1

Tensile Basic Creep: Measurements and Behavior at Early Age

Salah A. Altoubat and David A. Lange

Department of Civil Engineering

University of Illinois at Urbana-Champaign

Urbana, IL 61801

ABSTRACT

Creep and shrinkage of concrete under sealed and wet curing conditions have been

investigated to determine the tensile basic creep of concrete during the first days after

casting. The common practice of sealing concrete to measure basic creep was found

inaccurate because internal drying at this age is generally a significant factor. Instead, a

moist cover was placed on the concrete samples to successfully suppress early age

shrinkage. A basic creep model based on solidification theory was implemented to provide

insight on the behavior of plain and fiber reinforced concrete. The results revealed a high

rate of basic tensile creep during the first 20 hours of loading which decreased afterward

and approached a bound limit. More important, the tensile basic creep was found sensitive

to age at loading only within the first few days and age- independent after 5-6 days. Finally,

steel fiber reinforcement lowered the initial rate of tensile basic creep.

Keywords: tensile creep, basic creep, autogenous shrinkage, early age behavior, fiber

reinforcement, steel fiber, young concrete, curing

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Salah A. Altoubat has received his Ph.D in civil engineering from the University of Illinois

at Urbana-Champaign (UIUC) in 2000. He received his MS in structural engineering from

the Jordan University of Science and Technology, Jordan in 1990. Currently he is a post-

doctorate researcher at the Department of Civil and Environmental Engineering at UIUC.

His current research interest includes early age behavior of concrete, creep, shrinkage and

cracking.

ACI Member David A. Lange is an Associate Professor of Civil Engineering at the

University of Illinois at Urbana-Champaign. He received his Ph.D. from Northwestern

University. He is a member of ACI Committees E802, Teaching Methods and Materials;

544, Fiber Reinforced Concrete; 549, Thin Reinforced Cement Products, and serves as

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.

RESEARCH SIGNIFICANCE

Basic creep of concrete during the first days after casting is an important

component of the behavior of young concrete. The behavior is not well understood for

concrete in tension because of the complexity of the material behavior and a lack of

experimental data to support sound theoretical modeling. Creep tests on sealed concrete

and moist-covered concrete were conducted to address the appropriate experimental

conditions for young concrete and to isolate the true basic creep behavior. The results are

3

useful for characterizing tensile basic creep behavior of concrete and establishing models

for young concrete.

INTRODUCTION

Basic creep of concrete is a material property, defined as the creep of concrete

when moisture content remains constant. Mechanisms of basic creep of concrete in

compression have been a matter of research since the turn of the century and a great deal of

understanding has been achieved. However, the behavior in tension has been less often

studied, primarily because the required experiments are considerably more difficult to

execute. In particular, experimental data on tensile basic creep of concrete in the early days

after casting are very scarce in the literature because of the complexity of the material

properties at this age. The complexity arises from the fact that concrete experiences

physical and chemical changes in the early days that make measurement and interpretation

of basic creep difficult. For example, sealing concrete is often used to measure basic creep

[e.g. 1,2,3]. But sealing may not eliminate internal drying that concrete experiences at early

age, and therefore the measured creep of sealed concrete will not be the true basic creep

because it will include interaction with autogenous shrinkage.

In this study, creep tests under sealed and moist-covered conditions were conducted

to quantify the basic creep of concrete in the first days after casting. The sealed test samples

were sealed using a self-adhesive aluminum, while the moist test samples were covered

with moist cloths. Normal plain and steel fiber reinforced concrete mixtures with different

w/c ratios were tested to provide data on tensile basic creep of young concrete. The results

were used to calibrate a basic creep model based on solidification theory [4,5]. The basic

4

creep of early age concrete and the effects of w/c ratio and fiber reinforcement will be

discussed.

EXPERIMENTAL INVESTIGATION

Basic Creep Test

A uniaxial tensile loading device developed originally to test restrained shrinkage

[6] was used to measure basic creep of concrete. The system tests two identical “dog-bone”

samples; one is loaded and the other is free of load. Each sample is 1000 mm long and

76.6x76.6 mm in cross-section. The experiment is controlled by a closed loop system

capable of highly accurate measurements and smooth loading. Reliability of the system and

reproducibility of test results were extensively examined, and satisfactory results were

obtained [6].

