numericalstudyondiffusionofchlorideandinducedrebar ...xitu ,1,2 jindi,1,2 cunjunpang,1,2...

Research ArticleNumerical Study on Diffusion of Chloride and Induced RebarCorrosion by Two-Dimensional Multiscale Approach

Xi Tu 12 Jin Di12 Cunjun Pang12 and Xiaoqing Xu 12

1Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University) Ministry of EducationChongqing China2College of Civil Engineering Chongqing University Chongqing China

Correspondence should be addressed to Xi Tu tuxicqueducn

Received 15 November 2018 Accepted 12 December 2018 Published 31 December 2018

Guest Editor Qing-feng Liu

Copyright copy 2018 Xi Tu et al -is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Modeling approach for mesoscopic model of concrete depicting mass transportation and physicochemical reaction is importantsince there is growing demand for accuracy and computational efficiency of numerical simulation Mesoscopic numericalsimulation considering binder aggregate and interfacial transition zone (ITZ) generally produces huge number of DOFs which isinapplicable for full structure In this paper a two-dimensional multiscale approach describing three-phase structure of concretewas discussed numerically An effective approach generating random aggregate in polygon based on checking centroid distanceand intersection of line segment was introduced Moreover ITZ elements were built by parallel expanding the edge of aggregateson inner side By combining mesoscopic model including full-graded aggregate and macroscopic model cases related to dif-fusivity and width of ITZ volume fraction and grade of aggregate were studied regarding the consideration of multiscalecompensation Result clearly showed that larger analysis model in multiscale model expanded the diffusion space of chloride ionand decreased chloride content in front of rebar Finally this paper addressed some noteworthy conclusions about the chloridedistribution and rebar corrosion regarding the configuration of rebar diameter concrete cover and exposure period

1 Introduction

Corrosion of rebar induced by chloride ion could signifi-cantly deteriorate the serviceability of concrete structures[1] -e protective film of rebar was depassivated by chlorideion penetrated from surface of concrete and thus corrosionof rebar initiates once the chloride content on surface ofrebar reaches a certain thresholding value defined as criticalchloride content Afterwards corrosion of rebar keepspropagating and induces further cracking and spalling dueto expansion of rust -erefore it is important to accuratelyassess the diffusion process of chloride ion within concretewhich is meaningful for further evaluation of durability ofreinforced concrete structures

In the view of mesoscopic numerical simulation concretewas recognized as the heterogeneous composite of threephases including cement paste aggregate and interfacialtransition zone (ITZ) [2] ITZ was identified as a fine cementpaste zone enclosing aggregate and rebar providing higher

water-to-cement ratio higher porosity and lower cementcontent compared with normal bulk cement paste regions-us ITZ was generally considered as an individual phase[3ndash5] -ough the porosity of ITZ decreases with increase ofdistance from aggregate surface [6] ITZ was simplified as ahomogenous thin layer in most studies Significant influenceon the overall behavior of concrete attributes to ITZ due to itsfraction of the total paste volume such as diffusivity andstrength [4 6ndash8]

In the view of mesoscopic numerical simulation due tolarge amount of nodes and elements an optimized approachwas that three-phase composite of concrete was simplifiedinto two-phase composite including cement paste and ho-mogenized equivalent aggregate [4 7 9ndash13] Diffusivity ofITZ was transferred by means of deriving the analyticalsolution of general effective chloride diffusivity whichmeans modeling of ITZ is unnecessary

Generally modeling and analysis for cement-based ma-terial were categorized in microscopic scale mesoscopic scale

HindawiModelling and Simulation in EngineeringVolume 2018 Article ID 1932813 20 pageshttpsdoiorg10115520181932813

and macroscopic scale [14 15] Recently a number of theoryresearch and modeling efforts have been devoted to studyingmultiscale modeling Multiscale modeling was usually definedas the integrated numerical process of transferring me-chanical and chemical response between lower scale andhigher scale [16 17] A significant advantage of multiscalemodeling is optimizing computing loading and enhancing theprecision According to available literature researchersgenerally focused on the transferring process of materialresponse between scales

As the major purpose of multiscale modeling to reducecalculation loading heterogeneous model was alwaysmodeled for transferring damage and mass transportation ofcritical regions from the macroscale to the mesoscale whichprovided coupling of subdomains [18] Balance of accuracyand efficiency is the major consideration of multiscalemodeling for numerical simulation By means of macro-scopic model substituting for a part of mesoscopic modelmultiscale modeling is able to provide relatively smaller sizeof mesoscopic model and generate the same filling rate ofaggregate and less amount of aggregate which is no doubtbeneficial for raising success rate of meshing [19]

For mesoscopic structure of concrete both of size andshape of aggregates are generated as given design Regardingtwo-dimensional space general process was divided into twosteps including modeling of geometric model and meshingAngular aggregate was generated based on inscribed convexpolygon within elongated ellipse [20]Wang et al proposed aprocedure for generating random aggregate structures forangular aggregates by means of Monte Carlo samplingwhich was compatible for concave polygon [21] An in-evitable algorithm was intersection check of convex poly-gons which was achieved by detecting space independenceof two polygons [22 23] In terms of meshing mortar plussmaller aggregates embedding coarse aggregate was dis-cretized into finite elements by free meshing [20 24] oruniform background grid [25ndash27]

Another major factor for durability of reinforced con-crete structures is corrosion of steel rebar Researchersdevoted efforts on laboratorial research by means of naturalexperiments [28ndash32] and accelerated experiments [33ndash38]about the process of chloride diffusion and corrosion On theother hand some types of simplified approximate law forcorrosion were introduced Biondini introduced a reason-able linear damage model for corrosion of rebar underaggressive agent which evaluates corrosion rate according tothe real-time chloride content surrounding rebar [39ndash42]Despite the complex principle of corrosion based on thenatural damagemode of corrosion this linear damagemodelis able to provide acceptable description of damage process

-is paper discussed two important aspects regardingmultiscale modeling for numerical simulation of chlorideion diffusing within concrete Firstly a comprehensivemodeling approach for concrete considering both multiscalemodeling including interfacial transition layer (ITL) andthree-phase mesoscale structure including ITZ Secondly bymeans of the multiscale numerical simulation tool the in-fluence of ITZ on diffusion of chloride ion within concrete inmesoscale was studied in detail where ITZ was modeled as

an individual phase in FE model for chloride diffusion inconcrete Besides the corrosion of rebar in straight edge ofconcrete induced by diffusion of chloride ion was alsocalculated to study the time evolution of corrosion process

2 Multiscale Modeling and Discussion

21 Multiscale Modeling eory In mesoscopic numericalsimulation for chloride diffusion usually 100sim200mm sizeof specimen in square or rectangle was considered Withinthis typical size of analysis space enough number of ag-gregates with various sizes were included for in-depth studyWithin limited analysis space chloride ion would able topenetrate and saturate the whole space within the assessingperiod indicating the whole space was inadequate for fur-ther simulation However it would be impossible to in-creasing the size of analysis space due to two reasons Firstseveral times of original size of analysis space will generatemuch more nodes and elements especially for three-dimensional problem Second to control computing load-ing changing the grading curve and ignoring fine aggregatewill cause inaccuracy of numerical simulation

In this paper a scheme of multiscale modeling wasintroduced in terms of balancing amount of nodes andelements and calculation accuracy (Figure 1) In the view ofmultiscale modeling based on original mesoscopic modelincluding multiphase components which was defined as corepart a macroscopic compensationmodel which was definedas compensation part was modeled -e aim of introducingcompensation part was creating addition space to absorb thechloride within core part and adjusting the distribution ofchloride content within core part which means re-distribution of chloride in larger space

Due to different definition of nodal chloride content anddiffusion coefficient in mesoscopic model and macroscopicmodel the two types of models cannot be directly combinedand analyzed simultaneously In this paper interfacialtransition layer (ITL) was introduced to connect bothmodels at the interface which consists of a group of nodesand elements shown in Figure 1 ITL was designed as abanded shape transition zone allowing chloride ion diffusingfrom core part into compensation part Within each timestep core part and compensation part were analyzed se-quentially and the chloride content at interface of the twoparts was transferred based on the function of ITL

It is worth noting that the most important preconditionis the mechanism of ITL for transporting the chloride ionwhich generates equivalent diffusion and distribution ofchloride within the model on the same scale ITL could becomposed by a row of common nodes occupied by bothmesoscopic model and macroscopic model as well as anamount of elements with certain thickness stuck by bothmodels

-e process of transferring chloride ion within ITL inone-dimension was illustrated in Figure 2 For initial stateanalysis space of three phases including core part com-pensation part and ITL was modeled respectivelyBoundary condition was set at surface of concrete whichwas the top of core part shown in Figure 2

2 Modelling and Simulation in Engineering

-is mixed model behaved in sequential multiscaleprocess For themixed case that core part is inmesoscale andcompensation part in macroscale equivalent chloridecontent in ITL will be calculated and transferred Definitionsof chloride content in both parts were different Chloridecontent in macroscopic model was measured in concreteand the value in mesoscopic model was measured in cement-erefore a necessary procedure was included that the valueof chloride content in ITL should be calculated for eachstage Simulation of chloride diffusion within mixed modelwas divided into two stages of diffusion and two steps ofconversion

(1) -e first stage of diffusion core part and ITL wereconnected as common interface while ITL andcompensation part were disconnected With onetime step chloride ion penetrated into core part fromboundary condition During current stage diffusionof chloride ion restrained within core part and ITL-e chloride content of core part and ITL rose upfrom previous content while compensation part keptunchanged

Find out all of the elements with the centroid locatedwithin the elements from compensation model

Calculate the weighted mean content of all these ele-ments in core model -is content is the represented contentfor the element in compensation model

(2) Conversion from mesoscale to macroscale withinITL the simulated result in region in core partcovered by ITL was converted from mesoscale tomacroscale within this step For the instance ofcenter bottom of concrete boundary compensationpart was modeled as simply one-dimensional modelWithin core part elements with their centroid in-cluded in interfacial transfer layer were identified(the region enclosed by red dashed line in Figure 3)Weighted mean value of chloride content of theseinvolved elements was calculated for the nodal valueof ITL in macroscale

