Kein de 2014

This article was downloaded by: [University of Saskatchewan Library]On: 18 March 2015, At: 23:57Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Click for updates

European Journal of Environmental andCivil EngineeringPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/tece20

Effect of the interfacial transition zoneand the nature of the matrix-aggregateinterface on the overall elastic andinelastic behaviour of concrete undercompression: a 3D numerical studyDame Keindeab, Siham Kamali-Bernarda, Fabrice Bernarda &Ibrahima Cisseb

a Laboratoire GCGM, Institut National des Sciences Appliquées,Université Européenne de Bretagne, Rennes, Franceb Ecole Supérieure Polytechnique de Dakar, Département GénieCivil, Dakar, SénégalPublished online: 17 Mar 2014.

To cite this article: Dame Keinde, Siham Kamali-Bernard, Fabrice Bernard & Ibrahima Cisse(2014) Effect of the interfacial transition zone and the nature of the matrix-aggregate interfaceon the overall elastic and inelastic behaviour of concrete under compression: a 3D numericalstudy, European Journal of Environmental and Civil Engineering, 18:10, 1167-1176, DOI:10.1080/19648189.2014.896757

To link to this article: http://dx.doi.org/10.1080/19648189.2014.896757

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.

This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Dow

nloa

ded

by [

Uni

vers

ity o

f Sa

skat

chew

an L

ibra

ry]

at 2

3:57

18

Mar

ch 2

015

Effect of the interfacial transition zone and the nature of thematrix-aggregate interface on the overall elastic and inelasticbehaviour of concrete under compression: a 3D numerical study

Dame Keindea,b, Siham Kamali-Bernarda*, Fabrice Bernarda and Ibrahima Cisseb

aLaboratoire GCGM, Institut National des Sciences Appliquées, Université Européenne deBretagne, Rennes, France; bEcole Supérieure Polytechnique de Dakar, Département Génie Civil,Dakar, Sénégal

(Received 11 October 2013; accepted 7 February 2014)

A 3D numerical model is developed to study the elastic and inelastic behaviour ofconcrete with consideration of the interfacial transition zone and the nature of thematrix – aggregate interface. Concrete is represented as a bi-phasic or tri-phasicmaterial, consisting of spherical aggregates embedded in a matrix (mortar) surroundedor not by a transition zone. The matrix–aggregates interface is modelled taking intoaccount a perfect contact and a sliding one. Numerical elastic modelling results are ina good agreement with those obtained by Hashin and Monteiro analytical model.Numerical results of the overall behaviour modelling show a slight influence of thetransition zone on the mechanical behaviour of concrete. In contrast, a significantinfluence of the nature of the matrix – aggregate contact is demonstrated andexplained based on local analysis of stress distribution in the material.

Keywords: concrete; modelling; ITZ; sliding; compression; elastic modulus

1. Introduction

Concrete is usually represented as a matrix with inclusions representing aggregates sur-rounded by an interfacial transition zone (ITZ). The presence of this zone was proposedin 1953 by Farran according to microscopic investigations (Farran, 1953). This zone iscreated due to the wall effect generated by the aggregates (which is a limitation in thepacking of cement particles in the vicinity of the aggregates). Cohen, Goldman, andChen (1994) showed that the transition zone can have a significant volume and higherporosity, and hence lower mechanical properties than the bulk matrix. Consequently, theelastic modulus and mechanical strength of mortar and concrete can be affected. More-over, the nature of the aggregates strongly influences the quality of the transition zone.Limestone aggregates develop a stronger transition zone because of the chemical reac-tions that occur over time with the matrix. The increase in the strength of concrete withreactive aggregates was also observed by Malier (1992) whereas weak adherence andno change in time were found for siliceous aggregates. Other researchers were interestedto evaluate the influence of ITZ properties on the overall mechanical behaviour of mor-tar and concrete using analytical models. However, these models are limited to elasticcalculations and do not take into account the possible sliding between the cement pasteor mortar and aggregates. The objective of this paper is to investigate and quantify the

