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Composite Structures 183 (2018) 371–380

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Composite Structures

journal homepage: www.elsevier .com/locate /compstruct

Ionic transport features in concrete composites containing variousshaped aggregates: a numerical study

http://dx.doi.org/10.1016/j.compstruct.2017.03.0880263-8223/� 2017 Elsevier Ltd. All rights reserved.

⇑ Corresponding author at: State Key Laboratory of Ocean Engineering, School ofNaval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University,Shanghai, China.

E-mail addresses: [email protected] (Q.-f. Liu), [email protected] (J. Yang).

Qing-feng Liu a,b, Gan-lin Feng c, Jin Xia d, Jian Yang a,e,⇑, Long-yuan Li c

a State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai, ChinabCollaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE), Shanghai, Chinac School of Marine Science and Engineering, University of Plymouth, UKd Institute of Structural Engineering, Zhejiang University, Hangzhou, Chinae School of Civil Engineering, University of Birmingham, UK

a r t i c l e i n f o a b s t r a c t

Article history:Received 18 January 2017Revised 16 March 2017Accepted 25 March 2017Available online 28 March 2017

Keywords:DurabilityNumerical modellingConcrete compositesInner structures of concreteAggregate shapeChloride migrationHeterogeneityMulti-phaseMulti-speciesIonic interactionBinding

The service life of concrete-based infrastructure and buildings is seriously shortened due to the chloride-induced durability problems. In order to clarify the transport mechanism associated with the response ofinclusion structures, this paper presents a numerical study on the influence caused by morphology andheterogeneity of individual phases, in which the concrete is treated as a three-phase composite includingmortar, aggregates and interfacial transition zone (ITZ). A series of meso-scale numerical models with dif-ferent shapes and volume fractions of aggregates are developed for examining the effects of aggregates onionic migration. Unlike in most of the existing published research work in this area, a multi-componentionic transport theory which takes ionic interactions into consideration has been utilised in this study. Bycoupling mass conservation and Poisson’s equations, the time-spatial concentration distribution resultsfor individual ionic species are obtained. Other important factors such as the externally applied electricfield, concrete heterogeneity, ionic binding and ITZ are also considered and examined in this study.Through this relatively thorough numerical analysis, some important features about the effect of aggre-gate shape based on multi-species modelling, which have previously not been properly investigated, arehighlighted.

� 2017 Elsevier Ltd. All rights reserved.

1. Introduction

Concrete is the most widely used man-made material in mod-ern construction industry. However, the service life of concrete-based infrastructure and buildings has been seriously shorteneddue to the durability problems, especially the corrosion of rein-forcement caused by the penetration of chloride ions. Once thechloride concentration around the reinforcing steel reaches athreshold value, depassivation of the reinforcement will occur[1,2]. To this end, it is important to clarify the transport mechanismassociated with changes in ionic concentration in concrete, andhow individual phases in concrete composites behave during chlo-rides penetration.

During the last few decades, a number of studies have been pro-duced around the theme of assessment of ionic transport in con-

crete by using traditional methods, including analytical models[3–10] and experimental techniques [11–23]. Concrete is a com-posite material consisting of meso- and micro-structural organisa-tions, which has a complicated heterogeneous nature.Unfortunately, most of the previous analytical studies are only cap-able of tackling one dimensional transport problems in a single-phase medium and are generally suitable for cement or mortarmatrices, but not for concrete. Experimental studies have theadvantage of providing credible and valuable data on transportproperties of concrete; however, they are weak in clarifying theindividual effects of different factors, as well as usually beingtime-consuming and expensive.

It seems that none of these earlier experimental or analyticalmethods is suitable for evaluating the influence of individual com-ponents on chloride transport in concrete. To deal with this, fromthe mechanics point of view, if the properties of each individualmaterial involved in the concrete are known then the propertiesof the concrete composite should be predictable. For this concern,advanced numerical concrete models, which are originally devel-oped for structural stress analysis [24,25], have recently been uti-

372 Q.-f. Liu et al. / Composite Structures 183 (2018) 371–380

lized to investigate the ionic transport properties of concrete, treat-ing it as a multi-phase composite material [26–42]. By using thesemulti-phase computational models, it can be easy to clarify andquantify the influence of the different component parts of concrete,i.e. coarse/fine aggregate inclusion, mortar/cement and interfacialtransition zones (ITZs), which could not be achieved with onedimensional (1-D) analytical models. However, most of the exist-ing modelling work assumes that the shape of an aggregate parti-cle is circular or spherical. This rough simplification may causesimulation results to be inaccurate. More recently, meso-structures of concrete with several aggregate shapes have beenestablished to explore the effect of aggregate shape on the durabil-ity properties of concrete. As a typical example, Larrard et al. [44]numerically generated 3-D, 2-phase samples with and withoutsteel bars to study the effects of the aggregate shape on dryingand atmospheric carbonation. It was found that, regarding macro-scopic indicators, the influence of the coarse aggregate shapesappears negligible when compared to the effect of their volumefractions. Li et al. [45] established 3-D meso-scale models to inves-tigate the effective permeability during steady state flow, andclaimed that the tortuosity effect is more pronounced when differ-ent aggregate shapes are employed. Abyaneh et al. [46] numeri-cally explored the effect of aggregate size, shape and volumefraction on the capillary absorption. They solved the non-linear,non-steady state Fick’s equation in a 3-D mesoscale model andfound the shape of aggregate particles may have a significant effecton the water penetration profile and sorptivity. Using chloride dif-fusivity as a durability indicator, Zheng et al. [39] applied a 2-D, 3-phase model using lattice method to investigate the effect of aggre-gate shape on chloride diffusion through concrete, in which theaggregate particles are assumed to be elliptical. They concludedthat the chloride diffusivity in concrete decreases with an increasein the aspect ratio of elliptical aggregate particles. Abyaneh et al.[47] conducted a series of numerical simulations with a 3-D finitedifference model to study the effect of the shape of various spher-oidal aggregates (i.e. spherical, tri-axial ellipsoidal, prolate spheroi-dal and oblate spheroidal). The results showed that the diffusivitydecreased significantly when spherical aggregate particles werereplaced by ellipsoidal aggregate particles, particularly for higheraggregate fractions and aspect ratios.

