1 INTRODUCTION

In common practice, it is usually assumed thatlinear visco-elasticity takes place for low loadlevels and that the instantaneous mechanicalbehaviour of concrete is elastic. For high loadlevels, deviation from linearity of the creepbehaviour of concrete is expected. Under highsustained loads, cracks grow and interact withvisco-elasticity. Some experimental and analyticalresults concerning non-linear creep can be found inthe literature (see among others Bazant, 1988,Gettu and Bazant 1992, Mazzotti and Savoia 2003,Rüsch et al. 1957, Rüsch 1958) but much remainsto be learned.

Modelling non linear creep of concrete is offundamental importance for severely loadedstructures as creep may decrease the materialstrength with increasing time. The evaluation of theresidual carrying capacity of structural componentsis a problem of growing importance for civilengineering structures such as nuclear powerplants. Actually, these structures are often exposedto high stresses for a long time, due to whatdamage develops. Therefore, the results arisingfrom short time tests cannot be considered a

sufficient basis for judging the safety of suchstructures and it is of great interest to devisemethods for evaluating their residual capacity.

This problem has drawn the attention of manyauthors, among them Rüsch and co-workers (1957,1958), who have carried out the first experimentsin order to determine the effect of continuousloading duration on the resistance and deflectionsof concrete specimens under compression tests.They found that the capacity of a structuresubjected to creep loads seems to be 70 to 80% ofthat observed in short time compression tests.

In the present paper, the main results of a set ofexperimental creep tests on concrete three pointsbend specimens at different load levels arepresented. The objective is to investigate the rangesof variation of the time response under constantload due to variations of the load level. For eachcreep test, a different load level has been applied,starting from low levels (36% of peak load) wherelinear visco-elasticity applies, to high levels (80%of peak load) where tertiary creep causing failure ata finite time can be observed.

Also, this paper deals with the evaluation of theresidual capacity of concrete after creep. ConcreteB11 used for the construction of the Civaux power

Creep load influence on the residual capacity of concrete structure:Experimental investigation

Mirvat Omar, Khalil Haidar, Ahmed Loukili, and Gilles Pijaudier-Cabot

R&DO, Institut de recherches en Génie civil et Mécanique, Ecole Centrale de Nantes,

BP 92101, F-44321 Nantes cedex 3, France

ABSTRACT: Recent experiences and results investigating flexural creep tests with various loading levelsare presented. The aim of the study is to analyse the influence of creep on the residual capacity of concretebeams. The load level effects on creep strain are also discussed. Results show that for bending beamssubjected to 60% of their load capacity during 40 days, the residual carrying capacity is reduced about20%. This effect is essentially due to drying creep. Basic creep experiments show that for high load levelsthere is a coupled effect between creep and damage as tertiary creep is observed. Acoustic emissionanalyses underline also that damage occurs during creep. These results, which include size effect fracturetests, may serve for the development and the validation of coupled creep-damage models.

Keywords: flexural creep, loading level, residual capacity, acoustic emission

plant in France and tested by Granger (1995) isbeing used in this experimental program.

2 FRACTURE AND CREEP TESTS

Experimental investigation on concrete B11 wasperformed, involving fracture properties, as well asthe visco-elastic behaviour of concrete via creeptests. The experimental program aimed atdetermining the mechanical characteristics (e.g.tensile strength, compressive strength, fractureenergy) of concrete specimens, in order to performin a next step flexural creep tests on prismaticbending beams.

2.1 Mix proportions of concrete

All the specimens were made with a mix whichconsisted of ordinary Portland cement CPA-CEMII42.5, fine sand with a maximum size of 5 mm,crushed gravel of size 5 to 25 mm, asuperplasticizer a gent (Glenium 21) and water.Mix proportions are shown in table 1. This mixtureis characterised by a water-cement ratio of 0.56 anda slump of 4 cm.

________________________________________________________________________________Constituents Concrete B11_______________ __________________________

Kg/m3_________________________________________________Portland cement 350Gravel G:12.5/25 784Gravel g:5/12.5 316Sand 772Water 195Superplasticizer 1.3Mass Density 2360________________________________________________________________________________

Table 1. Concrete mixture proportions

2.2 Fracture tests

Three different types of tests were performed inorder to determine the mechanical characteristics ofconcrete. Six cylindrical concrete specimens ofdiameter 16 cm and length 32 cm were used forcompressive and splitting tests. The compressiontests were performed using 300 KN capacityhydraulic testing machine at a loading rate of 0.5MPa/s until failure.

