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by Alkali-Silica ReactionStéphane Multon, Ph.D.1; Jean-François Seignol, Ph.D.2; and François Toutlemonde, Ph.D.3

Abstract: The alkali-silica reaction �ASR� is a chemical reaction that causes expansions and unexpected deformations of concretestructures. A methodology of assessment of ASR-damaged structures is required in order to evaluate their structural stability. Chemome-chanical calculations have been performed in order to investigate the assumption of modeling ASR-induced expansions as imposedstrains. The input data for the model comprises the moisture distribution in the damaged structures, ASR-induced potential strains, and theinfluence of ASR on the concrete mechanical properties. The results of calculations have been compared with experimental data obtainedfrom ASR-damaged beam specimens. The role of water supply and reinforcement has been analyzed in comparing the deformations ofplain and reinforced concrete beams subjected to a moisture gradient. Calculations show that cracking and compressive stresses �hereinduced by steel reinforcement� have a large influence on the anisotropy of the ASR swellings. This induced anisotropy is shown to be oneof the main factors that should be considered while predicting the mechanical behavior of ASR-damaged structures.

DOI: XXXX

CE Database subject headings: Anisotropy; Durability; Concrete, reinforced; Gradient; Concrete beams.

Introduction

A significant number of civil engineering structures �bridges, roadpavements, dams, etc.� are damaged by the alkali-silica reaction�ASR�. This chemical reaction between alkalis and certain sili-ceous aggregate, containing reactive particles, causes expansionsin concrete and large cracking and deformations in structures.Determining the consequences of such a reaction is of great prac-tical significance for the owners of ASR-damaged civil engineer-ing structures. The magnitude and time-evolution of ASR-inducedstrains depend on: �1� reactive compound content �alkali and re-active silica�; �2� environmental conditions �temperature, relativehumidity �RH�� �Olafsson 1986�; �3� water supply �Larive 1998;Larive et al. 2000b�; and �4� stress conditions due either to me-chanical loading �Larive et al. 1996; Gravel et al. 2000; Multon2004; Multon et al. 2004� or to restraint of ASR expansion pro-vided by the steel reinforcement �Swamy and Al-Asali 1990; Fanand Hanson 1998; Monette et al. 2002; Multon et al. 2005�.

Moreover, ASR expansions appear to be highly anisotropic de-pending on the casting direction �Clark 1991; Larive 1998; Lariveet al. 2000a; Smaoui 2003�. The consequences of ASR on con-crete mechanical properties are still debated and appear to bedifferent depending on the nature of the reactive aggregate. Someauthors observed a decrease in all the mechanical properties�Pleau et al. 1989; Smaoui 2003� while others found that concretemixtures exhibited mostly a decrease in the Young’s modulus�Larive 1998; Monette et al. 2002�. Models developed to predictthe structural behavior of such damaged structures �Ulm et al.2000; Li and Coussy 2002; Capra and Sellier 2003� take intoaccount most of these phenomena. However the ASR anisotropyand the effect of stresses on ASR expansions are still not perfectlydescribed by these predictive models.

The aim of the present research was to investigate the possi-bility of modeling ASR expansions as imposed strains that dependon the concrete mix-design and environmental conditions as de-scribed in the thermohydrochemomechanical model developed byUlm et al. �2000� and Li and Coussy �2002�. In this approach, therequired external input data are the temperature and the moistureconditions �determined by in situ measurements�. The ASR-induced strains are computed knowing the potential expansiondue to the concrete mix-design �measured by residual expansiontests �Bérubé et al. 2002��. The merit of this method is the sim-plicity in obtaining the input data. The thermohydro calculationsuse already validated models �Maingy et al. 1999�. The aim ofthis paper is to validate the chemomechanical part of the struc-tural assessment method according to chemoelastic calculationsbased on the strength of materials assumptions, by comparisonwith experimental data obtained on damaged beams in Multon�2004� and Multon et al. �2005�. The effects of water supply andreinforcement on ASR-induced strains have been studied bothexperimentally and numerically, focusing on induced expansionanisotropy.

1Graduate Teacher, Dept. of Civil Engineering, INSA/LMDC, 135,Ave de Rangueil, 31077 Toulouse Cedex, France. E-mail: multon@insa-toulouse.fr

2Research Engineer, LCPC, 58, Bld. Lefebvre, 75732 Paris, Cedex 15,France. E-mail: seignol@lcpc.fr

3Head of Structural Laboratory, Professor of Research Engineering,LCPC, 58, Bld. Lefebvre, 75732 Paris, Cedex 15, France. E-mail:toutlemo@lcpc.fr

Note. Associate Editor: Kolluru V. Subramaniam. Discussion openuntil January 1, 2007. Separate discussions must be submitted for indi-vidual papers. To extend the closing date by one month, a written requestmust be filed with the ASCE Managing Editor. The manuscript for thispaper was submitted for review and possible publication on July 19,2004; approved on July 6, 2005. This paper is part of the Journal ofMaterials in Civil Engineering, Vol. 18, No. 4, August 1, 2006. ©ASCE,ISSN 0899-1561/2006/4-1–XXXX/$25.00.

