Research Article Evaluation Technique of Chloride Penetration … · 2019. 7. 31. · Evaluation Technique of Chloride Penetration Using Apparent Diffusion Coefficient and Neural

Research ArticleEvaluation Technique of Chloride Penetration Using ApparentDiffusion Coefficient and Neural Network Algorithm

Yun-Yong Kim1 Byung-Jae Lee2 and Seung-Jun Kwon3

1 Civil Engineering Chungnam National University 99 Daehak-ro Yuseong-gu Daejeon 305-764 Republic of Korea2 RampD Center JNTINC Co Ltd No 9 Hyundaikia-ro 830beon-Gil Bibong-myeon HwaseongGyeonggi-do 445-842 Republic of Korea

3 Civil and Environmental Engineering Hannam University 133 Ojeong-dong Daedeok-gu Daejeon 306-791 Republic of Korea

Correspondence should be addressed to Seung-Jun Kwon jjuni98hannamackr

Received 3 June 2014 Accepted 11 August 2014 Published 11 September 2014

Academic Editor Tao Zhang

Copyright copy 2014 Yun-Yong Kim et alThis 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

Diffusion coefficient from chloride migration test is currently used however this cannot provide a conventional solution like totalchloride contents since it depicts only ion migration velocity in electrical field This paper proposes a simple analysis technique forchloride behavior using apparent diffusion coefficient from neural network algorithm with time-dependent diffusion phenomenaFor this work thirty mix proportions of high performance concrete are prepared and their diffusion coefficients are obtainedafter long term-NaCl submerged test Considering time-dependent diffusion coefficient based on Fickrsquos 2nd Law and NNA (neuralnetwork algorithm) analysis technique for chloride penetration is proposedThe applicability of the proposed technique is verifiedthrough the results from accelerated test long term submerged test and field investigation results

1 Introduction

Chloride ions induced into concrete cause a severe corrosionin embedded steel and the durability degradation propagatesto structural safety problem [1] In the earlier researches ondeterioration of chloride attack studies based on field inves-tigations and apparent diffusion have been performed [2ndash4]Recently micromodels based on mass conservation law andbehaviors in early aged concrete like porosity hydration andsaturation have been proposed [5ndash7] Furthermore variousphenomena like enlarged diffusion and permeation due tocracks and cold joint are considered for quantitativemodelingon chloride penetration [8 9]

Apparent diffusion coefficient based on Fickrsquos 2nd law isconventionally utilized for evaluating chloride behavior how-ever migration test and the related techniques are frequentlyutilized for measuring a resistance to chloride penetration[10 11] since apparent diffusion coefficient experimentallyobtained needs considerably long period Chloride diffusioncoefficients frommigration tests indicate ion velocity in elec-trical field so that they cannot be directly employed to Fickrsquo

2nd law For evaluation of chloride behavior using diffusioncoefficient from migration test complicated analysis frameis required [12 13] For evaluation of total chloride contentspecial relationship between free and bound chloride ionso called isotherm should be considered in the analysisframe [6 14 15] Apparent diffusion coefficient can providedirect solution-chloride content based on Fickrsquos 2nd Law toengineers and this technique has been widely applied for itssimple formulation and several familiar-powerful programslike Life 365 [3 16] Additionally several engineering advan-tages like easy employing time effect on diffusion behavior[16] and random variables for stochastic approach [8] arefound through treating apparent diffusion coefficient

NNA (neural network algorithm) is one of the optimiza-tion techniques and this has been widely utilized for determi-nation ofmix proportions and strength evaluation in concreteresearch field [17ndash20] For analysis of chloride behavior andcarbonation NNA technique is recently adopted [21 22]but the related analysis technique needs such complicatedmicromodels andmajor assumptions that it is notwidely usedfor engineers

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2014 Article ID 647243 13 pageshttpdxdoiorg1011552014647243

2 Advances in Materials Science and Engineering

Table 1 Chemical and physical properties of cement and mineral admixtures

TypesItems

Chemical composition () Physical propertiesSiO2 Al2O3 Fe2O3 CaO MgO SO3 Ig loss Specific gravity (gcm3) Blaine (cm2g)

OPC 2196 527 344 6341 213 196 079 316 3214GGBFS 3274 1323 041 4414 562 184 02 289 4340FA 5566 2776 704 270 114 049 43 219 3621SF 933 05 121 027 103 002 11 221 190620

30 mix proportions for HPC

Measurement of apparent diffusion coefficient after 6 months in submerged condition

Measurement of compressive strength at 28 days

Simulation of apparent diffusion coefficient

through NN

Selection of neurons (mix proportions)wb unit content of cement GGBFS FA SF and

finecoarse aggregate

Data processing(normalization of input and output values)

Learning and training(back propagation algorithm)

Comparison with data set and previous test results

regarding output (apparent diffusion coefficient)

Time-dependentdiffusion coefficient

Governing equation for chloridebehavior based on Fickrsquos 2nd law

Integration with diffusion coefficient from NN and governing equation

Verification of the proposed technique (chloride profile comparison)

Figure 1 Flowchart for this study

In this paper apparent diffusion coefficients which canprovide a direct solution (chloride content) are obtainedfrom chloride-submerged condition for 6 months Majormix components are selected as neurons and training forlearning is carried out for optimum apparent diffusion

coefficients The simulated diffusion coefficients areverified with test results A simple and deterministic analysistechnique for chloride behavior is proposed consideringtime-dependent diffusion characteristics and the apparentdiffusion coefficient from NNA In this paper diffusion

Advances in Materials Science and Engineering 3

Error

Error

Target output

Calculation of data fows forwards

Error backpropagates to adjust the weights and thresholds

h

ij

+

+minus

minus

xp1

xp2

xpN

whiwjh

(a) Simple neural network architecture

x1j

x2j

xij

xmj

w

0

11j

w2j

wij

wmj

120579j

y = f(x)

x

y

Oj = f( msumsum i=1

120579j)wijxij minus

(b) Activation function

Figure 2 Schematic diagram for simple NNA architecture [22 24]

0

10

20

30

40

50

60

70

80

o100 g30o70 g50o50 f10o90 f20o80 f30o70 f10s05 f20s05 g30s05 g35f15

Com

pres

sive s

treng

th (M

Pa)

(a) wb 037 series

0

10

20

30

40

50

60

70

80


Com

pres

sive s

treng

th (M

Pa)

(b) wb 042 series

0

10

20

30

40

50

60

70

80


Com

pres

sive s

treng

th (M

Pa)

7 days28 days

91 days270 days

(c) wb 047 series

Figure 3 Strength development with admixtures and curing periods

coefficients from various HPC (high performance concrete)mix proportions NNA application for reasonable selectionof diffusion coefficients and simple technique for chloridepenetration prediction are dealt with In Figure 1 flow chartfor the work is shown

2 Outline of NNA

It is reported that NNA was started by McCulloch and Pitt[23] A neuron as a unit with process of stimulus and reactionis modeled in the system The training for learning a data set


o100-37o100-42o100-47

g30o70-37g30o70-42g30o70-47g50o50-37g50o50-42g50o50-47

0 1 2 3 4 5 6 7 8

Apparent diffusion coefficient (1012 m2s)

(a) OPC and slag mixture series with various wb ratios

o100-37o100-42o100-47

f10o90-37f10o90-42f10o90-47f20o80-37f20o80-42f20o80-47

0 1 2 3 4 5 6 7 8


(b) OPC and fly ash series with various wb ratios

o100-37o100-42o100-47

f10s05-37f10s05-42f10s05-47f20s05-37f20s05-42f20s05-47g30s05-37g30s05-42g30s05-47g35f15-37g35f15-42g35f15-47

0 1 2 3 4 5 6 7 8


(c) OPC and combined mixture series with various wb ratios

Figure 4 Comparison of measured diffusion coefficient with OPC concrete

Table 2 Physical properties of aggregates

Types Items119866max(mm)

Specific gravity(gcm3)

Absorption() FM

Fine aggregate mdash 258 101 290Coarse aggregate 25 264 082 687

is conductedwith connection strength transfer function andbiasesThe errors between calculated and expected results arereduced with increasing epochs The training for learning iscompleted when the error decreases to a target convergencelevel In this paper a back-propagation algorithm is adoptedfor the neural network Figure 2 shows an outline of simpleneural network architecture [22 24]

In this network each element of input is connected toeach neuron input through the weight matrix Neurons (119873119895)and activated values (119867119895) in the hidden layer are formulated

as (1) and (2) Activated value 119874119896 can be written as (3)Consider

119873119895 = sum119882119895119894119868119894 (1)

119867119895 = 119891 (119873119895 + 119861119895) (2)

119874119896 = 119891 (sum119882119896119895119867119895 + 119861119896) (3)

where 119868119895 is input vector119882119895119894 is weight or connection strength119891 is transfer function and119861119895 is bias In the back-propagationerror (119864) is calculated through (4) considering target value(119879119896) Consider

119864 =1

2(sum

119896=1

119874119896 minus 119879119896)

2

(4)