The third kind of tests consisted on three pointsbend size effect experiments on prismaticgeometrically similar notched beams. Threedifferent sizes were used, the depths were D1 =10cm, D2= 20cm, and D3= 40 cm with respectivelengths 35, 70, and 140 cm while the thickness was

kept constant for all the specimens b = 10 cm. Thespan to depth ratio was l/D = 3 for all specimens.One notch of depth 0.15D and thickness 3 mm(same for all dimensions) was performed in eachspecimen by placing a plastic plate at the midpointperpendicular to the long direction of the mouldbefore casting (Fig. 1). Nine prismatic specimenswere cast, three for each size.

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Figure 1. (a) Three point bend experiments on notchedspecimen; (b) Description of the instrumentation of themechanical test

Size effect tests followed the guidelinesestablished by RILEM (1990) using a closed – looptesting machine, (160 KN capacity INSTRONmachine), under crack mouth opening displacement(CMOD) control. A general view of theexperimental set-up is provided in figure 2. Prior tothe test, two steel plates with lips to fit into thenotch were glued on both sides of the notch. Theclip gage used to measure the CMOD was thenplaced between knife edges attached to the steelplates. In order to measure the deflection of acentral point of the beam, a laser extensometer wasused. This extensometer was attached at mid - spanto a steel beam which was fixed to the concretebeam on two supports at half height and at the endsof it. A metallic plate glued on the specimen at midspan and half height reflect the ray emitted by thelaser extensometer and permit to measure thedeflection. Deflection was measured in this way soas not to include the effect of local deformations atthe support and load points. A data acquisitionsystem was used to record the load, the CMOD,and the deflection with time. Figure 3 shows theaverage responses for all dimensions. Curing

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conditions for all specimens were 28 days at 50%RH and controlled temperature of 20° C. Meanvalues of physical and mechanical properties aresummarised in table 2.

Figure 2. general view of experimental fracture test set-up

Figure 3. average load-deflection curves for small (D1), medium(D2) and large (D3) sizes

________________________________________________________________________________Properties Mean values_________________________________________________f '

c (MPa) 41.25f '

t (MPa) 3.48Edyn (MPa) 39000D1 : Fmax (daN) 863.42 σN (MPa) 5.61D2 : Fmax (daN) 1401.13 σN (MPa) 4.42D3 : Fmax (daN) 2377.31 σN (MPa) 4.81Gf (N/m) 180________________________________________________________________________________

Table 2. Physical and mechanical properties of concrete

Another set of three points bending tests wascarried out on beams of size D2:10x20x70 cmwithout notches. These tests were aimed at

determining the maximum load of unotched beamsin order to calibrate the applied load in the creeptests, where beams having the same geometry havebeen used. The average maximum load determinedfrom flexural tests on three specimens is about2409 daN.

2.3 Creep tests

The creep tests were performed on frames designedat R&DO. The aim is to load concrete flexuralbeams with a constant force. The frames have acapacity ranging from 5 to 50 KN and canaccommodate geometrically similar specimens ofthree different sizes. The load is applied by gravitywith a weight and counter-weight system whichenables a fine tuning of the load. Figure 4 shows ageneral view of these creep frames.

Figure 4. general view of creep frames

The specimens tested have the same thickness of10 cm. The smallest D1 is 10 cm high and 35 cmlong. The medium D2 is 20 cm high and 70 cmlong and the largest D3 is 40 cm high and 140 cmlong. Two kinds of creep tests have beenperformed. The first one is intended to study theinfluence of the load level on creep. In the secondkind of test (which is still in progress), theinteraction between creep and fracture of concreteis considered via the associated size effect instructures and the decrease of the fracture energydue to creep. The applied loads in the creep testshave been determined from the previous fracturetests on the same material and the same geometry.

2.3.1 Load level testsIt is expected that visco-elasticity and crack growthinteraction is related to the solicitation level. Thus,under high sustained loads, damage occurs and therole of microcracking on creep evolution isexhibited. It has also been verified that creep in

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compression is significantly affected by the appliedload amplitude. The greater the load level, thelarger the creep strain magnitude.