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Chemoelastic Approach

Parameters

Temperature has an accelerating effect on ASR expansion, but itdoes not affect the range of expansion. The effects on kinetics canbe modeled by the Arrhenius law �Larive 1998; Ulm et al. 2000�.Because the effect of temperature has already been studied�Ulm et al. 2000�, it was not chosen as a parameter for this study.

The effect of water supply on the range of ASR swellings iscommonly known �Olafsson 1986; Larive et al. 2000b�. Realstructures are submitted to drying, resulting in moisture gradients,and differential water supply. Such conditions lead to differentialexpansions between the parts submitted to high moisture contentand the parts submitted to drying. Models have to predict thesignificant consequences of such moisture gradients on the struc-tural behavior of ASR-damaged structures. Moreover, compres-sive stresses appear to reduce ASR expansions along the mostcompressed direction �Larive et al. 1996; Gravel et al. 2000;Multon 2004; Multon et al. 2004�. Compressive stresses can ei-ther be caused by mechanical loading of the structure, or inducedby the presence of steel reinforcement �Swamy and Al-Asali1990; Fan and Hanson 1998; Monette et al. 2002�. The role ofwater supply and compressive stresses in ASR expansion is in-vestigated in this paper.

Experiments on Reactive Beams

An experimental program is used in this paper to validatecalculations �Multon 2004; Multon et al. 2005�. These experimen-tations were carried out on 3-m-long, 0.25-m-thick, and 0.50-m-high simply supported beam specimens �with a 2.80 m span; Fig.1�. The beams were submitted to a vertical moisture gradientobtained by original environmental conditions in order to studythe effect of water on ASR expansion. The lower parts of thebeams were immersed in water while the upper faces were ex-posed to air at 30% RH �Fig. 1�. The lateral faces were sealedusing a watertight cover. This vertical moisture gradient led tostrain gradients �with shrinkage in the upper part and large ASR

expansions in the bottom� and thus to flexural deflections. Bothplain and reinforced concrete beams �using rebars with a500 MPa yield stress� were monitored in the program �Table 1�.All the specimens were exposed to a constant 38°C environmentfor about one year, leading to significant expansions after somemonths.

Modeling Methodology

Because temperature was kept constant, calculations are based onthree input variables: �1� the water distribution in the structures;�2� the potential ASR-induced strains �depending on moistureconditions�; and �3� the �possibly time-dependent� concrete me-chanical properties. The distribution of ASR-induced strains inthe whole structure was determined by using the first two inputdata. This distribution of chemical strains can be used as theinitial imposed strains in the equations of strength of materials�equilibrium of plane cross sections� to predict the behavior of thethree reactive beams. Experimental measurements provide for theinput data: water distribution was measured on the beams, poten-tial ASR-induced strains were obtained on companion standardspecimens, and the evolution of mechanical properties was char-acterized at different times. Experimental results also provide forthe strains and deflections necessary to validate the models.

Input Data

Imposed strains depend on moisture distribution in the damagedstructures and on the response of reactive concrete to these localmoisture conditions.

Table 1. Characteristics of Three ASR-Damaged Beams

Beams Lower reinforcement Upper reinforcement

B1 None None

B3 2 ribbed #16 bars �d=0.450 m� 2 ribbed #10 bars �d�=0.045 m�B4 2 ribbed #32 bars �d=0.420 m� 2 ribbed #20 bars �d�=0.050 m�

Fig. 1. Environmental conditions of three beams

Fig. 2. Profiles of mass variation along height of beams

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Moisture Distribution in ASR-Damaged BeamsWater movements in the beams were produced by the environ-mental boundary shown in Fig. 1. Moisture distribution can bedescribed by profiles of mass variations �Fig. 2� as follows: �1�mass increase due to water absorption in the bottom of the beams;�2� mass variations lower than the accuracy of the measurementdevice and hence assumed as null in the middle part of the beam;and �3� mass loss due to drying in the upper 140 mm, measuredusing a gammadensitometry device �Multon and Toutlemonde2004; Multon et al. 2005�. The profiles of mass variation wereobtained considering the penetration of water in the bottom part

of the beam as an idealized imbibition front propagating as thesquare root of time, as described in Hall �1989�, with a meansorptivity S of about 6 .10−3 m·day−1/2.

ASR-Induced Potential ExpansionFollowing Larive et al. �2000b� in using the mass variations dueto water supply as the influent parameter, Fig. 3 shows the massvariation and the strains of the concrete mixture under three mois-ture conditions at 38°C: in water, sealed under watertight alumi-num cover, and in air at 30% RH. Shrinkage is observed for largemass losses and expansion for mass increase or mass losses lowerthan 1%. Therefore, it has been assumed in the following calcu-lations that shrinkage occurred for concrete with mass losseshigher than 1% and ASR expansions occurred for concrete withmass losses lower than 1%. It can be observed in Fig. 3 that thelarger the water supply, the larger the ASR-induced expansions, asalready shown in Larive et al. �2000b�. These expansions mea-sured on specimens have been directly used in the following cal-culations, as explained subsequently.

