2 90 d
Z998400
Z998400998400
10 20 30 40 50Data point
minus08
minus06
minus04
minus02
00
02
04
06
08
Resid
uals
()
(c) Specimen number GS2 90 dZ
998400Z
998400998400
10 20 30 40 50Data point
minus15
minus10
minus05
00
05
10
Resid
uals
()
(d) Specimen number SF2 90 d
Figure 12 Validation results
Journal of Engineering 7
of Voigt model fitting Equation (10) is used to calculate theresiduals
Residuals (Re119885) = (119885Re minus 119885Re-cal)2
1198852Re
Residuals (Im119885) = (119885Im minus 119885Im-cal)21198852Im
(10)
where 119885Re and 119885Im are real part and the imaginary part ofthe measured impedance respectively and119885Re-cal and119885Im-calare the fitted values obtained by using the Voigt model Smallresiduals correspond to better validity
Only measured data that passed the KramersndashKronig testcan be used for further numerical fitting Figure 12 showsthat the obtained impedance data shows good validity whichcan be attributed to the measures employed in this sectionMoreover the repeatability of the test data is good becauseof reliable close contact between the test block and theelectrodes
Parameters 1198770 1198771 and 1198621 can be obtained throughnumerical fitting of the measured impedance data and thepreset equivalent circuit shown in Figure 5 The chloride iondiffusion coefficient can be calculated by using119877CCP = 1198770+1198771and (9)
The method of determining chloride ion diffusion coeffi-cient based on the AC impedance technique is performed asfollows
(1) Prepare Φ100mm times 50mm specimens and conductvacuum Clminus saturating using 1molL NaCl solution(the saturating regime is the same as that of ASTMC1202)
(2) Carry out AC impedance testing to obtain impedancespectroscopy data
(3) Perform data validation(4) Obtain 119877CCP from equivalent circuit fitting(5) Calculate chloride ion diffusion coefficient using (9)(6) Modify the diffusion coefficient according to the
cementitious material that was used
The rapid chloride permeability test ASTM C1202 hasbeen adopted as national standard by many countriesincluding China the United States and Canada The ASTMC1202 method specifies the rating of chloride permeability ofconcrete based on the charge passed through the specimenduring 6 h of testing period ASTM C1202 tests that use thesame concrete blocks were conducted to perform a compar-ison Figure 13 shows the relationship between chloride iondiffusion coefficients obtained from impedance-based tech-nology and 6 h electric flux A linear correlation (119876C1202 =930 times 119863Clminus ) between the rapid chloride permeability testand the proposed method was obtained with a correlationcoefficient of 09 see Figure 13 for details
As can be seen from Figure 13 some data points devi-ate from the straight line As reported by Shi [11] theASTMC1202 method is virtually a measurement of electricalconductivity of concrete which depends on both the pore
Testing resultLinear fit
0
1000
2000
3000
4000
Char
ge p
asse
d (C
oulo
mb)
1 2 3 4 50
DClminus (10minus12 m2sminus1)
Figure 13 Relationship between chloride ion diffusion coefficientusing ACIS and 6 h electric flux from ASTM C1202 tests
structure characteristics and pore solution chemistry ofconcrete Supplementary cementing materials such as silicafume fly ash and ground blast furnace slag may have asignificant effect on the chemistry or electrical conductivityof pore solution depending on the alkali content of the sup-plementary cementing material replacement level and agewhich has little to do with the chloride permeability ASTMC1202 method is susceptible to pore solution conductanceHowever the proposed method eliminates the effect of poresolution conductivity on permeability by using a carefullydesigned technique This effect may be an important reasonfor the moderate correlation between the two methods
5 Conclusions
(1) High-frequency AC impedance spectroscopy can reflectthe mesostructural properties of materials which enables usto indirectly study the permeability of concrete An equiva-lent circuit model with a clear physical meaning was adoptedthrough an investigation of AC conduction paths in concreteThrough numerical fitting of theNyquist plot of themeasuredimpedance spectroscopy and a preset model a parameterthat characterizes diffusion resistance that depends on theinterconnected porosity and pore solution conductivity wasobtained Based on the EinsteinndashSmoluchowski equationthe chloride ion diffusion coefficient was derived and theproposed formula was modified to eliminate the influenceof pore solution conductivity on diffusion coefficient mea-surementThen an accurate formula that reflects chloride iondiffusion resistance was obtained(2) With test block size specimen pretreatment im-