Materials and Test Program

This study is a continuation of a previous work that investigated the total tensile

creep in restrained shrinkage tests [7]. In both studies, same materials and mix proportions

of plain concrete (NC) and steel fiber concrete (SF) were used. The constituent materials

were Type I portland cement, crushed limestone aggregates with maximum size of 25.4

mm, and natural sand. The gradation of coarse and fine aggregates satisfied ASTM C33

requirements, and the natural sand had a fineness modulus of 2.2. The steel fibers were

30mm long and 0.4mm in diameter, and were used at a volume fraction of 0.5 %.

The concrete mixtures had a paste volume fraction of 0.35 and w/c ratio of 0.4 and

0.5. No modifications to the concrete proportions were allowed when fibers were included.

The mixture proportions for the tested concrete are presented in Table 1.

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The applied loads in the basic creep tests were determined by restrained drying

shrinkage tests in the previous study [7]. The basic creep and the resolved total tensile

creep under restrained shrinkage stresses can be used to quantify various creep

components. This study focused on the basic creep component. The patterns and

magnitudes of the applied stresses are shown in Figure 1. It should be noted that identical

loads were applied on both plain and fiber reinforced concrete samples for the concrete

mixture with w/c-ratio of 0.5.

A series of creep tests under both sealed and moist-cover conditions were

conducted for the four concrete mixtures considered in this study. The creep test conducted

under the sealed condition was repeated under the moist-cover condition for all concrete

mixtures. Two specimens were cast for each test; one was loaded to measure elastic and

creep strains and the other was free of load to measure free shrinkage. The side molds were

removed off at the age of 12 hours. Both concrete samples were then sealed with self-

adhesive aluminum foil in the sealed test, whereas they were covered with continuously

moist cloths in the moist test. The moist cloths provide a continuous wet surface similar to

the condition achieved in a standard moist curing of concrete. Loads were applied as in

Figure 1 and the computer program recorded measurements every five minutes throughout

the test duration.

RESULTS AND DISCUSSIONS

Sealed Tests

The significance of concrete behavior under sealed conditions lies in its relation to

basic creep and its interaction with shrinkage. The common practice for many years has

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been to assume that shrinkage deformation is effectively prevented by sealing. However,

this study showed that autogenous shrinkage is an important issue for young concrete, even

at w/c ratios as high as 0.5. The sealed concrete samples exhibited significant shrinkage as

shown in Figure 2. The shrinkage strain at the age of 7 days reached 120 and 82

microstrain for the NC-0.4 and NC-0.5 mixtures, respectively. It is well known that

concrete with w/c-ratio less than 0.42 will exhibit shrinkage under sealed conditions

because of internal drying (self-desiccation). However, even the concrete with w/c-ratio of

0.5 exhibited measurable autogenous shrinkage. This result suggests that even partial

drying that removes water from the large capillary pores is capable of generating

substantial drying stress. In addition, chemical shrinkage affiliated with cement hydration

at early age may contribute to the observed deformation. Chemical shrinkage develops

continuously from the point of cement-water contact as a result of the loss of volume due to

hydration (volume of reactions products is smaller than the volume of the reactants).

Clearly, sealing the young concrete will not eliminate the early age shrinkage even for

normal concrete. Consequently, the measured creep under sealed conditions will not be the

basic creep since it includes interaction with autogenous shrinkage.

The measurement of creep and shrinkage of sealed concrete is sensitive to the age

at which sealing is applied. Figure 3 presents results of creep and shrinkage for similar sets

of concrete samples subjected to same load profile (loading starts at age of 27.5 hours) but

sealed at different ages (14 hours and 27 hours). The results reveal variation in the

magnitude of creep and shrinkage between the two sets. The results suggest that sealing the

concrete, particularly at early age, temporarily disturbs its thermodynamic equilibrium with

the environment. Subsequent deformation of concrete is expected to reflect this

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disturbance. The level of disturbance is mainly influenced by the age of concrete and its

moisture content at the onset of sealing. Sealing the concrete increases the internal vapor

pressure and causes reduction of the capillary surface tension, and consequent swelling as

suggested by Kovler [8]. The degree of swelling depends on the internal vapor pressure at

the time of sealing and volume and size of empty pores, both of which are actively

changing in young concrete. This adds one more complication to the measurement and

interpretation of basic creep from sealed tests.

Basic Creep Identification

The experimental measurement of basic creep of concrete requires that drying

shrinkage be prevented, a condition that could not be achieved by sealing the concrete in

this study. A moist curing technique was adopted to suppress early age autogenous

shrinkage so that basic creep could be measured. In this method, the concrete samples were

covered by wet cloths throughout the test duration. Typical results of creep and shrinkage

are shown in Figure 4.