Expansion measurements presented in Fig. 3 were performedon six specimens, cast from the same batch and stored in the sameenvironment. The standard deviation �Fig. 3� is still high in spiteof the similarity of the specimens. This can be explained by theheterogeneous repartition of the reactive silica inside the lime-stone aggregate �Larive 1998; Larive et al. 2000a�. Moreover, themeasurements were carried out along two perpendicular direc-tions relative to the casting direction. The ASR expansionsshowed anisotropy; expansions along the casting direction weretwice as large as along the perpendicular direction �Clark 1991;Larive 1998; Larive et al. 2000a; Smaoui 2003�.

Imposed Strains DistributionImposed strains distribution in the beams �Fig. 4� is determinedby combining the input data on the moisture distribution �Fig. 2�and ASR-induced potential expansion �Fig. 3� as described here-after:• ASR-induced strains �wat are measured on specimens kept in

water. They are representative for concrete within the im-mersed part, or reached by the water penetration:

zwat � z � h ⇒ �imp�t,z� = �wat�t� �1�

where zwat=h− �0.07+S�t� represents the depth of the imbibi-tion front.

• ASR-expansions ��m=0 are representative for concrete with-out mass variation and are obtained from measurements onspecimens kept in water and under aluminum. The expansions

Fig. 3. �a� Mass variation and �b� potential expansion of reactiveconcrete

Fig. 4. Profile of imposed strains along height of beams

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are calculated by assuming proportionality between the ASRexpansions and the mass variations �Larive 1998; Larive et al.2000b�. Fig. 5 shows how to obtain the following equation tocalculate the imposed strain in concrete without massvariation:

zd � z � zwat

⇒ �imp�t,z� = ��m=0�t� = �wat�t� −�wat�t� − �seal�t�

��m

m�

wat�t� − ��m

m�

seal�t�

�2�

• ASR expansions �seal measured on sealed specimens are usedfor concrete with mass losses lower than 1% as explainedpreviously:

zshr � z � zd ⇒ �imp�t,z� = �seal�t� �3�

• The profile of imposed strains is assumed to be linear with thedepth for concrete with mass losses higher than 1% �Fig. 4�.Shrinkage at the upper face �shr is taken as proportional to themass variation �Torrenti et al. 1999� and equal to zero at zshr

�depth where the mass variation is equal to −1%�. The rela-tionship between mass losses and shrinkage was deduced frommeasurements performed on specimens kept in air at 30% RHas presented in Fig. 3

�shr��m

m� = 0.013

�m

m+ 0.007 �4�

The equation of the straight line representing the shrinkagestrain �Fig. 4� can be deduced from the drying depth zshr �obtainedin Fig. 2� and the drying shrinkage �shr��m /m� �Eq. �4��

0.0 � z � zshr ⇒ �imp��m

m� = �shr��m

m� �− z + zshr�

zshr�5�

In this part, the shrinkage-induced strains are considered as im-posed strains.

Mechanical PropertiesMechanical properties were measured at five time steps during theexperimental program �Multon 2004; Multon et al. 2005�. Com-pressive and tensile strengths had the same evolution as for non-reactive concrete, as already observed in Larive �1998� and Mon-ette et al. �2002� with compressive and splitting tensile strengths

of about 38 and 3 MPa. The concrete Young’s modulus at 28 daysafter casting is equal to 37,300 MPa. It is constant during the first60 days of exposure, decreases about 20% between 60 and 150days, and stays equal to 30,100 MPa during the following year�Multon 2004; Multon et al. 2005�. The reduction can be ex-plained by the initiation of ASR cracks. Predictive models shouldtake into account the decrease in the Young’s modulus.

Chemoelastic Calculation

Longitudinal strain measurements carried out on the beams showthat the plane cross sections remained plane during the wholeexperiment, as shown in Fig. 6 for Beam B1 and reported for thethree beams in Multon �2004� and Multon et al. �2005�. Thus, thebeams fulfill Navier-Bernoulli’s assumption, and calculations ac-cording to strength of materials hypotheses can be used.

Strength of MaterialsChemoelastic calculations have been performed to predict theflexural behavior of the ASR-damaged beams. Strains due to self-weight of the structures �about 5 �m/m� can be neglected ascompared to shrinkage and chemically induced strains �between500 and 2,500 �m/m�. The equations of equilibrium of the planecross sections for reinforced concrete beams are

�N�t� =�0

h

��t,z� · b · dz + A�s�t,d� + A��s�t,d�� = 0

Mf�t� =�0

h

��t,z� · z · b · dz + dA�s�t,d� + d�A��s�t,d�� = 0�6�

with A , A� , d, and d� given in Table 1.Shrinkage and ASR-induced strains are assumed to be im-

posed strains. In the elastic range, the chemoelastic concrete con-stitutive law reads:

��t,z� = Ec�t� · ���t,z� − �imp�t,z�� �7�

where Ec stands for concrete equivalent Young’s modulus for longterm calculations.