Most of transport models described above focus on the diffusionmechanism and employ Fick’s law to describe the steady-statechloride diffusion in concrete with spheroidal aggregates. The ionictransport behaviour in saturated electrolyte solution is classifiedinto both diffusion and migration, particularly for cases where anexternally applied electric field is involved, such as in the rapidchloride permeability/migration test (RCPT/RCM) [21–23], andthe electrochemical chloride removal (ECR) treatment [48]. Theformer is one of the most widely used test methods in durabilitytesting; whereas the latter has recently become a popular rehabil-itation method due to both its cost and efficiency. It is clearlyessential for the numerical models to extend the ionic diffusionto a more complicated migration dominated process. In recentyears, great efforts have been made on this issue [49–67]. How-ever, the presence of an external electric field, and couplingbetween different species leads the transport equations to a highlynonlinear form. In order to achieve convergent solutions, mostexisting numerical simulations regarding migration only adopt a1-D model or 2-D model, but incorporate a number of simplifica-tions (e.g. circular aggregates).

The above literature review shows that the influence of innerstructures morphology, i.e., various shaped aggregates on ionictransport in a multiple ionic electro-migration process within mor-tar or concrete has not been investigated in the existing models. Inthis paper, a numerical study is presented to simulate the chloridemigration process by treating the concrete as a three-phase com-

posite including mortar, ITZs and aggregates with various shapesand volume fractions. A series of meso-scale models are developedfor a theoretical investigation. The previous studies on the effect ofaggregate shape [39,47] did not discuss or show the details of chlo-ride transport in concrete, such as the time-dependent concentra-tion distribution and penetration depth (which are the keyinformation for predicting the depassivation process or chloridediffusivity), and they modelled concrete with only spheroidalshaped inclusions. The study presented in this paper examinesboth spheroidal and polygonal aggregates, and also providestime-spatial distribution results for the four ionic species involved(K+, Na+, Cl�, OH�) by solving coupled mass conservation and Pois-son’s equations. Other important factors such as the externallyapplied electric field, concrete heterogeneity, ionic binding andthe ITZs are also considered and examined in this study. Throughthis thorough numerical analysis based on multi-phase andmulti-species modelling, some important features about the effectof aggregate shape, which have not previously been properlyinvestigated, are highlighted.

2. Theoretical background

In order to discuss the ionic transport features in heterogeneousconcrete subjected to an external electric field, more attentionshould be devoted to the definitions of driving forces, ionic bind-ing, time-dependent concentration and electrical potential per unitof medium.

Fick’s law is not adequate to describe the ionic transport otherthan the diffusion process. When a transport process includes var-ious driving forces such as concentration gradient, electric field,pressure flow and chemical activity, the flux of ionic species canbe presented by the extended Nernst-Planck equation as follows,

Jk ¼ �DkrCk � zkFRT

DkCkrUþ Ckuk � Ck

ckrck ð1Þ

where Jk and Ck are the flux and the concentration of the kth species,respectively, Dk is the diffusion coefficient, uk is the advectivevelocity, ck is the chemical activity coefficient, zk is the chargenumber, F = 9.648 � 104 Cmol�1 is the Faraday constant,R = 8.314 J mol�1 K�1 is the ideal gas constant, T = 298 K is the abso-lute temperature, and U is the electrostatic potential. For the RCMtest, as the pore solution is fully saturated with diluted solutionand there are no pressure differences, the terms of convection andchemical activity can be ignored. Hence, the extended Nernst-Planck equation can be simplified to a diffusion-migration form, asfollows:

Jk ¼ �DkrCk � zkFRT

DkCkrU ð2Þ

To quantitatively describe the time-spatial distribution of ionicconcentrations, each ionic species involved in the electrolyte solu-tion is also subjected to the mass conservation equations asdescribed in Eq. (3),

@Ck

@t¼ �r � Jk ð3Þ

where t is time. As the effect of the aggregate is involved in thisstudy, the concrete considered here is modelled as a compositestructure consisting of aggregate-, cement paste- and ITZ-phasesat mesoscopic level. The cement paste phase and ITZ phase are trea-ted as two different porous materials; different microstructureproperties are applied in the numerical simulation to show theirdifferent transport properties. Thus the governing equations forionic transport in this study should be rewritten and taken influ-ences of the microstructure properties of the porous materials intoaccount. In this study, porosity and tortuosity of the pore structure

Fig. 1. Geometry sample of 2D multi-phase concrete model: section of concrete,Vagg = 0.5.