The moist-cover condition successfully suppressed the early age autogenous

shrinkage, which could be attributed to two factors. First, covering the concrete with wet

cloths increases its internal vapor pressure and the concrete swells, which offsets part of the

autogenous shrinkage caused by hydration. Second, extra moisture migrates to the concrete

by capillary transport, which compensates for consumed moisture by continuing hydration.

The relative humidity inside the concrete was measured and found to remain constant when

moist curing was used. The constancy of the measured RH explains, at least in part, the

near-zero shrinkage. Consequently, the measured tensile creep of the concrete under moist-

cover condition is equal to its basic creep because shrinkage was eliminated. In this study,

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the basic creep as a material property was extracted from the tests under moist-cover

conditions. Figures 5 and 6 present results of basic creep for fiber and plain concrete for the

NC-0.5 and NC-0.4 mixtures, respectively.

Effect of Fibers on Basic Creep

The effect of fiber reinforcement on creep can be ascertained from the basic creep

results. The steel fibers tend to reduce the rate of creep in the very early age as shown in

Figures 5 and 6. The lower rate of creep of FRC can be attributed to the fibers controlling

microcracking in the concrete and providing a better load transfer. Concrete generally

exhibits some level of microcracking in the first 12-24 hours. Thus, the fiber concrete

initially suppresses microcracking and engages greater volume of the matrix in stress

transfer. This leads to a more uniform but lower internal stress intensity, which causes the

initial low rate of creep of FRC.

The impact of fibers on creep seems to depend on test conditions. For example,

fibers reduced the initial rate of creep under moist curing conditions whereas, another study

[6] found that fibers did not modify the initial rate of creep under drying conditions. The

explanation may be related to the degree of microcracking develops under different curing

conditions; wet cover reduces microcracking while drying condition promotes surface

microcracking. Different curing conditions seem to invoke different creep mechanisms.

Therefore, it is important to define the test condition when effect of fibers on early age

creep is examined.

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ANALYSIS

This section presents ana lysis of the basic creep data and discusses test results. The

analysis used a basic creep model with aging based on the principles of solidification

theory [4,5] to characterize the basic creep behavior of plain and fiber reinforced concrete

at early age. Numerical analysis based on the principle of superposition was performed, in

which the response to varying stress was considered as the sum of the responses to each

stress taken separately. The outcome provides behavioral information such as the effects of

age at loading and fiber reinforcement on basic creep of concrete at early age.

Review of Basic Creep Model with Aging

Solidification theory considers the creep function of the viscoelastic material to be

age-independent, but recognizes that the volume of this material )(tv is increased with time

[4,5]. This model makes it possible to apply the classical theory of non-aging

viscoelasticity. The model defined the creep strain as the sum of two components:

viscoelastic strain )(tvε& and viscous strain )(tfε& . The creep strain rate of the solid )(tvε& is

expressed as the product of the age- independent strain rate of solid )(tγ& , and the increase

of the volume fraction, )(tv , of the solid:

)()(

))(()( t

tvtF

tv γσ

ε && = 1

where function ))(( tF σ is introduced to reflect nonlinear behavior at high stress. The

viscoelastic microstrain )(tγ is represented by a Kelvin chain model with N Kelvin units.

Each unit consists of a spring with age-independent elastic modulus µE and a dashpot with

age-independent viscosity µη . The solution for this spring-dashpot system is:

10

µ

µµ

τ

µ µ

ητσγ ϖ

Ee

Et tt

N

=−= ′−−

=∑ )1(

1)( /)(

1

2

where µτ is a constant called the retardation time, and must be chosen upfront. The viscous

strain term is:

)()())((

)( 3 ttv

tFqtf σ

σε =& 3

where 3q is an empirical constant that depends on the composition of the concrete.

However, the viscous term can be neglected for tensile creep at early age [6]. The inclusion

of the high stress factor ))(( tF σ did not improve the data fit in this study, and it was also

neglected. Therefore, two main parameters remain to describe the model: v(t) and µE/1 .