Fig. 5. Imposed strains interpolated from measurements onspecimens kept in water and under aluminum for concrete withoutmass variation

Fig. 6. Plane cross sections of plain concrete beam �B1� duringexperiment

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T For long term calculations, it is necessary to take into consid-

eration the delayed strains due to concrete creep. The ratio be-tween the delayed and instantaneous strains for this concrete mix-ture was estimated at about 3 �determination from long termloaded specimens �Multon 2004; Multon et al. 2004��. An equiva-lent long term Young’s modulus can be obtained by dividing by 4the “instantaneous” Young’s modulus measured on specimens.

Because plane cross sections remained plane during the wholeexperiment, longitudinal strains read

��t,z� = �0��t� · z + �0�t� �8�

where �0��t� and �0�t� are two unknown variables. Assuming per-fect bond between the concrete and the reinforcement steel, stress

in the lower �Eq. �9�� and upper reinforcing bars �Eq. �10�� read

�s�t;d� = Es��0�d + �0� �9�

�s�t;d�� = Es��0�d� + �0� �10�

with Es=200,000 MPa.At each time step, Eq. �11� derives from Eqs. �6�–�10� �with

n=Es /Ec�

��0��h2

2+

n

b�dA + d�A��� + �0�h +

n

b�A + A��� =�

0

h

�imp�z�dz = IN

�0��h3

3+

n

b�d2A + d�2A��� + �0�h2

2+

n

b�dA + d�A��� =�

0

h

�imp�z� · z · dz = IM �11�

where IN and IM derive from Eqs. �1�–�4�:

�IN = �wat�h − zwat� + ��m=0�zwat − zd� + �seal�zd − zshr� +zshr · �shr

2

IM =�wat

2�h2 − zwat

2 � +��m=0

2�zwat

2 − zd2� +

�seal

2�zd

2 − zshr2 � +

zshr2 · �shr

6 �12�

where zd=depth of the drying front �m�; zshr=depth along whichshrinkage occurred �m�; and zwat=depth reached by the waterpenetration �m�.

Eq. �11� has been numerically solved for every time step, andthus the structural behavior of the ASR-damaged beams has beenpredicted from the input data �moisture distribution, ASR-inducedpotential expansion, and mechanical evolution of concrete�. Be-cause the cross sections remained plane during the whole experi-ment, the longitudinal behavior of the beams can be described byonly two variables, for instance, by the longitudinal strain at thedepth of 0.23 m and the midspan deflection. These experimentaldata can be compared to the calculated ones:

��0.23� = 0.23�0� + �0 �13�

dms = �0� ·l2

8�14�

Accuracy of Calculations

The uncertainty of the calculations results from uncertainty con-cerning the moisture distribution and from the large scatter in theASR-induced strains measured on the specimens. For the depth ofthe drying front zd, accuracy is related to the resolution of thegammadensitometry device �uzd=0.01 m�. For the depth of waterpenetration zwat, accuracy is related to the uncertainty of the sorp-tivity S�uS=1.5�10−3 m·day−1/2�. For the ASR-induced strains,the heterogeneity of ASR expansion is significantly larger thanthe measurement accuracy. Accuracy can be taken as equal to thestandard deviation of shrinkage and the ASR-induced strain val-ues measured on the specimens �Fig. 3�. Uncertainty of the cal-culations can thus be estimated by derivation of the formulascorresponding to solving Eq. �11�. For the strains at a depth of0.23 m, thus reads:

u��z� =�� ���z���wat

uwat�2

+ � ���z����m=0

u�m=0�2

+ � ���z���shr

ushr�2

+ � ���z��S

uS�2

+ � ���z��zd

uzd�2

�15�

The same calculation can be carried out for the midspan deflection. This uncertainty is represented as the half-height of the intervalaround the computed value in Figs. 7, 9, 11, and 13.

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Structural Assessment of Plain Concrete Beam

Calculation 1: Effect of Casting Directionon Anisotropy

The anisotropy of ASR expansions is commonly observed relativeto the casting direction �Clark 1991; Larive 1998; Larive et al.2000a; Smaoui 2003�. For the beams studied, the longitudinaldirection was perpendicular to the casting direction. Eq. �12� hasbeen solved for the plain concrete beam �A=A�=0� with the as-sumption that ASR-induced strains were equal to the strains mea-sured on specimens perpendicular to the casting direction. Thepredicted values of mean strain and midspan deflection show agood agreement with the measurements performed on the beamduring the first 150 days �Fig. 7�. The structural behavior afterthis period is not correctly predicted. It had to be noted that crack-ing of the beam was observed on the immersed part 160 daysafter the beginning of measurement �Fig. 8�. The initiation ofcracking of the immersed face can be considered as predicted bythe chemomechanical calculations, because tensile stresses calcu-lated in the lower part of the beam reach 4 MPa after 150 days.Eq. �7� should not be used in the cracked concrete. Cracks causeddiscontinuities in concrete and thus a reduction of the section ofthe beam. Preliminary calculations were carried out to calculatethe height of the cracked part and thus to determine the reduction

of the section of the beam. However, observations showed thatthe cracks were filled by ASR gel. The ASR gel kept on swellingand pushed on the two faces of cracks. Preliminary calculationsthat did not consider the cracked part also neglected the ASRexpansions in this part and did not lead to satisfactory agreementin computing postcracking evolution. After these preliminary cal-culations, it was assumed that Eq. �7� could be used in spite ofcracking. This computation is shown in Calculation 2.

