Probability-Based Sensitivity of Service Life of Chloride...

Research ArticleProbability-Based Sensitivity of Service Life of Chloride-AttackedConcrete Structures with Multiple Cover Concrete Repairs

Aruz Petcherdchoo

Associate Professor Department of Civil Engineering Faculty of EngineeringKing Mongkutrsquos University of Technology North Bangkok Bangkok 10800 ampailand

Correspondence should be addressed to Aruz Petcherdchoo aruzpengkmutnbacth

Received 6 July 2018 Revised 28 September 2018 Accepted 22 October 2018 Published 4 December 2018

Academic Editor Constantin Chalioris

Copyright copy 2018Aruz Petcherdchoo(is is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

(is paper presents probabilistic and sensitivity analysis of service life (or time to repairs) for attaining corrosion-free condition ofconcrete structures under chloride attack Four groups of probabilistic parameters are determined ie (1) time-dependentchloride content (2) mean and median of corrosion initiation and repair application times (3) percent confidence of repairs and(4) total expected number of repairs To achieve this this paper proposes a computational approach and probabilistic data (eproposed approach which combined the Latin Hypercube technique with the CrankndashNicolson-based finite difference approachis developed for predicting probabilistic chloride diffusion in concrete with repairs by cover concrete replacement Probabilisticdata of four governing random variables (surface chloride diffusion coefficient concrete cover depth and critical chloride) and sixrepair strategies for corrosion-free condition are introduced Numerical assessment is then shown From the study it is revealedthat the reduction of the amount of chloride ions at the threshold depth due to using higher depth of cover concrete repairs isbetter than that using higher quality of repair materials However the excessive depth of repairs is not always recommended due toanother control factor such as the immediate amount of chloride ions at the repair depth cost of repairs etc From the sensitivityanalysis the cover depth is found to be the most important parameter in the design of chloride-attacked concrete structures toextend the corrosion initiation and repair application times and to reduce the total expected number of repairs

1 Introduction

(e time-dependent deterioration of civil structures wasmostly due to the result of aging of materials continuoususe overloading aggressive exposure conditions lack ofsufficient maintenance and difficulties encountered inproper inspection methods [1] Chloride attack by diffusionwas not only categorized as aggressive exposure conditionsfor the deterioration of concrete structures located inmarine environment but also considered as one of themost concerning issues for long-term durability of rein-forced concrete structures [2] Whenever the thresholdamount of diffused chloride ions at reinforcement wasreached a thin oxide layer so called ldquopassivation filmrdquocould be broken down [3] (is may initiate reinforce-ment corrosion that subsequently leads to three signifi-cant phenomena reduction of the cross-sectional areaof reinforcement loss of bonds between concrete and

reinforcement [4 5] and concrete cracking (ese threephenomena can possibly result in severe structural de-terioration As a result the diffusion of chloride ions andthe reinforcement corrosion not only adversely affect thesafety and serviceability of concrete structures but alsoshorten their service life [6] However in real practicesevere structural deterioration is not preferable due to therisk of human life To avoid such kind of deteriorationthere are two main remedial approaches use of durableconcrete for reinforcement protection [7ndash9] and applica-tion of appropriate repair and maintenance [10ndash12] Forthe latter there are many kinds of maintenance actions inthe market [13 14] To efficiently apply these actionsmaintenance (or repair) application times such as the timeprior to reinforcement corrosion [15 16] are of signifi-cance (erefore a method to predict the appropriate re-pair application time which was occasionally defined asservice life [17 18] is required

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 4525646 17 pageshttpsdoiorg10115520184525646

In studying the service life and the repair applicationtime of concrete structures under chloride attack a quan-titative assessment is preferable [19 20](e diffusion theorybased on Fickrsquos second law can be used to predict thepenetration of chloride ions through concrete structures Inthe study of researchers [21ndash23] if the attack of chloride ions(in terms of surface chloride) and the resistance of concrete(in terms of diffusion coefficient) were both assumed con-stant the one-dimensional partial differential equation ofFickrsquos second law could analytically be solved and used topredict the service life However these studies are based ondeterministic data that are not suitable for considering agroup of concrete structures in which uncertainties play animportant role Moreover even an individual concretestructure itself contains uncertainties in terms of surfacechloride diffusion coefficient concrete cover depth andcritical chloride value Hence several researchers carried outprobabilistic studies on service life prediction as follows In2006 Zhang and Lounis [24] performed a sensitivity analysison the diffusion-based corrosion initiation model forreinforced concrete structures built in chloride-laden en-vironments by using analytical differentiation techniques(ey found that the time to corrosion initiation for con-ventional carbon steels was most sensitive to concrete coverdepth followed by chloride diffusion coefficient Howeverthe time to corrosion initiation for corrosion-resistant steelswas most sensitive to the surface chloride concentration andchloride threshold level followed by the concrete coverdepth and chloride diffusion coefficient Later Bastidas-Arteaga et al [25] utilized a stochastic approach for de-termining the influence of weather conditions and globalwarming on chloride ingress into concrete In their study asimplified model of temperature and humidity includingseasonal variations and global warming was proposedFurthermore three scenarios of global warming were de-fined based on gas emissions global population growthintroduction of new and clean technologies and use of fossilsources of energy It was found that the lifetime reductioninduced by global warming was more significant forstructures located in chloride-contaminated environmentsfar from the sea (e results also indicated that the climatechange effect was higher for structures located in oceanicenvironments and could lead to lifetime reductions rangingfrom 2 to 18 Hackl and Kohler [26] presented a genericframework for the stochastic modeling of reinforced con-crete deterioration caused by corrosion (eir frameworkenabled the coupling of probabilistic models for the initi-ation and propagation of corrosion in service life models Intheir framework existing probabilistic models for chlorideand carbonation initiation with models for the propagationand consequences of corrosion were coupled To achieve thetask they combined structural reliability analysis withBayesian networks in order to estimate the probability offailure of a reinforced concrete structure In 2016 Pang andLi [27] carried out the filed investigations of seventeenhighpile wharf structures located at the south coast of China(ey compared the obtained results with the long-termexposure test results in terms of chloride ingress profile(e probability models for surface chloride content and

chloride diffusion coefficient were derived accordingly (eyalso investigated the effects of different models of chlorideingress parameters based on exposure trails or based on realstructure surveys on the expected service life of marinestructures It was found that the height-dependency ofsurface chloride indicated the existence of a ldquosemisplashrdquozone and the existence of semisplash zone and the additionof BFS in concrete have significant effects on the service lifeof concrete structures Yang et al [28] carried out design andoptimization of the maintenance works of reinforced con-crete (RC) elements in a long life-span marine port inShanghai China In their study the deterioration of RCelements was dominated by the reinforcement steel corro-sion induced by external chloride penetration (e de-terioration model was established for the RC elements withprescribed durability limit state and the failure probabilityevolution was calculated through Monte Carlo simulationsFurthermore the preventive necessary and mandatorymaintenances corresponded respectively to probabilitylevels of 2 5 and 20 and also three schemes of mainte-nance planning were investigated unsynchronized syn-chronized and coating-synchronized schemes From theiranalysis it was found that the coating-synchronized schemeachieved the optimal cost as well as delayed the deteriorationrate of beam elements In their study they also assumed thatwith maintenances the durability state of RC elements wasassumed to be totally restored to its initial state Howeverthis assumption shows the limitation of their study (is isdue to the fact that after concrete repairs the influence ofremaining chloride ions which are used to indicate thedurability in their study should also be taken into account

Although the aforementioned researchers studied theprobabilistic service life of concrete structures without orwith repairs they did not consider multiple repairs ac-companied with the interaction of chloride transport afterconcrete repairs (at kind of repairs is important inparticular in the current situation at which many structuresdrastically deteriorate after operating for a period of timeBased on further literature reviews there were researcherswho studied such kind of repairs For example the study ofPetcherdchoo [29] carried out probabilistic assessment ofchloride ions in concrete with repairs (e study simplifiedthe assessment by focusing on only two random variablesie surface chloride and diffusion coefficient Howeverthere are two observations in that study First in realpractice not only the surface chloride and diffusion co-efficient are random but also threshold depth (cover depth)and critical chloride value do so Second that study definedcritical time as the application repair time for preventingconcrete cracking However in real practice the time afterconcrete cracking to severe concrete deterioration is rela-tively short If this kind of concrete cracking limit state isfocused it would be too risky for concrete structures Hencemany researchers are interested in the time of corrosioninitiation rather than concrete cracking Due to these twoobservations that study is limited In 2014 Rahimi et al [30]studied probabilistic approaches for modeling the residualservice life of marine concrete structures after concreterepairs However their study has two restrictions First in

2 Advances in Civil Engineering

their study they considered three repair cases as follows Inthe first case the cover concrete was entirely removed andreplaced with a repair material And the remaining layer ofconcrete behind the reinforcement was assumed unaffectedby chloride ions Hence the design of the service life of astructure with regard to chloride-induced corrosion of thereinforcement was based on a common 1-layer system Inthe second case the cover concrete was only partially re-moved and replaced with a repair material Moreover theremaining layer of concrete in the cover and behind thereinforcement was assumed unaffected by chloride ions Inthe third case the concrete cover is only partially removedand replaced with repair material And the remaining layerof concrete contained residual chloride ions Because themost important location in concrete structures is the po-sition of reinforcement it would be more appropriate toreduce the amount of chloride ions at the location of re-inforcement (cover depth) rather than partial concretecover Hence the second and third cases in their study arenot sufficient Although the first case considered the removalof the entire cover concrete the remaining layer of concretebehind the reinforcement was assumed unaffected bychloride ions Such kind of residual chloride ions is im-portant because they are near the location of the re-inforcement As a result both removing at least the entirecover concrete and considering the effect of residual chlorideions are necessary Second they evaluated the residualservice life of concrete structure after only one repairHowever multiple repairs for service life extension canoccur over the lifetime of concrete structures In order tobridge these gaps this study aims at reporting probabilisticand sensitivity analysis of service life (time to concrete re-pairs) and associated parameters for attaining corrosion-freecondition of chloride-attacked concrete structures More-over concrete structures are multiply repaired at least up toconcrete cover depth Four groups of parameters are studied(1) time-dependent chloride content (2) mean and medianof corrosion initiation and repair application times (3)percent confidence of repairs and (4) the total expectednumber of repairs To achieve these a computational ap-proach and probabilistic data (surface chloride diffusioncoefficient cover depth and critical chloride) for chloridetransport in concrete without and with multiple repairs areintroduced for study (ese are explained as follows

2 Computational Approach

(e computational approach in this study is an approachwhich combines the Latin Hypercube technique with aCrankndashNicolson-based finite difference approach (eflowchart of the proposed approach is shown in Figure 1It consists of two main shaded areas or loops (e internalloop represents the CrankndashNicolson-based finite differ-ence approach for determining chloride transport in con-crete without and with repairs by cover replacementwhereas the external loop represents the approach that usesthe Latin Hypercube technique for sampling randomnumbers and feeding all random numbers into the internalloop (e models for chloride transport in concrete without

and with repairs using the CrankndashNicolson-based finitedifference approach and the sampling method using theLatin Hypercube technique are explained as follows

21 Model of Chloride Transport in Concrete without Repairs(e one-dimensional partial differential equation (1-D PDE)for chloride diffusion in concrete structures [21 31] canfundamentally be written as

zC

zt

z

zxD

zC

zx (1)

where C is the chloride content as a function of position x

and time t and D is the chloride diffusion coefficient ofconcrete If the initial condition (initial chloride content)boundary condition (surface chloride CS) and materialproperty (chloride diffusion coefficient D) are assumed tobe zero constant and constant respectively a simple so-lution for Equation (1) can be derived as

C(x t) CS 1minus erfx

2Dt

radic1113888 11138891113890 1113891 (2)

where erf(middot) is an error function (is equation can be usedto predict the diffusion of chloride ions through concrete ifthe surface chloride and diffusion coefficient are knownSeveral researchers proposed deterministic data to represent

Start

Read input file

Latin hypercube technique

Consider j time step

Set sample number i = 1Set time step j = 1

Consider i sample

j = total no of time steps

Yes

Chloride diffusion computation byCrankndashNicolson finite difference method

No

j = j + 1

i = i + 1

i = total no of samplesNo

Stop

Yes

Figure 1 Flowchart for the developed program

Advances in Civil Engineering 3

these two variables such as those shown in literatures[22 32ndash34]

22 Model of Chloride Transport in Concrete with Repairs(e flowchart for determining the transport of chloride ionsas shown in the internal loop of Figure 1 can be used todetermine the transport of chloride ions in concrete withrepairs by cover concrete replacement Whenever concreterepairs in terms of cover concrete replacement is applied thesolution such as that in Equation (2) is complex to obtain Toexplain this difficulty let us consider Figure 2(a) At time tjthe repair action by cover concrete replacement is appliedHence the concrete with the cover (threshold) depth of Xc istaken off and a repair material (shown by shaded zone) isreplaced for the taken-off concrete(e thickness of replacedconcrete is called repair depth or Xp which is not necessaryto be the same as the concrete cover depth Xc After thatthere are three principle stages as shown in Figure 2(b) Firstat time tj the chloride ions in the original (old) concrete areabout to redistribute from the original concrete through therepair material due to differential chloride ions in oldconcrete and repair materials [35] So the problem willinvolve solving the PDE with nonlinear chloride ion profileor C(x tj)

Secondly when the redistributing chloride ions pene-trate from the original concrete to the repair material theproblem involving space-dependent diffusion coefficient orD(x) will be encountered due to the difference of the dif-fusion coefficient between the original concrete and therepair material Mathematically the PDE based on Fickrsquossecond law can be written as

zC

zt

z

zxD(x)

zC

zx (3)