Table 3 Mix proportions for HPC

Names of mix

Items

wbUnit weight (kgm3) Binder times

W Binder Materials S G AdmixtureC GGBS FA SF SP AE

o100-37 037 168 454 mdash mdash mdash 767 952 10 0017o100-42 042 168 400 mdash mdash mdash 787 976 09 0015o100-47 047 168 357 mdash mdash mdash 838 960 085 0017g30o70-37 037 168 318 136 mdash mdash 762 946 08 0018g30o70-42 042 168 280 120 mdash mdash 783 972 075 0013g30o70-47 047 168 250 107 mdash mdash 835 956 065 0015g50o50-37 037 168 227 227 mdash mdash 760 943 075 0017g50o50-42 042 168 200 200 mdash mdash 780 969 07 00135g50o50-47 047 168 178 179 mdash mdash 832 853 06 0015f10o90-37 037 168 409 mdash 45 mdash 760 943 075 0018f10o90-42 042 168 360 mdash 40 mdash 780 969 09 0021f10o90-47 047 168 321 mdash 36 mdash 832 952 075 0017f20o80-37 037 168 363 mdash 91 mdash 752 934 075 0018f20o80-42 042 168 320 mdash 80 mdash 774 961 085 0025f20o80-47 047 168 286 mdash 71 mdash 826 946 07 0017f30o70-37 037 168 318 mdash 136 mdash 745 952 075 02f30o70-42 042 168 280 mdash 120 mdash 768 953 075 0015f30o70-47 047 168 250 mdash 107 mdash 820 939 065 0019f10s05-37 037 168 386 mdash 45 23 756 938 10 0023f10s05-42 042 168 340 mdash 40 20 777 965 09 0021f10s05-47 047 168 303 mdash 36 18 829 950 09 0021f20s05-37 037 168 340 mdash 91 23 749 929 09 0023f20s05-42 042 168 300 mdash 80 20 771 957 085 0025f20s05-47 047 168 268 mdash 71 18 810 927 09 0025g30s05-37 037 168 295 136 mdash 23 759 942 075 0015g30s05-42 042 168 260 120 mdash 20 765 949 075 0015g30s05-47 047 168 232 107 mdash 18 832 952 08 0015g35f15-37 037 168 227 159 68 mdash 751 932 065 0014g35f15-42 042 168 200 140 60 mdash 773 959 065 0014g35f15-47 047 168 178 125 54 mdash 804 921 07 0014wb water to binder ratioG gravelAE air entrainerS sandSP superplasticizer

For minimizing the error connection strength (119882119894119895) is mod-ified backward form neurons in output layer like

Δ119882119896119895 = 120578120575119896119867119895 Δ119861119896 = 120578120575119896 120575119896 = (119879119896 minus 119874119896) 1198911015840(119873119896)

Δ119882119895119894 = 120578120575119895119867119894 Δ119861119895 = 120578120575119895 120575119895 = (119882119896119895120575119896) 1198911015840(119873119895)

(5)

where 120575119895 and 120575119896 are gradients of the total error and 120578 is thelearning rate

After the modification of connection strength NNArepeats the process of calculation and modification until theerror decreases within the target convergence

For the data set each input should have boundary limitsfrom 00 to 10 Through data process like (6) each valuesatisfies the boundary limit Consider

119875119899 =119875act minus 119875min119875max minus 119875min

(6)

where 119875119899 is input value for training 119875act is actual input dataand 119875max and 119875min are maximum and minimum values ofinput data After calculation the output value with a range of00sim10 is obtained and it should be converted to actual valueusing (6)


Table 4 Results of apparent diffusion coefficient

Mixture Diffusion coefficient (m2sec)o100-37 41119864 minus 12

o100-42 52119864 minus 12

o100-47 73119864 minus 12

g30o70-37 21119864 minus 12

g30o70-42 30119864 minus 12

g30o70-47 32119864 minus 12

g50o50-37 14119864 minus 12

g50o50-42 16119864 minus 12

g50o50-47 17119864 minus 12

f10o90-37 35119864 minus 12

f10o90-42 52119864 minus 12

f10o90-47 62119864 minus 12

f20o80-37 32119864 minus 12

f20o80-42 40119864 minus 12

f20o80-47 59119864 minus 12

f30o70-37 39119864 minus 12

f30o70-42 43119864 minus 12

f30o70-47 59119864 minus 12

f10s05-37 22119864 minus 12

f10s05-42 28119864 minus 12

f10s05-47 33119864 minus 12

f20s05-37 25119864 minus 12

f20s05-42 36119864 minus 12

f20s05-47 38119864 minus 12

g30s05-37 14119864 minus 12

g30s05-42 19119864 minus 12

g30s05-47 18119864 minus 12

g35f15-37 18119864 minus 12

g35f15-42 19119864 minus 12

g35f15-47 23119864 minus 12

3 Test Program for ApparentDiffusion Coefficient

31 Outline of Test Program In this section tests for learningand training of NNA are explained Thirty mix proportionsfor HPC are prepared Target slump and air content are150 plusmn 15mm and 45 plusmn 10 respectively Three wb (waterto binder) ratios are set as as 037 042 and 047 After28 days of water curing the specimens were kept in 35of NaCl solution for 6 months For 1-dimensinal intrusionof chloride ion sides and bottoms were coated with epoxyexcept top surface After 6 months of submerging in NaClsolution chloride profiles weremeasured based on AASHTOT 260 Through regression of chloride profile surface chlo-ride contents and apparent diffusion coefficients are obtainedFor binding materials OPC (ordinary portland cement) wasused GGBFS (ground granulated blast furnace slag) FA (flyash) and SF (silica fume) were added formineral admixturesIn Table 1 chemical compositions and physical propertiesof cement and the used mineral admixtures are listed

20

40

60

80

1 2 3 4 5 6 7 8

Com

pres

sive s

treng

th (M

Pa)

7 days 28 days91 days 270 days(7 days) (28 days)(91 days) (270 days)

Equation (7a)

Equation (7b)

Equation (7c)Equation (7d)

Diffusion coefficient (E12m2s)

Figure 5 Relationship between compressive strength and diffusioncoefficient

0 100 200 300 400 500 600 700 800 900 1000

Mea

n sq

uare

d er

ror (

mse

)

Epochs

10minus2

10minus4

10minus6

10minus10

10minus8

10minus12

Figure 6 Decrease in errors with increasing epochs

The physical properties of aggregates are listed in Table 2Thirty mix properties which are used for learning andtraining of NNA are listed in Table 3

32 Test Results

321 Compressive Strength with Ages Compressive strengthis measured at the age of 7 28 91 and 270 days In Figure 3the results of compressive strength with different ages areshownThe results show typical strength development higherstrength with lower wb ratio The smallest strength at theage 7 days is measured in f30o70 (30 replacement ofFA) in Figure 3 Compared with the results in OPC thestrength ratio is only 699 however in the long term (270days) concrete withmineral admixturesmostly shows higherstrength than OPC concrete It is reported that the ability ofa mineral admixture to react with calcium hydroxide presentin the hydrated Portland cement paste and to form additionalcalcium silicate hydrates can lead to significant reduction in


Table 5 Result of multiregression analysis

119863 = [1198861(119908119887) + 1198862(119862119890) + 1198863(GGBFS) + 1198864(FA) + 1198865(SF) + 1198866(119878) + 1198867(119866) + 119868] times 10minus15

1198861 1198862 1198863 1198864 1198865 1198866 1198867 119868

29386 2658 1101 2434 minus4241 1278 1180 minus3949161

Table 6 Mix proportions for verification (long-term submerged condition)

Type wb Binder (kgm3) Sand (kgm3) Coarse aggregate (kgm3)C FA

OPC 100 381 449 0 616 1050OPC 80 and FA 20 381 359 90 616 1050

porosity of both the matrix and the transition zone Conse-quently considerable improvement in ultimate strength andwater-tightness can be achieved by incorporation of mineraladmixtures [25] Silica fume is very effective to strengthdevelopment both in the short and in the long term In thecase of 270 days the highest strength is measured in f10s05(175 increase for OPC result wb 037) g30s05 (167increase forOPC result wb 042) and g30s05 (310 increasefor OPC result wb 047) In many researches the effect ofsilica fume is found to be considerable both to strength andto durability [26 27]

322 Apparent Diffusion Coefficient In Table 4 the resultsof apparent diffusion coefficient are listed The maximumand minimum results are measured in o100-47 (73 times

10minus12m2sec) and g30s05-37 (14times 10minus12m2sec) respectivelyThe lower wb ratio concrete has the lower diffusion coef-ficients are measured The mix proportions with mineraladmixture have lower results than thosewith onlyOPC Sincethe mix proportions with lower wb ratio and large amountof binder have more hydrates amount and smaller porositypenetration of chloride ion is impeded [7 13 15] Concretewith FA can have large amount of hydrates due to pozzolanreaction and this leads low diffusion of chloride ion In thecase of GGBFS low diffusion coefficients are measured dueto the small porosity from latent hydraulic properties andchemical binding of chloride ion [5 6 28] The comparisonsof mineral admixture group with OPC series are shown inFigure 4

In order to evaluate the relationship between strength anddiffusion coefficient linear regression analysis is performedand the results are shown in Figure 5 with test results

The regression results are listed in (7a)sim(7d)Consider

1198623 = minus13477119863 + 37064 (7a)

11986228 = minus18815119863 + 46954 (7b)

11986291 = minus28811119863 + 61963 (7c)

119862270 = minus30938119863 + 68342 (7d)

where 119862119894 denotes the compressive strength (MPa) at 119894 days119863 is measured diffusion coefficient (times1012m2sec) It is

observed the gradients of (7a) (7b) (7c) and (7d) increasewith ages and this shows higher strength is related with lowerdiffusion coefficient with aging