(3) -e second stage of diffusion a new barrier wasinserted at common border of core part and ITLwhich was equal to cut down the connection of theseparts -e existing barrier at common border ofcompensation part and ITL was removed Duringthis stage chloride redistributes within the regionincluding ITL and compensation part

(4) Conversion from macroscale to mesoscale withinITL as the inverse process of the 2nd step the nodalcontent of mesoscopic core part was interpolatedfrom macroscopic compensation part in the form ofregular rectangle element As was illustrated inFigure 4 the outer rectangle represents the uniformquadrilateral model in compensation part and thetarget node denotes the node included within corepart Four nodes of the quadrilateral were numberedin counterclockwise

22 Analytical Study for Finite Space with Exposed and Time-Dependent Boundary In following section this paper dis-cussed about the feasibility of multiscale model in analyticalapproach Due to the sectional design of rebar in concretemember some research studies on chloride diffusion weretransformed within two-dimensional space equivalently Forthe case on center of bottom of concrete section concreteand outer atmosphere were divided into two infinite half-space into which the boundary plane divides the three-dimensional space Regarding numerical simulation forthe same configuration of boundary condition and diffu-sivity of concrete all points in concrete at the same depthfrom the boundary behave in the same characteristics ofdiffusion In simplification the chloride diffusion in three-dimensional and two-dimensional space was equivalent toone-dimensional one -erefore the problem was simplifiedto one-dimensional macroscopic model and the analyticalsolution for finite space with both exposed and sealingboundary was discussed Usually diffusion of chloride withinsolution was expressed by linear Fickrsquos second law

zC

zt D middot nabla2C (1)

where D is the diffusion coefficient of concrete C denotesthe chloride content Considering the boundary condition ofC(0 t) Cs and C(infin t) C0 As was widely knownaccording to Laplace transform the analytical solution ofabove partially derivative equation was

Core part

Compensationpart

Clndash ne 0

Clndash ne 0

Clndash = 0

ti + Δt

ti

Barrier

Core part

Compensationpart

Cndash ne 0

Clndash ne 0

Clndash ne 0

ti + Δt

ti + Δt

Barrier

Figure 2 -e two stages of chloride diffusion at the interfacialtransition layer connectingmacroscopic andmesoscopic model (a)First stage (b) Second stage

Compensation part

Core part

Interfacial transition layer

Boundary Clndash

Figure 1 Two-dimensional multiscale model with core part andcompensation part for simulating chloride diffusion within concrete

Modelling and Simulation in Engineering 3

C(x t) C0 + Cs minusC0( 1113857 1minus erfx

2Dt

radic1113888 11138891113890 1113891 (2)

where erf is Gauss error function -e limitation of theabove solution is the premise of infinite space for boundarycondition which is suitable for concrete members with largethickness compared with thickness of concrete cover butinaccurate for typical beams and slabs For finite spacethree-dimensional analytical solution by means of separa-tion of variables was discussed and deduced by Li et al [43]For one-dimensional space assuming the total length ofdiffusion space is l x axis is the longitudinal direction of theone-dimensional model Initial condition for diffusionspace C(x 0) C0 and boundary condition exposedboundary C(Γ1 t) Cs and sealing boundary zCzx|Γ2 0were all considered -e schematic illustration is shown inFigure 4

-e simplified function of chloride content including thevariables of time and depth in one-dimensional spaceaccording to Lirsquos solution was expressed as follows

C Cs + C0 minusCs( 1113857 1113944

infin

n1

4(2nminus 1)π

sin2nminus 12l

πx1113874 1113875eminusD(((2nminus1)2l)π)2t

(3)

If zero chloride content for initial condition C0 0 wasconsidered equation (3) was simplified as given below

C Cs 1minus 1113944infin

n1

4(2nminus 1)π

sin2nminus 12l

πx1113874 1113875eminusD(((2nminus1)2l)π)2t⎡⎣ ⎤⎦

(4)

-e aim of following section was to deduce the ex-pression of analytical solution of chloride content with bothexposed boundary and time-dependent boundary accordingto Lirsquos deduction process and prove that the development incore model with predefined time-dependent boundarycondition is same as the part in full model For the con-sideration of compensation for chloride diffusion a part ofthe full model was extracted and called as Core Model -eschematic illustration of core model was shown in Figure 5-e length of core model was l1 while assuming the length offull model was l2(l2 gt l1)

Being different with the precondition of Lirsquos solution[43] the boundary condition Γ2 of core model was modifiedinto the function of time-dependent boundary Γ2prime strictlydefined by equation (4) set at l1 expressed in equation (5)-e other parameters and definition were the same as beforeFor simplification zero chloride content for initial condi-tion C0 0 was considered

C(t)|Γ2

Cs 1minus 1113944infin

n1

4(2nminus 1)π

sin2nminus 12l2

πl11113888 1113889eminusD (2nminus1)2l2π( )

2t⎡⎣ ⎤⎦

(5)

Considering a temporary variable V

V CminusCs (6)

Apart from initial condition and boundary conditionthe time-dependent boundary Γ2prime was expressed as

V|xl1 minusCs 1113944

infin

n1

4(2nminus 1)π

sin2nminus 12l2


2t

(7)

By means of separation of variables V was expressed as

V(x t) X(x) middot T(t) (8)

By introducing boundary condition of exposed surfaceΓ1 the general solution of X was simplified as

X(x) B sin(αx) (9)

For time-dependent boundary Γ2prime by combining equa-tions (7) and (9) we obtained the expression of α

αn 2nminus 12l2

π (n 1 2 ) (10)

-us particular solution of X was

Xn(x) kn sin2nminus 12l2

πx1113888 1113889 (11)

-e particular solution of T was solved as

Tn minusdneminusDα2nt

(12)

Interfacial transfer

layer

Impermeable aggregate

Centroid of sectional element

Figure 3 First step of conversion calculation of nodal chloridecontent of compensation part from involved elements in core part(red dashed coverage of nodes in compensation part blue in-volved elements in core part yellow uninvolved elements)

Γ1 Γ2

l

xO

C (Γ1 t) = Cs(Cx) Γ2 = 0

C (x t) = C0

Figure 4 Analysis model for analytical deduction


-us general solution of V was

Vn en sin2nminus 12l2

πx1113888 1113889eminusDα2nt

(13)

where en was the nth order of unknown expression anden kn middot dn Considering initial condition (t 0) we ob-tained the following from equation (13)

1113944

infin

n1en sin

2nminus 12l2

πx1113888 1113889 minusCs (14)

Due to orthogonality of the following function series

1113946l

0sin αmx( 1113857 sin αnx( 1113857dx

0 mne n

l2 m n1113896 (15)

Combining equations (14) and (15) we obtained

en minus4Cs

(2nminus 1)π (16)

By combining equations (6) (13) and (16) finally weobtained


n1

4(2nminus 1)π

sin2nminus 12l2

πx1113888 1113889eminusD (2nminus1)2l2π( )( )

2t⎡⎣ ⎤⎦

x isin 0 l11113858 1113859( 1113857

(17)

-erefore even considering the time-dependent bound-ary the development of diffusion within core model wasexactly the same as the original model which proved thefeasibility of compensation for chloride diffusion

3 Mesoscopic Modeling Approach

31 Generation of Two-Dimensional Random AggregateIn two-dimensional space the major consideration of gen-erating mesoscopic model is requirement of both grading ofaggregates and its volume fraction in concrete Generally themesoscopic structure of aggregate is randomly generated bydispersing particles in given shape and size in a limited squareor rectangle space -is process was fulfilled by two essentialsteps including constructing qualified aggregate and dis-persing the aggregate An applicable approach introduced inthis paper was depicted as follows

(1) Construction of aggregate in given shape and sizeregarding grading of concrete the convex polygonof an applicable aggregate is connected along thepoints on the curve of a randomly generated el-lipse the area of which meets the requirement of

design particle size -en the preliminary inscri-bed polygon is enlarged to match the same area ofdesigned ellipse

Two additional points to guarantee reasonable shape ofaggregate should be noted In practical concrete engineeringelongated aggregate (with dimension ratio over 2 1) shouldbe avoided considering its poor structural performance-usin aggregate generation program all vertices of polygon arewell distributed on ellipse in terms of the included angledefined by the connecting line of vertices of polygon and itscentroid (Figures 6(a) and 6(b)) Another measurement iscontrolling the area occupancy of polygon within the designellipse (Figures 6(c) and 6(d)) Detailed values for minimumincluded angle andminimum area occupancy are designed bydomestic specification for aggregates

(2) Dispersing aggregate by judgement of overlapping ofaggregates within two-dimensional space for onenewly dispersed aggregate checking its involvementwithin given rectangle analysis region and over-lapping with all existing aggregates are required -efirst condition can be met by checking whether themaximum and minimum coordinates of polygon arecovered by the rectangle -e detailed judgement foroverlapping of convex polygon was described asfollows Terms quoted are shown in Figure 7

(i) For each pair of aggregates judge whether sumof outer radius (R0 + R0prime) is larger than distanceof centroids (dagg) Here outer radius is definedas the maximum radical distance from anyvertex to centroid If no ((R0 + R0prime)ledagg) thereis no overlapping of aggregate and the newlydispersed aggregate is accepted If yes ((R0+

R0prime)ge dagg) possible overlapping cannot be avoi-ded and continue to next step for further check

(ii) Judge whether sum of inner radius (Ri + Riprime) issmaller than distance of centroids (dagg) Hereinner radius is defined as the minimum radicaldistance from any side to centroid If no((Ri + Riprime)gtdagg) solid overlapping appears anda redispersion of new aggregate is required Ifequal ((Ri + Riprime) dagg) a rare case representingparallel sides of aggregates is inappropriatewhich is also unaccepted If yes ((Ri + Riprime)ltdagg) intersected sides cannot be avoided con-tinue to next step for further check