Twelve prismatic beams were used. For eachcreep test, a different load level has been applied,starting from low levels to very high levels. Theapplied loads are given in table 3._______________________________________Applied load notched beams unotched beams

D1 D2 D2_______________ __________________________ _________________daN daN daN_________________________________________________

36% Fpeak 313 - - 50% Fpeak - - 119860% Fpeak 510 746 144470% Fpeak - - 167880% Fpeak 672 1033 1940________________________________________________________________________________

Table 3. Applied loads in creep tests

The first set consists of 4 unotched beams ofdimension D2 loaded at 50%, 60%, 70% and 80%of the maximum load. These tests are performed at20°C and 50% RH and the specimens are notprotected. Therefore, basic creep and drying creepoccur at the same time. The age of concrete at thebeginning of the creep tests is 28 days. Figure 5presents the total displacement (creep displacementplus instantaneous displacement) measured on thespecimens versus time for the first three loadinglevels. These curves indicate that for all loadinglevels creep kinetics are comparable, with theexception of the specimen loaded at 70% frompeak load, where failure due to tertiary creepoccurs after 8 days. In this test, we observed animportant acceleration of the creep kinetic and thenfailure. Concerning the specimen loaded at 80%from peak load, total failure occured 2 minutesafter applying the load.

Figure 5. Deflection of unotched beams D2 for different loadlevels

The second test series consists of two notchedbeams of dimension D1 loaded at 60 % and 36 %of the maximum load and one notched beam ofdimension D2 loaded at 60% of the maximum load.These tests were followed by a third set consistingof two notched beams of dimension D2 and threenotched beams of dimension D1 loaded at 80% ofthe peak load, one of these beams failed after 4days from loading. Results obtained for this test arenot reported here.

Specimens in the second and third test serieswere protected from desiccation by a double layerof self-adhesive aluminium paper. Hence basiccreep was considered only. The experimentalmeasurement of basic creep of concrete requiresalso that drying shrinkage be prevented. The curingconditions (3 months at 100% RH and 20°C)guaranteed to avoid early age autogeneousshrinkage so that basic creep could be measuredonly. The basic creep displacement was determinedby subtracting the instantaneous elasticdisplacement from the total displacement.

Figure 6 compare the displacements due to basiccreep for the smaller specimens (size D1). It showsthe influence of the load level on the basis creepevolution versus the elapsed time.

Figure 6. Basic creep displacement of notched beams D1 for36% , 60% , and 80% of peak load

As expected, increasing the applied loadincreases the basic creep magnitude. Moreover,creep develops very fast in the first days of loadingand stabilises after a few weeks for the two lowerloading levels. The specimens loaded at 36% and60% of the maximum load were cast from the samebatch. The results show a variation of theamplitude of basic creep of the 36% and 60%loaded specimens, which increases and decreasesagain between 40 days and 50 days of loading.This variation is due to a temperature regulation

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problem, which occurred on the climate controlsystem and which lead to this elevation in themagnitude of deflections measured on loadedspecimens. The specimen loaded at 80% is part ofthe third set of creep tests. It was made fromanother batch and loaded at a different time butfollowed the same curing conditions. For thisspecimen, basic creep increases rapidly. Figure 7shows the creep test results for the beams of sizeD2. These plots exhibit the same trend as those inFig. 6.

Figure 7. Basic creep displacement of notched beams D2 for60% , and 80% of peak load

Figure 8 presents a comparison between basiccreep displacements obtained on two specimens ofsize D1 and D2, both of them loaded at 60% fromtheir corresponding maximum load. These resultsshow that the basic creep kinetic for dimension D2is greater than that of dimension D1.

Figure 8. Basic creep displacement of notched beams D1 andD2 loaded at 60% of peak load

This difference is more obvious in the case of a80% loading level as seen in figure 9. On this plot,we show also the results obtained for the two

specimens of each size subjected to the same creepload. The reproducibility of the test is quitesatisfactory.