(irdly at time tj+2 the penetrating chloride ions fromconcrete surface merge with the redistributing chloride ionsat the point xm as shown in Figure 2(b) (is causes theinteraction between chloride ions in the old concrete andthose in the repair material Moreover the problem insolving the PDE will be encountered It will be even morecomplicated if the number of repairs is more than one dueto multiple repairs In order to avoid all of these difficulties aCrankndashNicolson-based numerical scheme [36] is used as

cij+1 minus cij

Δt12

1113888lfloorDi+12 ci+1 minus ci( 1113857j+1minusDiminus12 ci minus ciminus1( 1113857j+1rfloor

(Δx)2

+lfloorDi+12 ci+1 minus ci( 1113857jminusDiminus12 ci minus ciminus1( 1113857jrfloor

(Δx)21113889

(4)

where cij and cij+1 are the chloride contents at a mesh pointi at time j and j + 1 respectively and Di+12 and Diminus12 arethe diffusion coefficients at mesh point i + 12 and iminus 12respectively Moreover they are equal to (Di + Di+1)2 and(Diminus1 + Di)2 respectively In this study Δt and Δx are theincremental time step (1 week) and the mesh point size(1mm) respectively It is noted that there is another methodcalled multispecies approach which is based on the

NernstndashPlanck equation Truc et al [37] stated that thisapproach described the diffusion and the ionic interactionbetween several chemical species and included both thephysical and chemical phenomena in chloride ingressHowever this approach required the greater number ofinput data making it inappropriate in many situationseg probabilistic study in spite of its most completemodeling [38] As a result the multispecies approach is notused in this study

To calculate the diffusion of chloride ions Equation (4)must iteratively be solved over time Whenever the amountof chloride ions at the threshold depth (Xc) reaches a specificcritical chloride value the repair by cover concrete re-placement is applied as shown in Figure 2 Hence coverconcrete is replaced over the repair depth (Xp) and thediffusion coefficient of cover concrete will be updated incomputation for instance (DXp

)0 is updated as (DXp)rep It

is noted that (DXp)0 and (DXp

)rep are defined as thediffusion coefficient of original concrete and repair materialrespectively at the repair depth Xp

23 Probabilistic Sampling Method Most of researchers[24 26 28] generally used the Monte Carlo simulationtechnique as a sampling method in their probabilistic studydue to its simplicity However this technique requires a largeamount of random samples for satisfactory confidence levelIf it is combined with the iterative computation that isunavoidable in numerical prediction of chloride transport inconcrete with repairs the computational time is a big issueHence another sampling method which is more effectivemust be introduced

(e report in a study [39] stated that the Latin Hy-percube sampling technique [40 41] was able to reduce thenumber of random samples in computation to a certainamount with satisfactory confidence level Hence the LatinHypercube sampling technique is used in this study Bycombining the chloride diffusion computation by theCrankndashNicolson-based finite difference method with theLatin Hypercube technique the computational approach isdeveloped in this study according to the flowchart inFigure 1

3 Probabilistic Data

In probabilistic assessment there can be two groups ofuncertainties to be categorized ie the uncertainty related tochloride diffusion and that related to assessing criteria Forthe first group two random variables can be consideredie surface chloride and diffusion coefficient for originalconcrete (e uncertainty in the surface chloride whichrepresents the degree of chloride attack occurs due todifferent or random chloride environment (e uncertaintyin diffusion coefficient which represents the resistance ofconcrete to chloride diffusion occurs due to different orrandom concrete material properties Although concretestructures have the same mix design their material prop-erties are probably different due to different environmentquality control etc For the uncertainty related to the


assessing criteria two random variables can be consideredie cover depth and critical chloride value (e uncertaintyin the cover depth is related to quality control while that inthe critical chloride value can be considered due to randomconcrete material properties

(e study in the literature [42] both conducted tests andcollected data for their study(en a set of probabilistic datafor four governing random variables (surface chloridediffusion coefficient concrete cover depth and criticalchloride value) was proposed by considering the goodness-of-fit tests such as the Chi-square test the KolmogorovndashSmirnov test and the CramerndashVon Mises test Howevertheir data are found to be inappropriate for this study due totwo reasons First the distribution type of some parametersis inappropriate For example the distribution type of thediffusion coefficient was proposed as the Weibull distribu-tion However this kind of distribution type is not alwaysbell-like because it is highly sensitive to their descriptorsie scale and shape factors As a result it is not appropriateto use the Weibull distribution in this study In particularthe sensitivity study of random variables will be carried outFor the second reason all the four random variables shouldbe limited within a practical range For example the dis-tribution type of the cover depth in their study was proposedas the normal distribution However it is impossible that thecover depth which is directly related to the prediction ofchloride diffusion through concrete without and with re-pairs is negative Although the probability of occurrence islow the negative value of the cover depth might be obtainedfrom numerical sampling If this occurs numerical com-putation cannot be completed From these two reasons theprobabilistic assessment data in their study require revision

Based on the raw data [42] a set of appropriate descriptorsfor the four random variables is proposed and compared withthe raw data [42] as shown in Figure 3 In revising these databoth the goodness-of-fit tests and appropriateness of thedescriptors are considered Table 1 shows these proposedrandom variables surface chloride (Cs) diffusion coefficient(Do) concrete cover depth (Xc) and critical chloride (CCrit) Itis noted that the dispersion of the cover depth in terms ofstandard deviation (σ) is highest while that in terms of co-efficient of variation (COV) is lowest

4 Proposed Repair Strategies for Corrosion-Free Condition

In this study it is assumed that the amount of oxygen andmoisture is much enough to cause reinforcement corrosionwhenever the chloride content at the threshold depth (orconcrete cover depth) reaches the critical chloride value (etime at which the critical value is reached is defined as theservice life of concrete structures or the time of repair ap-plications In addition it can be predicted by using theproposed approach explained in Section 2 Six repair strat-egies for corrosion-free condition are proposed as shown inTable 2 and applied at the time of repair applications (ediffusion coefficient is chosen as Do 075Do or 05Do whilethe depth of repairs is chosen as equal to the cover depth (Xc)Xc + 35 or Xc + 50mm For the abbreviation in Table 2 forexample S4 means the repair strategy number 4 and 75DC35means that the diffusion coefficient of the repair material andthe depth of repairs are equal to 075Do and Xc + 35mmrespectively In addition the design time period for corrosion-free condition is chosen as equal to 100 years

5 Numerical Assessment

(is study represents two main kinds of numerical assess-ment deterministic and probabilistic (e deterministicassessment is to show the behaviors of chloride diffusionthrough concrete structures with multiple repairs (eprobabilistic assessment consists of three parts the assess-ment with 5 samples that with 2000 samples and thesensitivity analysis (e first part is to show how to assess theprobabilistic chloride diffusion in concrete with repairs (esecond and third ones are to perform the probabilistic andsensitivity analysis respectively

51 Deterministic Assessment (e surface chloride thediffusion coefficient of original concrete the cover depthand the critical chloride are chosen as their mean valueshown in the third column of Table 1 Moreover six repairstrategies in Table 2 are considered for comparison It isnoted that if for example the repair strategy of S6 is studied

Repairmaterial

Depth

Clndash co

ncen

trat

ion

0

Oldconcrete

Clndash from outersurface Cs

Clndash profile immediatelyaer repair at time tj

Drep D0

Xc Xp

(a)

Depth(σt)

Repair material Drep


Clndash co

ncen

trat

ion

0

Old concrete D0

Clndash from surfaceat time tj+1

Clndash fromsurface attime tj+2

CsOld Clndash at time tj+1

Old Clndash at time tj+2

Xc XpXm

(b)

Figure 2 Chloride profiles after cover concrete replacement (a) Immediately after repair (b) After repair


150

5

10

15

20

25

18 21 24 27 30 33 36 39 42 45 48 5100

02

04

06

08

10

PDF

of su

rface

chlo

ride

Num

ber o

f tes

ts

Surface chloride ( binder)

Song et al [42] (tests)is study T (157 24 486)

(a)

10 15 20 25 30 35 40 45 50 55 60 650

5

10

15

20

25

Num

ber o

f tes

ts

000

011

022

033

044

055

PDF

of d

iffus

ion

coeffi

cien

t

Diffusion coefficient (m2s times 10ndash12)


(b)


76 80 84 88 92 96 100 104 108 112 116 1200

5

10

15

20

25

0000

0015

0030

0045

0060

0075PD

F of

cove

r dep

th

Num

ber o

f tes

ts

Cover depth (mm)

(c)

00 02 04 06 08 10 12 14 16 180

5

10

15

20

25

000

031

062

093

124

155

PDF

of cr

itica

l chl

orid

e

Critical chloride ( binder)

Song et al [42] (literatures)is study T (01 06 171)

Num

ber o

f tes

ts

(d)

Figure 3 Raw data and proposed descriptors (a) Surface chloride (b) Diffusion coefficient (c) Cover depth (d) Critical chloride

Table 1 Proposed descriptors for four random variables

Random variables Descriptors Mean (μ) Standard deviation (σ) Coefficient of variation (COV)Cs ( binder) T (157 24 486) 294 07 024Do (times10minus12m2s) T (112 45 625) 396 106 027Xc (mm) T (78 92 118) 96 829 0087CCrit ( binder) T (01 06 171) 08 034 042T (a b c) means triangular distribution with minimum mode and maximum of a b and c respectively

Table 2 Six proposed repair strategies for corrosion-free condition

Code of repairs Repair application time Diffusion coefficient of repair material Drep Depth of repairs Xp

S1 DC

Whenever ClTHT CCrit

Do CoverS2 DC35 Do Cover + 35mmS3 75DC 075Do CoverS4 75DC35 075Do Cover + 35mmS5 75DC50 075Do Cover + 50mmS6 50DC50 05Do Cover + 50mmClTHT means chloride content at the threshold depth TH and time T CCrit means critical chloride


the diffusion coefficient of the repair material and the repairdepth are equal to 198 times 10minus12 m2s (05Do) and 146mm(96 + 50) respectively

(e chloride diffusion through the depth of a concretestructure with S1 and S6 is shown in form of space-dependentchloride profiles in Figures 4(a)ndash4(d) From Figure 4(a) thechloride ions continuously penetrate through the originalconcrete In year 30 (about 31 weeks after the year 30) thechloride profile reaches the critical value at the thresholddepth (cover depth) as shown by the profile at year 30B (ldquoBrdquomeans Before repair) If the repair strategy S1 is selected theconcrete cover over 96mm is replaced by the repair materialhaving the diffusion coefficient of 396 times 10minus12 m2s as shownby the shaded zone in Figure 4(b) Immediately after therepair the chloride profile becomes the profile at year 30A(ldquoArdquo means After repair) At year 31 the chloride ions fromthe surface of concrete penetrate through the cover concreteand the remaining chloride ions in the original concrete (nearthe threshold depth) will both redistribute through the repairmaterial and distribute further through the original concreteAfter that the chloride ions will continuously penetratethrough the concrete as shown

But if S6 is selected instead the concrete cover over146mm is replaced by the repair material having the diffusioncoefficient of 198 times 10minus12 m2s as shown by the shaded zonein Figure 4(d) (e behaviors of chloride ion penetration nearthe surface and the threshold depth of concrete with S6 areidentical with those with S1 except that the chloride profilesare not exactly the same By comparing the chloride profiles atyears 31 to 45 between Figures 4(b) and 4(d) there are twoobservations First the chloride penetration from the surfaceof concrete with S6 in Figure 4(d) is slower than that with S1in Figure 4(b) because of lower diffusion coefficient (betterquality) of the repair material of S6 Second the chlorideredistribution from the original concrete to the thresholddepth of concrete with S6 is slower than that with S1 becauseof deeper repair depth of S6

(e comparison of time-dependent chloride profileswithout and with repair by S1 and S6 is shown in Figure 5Without repair the chloride content at the cover depth of96mmwill continuously increase causing possible corrosionof reinforcement in the concrete structure If the time whichthe chloride profile reaches the critical value of 08 binder(mean value ofCCrit in Table 1) is defined as the service life ofconcrete structures or the time to repair the time to the firstrepair is approximately equal to 30 years If the repairstrategy of S1 is applied in the year 30 the chloride content atthe reinforcement will be controlled below the critical valueImmediately after the repair the time-dependent chloridecontent at the reinforcement as shown in Figure 5 decreasesto zero due to removing the chloride ions with the taken-offconcrete (see also the chloride profile in the year 30A inFigure 4(b)) However the chloride content suddenly in-creases because of immediate redistribution of chloride ionsfrom the original concrete (see also the chloride profile in theyear 31 in Figure 4(b)) (is immediate redistribution ofchloride ions occurs because the microstructure of the freshrepair material is not dense yet leading to a very low chloride

diffusion resistance of repair material [43] By the effect ofthe first repair the time which the chloride profile crossesthe critical value to start reinforcement corrosion will beprolonged After the first repair the chloride profile reachesthe critical value two more times within the design timeperiod of 100 years and the same kind of concrete repair asS1 is reapplied as shown in Figure 5

But instead if the repair strategy of S6 is applied in theyear 30 the behavior of chloride penetration is different fromapplying S1 Immediately after the repair by S6 the chloridecontent decreases to zero and then gradually increases (isgradual increase compared to S1 occurs because of tworeasons longer distance of chloride redistribution fromthe original concrete to the threshold depth (Figures 4(b) and4(d)) and lower diffusion coefficient of the repair material(Table 2) (e effect of the first repair by S6 lasts until year 90and then the second repair is applied After that the chlorideprofile will never reach the critical value any more within 100years In comparison between S1 and S6 the number ofrepairs is equal to thrice and once respectively Hence betterrepair material and deeper repair depth by S6 lead to fewernumbers of repairs within the design time period