Calculation 2: Effect of Cracking on Anisotropy

ASR-induced cracking of specimens is mainly perpendicular tothe casting direction, and the larger ASR expansions have alwaysbeen measured perpendicular to cracks �Clark 1991; Larive 1998;Larive et al. 2000a�. This can be explained by the intrinsic aniso-tropy of concrete, which would favor the opening of horizontalcracks. The formation of ASR gels would then be favored in thesehorizontal cracks, which would cause larger expansions along thedirection perpendicular to the cracks �Larive 1998; Larive et al.2000a�. Observations on the present beam prove that most of thecracks were in transverse direction �Fig. 8�. Larger ASR-imposedstrains could have occurred along the cracked part of the beam.New calculations have thus been performed with the assumptionthat imposed strains were equal to strains measured on specimensperpendicular to the casting direction in the whole beam, exceptin the cracked part. In this part, imposed strains have been takenas equal to the largest strains �measured along the casting direc-tion�. The effect of cracking is thus included in the calculation byconsidering the anisotropy of ASR expansions induced by theinitiation of cracks. Because cracks were first observed after 160days and reached a depth between 0.04 and 0.10 m at 425 days, alinear time evolution of the cracked height has been assumed tocarry out the calculations between 150 and 425 days, first with afinal cracked height of 0.04 m �Calculation 2a�, then with a finalcracked height of 0.10 m �Calculation 2b�. The stiffness is modi-fied following the evolution of the measured Young’s modulusdescribed hereafter. Calculations taking into account the effect ofcracking on ASR anisotropy show better agreement, especiallywith respect to midspan deflection �Fig. 7�b��. This illustrates that

Fig. 7. �a� Measured and calculated strain at depth of 0.23 m; and �b�midspan deflection of plain concrete beam �B1� assuming thatanisotropy depends on casting direction �Calculation 1� and takinginto account the effect of cracking direction on anisotropy�Calculations 2a and 2b�

Fig. 8. Cracking of plain concrete and reactive beam �B1�, central1 m-part: �a� lateral face; �b� lower immersed face

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ASR models should consider this phenomenon. However, themean strain was hardly better predicted �Fig. 7�a��, and furtherassumptions were studied.

Calculation 3: Isotropy for Concretewithout Cracking

Taking into account the effect of cracking on ASR anisotropy, itappears to be more realistic to consider isotropic expansion in thepart of the beam where little cracking takes place, and largerexpansion in the cracked part. The isotropic potential expansionhas been evaluated from the strains measured on the specimens�Fig. 3� as reported in Seignol et al. �2004�

�iso =�cast_dir + 2�perp

3�15��

where �cast_dir=ASR expansion measured along the casting direc-tion; and �perp=expansion measured perpendicular to the castingdirection.

The ASR-imposed strains have been taken as equal to the iso-tropic expansion in the whole beam except for the cracked part. Inthe cracked part, imposed strains have been taken as equal to thestrains measured on the specimens along the casting direction. Alinear time evolution of the cracked height has been still assumedbetween 150 and 425 days with a final depth of cracking equal to0.04 m �which was measured along the main part of the cross

section�. This allows good predictions to be obtained �Fig. 9�,especially after 250 days. However, the predicted structural be-havior in the first 200 days is worse than for the previouscalculations.

Discussion 1 „Plain Concrete Beam…

Previous assumptions and calculations show that the anisotropymeasured on specimens cannot be used directly for structural cal-culations. However, the complex effects of cracking on ASR an-isotropy should be considered in order to predict the mechanicalbehavior of ASR-damaged structures. Calculation 3 is consistentwith observations performed on the beam. Indeed, it predicts ten-sile stresses higher than 3 MPa after 50 days, which explains thetransverse cracks observed on the upper face during the experi-ment �Multon et al. 2005�. It also predicts the cracking of thelower face with tensile stresses higher than 4 MPa in the bottomof the beam after 150 days. However, even if the structural be-havior can be simulated, the accuracy relative to the computeddeflection is about 0.70 mm for a 5.2 mm deflection �about 15%�,mainly due to the scatter in the ASR expansion.