Q.-f. Liu et al. / Composite Structures 183 (2018) 371–380 373

are considered to represent the microstructure effect. Adsorptionand desorption of ions [68] at the pore walls while ions transportin the pore structures are also considered. Normally the porosityand tortuosity effects are considered by adjusting the diffusioncoefficient, but in this study these two parameters are consideredby using the ionic transport equations in porous media. Adsorptionand desorption are considered using existing ionic binding models.Finally Eq. (3) should be modified as follows:

@ð/CkÞ@t

þ @½ð1� /ÞSk�@t

¼ �/r � Jk ð4Þ

where u is the porosity and Sk is the concentration of bound ions.Three different methods (linear, Langmuir or Freundlich isotherm[69]) can be used to approximate the ratio between the boundand free chloride ions and the binding is nearly independent ofthe ionic transport rate. To enhance numerical stability, a simplelinear isotherm [70] is used here:

ð1� /Þ/

Sk ¼ kkCk ð5Þ

where kk > 0 is a dimensionless fitting constant for the kth species.Substituting Eqs. (2) and (5) into Eq. (4) yields:

ð1þ kÞ @Ck

@t¼ rðDkrCkÞ þ r zkDkF

RT

� �CkrU

� �ð6Þ

During the ionic migration process, the electrostatic potential,U, in Eq. (6) is governed not only by the externally applied electricfield, but also by the internal concentration imbalance betweendifferent species caused by different flow rate. The electrostaticpotential should be decided by Gauss’s law [71] as the followingform of Poisson’s equation,

r2U ¼ � Fe0er

XNk¼1

zkCk ð7Þ

where eo = 8.854 � 10�12 CV�1 m�1 is the permittivity of vacuum,er = 78.3 is the relative permittivity of water at 298 K, and N is thetotal number of species involved in the simulation. Most of theexisting work on multi-species transport is based on the assump-

tion of electro-neutrality conditionPN

k¼1zkCk ¼ 0� �

replacing Eq.

(7) and thus r2U ¼ 0, which means that the electrostatic potential,U, in Eq. (6) is only determined by the externally applied electricfield. Though this assumption can reduce the computational diffi-culty, the ionic electro-coupling between different species cannotbe realised, which can lead to questionable results. Literatures alsoindicate that the numerical models with consideration of interac-tions between multiple ionic species controlled by Poisson’s equa-tion, which is the more correct relationship between theelectrostatic potential and the charge density, can provide moreaccurate results than those considering only one ionic species, orthose considering multi-species in the pore solution but using theassumption of the electro-neutrality condition [50–54]. However,Poisson’s equation brings huge difficulties in achieving convergentsolutions and for now only the 1-D or 2-D simulation result formulti-species transport is available. N, this study will solve Eqs.(6) and (7) with given initial and boundary conditions to obtainthe distribution profiles of electrostatic potentialU and the concen-tration profiles of individual ionic species, at any place and any timein the solution domain.

3. Modelling

The concrete specimen modelled in this study is considered as acomposite material with three phases, consisting of cement mortarmatrix, coarse aggregates and ITZs. For simplification, in most ofthe existing multi-phase concrete models [26–43] including the

authors’ previous works [54,63–66], the shape of the coarse aggre-gate was assumed to be circular or spherical. In reality, the shape ofcoarse aggregates is not spherical in most cases. One of the 2-Dmulti-phase concrete models, with a sample size of 50 � 50 mm,is shown in Fig. 1. The volume fraction of aggregate Vagg is 0.5 inthis model. The circles represent the impermeable aggregates withradii ranging from 1.5 mm to 10 mm with Fuller aggregate grada-tion. The locations of the aggregates were randomly determinedusing a MATLAB program. Regarding the statistical effects, at a cer-tain volume fraction of aggregate, the diffusivity of a 2-D concreteperforms a decent reproducibility due to the use of the same aggre-gate gradation. The ITZs are considered as thin shell layers outsideeach aggregate particle, and the thickness of the ITZ layers in themodel is assumed to be 40 lm due to numerical difficulties inmesh size (the ITZ thickness is usually supposed to be 20–50 lmin normal concrete [73,74]). The remaining part of the model rep-resents the cement mortar matrix. As well as using the aggregatevolume fraction of 0.5, this study also conducted simulations withdifferent concrete geometries and volume fractions (ranging from0.1 to 0.5) of various shaped aggregates but these are not displayedhere.

In order to further study the effect caused by different aggregateshapes and volume fractions, a set of newly developed 2-D modelswith various shapes and volume fractions of coarse aggregates areused in this study. Fig. 2 shows the models with the same volumefraction of aggregate (Vagg = 0.5) but different aggregate shapes,which are elliptical, triangular, rectangular, and mixed shapes.The various shaped ITZs wrapped around the aggregate particlesare shown in the zoomed-in figure on the right-hand side ofFig. 2, and are highlighted in blue. The finite element meshes arealso shown in Fig. 2, which shows that only the cement mortarphase and ITZs are meshed during modelling. The coarse aggregateparticles are assumed to be impermeable to save the simulationtime. Note that due to the issue of Peclet number [54] and tinyscale of ITZs, the element size need to be finely meshed to achieveconvergent solutions. Denser meshes bring more accurate resultbut much more time for computing. In this study, a minimum ele-ment size of 6.25 lm has been chosen to balance between theaccuracy and computation time. It is also noticeable from Fig. 2