For a constant stress, the basic creep strain according to the model can be given as:

[ ])1(...)1()1()(

/)(/)(2

/)(1

21 no

n

oo ttttttcr eAeAeA

tvτττσ

ε −−−−−− −+−+−= 4

where t is the age of concrete, to is the age at loading, and Ai=1/Ei and τi are constants for

the ith unit of the Kelvin chain. The model describes the volume fraction growth as:

αλ

+

=

mo

ttv )(1

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where m and α are empirical constants and oλ is a constant that can be taken as 24 when

the age is expressed in hours [6]. Equation 4 was used as the primary analytical function for

basic creep, and the model parameters were identified from the experimental data by

optimization techniques. In this form, the optimization problem is nonlinear, which

requires iterative methods for solution. Statistics Toolbox built in computational MATLAB

software [9] was used for the optimization.

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Analysis based on principle of superposition

Creep functions at different ages at loading were analytically extracted from the

superposition- based analysis using the model described above. This was achieved by

finding the creep function that resulted in the best fit between analysis and experimental

data. Several choices for retardation times were considered, and reasonable fits were

achieved by using two terms in the exponential series of Equation 4, with retardation times

of 10 hrs and 100 hrs. The function for optimization was reduced to:

[ ])1()1()(

)(1.02

)(01.01

oo ttttcr eAeA

tv−−−− −+−=

σε 6

where )(tv is given by Equation 5. The choice of retardation times covers most of the time

domain relevant to the experiment. The model coefficients are presented in Table 2, and

typical fits of the basic creep data are shown in Figures 7 and 8.

Creep Functions for Plain Concrete

The calibrated model was used to generate specific basic creep functions at

different ages at loading. The functions were generated using Equation 5 for aging and

Equation 6 for creep, and the results are shown in Figures 9 and 10 for the plain concrete

mixtures NC-0.5 and NC-0.4, respectively. The results reveal a high initial rate of tensile

basic creep during the first 10-20 hours of loading. This suggests that a major portion of the

tensile creep of plain concrete occurs during the first 20 hours after loading while the rate

decreases substantially afterward and the creep asymptotically approaches a constant value.

Moreover, the initial rate of creep for plain concrete is not only high, but also sensitive to

the age at loading, particularly in the very early ages; the earlier the age at loading the

higher the initial rate of creep as shown in Figures 9 and 10. This suggests faster tensile

stress relaxation in young concrete.

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However, the sensitivity to age at loading ceases after a few days and the tensile

creep of concrete becomes age-independent afterward. For example, the NC-0.5 mixture

exhibited similar specific creep functions when the age at loading exceeded 96 hours as

shown in Figure 9. Likewise, the NC-0.4 mixture exhibited similar creep behavior when

the age at loading exceeded 72 hours. Apparently, the effect of aging on basic tensile creep

is only substantial in the first few days, and more pronounced in concrete with low w/c-

ratio. In fact, the NC-0.4 mixture exhibited a decrease in the creep at the ages of loading of

24 hours and 27 hours. This decrease in creep of young concrete was due to the strong

effect of aging. A decrease in creep has also been reported in a paper published by

Bournazel and Martineau [10] in which the authors called the decrease in creep as a

maturation creep induced by aging. Experimental results reported by Westman [11] and

Morimoto and Koyanagi [12] support this finding. For example, Westman observed an

unchanged response of compressive creep after the age of 48 hours, and Morimoto and

Koyanagi observed that tensile relaxation of young concrete terminates in a shorter period

than compressive relaxation and the half-relaxation time was not influenced by age at

loading after 3 days.

Unlike compressive creep, the aging of tensile basic creep seems to vanish after a

few days (around 5 days) as revealed by the analysis. It is an interesting feature that may be

useful for designing tensile creep experiments and modeling general behavior of concrete

in tension.

Creep Functions for Fiber Reinforced Concrete

Specific creep functions for the fiber reinforced concrete mixtures SF-0.4 and SF-

0.5 are presented in Figures 11 and 12, respectively. As with plain concrete, a high initial

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rate of creep was seen in the first 20 hours of loading, and the rate was sensitive to age at

loading in the very early age. The age-sensitivity of the creep rate diminishes, and tensile

creep becomes age-independent after a few days. The age-independence was also

illustrated by the effective load-bearing volume growth, which exhibited little change after

6 days as shown in Figure 13. Basic tensile creep becomes age-independent at the age of 5

to 6 days.