(iii) Judge whether the vertices of polygon repre-senting aggregate are inclusion of the existingaggregate (Figure 8) If yes overlapping isproved and a redispersion of new aggregate isrequired If no a complicated case of over-lapping that intersection polygons without anyvertex located within each polygon still cannotbe assured and continue to next step

(iv) -e last step is judging whether there are anyshared nodes of background meshing grid forboth polygons (Figure 9) If yes overlapping isproved and a redispersion of new aggregate is

C (Γ1 t) = Cs

C (x t) = C0Γ1 Γ2

xOl1

C(t) Γ2

Figure 5 Illustration of core model for diffusion withcompensation


required If no the newly dispersed aggregate isaccepted

-e above process was illustrated in Figure 10Two typical models with elongated aggregate are shown inFigure 11

Ro

Ri

Riprime

Roprime

Agg1

Agg2

dagg

Figure 7 Inner radius outer radius and distance of centroids oftwo intersected aggregates

Figure 8 Inclusion of vertices owned by dispersed aggregate inexisting aggregate

Figure 9 Shared nodes of background meshing grid for bothpolygons

(c) (d)

(a) (b)

Figure 6 Generating polygon of aggregate based on ellipse (a)Acceptable aggregate (b) Elongated aggregate (c) Low area pro-portion (d) Fair area proportion

Start

Calculate total amount and partical size of aggregatescreate background meshing grid

Sum of outer radius is larger than distance of centroids

Ro + Roprime gt dagg

Sum of inner radius is smaller than distance of centroids

Ri + Riprime lt dagg

Inclusion of vertices in existing aggregate

Any shared nodes of background meshing grid

Dispersion succeeds

Yes

Yes

No

No

Disperse next aggregate until end of dispersion

End

No

Yes

No

Yes

Dispersing a new aggregate

Figure 10 Process of generating random polygonal aggregates


Additional process for modeling is meshing the geom-etry space including significantly irregular distribution ofaggregate Conventional commercial software was adoptedfor meshing process However low success rate of meshingin refined quadrilateral element cannot be avoided for mostcommercial software due to the complex model -us anoptimized way adopted in this paper was meshing the spacein triangle element and subdividing one triangle into foursmall quadrilaterals which was proved as high meshingsuccess rate and high efficiency

32 Modeling of ITZ Based on Meshed Space Modelingapproach for ITZ was determined by the mechanism ofsimulating chloride diffusion within ITZ ITZ was recog-nized as an indeterminate zone around aggregates and bulkin linearly decreasing porosity with increase of distance fromaggregate surface Existing approaches describe ITZ as anindividual layer or compensation on equivalent diffusivity ofaggregate [44ndash46] In terms of aggregates in randompolygon the way of building actual elements of ITZ wasadopted in this paper -us more DOFs were introducedwhich significantly increased time consumption of assem-bling global diffusion matrix and solving it

Since ITZ was identified as the individual phase sur-round aggregate additional uniform width of elementsadhering on the edge of aggregates might induce un-necessary overlapping of ITZ elements in some cases that thepair of aggregate was too close to each other In order toavoid the above circumstance ITZ elements were assignedon the inner side of edge of aggregate instead of outer sideAccording to minor area proportion of ITZ it was ac-ceptable slightly decreasing the size of aggregate -ere aretotally three steps for this process

(i) For the first step for any aggregate the lines on itsedge were parallel offset inside by the designedwidth h shown as the dashed line in Figure 12(a)

(ii) For the second step all intersection of the offsetlines were found the total number of which were

equal to vertices of aggregate shown as the blackpoint in Figure 12(b) Additionally a special sub-routine called ldquofunc_L2Lrdquo was developed to identifythe relationship of a pair of line segments Its outputresult provided whether the two line segments in-tersect and the coordinate of their intersection

(iii) For the third step combining the previous availablenodes of aggregate and newly generated nodes(intersection) a group of quadrilateral elements wasbuilt in counterclockwise order which representedITZ -eir physical properties were set individuallybeing different from existing cement paste

-e above entire process of modeling FE model ofconcrete involving ITZ is shown in Figure 13

4 Basis of Assessing Approach

41 Diffusion Model of Chloride Transportation of chlorideion in porous medium such as cementitious materials ismainly a diffusive phenomenon due to concentration gra-dients [47] -e diffusion of chloride ion within concretecomponents was admitted as a complex process which wasinfluenced by many factors including watercement ratioporosity of cement additive aggregate temperature hu-midity environmental chloride content binding effect ofbinder and hydration of cement-e above process could besimulated by numerical approach based on available envi-ronmental attacking condition and material propertiesFickrsquos second law was widely adopted as the expression ofprinciple differential equation [48]

ωezCf

zt

z

zxDeωe

zCf

zxminus

zCb

zt

Ct Cb + Cf middot ωe

(18)

where Cf is the free chloride content (in kgm3 of solution)Cb is the bound chloride content (in kgm

3 of concrete) Ct isthe total chloride content (in kgm3 of concrete) De is the

(a) (b)

Figure 11 Generated aggregates with limitation on dimension ratio (a) Allowable dimension ratio up to 2 1 (b) Allowable dimension ratioup to 5 1


effective diffusivity and ωe is the evaporable water content(in volume percentage of concrete) Considering complexityof cross sections of bridge pier appropriate preliminarydivision and meshing grid are processed by means of somemeshing tools or commercial FE software Experimentaldata indicated that due to cement hydration and chloridecontent the chloride diffusion coefficient is strongly de-pendent on the exposure period of concrete [49]

42 Corrosion Model of Rebar Corrosion of rebar initiates inthe form of galvanic reaction between ferrous and oxygenaccelerated by the presence of active free chloride ion once theprotection of high pH (gt125) hydration products wasdepassivated Corrosion continues with the cycle of electriccurrent between cathode and anode which was influenced byhigh chloride concentration at the level of the rebar envi-ronmental temperature electrical resistivity of concrete andhydration of cement-e corrosionmodel regressed by Liu andWeyers [34] based on experimental data included the influenceof chloride content temperature concrete cover resistance andtime of cement hydration which was expressed as

ln 108icorr( 1113857 837 + 0618 middot ln(169Cl)minus3034

T

minus 0000105Rc + 232tminus0215

(19)

where icorr is corrosion current intensity (μAcm2) Cl ischloride content (kgm3) which was obtained from nu-merical simulation result of chloride diffusion T is tem-perature at the depth of steel surface (in degree Kelvin) Rc isthe resistance of the cover concrete (ohms) and t is cor-rosion time duration (years) With the data chloride contentobtained by numerical simulation and the other parametersassumed previously the real-time corrosion current rate ateach time step of numerical simulation was calculated byequation (19) -us the corrosion depth on surface of rebarwas calculated as [50]

Dt+Δt Dt minus 0023 middot icorrΔt (20)

where Dt is remaining rebar diameter (mm) at t yearshere 20mm adopted Dt+Δt is reduced rebar diameter (mm)at t + Δt years and ΔD|Δt is reduction of rebar diameter(mm) for the period of propagation for the duration time ofΔt years

5 Numerical Simulation for Diffusion ofChloride Including Compensation

51 Influence of ITZ Properties regarding CompensationConsidering that characteristics of ITZ significantly influ-ence diffusion chloride within concrete critical properties of

h

(a) (b) (c)

Figure 12 Process of generating new elements and nodes for ITZ (a) Step 1 offset outline with ITZ width h (b) Step 2 find intersection(nodes) of outline (c) Step 3 form elements of ITZ

Random aggregate model

Meshed FEM model

Creates inner parallel offset line-segment

Find intersection of line-segment pair

Form ITZ quadrilateral element in counterclockwise ordering

Adjust and merge nodes and elements

Find all nodes on boundary and organize in group

ITZ widthOrganize nodes in group

and counterclockwise

Obtain outline nodegroups for aggregates

Geometric properties of linesegment

Subroutine ldquofunc_L2Lrdquo

Figure 13 Flow chart for modeling of ITZ based on meshed FEM model


ITZ were detailed studied in this section including diffu-sivity and width of ITZ aggregate volume fraction andgrade of aggregate Furthermore chloride content on surfaceof rebar was also researched regarding presence of ITZ

Another major consideration of this paper was the effectof compensation in multiscale modeling A 100times100mmtwo-dimensional square space was modeled for mesoscopiccore part and another 100times 200mm rectangle space wasmodeled for macroscopic compensation part (Figure 14)Width of ITL was set at 10mm whichmeans 10 area of corepart and 5 area of compensation part were overlapped Onthe other hand for the case without compensation macro-scopic compensation part was deleted and chloride ion canonly diffuse within smaller mesoscopic core part

For the other parameters transportation mechanism ofchloride ion between both parts was described in previoussection of this paper For all simplified cases studied in thissection the analytical apparent surface chloride content of071 (wc) and apparent concrete diffusivity of 184 times

10minus12m2s were adopted for macroscopic model which wereregressed based on Zhaorsquos data [51] Meanwhile the ag-gregate was considered as impermeable and correspondingmodeling of FEM was ignored Boundary condition anddiffusivity of cement paste were calculated by these resultsRegarding generating random aggregate of mesoscopicmodel Fullerrsquos curve was adopted as the grading of ag-gregate Both types of cases with compensation and withoutcompensation were studied

Significant random distribution of aggregate was themajor factor for uncertainty of chloride diffusion -ustotally 100 specimens of aggregate model for each case weregenerated and analyzed considering reasonable accurate andacceptable time consumption After all specimens wereanalyzed mean results of these cases were calculated forfurther comparison

511 Diffusivity of ITZ Firstly diffusivity of ITZ wasstudied which was represented by the ratio of DITZDCPHereDITZ andDCP denoted the diffusivity in ITZ and cementpaste respectively As was discussed by Zheng et al [4] DITZDCP would vary within 1sim5 considering different configu-ration of wc aggregate size hydration time and aggregatefraction theoretically which were discussed by means of theapproach introduced in this paper 50 μm of ITZ width wasmodeled by expanding the edge of aggregate and rebarMaximum aggregate size in 20mm was considered