323 NNA Application to Diffusion Coefficient NNA tech-nique is applied to simulation of diffusion coefficient andthe results are compared with those from multiregressionanalysis Seven mix components like wb ratio unit contentof cement GGBFS FA SF sand and coarse aggregate areconsidered as input neurons Output neuron is fixed asapparent diffusion coefficient MATLAB program is usedfor this regression analysis Back propagation algorithmis adopted and Tan-Sigmoid function is used for transferfunction among various functions like linear transfer and log-sigmoid [24] Training number is set as 2000 and the errorto target convergence is set as 10minus12 for learning process Thenumber of neuron is only 7 so that the simulation is usuallycompleted within 2000 trials The decrease in error withincreasing epoch is shown in Figure 6

In Table 5 the result from multiregression analysis islisted From the analysis the average of relative error is198 which is reasonable however 706 of relative erroris calculated in the case of g50o50-47

In Figure 7 the results from multiregression in Table 5are compared with those from NNA and experiment Theresults from NNA show more reasonable prediction withaverage relative error of 41 which is very close to testresults compared with 198 of average relative error frommultiregression analysis The comparisons of relative errorfrom each technique are shown in Figure 8

The chloride profiles based on the diffusion coefficientfrom NNA are compared with test results which were keptin submerged condition for 6 months in Figure 9 Concretewith lower wb ratio and larger mineral admixture shows themore reduced chloride penetration The proposed techniqueshows reasonable prediction for chloride penetration

4 Analysis Technique of Chloride Penetrationwith Time-Dependent Diffusion

41 Time-Dependent Diffusion of Chloride Ion It is reportedthat chloride diffusion coefficient based on Fickrsquos 2nd lawdecreases with time [3 8] The governing equation for


Table 7 Analysis conditions for verification (submerged condition)

Type 119898119863 from NNA 11986328 Surface chloride content(m2sec) (10minus12 m2sec) ( of concrete wt)

OPC 100 02 2509 2912 0709OPC 80 and FA 20 036 1801 2252 0709

0

2000

4000

6000

8000

o100

-37

o100

-42

o100

-47

g30

o70

-37

g30

o70

-42

g30

o70

-47

g50

o50

-37

g50

o50

-42

g50

o50

-47Ap

pare

nt d

iffus

ion

coeffi

cien

t(E

-15

m2s

)

(a) OPC and GGBFS series

0

2000

4000

6000

8000

Appa

rent

diff

usio

n co

effici

ent

(E-15

m2s

)

f10

o90

-42

f10

o90

-47

f20

o80

-37

f20

o80

-42

f20

o80

-47

f30

o70

-37

f30

o70

-42

f30

o70

-47

(b) FA series

f10

s05

-37

f10

s05

-42

f10

s05

-47

f20

s05

-37

f20

s05

-42

f20

s05

-47

g30

s05

-37

g30

s05

-42

g30

s05

-47

g35

f15

-37

g35

f15

-42

g35

f15

-47

Test resultsMultiregressionNeural network

0

2000

4000

6000

8000

Appa

rent

diff

usio

n co

effici

ent

(E-15

m2s

)

(c) Combined series

Figure 7 Comparison with results from test multiregression and NNA

chloride penetration is listed in (8) and time-dependentdiffusion coefficient is listed in (9) [3 8 16] Consider

119862 (119909 119905) = 119862119904 [1 minus erf ( 119909

2radic119863 (119905) sdot 119905)] (8)

119863 (119905) = 1198630(1199050

119905)

119898

(9)

where 1199050 and 1198630 are reference time (28 days) and diffusioncoefficient at reference time119863(119905) is time-dependent diffusioncoefficient 119898 is time exponent which is changed with typeand amount of mineral admixtures [3 16] which is definedas

119898 = 02 + 04 (FA50

+SG70

) (10)

where FA and SG denote the replacement ratio of fly ash andslag For solving (8) with (9) numerical analysis like finite

differential method should be employed however if timeterm is fixed averaged diffusion coefficient can be derived as(11a) and (11b) [29] Consider

119863 (119905) =1

119905int

119905

0

1198630 (1199050

120591) 119889120591 = 1198630

1199051198980

119905[1205911minus119898

1 minus 119898]

119905

0

=1198630

1 minus 119898(1199050

119905)

119898

(119905 lt 119905119888)

(11a)

119863 (119905) = 1198630 [1 +119905119888

119905(

119898

1 minus 119898)](

1199050

119905119888

)

119898

(119905 ge 119905119888) (11b)

where 119905119888 is the time after which diffusion coefficient keepsalmost constant and it is usually assumed as 30 years

42 Chloride Penetration Analysis Using NNA and Time-Dependent Diffusion Coefficient The diffusion coefficientsfrom NNA are the results based on the test data which is


0 20 40 60 80 100NPC100-37NPC100-42NPC100-47G30N70-37G30N70-42G30N70-47G50N50-37G50N50-42G50N50-47F10N90-37F10N90-42F10N90-47F20N80-37F20N80-42F20N80-47F30N70-37F30N70-42F30N70-47F10S05-37F10S05-42F10S05-47F20S05-37F20S05-42F20S05-47G30S05-37G30S05-42G30S05-47G35F15-37G35F15-42G35F15-47

Relative error ()

Type

of m

ixtu

re

From NNAFrom linear regression

0

5

10

15

20

25

Linear regression NNA technique

Aver

aged

relat

ive e

rror

()

Figure 8 Comparison of relative errors from NNA and linear regression analysis with averaged relative errors

obtained from 6 months submerged condition so that theyare converted to diffusion coefficient at the reference time (28days) In Figure 10 analysis technique for chloride behaviorusing NNA is depicted

43 Comparison with Previous Test Results In this sectionthe results from the proposed technique are compared withthe previous test results of chloride profiles In the previoustest [28] two types of concrete (FA and OPC) were keptin 35 NaCl solution for 46 weeks Table 6 shows the mixproportions [28]

Conditions for analysis are listed in Table 7 and theanalysis results are shown in Figure 11 From Figure 11 it isfound that the obtained diffusion coefficient seems to be smallbut the results from the analysis reasonably agree with theprevious chloride profiles

Another verification is performed using the results fromfield investigation In the previous research [28] the chlorideprofileswere obtained fromRCcolumns after 1 and 10 years insubmerged condition Unfortunately mix proportions couldnot be obtained but it was found that it was made up withOPC concrete and wc (water to cement ratio) was 055Conventional mix proportions are assumed as Table 8 basedon the domestic typical mix proportions [30] and analysisconditions are listed in Table 9

Table 8 Mix proportions for verification (field investigation)

Type wc Cement(kgm3)

Sand(kgm3)

Coarse aggregate(kgm3)

OPC 100 550 352 653 1173

Table 9 Analysis condition for verification (field investigation)

Type 119898119863 from NNA 11986328 Surface chloride content(m2sec) (m2sec) ( of concrete wt)

OPC100 02 3647 4233 0709

In Figure 12 chloride profiles from field investigation arecompared with the results from this studyWith elapsed timechloride profile moves to inside of concrete and the proposedtechnique is evaluated to reasonably predict the chloridepenetration

This study extends the applicability of NNA which islimitedly utilized for concrete strength and mix proportionsto the research on durability Through learning and trainingof diffusion coefficient target value (diffusion coefficient)can be simulated in a given mix proportions However thistechnique has still limitation since NNA technique closely


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)

(a) Chloride profile in o100 series

0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)

(b) Chloride profile in g30o70 series

0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)

(c) Chloride profile in g50o50 series

0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)

(d) Chloride profile in f10o90 series

0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)

Analysis wb 37Analysis wb 42Analysis wb 47

Test wb 37Test wb 42Test wb 47

(e) Chloride profile in f20o80 series



0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)

(f) Chloride profile in f30o70 series

Figure 9 Continued


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)

(g) Chloride profile in f10s05 series

0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)

(h) Chloride profile in f20s05 series

0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)



(i) Chloride profile in g30s05 series

0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)



(j) Chloride profile in g35f15 series

Figure 9 Comparison of chloride profile between NNA and test results

depends on data set for training The data in this paperhas limitary material properties like wb (037sim047) anddiffusion coefficient (14sim73 times 10minus12msec2) so that it is nec-essary to extend the range for enhancing application Variousmix proportions with mineral admixtures and variability ofsurface chloride content will be considered for future study

5 Conclusions

The conclusions evaluation technique of chloride penetrationusing apparent diffusion coefficient and neural networkalgorithm are as follows

(1) Thirty mix proportions for HPC containing GGBFSFA and SF are prepared and apparent diffusioncoefficients are obtained after 6-month submergedcondition of NaCl 35 Seven mix components(wb unit content of cement GGBFS FA SF andfinecoarse aggregate) are selected as neurons andNNA is applied to simulation of diffusion coefficientThe simulated data shows only 41 of relative errorwhich is very accurate comparedwith the results frommultiregression analysis showing 198

(2) Utilizing diffusion coefficient from NNA and time-dependent diffusion chloride profiles are evaluated


Obtaining mix components

Derivation of apparent diffusion coefficient through NN (age 6 month)

Calculation of apparent diffusion coefficient at the reference time

(28 days) considering

Chloride behavior analysis

or

neural network

InputLayer Layer

Outputw

b+

w+

b

D(t) = D0 and m = 02 + 04(FA50 + SG70)

C(x t) = Cs[1minus erf( x

2radicD(t) middot t)]

D(t) = D0[1+ tct( m

1 minus m)]

tc (t ge tc)( t0

120591)d120591 = D0

tm0t[ 1205911minusm

1minus m]t

0=

D01minus m

( t0t)m ( t lt tc)

( t0t)m

( t0 )mD(t) =1

tintt0D0

Figure 10 Prediction of chloride penetration using NNA and time-dependent diffusion

0

02

04

06

08

0 10 20 30 40

Chlo

ride c

onte

nt (c

onc

wt

)

Cover depth (mm)