Although both the plain concrete and FRC exhibit high initial rate of creep, the

fiber reinforcement alters the creep behavior as shown in Figure 14. The initial creep rate

for fiber reinforced concrete is lower than that for the plain concrete, but the long term

creep of FRC is greater. Therefore, relaxation by creep mechanisms in fiber concrete

continues for a longer time than in plain concrete. This behavior was exhibited by both

FRC mixes, and was more pronounced in the mixture with low w/c ratio. Apparently, the

fiber reinforcement reduces the initial rate of creep but increases the long-term creep. This

behavior is attributed to the ability of fibers to suppress microcracks and to engage greater

volume of the matrix in stress transfer. The control of microcracking leads to a lower and

more uniform internal stress intensity, which lowers the initial creep rate, but the greater

volume of the matrix engaged in stress transfer increases the volume of material subjected

to creep mechanisms, thus increasing potential for the long-term creep.

Effect of Water-Cement Ratio

The effect of w/c-ratio of concrete on tensile creep is seen in Figure 14. The results

revealed higher tensile basic creep in the concrete with lower w/c-ratio. This observation

contradicts the general behavior reported in the literature for mature concrete. Creep is

generally thought to increase as w/c-ratio increases, however the opposite is revealed in this

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study. This suggests that the tensile creep behavior at early age is governed by different

factors than mature concrete.

Although a similar trend was exhibited in both plain and fiber reinforced concrete

mixtures, the FRC seems more sensitive to the w/c- ratio. For example, the results in Figure

14 indicate that the tensile creep at 150 hours of loading increased by 57 % when the w/c-

ratio decreased from 0.5 to 0.4 for FRC, whereas it only increased by 10% for plain

concrete. The higher sensitivity of fiber reinforced concrete to the w/c-ratio is important for

optimal design of fiber concrete to reduce the risk of shrinkage cracking.

SUMMARY AND CONCLUSIONS

This study reveals the complexity of measuring tensile basic creep of young concrete.

The complexity arises from the fact that concrete experiences internal drying. Sealing of

the concrete alone does not eliminate the early age shrinkage, even for normal concrete.

Therefore, the common practice of measuring basic creep from sealed concrete samples is

inaccurate in the early days after casting.

For more accurate measurement of tensile basic creep, the study recommends moist

curing conditions to suppress early age shrinkage. The method successfully eliminates the

shrinkage from the measurement and allows tensile basic creep to be differentiated as a

material property.

The basic creep model based on solidification theory satisfactorily describes the tensile

creep behavior at early age. The model captures the various characteristics of basic tensile

creep and provides valuable information on aging. The tensile basic creep function of

young concrete is characterized by a high initial rate in the first 10-20 hours of loading.

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Thereafter, the rate decreases and the creep function approaches a stable value. This trend

was observed in both plain and fiber reinforced concrete. The subsidence of the creep

function is faster for the plain concrete than for the FRC. The tensile basic creep is very

sensitive to age at loading during the first two days after casting, and becomes age-

independent after a few days. This finding is useful for the characterization of tensile basic

creep and for the design of experiments.

Steel fiber reinforcement alters the rate and magnitude of basic tensile creep at very

early ages. The initial creep rate of plain concrete is higher than that of fiber reinforced

concrete. This suggests that microcracking initially dominates the creep of plain concrete

while it is more suppressed in fiber reinforced concrete. Although, the creep rate of plain

concrete is higher than that of FRC, the creep function of plain concrete stabilizes earlier

than that of FRC, suggesting that FRC provides stress relaxation for a longer period of

time.

ACKNOWLEDGMENT

This research project was supported by the Federal Aviation Administration (FAA) Center

of Excellence (COE) at the University of Illinois and by the National Science Foundation

(CAREER Award # CMS-9623467).

REFERENCES

1 De Schutter G. and Taerwe L., “ Towards a more fundamental non- linear basic creep

model for early age concrete,” Magazine of Concrete Research, Vol. 49, No. 180, 1997,

pp. 195-200.

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2 Bissonnette B. and Pigeon M., “ Tensile creep at early ages of ordinary, silica fume and

fiber reinforced concretes,” Cement and Concrete Research, Vol. 25, No. 5, 1995, pp.

1075-1085.

3 Kovler K., “ A new look at the problem of drying creep of concrete under tension,”

Journal of Materials in Civil Engineering, Vol. 11, No. 1, Feb, 1999, pp. 84-87.

4 Bazant Z. P. and Prasannan S., “ Solidification theory for concrete creep. I:

Formulation,” Journal of Engineering Mechanics, Vol. 115, No. 8, 1989, pp. 1691-

1703.

