Measurement and modeling of concrete tensile creep and shrinkage at early age

AUTHOR NAMES M. D. D’Ambrosia, D. A. Lange, and Z. C. Grasley

TITLE OF PAPER Measurement and Modeling of Concrete Tensile Creep

and Shrinkage at Early Age

PAGE NUMBER 1

Measurement and Modeling of Concrete Tensile Creep and Shrinkage at Early Age

by M. D. D’Ambrosia, D. A. Lange, and Z. C. Grasley Synopsis: Volumetric instability of concrete is a primary cause for early age cracking of concrete pavements and structures. Creep and shrinkage of concrete were studied under restrained conditions and under constant applied load during the first week after casting. Early age behavior was characterized by a uniaxial test that measures shrinkage strain and restrained shrinkage stress. The extent of stress relaxation by tensile creep is determined using simple superposition analysis. The experimental measurements are compared with some current creep and shrinkage models to assess their validity for early age prediction. The B3 model has been previously modified to accommodate early age creep, and this modification was employed in the current study. Test results for normal concrete mixes with different w/c are discussed and compared to model predictions. Comparisons show that the B3 model is accurate when the early age modifications are employed.




PAGE NUMBER 2

Keywords: restrained drying; creep; shrinkage; early age; modeling;




PAGE NUMBER 3

ACI member Matthew D. D'Ambrosia is a PhD candidate at the University of Illinois at Urbana-Champaign. His research interests include early age creep and shrinkage of concrete, early age stress and cracking, high performance concrete, shrinkage reducing admixtures, and self-consolidating concrete. ACI Fellow David A. Lange is an associate professor of civil engineering at the University of Illinois at Urbana-Champaign. He received his PhD from Northwestern University. He is a member of ACI Committees E 802, Teaching Methods and Materials; E 803, Faculty Network Coordinating Committee; 544, Fiber Reinforced Concrete; and 549, Thin Reinforced Cement Products. He has served as the chair of Committee 236, Materials Science of Concrete. His research interests include early age properties of concrete, microstructure of porous materials, water transport in repair and masonry materials, and industrial applications of high-performance cement-based materials. ACI member Zachary C. Grasley is a graduate research assistant at the University of Illinois at Urbana-Champaign. His research interests include internal relative humidity and early age stress development of concrete.

INTRODUCTION Concrete is sensitive to environmental changes, especially during the first few days after casting. Volumetric changes due to drying, temperature, and autogenous shrinkage are often observed. These changes are critical during early ages when the concrete is most vulnerable to cracking. Drying shrinkage and tensile creep are especially important because if concrete is restrained, tensile stress will develop due to shrinkage and may cause cracking. Autogenous shrinkage may be significant at early age, even for normal w/c materials. Tensile creep is beneficial as a stress relaxation mechanism, relieving part of the tensile stress that develops due to shrinkage. These issues complicate the prediction of early age creep and shrinkage behavior. An experiment that provides early age measurements of stress and strain was used for comparison with several prediction models. They were reviewed for their usefulness at early age.

SHRINKAGE AND CREEP TESTING OF CONCRETE A widely accepted method to measure early age concrete behavior in tension is to use a uniaxial test specimen in a frame that is capable of simulating restraint according to the feedback of the test specimen. Paillere et al. developed a system to measure the stress developed due to restrained shrinkage [1]. A uniaxial specimen with dovetail ends was cast into a frame that applied a restraining force