FA 20OPC 100

Analysis FA 20Analysis OPC

Figure 11 Chloride profile between results from test and this study

From the comparison with results of long termsubmerging test and field investigation the proposedtechnique is evaluated to reasonably predict theinduced chloride profile

(3) The proposed technique is closely dependent onquantitative data set for training and learning With

0

02

04

06

08

0 20 40 60 80 100

Chlo

ride c

onte

nt (5

of c

onc

wt)

Concrete depth (mm)

Test (1 year)Test (10 year)

Analysis (1 year)Analysis (10 year)

Figure 12 Chloride profile between results from field investigationand this study

more extendedmix proportions and the related diffu-sion coefficients this technique can be modified andmore applicable to evaluation of chloride penetration


Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research was supported by Grant (Code 11-TechnologyInnovation-F04) from Construction Technology ResearchProgram (CTIP) funded by Ministry of Land Infrastructureand Transport

References

[1] J P Broomfield Corrosion of Steel in Concrete UnderstandingInvestigation and Repair EE amp FN Spon London UK 1997

[2] RILEM ldquoDurability design of concrete structuresrdquo Report ofRILEM technical committee 130-CSL EampFN 1994

[3] M D A Thomas and E C Bentz Computer Program forPredicting the Service Life and Life-Cycle Costs of ReinforcedConcrete Exposed to Chlorides Life 365 Manual SFA 2002

[4] CEB-FIP ldquoModel code for service life designrdquo InternationalFederation for Structural Concrete (fib) Task Group 56 2006

[5] H-W Song S-W Pack C H Lee and S -J Kwon ldquoService lifeprediction of concrete structures under marine environmentconsidering coupled deteriorationrdquo Restoration of Buildings andMonuments vol 12 pp 265ndash284 2006

[6] K Maekawa T Ishida and T Kishi ldquoMulti-scale modeling ofconcrete performancerdquo Journal of Advanced Concrete Technol-ogy vol 1 no 2 pp 91ndash126 2003

[7] H-W Song S-J Kwon K-J Byun and C-K Park ldquoA study onanalytical technique of chloride diffusion considering charac-teristics of mixture design for high performance concrete usingmineral admixturerdquo Journal of Korean Society of Civil Engineersvol 25 no 1A pp 213ndash223 2005

[8] S J Kwon U J Na S S Park and S H Jung ldquoServicelife prediction of concrete wharves with early-aged crackprobabilistic approach for chloride diffusionrdquo Structural Safetyvol 31 no 1 pp 75ndash83 2009

[9] S-S Park S-J Kwon and S-H Jung ldquoAnalysis techniquefor chloride penetration in cracked concrete using equivalentdiffusion and permeationrdquoConstruction andBuildingMaterialsvol 29 pp 183ndash192 2012

[10] NORDTEST ldquoChloride migration coefficient from non-steady-state migration experimentsrdquo NT BUILD 492 1999

[11] L Tang Chloride Transport in Concrete Publication P-966Division of Building Materials Chalmers University of Tech-nology Sweden 1996

[12] S Park S Kwon S H Jung and S Lee ldquoModeling of waterpermeability in early aged concrete with cracks based on micropore structurerdquoConstruction and BuildingMaterials vol 27 no1 pp 597ndash604 2012

[13] K Maekawa T Ishida and T Kishi Multi-Scale Modeling ofStructural Concrete TylorampFrancis London UK 1st edition2009

[14] L Tang ldquoElectrically accelerated methods for determiningchloride diffusivity in concrete-current developmentrdquo Maga-zine of Concrete Research vol 48 no 176 pp 173ndash179 1996

[15] C Arya N R Buenfeld and J B Newman ldquoFactors influencingchloride-binding in concreterdquo Cement and Concrete Researchvol 20 no 2 pp 291ndash300 1990

[16] M D A Thomas and P B Bamforth ldquoModelling chloridediffusion in concrete effect of fly ash and slagrdquoCement and Con-crete Research vol 29 no 4 pp 487ndash495 1999

[17] J Wang H Ni and J He ldquoThe application of automatic acqui-sition of knowledge to mix design of concreterdquo Cement andConcrete Research vol 29 no 12 pp 1875ndash1880 1999

[18] I-C Yeh ldquoModeling of strength of high-performance concreteusing artificial neural networksrdquoCement andConcrete Researchvol 28 no 12 pp 1797ndash1808 1998

[19] J A Stegemann and N R Buenfeld ldquoPrediction of unconfinedcompressive strength of cement paste with pure metal com-pound additionsrdquo Cement and Concrete Research vol 32 no6 pp 903ndash913 2002

[20] K-B Park T Noguchi and J Plawsky ldquoModeling of hydrationreactions using neural networks to predict the average proper-ties of cement pasterdquoCement and Concrete Research vol 35 no9 pp 1676ndash1684 2005

[21] H-W Song and S-J Kwon ldquoEvaluation of chloride penetrationin high performance concrete using neural network algorithmand micro pore structurerdquo Cement and Concrete Research vol39 no 9 pp 814ndash824 2009

[22] S Kwon and H Song ldquoAnalysis of carbonation behavior inconcrete using neural network algorithm and carbonationmodelingrdquoCement andConcrete Research vol 40 no 1 pp 119ndash127 2010

[23] W McCulloch and W Pitt ldquoA logical calculus of the ideasimmanentrdquo The Bulletin of Mathematical Biophysics vol 5 no4 pp 115ndash133 1943

[24] H Demuth andM BealeNeural Network Toolbox Userrsquos GuideThe MathWorks 1997

[25] A M Neville Properties of Concrete Longman 4th and finaledition 1996

[26] H-W Song J-C Jang V Saraswathy and K-J Byun ldquoAnestimation of the diffusivity of silica fume concreterdquo Buildingand Environment vol 42 no 3 pp 1358ndash1367 2007

[27] S A Khedr and M N Abou-Zeid ldquoCharacteristics of silica-fume concreterdquo Journal of Materials in Civil Engineering vol 6no 3 pp 357ndash375 1994

[28] S Y Jang Modeling of chloride transport and carbonationin concrete and prediction of service life of concrete struc-tures considering corrosion of steel reinforcement [PhD thesis]Department of Civil Engineering Seoul National UniversitySeoul Republic of Korea 2003

[29] E Poulsen ldquoOn a model of chloride ingress into concreterdquo inProceedings of the Nordic Mini-Seminar on Chloride Transportpp 1ndash8 Department of BuildingMaterials ChalmersUniversityof Technology Gothenburg Sweden 1993

[30] KREA-Korean Remicon Engineering Association ldquoConcreteMix Proportionsrdquo 2005 (Korean)

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


Table 1 Chemical and physical properties of cement and mineral admixtures

TypesItems

Chemical composition () Physical propertiesSiO2 Al2O3 Fe2O3 CaO MgO SO3 Ig loss Specific gravity (gcm3) Blaine (cm2g)

OPC 2196 527 344 6341 213 196 079 316 3214GGBFS 3274 1323 041 4414 562 184 02 289 4340FA 5566 2776 704 270 114 049 43 219 3621SF 933 05 121 027 103 002 11 221 190620

30 mix proportions for HPC

Measurement of apparent diffusion coefficient after 6 months in submerged condition

Measurement of compressive strength at 28 days

Simulation of apparent diffusion coefficient

through NN

Selection of neurons (mix proportions)wb unit content of cement GGBFS FA SF and

finecoarse aggregate

Data processing(normalization of input and output values)

Learning and training(back propagation algorithm)

Comparison with data set and previous test results

regarding output (apparent diffusion coefficient)

Time-dependentdiffusion coefficient

Governing equation for chloridebehavior based on Fickrsquos 2nd law

Integration with diffusion coefficient from NN and governing equation

Verification of the proposed technique (chloride profile comparison)

Figure 1 Flowchart for this study

In this paper apparent diffusion coefficients which canprovide a direct solution (chloride content) are obtainedfrom chloride-submerged condition for 6 months Majormix components are selected as neurons and training forlearning is carried out for optimum apparent diffusion

coefficients The simulated diffusion coefficients areverified with test results A simple and deterministic analysistechnique for chloride behavior is proposed consideringtime-dependent diffusion characteristics and the apparentdiffusion coefficient from NNA In this paper diffusion


Error

Error

Target output



h

ij

+

+minus

minus

xp1

xp2

xpN

whiwjh


x1j

x2j

xij

xmj

w

0

11j

w2j

wij

wmj

120579j

y = f(x)

x

y

Oj = f( msumsum i=1




0

10

20

30

40

50

60

70

80


Com

pres

sive s

treng

th (M

Pa)

(a) wb 037 series

0

10

20

30

40

50

60

70

80


Com

pres

sive s

treng

th (M

Pa)

(b) wb 042 series

0

10

20

30

40

50

60

70

80


Com

pres

sive s

treng

th (M

Pa)

7 days28 days

91 days270 days

(c) wb 047 series



2 Outline of NNA



o100-37o100-42o100-47

g30o70-37g30o70-42g30o70-47g50o50-37g50o50-42g50o50-47

0 1 2 3 4 5 6 7 8



o100-37o100-42o100-47

f10o90-37f10o90-42f10o90-47f20o80-37f20o80-42f20o80-47

0 1 2 3 4 5 6 7 8



o100-37o100-42o100-47


0 1 2 3 4 5 6 7 8







Absorption() FM





119873119895 = sum119882119895119894119868119894 (1)

119867119895 = 119891 (119873119895 + 119861119895) (2)

119874119896 = 119891 (sum119882119896119895119867119895 + 119861119896) (3)