In comparison among six repair strategies the repairapplication time and the number of repairs can be calculatedas shown in Table 3 Within the design time period of 100years the concrete structure with S1 and S2 requires threerepairs while that with S3 to S6 requires two repairs (isimplies that lower diffusion coefficient (better quality) ofrepair materials in S3 to S6 is more effective due to lowernumber of repairs

52 Probabilistic Assessment

521 With 5 Samples From the Latin Hypercube samplingtechnique five simulations for random numbers of fourrandom variables are generated as shown in Table 4 It is notedthat the original values of the cover depth Xc in the simulationnumbers 1 and 2 are randomly generated as 994332 and87883 respectively However they are rounded as 99 and88mm in order to be consistent with the unit of themesh pointsize which are in millimeters as mentioned in Section 22

If the repair strategy of S6 is selected the time-dependentchloride profiles can be calculated as shown in Figure 6(ereare six profiles ie five sample profiles and the mean of thefive samples profiles(e five sample profiles can be separatedinto two groups three with need of repairs and the other twowith no need of repairs (e chloride content of the threeprofiles with need of repairs increases up to their own criticalvalue (see also Table 4) and decrease to zero due to repairswhile that with no need of repairs will continuously increase(see the two hidden lines) It is noted that the two profiles haveno need of repair because they are always below their owncritical value Although one of them crosses the mean of thecritical chloride a repair is still not applied (e mean profileat time t can be computed based on the five sample profiles as

μt 1113936

ni1cit

n (5)


where cit is the chloride content of the i-th sample at time tand n is the total number of samples It is noted that themean profile (the darkest line) never reaches the mean of

the critical value nor decreases to zero because it is theaverage value which falls within the range of the five sampleprofiles

522 With 2000 Samples In this part all random variablesie surface chloride diffusion coefficient concrete coverdepth and critical chloride from Table 1 are used for studyFor repairs concrete structures with six repair strategies inTable 2 will be compared By using these data in the proposedcomputational approach observations can be drawn as follows

In case of no repair Figure 7 shows the comparison oftwo kinds of assessment deterministic and probabilistic For

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)

Do = 396 times 10ndash12 m2s Do = 396 times 10ndash12 m2s

Cs = 294 binder

rs dep = 96mm

Year 30B

ClCrit = 08

Year 1

21

714

(a)

0 50 100 150 200

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

Depth (mm)

DRep = 396 times 10ndash12 m2s Do = 396 times 10ndash12 m2s

Cs = 294 binder

rs dep = 96mm

Year 30A

Deph of 1st repair = 96mm

Year 31

35 4045

ClCrit = 08

(b)

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30A


Year 3135 40

45ClCrit = 08

(c)

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)

DRep = 198 times 10ndash12 m2s Do = 396 times10ndash12 m2sCs = 294 binder

rs dep = 96mm

Year 30A


Year 313540

45 ClCrit = 08

(d)

Figure 4 Deterministic space-dependent chloride profiles with S1 S4 and S6 (a) Year 1 to year 30B (b) Year 30A to year 45 (with S1)(c) Year 30A to year 45 (with S4) (d) Year 30A to year 45 (with S6)

000

04

08

12

16

20

20Time (yrs)

No repair

Repair

No repair

Repair S6 50DC50Repair S1 DC

40 60 80 100

Chlo

ride c

onte

nt (

bin

der)

ClCrit = 08

Thrs dep = 96mmCs = 294 binderDo = 396 times 10ndash12 m2s

Figure 5 Deterministic time-dependent chloride profiles withoutand with S1 and S6

Table 3 Number of repairs and repair application time for sixstrategies by deterministic assessment

StrategyRepair application time yrs

Number of repairsFirst Second (ird Fourth

S1 306 554 79 gt100 3S2 306 606 905 gt100 3S3 306 668 gt100 gt100 2S4 306 694 gt100 gt100 2S5 306 712 gt100 gt100 2S6 306 905 gt100 gt100 2


the deterministic assessment the chloride profile as wellas the lower and upper bounds of chloride content isshown For these profiles the surface chloride the diffusion

coefficient of original concrete and the cover depth arechosen as equal to their mean value as well as equal to theirupper and lower limits as shown in Table 5 For theprobabilistic assessment the mean profile and the yearlyprobability density functions (PDFs) of chloride content areshown From comparison the deterministic profile isslightly different from the mean profile (is differenceoccurs because all the randomly generated values of thecover depth in the probabilistic assessment are alwaysrounded as integers in order to be consistent with the meshpoint size (see Xc in Table 4) It is also observed that at theyears of 20 40 60 and 80 the PDF falls within the upper andlower bounds In addition from the PDF the dispersion ofchloride content increases with time

Other than the PDF of chloride content the dispersionof the chloride content can be shown in terms of thestandard deviation (σt) and the coefficient of variation(COVt) respectively by using the following equations

σt

1113936

ni1c

2it

n1113888 1113889minus micro2t

1113971

COVt σt

microt

(6)

(e time-dependent profiles of the mean the standarddeviation and the coefficient of variation of chloride contentfor concrete structures without and with the repair strategyof S1 can be compared in Figure 8 It can be seen that themean profile for concrete with S1 is lower than that withoutbecause the chloride content of all samples for concrete withS1 is limited below its critical chloride value due to repairsMoreover the dispersion in terms of the standard deviationis also lower but that in terms of the coefficient of variation(COV) is higher In fact if two random variables ie bothDrep and Xp are combined in consideration due to applyingS1 the dispersion must theoretically increase (e increaseoccurs because the uncertainty of the two random variablesis combined (is observation agrees with the dispersion interms of the coefficient of variation (COV) As a result thedispersion should be calculated in terms of the coefficient ofvariation rather (COV) than the standard deviation

(e probabilistic time to repairs can be represented interms of the PDF (probability density function) and CDF(cumulative distribution function) of repair applicationtime From computation Figures 9(a) and 9(b) show thePDF and CDF respectively for concrete structures with S1(ere are two approaches to define the time to repairsie (1) mean and standard deviation and (2) median (or 50-percentile) From the PDF in Figure 9(a) the mean and thestandard deviation of the first application time for S1 can becalculated as equal to 34 and 201 years respectively Bothvalues are calculated based on the 924 confidence which isshown at the year 100 of the CDF of repair application timein Figure 9(b) (0924) (is implies that 76 of the totalnumber of concrete structures do not need any repair withinthe design time period of 100 years If more percent con-fidence is needed the design time period must be longer sothat the CDF of repair application time can be completely

00

171

01

04

08

12

16

20

24

0 20 40 60 80 100Time (yrs)

3 samples need of repairs2 samples no need of repairsMean of five samples

Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Cs = T (157 24 486)rs Dep = 96 mm

Do = T (112 45 625)Xc = T (78 92 118)

With S650DC50CCrit= T (01 06 171)

Figure 6 Probabilistic time-dependent chloride profiles based onfive sets of random samples

000

08

16

24

32

40

20 40

40

60

60

80

80

100

Chlo

ride c

onte

nt (

bin

der)

Time (yrs)

Year 20Deterministic

Deterministic profileMean profileUpper bound

Lower boundPDF of chloride content

Mean

Upperbound

Lowerbound

No repair2000 samples

Cs = T (157 24 486) binderDo = T (112 45 625) times 10ndash12 m2sXc = T (78 92 118) mm

micro(ClCrit) = 08

Figure 7 Deterministic and mean profiles upper and lowerbound and PDF of chloride content

Table 4 Five generated random numbers for concrete structureswith S6

Simulationnumber

Random variables S6 50DC50Cs Do Xc CCrit Drep 05Do Xp Xc + 50

1 315 383 99 132 1915 1492 429 224 88 082 112 1383 182 457 103 117 2285 1534 299 294 79 062 147 1295 228 187 112 102 0935 162


captured Moreover if the design time period is longer themean and standard deviation will be slightly different FromFigures 9(a) and 9(b) the mean the standard deviation andthe percent confidence for the second third and fourthapplications can be tabulated in Table 6 It is noted that if thedesign time period is longer those means and standarddeviations will be considerably changed In particular thoseof the fourth application will be most changed due to itslowest percent confidence (is shows that the mean andstandard deviation of repair application time are sensitive tothe design time period

By further considering Figure 9(b) the CDF of repairapplication time can be referred to the probability of repairapplications at any year For example there is 50 proba-bility of the first repair application time (05) at year 307Moreover there is a 25 probability of the first repairapplication time at year 192(is indicates the probability ofreinforcement corrosion initiation If there are for example2000 concrete structures exposed to chloride environment500 (or 25) of them are expected to have reinforcementcorrosion (erefore repair planning is recommended forthem However the deterministic assessment in Figure 5shows that the corrosion does not occur prior to or even inyear 29 and no repair is required Hence if only the de-terministic assessment using the mean of random variablesas shown in Figure 5 is considered the expected corrosioncannot be predicted (is reveals that repair planning by thedeterministic assessment is not enough

In terms of the median of repair application time thetime to repairs is defined as the time which 50 of the totalnumber of concrete structures starts to have reinforcement

corrosion and requires a repair for corrosion-free conditionFrom the CDF of repair application time in Figure 9(b) themedian of the first second and third repairs of S1 can betabulated in Table 6 (ey are approximately equal to 307(Figure 9) 554 and 79 In comparison the deterministicrepair time as shown in Table 3 is equal to 306 554 and 79respectively (is reveals that the deterministic repair timesare closer to their median than the aforementioned mean(Tables 3 and 6) (is occurs because the design time periodis not long enough to represent their mean with high percentconfidence If the design time period is longer the percentconfidence will be higher and the mean of repair applicationtime will be closer to their median

From Figure 9(b) the probability of the first second andthird repair applications at year 50 is approximately equal to755 457 and 237 respectively Moreover that at year100 is approximately equal to 924 802 and 636respectively Based on these three repairs the total expectednumber of repair applications at years 50 and 100 can becalculated as equal to 145 (a combination of 755 457and 237) and 236 (a combination of 924 802 and636) respectively But if eight repairs are considered thetotal expected number of repair applications at years 50 and100 is approximately equal to 163 and 377 respectively Incomparison at year 50 the consideration of the total ex-pected number of repair applications for three repairs is notmuch different from that for eight repairs (145 to 163)However at year 100 it is quite different (236 to 377) As aresult if the design time period is longer more number ofrepair applications should be included in calculating thetotal expected number of repair applications Otherwise itwill be miscalculated

(e mean profiles of chloride content of concretestructures with six proposed repair strategies are comparedin Figure 10 According to the effect of repairs the sixprofiles can be separated into two groups S1 and S3 and S2and S4 to S6 (ere are two further observations First if S1to S4 are compared it can be observed that the depth ofrepairs is more effective in reducing the mean profiles thanthe quality of repair materials (see also Table 2) Second if S4to S6 are compared it seems that both the depth of repairsand the quality of repair materials do not obviously influencethe mean profiles (ese two observations show that deeperdepth of repairs is not always better because it has a lim-itation on reducing the amount of chloride ions For moreexplanation let compare Figures 4(c)ndash4(d) At year 30A inFigures 4(c) and 4(d) the amount of remaining chloride ionsat the repair depth of 131 and 146mm respectively aresufficiently low However the 131mm repair depth inFigure 4(c) is found to be deep enough to reduce the chlorideions redistributing to the cover depth Hence too deeprepair such as the 146mm repair depth in Figure 4(d) is notrecommended On the other hand the repair depth alsodepends on the immediate amount of chloride ions redis-tributing to the cover depth It is noted that in real practiceother factors such as the cost of repairs and etc are alsofound to control the repair strategy

Although the mean profiles in Figure 10 can be used forcomparing concrete structures with repairs it is difficult to

0 20 40 60 80 100Time (yrs)

CCrit = T (01 06 171) binder

No repairWith S1DC

00

04

08

12

16

20

Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Mean

COVSt dev

2000 samplesCs = T (157 24 486) binderDo = T (112 45 625) times 10ndash12 m2sXc = T (78 92 118) mm

Figure 8 Probabilistic time-dependent chloride profiles withoutand with S1

Table 5 Parameters for deterministic assessment

Analysis type Cs ( binder) Do (m2s) Xc (mm)Deterministic profile 294 396 times 10minus12 96Upper bound 486 625 times 10minus12 78Lower bound 157 112 times 10minus12 118


Xc = T (78 92 118) mmCCrit = T (01 06 171) binder

PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

0 20 40 60 80 100 0 20 40 60 80

PDF

of re

pair

appl

icat

ion

time

100

PDF of repair application time for S1 DCCs = T (157 24 486) binderDo = T (112 45 625) times 10ndash12 m2s

First application time(mean st dev) = (34 201)

Second application time(mean st dev) = (502 215)

Time (yrs) Time (yrs)

0 20 40 60 80 100 0 20 40 60 80 100

ird application time(mean st dev) = (597 203)

Fourth application time(mean st dev) = (666 186)


(a)

CDF

of re

pair

appl

icat

ion

time

100

075

050

025

0000 20 40 60 80 100

377

Time (yrs)

2000 samplesCs = T (157 24 486)Do = T (112 45 625) times 10ndash12

Xc = T (78 92 118)CCrit = T (01 06 171)With S1DC

First application0924

0802

0636

049

2nd

3rd

4th

5th

6th7th

8th

0755

0457

0237

192

307

(b)