*Corresponding author. Email: [email protected]

© 2014 Taylor & Francis

European Journal of Environmental and Civil Engineering, 2014Vol. 18, No. 10, 1167–1176, http://dx.doi.org/10.1080/19648189.2014.896757

Dow

nloa

ded

by [

Uni

vers

ity o

f Sa

skat

chew

an L

ibra

ry]

at 2

3:57

18

Mar

ch 2

015

effect of two situations on the elastic modulus and inelastic behaviour of concrete underunidirectional compressive test. The first situation corresponds to the presence of a por-ous transition zone and the second one to the existence of sliding with friction betweenaggregates and the matrix.

For this purpose, 3D computational concrete with a realistic aggregate concentrationis simulated using Abaqus software. For the first case (presence of ITZ), the numericalconcrete is simulated as a three-phase composite material composed of aggregate sur-rounded by an ITZ, all are embedded in a matrix of mortar. The numerical results arethen discussed and the elastic ones compared with those obtained by the analyticalmodel of Hashin and Monteiro (2002). For the second case (sliding with frictionbetween aggregate and the matrix), the numerical concrete is simulated using two-phasematerial composed of aggregate and a matrix of mortar with a possible sliding betweenthe two phases. The mechanical results are then compared to those obtained with a per-fect contact (no sliding). The significant or non-significant effect of the presence of atransition zone or friction between aggregates and the matrix is then explained based onlocal analysis of stress distribution in the material.

2. Strategy of simulation

An ordinary concrete with a water-to-cement ratio equal to .4 and aggregatesconcentration equal to 35% by volume is considered. The aggregates are assumed to bespherical with 10 mm of diameter. A template material with a granular structurecharacterised by the repetition of a unit cell is established to control the position of thedifferent phases. In the following, the methodology adopted to obtain the numericalconcretes taking into account the presence of ITZ or a non-perfect contact betweenaggregates and matrix and their mechanical behaviour under compression are developed.

2.1. Simulation of concrete considering the presence of ITZ

In this case, concrete is considered as a three-phase material composed of aggregates,matrix (here the mortar) and a transition zone. The material is modelled with a cubewhere the matrix is modelled with several compartments holes. The matrix and the tran-sition zone are geometrically modelled using a single phase which is then partitionedinto two parts. The transition zone is modelled with 3D eight nodes linear continuumshell elements. In order to accurately compute the state of stresses through the thicknessa shell section integrated during analysis, which is also preferable in case of non-linearbehaviour, has been chosen. The Simpson’s integration rule with five integration pointsis considered. A dedicated sensitivity analysis on the number of integration pointsrevealed that increasing this number has insignificant influence on the homogenisedstress–strain curve of the composite material. The various components are then meshedand assembled as shown in Figures 1 and 2. Two values of transition zone thickness areconsidered: 50 and 100 μm. Different cube volumes are simulated in order to identifythe representative volume element (RVE).

2.2. Simulation of concrete considering the presence of a sliding between theaggregates and the matrix

In this case, concrete is considered as a two-phase material composed of aggregates anda matrix (here the mortar). Coulomb’s law is used to model the contact between the

1168 D. Keinde et al.

Dow

nloa

ded

by [

Uni

vers

ity o

f Sa

skat

chew

an L

ibra

ry]

at 2

3:57

18

Mar

ch 2

015

aggregates and the matrix. The presence of a transition zone is neglected. Differentcoefficients of friction were tested.

2.3. Simulation of compressive test and materials properties

To simulate a 1D compression test, a vertical displacement of .25 mm on the upper faceof the numerical cube of concrete is applied. The vertical displacement of the lower faceis blocked. The other faces are free. The mechanical behaviour of the aggregates isassumed to be purely elastic while the matrix and the transition zone follow a damagedplasticity law. The continuum, plasticity-based damage model proposed by Lubliner,Oliver, Oller, and Oñate (1989) and extended by Lee and Fenves (1998) is used torepresent their mechanical behaviours. This model is used in conjunction with a regular-isation method based on the definition of a characteristic length in order to alleviatestrain localisation effects and then mesh dependency. The characteristic length is basedon the element geometry and, for solid elements, is equal to the cube root of the inte-gration point volume. This constitutive model, also known as the Barcelona model, iswidely used in the literature. More information on the model may be found in Abaqus(2009), or more briefly in Krour, Bernard, and Tounsi (2013).