5 Bazant Z. P. and Prasannan S., “ Solidification theory for concrete creep. II:

Verification and Application,” Journal of Engineering Mechanics, Vol. 115, No. 8,

1989, pp. 1704-1725.

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

concrete,” Ph.D thesis in the Department of Civil Engineering at the Univ. of Illinois at

Urbana-Champaign, 2000.

7 Altoubat S. A. and Lange D. A., “ Creep, shrinkage and cracking of restrained concrete

at early age,” Submitted to ACI Materials

8 Kovler K., “ Why sealed concrete swells,” ACI Materials Journal, Vol. 93, No. 4, 1996,

pp. 334-340.

9 The MathWorks, INC,” MATLAB,” Natick, Massachusetts, 1997.

10 Bournazel, J. P., and Martineau, J. P., “ A laboratory test to analyze creep under tension

of young concrete,” Creep and Shrinkage of Concrete, Proc. of the Fifth International

RILEM Symposium, Z. P. Bazant and I., Carol, ed., E & FN SPON, New York, 1993,

pp. 57-62.

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11 Westman, G., “Basic creep and relaxation of young concrete,” In Thermal Cracking In

Concrete at Early Age, Proceedings of the International RILEM Symposium, Ed. by R.

Springenschmid, Munich, 1994 pp. 87-94.

12 Morimoto, H., and Koyanagi, W., “ Estimation of stress relaxation in concrete at early

ages,” In Thermal Cracking In Concrete at Early Age, Proceedings of the International

RILEM Symposium, Ed. by R. Springenschmid, Munich, 1994 pp. 95-102.

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LIST OF TABLES

Table 1 Proportions of concrete mixes

Table 2 Basic creep model coefficients

Table 1: Proportions of concrete mixtures

Constituents HPC-0.32 NC-0.4 NC-0.5 Coarse Agg. kg/m3 974.1 925.8 925.8 Fine Agg. kg/m3 622.8 741.8 741.8 Cement kg/m3 533.1 480 421.4

Silica fume kg/m3 117.0 ---- ---- Water kg/m3 208.0 192.0 210.7

Superplasticizer ml/m3 954.8 565.1 ---- Fiber Dose: Steel: 39.2 kg/m3, Polypropylene: 4.55 kg/m3

Table 2: Test Program

Drying Test @ RH Concrete Mix 50 % 80 %

Tensile Strength

Additional Tests Combined Curing

NC-0.5 X X X Sealing / Drying SF-0.5 X X Sealing / Drying

Drying / Wetting PP-0.5 X X NC-0.4 X X SF-0.4 X X

HPC-0.32 X X X HSF-0.32 X X

Table 3: Shrinkage stress and age at cracking

Concrete Mix

Stress (MPa) Age (hrs) Direct Tensile Strength (MPa)

Stress/Strength Delay factor

HPC-0.32 1.759 69.5 2.325 0.757 NA HSF-0.32 1.898 100.5 2.465 0.770 1.446 NC-0.4 2.130 144.7 2.649 0.804 NA SF-0.4 2.221 174.8 2.790 0.796 1.208 NC-0.5 1.782 159.5 2.214 0.805 NA SF-0.5 1.767 181.0 2.307 0.766 1.135 PP-0.5 1.887 134.5 2.083 0.906 0.843 HPC: High performance concrete, NC: Normal plain concrete, SF: Steel fiber, HSF: HPC

with steel fiber; PP: Polypropylene fiber, Delay factor = FRC fracture time / PC fracture time

19

LIST OF FIGURES

Figure 1 Profile and magnitude of the applied stresses

Figure 2 Free shrinkage under sealed conditions

Figure 3 Concrete age at the time of sealing influences shrinkage and creep

Figure 4 Creep and shrinkage under sealed and moist-cover conditions

Figure 5 Basic creep for plain and fiber reinforced concrete mixtures (w/c = 0.5)

Figure 6 Basic creep for plain and fiber reinforced concrete mixtures (w/c = 0.4)

Figure 7 Model fit of the basic creep data for the NC-0.5 mixture

Figure 8 Model fit of the basic creep data for the NC-0.4 mixture

Figure 9 Creep function at different ages at loading for the NC-0.5 mixture

Figure 10 Creep function at different ages at loading for the NC-0.4 mixture

Figure 11 Creep function at different ages at loading for the SF-0.5 mixture

Figure 12 Creep function at different ages at loading for the SF-0.4 mixture

Figure 13 Typical age-dependency of the tensile creep function

Figure 14 Effect of fiber reinforcement and w/c ratio on creep function

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Figure 1 General view of the experimental setup