119864 =1

2(sum

119896=1

119874119896 minus 119879119896)

2

(4)



Names of mix

Items





Δ119882119896119895 = 120578120575119896119867119895 Δ119861119896 = 120578120575119896 120575119896 = (119879119896 minus 119874119896) 1198911015840(119873119896)

Δ119882119895119894 = 120578120575119895119867119894 Δ119861119895 = 120578120575119895 120575119895 = (119882119896119895120575119896) 1198911015840(119873119895)

(5)





(6)





o100-42 52119864 minus 12

o100-47 73119864 minus 12

g30o70-37 21119864 minus 12

g30o70-42 30119864 minus 12

g30o70-47 32119864 minus 12

g50o50-37 14119864 minus 12

g50o50-42 16119864 minus 12

g50o50-47 17119864 minus 12

f10o90-37 35119864 minus 12

f10o90-42 52119864 minus 12

f10o90-47 62119864 minus 12

f20o80-37 32119864 minus 12

f20o80-42 40119864 minus 12

f20o80-47 59119864 minus 12

f30o70-37 39119864 minus 12

f30o70-42 43119864 minus 12

f30o70-47 59119864 minus 12

f10s05-37 22119864 minus 12

f10s05-42 28119864 minus 12

f10s05-47 33119864 minus 12

f20s05-37 25119864 minus 12

f20s05-42 36119864 minus 12

f20s05-47 38119864 minus 12

g30s05-37 14119864 minus 12

g30s05-42 19119864 minus 12

g30s05-47 18119864 minus 12

g35f15-37 18119864 minus 12

g35f15-42 19119864 minus 12

g35f15-47 23119864 minus 12



20

40

60

80

1 2 3 4 5 6 7 8

Com

pres

sive s

treng

th (M

Pa)


Equation (7a)

Equation (7b)




0 100 200 300 400 500 600 700 800 900 1000

Mea

n sq

uare

d er

ror (

mse

)

Epochs

10minus2

10minus4

10minus6

10minus10

10minus8

10minus12



32 Test Results





1198861 1198862 1198863 1198864 1198865 1198866 1198867 119868

29386 2658 1101 2434 minus4241 1278 1180 minus3949161



OPC 100 381 449 0 616 1050OPC 80 and FA 20 381 359 90 616 1050






1198623 = minus13477119863 + 37064 (7a)

11986228 = minus18815119863 + 46954 (7b)

11986291 = minus28811119863 + 61963 (7c)

119862270 = minus30938119863 + 68342 (7d)












OPC 100 02 2509 2912 0709OPC 80 and FA 20 036 1801 2252 0709

0

2000

4000

6000

8000

o100

-37

o100

-42

o100

-47

g30

o70

-37

g30

o70

-42

g30

o70

-47

g50

o50

-37

g50

o50

-42

g50

o50

-47Ap

pare

nt d

iffus

ion

coeffi

cien

t(E

-15

m2s

)


0

2000

4000

6000

8000

Appa

rent

diff

usio

n co

effici

ent

(E-15

m2s

)

f10

o90

-42

f10

o90

-47

f20

o80

-37

f20

o80

-42

f20

o80

-47

f30

o70

-37

f30

o70

-42

f30

o70

-47

(b) FA series

f10

s05

-37

f10

s05

-42

f10

s05

-47

f20

s05

-37

f20

s05

-42

f20

s05

-47

g30

s05

-37

g30

s05

-42

g30

s05

-47

g35

f15

-37

g35

f15

-42

g35

f15

-47


0

2000

4000

6000

8000

Appa

rent

diff

usio

n co

effici

ent

(E-15

m2s

)

(c) Combined series



119862 (119909 119905) = 119862119904 [1 minus erf ( 119909

2radic119863 (119905) sdot 119905)] (8)

119863 (119905) = 1198630(1199050

119905)

119898

(9)


119898 = 02 + 04 (FA50

+SG70

) (10)



119863 (119905) =1

119905int

119905

0

1198630 (1199050

120591) 119889120591 = 1198630

1199051198980

119905[1205911minus119898

1 minus 119898]

119905

0

=1198630

1 minus 119898(1199050

119905)

119898

(119905 lt 119905119888)

(11a)

119863 (119905) = 1198630 [1 +119905119888

119905(

119898

1 minus 119898)](

1199050

119905119888

)

119898

(119905 ge 119905119888) (11b)





Relative error ()

Type

of m

ixtu

re


0

5

10

15

20

25


Aver

aged

relat

ive e

rror

()








Sand(kgm3)


OPC 100 550 352 653 1173



OPC100 02 3647 4233 0709




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


Figure 9 Continued


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






5 Conclusions










or

neural network

InputLayer Layer

Outputw

b+

w+

b

D(t) = D0 and m = 02 + 04(FA50 + SG70)



D(t) = D0[1+ tct( m

1 minus m)]

tc (t ge tc)( t0

120591)d120591 = D0

tm0t[ 1205911minusm

1minus m]t

0=

D01minus m

( t0t)m ( t lt tc)

( t0t)m

( t0 )mD(t) =1

tintt0D0


0

02

04

06

08

0 10 20 30 40

Chlo

ride c

onte

nt (c

onc

wt

)

Cover depth (mm)

FA 20OPC 100





0

02

04

06

08

0 20 40 60 80 100

Chlo

ride c

onte

nt (5

of c

onc

wt)

Concrete depth (mm)








Acknowledgment


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Error

Error

Target output



h

ij

+

+minus

minus

xp1

xp2

xpN

whiwjh


x1j

x2j

xij

xmj

w

0

11j

w2j

wij

wmj

120579j

y = f(x)

x

y

Oj = f( msumsum i=1




0

10

20

30

40

50

60

70

80


Com

pres

sive s

treng

th (M

Pa)

(a) wb 037 series

0

10

20

30

40

50

60

70

80


Com

pres

sive s

treng

th (M

Pa)

(b) wb 042 series

0

10

20

30

40

50

60

70

80


Com

pres

sive s

treng

th (M

Pa)

7 days28 days

91 days270 days

(c) wb 047 series



2 Outline of NNA



o100-37o100-42o100-47

g30o70-37g30o70-42g30o70-47g50o50-37g50o50-42g50o50-47

0 1 2 3 4 5 6 7 8



o100-37o100-42o100-47

f10o90-37f10o90-42f10o90-47f20o80-37f20o80-42f20o80-47

0 1 2 3 4 5 6 7 8



o100-37o100-42o100-47


0 1 2 3 4 5 6 7 8







Absorption() FM





119873119895 = sum119882119895119894119868119894 (1)

119867119895 = 119891 (119873119895 + 119861119895) (2)

119874119896 = 119891 (sum119882119896119895119867119895 + 119861119896) (3)


119864 =1

2(sum

119896=1

119874119896 minus 119879119896)

2

(4)



Names of mix

Items





Δ119882119896119895 = 120578120575119896119867119895 Δ119861119896 = 120578120575119896 120575119896 = (119879119896 minus 119874119896) 1198911015840(119873119896)

Δ119882119895119894 = 120578120575119895119867119894 Δ119861119895 = 120578120575119895 120575119895 = (119882119896119895120575119896) 1198911015840(119873119895)

(5)





(6)





o100-42 52119864 minus 12

o100-47 73119864 minus 12

g30o70-37 21119864 minus 12

g30o70-42 30119864 minus 12

g30o70-47 32119864 minus 12

g50o50-37 14119864 minus 12

g50o50-42 16119864 minus 12

g50o50-47 17119864 minus 12

f10o90-37 35119864 minus 12

f10o90-42 52119864 minus 12

f10o90-47 62119864 minus 12

f20o80-37 32119864 minus 12

f20o80-42 40119864 minus 12

f20o80-47 59119864 minus 12

f30o70-37 39119864 minus 12

f30o70-42 43119864 minus 12

f30o70-47 59119864 minus 12

f10s05-37 22119864 minus 12

f10s05-42 28119864 minus 12

f10s05-47 33119864 minus 12

f20s05-37 25119864 minus 12

f20s05-42 36119864 minus 12

f20s05-47 38119864 minus 12

g30s05-37 14119864 minus 12

g30s05-42 19119864 minus 12

g30s05-47 18119864 minus 12

g35f15-37 18119864 minus 12

g35f15-42 19119864 minus 12

g35f15-47 23119864 minus 12



20

40

60

80

1 2 3 4 5 6 7 8

Com

pres

sive s

treng

th (M

Pa)


Equation (7a)

Equation (7b)




0 100 200 300 400 500 600 700 800 900 1000

Mea

n sq

uare

d er

ror (

mse

)

Epochs

10minus2

10minus4

10minus6

10minus10

10minus8

10minus12



32 Test Results





1198861 1198862 1198863 1198864 1198865 1198866 1198867 119868

29386 2658 1101 2434 minus4241 1278 1180 minus3949161



OPC 100 381 449 0 616 1050OPC 80 and FA 20 381 359 90 616 1050






1198623 = minus13477119863 + 37064 (7a)

11986228 = minus18815119863 + 46954 (7b)

11986291 = minus28811119863 + 61963 (7c)

119862270 = minus30938119863 + 68342 (7d)












OPC 100 02 2509 2912 0709OPC 80 and FA 20 036 1801 2252 0709

0

2000

4000

6000

8000

o100

-37

o100

-42

o100

-47

g30

o70

-37

g30

o70

-42

g30

o70

-47

g50

o50

-37

g50

o50

-42

g50

o50

-47Ap

pare

nt d

iffus

ion

coeffi

cien

t(E

-15

m2s

)