Figure 9 PDF and CDF of repair application time for S1 (a) PDF of repair application time (b) CDF of repair application time


judge the best repair strategy (is is because all of the meanprofiles satisfy the corrosion-free condition Hence the useof the mean profiles as a criterion is not enough Anotherfactor ie the total expected number of repair applicationsis introduced here By the same method used for S1 inFigure 9 the total expected number of repair applicationsthe mean and median of repair application time and thepercent confidence for all repair strategies are compared inTable 6 It is seen that S6 is the best because the total expectednumber of repair applications is fewer (is agrees with theresults from the deterministic assessment in Table 3 in the waythat better repair material and deeper repair depth lead tofewer numbers of repairs From Table 6 it is also observedthat the number of repair applications is related to the percentconfidence For example the total expected number of repairapplications for S3 is equal to 292 as shown in the last columnof Table 6 (e percent confidence for the first second andthird repairs are larger than or approximately equal to 50but that for the fourth one is lower than 50(is implies thatif the percent confidence of the third repair is approximatelyequal to 50 then the total expected number of repair ap-plications is almost thrice It is also observed that if thepercent confidence of any repair is high eg 933 of the firstrepair of S4 the mean of repair application time will not bemuch different from its median But if the percent confidence

is not high enough eg 726 of the second repair of S3 itsmean will be quite different from its median

523 Sensitivity Analysis In this study the sensitivityanalysis is used for observing the relative significance of fourrandom variables ie surface chloride (Cs) diffusion co-efficient (Do) cover depth (Xc) and critical chloride (CCrit)on probabilistic parameters (e probabilistic parametersare composed of the chloride content the mean and medianof corrosion initiation time the total expected number ofrepair applications and the median of repair applicationtime To perform the sensitivity analysis the proposed de-scriptors ie minimum mode and maximum in Table 1will be added or subtracted so that either their mean or theirstandard deviation are disturbed by 10 as shown in Ta-bles 7 and 8 respectively

Without repair the sensitivity of the mean profiles ofchloride content to the mean and the standard deviation ofCs is shown in the left-handed and right-handed figures ofFigure 11 respectively It is found that the mean profiles aredirectly related to the mean of Cs but not sensitive to thestandard deviation of Cs

(e sensitivity of the mean and the median of corrosioninitiation time to the mean and the standard deviation offour random variables is shown in Figure 12 Its x-axis showsthe corrosion initiation time for the case without distur-bance while its y-axis shows that with disturbance FromFigure 12(a) the mean of corrosion initiation time is mostsensitive to the mean of Xc because the difference betweenthe means of corrosion initiation time without and withdisturbance falls approximately on 15 margin of errorHowever it is quite sensitive to the mean of the other threerandom variables because the difference falls within 10margin of error In addition the median of corrosion ini-tiation time is most sensitive to the mean of Xc (on 20margin of error) but quite sensitive to the mean of the otherrandom variables (on 10 margin of error) (ese obser-vations show that Xc (cover depth) is the most importantparameter in design of new concrete structures to extend thecorrosion initiation time From Figure 12(b) the mean andthe median of corrosion initiation time are however notsensitive to the standard deviation of all four randomvariables

With repairs the sensitivity of the total expected numberof repair applications by six repair strategies to the mean ofthe four random variables is shown in Figure 13 It reveals

Table 6 Comparison of six repair strategies from probabilistic assessment

StrategyMean of repair application time yrs ( confidence) Median of repair application time yrs

No of repairsFirst Second (ird Fourth First Second (ird Fourth

S1 34 (924) 502 (802) 597 (636) 666 (49) 307 554 79 gt100 377S2 34 (924) 515 (771) 617 (582) 685 (417) 307 591 87 gt100 337S3 34 (924) 552 (726) 65 (496) 727 (339) 307 674 gt100 gt100 292S4 34 (924) 553 (697) 67 (467) 739 (284) 307 688 gt100 gt100 271S5 34 (924) 564 (707) 668 (453) 731 (271) 307 702 gt100 gt100 268S6 34 (924) 621 (562) 733 (266) 776 (105) 307 884 gt100 gt100 194

Chlo

ride c

onte

nt (

bin

der)

12

10

08

06

04

02

000 20 40 60 80 100

Time (yrs)

2000 samples

CCrit = T (01 06 171) binderXc = T (78 92 118) mmDo = T (112 45 625) times 10ndash12 m2sCs = T (157 24 486) binder

μ(ClCrit) = 08

S4 S2S3S1

S5 S6

S1DCS2DC35S375DC

S475DC35S575DC50S650DC50

Figure 10 Mean profiles of chloride content with six proposedrepair strategies


that the total expected number of repair applications is mostsensitive to the mean of Xc (on 20 margin of error) andquite sensitive to the mean of the other random variables (on10 margin of error) Figure 14 shows the sensitivity of themedian of the second repair application time to 10 dis-turbance of the mean of the four random variables It revealsthat the median of the second repair application time is mostsensitive to the mean of Xc By the same method it can beshown that the total expected number of repair applications

and the median of repair application time are not sensitive tothe standard of the four random variables because thedifference is less than 2 margin of error

6 Conclusion

In this paper a study on probabilistic and sensitivity analysisof the service life (or time to repairs) for corrosion-freecondition of chloride-attacked concrete structures with

Table 8 Descriptors for sensitivity analysis of the standard deviation of four random variables

Random variables Disturbance Descriptors μ σ COV

Cs ( binder) σ(CS) + 10σ(CS) T (164 24 479) 294 067 023σ(CS)minus 10σ(CS) T (15 24 493) 073 025

Do (times10minus12m2s) σ(D0) + 10σ(D0) T (123 45 614) 396 102 026σ(D0)minus 10σ(D0) T (101 45 636) 111 028

Xc (mm) σ(Xc) + 10σ(Xc) T (79 92 117) 96 788 0082σ(Xc)minus 10σ(Xc) T (77 92 119) 869 0091

CCrit ( binder) σ(CCrit) + 10σ(CCrit) T (013 06 168) 08 032 040σ(CCrit)minus 10σ(CCrit) T (007 06 174) 035 044

T (a b c) means triangular distribution with minimum mode and maximum of a b and c respectively

Mea

n of

Clndash co

nten

t (

bin

der)

200

160

ndash10

+10

ndash10

+10

120

μ(CCrit) = 08 μ(CCrit) = 08

μ(Cs) + 10 μ(Cs)

μ(Cs) + 10 μ(Cs)Cs

080

040

0000 20 40 60 80 100

Mea

n of

Clndash co

nten

t (

bin

der)

200

160

120

080

040

000


Effect of μ(Cs) Effect of σ(Cs)

σ(Cs) + 10 σ(Cs)

σ(Cs) ndash 10 σ(Cs)Cs

0 20 40 60 80 100

Figure 11 Sensitivity of Cs to chloride profiles in concrete without repair

Table 7 Descriptors for sensitivity analysis of the mean of four random variables


Cs ( binder) μ(CS) + 10μ(CS) T (186 269 515) 324 07 022μ(CS)minus 10μ(CS) T (128 211 457) 265 026

Do (times10minus12m2s) μ(D0) + 10μ(D0) T (152 49 665) 435 106 024μ(D0)minus 10μ(D0) T (072 41 585) 356 03

Xc (mm) μ(Xc) + 10μ(Xc) T (88 102 128) 106 829 0079μ(Xc)minus 10μ(Xc) T (68 82 108) 86 0096

CCrit ( binder) μ(CCrit) + 10μ(CCrit) T (018 068 179) 088 034 038μ(CCrit)minus 10μ(CCrit) T (002 052 163) 072 047



Number of repairswithout disturbance on mean

Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10

+20μ(Cs) +ndash 10 μ(Cs)

ndash20ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

00

1

2

3

4

5

6

1 2 3 4 5 6

Equality-line

+10+20

μ(Xc) +ndash 10 μ(Xc)

ndash20ndash10


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line

+10+20

μ(CCrit) +ndash 10 μ(CCrit)

ndash20ndash10

Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean


0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10

+20μ(Do) +ndash 10 μ(Do)

ndash20ndash10

+10ndash10

+10ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

Figure 13 Sensitivity of the mean of four random variables to the total expected number of repair applications

Corrosion init time (yrs) without disturbance on mean

Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

mea

n

Mean of corrosioninitiation time

Median of corrosioninitiation time

Equality lin

e

ndash20 ndash line

+20 ndash line +10

ndash10

2020

24

24

28

28

32

32

36

36

40

40

44

44

μ(Cs) + 10 μ(Cs)μ(Cs) ndash 10 μ(Cs)μ(Do) + 10 μ(Do)μ(Do) ndash 10 μ(Do)

μ(Xc) + 10 μ(Xc)μ(Xc) ndash 10 μ(Xc)μ(CCrit) + 10 μ(CCrit)μ(CCrit) ndash 10 μ(CCrit)

(a)

Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

st d

ev

Corrosion init time (yrs) without disturbance on st dev



Equality lin

e

ndash20 ndash line

ndash10

+10+20 ndash line

20

24

28

32

36

40

44

20 24 28 32 36 40 44

σ(Cs) + 10 σ(Cs)σ(Cs) ndash 10 σ(Cs)σ(Do) + 10 σ(Do)σ(Do) ndash 10 σ(Do)

σ(Xc) + 10 σ(Xc)σ(Xc) ndash 10 σ(Xc)σ(CCrit) + 10 σ(CCrit)σ(CCrit) ndash 10 σ(CCrit)

(b)

Figure 12 Sensitivity to mean and median of corrosion initiation time (a) Effect of the mean of four random variables (b) Effect of thestandard deviation of four random variables


multiple repairs is carried out Four groups of probabilisticparameters are studied ie (1) time-dependent chloridecontent (2) mean and median of corrosion initiation andrepair application times (3) percent confidence of repairsand (4) the total expected number of repairs For these fourgoverning random variables (surface chloride diffusioncoefficient concrete cover depth and critical chloride value)and six repair strategies are considered By using the pro-posed computational approach observations can be foundas follows

(1) Both the deterministic and probabilistic studies showthat better repair material and deeper repair depthlead to fewer numbers of repairs

(2) If only the deterministic assessment is utilized thecorrosion initiation time is predicted as a discretetime (is however reveals that corrosion-freeplanning of concrete structures with long-term re-pairs which require the expected (or probabilistic)repair application time cannot properly be carriedout (is is due to the fact that the expected numberof concrete structures with reinforcement corrosioncannot be determined

(3) (e time-dependent dispersion of chloride contentshould be calculated in terms of the coefficient ofvariation rather than the standard deviation

(4) (ere are two approaches to assess the service lifeie the mean and standard deviation of repair ap-plication time and the median (or 50-percentile) ofrepair application time (e median is found to bemore effective because it is not sensitive to thedesign time period

(5) For existing concrete structures under chloride at-tack it seems that the depth of repairs is more ef-fective in reducing the mean profiles of chloridecontent than the quality of repair materials How-ever the excessive depth of repairs is not alwaysrecommended due to another control factor such asthe immediate amount of redistributing chlorideions at the repair depth It is also noted that inpractice other factors such as the cost of repairs andetc are also found to control the repair strategy Toalleviate this limitation this study however proposesto consider a terminology called the total expectednumber of repair applications

Median of repair time (yrs)without disturbance on mean

Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

Equality-line+10

+10

S1DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash10

+20

ndash20ndash10

μ(Cs) +ndash 10 μ(Cs)


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10+20

μ(Do) +ndash 10 μ(Do)

Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

00

20

20

40

40

60

60

80

80

100

100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10


+20

Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20

ndash10

+10+20


Equality-line

+10 ndash10

+10ndash10

+10ndash10

+10ndash10

+10ndash10

Figure 14 Sensitivity of the mean of four random variables to the median of second repair application time


(6) (e mean and median of repair application time(including corrosion initiation time) and the totalexpected number of repair applications are mostsensitive to the mean of the cover depth but notsensitive to the standard deviation of all four randomvariables (erefore the cover depth is the mostimportant parameter in design of new concretestructures exposed to chloride environment in orderto extend the repair application time as well ascorrosion initiation time

(7) (ere are two recommendations for further studyFor the first recommendation other control factorssuch as the cost of repairs should be taken intoaccount because it plays an important role for de-cision makers to obviously compare different repairstrategies For the second recommendation theflexural cracking of concrete members such asbeams due to serviceability loads requires furtherstudy because cracks caused by mechanical loadsreduce the chloride resistance of concrete and speedup the initiation of steel corrosion in concrete whichfrequently occurs in field applications [44]

Data Availability

Previously reported raw data were used to support this studyand are available at httpsdoiorg101016jconbuildmat200905007 (is prior study is cited at relevant placeswithin the text as reference [42] and the probabilistic dataused to support the findings of this study are also includedwithin the article

Conflicts of Interest

(e author declares that there are no conflicts of interest

Acknowledgments

(is research was funded by King Mongkutrsquos Universityof Technology North Bangkok (contract no KMUTNB-61-GOV-B-16) (e author would also like to acknowledge MsPaweena Narupankulchai for assisting in data collections

References

[1] M Sun W J Staszewski and R N Swamy ldquoSmart sensingtechnologies for structural health monitoring of civil engi-neering structuresrdquo Advances in Civil Engineering vol 2010Article ID 724962 13 pages 2010

[2] N Damrongwiriyanupap S Limkatanyu and Y Xi ldquoAthermo-hygro-coupled model for chloride penetration inconcrete structuresrdquo Advances in Materials Science and En-gineering vol 2015 Article ID 682940 10 pages 2015

[3] C L Page ldquoMechanism of corrosion protection in reinforcedconcrete marine structuresrdquo Nature vol 258 no 5535pp 514-515 1975

[4] I Saeligther ldquoBond deterioration of corroded steel bars inconcreterdquo Structure and Infrastructure Engineering vol 7no 6 pp 415ndash429 2011