Fig. 2. Finite element mesh of geometries with various shaped aggregates, Vagg = 0.5.


that elliptical, triangular, and rectangular type aggregates arealmost uniformly distributed within their respective concretegeometries, whereas the aggregates in the mixed shape modelare less uniformly distributed. An elaborate examination of themodel geometries including mixed shape aggregate particlesshows that smaller sized particles gather more in the region nearthe cathode (from x = 0 m to x = 0.025 m), whereas the larger sizedparticles gather more in the region near the anode (fromx = 0.025 m to x = 0.05 m). This mixed shape model has been inten-tionally developed in this way to investigate the influence of tortu-osity and to show the effect of aggregate size to some extent, whichis explained and discussed later.

The models described above are then employed to simulate theRCM test [21–23], in which concrete specimens are placedbetween two compartments and an external DC voltage of 24V isapplied between the two surfaces of the specimen. The compart-ment with the cathode inserted is filled with 0.52 mol/l NaCl solu-tion and the compartment with the anode inserted is filled with0.30 mol/l NaOH solution. The whole RCM test set-up is illustratedin Fig. 3. Four ionic species (i.e. K+, Na+, Cl�, OH�) are analysed in

Fig. 3. Schematic representation of 2-D plain concrete specimen in a RCM test.

the simulations. Other ionic species (e.g. Ca2+ and SO42�) are not

considered in the present simulations owing to their low concen-trations in the concrete specimen. The ionic transport parametersemployed in this numerical study are listed in Table 1, and the ini-tial and boundary conditions are shown in Table 2 [72]. For theconditions shown in Table 2 and the aforementioned meshing set-tings, it takes almost one day to achieve one convergent result on aPC of 2.5 GHz quad-core processors and 16G RAM, depending onthe number of degree of freedom which is, for example, 0.98 mil-lion in the model shown in Fig. 2 (southeast).

4. Results and discussion

With given initial and boundary conditions, the five field vari-ables (i.e. electrostatic potential and concentrations of K+, Na+,Cl�, and OH�) in the simulated 3-phase concrete specimens canbe numerically calculated by solving the mass conservation equa-tion and the Poisson equation. The 3-D plots shown in Figs. 4 and 5provide a good visualized view of the evolution of the variables, inwhich the two plane coordinates represent the position of the 2-Dconcrete model with 50% volume fraction of various shaped aggre-gates, and the vertical coordinate is the results of the variable. Eachframe of an individual variable represents one unique momentduring the first 4 h of the simulated RCM test. It can be seen fromFig. 4 that when using Poisson’s equation to control the multi-species ionic transport, electrostatic potential increases fromU = 0 at the cathode to U = 24 V at the anode, but this relationshipis clearly not linear. It is interesting to note from the 3-D plot thatthe electrostatic potential curve varies from a convex shape afterthe first hour to a concave shape after the fourth hour. This meansthat initially migration speed of ionic species is higher in the regionnear the cathode, but over time the zone with higher ionic migra-tion speed moves to the anode. The results show that migrationspeed of chloride ions is not be constant and varies not only in timebut also in space.

In terms of the four ionic concentrations, because the penetra-tion of chloride ions and the effect of aggregate shape on it are ofparticular interest, only the distribution profiles of chloride con-

Table 1Ionic transport properties in different phases.

Field variables Potassium Sodium Chloride Hydroxide

Charge number 1 1 �1 �1Diffusion coefficient in aggregates, DA 0 0 0 0Diffusion coefficient in bulk mortar, DB, � 10�10 m2/s 1.96 1.33 2.03 5.26Diffusion coefficient in ITZs, DI � 10�10 m2/s 9.80 6.65 10.15 26.30

Table 2Initial and boundary conditions of individual species.

Field variables Potassium Sodium Chloride Hydroxide Electrostatic potential

Concentration boundary conditions, mole/m3 x = 0 0 520 520 0 0x = L 0 300 0 300 24 V

Flux boundary conditions y = 0 J = 0 J = 0 J = 0 J = 0 әU/әy = 0y = L J = 0 J = 0 J = 0 J = 0 әU/әy = 0

Initial conditions, mole/m3 t = 0 200 100 0 300 0

Fig. 4. Electrostatic potential distribution profiles (for aggregates with mixedshapes).

Fig. 5. a. Concentration distribution profiles of chloride ions (for aggregates with acircular shape). Concentration distribution profiles of chloride ions (for aggregateswith an elliptical shape). Concentration distribution profiles of chloride ions (foraggregates with a triangular shape). Concentration distribution profiles of chlorideions (for aggregates with a rectangular shape). Concentration distribution profilesof chloride ions (for aggregates with mixed shapes).


centration are shown in the form of a 3-D plot in Fig. 5. With thesame aggregate volume fraction, the evolution of ionic transportin the models with elliptical, triangular, rectangular and mixedshape aggregate particles is very similar to that in the circularaggregate model which has been validated against experimentaldata [64]. The negatively charged chloride ions are driven steadilyfrom the cathode towards the anode in the migration process alongthe x-axis, which can be observed through the visible ‘migrationwave front’. It can also be seen from the figures that the migrationwave fronts of chloride ions are split into sections by the imperme-able aggregate particles, which makes the wave front act like a ‘wa-terfall’. Generally, the moving velocity of the wave front ‘waterfall’is almost the same along the y-axis, apart from in the model usingtriangular shaped aggregate, as shown in Fig. 5c. This phenomenoncan be explained by the effect of tortuosity. The sharp angles of thetriangular shape significantly increase the length of the flow pathand create a lot of local corner pockets in the electrolyte solution,which slows down the transport of ions in corresponding areas.