To complete the definition of the constitutive model, it is necessary to provide theevolution of the compressive stress according to the inelastic strain. These outcomes arehere taken directly from the compressive 1D stress–strain curve given by the CEB-FIPmodel (1990). The tensile behaviour is represented with a smeared crack approach andthe evolution of the post-peak stress is implemented as a tabular function of the

Figure 1. Meshes representing the matrix and the transition zone before (left) and after addingthe aggregate (right).

Figure 2. Methodology used to simulate the three-phase concrete.

European Journal of Environmental and Civil Engineering 1169

Dow

nloa

ded

by [

Uni

vers

ity o

f Sa

skat

chew

an L

ibra

ry]

at 2

3:57

18

Mar

ch 2

015

displacement across the crack (crack opening distance). The CEB-FIP model is anothertime considered. Finally, only the compressive strength (Rc) of the two phases (matrix,ITZ) are input data. All the other parameters can be deduced from this value.

For a considered concrete, the elastic modulus and compressive strength values ofthe matrix should be different when a transition zone is considered or not. Indeed, inorder to properly take into account the presence of a more porous ITZ, it is important totake into account the reduction of the porosity far from this zone. For this purpose,Dridi’s formula (2008) is used to determine the porosity of the matrix and that of theITZ from the one of the matrix when no ITZ is considered (Equation (1)). Then Bernardand Kamali-Bernard’s (2012) formula, resulting from a hierarchical multi-scale strategy,is used to calculate the new Rc values of matrix according to the new values of porosity(Equation (2)).

/matrix ¼ /pasteVmatrix þ VITZ

Vmatrix þ aVITZ

� �and a ¼ /ITZ

/matrixwith a 2 ½1:5; 2� (1)

where ϕmatrix: porosity of the paste when a transition zone is considered; ϕpaste: porosityof the paste with absence of a transition zone; ϕITZ: porosity of transition zone; Vb: vol-ume of the matrix and VITZ: volume of transition zone.

Rc ¼ 95:19 � ð1� /pasteÞ2:595 (2)

In Equation (2), Rc and the factor 95.19 are expressed in MPa. This formula is only avail-able for the considered mortar (made with a CEM I 42.5 cement and a w/c ratio of .4).For this study, the porosity of the cement paste is considered equal to 17.6%. This valuewas taken from previous studies on the modelling of cement pastes with w/c equal to .4(Kamali-Bernard & Bernard, 2009, 2011). The mechanical properties data used innumerical simulations are resumed in Table 1.

3. Modelling results

3.1. Effect of ITZ on elastic and non-elastic mechanical behaviour

3.1.1. Identification of the RVE

The question of the existence of the RVE for softening materials, such as concrete, is acurrent important topic (Gitman, Askes, & Sluys, 2007; Phu Nguyen, Lloberas-Valls,Stroeven, & Johannes Sluys, 2010). To address this controversial issue, various numeri-cal samples containing the same aggregates concentration have been considered. In the

Table 1. Values of the material properties using in the simulations (porosities calculated fromEquation (1) with α = 2. Rc and E deduced from Equation (2) and CEB-FIP model).