0

2000

4000

6000

8000

Appa

rent

diff

usio

n co

effici

ent

(E-15

m2s

)

f10

o90

-42

f10

o90

-47

f20

o80

-37

f20

o80

-42

f20

o80

-47

f30

o70

-37

f30

o70

-42

f30

o70

-47

(b) FA series

f10

s05

-37

f10

s05

-42

f10

s05

-47

f20

s05

-37

f20

s05

-42

f20

s05

-47

g30

s05

-37

g30

s05

-42

g30

s05

-47

g35

f15

-37

g35

f15

-42

g35

f15

-47


0

2000

4000

6000

8000

Appa

rent

diff

usio

n co

effici

ent

(E-15

m2s

)

(c) Combined series



119862 (119909 119905) = 119862119904 [1 minus erf ( 119909

2radic119863 (119905) sdot 119905)] (8)

119863 (119905) = 1198630(1199050

119905)

119898

(9)


119898 = 02 + 04 (FA50

+SG70

) (10)



119863 (119905) =1

119905int

119905

0

1198630 (1199050

120591) 119889120591 = 1198630

1199051198980

119905[1205911minus119898

1 minus 119898]

119905

0

=1198630

1 minus 119898(1199050

119905)

119898

(119905 lt 119905119888)

(11a)

119863 (119905) = 1198630 [1 +119905119888

119905(

119898

1 minus 119898)](

1199050

119905119888

)

119898

(119905 ge 119905119888) (11b)





Relative error ()

Type

of m

ixtu

re


0

5

10

15

20

25


Aver

aged

relat

ive e

rror

()








Sand(kgm3)


OPC 100 550 352 653 1173



OPC100 02 3647 4233 0709




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


Figure 9 Continued


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






5 Conclusions










or

neural network

InputLayer Layer

Outputw

b+

w+

b

D(t) = D0 and m = 02 + 04(FA50 + SG70)



D(t) = D0[1+ tct( m

1 minus m)]

tc (t ge tc)( t0

120591)d120591 = D0

tm0t[ 1205911minusm

1minus m]t

0=

D01minus m

( t0t)m ( t lt tc)

( t0t)m

( t0 )mD(t) =1

tintt0D0


0

02

04

06

08

0 10 20 30 40

Chlo

ride c

onte

nt (c

onc

wt

)

Cover depth (mm)

FA 20OPC 100





0

02

04

06

08

0 20 40 60 80 100

Chlo

ride c

onte

nt (5

of c

onc

wt)

Concrete depth (mm)








Acknowledgment


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




o100-37o100-42o100-47

g30o70-37g30o70-42g30o70-47g50o50-37g50o50-42g50o50-47

0 1 2 3 4 5 6 7 8



o100-37o100-42o100-47

f10o90-37f10o90-42f10o90-47f20o80-37f20o80-42f20o80-47

0 1 2 3 4 5 6 7 8



o100-37o100-42o100-47


0 1 2 3 4 5 6 7 8







Absorption() FM





119873119895 = sum119882119895119894119868119894 (1)

119867119895 = 119891 (119873119895 + 119861119895) (2)

119874119896 = 119891 (sum119882119896119895119867119895 + 119861119896) (3)


119864 =1

2(sum

119896=1

119874119896 minus 119879119896)

2

(4)



Names of mix

Items





Δ119882119896119895 = 120578120575119896119867119895 Δ119861119896 = 120578120575119896 120575119896 = (119879119896 minus 119874119896) 1198911015840(119873119896)

Δ119882119895119894 = 120578120575119895119867119894 Δ119861119895 = 120578120575119895 120575119895 = (119882119896119895120575119896) 1198911015840(119873119895)

(5)





(6)





o100-42 52119864 minus 12

o100-47 73119864 minus 12

g30o70-37 21119864 minus 12

g30o70-42 30119864 minus 12

g30o70-47 32119864 minus 12

g50o50-37 14119864 minus 12

g50o50-42 16119864 minus 12

g50o50-47 17119864 minus 12

f10o90-37 35119864 minus 12

f10o90-42 52119864 minus 12

f10o90-47 62119864 minus 12

f20o80-37 32119864 minus 12

f20o80-42 40119864 minus 12

f20o80-47 59119864 minus 12

f30o70-37 39119864 minus 12

f30o70-42 43119864 minus 12

f30o70-47 59119864 minus 12

f10s05-37 22119864 minus 12

f10s05-42 28119864 minus 12

f10s05-47 33119864 minus 12

f20s05-37 25119864 minus 12

f20s05-42 36119864 minus 12

f20s05-47 38119864 minus 12

g30s05-37 14119864 minus 12

g30s05-42 19119864 minus 12

g30s05-47 18119864 minus 12

g35f15-37 18119864 minus 12

g35f15-42 19119864 minus 12

g35f15-47 23119864 minus 12



20

40

60

80

1 2 3 4 5 6 7 8

Com

pres

sive s

treng

th (M

Pa)


Equation (7a)

Equation (7b)




0 100 200 300 400 500 600 700 800 900 1000

Mea

n sq

uare

d er

ror (

mse

)

Epochs

10minus2

10minus4

10minus6

10minus10

10minus8

10minus12



32 Test Results





1198861 1198862 1198863 1198864 1198865 1198866 1198867 119868

29386 2658 1101 2434 minus4241 1278 1180 minus3949161



OPC 100 381 449 0 616 1050OPC 80 and FA 20 381 359 90 616 1050






1198623 = minus13477119863 + 37064 (7a)

11986228 = minus18815119863 + 46954 (7b)

11986291 = minus28811119863 + 61963 (7c)

119862270 = minus30938119863 + 68342 (7d)












OPC 100 02 2509 2912 0709OPC 80 and FA 20 036 1801 2252 0709

0

2000

4000

6000

8000

o100

-37

o100

-42

o100

-47

g30

o70

-37

g30

o70

-42

g30

o70

-47

g50

o50

-37

g50

o50

-42

g50

o50

-47Ap

pare

nt d

iffus

ion

coeffi

cien

t(E

-15

m2s

)


0

2000

4000

6000

8000

Appa

rent

diff

usio

n co

effici

ent

(E-15

m2s

)

f10

o90

-42

f10

o90

-47

f20

o80

-37

f20

o80

-42

f20

o80

-47

f30

o70

-37

f30

o70

-42

f30

o70

-47

(b) FA series

f10

s05

-37

f10

s05

-42

f10

s05

-47

f20

s05

-37

f20

s05

-42

f20

s05

-47

g30

s05

-37

g30

s05

-42

g30

s05

-47

g35

f15

-37

g35

f15

-42

g35

f15

-47


0

2000

4000

6000

8000

Appa

rent

diff

usio

n co

effici

ent

(E-15

m2s

)

(c) Combined series



119862 (119909 119905) = 119862119904 [1 minus erf ( 119909

2radic119863 (119905) sdot 119905)] (8)

119863 (119905) = 1198630(1199050

119905)

119898

(9)


119898 = 02 + 04 (FA50

+SG70

) (10)



119863 (119905) =1

119905int

119905

0

1198630 (1199050

120591) 119889120591 = 1198630

1199051198980

119905[1205911minus119898

1 minus 119898]

119905

0

=1198630

1 minus 119898(1199050

119905)

119898

(119905 lt 119905119888)

(11a)

119863 (119905) = 1198630 [1 +119905119888

119905(

119898

1 minus 119898)](

1199050

119905119888

)

119898

(119905 ge 119905119888) (11b)





Relative error ()

Type

of m

ixtu

re


0

5

10

15

20

25


Aver

aged

relat

ive e

rror

()








Sand(kgm3)


OPC 100 550 352 653 1173



OPC100 02 3647 4233 0709




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


Figure 9 Continued


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






5 Conclusions










or

neural network

InputLayer Layer

Outputw

b+

w+

b

D(t) = D0 and m = 02 + 04(FA50 + SG70)



D(t) = D0[1+ tct( m

1 minus m)]

tc (t ge tc)( t0

120591)d120591 = D0

tm0t[ 1205911minusm

1minus m]t

0=

D01minus m

( t0t)m ( t lt tc)

( t0t)m

( t0 )mD(t) =1

tintt0D0


0

02

04

06

08

0 10 20 30 40

Chlo

ride c

onte

nt (c

onc

wt

)

Cover depth (mm)

FA 20OPC 100





0

02

04

06

08

0 20 40 60 80 100

Chlo

ride c

onte

nt (5

of c

onc

wt)

Concrete depth (mm)








Acknowledgment


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





Names of mix

Items





Δ119882119896119895 = 120578120575119896119867119895 Δ119861119896 = 120578120575119896 120575119896 = (119879119896 minus 119874119896) 1198911015840(119873119896)

Δ119882119895119894 = 120578120575119895119867119894 Δ119861119895 = 120578120575119895 120575119895 = (119882119896119895120575119896) 1198911015840(119873119895)

(5)





(6)





o100-42 52119864 minus 12

o100-47 73119864 minus 12

g30o70-37 21119864 minus 12

g30o70-42 30119864 minus 12

g30o70-47 32119864 minus 12

g50o50-37 14119864 minus 12

g50o50-42 16119864 minus 12

g50o50-47 17119864 minus 12

f10o90-37 35119864 minus 12

f10o90-42 52119864 minus 12

f10o90-47 62119864 minus 12

f20o80-37 32119864 minus 12

f20o80-42 40119864 minus 12

f20o80-47 59119864 minus 12

f30o70-37 39119864 minus 12

f30o70-42 43119864 minus 12

f30o70-47 59119864 minus 12

f10s05-37 22119864 minus 12

f10s05-42 28119864 minus 12

f10s05-47 33119864 minus 12

f20s05-37 25119864 minus 12

f20s05-42 36119864 minus 12

f20s05-47 38119864 minus 12

g30s05-37 14119864 minus 12

g30s05-42 19119864 minus 12

g30s05-47 18119864 minus 12

g35f15-37 18119864 minus 12

g35f15-42 19119864 minus 12

g35f15-47 23119864 minus 12



20

40

60

80

1 2 3 4 5 6 7 8

Com

pres

sive s

treng

th (M

Pa)