Structural Assessment of Reinforced ConcreteBeams

Numerous papers have emphasized the reduction of the observedASR-induced strains due to reinforcing bars �Swamy andAl-Asali 1990; Fan and Hanson 1998; Monette et al. 2002�. Inthis part of the paper, the effect of reinforcing steel on the struc-tural behavior of the ASR-damaged reinforced beams is investi-gated and analyzed following the same strength of materialsmethodology.

Effect of Cracking Direction on ASR Anisotropy

The previous calculations have shown the influence of crackingdirection on ASR anisotropy in structures. In order to assess thestructural behavior of the tested reinforced concrete beams, twocalculations have been carried out:• The first calculation assumes that ASR expansion in the beam

is isotropic. Only the elastic effect of the steel reinforcement isconsidered.

Fig. 9. �a� Measured and calculated strain at depth of 0.23 m; and �b�midspan deflection of Plain Concrete Beam B1 taking into accountisotropic expansion in the whole beam except for cracked part

Fig. 10. Cracking of reinforced and reactive beam �B3�, central1 m-part: �a� lateral face; �b� lower immersed face

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• The second calculation takes into account the effect of crack-ing direction on ASR-imposed strains. For the reinforcedbeams, cracking was mainly longitudinal Fig. �10�. Imposedstrains have been taken as equal to the average isotropic valuein the whole beam except in the �bottom� cracked part. In thispart, imposed strains have been taken as equal to the ASRexpansions measured perpendicular to the casting direction�and thus parallel to the cracking direction�. Cracks appearedat 90 and 200 days for B3 and B4, respectively, and reachedmaximum depths estimated at 0.12 and 0.15 m. A linear time

evolution of the depth of cracking has been assumed betweenthe initiation of cracks and the 425th day, when the deforma-tions were stabilized.The system of Eq. �11� has been solved for the Reinforced

Beam B3 �with A, d, A�, and d� in Table 1�. The calculationsshow a bad prediction of its structural behavior �Fig. 11�, particu-larly for the midspan deflection, even when the effect of crackingon ASR anisotropy is taken into consideration. The structural be-havior of the reinforced beams thus cannot be explained only bythe elastic effect of reinforcing bars. A large decrease in the im-posed strains in the lower part of the beam appeared as a neces-sary cause of the observed behavior. This could be explained bythe effect of the compressive stresses around the reinforcing bars.

Effect of Compressive Stresses on ASR-InducedAnisotropy

Calculations of the stresses along the height of the beam �Eq. �7��show that two parts were subjected to significant compressions:�1� the immersed concrete, close to the lower reinforcing bars;and �2� the concrete at midheight �Fig. 12�. In the lower part, thecompressive stresses were caused by the confinement of ASRexpansions due to reinforcing steels. Whatever the imposedstrains, calculated compressive stresses were higher than 5 MPaafter about 50 days close to the reinforcing bars. Compressivestresses in the intermediate zone are mainly explained by theassumed discontinuous profile of imposed strains close to zd. In

Fig. 11. �a� Measured and calculated strain at depth of 0.23 m; and�b� midspan deflection of reinforced and reactive beam �B3�

Fig. 12. Profile of imposed strains and plane cross section at 150days for reinforced and reactive beam �B3�

Fig. 13. �a� Measured and calculated strain at depth of 0.23 m; and�b� midspan deflection of two reinforced and reactive beams �B3, B4�taking into account the effect of compressive stresses

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T reality, the imposed strains should be more continuous in thispart. This could cause a diminution of these compressive stresses.Moreover, this zone is smaller than the first one. Therefore, thecompressive stresses in the concrete at midheight are neglected inthe subsequent calculation. While unsatisfactory for predictivecalculations, this allows the effect of compression stresses onstructural behavior of ASR-damaged beams to be investigated.

Compressive stresses higher than 5 MPa may largely reduceASR expansions along the compressed direction due either tomechanical loading �Larive et al. 1996; Gravel et al. 2000;Multon 2004; Multon et al. 2004� or to restraint of ASR expan-sion by steel reinforcement �Swamy and Al-Asali 1990; Fan andHanson 1998; Monette et al. 2002; Multon et al. 2005�. ASRexpansions are not only counteracted by the compressive stresses,they appear to be largely prevented in the compressed directions.Therefore, ASR-induced strains had been assumed to be signifi-cantly reduced in the compressed part. In order to assess simplythe structural behavior of the reinforced concrete beams, a reduc-tion factor ��� has been affected on the ASR-imposed strains inthe immersed part. Eq. �1� now becomes

h − �0.07 + S�t� � z � h ⇒ �imp�t,z� = � · �wat�t� �16�

This reduction factor has been determined for each beam to mini-mize the quadratic deviation between the calculated and measuredstrains at 0.23 m depth and midspan deflections. These calcula-tions show good agreement with the measurements using a reduc-tion factor of 0.45 and 0.30 for B3 and B4, respectively �standarddeviation of about 0.005% for the strain and 0.100 mm for thedeflection; Fig. 13�. This suggests that the compressive stressescaused a decrease in ASR-imposed strains of about 55 and 70%.The stresses in the reinforcing steels could be estimated to 160and 100 MPa for B3 and B4, respectively. This estimation ap-pears realistic, even if it could not be compared to direct mea-sures. It confirms that significant ASR-induced stresses in thesteel reinforcement should be accounted for in assessment ofASR-damaged structures.