For a more quantitative study, Figs. 6–9 employ traditional 2-Dplots to show comparisons of the concentration profiles of four

ionic species with five different aggregate shapes. Consideringthe results of the different ionic species, as a result of the nonlinearelectrostatic potential gradient, the ionic species coupling can beobserved by the similar migration speed of the same charged ions.Considering the results of different aggregate shapes, it is clear thatthere is only a tiny difference in the migration velocities betweenthe models with the ‘‘obtuse” shapes (i.e. circular, elliptical andrectangular), which gives a similar tortuosity. In contrast, fromthe overall point of view, the migration velocities with the modelusing triangular aggregate are the lowest among the five differentmodels, which is mainly due to the higher tortuosity.

More interesting features can be found upon closer examinationof the curves of the mixed shape model. As mentioned above, thedifferent shaped aggregates are deliberately arranged to be lessuniformly distributed (the small sized particles gather more nearthe cathode side, and the larger ones gather more near the anode

Fig. 5. dFig. 5. b

Fig. 5. cFig. 5. e


side). The tortuosity of this model is correspondingly less uniform(with higher tortuosity in the area near the cathode, and lower tor-tuosity in the area near the anode). As a consequence, the speed ofthe migration wave front of the negatively charged ions (Cl� andOH�) in the mixed shape model is much slower than that in themodels using circular, elliptical and rectangular aggregates in thesection from x = 0 m to x = 0.025 m, but it is a little higher than thatin the triangular shape model. In the section from x = 0.025 m tox = 0.05 m, close to the anode, the speed of the migration wavefront of the negatively charged ions in the mixed shape model ismuch higher than that in the triangular shape model, and is nearlythe same as the results in the obtuse shape models. Governed bythe electrochemical multi-species coupling, the results for the pos-itively charged ions (K+ and Na+) show exactly the opposite trend.The phenomenon discussed above clearly shows how the tortuos-ity (caused by aggregate size) regionally affects ionic transport inconcrete.

The above findings show that under the condition of identicalvolume fraction but with different aggregate distribution scenar-ios, the effect of aggregate shape has a significant impact on ionicmigration. The aggregate particles lead to higher tortuosity of con-crete in the triangular shape model, but in the circular, ellipticaland rectangular shape models the aggregate shape has littleimpact, leading to lower tortuosity of concrete in these cases. Inter-estingly, this phenomenon is similar to what happened in Abya-neh’s model [46,47]. The triangle aggregate herein acts like thetri-axial ellipsoidal and oblate spheroidal aggregates of higheraspect ratios. This shows that the tortuosity effect can play signif-icant roles in both 2-D migration and 3-D penetration/diffusionmodels. To further demonstrate this finding, more examples areprovided here of different aggregate particle shapes with variousvolume fractions (ranging from 0% to 50%). Figs. 10–12 show thecomparisons of different shapes under the aggregate volume frac-tions of 30%, 40% and 45%, respectively. As expected, the earlier

Fig. 6. Comparisons of potassium concentration profiles for different aggregateshapes, Vagg = 0.5.

Fig. 7. Comparisons of sodium concentration profiles for different aggregateshapes, Vagg = 0.5.

Fig. 8. Comparisons of chloride concentration profiles for different aggregateshapes, Vagg = 0.5.

Fig. 9. Comparisons of hydroxide concentration profiles for different aggregateshapes, Vagg = 0.5.


observations from the simulations under the condition of identicalvolume fraction of aggregate can be seen in simulations withdifferent volume fractions of aggregate. Figs. 10–12 again showthat the migration velocities of chloride ions are approximatelyidentical when comparing the models with various shapes, apartfrom in the model using triangular aggregates, which leads to asignificantly higher tortuosity. Moreover, by referring to the resultsunder the condition of different volume fractions of aggregates (i.e.50%, 45%, 40% and 30%), it can be found that the effect of aggregateshape increases with the aggregate volume fraction. Note that theaggregates of mixed shapes in the models with 30%, 40% and 45%fractions are randomly distributed. Therefore, the special phe-nomenon caused by the tortuosity difference which occurs inFigs. 6–9 disappears in Figs. 10–12.

Fig. 13 shows the distribution profiles of Cl� concentration com-paring three different aggregate volume fractions. As expected, thesmaller the aggregate volume fraction is, the quicker the chloride

ions travel. This is likely to be due to the tortuosity effect. As theaggregate volume fraction increases, tortuosity gets higher, thusthe ionic transport slows down. However, due to the presence ofthe ITZ phase (in which the ions travel much faster than in bulkmortar), the discrepancy in the results between different volumefractions is not so remarkable. It can be seen that the higher aggre-gate volume fraction is also accompanied by a higher ITZ volumefraction. It can also be seen by careful examination of the influenceof aggregate shape, as shown in the concentration profiles(Figs. 8 and 13), that the impact of aggregate shape appears to bemore significant than the effect of their volume fractions. Forexample, the variation in velocity between circular and triangularshapes is greater than that between 30% and 50% volume fractions;the variation in velocity between the other three shapes is alsoclose to that between the 40% and 50% volume fractions. Thesefindings clearly emphasise the significance of exploring the aggre-gate shape effect on ionic electro-migration in multi-phase models.