pedance test parameters equivalent circuit selection anddiffusion coefficient formula modification taken into consid-eration a method of determining the chloride ion diffusioncoefficient based on AC impedance spectroscopy was estab-lished In addition the test procedure was summarized forpractical purposes
8 Journal of Engineering
(3)The relationship between the proposed method andthe traditional ASTMC1202 method was established Resultsshowed that a certain but not very high degree of linear cor-relation exists which can be attributed to the fact that ASTMC1202 method is essentially a conductance method influ-enced by pore solution conductivity whereas pore solutionconductivity has little effect compared with interconnectedporosity on chloride ion diffusion behavior in concrete
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors acknowledge the support from National NaturalScience Foundation of China (Grant nos 51408379 and51508350) and Natural Science Foundation of Hebei China(Grant no E2013210125)
References
[1] L Kong and Y Du ldquoEffect of lightweight aggregate and theinterfacial transition zone on the durability of concrete basedon grey correlationrdquo Indian Journal of Engineering andMaterialsSciences vol 22 no 1 pp 111ndash119 2015
[2] A E Long G D Henderson and F R Montgomery ldquoWhyassess the properties of near-surface concreterdquo Constructionand Building Materials vol 15 no 2-3 pp 65ndash79 2001
[3] M Cabeza M Keddam X R Novoa I Sanchez and HTakenouti ldquoImpedance spectroscopy to characterize the porestructure during the hardening process of Portland cementpasterdquo Electrochimica Acta vol 51 no 8-9 pp 1831ndash1841 2006
[4] G Dotelli and C M Mari ldquoThe evolution of cement pastehydration process by impedance spectroscopyrdquo Materials Sci-ence and Engineering A vol 303 no 1-2 pp 54ndash59 2001
[5] M Cabeza P Merino X R Novoa and I Sanchez ldquoElectricaleffects generated by mechanical loading of hardened Portlandcement pasterdquo Cement and Concrete Composites vol 25 no 3pp 351ndash356 2003
[6] P Gu P Xie J J Beaudoin and R Brousseau ldquoAC impedancespectroscopy (I) a new equivalent circuit model for hydratedportland cement pasterdquo Cement and Concrete Research vol 22no 5 pp 833ndash840 1992
[7] G Song ldquoEquivalent circuit model for AC electrochemicalimpedance spectroscopy of concreterdquo Cement and ConcreteResearch vol 30 no 11 pp 1723ndash1730 2000
[8] M Shi Z Chen and J Sun ldquoDetermination of chloridediffusivity in concrete by AC impedance spectroscopyrdquo Cementand Concrete Research vol 29 no 7 pp 1111ndash1115 1999
[9] C Andrade ldquoCalculation of chloride diffusion coefficients inconcrete from ionic migration measurementsrdquo Cement andConcrete Research vol 23 no 3 pp 724ndash742 1993
[10] J M Esteban and M E Orazem ldquoOn the application ofthe Kramers-Kronig relations to evaluate the consistency ofelectrochemical impedance datardquo Journal of the ElectrochemicalSociety vol 138 no 1 pp 67ndash76 1991
[11] C Shi ldquoEffect of mixing proportions of concrete on its elec-trical conductivity and the rapid chloride permeability test
(ASTMC1202 or ASSHTOT277) resultsrdquoCement and ConcreteResearch vol 34 no 3 pp 537ndash545 2004
Figure 11 Nyquist plot of spectroscopy test results of specimen number C0
Z998400
Z998400998400
minus2
minus1
0
1
2
3
Resid
uals
()
10 20 30 405 15 25 35Data point
(a) Specimen number C0 90 dZ
998400Z
998400998400
minus2
minus1
0
1
2
Resid
uals
()
10 20 30 40Data point
(b) Specimen number FA2 90 d
Z998400
Z998400998400
10 20 30 40 50Data point
minus08
minus06
minus04
minus02
00
02
04
06
08
Resid
uals
()
(c) Specimen number GS2 90 dZ
998400Z
998400998400
10 20 30 40 50Data point
minus15
minus10
minus05
00
05
10
Resid
uals
()
(d) Specimen number SF2 90 d
Figure 12 Validation results
Journal of Engineering 7
of Voigt model fitting Equation (10) is used to calculate theresiduals
Residuals (Re119885) = (119885Re minus 119885Re-cal)2
1198852Re
Residuals (Im119885) = (119885Im minus 119885Im-cal)21198852Im
(10)
where 119885Re and 119885Im are real part and the imaginary part ofthe measured impedance respectively and119885Re-cal and119885Im-calare the fitted values obtained by using the Voigt model Smallresiduals correspond to better validity