[5] G G Triantafyllou T C Rousakis and A I KarabinisldquoCorroded RC beams patch repaired and strengthened in

flexure with fiber-reinforced polymer laminatesrdquo CompositesPart B Engineering vol 112 pp 125ndash136 2017

[6] A Petcherdchoo ldquoPseudo-coating model for predictingchloride diffusion into surface-coated concrete in tidal zoneTime-dependent approachrdquo Cement and Concrete Compos-ites vol 74 pp 88ndash99 2016

[7] R D Hooton M R Geiker and E C Bentz ldquoEffects of curingon chloride ingress and implications on service liferdquo ACIMaterials Journal vol 99 no 2 pp 201ndash206 2002

[8] W Sanawung T Cheewaket W Tangchirapat andC Jaturapitakkul ldquoInfluence of palm oil fuel ash and WBratios on compressive strength water permeability andchloride resistance of concreterdquo Advances in MaterialsScience and Engineering vol 2017 Article ID 49276408 pages 2017

[9] B Dong Z Gu Q Qiu et al ldquoElectrochemical feature forchloride ion transportation in fly ash blended cementitiousmaterialsrdquo Construction and Building Materials vol 161pp 577ndash586 2018

[10] J Paulsson-Tralla ldquoService life prediction of concrete bridgedecks repaired with bonded concrete overlaysrdquoMaterials andStructures vol 34 no 1 pp 34ndash41 2001

[11] Y Li and T Vrouwenvelder ldquoService life prediction andrepair of concrete structures with spatial variabilityrdquo Heronvol 52 pp 251ndash67 2007

[12] M D Pritzl H Tabatabai and A Ghorbanpoor ldquoLaboratoryassessment of select methods of corrosion control and repairin reinforced concrete bridgesrdquo International Journal ofCorrosion vol 2014 Article ID 175094 11 pages 2014

[13] Maunsell Ltd Optimum Maintenance Strategies for DifferentBridge Type Highway Agency Guildford UK 2000

[14] P Duan C Yan andW Luo ldquoA novel waterproof fast settingand high early strength repair material derived from meta-kaolin geopolymerrdquo Construction and Building Materialsvol 124 pp 69ndash73 2016

[15] A Petcherdchoo ldquoClosed-form solutions for modelingchloride transport in unsaturated concrete under wet-drycycles of chloride attackrdquo Construction and Building Mate-rials vol 176 pp 638ndash651 2018

[16] A A Abouhussien and A A A Hassan ldquoExperimental andempirical time to corrosion of reinforced concrete structuresunder different curing conditionsrdquo Advances in Civil Engi-neering vol 2014 Article ID 595743 9 pages 2014

[17] A Petcherdchoo ldquoService life and environmental impact dueto repairs by metakaolin concrete after chloride attackrdquo inRILEM Bookseries pp 35ndash41 Springer Nature Basel Swit-zerland 2015

[18] A Petcherdchoo ldquoRepairs by fly ash concrete to extendservice life of chloride-exposed concrete structures consid-ering environmental impactsrdquo Construction and BuildingMaterials vol 98 pp 799ndash809 2015

[19] REHABCON ldquoFinal report on the evaluation of alternativerepair and upgrading options strategy for maintenance andrehabilitation in concrete structuresrdquo EC Innovation andSME Programme Project No IPS-2000-0063 Department ofBuilding Materials LIT Lund Sweden 2004

[20] A Petcherdchoo ldquoEnvironmental impacts of combined re-pairs on marine concrete structuresrdquo Journal of AdvancedConcrete Technology vol 13 no 3 pp 205ndash213 2015

[21] J Crank ampe Mathematics of Diffusion (e ClarendonPressOxford UK 1975

[22] M K Kassir and M Ghosn ldquoChloride-induced corrosion ofreinforced concrete bridge decksrdquo Cement and ConcreteResearch vol 32 no 1 pp 139ndash143 2002


[23] A Petcherdchoo ldquoClosed-form solutions for bilinear surfacechloride functions applied to concrete exposed to deicingsaltsrdquo Cement and Concrete Research vol 102 pp 136ndash1482017

[24] J Zhang and Z Lounis ldquoSensitivity analysis of simplifieddiffusion-based corrosion initiation model of concretestructures exposed to chloridesrdquo Cement and Concrete Re-search vol 36 no 7 pp 1312ndash1323 2006

[25] E Bastidas-Arteaga A Chateauneuf M Sanchez-SilvaP Bressolette and F Schoefs ldquoInfluence of weather and globalwarming in chloride ingress into concrete a stochastic ap-proachrdquo Structural Safety vol 32 no 4 pp 238ndash249 2010

[26] J Hackl and J Kohler ldquoReliability assessment of deterioratingreinforced concrete structures by representing the coupledeffect of corrosion initiation and progression by Bayesiannetworksrdquo Structural Safety vol 62 pp 12ndash23 2016

[27] L Pang and Q Li ldquoService life prediction of RC structures inmarine environment using long term chloride ingress datacomparison between exposure trials and real structure sur-veysrdquo Construction and Building Materials vol 113pp 979ndash987 2016

[28] L Yang K Li and X Pang ldquoDesign and optimization ofmaintenance strategies for a long life-span port projectrdquoMaterials and Structures vol 46 no 1-2 pp 161ndash172 2013

[29] A Petcherdchoo ldquoProbabilistic assessment of CO2 due toconcrete repairs for crack-free condition of marine concretestructuresrdquo Advanced Materials Research vol 931-932pp 426ndash430 2014

[30] A Rahimi C Gehlen T Reschke and A WestendarpldquoApproaches for modelling the residual service life of marineconcrete structuresrdquo International Journal of Corrosionvol 2014 Article ID 432472 11 pages 2014

[31] V A Saetta V R Scotta and V R Vitaliani ldquoAnalysis ofchloride diffusion into partially saturated concreterdquo ACIMaterials Journal vol 90 no 5 pp 441ndash51 1993

[32] K Uji Y Matsuoka and T Maruya ldquoFormulation of anequation for surface chloride content of concrete due topermeation of chloriderdquo in Corrosion of Reinforcement inConcrete C L Page K W J Treadaway and P B BamforthEds SCI London UK 1990

[33] A Costa and J Appleton ldquoChloride penetration into concretein marine environment-part II prediction of long termchloride penetrationrdquoMaterials and Structures vol 32 no 5pp 354ndash359 1999

[34] A Petcherdchoo ldquoTime dependent models of apparent dif-fusion coefficient and surface chloride for chloride transportin fly ash concreterdquo Construction and Building Materialsvol 38 pp 497ndash507 2013

[35] P Skoglund J Silfwerbrand J Holmgren and J TragardhldquoChloride redistribution and reinforcement corrosion in theinterfacial region between substrate and repair concretemdashalaboratory studyrdquo Material and Structures vol 41 no 6pp 1001ndash1014 2008

[36] W H Press S A Teukolsky W T Vetterling andB P Flannery Numerical Recipes in C the Art of ScientificComputing Cambridge University Press Cambridge UK1999

[37] O Truc J P Ollivier and L O Nilsson ldquoNumerical simu-lation of multi-species transport through saturated concreteduring a migration test - MsDiff coderdquo Cement and ConcreteResearch vol 30 no 10 pp 1581ndash1592 2000

[38] F Deby M Carcasses and A Sellier ldquoProbabilistic approachfor durability design of reinforced concrete in marine

environmentrdquo Cement and Concrete Research vol 39 no 5pp 466ndash471 2009

[39] L C Neves Life cycle analysis of bridges considering conditionsafety and maintenance cost interaction PhD thesis Uni-versity of Minho Guimaratildees Portugal 2005

[40] M McKay W Conover and R A Beckman ldquoComparison ofthree methods for selecting values of input variables in theanalysis of output from a computer coderdquo Technometricsvol 21 no 2 pp 239ndash245 1979

[41] A Olsson G Sandberg and O Dahlblom ldquoOn Latin Hy-percube sampling for structural reliability analysisrdquo StructuralSafety vol 25 no 1 pp 47ndash68 2003

[42] H W Song S W Pack and K Y Ann ldquoProbabilistic as-sessment to predict the time to corrosion of steel in reinforcedconcrete tunnel box exposed to sea waterrdquo Construction andBuilding Materials vol 23 no 10 pp 3270ndash3278 2009

[43] A Rahimi C Gehlen T Reschke and A WestendarpldquoChloride transport in concrete structural elements afterrepairrdquo in Proceeding of the International Concrete-Innovation and Design FIB Symposium 2015 CopenhagenDenmark May 2015

[44] Q Wang W Sun L Guo C Gu and J Zong ldquoModelingchloride diffusion coefficient of steel fiber reinforced concreteunder bending loadrdquo Advances in Civil Engineering vol 2018Article ID 3789214 6 pages 2018


International Journal of

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Journal of

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Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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SensorsJournal of



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Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


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Hindawi

wwwhindawicom Volume 2018

Advances in

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Submit your manuscripts atwwwhindawicom

In studying the service life and the repair applicationtime of concrete structures under chloride attack a quan-titative assessment is preferable [19 20](e diffusion theorybased on Fickrsquos second law can be used to predict thepenetration of chloride ions through concrete structures Inthe study of researchers [21ndash23] if the attack of chloride ions(in terms of surface chloride) and the resistance of concrete(in terms of diffusion coefficient) were both assumed con-stant the one-dimensional partial differential equation ofFickrsquos second law could analytically be solved and used topredict the service life However these studies are based ondeterministic data that are not suitable for considering agroup of concrete structures in which uncertainties play animportant role Moreover even an individual concretestructure itself contains uncertainties in terms of surfacechloride diffusion coefficient concrete cover depth andcritical chloride value Hence several researchers carried outprobabilistic studies on service life prediction as follows In2006 Zhang and Lounis [24] performed a sensitivity analysison the diffusion-based corrosion initiation model forreinforced concrete structures built in chloride-laden en-vironments by using analytical differentiation techniques(ey found that the time to corrosion initiation for con-ventional carbon steels was most sensitive to concrete coverdepth followed by chloride diffusion coefficient Howeverthe time to corrosion initiation for corrosion-resistant steelswas most sensitive to the surface chloride concentration andchloride threshold level followed by the concrete coverdepth and chloride diffusion coefficient Later Bastidas-Arteaga et al [25] utilized a stochastic approach for de-termining the influence of weather conditions and globalwarming on chloride ingress into concrete In their study asimplified model of temperature and humidity includingseasonal variations and global warming was proposedFurthermore three scenarios of global warming were de-fined based on gas emissions global population growthintroduction of new and clean technologies and use of fossilsources of energy It was found that the lifetime reductioninduced by global warming was more significant forstructures located in chloride-contaminated environmentsfar from the sea (e results also indicated that the climatechange effect was higher for structures located in oceanicenvironments and could lead to lifetime reductions rangingfrom 2 to 18 Hackl and Kohler [26] presented a genericframework for the stochastic modeling of reinforced con-crete deterioration caused by corrosion (eir frameworkenabled the coupling of probabilistic models for the initi-ation and propagation of corrosion in service life models Intheir framework existing probabilistic models for chlorideand carbonation initiation with models for the propagationand consequences of corrosion were coupled To achieve thetask they combined structural reliability analysis withBayesian networks in order to estimate the probability offailure of a reinforced concrete structure In 2016 Pang andLi [27] carried out the filed investigations of seventeenhighpile wharf structures located at the south coast of China(ey compared the obtained results with the long-termexposure test results in terms of chloride ingress profile(e probability models for surface chloride content and

chloride diffusion coefficient were derived accordingly (eyalso investigated the effects of different models of chlorideingress parameters based on exposure trails or based on realstructure surveys on the expected service life of marinestructures It was found that the height-dependency ofsurface chloride indicated the existence of a ldquosemisplashrdquozone and the existence of semisplash zone and the additionof BFS in concrete have significant effects on the service lifeof concrete structures Yang et al [28] carried out design andoptimization of the maintenance works of reinforced con-crete (RC) elements in a long life-span marine port inShanghai China In their study the deterioration of RCelements was dominated by the reinforcement steel corro-sion induced by external chloride penetration (e de-terioration model was established for the RC elements withprescribed durability limit state and the failure probabilityevolution was calculated through Monte Carlo simulationsFurthermore the preventive necessary and mandatorymaintenances corresponded respectively to probabilitylevels of 2 5 and 20 and also three schemes of mainte-nance planning were investigated unsynchronized syn-chronized and coating-synchronized schemes From theiranalysis it was found that the coating-synchronized schemeachieved the optimal cost as well as delayed the deteriorationrate of beam elements In their study they also assumed thatwith maintenances the durability state of RC elements wasassumed to be totally restored to its initial state Howeverthis assumption shows the limitation of their study (is isdue to the fact that after concrete repairs the influence ofremaining chloride ions which are used to indicate thedurability in their study should also be taken into account

Although the aforementioned researchers studied theprobabilistic service life of concrete structures without orwith repairs they did not consider multiple repairs ac-companied with the interaction of chloride transport afterconcrete repairs (at kind of repairs is important inparticular in the current situation at which many structuresdrastically deteriorate after operating for a period of timeBased on further literature reviews there were researcherswho studied such kind of repairs For example the study ofPetcherdchoo [29] carried out probabilistic assessment ofchloride ions in concrete with repairs (e study simplifiedthe assessment by focusing on only two random variablesie surface chloride and diffusion coefficient Howeverthere are two observations in that study First in realpractice not only the surface chloride and diffusion co-efficient are random but also threshold depth (cover depth)and critical chloride value do so Second that study definedcritical time as the application repair time for preventingconcrete cracking However in real practice the time afterconcrete cracking to severe concrete deterioration is rela-tively short If this kind of concrete cracking limit state isfocused it would be too risky for concrete structures Hencemany researchers are interested in the time of corrosioninitiation rather than concrete cracking Due to these twoobservations that study is limited In 2014 Rahimi et al [30]studied probabilistic approaches for modeling the residualservice life of marine concrete structures after concreterepairs However their study has two restrictions First in







zC

zt

z

zxD

zC

zx (1)