Fig. 13. Comparisons of chloride concentration profiles for different volumefractions (circular aggregates).



5. Conclusions

This paper presents a numerical investigation into the transportfeatures of chloride migration in concrete composite based on a 3-phase model, which considers various shapes (both spheroidal andpolygon) and volume fractions of aggregates. The model also con-siders ionic interactions, ionic binding, the non-steady state pro-cess and external voltage, to simulate a multi-componenttransport process during RCM testing. From this study the follow-ing conclusions can be drawn:

1) The proposed multi-phase, multi-component transportmodel provides a promising tool for demonstrating thetransport features, such as how ionic concentration changesin concrete and how individual phases behave while chlo-rides penetrate the concrete composites. In this model, theelectrostatic potential gradient, which is also the dominantsource of ionic transport, is no longer linear, but varies notonly in time but also in space.

2) The 2-D concentration distribution profiles show that theirregular tortuosity caused by various shaped aggregateswill markedly influence the length of the flow paths of ionsas well as the ionic diffusivity. In addition, the distributionscenario of coarse aggregates will also have an impact onionic transport.

3) Under the condition of identical volume fraction of aggre-gates, the effect of aggregate shape has significant impacton the ionic migration rate when the aggregate shapes havehigher tortuosity, whereas it has little impact when theaggregate shapes have lower tortuosity.

4) Under the condition of different volume fractions of aggre-gates, the effect of aggregate shape increases with the aggre-gate volume fraction.

5) The comparison between the effects of shape and volumefraction suggests that, in addition to the volume fractionof aggregates, the aggregate morphology is also animportant factor to consider in modelling the concretecomposites.


Acknowledgements

The work was supported by the Natural Science Foundation ofChina (51508324), the Shanghai Pujiang Program, China(15PJ1403800) and the Shanghai Chenguang Program, China(16CG06). The third author would also like to thank the supportfrom the Natural Science Foundation of China (51408537) andthe Key Project Supported by Zhejiang Provincial Natural ScienceFoundation of China (LZ16E080002).

References

[1] Bazant ZP. Physical model for steel corrosion in concrete sea structures—theory. J Struct Div 1979;105:1155–66.

[2] Yan F, Lin Z. Bond durability assessment and long-term degradation predictionfor GFRP bars to fiber-reinforced concrete under saline solutions. ComposStruct 2017;161:393–406.

[3] Atkinson A, Nickerson AK. The diffusion of ions through water-saturatedcement. J Mater Sci 1984;19:3068–78.

[4] Hobbs DW. Aggregate influence on chloride ion diffusion into concrete. CemConcr Res 1999;29:1995–8.

[5] Garboczi EJ. Permeability, diffusivity, and microstructural parameters: acritical review. Cem Concr Res 1990;20(4):591–601.

[6] Brakel JV, Heertjes PM. Analysis of diffusion in macroporous media in terms ofporosity, a tortuosity and a constrictivity factor. Int J Heat Mass Transf 1974;17(9):1093–103.

[7] Garboczi EJ, Bentz DP. Analytical formulas for interfacial transition zoneproperties. Adv Cem Based Mater 1997;6(3–4):99–108.

[8] Xu K, Daian JF, Quenard D. Multiscale structures to describe porous media partII: transport properties and application to test materials. Transp Porous Media1997;26(3):319–38.

[9] Xi Y, Bazant ZP. Modeling chloride penetration in saturated concrete. J MaterCiv Eng 1999;11:58–65.

[10] Byung HO, Seung YJ. Prediction of diffusivity of concrete based on simpleanalytical equations. Cem Concr Res 2004;34(3):463–80.

[11] AASHTO T 259. Standard method of test for resistance of concrete to chlorideion penetration. American Association of States Highway and TransportationOfficials. Washington; 2003.

[12] ASTM C1543. Standard Test Method for Determining the Penetration ofChloride Ion into Concrete by Ponding. ASTM International. WestConshohocken, PA; 2010.

[13] Amidi S, Wang J. Deterioration of the FRP-to-concrete interface subject tomoisture ingress: effects of conditioning methods and silane treatment.Compos Struct 2016;153:380–91.

[14] Whiting D. Rapid measurement of the chloride permeability of concrete.Public Roads 1981;45(3):101–12.

[15] Li H, Xiao H, Guan X, Wang Z, Yu L. Chloride diffusion in concrete containingnano-TiO2 under coupled effect of scouring. Compos B 2014;56:698–704.

[16] AASHTO T 277. Standard method of test for rapid determination of the chloridepermeability of concrete. American Association of States Highway andTransportation Officials. Washington; 1983.

[17] ASTM C 1202. Standard test method for electrical indication of concrete’sability to resist chloride ion penetration. American Society for Testing andMaterials. Philadelphia; 1994.