Aggregates Matrix without ITZ

Matrix with ITZdepth=100 μm

Matrix with ITZdepth=50 μm

VITZ/Vmatrix =8.81%

VITZ/Vmatrix =4.13%

Matrix ITZ Matrix ITZ

υ .2 .27 .27 .27 .27 .27Porosity (%) – 17.60 16.07 32.14 17.20 34.4E (GPa) 80 45.65 46.02 18.61 45.74 17.56Rc (MPa) – 57.60 60.42 34.80 58.33 31.87

1170 D. Keinde et al.

Dow

nloa

ded

by [

Uni

vers

ity o

f Sa

skat

chew

an L

ibra

ry]

at 2

3:57

18

Mar

ch 2

015

following, these numerical samples are defined by their edge size-to-aggregates diameterratio (L/D): 1.1, 2.2, 3.3, 5.5, 6.6, 7.7 and 8.8. A plot of homogenised normal compres-sive stress–strain diagrams is given in Figure 3. For such a compression test, it appearsthat the size of the RVE of the template material can be identified on the pre-peak partof the previous curve as well as in the softening one. However, these sizes are different:if an L/D ratio of 2.2 seems to be sufficient to well capture the Young’s modulus andthe compressive strength of the composite material, a ratio of 5.5 is more appropriatefor the softening behaviour. A large part of the softening behaviour can nevertheless bewell predicted with L/D ratio of 3.3 which corresponds to a cube of 33 × 33 × 33 mm.

The reason, usually cited, why the RVE cannot be found is that the material losesstatistical homogeneity upon strain localisation. This phenomenon is probably moreproblematic during tensile loading than for compressive one which is characterised bythe appearance of micro-cracks everywhere inside the sample and followed by the coa-lescence in several main cracks and not only one. The larger the sample is, the largerthe number of cracks is.

3.1.2. Elastic modulus – comparison with an analytical model

In order to check the validity of the proposed modelling strategy, the evolution of theYoung’s modulus according to the EITZ/Emat ratio has been compared to the predictionof the Hashin and Monteiro analytical three-phase model (2002).

In the literature, it is stated that the elastic modulus of the ITZ is in between 30 and50% of the matrix one (Ramesh, Sotelino, & Chen, 1996) and its thickness is about50 μm (Zohdi & Wriggers, 2001). The same authors estimated the modulus of elasticityof concrete using a volume fraction of the transition zone of 10%. Lee and Park (2008)used a volume fraction of about 1–7%. In this study the elastic modulus of the transitionzone is used in the range of 10–90% that of the matrix and the volume fraction of ITZused is equal to 4.13% (50 μm).

The evolution of the Young’s modulus according to the EITZ/Emat ratio given by themodelling and compared to Hashin and Monteiro analytical three-phase model has been

Figure 3. Effect of the L/D ratio on the homogenised stress–strain curve in compression.

European Journal of Environmental and Civil Engineering 1171

Dow

nloa

ded

by [

Uni

vers

ity o

f Sa

skat

chew

an L

ibra

ry]

at 2

3:57

18

Mar

ch 2

015

reported on Figure 4. Here, EITZ and Emat stand for the Young’s modulus of the transi-tion zone and the matrix (mortar), respectively.

Analytical and numerical results are coincident, especially for EITZ/Emat > .4. Theyshow that the higher the quality of the transition zone is, the lower is the loss in theelastic modulus of concrete and vice versa. However, this influence seems to be low.The small discrepancy observed for EITZ/Emat < .4 may be attributed to the lower accu-racy of the homogenisation analytical models when the contrasts between the mechani-cal properties of the components are great.

3.1.3. Stress–strain curves for various values of α= ϕITZ/ϕmat and ITZ volume

Figure 5 presents the numerical stress–strain curves of the composite material for fourvalues of ITZ porosity to matrix porosity ratio α:1 (without ITZ), 1.5, 1.75 and 2.

Young’s modulus (MPa)

Analytical modelling [HAS02]

Numerical modelling

Figure 4. Evolution of the Young’s modulus according to the EITZ/Emat ratio, numerical model-ling results compared to Hashin and Monteiro’s analytical three phases model ones.

Figure 5. Numerical stress–strain curves for various values of α.