Figure 15 showed typical distribution of chloride contentregarding different diffusivity in ITZ-emajor difference ofcontour line observed was the slightly higher chloridecontent due to the presence of ITZ in width of the mi-crometer scale It means higher diffusivity in ITZ comparedwith cement paste accelerated the diffusion of chloridewithin concrete

For mesoscopic numerical simulation distribution ofaggregate was recognized as the major influence factorfor development of chloride [52] Chloride content onsurface of rebar significantly varied with different ar-rangement and grading of aggregate -us both mean and

maximum distribution of chloride ion in terms of randomaggregate models became the major consideration Fig-ures 16 and 17 summarized average content and maximumversus depth regarding diffusivity of ITZ at 50 years and 100years respectively It was clearly noted that chloride contentincreased as the diffusivity of ITZ increased An interestingphenomenon observed was that the influence of compen-sation was larger in higher chloride content It attributed to alarger diffusion space released in mixed model includingcompensation part From the result of numerical simulationanother point should be noted that within the boundarylayer in width of 10mm from surface of concrete both meanand maximum chloride content were closed to boundarycondition which was recognized as the lower aggregatevolume fraction and smaller particle size in this region

512 ITZ Width -e second major factor for chloride dif-fusion is ITZ width A thin layer composed of quadrilateralelements in the width of 5μm 10μm 20μm 35μm and 50μmadhering to the edge of aggregates was modeled (Figure 18)For the other parameters diffusivity of ITZ in DITZDCP 5was adopted Maximum particle size of coarse aggregate waslimited within Dmax 20mm Figure 18 showed ITZ elementsin orange color of FE model in different width of ITZ

Figures 19 and 20 showed average content and maxi-mum versus depth regarding width of ITZ at 50 years and100 years respectively A clear conclusion was drawn thatthicker ITZ width induced higher volume fraction of ITZand enhanced diffusion of chloride ion

513 Aggregate Volume Fraction Aggregate volume frac-tion determined total amount of aggregates within givenspace and accordingly total length of perimeter was alsodetermined which was the key factor for proportion of ITZ

20

18

16

14

12

10

8

6

4

2

0

(kgm3)

Figure 14 Contour of chloride content of multiscale model


in concrete In this section the cases of aggregate volumefraction in 20 30 40 50 60 and 70 were dis-cussed by means of the approach introduced in this paperDiffusivity of ITZ in DITZDCP 5 and 50 μm of ITZ widthwere adopted Maximum aggregate size in 20mm and Fullergrading was adopted Both types of cases with compensationand without compensation were studied Figure 21 showedwith aggregate volume fraction from 20 to 70 the typicaldistribution of chloride content and aggregate with givenanalysis square space

Figure 22 described mean content and maximum versusdepth regarding aggregate volume fraction at 100 years

According to the result presence of ITZ provided greatereffect on higher aggregate volume fraction and thus reducedthe difference of chloride content profile in cases withdifferent aggregate volume fraction

514 Grade of Aggregate -e cases for grade of aggregatewith maximum aggregate size Dmax 5mm 10mm 15mm20mm 25mm and 30mm were discussed Both cases withor without ITZ were included Fuller grading was adoptedFor the case with ITZ diffusivity of ITZ in DITZDCP 5 wasadopted 50 μm of ITZ width was modeled by expanding the

16 164 168 172 176 18 184

(a)

16 164 168 172 176 18 184

(b)

Figure 15 Typical distribution of chloride content regarding diffusivity in ITZ (solid line denotes isoline of chloride content) (a) DITZDCP 1 (b) DITZDCP 5

0 20 40 60 808

10

12

14

16

18

20

Chlo

ride c

onte

nt (k

gm

3 )

Depth (mm)

DITZDCP = 1DITZDCP = 2

DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)

Figure 16 Average content and maximum vs depth regarding compensation and ITZ DITZDCP at 50 y of exposure (dashed wocompensation solid with compensation) (a) Mean chloride content (b) Maximum chloride content


edge of aggregate and rebar Both types of cases withcompensation and without compensation were studiedFigure 23 showed with maximum aggregate size from 5mmto 30mm the typical distribution of chloride content andaggregate with given analysis square space Figure 24 showedmean content and maximum versus depth regarding gradeof aggregate at 100 years

Figure 24 summarized mean and maximum chloridecontent vs depth from surface of concrete An interestingpoint should be noted that the lower aggregate volumefraction and smaller particle size in the region closed toboundary was not significant in the case with smallermaximum particle size Moreover presence of ITZ indeedenhanced diffusion of chloride ion especially in cases withsmaller maximum particle size

52 Chloride Content and Corrosion of Steel Rebar In thissection chloride content on the front of rebar in terms ofthe configuration was studied by the multiscale numericalsimulation introduced previously According to general

engineering design a group of concrete cover thickness andrebar diameter was devised for detailed comparison ofchloride diffusion and rebar corrosion shown in Table 1 Forthe purpose of comparison rebar in diameter of 16mm wasselected for the cases in different cover thickness and 50mmcover thickness for the comparison of rebar diameters Bymeans of the random aggregate generation approach andconsidering reasonable computing loading 100 two-dimensional samples for each combination of concretecover thickness and rebar diameter was modeled consid-ering random distribution of aggregate

Considering three-phase composite of concrete nodesand elements of ITZ were modeled not only surroundingaggregate but also on the surface of steel rebar It alsojustified to a certain extent that the formation of ITZ onsurface of steel rebar in the light of the same mechanism ofaggregate -erefore the same width and diffusivity ofITZ on surface of steel were adopted Chloride content onfront of rebar was extracted from the newly created nodes onthe edge of ITZ elements in terms of the neat surface of steelrebar

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)Ch

lorid

e con

tent

(kg

m3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)


(a) (b) (c) (d) (e)

Figure 18 FE model for cement paste and ITZ regarding ITZ width h (blue cement paste orange ITZ) (a) h 5 μm (b) h 10 μm(c) h 20 μm (d) h 35 μm (e) h 50 μm


-e placement of steel rebar on the center of straightedge was considered Rebar placed in the center of bottomside of concrete section (Figure 25(a) listed in Table 1was tested Term d denotes the cover thickness and thediameter D of circle refers to diameter of rebar A two-dimensional mesoscopic core model in the size of100times100mmwas created In order to guarantee the effect ofcompensation 100times 200mm total size of compensation

model was designed as two times of core model 10mmthickness of ITL was considered for compensation processApart from ITZ elements surrounding aggregates newelements adjacent to steel rebar were also modeled byexpanding outline -erefore chloride content on surfaceof rebar was extracted from the newly built nodes of ITZBoth types of cases with compensation and withoutcompensation were studied Diffusivity of ITZ in DITZ

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)

Figure 20 Average content and maximum vs depth regarding compensation and ITZ width at 100 y of exposure (dashed wo com-pensation solid with compensation) (a) Mean chloride content (b) Maximum chloride content

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



(a) (b) (c)

(d) (e) (f )

Figure 21 FE model and typical distribution of chloride content for different aggregate volume fraction fa (a) fa 20 (b) fa 30 (c)fa 40 (d) fa 50 (e) fa 60 (f ) fa 70

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)

Figure 22 Continued


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)

Figure 22 Average content and maximum vs depth regarding aggregate volume fraction (fa) and presence of ITZ at 100 y of exposure(dashed wo compensation solid with compensation) (a) Mean chloride content with ITZ (b) Mean chloride content wo ITZ (c) Maxchloride content with ITZ (d) Max chloride content wo ITZ

(a) (b) (c)

(d) (e) (f )

Figure 23 FE model and typical distribution of chloride content for different aggregate and gradation (a) Dmax 5mm (b) Dmax 10mm(c) Dmax 15mm (d) Dmax 20mm (e) Dmax 25mm (f) Dmax 30mm


DCP 5 was adopted 50 μm of ITZ width was modeled byexpanding the edge of aggregate and rebar Maximumaggregate size in 20mm was considered and Fuller gradingwas adopted

Figure 25(b) showed typical distribution of chloridecontent within core mesoscopic model and compensatedmacroscopic model at 100 years of exposure period for thecases of rebar placed in center of bottom -e contourclearly described sound transition of chloride content nearITL on both cases and proved the effect of compensation aswell

Dmax = 5 mmDmax = 10 mmDmax = 15 mm


Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)

Figure 24 Average content and maximum vs depth regarding grade of aggregate and presence of ITZ (dashed wo compensation solidwith compensation) (a) Mean with ITZ (b) Mean wo ITZ (c) Max with ITZ (d) Max wo ITZ

Table 1 Details of model comparison for concrete cover thicknessand rebar diameter regarding chloride diffusion and rebarcorrosion

Cover thickness C (mm)Rebar diameter D (mm)

12 16 20 25 2820 times

30 times

40 times

50 times times times times times

60 times


-e circle curve of rebar was meshed into a series ofnode and nodal chloride content was obtained from resultof FE analysis For all 100 samples of each research casemean value of chloride content on each node around rebarwas calculated and plotted in polar coordinate Figure 26showed the polar distribution of mean chloride content oncross section of rebar at 20 years (solid) and 100 years(dashed) of exposure period Depending on whethercompensation model or ITZ was considered chloridecontent was plotted in different colors shown in legend onthe bottom Distribution of chloride content developedtowards lower-middle which matched the configurationof boundary condition Result indicated higher chloridecontent was obtained for longer period of exposureMoreover lower value was observed in the cases withcompensation

Mean chloride content vs cover thickness for 16mmrebar and mean chloride content vs diameter for 50mmcover are summarized in Figure 27 An obvious resultshowed lower chloride content in compensation case sincesolid lines were all under corresponding dashed lines in thefigures which attributed the larger diffusion space incompensation cases

Another observation was the insignificant differencebetween the solid line of ldquoITZrdquo and ldquoITZ+Compensationrdquo(20 years) Since diffusion of chloride did not exceed theborder of core part and compensation part there was noclear difference for both diffusion spaces of ldquoITZrdquo andldquoITZ+Compensationrdquo which is the major reason

-e corrosion model regressed by Liu and Weyers [34]based on experimental data included the influence of

chloride content temperature concrete cover resistanceand time of cement hydration which was expressed as