Discussion 2 „Reinforced Concrete Beam…

For the plain concrete beam, these calculations cannot be consid-ered as predictive, because the behavior had to be known to de-termine the reduction factor. The analysis proves that not onlydoes steel reinforcement have the direct effect of “prestressing”the beams by restraining the expansions; but the compressivestresses due to local restraint by steels cause a reduction of ASR-induced expansion along the compressed direction as well. Re-duction may reach 50% even for a 0.45% reinforcement ratio�B3�. The accuracy relative to the computed deflections lies be-tween 0.5 and 0.7 mm for deflections of about 1.1 and 0.3 mm.This accuracy is mainly due to the heterogeneity of measuredASR expansions. The resulting scatter of calculated data is quiteconstant for all calculations �about 0.6 mm�. For the plain con-crete beam, this is only 15% of the measured deflection, but forthe reinforced beams, it is between 60 and 200% of the deflec-tions measured on the beams. This effect of ASR heterogeneity onpredictive calculations should not be ignored.

Finally, it is suggested that an isotropic ASR-induced straincould be taken as a basic input data. This “isotropic” data must beobtained by averaging the strains measured along the three direc-tions of standard specimens; for instance, it may account for axialand transverse expansions of cylinders. It should then be multi-plied by a factor corresponding either to a reduction �compressivestresses reduce ASR-induced strains along the compressed direc-

tion� or to an increase �tensile stresses induce cracks, which in-crease ASR expansion perpendicular to the cracking direction�.This factor is related to the local stress state, and structural as-sessments would be possible if it can be determined. One ap-proach is to try to determine the law linking the real ASR aniso-tropy in concrete to the local stress state. An attempt at directexperimental insight in determining this anisotropy factor, de-pending only on the stress deviator, is given in Multon �2004�;obtained values appear consistent with the fitted determinations of� �0.3–0.5� obtained in the present paper. Obviously, further in-vestigations are still necessary to validate such methods.

Conclusions

The concrete mixture, the environmental conditions, the potentialwater supply, and the stresses due to both mechanical loading andreinforced-induced restraint of ASR expansions are major param-eters to be considered while predicting the mechanical behaviorof ASR-damaged structures.

Predictive models using chemoelasticity concepts have stillnot solved how to take into consideration the effect of compres-sive stresses on ASR expansions. The development of concretecracking, the compressive stresses, and the effect of ASR-inducedstrains on the stresses within structures modify the directions offurther ASR-induced expansions and thus the ASR anisotropy.Therefore, iterative calculations appear to be necessary.

This paper proposes some modeling strategies to make predic-tive calculations. Ultimately, whatever the approach, ASR model-ing should take into consideration the effects of both cracking andcompressive stresses on ASR anisotropy for predicting the behav-ior of ASR-damaged structures.

Acknowledgments

The writers are pleased to thank S. Prené, H. Tournier, E. Bour-darot, A. Jeanpierre, and D. Chauvel �EDF� for their help inanalysis. They also thank particularly B. Godart and T. Kretz�LCPC� for their ideas for investigation.

Notation

The following symbols are used in this paper:A area of lower steel reinforcement �m2�;

A� area of upper steel reinforcement �m2�;b beams thickness �m�;d distance between center of gravity of lower steel

reinforcement and upper face of beam �m�;d� distance between center of gravity of upper steel

reinforcement and upper face of beam �m�;dms midspan deflection of beam �m�;Ec equivalent long term Young’s modulus for concrete

�MPa�;Es Young’s modulus of steel reinforcement �MPa�;h height of beam �m�;l span of beam �m�;

Mb bending moment �MN·m�;N axial force �N�;n Young’s modulus ratio �Es /Ec�;S sorptivity �m·day−1/2�;t time �day�;

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T z depth along height of beams �m�;

zd depth of drying front �m�;zshr depth along which shrinkage occurred �m�;zwat depth reached by water penetration �m�;

� reduction factor multiplying ASR-imposed strainsdue to compressive stresses;

�m /m relative mass variation;� strain;

�imp imposed strain;�s steel strain;� stress �MPa�; and

�s steel stress �MPa�.

References

Bérubé, M.-A., Duchesne, J., Dorion, J. F., and Rivest, M. �2002�. “Labo-ratory assessment of alkali contribution by aggregates to concrete andapplication to concrete structures affected by alkali-silica reactivity.”Cem. Concr. Res., 32�8�, 1215–1227.

Capra, B., and Sellier, A. �2003�. “Orthotropic modelling of alkali-aggregate reaction in concrete structures: Numerical simulations.”Mech. Mater., 35�8�, 817–830.

Clark, L. A. �1991�. “Modeling the structural effects of alkali-aggregatereaction on reinforced concrete.” Mat. J., 88�3�, 271–277.