1172 D. Keinde et al.

Dow

nloa

ded

by [

Uni

vers

ity o

f Sa

skat

chew

an L

ibra

ry]

at 2

3:57

18

Mar

ch 2

015

Figure 6 presents the result for two values of ITZ volume (4.13 and 8.81% obtained,respectively, with an ITZ thickness of 50 and 100 μm) and for α = 2. Very slight differ-ences between all these results are put into evidence showing the weak influence of theITZ on the homogenised compressive behaviour.

3.2. Effect of friction on the overall mechanical behaviour

The aim of this section is to investigate the effect of the aggregates – matrix contact onthe overall compressive behaviour of concrete neglecting the transition zone. TheCoulomb’s law is used to model this contact and various friction coefficients μ areconsidered. These coefficients are mainly dependent of the roughness of the aggregatessurface. The results of the simulation of a compression test, in terms of elastic modulusfor various values of μ, are provided in Table 2.

The whole stress–strain curves are plotted in Figure 7. It appears that a non-perfectcontact decreases significantly the Young’s modulus as well as the compressive strength.The lower the friction coefficient is, the lower these two mechanical characteristics are.After Gu, Hong, Wang, and Lin (2013), the range of values of the friction coefficientfor conventional aggregates is μ = .5–.8. For μ = .5, when compared to a perfect contact,the decreases of E and Rc, are respectively, 42 and 48%. The evolution of the norma-lised normal stress along a line which crosses all the phases is drawn in Figure 8 for aperfect contact and a sliding one. This result provides an explanation of the decreases: itis observed that the mechanical contribution of the matrix becomes higher than theaggregates one with a sliding contact, whereas it is the opposite for a perfect contact. Inthe first case, the aggregates do not offer all their mechanical contribution.

Figure 6. Numerical stress–strain curves for two ITZ volumes.

Table 2. Young’s modulus for various values of the friction coefficient. The value for a perfectcontact is 55500MPa.

μ .1 .15 .2 .25 .3 .4 1 2 4 5E (MPa) 37683 38264 38857 39461 40075 41330 46762 51295 52474 52523

European Journal of Environmental and Civil Engineering 1173

Dow

nloa

ded

by [

Uni

vers

ity o

f Sa

skat

chew

an L

ibra

ry]

at 2

3:57

18

Mar

ch 2

015

Figure 7. Numerical compressive stress–strain curves for various friction coefficients.

Aggregate

Matrix

2

1

2

1

Figure 8. Evolution of the normal stress and the corresponding stress maps inside the RVE for aperfect contact (down) and a sliding one between aggregate and matrix (top).

1174 D. Keinde et al.

Dow

nloa

ded

by [

Uni

vers

ity o

f Sa

skat

chew

an L

ibra

ry]

at 2

3:57

18

Mar

ch 2

015

4. Conclusion

The effect of the presence of a transition zone and the influence of the nature of thematrix – aggregate interface on the overall elastic and inelastic behaviour of concreteunder compression are investigated. For this purpose, a 3D numerical model using finiteelement methods is developed. Concrete is represented as a bi-phasic or tri-phasic mate-rial composed of spherical aggregates, matrix (mortar) and a transition zone. Matrix –aggregate interface is modelled taking into account a perfect contact and contact withfriction. A RVE analysis shows that a cube with L/D ≥ 3.3 is a REV for 1D compres-sive test simulations. The elastic numerical results are comparable to those obtainedwith the analytical model of Hashin and Monteiro. The proposed model makes it possi-ble to obtain the overall stress–strain curves. Simulation results show a slight influenceof the transition zone of the aggregates on the overall behaviour of concrete in compres-sion. However, a significant influence of the nature of the matrix – aggregate contact isdemonstrated when friction between the matrix and the aggregate is taken into account.This influence is quantified by varying the coefficient of friction. A local analysis of thestress distribution in the composite material has helped to explain the results.

ReferencesAbaqus (v6.9). (2009). User’s manual – Part V: Materials.Bernard, F., & Kamali-Bernard, S. (2012). Predicting the evolution of mechanical and diffusivity

properties of cement pastes and mortars for various hydration degrees – A numerical simula-tion investigation. Computational Materials Science, 61, 106–115.