T


(21)

where icorr is corrosion current intensity (μAcm2) Cl ischloride content (kgm3) which was obtained from nu-merical simulation result of chloride diffusion T istemperature at the depth of steel surface (in degreeKelvin) Rc is the resistance of the cover concrete (ohms)and t is corrosion time duration (years) For corrosioncalculation in the following discussion environmentaltemperature 293 K was adopted A generally adoptedvalue of concrete resistance 1500Ω was adopted Besidespitting of rebar was neglected With the data chloridecontent obtained by numerical simulation the real-timecorrosion current rate at each time step of numericalsimulation was calculated -e corrosion depth on surfaceof rebar was calculated as [50]


where Dt is remaining rebar diameter (mm) at t years here20mm adopted and Dt+Δt is reduced rebar diameter (mm) att + Δt years

A single mean chloride content for each time stepwas calculated as the attacking chloride content for rebar andmean corrosion depth of rebar was calculated basedon equation (19) Figure 28(a) (cover thickness) andFigure 28(b) (rebar diameter) showed corrosion process and

(kgm3)

Contour20

18

16

14

12

10

8

6

4

2

0

D

Boundary

(b)(a)

Core model

Compensation model

ITL

d

Rebar

Figure 25 Geometrical configuration and chloride content distribution of compensation case (a) Geometrical configuration of concreteanalysis space and rebar (b) Typical distribution of aggregate and chloride content in concrete 100 y


characteristics of rebar based on obtained distribution ofchloride content around rebar Ordinate in these figures in-dicated the ratio of diameter of corroded rebar to initial value

Obtained diagrams showed less corrosion of steel rebarin the cases with compensation due to larger space forchloride diffusion and lower distributed chloride contentMore obvious difference comparing between the result fromthe compensation model (solid) and the case withoutcompensation (dashed) due to a longer exposure period wasobserved

Moreover it should be noted that increasing concretecover provided slight effect on protecting steel rebar fromcorrosion -e higher diffusivity in ITZ adhering on steelrebar provided an equivalent express channel for diffusion ofchloride ion around steel rebar -us ITZ actually balancedthe difference of depth from surface of concrete for thesecases and insignificant difference was observed for cases indifferent covers Similar phenomenon was noticed thatcompensation decreased chloride content on surface ofrebar as well as its corrosion degree

05101520

OriginalCompensationITZITZ + compensation

(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)

Figure 26 Polar distribution of chloride content on cross section of rebar on center of bottom side (solid 20 y dashed 100 y) (a)R 16mm C 20mm (b) R 16mm C 30mm (c) R 16mm C 40mm (d) R 16mm C 50mm (e) R 16mm C 60mm (f)R 12mm C 50mm (g) R 20mm C 50mm (h) R 25mm C 50mm (i) R 28mm C 50mm


6 Conclusion

-is paper presented a study on the approach of multiscalemodeling for diffusion of chloride ion within concrete in-cluding ITZ A two-phase integrated model including corepart and compensation part was introduced where bothphases were connected by an overlapped zone called in-terfacial transition layer Nodes and elements of ITZ in FEmodel were built by expanding outline of aggregates whichwere randomly generated Cases considering multiscale andITZ were studied for obtaining chloride content profileMoreover corrosion of rebar on straight edge was discussed

by means of the multiscale approach-e conclusions of thisstudy are summarized as follows

(1) -e multiscale approach based on the theory ofcompensation for mesoscopic numerical simulationof chloride diffusion within concrete introduced inthis paper was applied by means of numericalsimulation -e presented work showed the influ-ence of compensated model on distribution ofchloride content which provided the basis for futurelarge-scale structural durability analysis in optimizedsize number of DOFs and time consumption

0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)

OriginalCompensation

ITZITZ + compensation

(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)

Figure 27 Mean chloride content of rebar on center of bottom side (solid 20 y dashed 100 y) (a) Mean chloride content vs coverthickness 16mm rebar (b) Mean chloride content vs diameter 50mm cover

20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)

Figure 28 Mean chloride content of rebar on center of bottom side (solid 20 y dashed 100 y) (a) Mean remaining diameter vs coverthickness 16mm rebar (b) Mean remaining diameter vs diameter 50mm cover


(2) Regarding diffusivity and width of ITZ volumefraction and grade of aggregate effects of ITZ ondistribution of chloride were compared in the pre-sented work-e result showed significant differenceon distribution of chloride content between differentconfiguration of ITZ and compensation

(3) In the light of corrosion model of steel rebar interms of surrounding chloride content presence ofITZ and multiscale compensation was discussed bynumerical simulation -e result obtained is relatedto the configuration of rebar diameter concretecover and exposure period It was clearly concludedthat consideration of both ITZ and compensationchanged significantly the distribution of chloridecontent as well as corrosion process of steel rebar

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is study was sponsored by the National Key Research andDevelopment Program of China (2016YFC0701202) -isstudy was also supported by the National Natural ScienceFoundation of China (51508053) the National NaturalScience Foundation of China (51808069) and the Fun-damental Research Funds for the Central Universities(106112014CDJZR200016) which were greatly appreciatedby the authors

References

[1] W Zhu R Franccedilois Q Fang and D Zhang ldquoInfluence oflong-term chloride diffusion in concrete and the resultingcorrosion of reinforcement on the serviceability of RC beamsrdquoCement and Concrete Composites vol 71 pp 144ndash152 2016

[2] Q-F Liu G-L Feng J Xia J Yang and L-Y Li ldquoIonictransport features in concrete composites containing variousshaped aggregates a numerical studyrdquo Composite Structuresvol 183 pp 371ndash380 2018

[3] U Angst B Elsener C K Larsen and Oslash VenneslandldquoCritical chloride content in reinforced concretendasha reviewrdquoCement and Concrete Research vol 39 no 12 pp 1122ndash11382009

[4] J-J Zheng H S Wong and N R Buenfeld ldquoAssessing theinfluence of ITZ on the steady-state chloride diffusivity ofconcrete using a numerical modelrdquo Cement and ConcreteResearch vol 39 no 9 pp 805ndash813 2009

[5] L-X Mao Z Hu J Xia et al ldquoMulti-phase modelling ofelectrochemical rehabilitation for ASR and chloride affectedconcrete compositesrdquo Composite Structures vol 207pp 176ndash189 2019

[6] J Xu and F Li ldquoAmeso-scale model for analyzing the chloridediffusion of concrete subjected to external stressrdquo Con-struction and Building Materials vol 130 pp 11ndash21 2017

[7] X Du L Jin and G Ma ldquoA meso-scale numerical method forthe simulation of chloride diffusivity in concreterdquo FiniteElements in Analysis and Design vol 85 pp 87ndash100 2014c

[8] F Bernard and S Kamali-Bernard ldquoNumerical study of ITZcontribution on mechanical behavior and diffusivity ofmortarsrdquo Computational Materials Science vol 102pp 250ndash257 2015

[9] J-J Zheng and X-Z Zhou ldquoEffective medium method forpredicting the chloride diffusivity in concrete with ITZ per-colation effectrdquo Construction and Building Materials vol 47pp 1093ndash1098 2013

[10] K Wu L Xu G D Schutter H Shi and G Ye ldquoInfluence ofthe interfacial transition zone and interconnection onchloride migration of portland cement mortarrdquo Journal ofAdvanced Concrete Technology vol 13 no 3 pp 169ndash1772015

[11] Z Zhang and Q Zhang ldquoSelf-healing ability of engineeredcementitious composites (ECC) under different exposureenvironmentsrdquo Construction and Building Materials vol 156pp 142ndash151 2017

[12] Z Zhang and Q Zhang ldquoMatrix tailoring of engineeredcementitious composites (ECC) with non-oil-coated lowtensile strength PVA fiberrdquo Construction and Building Ma-terials vol 161 pp 420ndash431 2018

[13] H Chen Z Zhu J Lin W Xu and L Liu ldquoNumericalmodeling on the influence of particle shape on ITZrsquos mi-crostructure and macro-properties of cementitious compos-ites a critical reviewrdquo Journal of Sustainable Cement-BasedMaterials vol 7 no 4 pp 248ndash269 2018

[14] J F Unger and S Eckardt ldquoMultiscale modeling of concreterdquoArchives of Computational Methods in Engineering vol 18no 3 pp 341ndash393 2011

[15] G-L Feng L-Y Li B Kim and Q-F Liu ldquoMultiphasemodelling of ionic transport in cementitious materials withsurface chargesrdquo Computational Materials Science vol 111pp 339ndash349 2016

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

[17] L Chen Z Qian and J Wang ldquoMultiscale numericalmodeling of steel bridge deck pavements consideringvehiclendashpavement interactionrdquo International Journal ofGeomechanics vol 16 no 1 article B4015002 2016

[18] Y Hiratsuka and K Maekawa ldquoMulti-scale and multi-chemo-physics analysis applied to fatigue life assessmentof strengthened bridge decksrdquo in Proceedings of XIIIInternational Conference on Computational Plasticity fun-damentals and applications pp 596ndash607 Barcelona SpainSeptember 2015

[19] X Tu et al ldquoA multiscale numerical simulation approach forchloride diffusion and rebar corrosion with compensationmodelrdquo Computers and Concrete vol 21 no 4 pp 471ndash4842018

[20] X Wang M Zhang and A P Jivkov ldquoComputationaltechnology for analysis of 3D meso-structure effects ondamage and failure of concreterdquo International Journal ofSolids and Structures vol 80 pp 310ndash333 2016

[21] Z M Wang A K H Kwan and H C Chan ldquoMesoscopicstudy of concrete I generation of random aggregate structureand finite element meshrdquo Computers and Structures vol 70no 5 pp 533ndash544 1999

[22] M Bailakanavar Y Liu J Fish and Y Zheng ldquoAutomatedmodeling of random inclusion compositesrdquo Engineering withComputers vol 30 no 4 pp 609ndash625 2012


[23] Z Y Ren and J Y W ldquoGeneration of spatial convex poly-hedron random aggregate modelrdquo in Proceedings of ICOME2006 Hefei China October 2006