Only measured data that passed the KramersndashKronig testcan be used for further numerical fitting Figure 12 showsthat the obtained impedance data shows good validity whichcan be attributed to the measures employed in this sectionMoreover the repeatability of the test data is good becauseof reliable close contact between the test block and theelectrodes
Parameters 1198770 1198771 and 1198621 can be obtained throughnumerical fitting of the measured impedance data and thepreset equivalent circuit shown in Figure 5 The chloride iondiffusion coefficient can be calculated by using119877CCP = 1198770+1198771and (9)
The method of determining chloride ion diffusion coeffi-cient based on the AC impedance technique is performed asfollows
(1) Prepare Φ100mm times 50mm specimens and conductvacuum Clminus saturating using 1molL NaCl solution(the saturating regime is the same as that of ASTMC1202)
(2) Carry out AC impedance testing to obtain impedancespectroscopy data
(3) Perform data validation(4) Obtain 119877CCP from equivalent circuit fitting(5) Calculate chloride ion diffusion coefficient using (9)(6) Modify the diffusion coefficient according to the
cementitious material that was used
The rapid chloride permeability test ASTM C1202 hasbeen adopted as national standard by many countriesincluding China the United States and Canada The ASTMC1202 method specifies the rating of chloride permeability ofconcrete based on the charge passed through the specimenduring 6 h of testing period ASTM C1202 tests that use thesame concrete blocks were conducted to perform a compar-ison Figure 13 shows the relationship between chloride iondiffusion coefficients obtained from impedance-based tech-nology and 6 h electric flux A linear correlation (119876C1202 =930 times 119863Clminus ) between the rapid chloride permeability testand the proposed method was obtained with a correlationcoefficient of 09 see Figure 13 for details
As can be seen from Figure 13 some data points devi-ate from the straight line As reported by Shi [11] theASTMC1202 method is virtually a measurement of electricalconductivity of concrete which depends on both the pore
Testing resultLinear fit
0
1000
2000
3000
4000
Char
ge p
asse
d (C
oulo
mb)
1 2 3 4 50
DClminus (10minus12 m2sminus1)
Figure 13 Relationship between chloride ion diffusion coefficientusing ACIS and 6 h electric flux from ASTM C1202 tests
structure characteristics and pore solution chemistry ofconcrete Supplementary cementing materials such as silicafume fly ash and ground blast furnace slag may have asignificant effect on the chemistry or electrical conductivityof pore solution depending on the alkali content of the sup-plementary cementing material replacement level and agewhich has little to do with the chloride permeability ASTMC1202 method is susceptible to pore solution conductanceHowever the proposed method eliminates the effect of poresolution conductivity on permeability by using a carefullydesigned technique This effect may be an important reasonfor the moderate correlation between the two methods
5 Conclusions
(1) High-frequency AC impedance spectroscopy can reflectthe mesostructural properties of materials which enables usto indirectly study the permeability of concrete An equiva-lent circuit model with a clear physical meaning was adoptedthrough an investigation of AC conduction paths in concreteThrough numerical fitting of theNyquist plot of themeasuredimpedance spectroscopy and a preset model a parameterthat characterizes diffusion resistance that depends on theinterconnected porosity and pore solution conductivity wasobtained Based on the EinsteinndashSmoluchowski equationthe chloride ion diffusion coefficient was derived and theproposed formula was modified to eliminate the influenceof pore solution conductivity on diffusion coefficient mea-surementThen an accurate formula that reflects chloride iondiffusion resistance was obtained(2) With test block size specimen pretreatment im-
pedance test parameters equivalent circuit selection anddiffusion coefficient formula modification taken into consid-eration a method of determining the chloride ion diffusioncoefficient based on AC impedance spectroscopy was estab-lished In addition the test procedure was summarized forpractical purposes
8 Journal of Engineering