Equation (7a)

Equation (7b)




0 100 200 300 400 500 600 700 800 900 1000

Mea

n sq

uare

d er

ror (

mse

)

Epochs

10minus2

10minus4

10minus6

10minus10

10minus8

10minus12



32 Test Results





1198861 1198862 1198863 1198864 1198865 1198866 1198867 119868

29386 2658 1101 2434 minus4241 1278 1180 minus3949161



OPC 100 381 449 0 616 1050OPC 80 and FA 20 381 359 90 616 1050






1198623 = minus13477119863 + 37064 (7a)

11986228 = minus18815119863 + 46954 (7b)

11986291 = minus28811119863 + 61963 (7c)

119862270 = minus30938119863 + 68342 (7d)












OPC 100 02 2509 2912 0709OPC 80 and FA 20 036 1801 2252 0709

0

2000

4000

6000

8000

o100

-37

o100

-42

o100

-47

g30

o70

-37

g30

o70

-42

g30

o70

-47

g50

o50

-37

g50

o50

-42

g50

o50

-47Ap

pare

nt d

iffus

ion

coeffi

cien

t(E

-15

m2s

)


0

2000

4000

6000

8000

Appa

rent

diff

usio

n co

effici

ent

(E-15

m2s

)

f10

o90

-42

f10

o90

-47

f20

o80

-37

f20

o80

-42

f20

o80

-47

f30

o70

-37

f30

o70

-42

f30

o70

-47

(b) FA series

f10

s05

-37

f10

s05

-42

f10

s05

-47

f20

s05

-37

f20

s05

-42

f20

s05

-47

g30

s05

-37

g30

s05

-42

g30

s05

-47

g35

f15

-37

g35

f15

-42

g35

f15

-47


0

2000

4000

6000

8000

Appa

rent

diff

usio

n co

effici

ent

(E-15

m2s

)

(c) Combined series



119862 (119909 119905) = 119862119904 [1 minus erf ( 119909

2radic119863 (119905) sdot 119905)] (8)

119863 (119905) = 1198630(1199050

119905)

119898

(9)


119898 = 02 + 04 (FA50

+SG70

) (10)



119863 (119905) =1

119905int

119905

0

1198630 (1199050

120591) 119889120591 = 1198630

1199051198980

119905[1205911minus119898

1 minus 119898]

119905

0

=1198630

1 minus 119898(1199050

119905)

119898

(119905 lt 119905119888)

(11a)

119863 (119905) = 1198630 [1 +119905119888

119905(

119898

1 minus 119898)](

1199050

119905119888

)

119898

(119905 ge 119905119888) (11b)





Relative error ()

Type

of m

ixtu

re


0

5

10

15

20

25


Aver

aged

relat

ive e

rror

()








Sand(kgm3)


OPC 100 550 352 653 1173



OPC100 02 3647 4233 0709




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


Figure 9 Continued


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






5 Conclusions










or

neural network

InputLayer Layer

Outputw

b+

w+

b

D(t) = D0 and m = 02 + 04(FA50 + SG70)



D(t) = D0[1+ tct( m

1 minus m)]

tc (t ge tc)( t0

120591)d120591 = D0

tm0t[ 1205911minusm

1minus m]t

0=

D01minus m

( t0t)m ( t lt tc)

( t0t)m

( t0 )mD(t) =1

tintt0D0


0

02

04

06

08

0 10 20 30 40

Chlo

ride c

onte

nt (c

onc

wt

)

Cover depth (mm)

FA 20OPC 100





0

02

04

06

08

0 20 40 60 80 100

Chlo

ride c

onte

nt (5

of c

onc

wt)

Concrete depth (mm)








Acknowledgment


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






o100-42 52119864 minus 12

o100-47 73119864 minus 12

g30o70-37 21119864 minus 12

g30o70-42 30119864 minus 12

g30o70-47 32119864 minus 12

g50o50-37 14119864 minus 12

g50o50-42 16119864 minus 12

g50o50-47 17119864 minus 12

f10o90-37 35119864 minus 12

f10o90-42 52119864 minus 12

f10o90-47 62119864 minus 12

f20o80-37 32119864 minus 12

f20o80-42 40119864 minus 12

f20o80-47 59119864 minus 12

f30o70-37 39119864 minus 12

f30o70-42 43119864 minus 12

f30o70-47 59119864 minus 12

f10s05-37 22119864 minus 12

f10s05-42 28119864 minus 12

f10s05-47 33119864 minus 12

f20s05-37 25119864 minus 12

f20s05-42 36119864 minus 12

f20s05-47 38119864 minus 12

g30s05-37 14119864 minus 12

g30s05-42 19119864 minus 12

g30s05-47 18119864 minus 12

g35f15-37 18119864 minus 12

g35f15-42 19119864 minus 12

g35f15-47 23119864 minus 12



20

40

60

80

1 2 3 4 5 6 7 8

Com

pres

sive s

treng

th (M

Pa)


Equation (7a)

Equation (7b)




0 100 200 300 400 500 600 700 800 900 1000

Mea

n sq

uare

d er

ror (

mse

)

Epochs

10minus2

10minus4

10minus6

10minus10

10minus8

10minus12



32 Test Results





1198861 1198862 1198863 1198864 1198865 1198866 1198867 119868

29386 2658 1101 2434 minus4241 1278 1180 minus3949161



OPC 100 381 449 0 616 1050OPC 80 and FA 20 381 359 90 616 1050






1198623 = minus13477119863 + 37064 (7a)

11986228 = minus18815119863 + 46954 (7b)

11986291 = minus28811119863 + 61963 (7c)

119862270 = minus30938119863 + 68342 (7d)












OPC 100 02 2509 2912 0709OPC 80 and FA 20 036 1801 2252 0709

0

2000

4000

6000

8000

o100

-37

o100

-42

o100

-47

g30

o70

-37

g30

o70

-42

g30

o70

-47

g50

o50

-37

g50

o50

-42

g50

o50

-47Ap

pare

nt d

iffus

ion

coeffi

cien

t(E

-15

m2s

)


0

2000

4000

6000

8000

Appa

rent

diff

usio

n co

effici

ent

(E-15

m2s

)

f10

o90

-42

f10

o90

-47

f20

o80

-37

f20

o80

-42

f20

o80

-47

f30

o70

-37

f30

o70

-42

f30

o70

-47

(b) FA series

f10

s05

-37

f10

s05

-42

f10

s05

-47

f20

s05

-37

f20

s05

-42

f20

s05

-47

g30

s05

-37

g30

s05

-42

g30

s05

-47

g35

f15

-37

g35

f15

-42

g35

f15

-47


0

2000

4000

6000

8000

Appa

rent

diff

usio

n co

effici

ent

(E-15

m2s

)

(c) Combined series



119862 (119909 119905) = 119862119904 [1 minus erf ( 119909

2radic119863 (119905) sdot 119905)] (8)

119863 (119905) = 1198630(1199050

119905)

119898

(9)


119898 = 02 + 04 (FA50

+SG70

) (10)



119863 (119905) =1

119905int

119905

0

1198630 (1199050

120591) 119889120591 = 1198630

1199051198980

119905[1205911minus119898

1 minus 119898]

119905

0

=1198630

1 minus 119898(1199050

119905)

119898

(119905 lt 119905119888)

(11a)

119863 (119905) = 1198630 [1 +119905119888

119905(

119898

1 minus 119898)](

1199050

119905119888

)

119898

(119905 ge 119905119888) (11b)





Relative error ()

Type

of m

ixtu

re


0

5

10

15

20

25


Aver

aged

relat

ive e

rror

()








Sand(kgm3)


OPC 100 550 352 653 1173



OPC100 02 3647 4233 0709




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


Figure 9 Continued


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






5 Conclusions










or

neural network

InputLayer Layer

Outputw

b+

w+

b

D(t) = D0 and m = 02 + 04(FA50 + SG70)



D(t) = D0[1+ tct( m

1 minus m)]

tc (t ge tc)( t0

120591)d120591 = D0

tm0t[ 1205911minusm

1minus m]t

0=

D01minus m

( t0t)m ( t lt tc)

( t0t)m

( t0 )mD(t) =1

tintt0D0


0

02

04

06

08

0 10 20 30 40

Chlo

ride c

onte

nt (c

onc

wt

)

Cover depth (mm)

FA 20OPC 100





0

02

04

06

08

0 20 40 60 80 100

Chlo

ride c

onte

nt (5

of c

onc

wt)

Concrete depth (mm)








Acknowledgment


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






1198861 1198862 1198863 1198864 1198865 1198866 1198867 119868

29386 2658 1101 2434 minus4241 1278 1180 minus3949161



OPC 100 381 449 0 616 1050OPC 80 and FA 20 381 359 90 616 1050






1198623 = minus13477119863 + 37064 (7a)

11986228 = minus18815119863 + 46954 (7b)

11986291 = minus28811119863 + 61963 (7c)

119862270 = minus30938119863 + 68342 (7d)