PAGE NUMBER 4

by means of an air pump. The tensile stress generated was then measured with a load cell. The deformation was monitored and the load was applied manually to produce a restrained condition. This test was performed both vertically and horizontally depending on the age of the specimen. It was found that a vertical test was problematic due to the dead load of the specimen. Bloom and Bentur developed a similar system in which a step motor was used to apply the restraining load [2]. Two flared end specimens were measured for simultaneous determination of free shrinkage and stress development. Creep was calculated as the difference in strain accumulation between the two specimens. Kovler further modified this system to include a closed- loop computer control system, and measured deformation with LVDT sensors instead of conventional dial gages [3]. When the load reached a predefined threshold, a restraining force was applied automatically to move the specimen to its original position. Another system developed by Pigeon et al., based on Kovler’s system, measured the stress due to restrained autogenous shrinkage [4]. This system also used a computer controlled loading system. Deformation was measured using a direct current displacement transducer for greater precision. Springenschmid et al. developed the Temperature Stress Testing Machine (TSTM) to measure the tensile stress in concrete due to the heat of hydration [5]. Attached to one end of a uniaxial concrete specimen was an adjustable crosshead. A computer controlled step motor applied a load to control the deformation of the concrete specimen as it reached a threshold of 0.001 mm (0.00004 in). Altoubat developed the system currently in use at the University of Illinois at Urbana-Champaign [6]. It was an improvement over the systems developed previously for several reasons. The 75x75 mm (3x3”) cross-section was large enough to allow tests of concrete with 1” coarse aggregate. The applied load generated using a servo-hydraulic actuator had superior load stability and was capable of high load application. In addition, the revised deformation measurement technique avoided grip-specimen interaction, which caused inaccurate strain measurements in preliminary tests [7].

EXPERIMENTAL METHODS The uniaxial test technique developed by Altoubat allows for simultaneous measurement of free shrinkage and deformation under restrained or constant tensile load [6]. The materials tested in this study were concretes with w/c ratio of 0.50 and 0.40 with the same aggregate type and content and same cement source. The mixture proportions are shown in Table 1. Two companion specimens were cast in a temperature and humidity controlled environmental chamber. The conditions during testing were 23ºC (±0.5º C) and 50% (±5 %) relative humidity. The dimensions of each specimen are given in Figure 1. The steel end grips, which transmit the applied load, remained in place for the duration of the test. Steel formwork was removed from the sides of the specimen at 23 hours. To avoid early load application from evaporative cooling associated with formwork removal, the specimens equilibrated to room conditions for one hour before starting the




PAGE NUMBER 5

measurements. Evaporative cooling may cause significant deformation during early age testing, which can then lead to misinterpretation of test data [6, 8]. A sealed barrier of self-adhesive aluminum foil was used to impose a condition of symmetric drying from only two sides. A rounded transition in specimen geometry minimizes stress concentrations and interactions between the specimen and the end grip. A 20 kN (5 kip) load cell in line with a 90 kN (20 kip) servo-hydraulic actuator controlled the load applied to the specimen. To minimize friction between the specimen and the table surface, a 3mm (1/8”) thick plastic sheet was used. Deformation was measured using an extensometer consisting of a linear variable differential transformer (LVDT) and a steel rod positioned on the top of the concrete specimen for a total gage length of 622.3 mm (24.5 in). Steel brackets with bolts anchored into the concrete specimen supported the measurement assembly. The test measurements began at 24 hrs for this study, but previous work has included successful measurements as early as 10 hours. The unrestrained specimen, shown in Figure 2, was used to measure free shrinkage and not subject to external loading or restraint. The second specimen, shown in Figure 3, was connected to the actuator and tested in a computer controlled closed-loop configuration. This configuration was used to conduct two different tests. First, a constant load test was performed with a stress/strength ratio of 0.4 based on the 1 day measured tensile strength. The second test simulated a restrained load condition (on a different specimen, but with the same equipment). The specimen was allowed to deform within a threshold strain value and then restrained by applying a load to compensate for this deformation once the threshold value was reached. For measuring tensile creep, compressive loads did not compensate for expansion. The applied load was feedback controlled and stopped once the specimen returned to its original length. A threshold value of 0.005 mm (8 µε) was used to simulate restraint. This value was determined experimentally to be the minimum effective value within the limitations of the measuring equipment.