[24] A Caballero C M Lopez and I Carol ldquo3D meso-structuralanalysis of concrete specimens under uniaxial tensionrdquoComputer Methods in Applied Mechanics and Engineeringvol 195 no 52 pp 7182ndash7195 2006

[25] F Biondini F Bontempi D M Frangopol and P G MalerbaldquoCellular automata approach to durability analysis of concretestructures in aggressive environmentsrdquo Journal of StructuralEngineering vol 130 no 11 pp 1724ndash1737 2004

[26] B Savija J Pacheco and E Schlangen ldquoLattice modeling ofchloride diffusion in sound and cracked concreterdquo Cementand Concrete Composites vol 42 pp 30ndash40 2013

[27] H Ma W Xu and Y Li ldquoRandom aggregate model formesoscopic structures andmechanical analysis of fully-gradedconcreterdquo Computers and Structures vol 177 pp 103ndash1132016

[28] R Franccedilois and G Arliguie ldquoEffect of microcracking andcracking on the development of corrosion in reinforcedconcrete membersrdquo Magazine of Concrete Research vol 51no 2 pp 143ndash150 1999

[29] T Vidal A Castel and R Franccedilois ldquoCorrosion process andstructural performance of a 17 year old reinforced concretebeam stored in chloride environmentrdquo Cement and ConcreteResearch vol 37 no 11 pp 1551ndash1561 2007

[30] T Vidal A Castel and R Franccedilois ldquoAnalyzing crack widthto predict corrosion in reinforced concreterdquo Cement andConcrete Research vol 34 no 1 pp 165ndash174 2004

[31] R Zhang A Castel and R Franccedilois ldquoConcrete cover crackingwith reinforcement corrosion of RC beam during chloride-induced corrosion processrdquo Cement and Concrete Researchvol 40 no 3 pp 415ndash425 2010

[32] R Zhang A Castel and R Franccedilois ldquo-e corrosion pattern ofreinforcement and its influence on serviceability of reinforcedconcrete members in chloride environmentrdquo Cement andConcrete Research vol 39 no 11 pp 1077ndash1086 2009

[33] C Andrade C Alonso and F J Molina ldquoCover cracking as afunction of bar corrosion Part I-Experimental testrdquoMaterialsand Structures vol 26 no 8 pp 453ndash464 1993

[34] T Liu and R W Weyers ldquoModeling the dynamic corrosionprocess in chloride contaminated concrete structuresrdquoCement and Concrete Research vol 28 no 3 pp 365ndash3791998

[35] L C Qing ldquoCorrosion initiation of reinforcing steel inconcrete under natural salt spray and service loadingmdashresultsand analysisrdquo Materials Journal vol 97 no 6 2000

[36] S M Pritpal and S E Mahmoud ldquoFlexural strength ofconcrete beams with corroding reinforcementrdquo ACI Struc-tural Journal vol 96 no 1 1999

[37] A A Torres-Acosta S Navarro-Gutierrez and J Teran-Guillen ldquoResidual flexure capacity of corroded reinforcedconcrete beamsrdquo Engineering Structures vol 29 no 6pp 1145ndash1152 2007

[38] A A Torres-Acosta andM Martnez-Madrid ldquoResidual life ofcorroding reinforced concrete structures in marine envi-ronmentrdquo Journal of Materials in Civil Engineering vol 15no 4 pp 344ndash353 2003

[39] F Biondini F Bontempi D M Frangopol and P G MalerbaldquoProbabilistic service life assessment and maintenanceplanning of concrete structuresrdquo Journal of Structural Engi-neering vol 132 no 5 pp 810ndash825 2006

[40] P Zhang D Li Y Qiao S Zhang C Sun and T Zhao ldquoEffectof air entrainment on the mechanical properties chloride

migration and microstructure of ordinary concrete and flyash concreterdquo Journal of Materials in Civil Engineeringvol 30 no 10 article 04018265 2018

[41] P Zhang F H Wittmann M Vogel H S Muller andT Zhao ldquoInfluence of freeze-thaw cycles on capillary ab-sorption and chloride penetration into concreterdquo Cement andConcrete Research vol 100 pp 60ndash67 2017

[42] P Zhang D Hou Q Liu Z Liu and J Yu ldquoWater andchloride ions migration in porous cementitious materials anexperimental and molecular dynamics investigationrdquo Cementand Concrete Research vol 102 pp 161ndash174 2017

[43] X Li F Wu and Z Huang ldquoAnalytical solution to chloridediffusion equation on concreterdquo Concrete(Chinese) vol 30no 10 pp 30ndash33 2009

[44] W Dridi ldquoAnalysis of effective diffusivity of cement basedmaterials by multi-scale modellingrdquoMaterials and Structuresvol 46 no 1-2 pp 313ndash326 2012

[45] G Sun Y Zhang W Sun Z Liu and C Wang ldquoMulti-scaleprediction of the effective chloride diffusion coefficient ofconcreterdquo Construction and BuildingMaterials vol 25 no 10pp 3820ndash3831 2011

[46] Z Zhu H Chen L Liu and X Li ldquoMulti-scale modelling fordiffusivity based on practical estimation of interfacial prop-erties in cementitious materialsrdquo Powder Technology vol 307pp 109ndash118 2017

[47] K Maekawa T Ishida and T Kishi Multi Scale Modeling ofStructural Concrete Taylor amp Francis Vol 670 Taylor ampFrancis Abingdon UK 2009

[48] Q Yuan C Shi G De Schutter K Audenaert and D DengldquoChloride binding of cement-based materials subjected toexternal chloride environment a reviewrdquo Construction andBuilding Materials vol 23 no 1 pp 1ndash13 2009

[49] P S Mangat and B T Molloy ldquoPrediction of long termchloride concentration in concreterdquoMaterials and Structuresvol 27 no 6 pp 338ndash346 1994

[50] B Savija M Lukovic J Pacheco and E Schlangen ldquoCrackingof the concrete cover due to reinforcement corrosion a two-dimensional lattice model studyrdquo Construction and BuildingMaterials vol 44 pp 626ndash638 2013

[51] Y Zhao et al ldquoConcrete surface chloride ion concentrationvarying with seasons in marine environment (Chinese)rdquoJournal of Zhejiang University (Engineering Science) vol 43no 11 pp 2120ndash2124 2009

[52] Z Pan A Chen and X Ruan ldquoSpatial variability of chlorideand its influence on thickness of concrete cover a two-dimensional mesoscopic numerical researchrdquo EngineeringStructures vol 95 pp 154ndash169 2015


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and macroscopic scale [14 15] Recently a number of theoryresearch and modeling efforts have been devoted to studyingmultiscale modeling Multiscale modeling was usually definedas the integrated numerical process of transferring me-chanical and chemical response between lower scale andhigher scale [16 17] A significant advantage of multiscalemodeling is optimizing computing loading and enhancing theprecision According to available literature researchersgenerally focused on the transferring process of materialresponse between scales

As the major purpose of multiscale modeling to reducecalculation loading heterogeneous model was alwaysmodeled for transferring damage and mass transportation ofcritical regions from the macroscale to the mesoscale whichprovided coupling of subdomains [18] Balance of accuracyand efficiency is the major consideration of multiscalemodeling for numerical simulation By means of macro-scopic model substituting for a part of mesoscopic modelmultiscale modeling is able to provide relatively smaller sizeof mesoscopic model and generate the same filling rate ofaggregate and less amount of aggregate which is no doubtbeneficial for raising success rate of meshing [19]

For mesoscopic structure of concrete both of size andshape of aggregates are generated as given design Regardingtwo-dimensional space general process was divided into twosteps including modeling of geometric model and meshingAngular aggregate was generated based on inscribed convexpolygon within elongated ellipse [20]Wang et al proposed aprocedure for generating random aggregate structures forangular aggregates by means of Monte Carlo samplingwhich was compatible for concave polygon [21] An in-evitable algorithm was intersection check of convex poly-gons which was achieved by detecting space independenceof two polygons [22 23] In terms of meshing mortar plussmaller aggregates embedding coarse aggregate was dis-cretized into finite elements by free meshing [20 24] oruniform background grid [25ndash27]

Another major factor for durability of reinforced con-crete structures is corrosion of steel rebar Researchersdevoted efforts on laboratorial research by means of naturalexperiments [28ndash32] and accelerated experiments [33ndash38]about the process of chloride diffusion and corrosion On theother hand some types of simplified approximate law forcorrosion were introduced Biondini introduced a reason-able linear damage model for corrosion of rebar underaggressive agent which evaluates corrosion rate according tothe real-time chloride content surrounding rebar [39ndash42]Despite the complex principle of corrosion based on thenatural damagemode of corrosion this linear damagemodelis able to provide acceptable description of damage process

-is paper discussed two important aspects regardingmultiscale modeling for numerical simulation of chlorideion diffusing within concrete Firstly a comprehensivemodeling approach for concrete considering both multiscalemodeling including interfacial transition layer (ITL) andthree-phase mesoscale structure including ITZ Secondly bymeans of the multiscale numerical simulation tool the in-fluence of ITZ on diffusion of chloride ion within concrete inmesoscale was studied in detail where ITZ was modeled as

an individual phase in FE model for chloride diffusion inconcrete Besides the corrosion of rebar in straight edge ofconcrete induced by diffusion of chloride ion was alsocalculated to study the time evolution of corrosion process

2 Multiscale Modeling and Discussion

21 Multiscale Modeling eory In mesoscopic numericalsimulation for chloride diffusion usually 100sim200mm sizeof specimen in square or rectangle was considered Withinthis typical size of analysis space enough number of ag-gregates with various sizes were included for in-depth studyWithin limited analysis space chloride ion would able topenetrate and saturate the whole space within the assessingperiod indicating the whole space was inadequate for fur-ther simulation However it would be impossible to in-creasing the size of analysis space due to two reasons Firstseveral times of original size of analysis space will generatemuch more nodes and elements especially for three-dimensional problem Second to control computing load-ing changing the grading curve and ignoring fine aggregatewill cause inaccuracy of numerical simulation