[18] Won JP, Yoon YN, Hong BT, Choi TJ, Lee SJ. Durability characteristics of nano-GFRP composite reinforcing bars for concrete structures in moist and alkalineenvironments. Compos Struct 2012;94:1236–42.

[19] Su HL, Yang J, Ling TC, Ghataora G, Dirar S. Properties of concrete preparedwith waste tyre rubber particles of uniform and varying sizes. J Cleaner Prod2015;91:288–96.

[20] Miyandehi BM, Feizbakhsh A, Yazdi MA, Liu QF, Yang J, Alipour P. Performanceand properties of mortar mixed with nano-CuO and rice husk ash. CementConcr Compos 2016;74:225–35.

[21] Tang L, Nilsson LO. Rapid determination of the chloride diffusivity in concreteby applying an electric field. ACI Mater J 1993;89(1):49–53.

[22] NT-Build 492. Nordtest method: concrete, mortar and cement-based repairmaterials: chloride migration coefficient from non-steady-state migrationexperiments; 1999.

[23] AASHTO TP 64-03. Standard method of test for prediction of chloridepenetration in hydraulic cement concrete by the rapid migration procedure.American Association of State Highway and Transportation Officials.Washington; 2003.

[24] Bernard F, Kamali-Bernard S. Predicting the evolution of mechanical anddiffusivity properties of cement pastes and mortars for various hydrationdegrees – A numerical simulation investigation. Comput Mater Sci2012;61:106–15.

[25] Alberti MG, Enfedaque A, Galvez JC, Reyes E. Numerical modelling of thefracture of polyolefin fibre reinforced concrete by using a cohesive fractureapproach. Compos B 2017;111:200–10.

[26] Bentz DP, Garboczi EJ. Percolation of phases in a three-dimensional cementpaste microstructural model. Cem Concr Res 1991;21(2–3):325–44.

[27] Bourdette B, Ringot E, Ollivier JP. Modeling of the transition zone porosity. CemConcr Res 1995;25(4):741–51.

[28] Garboczi EJ, Bentz DP. Multiscale analytical/numerical theory of the diffusivityof concrete. Adv Cem Based Mater 1998;8(2):77–88.

[29] Yang CC, Weng SH. A three-phase model for predicting the effective chloridemigration coefficient of ITZ in cement-based materials. Mag Concr Res2013;65(3):193–201.

[30] Caré S. Influence of aggregates on chloride diffusion coefficient into mortar.Cem Concr Res 2003;33(7):1021–8.

[31] Caré S, Hervé E. Application of a n-phase model to the diffusion coefficient ofchloride in mortar. Transp Porous Media 2004;56(2):119–35.

[32] Zeng YW. Modeling of chloride diffusion in hetero-structured concretes byfinite element method. Cement Concr Compos 2007;29:559–65.

[33] Zheng JJ, Wong HS, Buenfeld NR. Assessing the influence of ITZ on the steady-state chloride diffusivity of concrete using a numerical model. Cem Concr Res2009;39:805–13.

[34] Sun G, Zhang Y, Sun W, Liu Z, Wang C. Multi-scale prediction of the effectivechloride diffusion coefficient of concrete. Constr Build Mater2011;25:3820–31.

[35] Xiao J, Ying J, Shen L. FEM simulation of chloride diffusion in modeled recycledaggregate concrete. Constr Build Mater 2012;29:12–23.

[36] Jiang JY, Sun GW, Wang CH. Numerical calculation on the porosity distributionand diffusion coefficient of interfacial transition zone in cement-basedcomposite materials. Constr Build Mater 2013;39:134–8.

[37] Ying J, Xiao J, Shen L, Bradford MA. Five-phase composite sphere model forchloride diffusivity prediction of recycled aggregate concrete. Mag Concr Res2013;65(9):573–88.

[38] Li LY, Xia J, Lin SS. A multi-phase model for predicting the effective diffusioncoefficient of chlorides in concrete. Constr Build Mater 2012;26(1):295–301.

[39] Zheng JJ, Zhou XZ, Wu YW, Jin XY. A numerical method for the chloridediffusivity in concrete with aggregate shape effect. Constr Build Mater2012;31:151–6.

[40] Caporale A, Feo L, Luciano R. Damage mechanics of cement concrete modeledas a four-phase composite. Compos B 2014;65:124–30.

[41] Wang L, Bao J, Ueda T. Prediction of mass transport in cracked-unsaturatedconcrete by mesoscale lattice model. Ocean Eng 2016;127:144–57.

[42] Liu QF, Li LY, Easterbrook D, Li D. Prediction of chloride diffusion coefficients inconcrete using meso-scale multi-phase transport models. Mag Concr Res2017;69:134–44.

[43] Abyaneh SD, Wong HS, Buenfeld NR. Simulating the effect of microcracks onthe diffusivity and permeability of concrete using a three-dimensional model.Comput Mater Sci 2016;119:130–43.

[44] de Larrard T, Bary B, Adamc E, Kloss F. Influence of aggregate shapes on dryingand carbonation phenomena in 3D concrete numerical samples. ComputMater Sci 2013;72:1–14.

[45] Li X, Xu Y, Chen S. Computational homogenization of effective permeability inthree-phase mesoscale concrete. Constr Build Mater 2016;121:100–11.

[46] Abyaneh SD, Wong HS, Buenfeld NR. Computational investigation of capillaryabsorption in concrete using a three-dimensional mesoscale approach.Comput Mater Sci 2014;87:54–64.