2Dt

radic1113888 11138891113890 1113891 (2)


Start

Read input file




Consider i sample


Yes


No

j = j + 1

i = i + 1


Stop

Yes






zC

zt

z

zxD(x)

zC

zx (3)


cij+1 minus cij

Δt12


(Δx)2


(Δx)21113889

(4)




















Repairmaterial

Depth

Clndash co

ncen

trat

ion

0

Oldconcrete



Drep D0

Xc Xp

(a)

Depth(σt)



Clndash co

ncen

trat

ion

0

Old concrete D0





Xc XpXm

(b)



150

5

10

15

20

25

18 21 24 27 30 33 36 39 42 45 48 5100

02

04

06

08

10

PDF

of su

rface

chlo

ride

Num

ber o

f tes

ts



(a)

10 15 20 25 30 35 40 45 50 55 60 650

5

10

15

20

25

Num

ber o

f tes

ts

000

011

022

033

044

055

PDF

of d

iffus

ion

coeffi

cien

t



(b)


76 80 84 88 92 96 100 104 108 112 116 1200

5

10

15

20

25

0000

0015

0030

0045

0060

0075PD

F of

cove

r dep

th

Num

ber o

f tes

ts

Cover depth (mm)

(c)

00 02 04 06 08 10 12 14 16 180

5

10

15

20

25

000

031

062

093

124

155

PDF

of cr

itica

l chl

orid

e



Num

ber o

f tes

ts

(d)






S1 DC














μt 1113936

ni1cit

n (5)






08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30B

ClCrit = 08

Year 1

21

714

(a)

0 50 100 150 200

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30A


Year 31

35 4045

ClCrit = 08

(b)

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30A


Year 3135 40

45ClCrit = 08

(c)

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


rs dep = 96mm

Year 30A


Year 313540

45 ClCrit = 08

(d)


000

04

08

12

16

20

20Time (yrs)

No repair

Repair

No repair


40 60 80 100

Chlo

ride c

onte

nt (

bin

der)

ClCrit = 08











σt

1113936

ni1c

2it


1113971

COVt σt

microt

(6)



00

171

01

04

08

12

16

20

24

0 20 40 60 80 100Time (yrs)


Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Cs = T (157 24 486)rs Dep = 96 mm

Do = T (112 45 625)Xc = T (78 92 118)

With S650DC50CCrit= T (01 06 171)


000

08

16

24

32

40

20 40

40

60

60

80

80

100

Chlo

ride c

onte

nt (

bin

der)

Time (yrs)




Mean

Upperbound

Lowerbound



micro(ClCrit) = 08



Simulationnumber


1 315 383 99 132 1915 1492 429 224 88 082 112 1383 182 457 103 117 2285 1534 299 294 79 062 147 1295 228 187 112 102 0935 162









0 20 40 60 80 100Time (yrs)


No repairWith S1DC

00

04

08

12

16

20

Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Mean

COVSt dev







PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

0 20 40 60 80 100 0 20 40 60 80

PDF

of re

pair

appl

icat

ion

time

100





0 20 40 60 80 100 0 20 40 60 80 100




(a)

CDF

of re

pair

appl

icat

ion

time

100

075

050

025

0000 20 40 60 80 100

377

Time (yrs)




0802

0636

049

2nd

3rd

4th

5th

6th7th

8th

0755

0457

0237

192

307

(b)













Chlo

ride c

onte

nt (

bin

der)

12

10

08

06

04

02

000 20 40 60 80 100

Time (yrs)

2000 samples


μ(ClCrit) = 08

S4 S2S3S1

S5 S6

S1DCS2DC35S375DC

S475DC35S575DC50S650DC50





6 Conclusion









Mea

n of

Clndash co

nten

t (

bin

der)

200

160

ndash10

+10

ndash10

+10

120


μ(Cs) + 10 μ(Cs)


080

040

0000 20 40 60 80 100

Mea

n of

Clndash co

nten

t (

bin

der)

200

160

120

080

040

000



σ(Cs) + 10 σ(Cs)


0 20 40 60 80 100











Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

00

1

2

3

4

5

6

1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10

Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean


0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

+10ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50



Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

mea

n



Equality lin

e

ndash20 ndash line

+20 ndash line +10

ndash10

2020

24

24

28

28

32

32

36

36

40

40

44

44



(a)

Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

st d

ev




Equality lin

e

ndash20 ndash line

ndash10

+10+20 ndash line

20

24

28

32

36

40

44

20 24 28 32 36 40 44



(b)










Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

Equality-line+10

+10

S1DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash10

+20

ndash20ndash10



Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10+20


Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

00

20

20

40

40

60

60

80

80

100

100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10


+20

Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20

ndash10

+10+20


Equality-line

+10 ndash10

+10ndash10

+10ndash10

+10ndash10

+10ndash10





Data Availability




Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







zC

zt

z

zxD

zC

zx (1)




2Dt

radic1113888 11138891113890 1113891 (2)


Start

Read input file




Consider i sample


Yes


No

j = j + 1

i = i + 1


Stop

Yes






zC

zt

z

zxD(x)

zC

zx (3)


cij+1 minus cij

Δt12


(Δx)2


(Δx)21113889

(4)




















Repairmaterial

Depth

Clndash co

ncen

trat

ion

0

Oldconcrete



Drep D0

Xc Xp

(a)

Depth(σt)



Clndash co

ncen

trat

ion

0

Old concrete D0





Xc XpXm

(b)



150

5

10

15

20

25

18 21 24 27 30 33 36 39 42 45 48 5100

02

04

06

08

10

PDF

of su

rface

chlo

ride

Num

ber o

f tes

ts



(a)

10 15 20 25 30 35 40 45 50 55 60 650

5

10

15

20

25

Num

ber o

f tes

ts

000

011

022

033

044

055

PDF

of d

iffus

ion

coeffi

cien

t



(b)


76 80 84 88 92 96 100 104 108 112 116 1200

5

10

15

20

25

0000

0015

0030

0045

0060

0075PD

F of

cove

r dep

th

Num

ber o

f tes

ts

Cover depth (mm)

(c)

00 02 04 06 08 10 12 14 16 180

5

10

15

20

25

000

031

062

093

124

155

PDF

of cr

itica

l chl

orid

e



Num

ber o

f tes

ts

(d)






S1 DC














μt 1113936

ni1cit

n (5)






08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30B

ClCrit = 08

Year 1

21

714

(a)

0 50 100 150 200

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30A


Year 31

35 4045

ClCrit = 08

(b)

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30A


Year 3135 40

45ClCrit = 08

(c)

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


rs dep = 96mm

Year 30A


Year 313540

45 ClCrit = 08

(d)


000

04

08

12

16

20

20Time (yrs)

No repair

Repair

No repair


40 60 80 100

Chlo

ride c

onte

nt (

bin

der)

ClCrit = 08











σt

1113936

ni1c

2it


1113971

COVt σt

microt

(6)



00

171

01

04

08

12

16

20

24

0 20 40 60 80 100Time (yrs)


Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Cs = T (157 24 486)rs Dep = 96 mm

Do = T (112 45 625)Xc = T (78 92 118)

With S650DC50CCrit= T (01 06 171)


000

08

16

24

32

40

20 40

40

60

60

80

80

100

Chlo

ride c

onte

nt (

bin

der)

Time (yrs)




Mean

Upperbound

Lowerbound



micro(ClCrit) = 08



Simulationnumber


1 315 383 99 132 1915 1492 429 224 88 082 112 1383 182 457 103 117 2285 1534 299 294 79 062 147 1295 228 187 112 102 0935 162









0 20 40 60 80 100Time (yrs)


No repairWith S1DC

00

04

08

12

16

20

Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Mean

COVSt dev







PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

0 20 40 60 80 100 0 20 40 60 80

PDF

of re

pair

appl

icat

ion

time

100





0 20 40 60 80 100 0 20 40 60 80 100




(a)

CDF

of re

pair

appl

icat

ion

time

100

075

050

025

0000 20 40 60 80 100

377

Time (yrs)




0802

0636

049

2nd

3rd

4th

5th

6th7th

8th

0755

0457

0237

192

307

(b)













Chlo

ride c

onte

nt (

bin

der)

12

10

08

06

04

02

000 20 40 60 80 100

Time (yrs)

2000 samples


μ(ClCrit) = 08

S4 S2S3S1

S5 S6

S1DCS2DC35S375DC

S475DC35S575DC50S650DC50





6 Conclusion









Mea

n of

Clndash co

nten

t (

bin

der)

200

160

ndash10

+10

ndash10

+10

120


μ(Cs) + 10 μ(Cs)


080

040

0000 20 40 60 80 100

Mea

n of

Clndash co

nten

t (

bin

der)

200

160

120

080

040

000



σ(Cs) + 10 σ(Cs)


0 20 40 60 80 100











Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

00

1

2

3

4

5

6

1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10

Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean


0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

+10ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50



Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

mea

n



Equality lin

e

ndash20 ndash line

+20 ndash line +10

ndash10

2020

24

24

28

28

32

32

36

36

40

40

44

44



(a)

Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

st d

ev




Equality lin

e

ndash20 ndash line

ndash10

+10+20 ndash line

20

24

28

32

36

40

44

20 24 28 32 36 40 44



(b)










Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

Equality-line+10

+10

S1DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash10

+20

ndash20ndash10



Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10+20


Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

00

20

20

40

40

60

60

80

80

100

100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10


+20

Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20

ndash10

+10+20


Equality-line

+10 ndash10

+10ndash10

+10ndash10

+10ndash10

+10ndash10





Data Availability




Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





zC

zt

z

zxD(x)

zC

zx (3)


cij+1 minus cij

Δt12


(Δx)2


(Δx)21113889

(4)




















Repairmaterial

Depth

Clndash co

ncen

trat

ion

0

Oldconcrete



Drep D0

Xc Xp

(a)

Depth(σt)



Clndash co

ncen

trat

ion

0

Old concrete D0





Xc XpXm

(b)



150

5

10

15

20

25

18 21 24 27 30 33 36 39 42 45 48 5100

02

04

06

08

10

PDF

of su

rface

chlo

ride

Num

ber o

f tes

ts



(a)

10 15 20 25 30 35 40 45 50 55 60 650

5

10

15

20

25

Num

ber o

f tes

ts

000

011

022

033

044

055

PDF

of d

iffus

ion

coeffi

cien

t



(b)


76 80 84 88 92 96 100 104 108 112 116 1200

5

10

15

20

25

0000

0015

0030

0045

0060

0075PD

F of

cove

r dep

th

Num

ber o

f tes

ts

Cover depth (mm)

(c)

00 02 04 06 08 10 12 14 16 180

5

10

15

20

25

000

031

062

093

124

155

PDF

of cr

itica

l chl

orid

e



Num

ber o

f tes

ts

(d)






S1 DC














μt 1113936

ni1cit

n (5)






08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30B

ClCrit = 08

Year 1

21

714

(a)

0 50 100 150 200

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30A


Year 31

35 4045

ClCrit = 08

(b)

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30A


Year 3135 40

45ClCrit = 08

(c)

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


rs dep = 96mm

Year 30A


Year 313540

45 ClCrit = 08

(d)


000

04

08

12

16

20

20Time (yrs)

No repair

Repair

No repair


40 60 80 100

Chlo

ride c

onte

nt (

bin

der)

ClCrit = 08











σt

1113936

ni1c

2it


1113971

COVt σt

microt

(6)



00

171

01

04

08

12

16

20

24

0 20 40 60 80 100Time (yrs)


Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Cs = T (157 24 486)rs Dep = 96 mm

Do = T (112 45 625)Xc = T (78 92 118)

With S650DC50CCrit= T (01 06 171)


000

08

16

24

32

40

20 40

40

60

60

80

80

100

Chlo

ride c

onte

nt (

bin

der)

Time (yrs)




Mean

Upperbound

Lowerbound



micro(ClCrit) = 08



Simulationnumber


1 315 383 99 132 1915 1492 429 224 88 082 112 1383 182 457 103 117 2285 1534 299 294 79 062 147 1295 228 187 112 102 0935 162









0 20 40 60 80 100Time (yrs)


No repairWith S1DC

00

04

08

12

16

20

Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Mean

COVSt dev







PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

0 20 40 60 80 100 0 20 40 60 80

PDF

of re

pair

appl

icat

ion

time

100





0 20 40 60 80 100 0 20 40 60 80 100




(a)

CDF

of re

pair

appl

icat

ion

time

100

075

050

025

0000 20 40 60 80 100

377

Time (yrs)




0802

0636

049

2nd

3rd

4th

5th

6th7th

8th

0755

0457

0237

192

307

(b)













Chlo

ride c

onte

nt (

bin

der)

12

10

08

06

04

02

000 20 40 60 80 100

Time (yrs)

2000 samples


μ(ClCrit) = 08

S4 S2S3S1

S5 S6

S1DCS2DC35S375DC

S475DC35S575DC50S650DC50





6 Conclusion









Mea

n of

Clndash co

nten

t (

bin

der)

200

160

ndash10

+10

ndash10

+10

120


μ(Cs) + 10 μ(Cs)


080

040

0000 20 40 60 80 100

Mea

n of

Clndash co

nten

t (

bin

der)