TENSILE CREEP BEHAVIOR Strain measured from the unrestrained specimen was compared to the restrained or constant load specimen to obtain creep deformation. Typical deforma tion data is displayed in Figure 4. The difference in deformation between the unrestrained and the loaded specimen is attributed to creep. The total tensile creep strain is calculated as the difference between the accumulated restrained deformation and the free shrinkage according to

εc = εr - εf,

where εc is the total creep strain, εr is the restrained deformation and εf is unrestrained shrinkage.




PAGE NUMBER 6

Creep strain for the constant load test is initially higher than for the restrained test and then levels off since there is no accumulation of stress. Creep strain from a restrained test will eventually surpass the constant load test as it accumulates stress, sometimes leading to failure of the specimen. A component of this creep strain at high stress can be attributed to microcracking in the material. Figure 5 shows the typical difference in creep strain measurements for a constant stress test and a restrained stress test. The mechanism of creep at early age is highly sensitive to loading age, so as additional load is applied during the restrained test, the additional creep due to increasing restrained load is proportionally less. Therefore, instead of evaluating creep behavior using the magnitude of creep strain, it is common to define the creep coefficient parameter by normalizing the creep strain by the amount of elastic strain at the time of loading according to

el

cr

εε

φ = .

The creep coefficient, φ, applies to constant load creep tests where the elastic strain is measured during initial load application. It has also been applied to restrained creep tests [3, 6] where the creep strain under restrained conditions is normalized with the elastic strain at each load compensation cycle. At early age, the creep coefficient evolves over time and reflects the developing microstructure stiffness, which represents the ability of concrete to relax stresses. Values for early age tensile creep coefficient in the literature are limited, but are typically in the range of 0.3 to 0.5 initially and then increase to 0.5 to 1.5 in the first week after casting.

MODELING OF CONCRETE CREEP AND SHRINKAGE AT EARLY AGE The accurate prediction of early age cracking in concrete is essential for evaluating the durability of concrete structures. Cracking reduces durability by providing a path for water and aggressive ions to penetrate the material and induce corrosion of reinforcing steel. To predict cracking, it is necessary to understand how early age volume changes, such as drying shrinkage, produce stress and how creep mechanisms act to relax part of the stress. Analytical models have been developed that evaluate the creep and shrinkage behavior of concrete. Some current models include ACI 209 and RILEM Draft Recommendation B3 [9, 10]. The experimental data used to construct and validate these models was primarily based on compressive creep results from constant load tests on mature concrete. However, to predict early age cracking in concrete, we should consider tensile creep of early age concrete under restrained conditions. In the following paragraphs, we examine the usefulness of the ACI and B3 models for evaluating early age tensile creep at variable stress levels.




PAGE NUMBER 7

The models for concrete creep and shrinkage developed by ACI 209R-92 consist of empirical equations based on laboratory test data. The creep coefficient is given by

ut vtd

tv Ψ

Ψ

+= ,

where t is the time after loading in days, and d, and Ψ are constants. The parameter vu is the ultimate creep coefficient for a given material. Recommendations are given for each constant, based on standard test conditions. There are recommended modifications to each parameter for deviations from standard conditions. The ACI equation for creep coefficient was applied to a concrete mixture with a w/c of 0.50. Creep, drying shrinkage, compressive and tensile strength, and elastic modulus were measured for this mixture. A comparison between creep strain measurements from a constant load test and the ACI model prediction is shown in Figure 6 using two different values for vu, the ultimate creep coefficient. The lower curve reflects the ACI recommended constants modified for test conditions, and the other uses an ultimate creep coefficient vu of 13.5, which is beyond the recommended range of the parameter. Modifying the ultimate creep coefficient was the only way to fit the ACI equation to the dataset. The other parameters affect the shape of the curve more than the overall magnitude. The prediction fits the experimental data quite well – demonstrating that even early age creep can be modeled with the ACI equation – but only after the vu parameter has been modified beyond a realistic range. This finding confirms the current ACI equation that limits the model use to a minimum loading age of 7 days, which is reasonable for structural loads. For earlier loading ages from deformation due to drying and autogenous shrinkage or temperature change, modifications of some kind are necessary to apply this prediction. The B3 prediction model developed by Bažant et al. [11] is based in part on the solidification theory for concrete creep [12]. Total strain is calculated according to