[47] Abyaneh SD, Wong HS, Buenfeld NR. Modelling the diffusivity of mortar andconcrete using a three-dimensional mesostructure with several aggregateshapes. Comput Mater Sci 2013;78:63–73.

[48] Lankard DR, Slatter JE, Holden WA, Niest DE. Neutralization of chloride inconcrete, FHWA Report No. FHWA-RD-76-6, Battelle Columbus Laboratories;1975.

[49] Narsillo GA, Li R, Pivonka P, Smith DW. Comparative study of methods used toestimate ionic diffusion coefficients using migration tests. Cem Concr Res2007;37:1152–63.

[50] Johannesson B, Yamada K, Nilsson LO, Hosokawa Y. Multi-species ionicdiffusion in concrete with account to interaction between ions in the poresolution and the cement hydrates. Mater Struct 2007;40:651–65.

[51] Samson E, Marchand J. Modeling the transport of ions in unsaturated cement-based materials. Comput Struct 2007;85:1740–56.

[52] Krabbenhoft K, Krabbenhoft J. Application of the poisson-nernst-planckequations to the migration test. Cem Concr Res 2008;38:77–88.

[53] Xia J, Li LY. Numerical simulation of ionic transport in cement paste under theaction of externally applied electric field. Constr Build Mater 2013;39:51–9.

[54] Liu QF, Li LY, Easterbrook D, Yang J. Multi-phase modelling of ionic transport inconcrete when subjected to an externally applied electric field. Eng Struct2012;42:201–13.

[55] Jensen MM, Johannesson B, Geiker MR. Framework for reactive masstransport: Phase change modeling of concrete by a coupled mass transportand chemical equilibrium model. Comput Mater Sci 2014;92:213–23.

[56] Li LY, Page CL. Modelling and simulation of chloride extraction from concreteby using electrochemical method. Comput Mater Sci 1998;9:303–8.

[57] Frizon F, Lorente S, Ollivier JP, Thouvenot P. Transport model for the nucleardecontamination of cementitious materials. Comput Mater Sci2003;27:507–16.

[58] Truc O, Ollivier JP, Nilsson LO. Numerical simulation of multi-species transportthrough saturated concrete during a migration test–MSDIFF code. Cem ConcrRes 2000;30:1581–92.

[59] Wang Y, Li LY, Page CL. A two-dimensional model of electrochemical chlorideremoval from concrete. Comput Mater Sci 2001;20:196–212.


[60] Toumi A, Francois R, Alvarado O. Experimental and numerical study ofelectrochemical chloride removal from brick and concrete specimens. CemConcr Res 2007;37:54–62.

[61] Liu Y, Shi X. Ionic transport in cementitious materials under an externallyapplied electric field: Finite element modeling. Constr Build Mater2012;27:450–60.

[62] Šavija B, Lukovic M, Schlangen E. Lattice modeling of rapid chloride migrationin concrete. Cem Concr Res 2014;61–62:49–63.

[63] Liu QF, Xia J, Easterbrook D, Yang J, Li LY. Three-phase modeling ofelectrochemical chloride removal from corroded steel-reinforced concrete.Constr Build Mater 2014;70:410–27.

[64] Liu QF, Easterbrook D, Yang J, Li LY. A three-phase, multi-component ionictransport model for simulation of chloride penetration in concrete. Eng Struct2015;86:122–33.

[65] Liu QF, Yang J, Xia J, Easterbrook D, Li LY, Lu XY. A numerical study on chloridemigration in cracked concrete using multi-component ionic transport models.Comput Mater Sci 2015;99:396–416.

[66] Feng GL, Li LY, Kim B, Liu QF. Multiphase modelling of ionic transport incementitious materials with surface charges. Comput Mater Sci2016;111:339–49.

[67] Li LY, Easterbrook D, Xia J, Jin WL. Numerical simulation of chloridepenetration in concrete in rapid chloride migration tests. Cement ConcrCompos 2015;63:113–21.

[68] Geng J, Easterbrook D, Liu QF, Li LY. Effect of carbonation on release of boundchlorides in chloride-contaminated concrete. Mag Concr Res 2016;68:353–63.

[69] Tang L, Nilsson LO. Chloride binding capacity and binding isotherms of OPCpastes and mortars. Cem Concr Res 1993;23:247–53.

[70] Bentz DP, Garboczi EJ, Lu Y, Martys N, Sakulich AR, Weiss WJ. Modeling of theinfluence of transverse cracking on chloride penetration into concrete. CementConcr Compos 2013;38:65–74.

[71] Johannesson B. Comparison between the Gauss’ law method and the zerocurrent method to calculate multi-species ionic diffusion in saturateduncharged porous materials. Comput Geotech 2010;37:667–77.

[72] Yang CC, Cho SW. The relationship between chloride migration rate forconcrete and electrical current in steady state using the accelerated chloridemigration test. Mater Struct 2004;37:456–63.

[73] Diamond S, Huang JD. The ITZ in concrete – a different view based on imageanalysis and SEM observations. Cement Concr Compos 2001;23:179–88.

[74] Gao JM, Qian CX, Liu HF, Wang B, Li L. ITZ microstructure of concretecontaining GGBS. Cem Concr Res 2005;35:1299–304.

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