In this paper a scheme of multiscale modeling wasintroduced in terms of balancing amount of nodes andelements and calculation accuracy (Figure 1) In the view ofmultiscale modeling based on original mesoscopic modelincluding multiphase components which was defined as corepart a macroscopic compensationmodel which was definedas compensation part was modeled -e aim of introducingcompensation part was creating addition space to absorb thechloride within core part and adjusting the distribution ofchloride content within core part which means re-distribution of chloride in larger space

Due to different definition of nodal chloride content anddiffusion coefficient in mesoscopic model and macroscopicmodel the two types of models cannot be directly combinedand analyzed simultaneously In this paper interfacialtransition layer (ITL) was introduced to connect bothmodels at the interface which consists of a group of nodesand elements shown in Figure 1 ITL was designed as abanded shape transition zone allowing chloride ion diffusingfrom core part into compensation part Within each timestep core part and compensation part were analyzed se-quentially and the chloride content at interface of the twoparts was transferred based on the function of ITL

It is worth noting that the most important preconditionis the mechanism of ITL for transporting the chloride ionwhich generates equivalent diffusion and distribution ofchloride within the model on the same scale ITL could becomposed by a row of common nodes occupied by bothmesoscopic model and macroscopic model as well as anamount of elements with certain thickness stuck by bothmodels

-e process of transferring chloride ion within ITL inone-dimension was illustrated in Figure 2 For initial stateanalysis space of three phases including core part com-pensation part and ITL was modeled respectivelyBoundary condition was set at surface of concrete whichwas the top of core part shown in Figure 2










zC



Core part

Compensationpart

Clndash ne 0

Clndash ne 0

Clndash = 0

ti + Δt

ti

Barrier

Core part

Compensationpart

Cndash ne 0

Clndash ne 0

Clndash ne 0

ti + Δt

ti + Δt

Barrier


Compensation part

Core part


Boundary Clndash




2Dt

radic1113888 11138891113890 1113891 (2)



C Cs + C0 minusCs( 1113857 1113944

infin

n1

4(2nminus 1)π

sin2nminus 12l


(3)



n1

4(2nminus 1)π

sin2nminus 12l


(4)



C(t)|Γ2


n1

4(2nminus 1)π

sin2nminus 12l2


2t⎡⎣ ⎤⎦

(5)


V CminusCs (6)



infin

n1

4(2nminus 1)π

sin2nminus 12l2


2t

(7)




X(x) B sin(αx) (9)


αn 2nminus 12l2

π (n 1 2 ) (10)



πx1113888 1113889 (11)



(12)


layer




Γ1 Γ2

l

xO

C (Γ1 t) = Cs(Cx) Γ2 = 0

C (x t) = C0






(13)


1113944

infin

n1en sin

2nminus 12l2

πx1113888 1113889 minusCs (14)


1113946l

0sin αmx( 1113857 sin αnx( 1113857dx

0 mne n

l2 m n1113896 (15)


en minus4Cs

(2nminus 1)π (16)



n1

4(2nminus 1)π

sin2nminus 12l2


2t⎡⎣ ⎤⎦

x isin 0 l11113858 1113859( 1113857

(17)













C (Γ1 t) = Cs

C (x t) = C0Γ1 Γ2

xOl1

C(t) Γ2





Ro

Ri

Riprime

Roprime

Agg1

Agg2

dagg




(c) (d)

(a) (b)


Start








Dispersion succeeds

Yes

Yes

No

No


End

No

Yes

No

Yes














ωezCf

zt

z

zxDeωe

zCf

zxminus

zCb

zt


(18)



(a) (b)






T


(19)






h

(a) (b) (c)



Meshed FEM model

























20

18

16

14

12

10

8

6

4

2

0

(kgm3)







16 164 168 172 176 18 184

(a)

16 164 168 172 176 18 184

(b)


0 20 40 60 808

10

12

14

16

18

20

Chlo

ride c

onte

nt (k

gm

3 )

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)








Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)Ch

lorid

e con

tent

(kg

m3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)


(a) (b) (c) (d) (e)





h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)


h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



(a) (b) (c)

(d) (e) (f )


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)

Figure 22 Continued


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)


(a) (b) (c)

(d) (e) (f )







Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)




12 16 20 25 2820 times

30 times

40 times


60 times








T


(21)





(kgm3)

Contour20

18

16

14

12

10

8

6

4

2

0

D

Boundary

(b)(a)

Core model

Compensation model

ITL

d

Rebar






05101520


(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)



6 Conclusion




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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



Core part

Compensationpart

Clndash ne 0

Clndash ne 0

Clndash = 0

ti + Δt

ti

Barrier

Core part

Compensationpart

Cndash ne 0

Clndash ne 0

Clndash ne 0

ti + Δt

ti + Δt

Barrier


Compensation part

Core part


Boundary Clndash




2Dt

radic1113888 11138891113890 1113891 (2)



C Cs + C0 minusCs( 1113857 1113944

infin

n1

4(2nminus 1)π

sin2nminus 12l


(3)



n1

4(2nminus 1)π

sin2nminus 12l


(4)



C(t)|Γ2


n1

4(2nminus 1)π

sin2nminus 12l2


2t⎡⎣ ⎤⎦

(5)


V CminusCs (6)



infin

n1

4(2nminus 1)π

sin2nminus 12l2


2t

(7)




X(x) B sin(αx) (9)


αn 2nminus 12l2

π (n 1 2 ) (10)



πx1113888 1113889 (11)



(12)


layer




Γ1 Γ2

l

xO

C (Γ1 t) = Cs(Cx) Γ2 = 0

C (x t) = C0






(13)


1113944

infin

n1en sin

2nminus 12l2

πx1113888 1113889 minusCs (14)


1113946l

0sin αmx( 1113857 sin αnx( 1113857dx

0 mne n

l2 m n1113896 (15)


en minus4Cs

(2nminus 1)π (16)



n1

4(2nminus 1)π

sin2nminus 12l2


2t⎡⎣ ⎤⎦

x isin 0 l11113858 1113859( 1113857

(17)













C (Γ1 t) = Cs

C (x t) = C0Γ1 Γ2

xOl1

C(t) Γ2





Ro

Ri

Riprime

Roprime

Agg1

Agg2

dagg




(c) (d)

(a) (b)


Start








Dispersion succeeds

Yes

Yes

No

No


End

No

Yes

No

Yes














ωezCf

zt

z

zxDeωe

zCf

zxminus

zCb

zt


(18)



(a) (b)






T


(19)






h

(a) (b) (c)



Meshed FEM model

























20

18

16

14

12

10

8

6

4

2

0

(kgm3)







16 164 168 172 176 18 184

(a)

16 164 168 172 176 18 184

(b)


0 20 40 60 808

10

12

14

16

18

20

Chlo

ride c

onte

nt (k

gm

3 )

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)








Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)Ch

lorid

e con

tent

(kg

m3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)


(a) (b) (c) (d) (e)





h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)


h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



(a) (b) (c)

(d) (e) (f )


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)

Figure 22 Continued


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)


(a) (b) (c)

(d) (e) (f )







Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)




12 16 20 25 2820 times

30 times

40 times


60 times








T


(21)





(kgm3)

Contour20

18

16

14

12

10

8

6

4

2

0

D

Boundary

(b)(a)

Core model

Compensation model

ITL

d

Rebar






05101520


(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)



6 Conclusion




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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



2Dt

radic1113888 11138891113890 1113891 (2)



C Cs + C0 minusCs( 1113857 1113944

infin

n1

4(2nminus 1)π

sin2nminus 12l


(3)



n1

4(2nminus 1)π

sin2nminus 12l


(4)



C(t)|Γ2


n1

4(2nminus 1)π

sin2nminus 12l2


2t⎡⎣ ⎤⎦

(5)


V CminusCs (6)



infin

n1

4(2nminus 1)π

sin2nminus 12l2


2t

(7)




X(x) B sin(αx) (9)


αn 2nminus 12l2

π (n 1 2 ) (10)



πx1113888 1113889 (11)



(12)


layer




Γ1 Γ2

l

xO

C (Γ1 t) = Cs(Cx) Γ2 = 0

C (x t) = C0






(13)


1113944

infin

n1en sin

2nminus 12l2

πx1113888 1113889 minusCs (14)


1113946l

0sin αmx( 1113857 sin αnx( 1113857dx

0 mne n

l2 m n1113896 (15)


en minus4Cs

(2nminus 1)π (16)



n1

4(2nminus 1)π

sin2nminus 12l2


2t⎡⎣ ⎤⎦

x isin 0 l11113858 1113859( 1113857

(17)













C (Γ1 t) = Cs

C (x t) = C0Γ1 Γ2

xOl1

C(t) Γ2





Ro

Ri

Riprime

Roprime

Agg1

Agg2

dagg




(c) (d)

(a) (b)


Start








Dispersion succeeds

Yes

Yes

No

No


End

No

Yes

No

Yes














ωezCf

zt

z

zxDeωe

zCf

zxminus

zCb

zt


(18)



(a) (b)






T


(19)






h

(a) (b) (c)



Meshed FEM model

























20

18

16

14

12

10

8

6

4

2

0

(kgm3)







16 164 168 172 176 18 184

(a)

16 164 168 172 176 18 184

(b)


0 20 40 60 808

10

12

14

16

18

20

Chlo

ride c

onte

nt (k

gm

3 )

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)








Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)Ch

lorid

e con

tent

(kg

m3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)


(a) (b) (c) (d) (e)





h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)


h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



(a) (b) (c)

(d) (e) (f )


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)

Figure 22 Continued


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)


(a) (b) (c)

(d) (e) (f )







Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)




12 16 20 25 2820 times

30 times

40 times


60 times








T


(21)





(kgm3)

Contour20

18

16

14

12

10

8

6

4

2

0

D

Boundary

(b)(a)

Core model

Compensation model

ITL

d

Rebar






05101520


(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)



6 Conclusion




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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





(13)


1113944

infin

n1en sin

2nminus 12l2

πx1113888 1113889 minusCs (14)