ε(t) = J(t,t’)σ + εsh(t) + α∆T(t)

where J(t,t’) is the compliance function, t is the age of concrete, and t’ is the age at loading. J(t,t’) can be subdivided further into

J(t,t’) = q1 + Co(t,t’) + Cd(t,t’)

where q1 is the instantaneous compliance, Co(t,t’) is the basic creep component, and Cd(t,t’) is the drying creep component. Co(t,t’) and Cd(t,t’) are given by

Co(t,t’) = q2Q(t,t’) + q3ln[1+(t-t’)n] + q4ln(t/t’)

Cd(t,t’) = q5[exp{-8H(t)} – exp{-8H(t’)}]1/2

where H(t) = 1- (1-h)tanh [(t-to)/τsh],




PAGE NUMBER 8

q1 through q5 are constant parameters, and τsh is the shrinkage half time. H(t) represents the average relative humidity of a cross section as a function of time. The B3 model is attractive for describing early age tensile creep because is it based on real phenomena. However, application of the basic creep portion of this model to experimental results by Østergaard et al. has shown that the unmodified B3 model does not give accurate prediction at loading ages of one day or less [13]. To account for this discrepancy, an additional parameter was proposed in his work to capture very early creep. The additional term was incorporated into parameter q2 according to

−

=6

22 ''

'qt

tqq .

[Note: The new coefficient was originally called q5, but has been renamed q6 here to avoid confusion with the drying creep parameter q5]. The improvement to the model is illustrated in Figure 7, which shows a comparison between experimental data and the model before and after modification. Østergaard considered wet-cured samples and his analysis altered only the basic creep component of the prediction model to produce successful results. The modified B3 (MB3) model was used to predict creep and shrinkage for a concrete mixture with a 0.50 w/c ratio under constant load and drying conditions. The elastic modulus for this material was measured at one and eight days and the intermediate values were approximated using the ACI equation [9]. The model prediction fits adequately to the experimental data, as shown in Figure 8, with the same parameter values used by Østergaard et al. No additional terms were needed to account for drying at early age. Creep behavior of the same concrete mixture tested under restrained drying conditions was compared to MB3, shown in Figure 9. To adapt the MB3 model to a variable stress case, as seen in a restrained test condition, the model was applied incrementally and the stress was increased at each load step. In the restrained test experiments, the elastic modulus was measured at each load step, and these actual measured values of elastic modulus were used in the model. The additional benefit of using the measured elastic modulus is that it incorporates the effect of damage due to microcracking during the test. The same parameter values were used for modeling the restrained case as for the constant load case. The MB3 model was used to analyze the behavior of a concrete mixture with a 0.40 w/c ratio under restrained drying conditions. The model results and experimental data are shown in Figure 10. The values of model parameters were changed according to recommendations to reflect the change in material, but no additional terms were used to describe early age or autogenous shrinkage. The fit of the MB3 prediction model was excellent for this case and for several other materials not shown here. Overall, the model was capable of predicting early age tensile creep when employing only the proposed modification by Østergaard.




PAGE NUMBER 9

Drying shrinkage predictions were made using the original B3 model for the 0.40 and 0.50 w/c concrete mixtures. The results are shown in Figures 11 and 12. The model predicted the drying shrinkage strains with reasonable accuracy for both materials except for a small initial portion of the data, which is related to thermal change. The gap in the curve of 20 to 30 µε corresponds to a difference in temperature of 2-3°C, which was measured during the test. Assuming a typical value of 10 µε/°C for the coefficient of thermal dilation, this accounts for the difference in results. No modifications were needed for the original B3 model to account for drying or autogenous shrinkage in this study. However, it is reasonable to be cautious about applicability of the model to materials with lower w/c ratio beyond the range of the study. Lower w/c ratio materials with high autogenous shrinkage were no considered in the current study.