Figure 9. Basic creep displacement of notched beams D1 andD2 loaded at 80% of peak load

2.4 Acoustic Emission in basic creep tests

Acoustic emission (AE) occurs when there is asudden change in energy or energy release, due toflaws and defects nucleation or propagation in aspecimen. Most studies have focused on relatingacoustic emission characteristics to the propertiesof the fracture process zone (Maji and Shah 1988),and using AE source location analysis to evaluatedamage localisation (Berthelot et al. 1987). Weapplied this technique to the creep tests presentedabove.

The AE system used was comprised of an eight-channel MISTRAS system manufactured byPhysical Acoustic Corporation. Piezoelectrictransducers (R15/C, resonant frequency of 150KHz) were used. Transducers were placed aroundthe expected location of the process zone, on oneside of the specimen, and in a linear array (Fig. 10).

In the present study, the primary aim is tocorrelate the basic creep evolution and the totalnumber of acoustic events. In other terms, thisstudy is intended to clarify the qualitativerelationship between basic creep strain and damageoccurring inside the material. More accurateanalyses might be performed which includeacoustic event localisation in order to visualise thelocations of damage. Such tests which require alarge number of transducers placed on the samebeam will be performed in future experiments.

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Figure 11 presents the total number of acousticevents versus time and figure 12 shows thecorresponding basic creep evolution occurring atthe same time.

Figure 11. Total number of AE versus time for the 80% basiccreep loaded specimen D2

Figure 12. Deflection due to basic creep of a 80% loadedspecimen D2

We may observe that the number of AE eventsincreases as basic creep develops. The evolution ofthe AE number is almost linear. There is a changeof slope of the curve, which seems to correspond toa small peak in Fig. 12. This peak is due again to aslight defect in the room temperature control.

If one admits that AE events are due tomicrocracking, these results show clearly that thereis a coupling between creep and damage. It followsthat the mechanical responses of beams subjectedto creep compared to those not subjected to creep,ought to exhibit a difference due to initial damageaccumulated during creep loads. A reduction of theresidual carrying capacity due to basic creep has tobe expected in particular.

3 RESIDUAL CAPACITY TESTS

In order to investigate the variation of the residualcapacity due to creep, comparison specimens castat the same time than those subjected to creep werekept under the same conditions of temperature andrelative humidity. Three points bendingexperiments till failure were carried out on thecreep loaded and on the comparison specimens.

The first series of test results deals with unotchedbeams under combined drying and basic creep.After 40 days of loading, beams of dimension D2subjected to loads of 50% and 60% of themaximum load were removed from the creepframes and then immediately subjected to threepoint bending loading up to failure with a constantloading rate.

Figure 13. Residual capacity of unotched beams of dimensionD2

The chosen rate of loading is 0,1µm/s, which isthe same rate used as in the flexural experimentsintended to determine the average maximum loadfor this kind of specimens (see section 2.2). Figure13 displays the load-displacement curves obtainedfor the specimens after creep loading and for theunloaded comparison specimens. The maximumcarrying force of the specimens subjected to creepinitially is reduced of about 20% in comparison to

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Figure 14. Residual capacity of notched beams of dimensionD1

Figure 14 presents the results obtained on threepoints bend experiments carried out after 60 daysof basic creep tests. These are notched specimensof dimension D1 loaded at 36% and 60% of themaximum load. Contrarily to previous results, it isobserved that there is no influence of the 60 days ofbasic creep loading on the residual capacity ofbending beams, when compared to the responseobtained with the comparison specimens. Thedifferences are within the experimental dispersion.

4 DISCUSSION AND CLOSURE

The following conclusions can be drawn from theabove test results:

• For high load level, tertiary creep i.e. a visco-elastic response of the material coupled withan evolution of damage, occurs. In our bendingtests, tertiary creep is observed for load levelsthat are above 60% of the maximum carryingcapacity of the beam measured on initiallyunloaded specimens. This limit is consistentwith other experimental data, namely oncompression tests (Mazzotti and Savoia,2003).

• Basic creep on bending beams seems to be sizedependent. For two geometrically similarspecimens (sizes D1 and D2), the displacementdue to creep is neither equal nor multiplied by

two (which is the ratio between the sizes of thetwo beams).

• AE shows that there is some activity duringthe creep phase. Such an activity shouldcorrespond to the development of microcracks.It is an indication that damage should becoupled to creep.