(3)The relationship between the proposed method andthe traditional ASTMC1202 method was established Resultsshowed that a certain but not very high degree of linear cor-relation exists which can be attributed to the fact that ASTMC1202 method is essentially a conductance method influ-enced by pore solution conductivity whereas pore solutionconductivity has little effect compared with interconnectedporosity on chloride ion diffusion behavior in concrete
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors acknowledge the support from National NaturalScience Foundation of China (Grant nos 51408379 and51508350) and Natural Science Foundation of Hebei China(Grant no E2013210125)
References
[1] L Kong and Y Du ldquoEffect of lightweight aggregate and theinterfacial transition zone on the durability of concrete basedon grey correlationrdquo Indian Journal of Engineering andMaterialsSciences vol 22 no 1 pp 111ndash119 2015
[2] A E Long G D Henderson and F R Montgomery ldquoWhyassess the properties of near-surface concreterdquo Constructionand Building Materials vol 15 no 2-3 pp 65ndash79 2001
[3] M Cabeza M Keddam X R Novoa I Sanchez and HTakenouti ldquoImpedance spectroscopy to characterize the porestructure during the hardening process of Portland cementpasterdquo Electrochimica Acta vol 51 no 8-9 pp 1831ndash1841 2006
[4] G Dotelli and C M Mari ldquoThe evolution of cement pastehydration process by impedance spectroscopyrdquo Materials Sci-ence and Engineering A vol 303 no 1-2 pp 54ndash59 2001
[5] M Cabeza P Merino X R Novoa and I Sanchez ldquoElectricaleffects generated by mechanical loading of hardened Portlandcement pasterdquo Cement and Concrete Composites vol 25 no 3pp 351ndash356 2003
[6] P Gu P Xie J J Beaudoin and R Brousseau ldquoAC impedancespectroscopy (I) a new equivalent circuit model for hydratedportland cement pasterdquo Cement and Concrete Research vol 22no 5 pp 833ndash840 1992
[7] G Song ldquoEquivalent circuit model for AC electrochemicalimpedance spectroscopy of concreterdquo Cement and ConcreteResearch vol 30 no 11 pp 1723ndash1730 2000
[8] M Shi Z Chen and J Sun ldquoDetermination of chloridediffusivity in concrete by AC impedance spectroscopyrdquo Cementand Concrete Research vol 29 no 7 pp 1111ndash1115 1999
[9] C Andrade ldquoCalculation of chloride diffusion coefficients inconcrete from ionic migration measurementsrdquo Cement andConcrete Research vol 23 no 3 pp 724ndash742 1993
[10] J M Esteban and M E Orazem ldquoOn the application ofthe Kramers-Kronig relations to evaluate the consistency ofelectrochemical impedance datardquo Journal of the ElectrochemicalSociety vol 138 no 1 pp 67ndash76 1991
[11] C Shi ldquoEffect of mixing proportions of concrete on its elec-trical conductivity and the rapid chloride permeability test
(ASTMC1202 or ASSHTOT277) resultsrdquoCement and ConcreteResearch vol 34 no 3 pp 537ndash545 2004
of Voigt model fitting Equation (10) is used to calculate theresiduals
Residuals (Re119885) = (119885Re minus 119885Re-cal)2
1198852Re
Residuals (Im119885) = (119885Im minus 119885Im-cal)21198852Im
(10)
where 119885Re and 119885Im are real part and the imaginary part ofthe measured impedance respectively and119885Re-cal and119885Im-calare the fitted values obtained by using the Voigt model Smallresiduals correspond to better validity
Only measured data that passed the KramersndashKronig testcan be used for further numerical fitting Figure 12 showsthat the obtained impedance data shows good validity whichcan be attributed to the measures employed in this sectionMoreover the repeatability of the test data is good becauseof reliable close contact between the test block and theelectrodes
Parameters 1198770 1198771 and 1198621 can be obtained throughnumerical fitting of the measured impedance data and thepreset equivalent circuit shown in Figure 5 The chloride iondiffusion coefficient can be calculated by using119877CCP = 1198770+1198771and (9)
The method of determining chloride ion diffusion coeffi-cient based on the AC impedance technique is performed asfollows
(1) Prepare Φ100mm times 50mm specimens and conductvacuum Clminus saturating using 1molL NaCl solution(the saturating regime is the same as that of ASTMC1202)
(2) Carry out AC impedance testing to obtain impedancespectroscopy data
(3) Perform data validation(4) Obtain 119877CCP from equivalent circuit fitting(5) Calculate chloride ion diffusion coefficient using (9)(6) Modify the diffusion coefficient according to the
cementitious material that was used