CONCLUSIONS The study considered constant load and incremental restrained load cases for measurement and modeling of early age tensile creep and shrinkage of concrete. An experimental program measured early age tensile creep and shrinkage. The experimental results were compared to the ACI 209 and B3 prediction models. The following conclusions were drawn: n The ACI 209 model can be fit to early age tensile creep data, but only when the value of vu (ultimate creep coefficient) has been set beyond a realistic range. n The B3 model, modified by Østergaard, was successfully used to model early age tensile creep under both constant load and restrained drying conditions. No additional terms were needed in the model to account for differences in drying at early age, or to account for autogenous shrinkage for the materials considered in this study. n The B3 model predicted early age shrinkage with reasonable accuracy without any changes in its original formulation to account for autogenous shrinkage. However, lower w/c ratio materials should be investigated at early age to verify this conc lusion for materials beyond the range in this study. n A stepwise application of the modified B3 model was used effectively to predict creep under restrained drying conditions at early age.




PAGE NUMBER 10

REFERENCES

1. Paillère, A. M., Buil, M., Serrano, J. J., “Effect of Fiber Addition on the Autogenous Shrinkage of Silica Fume Concrete,” ACI Mat. J., V. 86, No. 2, 139-144, 1989

2. Bloom, R. and Bentur, A., “Free and Restrained Shrinkage of Normal and High

Strength Concretes,” ACI Mat. J, V. 92, No. 2, 211-217, 1995 3. Kovler, K., “Testing System for Determining the Mechanical Behavior of Early

Age Concrete under Restrained and Free Uniaxial Shrinkage,” Materials and Structures, V. 27, 324-330, 1994

4. Pigeon, M., Toma, G., Delagrave, A, Bissonnette, B., Marchand, J., and Prince, J.

C., “Equipment for the Analysis of the Behaviour of Concrete Undere Restrained Shrinkage at Early Ages,” Mag. Con. Res., V. 52, No. 4, Aug., 297-302, 2000

5. Springenschmid, R., Breitenbücher, R., and Mangold, M., “Development of

Thermal Cracking Frame and the Temperature-Stress Testing Machine,” in Thermal Cracking in Concrete at Early Ages, Proceedings of the International RILEM Symposium, Ed. By R. Springenschmid, Munich 1994, 137-144, 1995

6. Altoubat, S. A., “Early age stresses and creep-shrinkage interaction of restrained

concrete”, Ph.D. Thesis, Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 2000

7. Altoubat, S. A. and Lange, D. A. “Grip-specimen Interaction in Uniaxial

Restrained Test,” ACI SP-206, Concrete: Material Science to Application - A Tribute to Surendra P. Shah, 2002

8. K. Kovler, “Shock of evaporative cooling of concrete in hot dry climates”, ACI

Concrete International, V. 10, 65-69, 1995 9. American Concrete Institute (ACI) 209R-92 (Reapproved 1997). Prediction of

Creep Shrinkage and Temperature Effects in Concrete Structures, Farmington Hills, MI

10. RILEM Draft Recommendation, TC 107-GCS Guidelines for the Formulation of

Creep and Shrinkage Prediction Models, “Creep and Shrinkage Prediction Model for Analysis and Design of Concrete Structures – Model B3”, prepared by Bažant, Z. P. and Baweja, S., Materials and Structures, V. 28, 357-365, 1995

11. Bažant, Z. P. and Baweja, S., “Creep and Shrinkage Prediction Model for Analysis

and Design of Concrete Structures – Model B3”, Structural Engineering Report 94-10/603c, Northwestern University, 1994




PAGE NUMBER 11

12. Bažant, Z. P. and Prasannan, S., “Solidification Theory for Concrete Creep I: Formulation and II: Verification and Application,” J. of Eng. Mech. (ASCE), V. 115, No. 8, 1691-1725, 1989