• Residual capacity tests show that drying creephas a great influence on the residual carryingcapacity of the beams. For the tests presented,which are limited to low creep levels (50% and60% of the maximum load), basic creep doesnot influence the structural strength of thebeam.

These test results have now to be used for thedevelopment of a constitutive relation in whichcreep and damage are coupled. Some proposalsexist in the literature (see for instance Mazzotti etal. 2001, Mazzotti and Savoia 2003, Zi and Bazant2001, Bazant and Jirasek 1992, Omar et al. 2003,Benboudjema et al. 2001), and could be comparedwith the above results as well. Furthermore,additional test data dealing with larger sizes ofspecimen, higher load levels in basic creepexperiments followed by size effect tests areexpected to provide a more comprehensiveunderstanding of the creep damage interaction andof the influence of creep on the fracture energy ofconcrete.

5 ACKNOWLEDGMENTS

Financial support from the European Commissionthrough the MAECENAS project (FIS5-2001-00100) and from the partnership betweenElectricité de France and the R&DO group throughthe MECEN project are gratefully acknowledged.

6 REFERENCES

Bazant Z.P. 1988, Mathematical modeling of creepand shrinkage of concrete , John Wiley & SonsLtd.

Bazant, Z.P. and Jirasek, M. 1992, R-curvemodeling of rate effect in static fracture and itsinterference with size effect, in FractureMechanics of Concrete Structures. Proc. Int.Conf. On Fracture Mechanics of ConcreteStructures. Breckenridge, Colorado, June, ed.by Bazant Z.P., Elsevier Applied Science,London, pp. 918-923.

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Benboudjema F., Meftah F., Sellier A., HeinflingG. et Torrenti J.M. 2001, A basic creep modelfor concrete subjected to multiaxial loads,Fracture Mechanics of Concrete Structures, R.de Borst, J. Mazars, G. Pijaudier-Cabot andJ.G.M. Van Mier Eds., Swets & Zeitlinger,Lisse, The Netherlands, pp. 161-168, 2001.

Berthelot J.M. and Robert J.L., 1987. Modellingconcrete damage by acoustic emission. Journalof Acoustic Emission, 7, pp. 43 – 60.

Gettu, R., Bazant, Z.P. 1992, Rate effects and loadrelaxation: static fracture of concrete. ACIMaterials J. 89 (5), pp. 456-468.

Granger L. Comportement différé du béton dans lesenceintes de centrales nucléaires (analyse etmodélisation) . Thèse de doctorat de l’ENPC,1995.

Maji A.K. and Shah S.P., 1988. Process zone andacoustic emission in concrete. Experimentalmechanics, 28, pp. 27 – 33.

Mazzotti C. and Savoia M., 2003, Nonlinear creepdamage model for concrete under uniaxialcompression, J. Engrg. Mech. ASCE, 129, pp.1065-1075.

Mazzotti C., Savoia M., et Tralli A. 2001, Anisotropic damage model for non linear creepbehavior of concrete in compression, inFracture Mechanics of Concrete Structures, R.de Borst, J. Mazars, G. Pijaudier-Cabot andJ.G.M. Van Mier Eds., Swets & Zeitlinger,Lisse, The Netherlands, pp. 255-262.

Omar M., Pijaudier-Cabot G., and Loukili A. 2003,Etude du couplage endommagement –fissuration, Revue Française de Génie Civil, inpress.

RILEM Draft Recommendations, 1990. Size effectmethod for determining fracture energy andprocess zone size of concrete, 23, pp. 461-465.

Rüsch H. 1957, Versuche zur Bestimmung desEinflusses der Zeit auf Festigkeit andVerformung, (Experimental Determination ofthe effect of the Duration of Loading onStrength and Deformation), Final Report, FifthCongress, International Association for Bridgeand Structural Engineering, Portugal, pp. 237-244.

Rüsch H., Sell R., Rasch C., Stöckl S. 1958,Investigations on the Strength of Concreteunder Sustained Load, RILEM Symposium onthe Influence of Time on the Strength andDeformation of concrete, Munich.

Zi G., Bazant Z.P. 2001, Continuous relaxationrpectrum of concrete creep and its incorporationincorporation into microplane model M4, Proc.CONCREEP-6, F.J. Ulm et al. Eds, ElsevierPubs., pp. 239-243.