200

160

120

080

040

000



σ(Cs) + 10 σ(Cs)


0 20 40 60 80 100











Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

00

1

2

3

4

5

6

1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10

Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean


0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

+10ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50



Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

mea

n



Equality lin

e

ndash20 ndash line

+20 ndash line +10

ndash10

2020

24

24

28

28

32

32

36

36

40

40

44

44



(a)

Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

st d

ev




Equality lin

e

ndash20 ndash line

ndash10

+10+20 ndash line

20

24

28

32

36

40

44

20 24 28 32 36 40 44



(b)










Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

Equality-line+10

+10

S1DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash10

+20

ndash20ndash10



Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10+20


Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

00

20

20

40

40

60

60

80

80

100

100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10


+20

Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20

ndash10

+10+20


Equality-line

+10 ndash10

+10ndash10

+10ndash10

+10ndash10

+10ndash10





Data Availability




Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










Repairmaterial

Depth

Clndash co

ncen

trat

ion

0

Oldconcrete



Drep D0

Xc Xp

(a)

Depth(σt)



Clndash co

ncen

trat

ion

0

Old concrete D0





Xc XpXm

(b)



150

5

10

15

20

25

18 21 24 27 30 33 36 39 42 45 48 5100

02

04

06

08

10

PDF

of su

rface

chlo

ride

Num

ber o

f tes

ts



(a)

10 15 20 25 30 35 40 45 50 55 60 650

5

10

15

20

25

Num

ber o

f tes

ts

000

011

022

033

044

055

PDF

of d

iffus

ion

coeffi

cien

t



(b)


76 80 84 88 92 96 100 104 108 112 116 1200

5

10

15

20

25

0000

0015

0030

0045

0060

0075PD

F of

cove

r dep

th

Num

ber o

f tes

ts

Cover depth (mm)

(c)

00 02 04 06 08 10 12 14 16 180

5

10

15

20

25

000

031

062

093

124

155

PDF

of cr

itica

l chl

orid

e



Num

ber o

f tes

ts

(d)






S1 DC














μt 1113936

ni1cit

n (5)






08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30B

ClCrit = 08

Year 1

21

714

(a)

0 50 100 150 200

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30A


Year 31

35 4045

ClCrit = 08

(b)

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30A


Year 3135 40

45ClCrit = 08

(c)

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


rs dep = 96mm

Year 30A


Year 313540

45 ClCrit = 08

(d)


000

04

08

12

16

20

20Time (yrs)

No repair

Repair

No repair


40 60 80 100

Chlo

ride c

onte

nt (

bin

der)

ClCrit = 08











σt

1113936

ni1c

2it


1113971

COVt σt

microt

(6)



00

171

01

04

08

12

16

20

24

0 20 40 60 80 100Time (yrs)


Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Cs = T (157 24 486)rs Dep = 96 mm

Do = T (112 45 625)Xc = T (78 92 118)

With S650DC50CCrit= T (01 06 171)


000

08

16

24

32

40

20 40

40

60

60

80

80

100

Chlo

ride c

onte

nt (

bin

der)

Time (yrs)




Mean

Upperbound

Lowerbound



micro(ClCrit) = 08



Simulationnumber


1 315 383 99 132 1915 1492 429 224 88 082 112 1383 182 457 103 117 2285 1534 299 294 79 062 147 1295 228 187 112 102 0935 162









0 20 40 60 80 100Time (yrs)


No repairWith S1DC

00

04

08

12

16

20

Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Mean

COVSt dev







PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

0 20 40 60 80 100 0 20 40 60 80

PDF

of re

pair

appl

icat

ion

time

100





0 20 40 60 80 100 0 20 40 60 80 100




(a)

CDF

of re

pair

appl

icat

ion

time

100

075

050

025

0000 20 40 60 80 100

377

Time (yrs)




0802

0636

049

2nd

3rd

4th

5th

6th7th

8th

0755

0457

0237

192

307

(b)













Chlo

ride c

onte

nt (

bin

der)

12

10

08

06

04

02

000 20 40 60 80 100

Time (yrs)

2000 samples


μ(ClCrit) = 08

S4 S2S3S1

S5 S6

S1DCS2DC35S375DC

S475DC35S575DC50S650DC50





6 Conclusion









Mea

n of

Clndash co

nten

t (

bin

der)

200

160

ndash10

+10

ndash10

+10

120


μ(Cs) + 10 μ(Cs)


080

040

0000 20 40 60 80 100

Mea

n of

Clndash co

nten

t (

bin

der)

200

160

120

080

040

000



σ(Cs) + 10 σ(Cs)


0 20 40 60 80 100











Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

00

1

2

3

4

5

6

1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10

Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean


0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

+10ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50



Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

mea

n



Equality lin

e

ndash20 ndash line

+20 ndash line +10

ndash10

2020

24

24

28

28

32

32

36

36

40

40

44

44



(a)

Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

st d

ev




Equality lin

e

ndash20 ndash line

ndash10

+10+20 ndash line

20

24

28

32

36

40

44

20 24 28 32 36 40 44



(b)










Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

Equality-line+10

+10

S1DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash10

+20

ndash20ndash10



Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10+20


Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

00

20

20

40

40

60

60

80

80

100

100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10


+20

Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20

ndash10

+10+20


Equality-line

+10 ndash10

+10ndash10

+10ndash10

+10ndash10

+10ndash10





Data Availability




Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


150

5

10

15

20

25

18 21 24 27 30 33 36 39 42 45 48 5100

02

04

06

08

10

PDF

of su

rface

chlo

ride

Num

ber o

f tes

ts



(a)

10 15 20 25 30 35 40 45 50 55 60 650

5

10

15

20

25

Num

ber o

f tes

ts

000

011

022

033

044

055

PDF

of d

iffus

ion

coeffi

cien

t



(b)


76 80 84 88 92 96 100 104 108 112 116 1200

5

10

15

20

25

0000

0015

0030

0045

0060

0075PD

F of

cove

r dep

th

Num

ber o

f tes

ts

Cover depth (mm)

(c)

00 02 04 06 08 10 12 14 16 180

5

10

15

20

25

000

031

062

093

124

155

PDF

of cr

itica

l chl

orid

e



Num

ber o

f tes

ts

(d)






S1 DC














μt 1113936

ni1cit

n (5)






08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30B

ClCrit = 08

Year 1

21

714

(a)

0 50 100 150 200

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30A


Year 31

35 4045

ClCrit = 08

(b)

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30A


Year 3135 40

45ClCrit = 08

(c)

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


rs dep = 96mm

Year 30A


Year 313540

45 ClCrit = 08

(d)


000

04

08

12

16

20

20Time (yrs)

No repair

Repair

No repair


40 60 80 100

Chlo

ride c

onte

nt (

bin

der)

ClCrit = 08











σt

1113936

ni1c

2it


1113971

COVt σt

microt

(6)



00

171

01

04

08

12

16

20

24

0 20 40 60 80 100Time (yrs)


Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Cs = T (157 24 486)rs Dep = 96 mm

Do = T (112 45 625)Xc = T (78 92 118)

With S650DC50CCrit= T (01 06 171)


000

08

16

24

32

40

20 40

40

60

60

80

80

100

Chlo

ride c

onte

nt (

bin

der)

Time (yrs)




Mean

Upperbound

Lowerbound



micro(ClCrit) = 08



Simulationnumber


1 315 383 99 132 1915 1492 429 224 88 082 112 1383 182 457 103 117 2285 1534 299 294 79 062 147 1295 228 187 112 102 0935 162









0 20 40 60 80 100Time (yrs)


No repairWith S1DC

00

04

08

12

16

20

Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Mean

COVSt dev







PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

0 20 40 60 80 100 0 20 40 60 80

PDF

of re

pair

appl

icat

ion

time

100





0 20 40 60 80 100 0 20 40 60 80 100




(a)

CDF

of re

pair

appl

icat

ion

time

100

075

050

025

0000 20 40 60 80 100

377

Time (yrs)




0802

0636

049

2nd

3rd

4th

5th

6th7th

8th

0755

0457

0237

192

307

(b)













Chlo

ride c

onte

nt (

bin

der)

12

10

08

06

04

02

000 20 40 60 80 100

Time (yrs)

2000 samples


μ(ClCrit) = 08

S4 S2S3S1

S5 S6

S1DCS2DC35S375DC

S475DC35S575DC50S650DC50





6 Conclusion









Mea

n of

Clndash co

nten

t (

bin

der)

200

160

ndash10

+10

ndash10

+10

120


μ(Cs) + 10 μ(Cs)


080

040

0000 20 40 60 80 100

Mea

n of

Clndash co

nten

t (

bin

der)

200

160

120

080

040

000



σ(Cs) + 10 σ(Cs)


0 20 40 60 80 100











Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

00

1

2

3

4

5

6

1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10

Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean


0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

+10ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50



Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

mea

n



Equality lin

e

ndash20 ndash line

+20 ndash line +10

ndash10

2020

24

24

28

28

32

32

36

36

40

40

44

44



(a)

Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

st d

ev




Equality lin

e

ndash20 ndash line

ndash10

+10+20 ndash line

20

24

28

32

36

40

44

20 24 28 32 36 40 44



(b)










Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

Equality-line+10

+10

S1DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash10

+20

ndash20ndash10



Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10+20


Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

00

20

20

40

40

60

60

80

80

100

100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10


+20

Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20

ndash10

+10+20


Equality-line

+10 ndash10

+10ndash10

+10ndash10

+10ndash10

+10ndash10





Data Availability




Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












μt 1113936

ni1cit

n (5)






08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30B

ClCrit = 08

Year 1

21

714

(a)

0 50 100 150 200

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30A


Year 31

35 4045

ClCrit = 08

(b)

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30A


Year 3135 40

45ClCrit = 08

(c)

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


rs dep = 96mm

Year 30A


Year 313540

45 ClCrit = 08

(d)


000

04

08

12

16

20

20Time (yrs)

No repair

Repair

No repair


40 60 80 100

Chlo

ride c

onte

nt (

bin

der)

ClCrit = 08











σt

1113936

ni1c

2it


1113971

COVt σt

microt

(6)



00

171

01

04

08

12

16

20

24

0 20 40 60 80 100Time (yrs)


Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Cs = T (157 24 486)rs Dep = 96 mm

Do = T (112 45 625)Xc = T (78 92 118)

With S650DC50CCrit= T (01 06 171)


000

08

16

24

32

40

20 40

40

60

60

80

80

100

Chlo

ride c

onte

nt (

bin

der)

Time (yrs)




Mean

Upperbound

Lowerbound



micro(ClCrit) = 08



Simulationnumber


1 315 383 99 132 1915 1492 429 224 88 082 112 1383 182 457 103 117 2285 1534 299 294 79 062 147 1295 228 187 112 102 0935 162









0 20 40 60 80 100Time (yrs)


No repairWith S1DC

00

04

08

12

16

20

Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Mean

COVSt dev







PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

0 20 40 60 80 100 0 20 40 60 80

PDF

of re

pair

appl

icat

ion

time

100





0 20 40 60 80 100 0 20 40 60 80 100




(a)

CDF

of re

pair

appl

icat

ion

time

100

075

050

025

0000 20 40 60 80 100

377

Time (yrs)




0802

0636

049

2nd

3rd

4th

5th

6th7th

8th

0755

0457

0237

192

307

(b)













Chlo

ride c

onte

nt (

bin

der)

12

10

08

06

04

02

000 20 40 60 80 100

Time (yrs)

2000 samples


μ(ClCrit) = 08

S4 S2S3S1

S5 S6

S1DCS2DC35S375DC

S475DC35S575DC50S650DC50





6 Conclusion









Mea

n of

Clndash co

nten

t (

bin

der)

200

160

ndash10

+10

ndash10

+10

120


μ(Cs) + 10 μ(Cs)


080

040

0000 20 40 60 80 100

Mea

n of

Clndash co

nten

t (

bin

der)

200

160

120

080

040

000



σ(Cs) + 10 σ(Cs)


0 20 40 60 80 100











Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

00

1

2

3

4

5

6

1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10

Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean


0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

+10ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50



Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

mea

n



Equality lin

e

ndash20 ndash line

+20 ndash line +10

ndash10

2020

24

24

28

28

32

32

36

36

40

40

44

44



(a)

Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

st d

ev




Equality lin

e

ndash20 ndash line

ndash10

+10+20 ndash line

20

24

28

32

36

40

44

20 24 28 32 36 40 44



(b)










Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

Equality-line+10

+10

S1DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash10

+20

ndash20ndash10



Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10+20


Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

00

20

20

40

40

60

60

80

80

100

100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10


+20

Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20

ndash10

+10+20


Equality-line

+10 ndash10

+10ndash10

+10ndash10

+10ndash10

+10ndash10





Data Availability




Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30B

ClCrit = 08

Year 1

21

714

(a)

0 50 100 150 200

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30A


Year 31

35 4045

ClCrit = 08

(b)

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


Cs = 294 binder

rs dep = 96mm

Year 30A


Year 3135 40

45ClCrit = 08

(c)

08

00

16

24

32

40

Chlo

ride c

onte

nt (

bin

der)

0 50 100 150 200Depth (mm)


rs dep = 96mm

Year 30A


Year 313540

45 ClCrit = 08

(d)


000

04

08

12

16

20

20Time (yrs)

No repair

Repair

No repair


40 60 80 100

Chlo

ride c

onte

nt (

bin

der)

ClCrit = 08











σt

1113936

ni1c

2it


1113971

COVt σt

microt

(6)



00

171

01

04

08

12

16

20

24

0 20 40 60 80 100Time (yrs)


Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Cs = T (157 24 486)rs Dep = 96 mm

Do = T (112 45 625)Xc = T (78 92 118)

With S650DC50CCrit= T (01 06 171)