OPC 100 02 2509 2912 0709OPC 80 and FA 20 036 1801 2252 0709

0

2000

4000

6000

8000

o100

-37

o100

-42

o100

-47

g30

o70

-37

g30

o70

-42

g30

o70

-47

g50

o50

-37

g50

o50

-42

g50

o50

-47Ap

pare

nt d

iffus

ion

coeffi

cien

t(E

-15

m2s

)


0

2000

4000

6000

8000

Appa

rent

diff

usio

n co

effici

ent

(E-15

m2s

)

f10

o90

-42

f10

o90

-47

f20

o80

-37

f20

o80

-42

f20

o80

-47

f30

o70

-37

f30

o70

-42

f30

o70

-47

(b) FA series

f10

s05

-37

f10

s05

-42

f10

s05

-47

f20

s05

-37

f20

s05

-42

f20

s05

-47

g30

s05

-37

g30

s05

-42

g30

s05

-47

g35

f15

-37

g35

f15

-42

g35

f15

-47


0

2000

4000

6000

8000

Appa

rent

diff

usio

n co

effici

ent

(E-15

m2s

)

(c) Combined series



119862 (119909 119905) = 119862119904 [1 minus erf ( 119909

2radic119863 (119905) sdot 119905)] (8)

119863 (119905) = 1198630(1199050

119905)

119898

(9)


119898 = 02 + 04 (FA50

+SG70

) (10)



119863 (119905) =1

119905int

119905

0

1198630 (1199050

120591) 119889120591 = 1198630

1199051198980

119905[1205911minus119898

1 minus 119898]

119905

0

=1198630

1 minus 119898(1199050

119905)

119898

(119905 lt 119905119888)

(11a)

119863 (119905) = 1198630 [1 +119905119888

119905(

119898

1 minus 119898)](

1199050

119905119888

)

119898

(119905 ge 119905119888) (11b)





Relative error ()

Type

of m

ixtu

re


0

5

10

15

20

25


Aver

aged

relat

ive e

rror

()








Sand(kgm3)


OPC 100 550 352 653 1173



OPC100 02 3647 4233 0709




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


Figure 9 Continued


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






5 Conclusions










or

neural network

InputLayer Layer

Outputw

b+

w+

b

D(t) = D0 and m = 02 + 04(FA50 + SG70)



D(t) = D0[1+ tct( m

1 minus m)]

tc (t ge tc)( t0

120591)d120591 = D0

tm0t[ 1205911minusm

1minus m]t

0=

D01minus m

( t0t)m ( t lt tc)

( t0t)m

( t0 )mD(t) =1

tintt0D0


0

02

04

06

08

0 10 20 30 40

Chlo

ride c

onte

nt (c

onc

wt

)

Cover depth (mm)

FA 20OPC 100





0

02

04

06

08

0 20 40 60 80 100

Chlo

ride c

onte

nt (5

of c

onc

wt)

Concrete depth (mm)








Acknowledgment


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






OPC 100 02 2509 2912 0709OPC 80 and FA 20 036 1801 2252 0709

0

2000

4000

6000

8000

o100

-37

o100

-42

o100

-47

g30

o70

-37

g30

o70

-42

g30

o70

-47

g50

o50

-37

g50

o50

-42

g50

o50

-47Ap

pare

nt d

iffus

ion

coeffi

cien

t(E

-15

m2s

)


0

2000

4000

6000

8000

Appa

rent

diff

usio

n co

effici

ent

(E-15

m2s

)

f10

o90

-42

f10

o90

-47

f20

o80

-37

f20

o80

-42

f20

o80

-47

f30

o70

-37

f30

o70

-42

f30

o70

-47

(b) FA series

f10

s05

-37

f10

s05

-42

f10

s05

-47

f20

s05

-37

f20

s05

-42

f20

s05

-47

g30

s05

-37

g30

s05

-42

g30

s05

-47

g35

f15

-37

g35

f15

-42

g35

f15

-47


0

2000

4000

6000

8000

Appa

rent

diff

usio

n co

effici

ent

(E-15

m2s

)

(c) Combined series



119862 (119909 119905) = 119862119904 [1 minus erf ( 119909

2radic119863 (119905) sdot 119905)] (8)

119863 (119905) = 1198630(1199050

119905)

119898

(9)


119898 = 02 + 04 (FA50

+SG70

) (10)



119863 (119905) =1

119905int

119905

0

1198630 (1199050

120591) 119889120591 = 1198630

1199051198980

119905[1205911minus119898

1 minus 119898]

119905

0

=1198630

1 minus 119898(1199050

119905)

119898

(119905 lt 119905119888)

(11a)

119863 (119905) = 1198630 [1 +119905119888

119905(

119898

1 minus 119898)](

1199050

119905119888

)

119898

(119905 ge 119905119888) (11b)





Relative error ()

Type

of m

ixtu

re


0

5

10

15

20

25


Aver

aged

relat

ive e

rror

()








Sand(kgm3)


OPC 100 550 352 653 1173



OPC100 02 3647 4233 0709




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


Figure 9 Continued


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






5 Conclusions










or

neural network

InputLayer Layer

Outputw

b+

w+

b

D(t) = D0 and m = 02 + 04(FA50 + SG70)



D(t) = D0[1+ tct( m

1 minus m)]

tc (t ge tc)( t0

120591)d120591 = D0

tm0t[ 1205911minusm

1minus m]t

0=

D01minus m

( t0t)m ( t lt tc)

( t0t)m

( t0 )mD(t) =1

tintt0D0


0

02

04

06

08

0 10 20 30 40

Chlo

ride c

onte

nt (c

onc

wt

)

Cover depth (mm)

FA 20OPC 100





0

02

04

06

08

0 20 40 60 80 100

Chlo

ride c

onte

nt (5

of c

onc

wt)

Concrete depth (mm)








Acknowledgment


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





Relative error ()

Type

of m

ixtu

re


0

5

10

15

20

25


Aver

aged

relat

ive e

rror

()








Sand(kgm3)


OPC 100 550 352 653 1173



OPC100 02 3647 4233 0709




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


Figure 9 Continued


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






5 Conclusions










or

neural network

InputLayer Layer

Outputw

b+

w+

b

D(t) = D0 and m = 02 + 04(FA50 + SG70)



D(t) = D0[1+ tct( m

1 minus m)]

tc (t ge tc)( t0

120591)d120591 = D0

tm0t[ 1205911minusm

1minus m]t

0=

D01minus m

( t0t)m ( t lt tc)

( t0t)m

( t0 )mD(t) =1

tintt0D0


0

02

04

06

08

0 10 20 30 40

Chlo

ride c

onte

nt (c

onc

wt

)

Cover depth (mm)

FA 20OPC 100





0

02

04

06

08

0 20 40 60 80 100

Chlo

ride c

onte

nt (5

of c

onc

wt)

Concrete depth (mm)








Acknowledgment


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

Chlo

ride c

onte

nt (

of c

onc

wt)

0 5 10 15 20 25 30 35 40Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


Figure 9 Continued


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






5 Conclusions










or

neural network

InputLayer Layer

Outputw

b+

w+

b

D(t) = D0 and m = 02 + 04(FA50 + SG70)



D(t) = D0[1+ tct( m

1 minus m)]

tc (t ge tc)( t0

120591)d120591 = D0

tm0t[ 1205911minusm

1minus m]t

0=

D01minus m

( t0t)m ( t lt tc)

( t0t)m

( t0 )mD(t) =1

tintt0D0


0

02

04

06

08

0 10 20 30 40

Chlo

ride c

onte

nt (c

onc

wt

)

Cover depth (mm)

FA 20OPC 100





0

02

04

06

08

0 20 40 60 80 100

Chlo

ride c

onte

nt (5

of c

onc

wt)

Concrete depth (mm)








Acknowledgment


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)


0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)




0

02

04

06

08

0 5 10 15 20 25 30 35 40

Chlo

ride c

onte

nt (

of c

onc

wt)

Cover depth (mm)






5 Conclusions










or

neural network

InputLayer Layer

Outputw

b+

w+

b

D(t) = D0 and m = 02 + 04(FA50 + SG70)



D(t) = D0[1+ tct( m

1 minus m)]

tc (t ge tc)( t0

120591)d120591 = D0

tm0t[ 1205911minusm

1minus m]t

0=

D01minus m

( t0t)m ( t lt tc)

( t0t)m

( t0 )mD(t) =1

tintt0D0


0

02

04

06

08

0 10 20 30 40

Chlo

ride c

onte

nt (c

onc

wt

)

Cover depth (mm)

FA 20OPC 100





0

02

04

06

08

0 20 40 60 80 100

Chlo

ride c

onte

nt (5

of c

onc

wt)

Concrete depth (mm)








Acknowledgment


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials









or

neural network

InputLayer Layer

Outputw

b+

w+

b

D(t) = D0 and m = 02 + 04(FA50 + SG70)



D(t) = D0[1+ tct( m

1 minus m)]

tc (t ge tc)( t0

120591)d120591 = D0

tm0t[ 1205911minusm

1minus m]t

0=

D01minus m

( t0t)m ( t lt tc)

( t0t)m

( t0 )mD(t) =1

tintt0D0


0

02

04

06

08

0 10 20 30 40

Chlo

ride c

onte

nt (c

onc

wt

)

Cover depth (mm)

FA 20OPC 100





0

02

04

06

08

0 20 40 60 80 100

Chlo

ride c

onte

nt (5

of c

onc

wt)

Concrete depth (mm)








Acknowledgment


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






Acknowledgment


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



Documents

Research Article Evaluation Technique of Chloride Penetration … · 2019. 7. 31. · Evaluation Technique of Chloride Penetration Using Apparent Diffusion Coefficient and Neural