The rapid chloride permeability test ASTM C1202 hasbeen adopted as national standard by many countriesincluding China the United States and Canada The ASTMC1202 method specifies the rating of chloride permeability ofconcrete based on the charge passed through the specimenduring 6 h of testing period ASTM C1202 tests that use thesame concrete blocks were conducted to perform a compar-ison Figure 13 shows the relationship between chloride iondiffusion coefficients obtained from impedance-based tech-nology and 6 h electric flux A linear correlation (119876C1202 =930 times 119863Clminus ) between the rapid chloride permeability testand the proposed method was obtained with a correlationcoefficient of 09 see Figure 13 for details
As can be seen from Figure 13 some data points devi-ate from the straight line As reported by Shi [11] theASTMC1202 method is virtually a measurement of electricalconductivity of concrete which depends on both the pore
Testing resultLinear fit
0
1000
2000
3000
4000
Char
ge p
asse
d (C
oulo
mb)
1 2 3 4 50
DClminus (10minus12 m2sminus1)
Figure 13 Relationship between chloride ion diffusion coefficientusing ACIS and 6 h electric flux from ASTM C1202 tests
structure characteristics and pore solution chemistry ofconcrete Supplementary cementing materials such as silicafume fly ash and ground blast furnace slag may have asignificant effect on the chemistry or electrical conductivityof pore solution depending on the alkali content of the sup-plementary cementing material replacement level and agewhich has little to do with the chloride permeability ASTMC1202 method is susceptible to pore solution conductanceHowever the proposed method eliminates the effect of poresolution conductivity on permeability by using a carefullydesigned technique This effect may be an important reasonfor the moderate correlation between the two methods
5 Conclusions
(1) High-frequency AC impedance spectroscopy can reflectthe mesostructural properties of materials which enables usto indirectly study the permeability of concrete An equiva-lent circuit model with a clear physical meaning was adoptedthrough an investigation of AC conduction paths in concreteThrough numerical fitting of theNyquist plot of themeasuredimpedance spectroscopy and a preset model a parameterthat characterizes diffusion resistance that depends on theinterconnected porosity and pore solution conductivity wasobtained Based on the EinsteinndashSmoluchowski equationthe chloride ion diffusion coefficient was derived and theproposed formula was modified to eliminate the influenceof pore solution conductivity on diffusion coefficient mea-surementThen an accurate formula that reflects chloride iondiffusion resistance was obtained(2) With test block size specimen pretreatment im-
pedance test parameters equivalent circuit selection anddiffusion coefficient formula modification taken into consid-eration a method of determining the chloride ion diffusioncoefficient based on AC impedance spectroscopy was estab-lished In addition the test procedure was summarized forpractical purposes
8 Journal of Engineering
(3)The relationship between the proposed method andthe traditional ASTMC1202 method was established Resultsshowed that a certain but not very high degree of linear cor-relation exists which can be attributed to the fact that ASTMC1202 method is essentially a conductance method influ-enced by pore solution conductivity whereas pore solutionconductivity has little effect compared with interconnectedporosity on chloride ion diffusion behavior in concrete
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors acknowledge the support from National NaturalScience Foundation of China (Grant nos 51408379 and51508350) and Natural Science Foundation of Hebei China(Grant no E2013210125)
References
[1] L Kong and Y Du ldquoEffect of lightweight aggregate and theinterfacial transition zone on the durability of concrete basedon grey correlationrdquo Indian Journal of Engineering andMaterialsSciences vol 22 no 1 pp 111ndash119 2015
[2] A E Long G D Henderson and F R Montgomery ldquoWhyassess the properties of near-surface concreterdquo Constructionand Building Materials vol 15 no 2-3 pp 65ndash79 2001
[3] M Cabeza M Keddam X R Novoa I Sanchez and HTakenouti ldquoImpedance spectroscopy to characterize the porestructure during the hardening process of Portland cementpasterdquo Electrochimica Acta vol 51 no 8-9 pp 1831ndash1841 2006