Comité Euro-International du Béton (CEB), CEB-FIP model code 1990: Design code. (1990).Lausanne: Thomas telford services.

Cohen, M. D., Goldman, A., & Chen, W. F. (1994). The role of silica fume in mortar: Transitionzone vs. bulk paste modification. Cement and Concrete Research, 24, 95–98.

Dridi, W. (2008). Analytical modeling of the coupling between microstructure and effective diffu-sivity of cement-based materials. In E. Schlangen & G. De Schutter (Eds.), Proceedings ofInternational RILEM Symposium – CONMOD 08 (pp. 233–241). Deft: RILEM.

Farran, J. (1953). Sur l’adhérence entre ciments et matériaux enrobés [About the adherencebetween cement and embedded materials]. Comptes-Rendus de l’académie des Sciences(pp. 73–76). France: Académie des sciences.

Gitman, I. M., Askes, H., & Sluys, L. J. (2007). Representative volume: Existence and size deter-mination. Engineering Fracture Mechanics, 74, 2518–2534.

Gu, X., Hong, L., Wang, Z., & Lin, F. (2013). Experimental study and application of mechanicalproperties for the interface between cobblestone aggregate and mortar in concrete. Construc-tion and Building Materials, 46, 156–166.

Hashin, Z., & Monteiro, P. J. M. (2002). An inverse method to determine the elastic properties ofthe interphase between the aggregate and the cement paste. Cement and Concrete Research,32, 1291–1300.

Kamali-Bernard, S., & Bernard, F. (2009). Effect of tensile cracking on diffusivity of mortar: 3Dnumerical modelling. Computational Materials Science, 47, 178–185.

Kamali-Bernard, S., & Bernard, F. (2011). How to assess the long-term behaviour of a mortarsubmitted to leaching? European Journal of Environmental and Civil Engineering, 15,1031–1043.

Krour, B., Bernard, F., & Tounsi, A. (2013). Fibers orientation optimization for concrete beamstrengthened with a CFRP bonded plate: A coupled analytical–numerical investigation. Engi-neering Structures, 56, 218–227.

Lee, J., & Fenves, G. (1998). Plastic-damage model for cyclic loading of concrete structures.Journal of Engineering Mechanics, 124, 892–900.

Lee, K. M., & Park, J. H. (2008). A numerical model for elastic modulus of concrete consideringinterfacial transition zone. Cement and Concrete Research, 38, 396–402.

European Journal of Environmental and Civil Engineering 1175

Dow

nloa

ded

by [

Uni

vers

ity o

f Sa

skat

chew

an L

ibra

ry]

at 2

3:57

18

Mar

ch 2

015

Lubliner, J., Oliver, J., Oller, S., & Oñate, E. A. (1989). A plastic-damage model for concrete.International Journal of Solids and Structures, 25, 299–326.

Malier, Y. (1992). Les bétons à hautes performances: caractérisation, durabilité, applications[High performance concrete: Characterisation, durability and applications] (2ème éd., 673 p).Paris: Presses de l’E.N.P.C.

Phu Nguyen, V., Lloberas-Valls, O., Stroeven, M., & Johannes Sluys, L. J. (2010). On the exis-tence of representative volumes for softening quasi-brittle materials – A failure zone averagingscheme. Computer Methods in Applied Mechanics and Engineering, 199, 3028–3038.

Ramesh, G., Sotelino, E. D., & Chen, W. F. (1996). Effect of transition zone on elastic moduli ofconcrete materials. Cement and Concrete Research, 26, 611–622.

Zohdi, T. I., & Wriggers, P. (2001). Computational micro–macro material testing. Archives ofComputational Methods in Engineering, 8, 131–228.

1176 D. Keinde et al.

Dow

nloa

ded

by [

Uni

vers

ity o

f Sa

skat

chew

an L

ibra

ry]

at 2

3:57

18

Mar

ch 2

015