Fan, S., and Hanson, J. M. �1998�. “Length expansion and cracking ofplain and reinforced concrete prisms due to alkali-silica reaction.”Struct. J., 95�4�, 480–487.

Gravel, C., Ballivy, G., Khayat, K., Quirion, M., and Lachemi, M.�2000�. “Expansion of AAR concrete under triaxial stresses: Simula-tion with instrumented concrete block.” Proc., 11th Int. Conf. on AAR,Centre de Recherche Interuniversitaire sur le Béton, Quebec, Canada,949–958.

Hall, C. �1989�. “Water sorptivity of mortars and concretes: A review.”Mag. Concrete Res., 41�147�, 51–61.

Larive, C. �1998�. “Apports combinés de l’expérimentation et de lamodélisation à la compréhension de l’alcali-réaction et de ses effetsmécaniques.” Rep. OA 28, ERLPC Collection, Laboratoire Central desPonts et Chaussées, Paris �in French�.

Larive, C., Joly, M., and Coussy, O. �2000a�. “Heterogeneity and aniso-tropy in ASR-affected concrete: Consequences for structural assess-ment.” Proc., 11th Int. Conf. on AAR, Centre de Recherche Interuni-versitaire sur le Béton, Quebec, Canada, 969–978.

Larive, C., Laplaud, A., and Coussy, O. �2000b�. “The role of water inalkali-silica reaction.” Proc., 11th Int. Conf. on AAR, Centre de Re-cherche Interuniversitaire sur le Béton, Quebec, Canada, 61–70.

Larive, C., Laplaud, A., and Joly, M. �1996�. “Behavior of AAR-affected

concrete: Experimental data.” Proc., 10th Int. Conf. on AAR, A.Shayan, ed., Melbourne, Australia, 670–677.

Li, K., and Coussy, O. �2002�. “Concrete ASR degradation: From mate-rial modeling to structure assessment.” Concr. Sci. Eng., 4�13�,35–46.

Maingy, M., Coussy, O., and Eymard, R. �1999�. “Modélisation destransferts hydriques isothermes en milieu poreux: Application auséchage des matériaux à base de ciment.” Rep. OA 32, ERLPC Col-lection, Laboratoire Central des Ponts et Chaussées, Paris �in French�.

Monette, L. J., Gardner, N. J., and Grattan-Bellew, P. E. �2002�. “Re-sidual strength of reinforced concrete beams damaged by alkali-silicareaction: Examination of damage rating index method.” Mat. J.,99�1�, 42–50.

Multon, S. �2004�. “Evaluation expérimentale et théorique des effets del’alcali-réaction sur des structures modèles.” Rep. OA 46, ERLPCCollection, Laboratoire Central des Ponts et Chaussées, Paris �inFrench�.

Multon, S., Leclainche, G., Bourdarot, E., and Toutlemonde, F. �2004�.“Alkali-silica reaction in specimens under multi-axial mechanicalstresses.” Proc., CONSEC’04, B. H. Oh, et al., eds., Seoul NationalUniv., Seoul, Korea, 2004–2011.

Multon, S., Seignol, J.-F., and Toutlemonde, F. �2005�. “Structural behav-ior of concrete beams affected by ASR.” Mat. J., 102�2�, 67–76.

Multon, S., and Toutlemonde, F. �2004�. “Water distribution in concretebeams.” Mater. Struct., 37�270�, 378–386.

Olafsson, H. �1986�. “The effect of relative humidity and temperature onalkali expansion of mortar bars.” Proc., 7th Int. Conf. on AAR, Noyes,Park Ridge. N.J., 461–465.

Pleau, R., Bérubé, M. A., Pigeon, M., Fournier, B., and Raphael, S.�1989�. “Mechanical behavior of concrete affected by ASR.” Proc.,8th Int. Conf. on AAR, Elsevier, London, 721–726.

Seignol, J.-F., Barbier, F., Multon, S., and Toutlemonde, F. �2004�. “Nu-merical simulation of ASR-affected beams, comparison to experimen-tal data.” Proc., 12th Int. Conf. on AAR, International Academic,Beijing, China, 198–206.

Smaoui, N. �2003�. “Contribution à l’évaluation du comportement struc-tural des ouvrages d’art affectés de réaction alcali-silice �RAS�.”Ph.D. thesis, Faculté des Sciences et de Génie de l’Université deLaval, Québec, Canada �in French�.

Swamy, R. N., and Al-Asali, M. M. �1990�. “Control of alkali-silicareaction in reinforced concrete beams.” Mat. J., 87�1�, 38–46.

Torrenti, J.-M., Granger, L., Diruy, M., and Genin, P. �1999�. “Modelingconcrete shrinkage under variable ambient conditions.” Mat. J.,96�1�, 35–39.

Ulm, F.-J., Coussy, O., Kefei, L., and Larive, C. �2000�. “Thermo-chemo-mechanics of ASR expansion in concrete structures.” J. Eng. Mech.,126�3�, 233–242.

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