[4] G Dotelli and C M Mari ldquoThe evolution of cement pastehydration process by impedance spectroscopyrdquo Materials Sci-ence and Engineering A vol 303 no 1-2 pp 54ndash59 2001
[5] M Cabeza P Merino X R Novoa and I Sanchez ldquoElectricaleffects generated by mechanical loading of hardened Portlandcement pasterdquo Cement and Concrete Composites vol 25 no 3pp 351ndash356 2003
[6] P Gu P Xie J J Beaudoin and R Brousseau ldquoAC impedancespectroscopy (I) a new equivalent circuit model for hydratedportland cement pasterdquo Cement and Concrete Research vol 22no 5 pp 833ndash840 1992
[7] G Song ldquoEquivalent circuit model for AC electrochemicalimpedance spectroscopy of concreterdquo Cement and ConcreteResearch vol 30 no 11 pp 1723ndash1730 2000
[8] M Shi Z Chen and J Sun ldquoDetermination of chloridediffusivity in concrete by AC impedance spectroscopyrdquo Cementand Concrete Research vol 29 no 7 pp 1111ndash1115 1999
[9] C Andrade ldquoCalculation of chloride diffusion coefficients inconcrete from ionic migration measurementsrdquo Cement andConcrete Research vol 23 no 3 pp 724ndash742 1993
[10] J M Esteban and M E Orazem ldquoOn the application ofthe Kramers-Kronig relations to evaluate the consistency ofelectrochemical impedance datardquo Journal of the ElectrochemicalSociety vol 138 no 1 pp 67ndash76 1991
[11] C Shi ldquoEffect of mixing proportions of concrete on its elec-trical conductivity and the rapid chloride permeability test
(ASTMC1202 or ASSHTOT277) resultsrdquoCement and ConcreteResearch vol 34 no 3 pp 537ndash545 2004
(3)The relationship between the proposed method andthe traditional ASTMC1202 method was established Resultsshowed that a certain but not very high degree of linear cor-relation exists which can be attributed to the fact that ASTMC1202 method is essentially a conductance method influ-enced by pore solution conductivity whereas pore solutionconductivity has little effect compared with interconnectedporosity on chloride ion diffusion behavior in concrete
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors acknowledge the support from National NaturalScience Foundation of China (Grant nos 51408379 and51508350) and Natural Science Foundation of Hebei China(Grant no E2013210125)
References
[1] L Kong and Y Du ldquoEffect of lightweight aggregate and theinterfacial transition zone on the durability of concrete basedon grey correlationrdquo Indian Journal of Engineering andMaterialsSciences vol 22 no 1 pp 111ndash119 2015
[2] A E Long G D Henderson and F R Montgomery ldquoWhyassess the properties of near-surface concreterdquo Constructionand Building Materials vol 15 no 2-3 pp 65ndash79 2001
[3] M Cabeza M Keddam X R Novoa I Sanchez and HTakenouti ldquoImpedance spectroscopy to characterize the porestructure during the hardening process of Portland cementpasterdquo Electrochimica Acta vol 51 no 8-9 pp 1831ndash1841 2006
[4] G Dotelli and C M Mari ldquoThe evolution of cement pastehydration process by impedance spectroscopyrdquo Materials Sci-ence and Engineering A vol 303 no 1-2 pp 54ndash59 2001
[5] M Cabeza P Merino X R Novoa and I Sanchez ldquoElectricaleffects generated by mechanical loading of hardened Portlandcement pasterdquo Cement and Concrete Composites vol 25 no 3pp 351ndash356 2003
[6] P Gu P Xie J J Beaudoin and R Brousseau ldquoAC impedancespectroscopy (I) a new equivalent circuit model for hydratedportland cement pasterdquo Cement and Concrete Research vol 22no 5 pp 833ndash840 1992
[7] G Song ldquoEquivalent circuit model for AC electrochemicalimpedance spectroscopy of concreterdquo Cement and ConcreteResearch vol 30 no 11 pp 1723ndash1730 2000
[8] M Shi Z Chen and J Sun ldquoDetermination of chloridediffusivity in concrete by AC impedance spectroscopyrdquo Cementand Concrete Research vol 29 no 7 pp 1111ndash1115 1999
[9] C Andrade ldquoCalculation of chloride diffusion coefficients inconcrete from ionic migration measurementsrdquo Cement andConcrete Research vol 23 no 3 pp 724ndash742 1993
[10] J M Esteban and M E Orazem ldquoOn the application ofthe Kramers-Kronig relations to evaluate the consistency ofelectrochemical impedance datardquo Journal of the ElectrochemicalSociety vol 138 no 1 pp 67ndash76 1991
[11] C Shi ldquoEffect of mixing proportions of concrete on its elec-trical conductivity and the rapid chloride permeability test
(ASTMC1202 or ASSHTOT277) resultsrdquoCement and ConcreteResearch vol 34 no 3 pp 537ndash545 2004