1113946l

0sin αmx( 1113857 sin αnx( 1113857dx

0 mne n

l2 m n1113896 (15)


en minus4Cs

(2nminus 1)π (16)



n1

4(2nminus 1)π

sin2nminus 12l2


2t⎡⎣ ⎤⎦

x isin 0 l11113858 1113859( 1113857

(17)













C (Γ1 t) = Cs

C (x t) = C0Γ1 Γ2

xOl1

C(t) Γ2





Ro

Ri

Riprime

Roprime

Agg1

Agg2

dagg




(c) (d)

(a) (b)


Start








Dispersion succeeds

Yes

Yes

No

No


End

No

Yes

No

Yes














ωezCf

zt

z

zxDeωe

zCf

zxminus

zCb

zt


(18)



(a) (b)






T


(19)






h

(a) (b) (c)



Meshed FEM model

























20

18

16

14

12

10

8

6

4

2

0

(kgm3)







16 164 168 172 176 18 184

(a)

16 164 168 172 176 18 184

(b)


0 20 40 60 808

10

12

14

16

18

20

Chlo

ride c

onte

nt (k

gm

3 )

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)








Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)Ch

lorid

e con

tent

(kg

m3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)


(a) (b) (c) (d) (e)





h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)


h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



(a) (b) (c)

(d) (e) (f )


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)

Figure 22 Continued


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)


(a) (b) (c)

(d) (e) (f )







Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)




12 16 20 25 2820 times

30 times

40 times


60 times








T


(21)





(kgm3)

Contour20

18

16

14

12

10

8

6

4

2

0

D

Boundary

(b)(a)

Core model

Compensation model

ITL

d

Rebar






05101520


(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)



6 Conclusion




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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




Ro

Ri

Riprime

Roprime

Agg1

Agg2

dagg




(c) (d)

(a) (b)


Start








Dispersion succeeds

Yes

Yes

No

No


End

No

Yes

No

Yes














ωezCf

zt

z

zxDeωe

zCf

zxminus

zCb

zt


(18)



(a) (b)






T


(19)






h

(a) (b) (c)



Meshed FEM model

























20

18

16

14

12

10

8

6

4

2

0

(kgm3)







16 164 168 172 176 18 184

(a)

16 164 168 172 176 18 184

(b)


0 20 40 60 808

10

12

14

16

18

20

Chlo

ride c

onte

nt (k

gm

3 )

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)








Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)Ch

lorid

e con

tent

(kg

m3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)


(a) (b) (c) (d) (e)





h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)


h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



(a) (b) (c)

(d) (e) (f )


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)

Figure 22 Continued


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)


(a) (b) (c)

(d) (e) (f )







Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)




12 16 20 25 2820 times

30 times

40 times


60 times








T


(21)





(kgm3)

Contour20

18

16

14

12

10

8

6

4

2

0

D

Boundary

(b)(a)

Core model

Compensation model

ITL

d

Rebar






05101520


(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)



6 Conclusion




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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












ωezCf

zt

z

zxDeωe

zCf

zxminus

zCb

zt


(18)



(a) (b)






T


(19)






h

(a) (b) (c)



Meshed FEM model

























20

18

16

14

12

10

8

6

4

2

0

(kgm3)







16 164 168 172 176 18 184

(a)

16 164 168 172 176 18 184

(b)


0 20 40 60 808

10

12

14

16

18

20

Chlo

ride c

onte

nt (k

gm

3 )

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)








Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)Ch

lorid

e con

tent

(kg

m3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)


(a) (b) (c) (d) (e)





h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)


h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



(a) (b) (c)

(d) (e) (f )


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)

Figure 22 Continued


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)


(a) (b) (c)

(d) (e) (f )







Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)




12 16 20 25 2820 times

30 times

40 times


60 times








T


(21)





(kgm3)

Contour20

18

16

14

12

10

8

6

4

2

0

D

Boundary

(b)(a)

Core model

Compensation model

ITL

d

Rebar






05101520


(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)



6 Conclusion




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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





T


(19)






h

(a) (b) (c)



Meshed FEM model

























20

18

16

14

12

10

8

6

4

2

0

(kgm3)







16 164 168 172 176 18 184

(a)

16 164 168 172 176 18 184

(b)


0 20 40 60 808

10

12

14

16

18

20

Chlo

ride c

onte

nt (k

gm

3 )

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)








Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)Ch

lorid

e con

tent

(kg

m3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)


(a) (b) (c) (d) (e)





h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)


h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



(a) (b) (c)

(d) (e) (f )


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)

Figure 22 Continued


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)


(a) (b) (c)

(d) (e) (f )







Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)




12 16 20 25 2820 times

30 times

40 times


60 times








T


(21)





(kgm3)

Contour20

18

16

14

12

10

8

6

4

2

0

D

Boundary

(b)(a)

Core model

Compensation model

ITL

d

Rebar






05101520


(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)



6 Conclusion




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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














20

18

16

14

12

10

8

6

4

2

0

(kgm3)







16 164 168 172 176 18 184

(a)

16 164 168 172 176 18 184

(b)


0 20 40 60 808

10

12

14

16

18

20

Chlo

ride c

onte

nt (k

gm

3 )

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)








Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)Ch

lorid

e con

tent

(kg

m3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)


(a) (b) (c) (d) (e)





h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)


h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



(a) (b) (c)

(d) (e) (f )


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)

Figure 22 Continued


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)


(a) (b) (c)

(d) (e) (f )







Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)




12 16 20 25 2820 times

30 times

40 times


60 times








T


(21)





(kgm3)

Contour20

18

16

14

12

10

8

6

4

2

0

D

Boundary

(b)(a)

Core model

Compensation model

ITL

d

Rebar






05101520


(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)



6 Conclusion




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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






16 164 168 172 176 18 184

(a)

16 164 168 172 176 18 184

(b)


0 20 40 60 808

10

12

14

16

18

20

Chlo

ride c

onte

nt (k

gm

3 )

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)








Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)Ch

lorid

e con

tent

(kg

m3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)


(a) (b) (c) (d) (e)





h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)


h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



(a) (b) (c)

(d) (e) (f )


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)

Figure 22 Continued


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)


(a) (b) (c)

(d) (e) (f )







Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)




12 16 20 25 2820 times

30 times

40 times


60 times








T


(21)





(kgm3)

Contour20

18

16

14

12

10

8

6

4

2

0

D

Boundary

(b)(a)

Core model

Compensation model

ITL

d

Rebar






05101520


(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)



6 Conclusion




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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 (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(a)Ch

lorid

e con

tent

(kg

m3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)


DITZDCP = 3

DITZDCP = 4

DITZDCP = 5

(b)


(a) (b) (c) (d) (e)





h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)


h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



(a) (b) (c)

(d) (e) (f )


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)

Figure 22 Continued


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)


(a) (b) (c)

(d) (e) (f )







Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)




12 16 20 25 2820 times

30 times

40 times


60 times








T


(21)





(kgm3)

Contour20

18

16

14

12

10

8

6

4

2

0

D

Boundary

(b)(a)

Core model

Compensation model

ITL

d

Rebar






05101520


(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)



6 Conclusion




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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




h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)


h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

h = 5 μmh = 10 μmh = 20 μm

h = 35 μmh = 50 μm

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



(a) (b) (c)

(d) (e) (f )


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)

Figure 22 Continued


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)


(a) (b) (c)

(d) (e) (f )







Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)




12 16 20 25 2820 times

30 times

40 times


60 times








T


(21)





(kgm3)

Contour20

18

16

14

12

10

8

6

4

2

0

D

Boundary

(b)(a)

Core model

Compensation model

ITL

d

Rebar






05101520


(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)



6 Conclusion




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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


(a) (b) (c)

(d) (e) (f )


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)

Figure 22 Continued


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)


(a) (b) (c)

(d) (e) (f )







Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)




12 16 20 25 2820 times

30 times

40 times


60 times








T


(21)





(kgm3)

Contour20

18

16

14

12

10

8

6

4

2

0

D

Boundary

(b)(a)

Core model

Compensation model

ITL

d

Rebar






05101520


(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)



6 Conclusion




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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


fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)

fa = 20fa = 30fa = 40

fa = 50fa = 60fa = 70

Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)


(a) (b) (c)

(d) (e) (f )







Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)




12 16 20 25 2820 times

30 times

40 times


60 times








T


(21)





(kgm3)

Contour20

18

16

14

12

10

8

6

4

2

0

D

Boundary

(b)(a)

Core model

Compensation model

ITL

d

Rebar






05101520


(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)



6 Conclusion




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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 (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(a)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(b)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(c)



Chlo

ride c

onte

nt (k

gm

3 )

0 20 40 60 808

10

12

14

16

18

20

Depth (mm)

(d)




12 16 20 25 2820 times

30 times

40 times


60 times








T


(21)





(kgm3)

Contour20

18

16

14

12

10

8

6

4

2

0

D

Boundary

(b)(a)

Core model

Compensation model

ITL

d

Rebar






05101520


(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)



6 Conclusion




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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








T


(21)





(kgm3)

Contour20

18

16

14

12

10

8

6

4

2

0

D

Boundary

(b)(a)

Core model

Compensation model

ITL

d

Rebar






05101520


(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)



6 Conclusion




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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





05101520


(a)

05101520


(b)

05101520


(c)

05101520


(d)

05101520


(e)

05101520


(f )

05101520


(g)

05101520


(h)

05101520


(i)



6 Conclusion




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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




0 10 20 30 40 50 600

5

10

15

20Ch

lorid

e con

tent

(kg

m3 )

Cover (mm)



(a)Ch

lorid

e con

tent

(kg

m3 )

10 15 20 25 300

5

10

15

20

Rebar diameter (mm)



(b)


20 30 40 50 6005

06

07

08

09

10

t = 100a

Cover (mm)



t = 20yrs

DtD

0

(a)



10 15 20 25 3005

06

07

08

09

10

t = 20yrs

t = 100a

DtD

0

Rebar diameter (mm)

(b)





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


numericalstudyondiffusionofchlorideandinducedrebar ...xitu ,1,2 jindi,1,2 cunjunpang,1,2...

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