13. Østergaard, L., Lange, D A., Altoubat, S A., Stang, H., “Tensile basic creep of early-age concrete under constant load,” Cement & Concrete Research, V. 31, No. 12, 1895-1899, 2001




PAGE NUMBER 12

Table 1. Concrete mixture proportions

w/c

Material SG 0.40 0.50

Cement (Type I) 3.15 809 710

Coarse Aggregate (SSD) 2.67 1560 1560

Fine Aggregate (SSD) 2.60 1250 1250

Water 1.00 324 355

Type F Superplasticizer 1.20 0.11

Note: Batch weights are lb/yd3 for dry ingredients and water, gal/yd3 for chemical admixtures




PAGE NUMBER 13

Figure 1. Companion specimen diagram




PAGE NUMBER 14

Figure 2. Unrestrained uniaxial test s pecimen




PAGE NUMBER 15

Figure 3. Restrained uniaxial test specimen with servo-hydraulic system




PAGE NUMBER 16

-300

-250

-200

-150

-100

-50

0

50

100

150

200

0 1 2 3 4 5 6 7Time (days)

Str

ain

(µε)

0

1

2

3

4

5

6

7

8

9

10A

pplied Load (kN)

Restrained Specimen

Free Specimen

Load (kN)

Creep

Cumulative Shrinkage + Creep

-300

-250

-200

-150

-100

-50

0

50

100

150

200

0 1 2 3 4 5 6 7Time (days)

Str

ain

(µε)

0

1

2

3

4

5

6

7

8

9

10A

pplied Load (kN)

Restrained Specimen

Free Specimen

Load (kN)

CreepCreep



Free Shrinkage Load

Restrained

Figure 4. Typical restrained test data




PAGE NUMBER 17

Figure 5. Relationship between constant and restrained tensile creep tests




PAGE NUMBER 18

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10Age (days)

Cre

ep S

trai

n (x

10-6

)Control w/c=0.50

ACI 209 - Fit

ACI209 - Original parameters vu = 13.5

vu = 2.35

Figure 6. Prediction of creep strain with ACI 209 equation and different values for vu




PAGE NUMBER 19

Figure 7. B3 creep prediction before (a) and after (b) modification (from Østergaard [13])




PAGE NUMBER 20

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10Age (days)

Cre

ep S

trai

n (x

10-6

)

Control w/c=0.50

ec(t,t') - B3

Figure 8. Prediction of constant load tensile creep with modified B3 for w/c = 0.50

B3 Prediction




PAGE NUMBER 21

0

50

100

150

200

250

300

0 2 4 6 8 10Age (days)

Cre

ep S

train

(x

10-6

)

ec(t,t') - B3

Control w/c=0.50

B3 Prediction

Figure 9. Prediction of restrained tensile creep with modified B3 for w/c = 0.50




PAGE NUMBER 22

0

50

100

150

200

250

300

0 2 4 6 8 10Age (days)

Cre

ep S

trai

n (x

10-6

)

ec(t,t') - B3

Control w/c=0.40

B3 Prediction

Figure 10. Prediction of restrained tensile creep with modified B3 for w/c = 0.40




PAGE NUMBER 23

-350

-300

-250

-200

-150

-100

-50

0

0 2 4 6 8 10Age

Shr

inka

ge S

train

(x1

0-6)

esh(t, to) - B3

Control w/c=0.40

B3 Prediction

(days)

Figure 11. Prediction of drying shrinkage with B3 for w/c = 0.40




PAGE NUMBER 24

-300

-250

-200

-150

-100

-50

0

0 2 4 6 8 10Age

Shr

inka

ge S

trai

n (x

10-6

)esh(t, to) - B3

Control w/c = 0.50

B3 Prediction

(days) Figure 12. Prediction of drying shrinkage with B3 for w/c = 0.50

Measurement and modeling of concrete tensile creep and shrinkage at early age

Documents