000

08

16

24

32

40

20 40

40

60

60

80

80

100

Chlo

ride c

onte

nt (

bin

der)

Time (yrs)




Mean

Upperbound

Lowerbound



micro(ClCrit) = 08



Simulationnumber


1 315 383 99 132 1915 1492 429 224 88 082 112 1383 182 457 103 117 2285 1534 299 294 79 062 147 1295 228 187 112 102 0935 162









0 20 40 60 80 100Time (yrs)


No repairWith S1DC

00

04

08

12

16

20

Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Mean

COVSt dev







PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

0 20 40 60 80 100 0 20 40 60 80

PDF

of re

pair

appl

icat

ion

time

100





0 20 40 60 80 100 0 20 40 60 80 100




(a)

CDF

of re

pair

appl

icat

ion

time

100

075

050

025

0000 20 40 60 80 100

377

Time (yrs)




0802

0636

049

2nd

3rd

4th

5th

6th7th

8th

0755

0457

0237

192

307

(b)













Chlo

ride c

onte

nt (

bin

der)

12

10

08

06

04

02

000 20 40 60 80 100

Time (yrs)

2000 samples


μ(ClCrit) = 08

S4 S2S3S1

S5 S6

S1DCS2DC35S375DC

S475DC35S575DC50S650DC50





6 Conclusion









Mea

n of

Clndash co

nten

t (

bin

der)

200

160

ndash10

+10

ndash10

+10

120


μ(Cs) + 10 μ(Cs)


080

040

0000 20 40 60 80 100

Mea

n of

Clndash co

nten

t (

bin

der)

200

160

120

080

040

000



σ(Cs) + 10 σ(Cs)


0 20 40 60 80 100











Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

00

1

2

3

4

5

6

1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10

Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean


0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

+10ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50



Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

mea

n



Equality lin

e

ndash20 ndash line

+20 ndash line +10

ndash10

2020

24

24

28

28

32

32

36

36

40

40

44

44



(a)

Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

st d

ev




Equality lin

e

ndash20 ndash line

ndash10

+10+20 ndash line

20

24

28

32

36

40

44

20 24 28 32 36 40 44



(b)










Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

Equality-line+10

+10

S1DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash10

+20

ndash20ndash10



Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10+20


Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

00

20

20

40

40

60

60

80

80

100

100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10


+20

Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20

ndash10

+10+20


Equality-line

+10 ndash10

+10ndash10

+10ndash10

+10ndash10

+10ndash10





Data Availability




Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





σt

1113936

ni1c

2it


1113971

COVt σt

microt

(6)



00

171

01

04

08

12

16

20

24

0 20 40 60 80 100Time (yrs)


Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Cs = T (157 24 486)rs Dep = 96 mm

Do = T (112 45 625)Xc = T (78 92 118)

With S650DC50CCrit= T (01 06 171)


000

08

16

24

32

40

20 40

40

60

60

80

80

100

Chlo

ride c

onte

nt (

bin

der)

Time (yrs)




Mean

Upperbound

Lowerbound



micro(ClCrit) = 08



Simulationnumber


1 315 383 99 132 1915 1492 429 224 88 082 112 1383 182 457 103 117 2285 1534 299 294 79 062 147 1295 228 187 112 102 0935 162









0 20 40 60 80 100Time (yrs)


No repairWith S1DC

00

04

08

12

16

20

Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Mean

COVSt dev







PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

0 20 40 60 80 100 0 20 40 60 80

PDF

of re

pair

appl

icat

ion

time

100





0 20 40 60 80 100 0 20 40 60 80 100




(a)

CDF

of re

pair

appl

icat

ion

time

100

075

050

025

0000 20 40 60 80 100

377

Time (yrs)




0802

0636

049

2nd

3rd

4th

5th

6th7th

8th

0755

0457

0237

192

307

(b)













Chlo

ride c

onte

nt (

bin

der)

12

10

08

06

04

02

000 20 40 60 80 100

Time (yrs)

2000 samples


μ(ClCrit) = 08

S4 S2S3S1

S5 S6

S1DCS2DC35S375DC

S475DC35S575DC50S650DC50





6 Conclusion









Mea

n of

Clndash co

nten

t (

bin

der)

200

160

ndash10

+10

ndash10

+10

120


μ(Cs) + 10 μ(Cs)


080

040

0000 20 40 60 80 100

Mea

n of

Clndash co

nten

t (

bin

der)

200

160

120

080

040

000



σ(Cs) + 10 σ(Cs)


0 20 40 60 80 100











Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

00

1

2

3

4

5

6

1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10

Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean


0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

+10ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50



Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

mea

n



Equality lin

e

ndash20 ndash line

+20 ndash line +10

ndash10

2020

24

24

28

28

32

32

36

36

40

40

44

44



(a)

Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

st d

ev




Equality lin

e

ndash20 ndash line

ndash10

+10+20 ndash line

20

24

28

32

36

40

44

20 24 28 32 36 40 44



(b)










Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

Equality-line+10

+10

S1DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash10

+20

ndash20ndash10



Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10+20


Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

00

20

20

40

40

60

60

80

80

100

100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10


+20

Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20

ndash10

+10+20


Equality-line

+10 ndash10

+10ndash10

+10ndash10

+10ndash10

+10ndash10





Data Availability




Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









0 20 40 60 80 100Time (yrs)


No repairWith S1DC

00

04

08

12

16

20

Chlo

ride c

onte

nt (

bin

der)

micro(ClCrit) = 08

Mean

COVSt dev







PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

0 20 40 60 80 100 0 20 40 60 80

PDF

of re

pair

appl

icat

ion

time

100





0 20 40 60 80 100 0 20 40 60 80 100




(a)

CDF

of re

pair

appl

icat

ion

time

100

075

050

025

0000 20 40 60 80 100

377

Time (yrs)




0802

0636

049

2nd

3rd

4th

5th

6th7th

8th

0755

0457

0237

192

307

(b)













Chlo

ride c

onte

nt (

bin

der)

12

10

08

06

04

02

000 20 40 60 80 100

Time (yrs)

2000 samples


μ(ClCrit) = 08

S4 S2S3S1

S5 S6

S1DCS2DC35S375DC

S475DC35S575DC50S650DC50





6 Conclusion









Mea

n of

Clndash co

nten

t (

bin

der)

200

160

ndash10

+10

ndash10

+10

120


μ(Cs) + 10 μ(Cs)


080

040

0000 20 40 60 80 100

Mea

n of

Clndash co

nten

t (

bin

der)

200

160

120

080

040

000



σ(Cs) + 10 σ(Cs)


0 20 40 60 80 100











Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

00

1

2

3

4

5

6

1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10

Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean


0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

+10ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50



Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

mea

n



Equality lin

e

ndash20 ndash line

+20 ndash line +10

ndash10

2020

24

24

28

28

32

32

36

36

40

40

44

44



(a)

Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

st d

ev




Equality lin

e

ndash20 ndash line

ndash10

+10+20 ndash line

20

24

28

32

36

40

44

20 24 28 32 36 40 44



(b)










Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

Equality-line+10

+10

S1DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash10

+20

ndash20ndash10



Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10+20


Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

00

20

20

40

40

60

60

80

80

100

100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10


+20

Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20

ndash10

+10+20


Equality-line

+10 ndash10

+10ndash10

+10ndash10

+10ndash10

+10ndash10





Data Availability




Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

PDF

of re

pair

appl

icat

ion

time

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

004

003

002

001

000

0 20 40 60 80 100 0 20 40 60 80

PDF

of re

pair

appl

icat

ion

time

100





0 20 40 60 80 100 0 20 40 60 80 100




(a)

CDF

of re

pair

appl

icat

ion

time

100

075

050

025

0000 20 40 60 80 100

377

Time (yrs)




0802

0636

049

2nd

3rd

4th

5th

6th7th

8th

0755

0457

0237

192

307

(b)













Chlo

ride c

onte

nt (

bin

der)

12

10

08

06

04

02

000 20 40 60 80 100

Time (yrs)

2000 samples


μ(ClCrit) = 08

S4 S2S3S1

S5 S6

S1DCS2DC35S375DC

S475DC35S575DC50S650DC50





6 Conclusion









Mea

n of

Clndash co

nten

t (

bin

der)

200

160

ndash10

+10

ndash10

+10

120


μ(Cs) + 10 μ(Cs)


080

040

0000 20 40 60 80 100

Mea

n of

Clndash co

nten

t (

bin

der)

200

160

120

080

040

000



σ(Cs) + 10 σ(Cs)


0 20 40 60 80 100











Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

00

1

2

3

4

5

6

1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10

Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean


0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

+10ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50



Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

mea

n



Equality lin

e

ndash20 ndash line

+20 ndash line +10

ndash10

2020

24

24

28

28

32

32

36

36

40

40

44

44



(a)

Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

st d

ev




Equality lin

e

ndash20 ndash line

ndash10

+10+20 ndash line

20

24

28

32

36

40

44

20 24 28 32 36 40 44



(b)










Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

Equality-line+10

+10

S1DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash10

+20

ndash20ndash10



Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10+20


Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

00

20

20

40

40

60

60

80

80

100

100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10


+20

Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20

ndash10

+10+20


Equality-line

+10 ndash10

+10ndash10

+10ndash10

+10ndash10

+10ndash10





Data Availability




Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












Chlo

ride c

onte

nt (

bin

der)

12

10

08

06

04

02

000 20 40 60 80 100

Time (yrs)

2000 samples


μ(ClCrit) = 08

S4 S2S3S1

S5 S6

S1DCS2DC35S375DC

S475DC35S575DC50S650DC50





6 Conclusion









Mea

n of

Clndash co

nten

t (

bin

der)

200

160

ndash10

+10

ndash10

+10

120


μ(Cs) + 10 μ(Cs)


080

040

0000 20 40 60 80 100

Mea

n of

Clndash co

nten

t (

bin

der)

200

160

120

080

040

000



σ(Cs) + 10 σ(Cs)


0 20 40 60 80 100











Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

00

1

2

3

4

5

6

1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10

Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean


0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

+10ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50



Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

mea

n



Equality lin

e

ndash20 ndash line

+20 ndash line +10

ndash10

2020

24

24

28

28

32

32

36

36

40

40

44

44



(a)

Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

st d

ev




Equality lin

e

ndash20 ndash line

ndash10

+10+20 ndash line

20

24

28

32

36

40

44

20 24 28 32 36 40 44



(b)










Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

Equality-line+10

+10

S1DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash10

+20

ndash20ndash10



Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10+20


Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

00

20

20

40

40

60

60

80

80

100

100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10


+20

Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20

ndash10

+10+20


Equality-line

+10 ndash10

+10ndash10

+10ndash10

+10ndash10

+10ndash10





Data Availability




Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




6 Conclusion









Mea

n of

Clndash co

nten

t (

bin

der)

200

160

ndash10

+10

ndash10

+10

120


μ(Cs) + 10 μ(Cs)


080

040

0000 20 40 60 80 100

Mea

n of

Clndash co

nten

t (

bin

der)

200

160

120

080

040

000



σ(Cs) + 10 σ(Cs)


0 20 40 60 80 100











Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

00

1

2

3

4

5

6

1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10

Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean


0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

+10ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50



Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

mea

n



Equality lin

e

ndash20 ndash line

+20 ndash line +10

ndash10

2020

24

24

28

28

32

32

36

36

40

40

44

44



(a)

Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

st d

ev




Equality lin

e

ndash20 ndash line

ndash10

+10+20 ndash line

20

24

28

32

36

40

44

20 24 28 32 36 40 44



(b)










Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

Equality-line+10

+10

S1DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash10

+20

ndash20ndash10



Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10+20


Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

00

20

20

40

40

60

60

80

80

100

100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10


+20

Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20

ndash10

+10+20


Equality-line

+10 ndash10

+10ndash10

+10ndash10

+10ndash10

+10ndash10





Data Availability




Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

00

1

2

3

4

5

6

1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10


Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line

+10+20


ndash20ndash10

Num

ber o

f rep

airs

w

ithou

t dist

urba

nce o

n m

ean


0

1

2

3

4

5

6

0 1 2 3 4 5 6

Equality-line+10


ndash20ndash10

+10ndash10

+10ndash10

+10ndash10

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50



Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

mea

n



Equality lin

e

ndash20 ndash line

+20 ndash line +10

ndash10

2020

24

24

28

28

32

32

36

36

40

40

44

44



(a)

Corr

osio

n in

itiat

ion

time (

yrs)

w

ith d

istur

banc

e on

st d

ev




Equality lin

e

ndash20 ndash line

ndash10

+10+20 ndash line

20

24

28

32

36

40

44

20 24 28 32 36 40 44



(b)










Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

Equality-line+10

+10

S1DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash10

+20

ndash20ndash10



Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10+20


Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

00

20

20

40

40

60

60

80

80

100

100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10


+20

Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20

ndash10

+10+20


Equality-line

+10 ndash10

+10ndash10

+10ndash10

+10ndash10

+10ndash10





Data Availability




Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

Equality-line+10

+10

S1DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash10

+20

ndash20ndash10



Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10+20


Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

00

20

20

40

40

60

60

80

80

100

100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20ndash10

+10


+20

Equality-line

+10 ndash10


Med

ian

of re

pair

time (

yrs)

w

ithou

t dist

urba

nce o

n m

ean

0

20

40

60

80

100

0 20 40 60 80 100

S1 DC

S2DC35 S375DC

S475DC35

S5 75DC50S650DC50

ndash20

ndash10

+10+20


Equality-line

+10 ndash10

+10ndash10

+10ndash10

+10ndash10

+10ndash10





Data Availability




Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Data Availability




Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Probability-Based Sensitivity of Service Life of Chloride...

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Transcript of Probability-Based Sensitivity of Service Life of Chloride...