Free Shrinkage

Creep + Shrinkage

Creep

Drying Time

Strain

Recovery cycleThreshold

Figure 2 Schematic diagram of the test mechanism

Free Shrinkage Sample

Restrained Sample

21

-300

-200

-100

0

100

200

0 50 100 150 200

Str

ain

(µm

/ m

)

Age (hrs)

Creep

ShrinkageNC-0.5

NC-0.4HPC-0.32

NC-0.5

NC-0.4HPC-0.32

Figure 3 Shrinkage and creep strains for plain concrete mixtures

-300

-200

-100

0

100

200

0 50 100 150 200

Str

ain

(µm

/ m

)

Age (hrs)

Creep

ShrinkageSF-0.5

SF-0.4

PP-0.5

HSF-0.32

SF-0.5

SF-0.4HSF-0.32

Figure 4 Shrinkage and creep strains for fiber reinforced concrete mixtures

22

0

0.5

1

1.5

2

2.5

0 50 100 150 200

Sh

rin

kag

e S

tres

s (M

Pa)

Age (hrs)

NC-0.5

NC-0.4HPC-0.32

Failure

Figure 5 Shrinkage stress for plain concrete mixtures

0

0.5

1

1.5

2

2.5

0 50 100 150 200

Sh

rin

kag

e S

tres

s (M

Pa)

Age (hrs)

SF-0.5

PP-0.5

SF-0.4

HSF-0.32

Failure

Figure 6 Shrinkage stress for fiber reinforced concrete mixtures

23

-350

-300

-250

-200

-150

-100

-50

0

50

0 50 100 150 200

Fre

e S

hri

nka

ge

(µm

/ m

)

Age (hrs)

HPC-0.32

HSF-0.32PP-0.5

NC-0.5

SF-0.5

Figure 7 Shrinkage strain of plain and fiber reinforced concrete

-250

-200

-150

-100

-50

0

50

0 50 100 150 200

RH = 50 %

RH = 80 %

Fre

e S

hri

nka

ge

(µm

/ m

)

Drying Time (hrs)

Figure 8 Shrinkage strain at different drying conditions

W/C = 0.5

24

0

0.5

1

1.5

0 50 100 150 200

Cre

ep C

oef

fici

ent

Age (hrs)

NC-0.4NC-0.5

HPC-0.32

Figure 9 Creep coefficient for plain concrete mixtures

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 50 100 150 200

Cre

ep /

Sh

rin

kag

e

Age (hrs)

NC-0.4

NC-0.5HPC-0.32

Figure 10 Creep-shrinkage ratio for plain concrete mixtures

25

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 50 100 150 200

SF-0.4SF-0.5PP-0.5HSF-0.32C

reep

/ S

hri

nka

ge

Age (hrs)

Figure 11 Creep-shrinkage ratio for fiber reinforced concrete mixtures

-0.5

0

0.5

1

1.5

2

0 50 100 150 200

NC-dryingSF-dryingNC-initially sealedSF-initially sealed

Sh

rin

kag

e S

tres

s (M

Pa)

Age (hrs)

Sealing period

W/C = 0.5

Figure 12 Effect of initial sealing on stress evolution and shrinkage cracking

26

-250

-200

-150

-100

-50

0

50

100

0 50 100 150 200

Str

ain

(µm

/ m

)

Age (hrs)

Sealing

Creep

Shrinkage

Drying

SF-0.5

SF-0.5

NC-0.5

NC-0.5

Figure 13 Creep and shrinkage under sealing/drying conditions

0

0.5

1

1.5

2

0 30 60 90 120 150 180

Sh

rin

kag

e S

tres

s (M

Pa)

Age (hrs)

Re-DryingDrying

Wetting

W/C = 0.50

Figure 14 Shrinkage stress under drying/wetting conditions

27

-150

-100

-50

0

50

100

0 30 60 90 120 150 180

Str

ain

(µm

/ m

)

Age (hrs)

Re-DryingDrying

Wetting

Creep

Shrinkage

SF-0.5

Figure 15 Creep and shrinkage under drying/wetting conditions

LIST OF SYMBOLS

)(tvε& : Viscoelastic strain rate of the solid

)(tvγ& : Age- independent strain rate of the solidified matter

28

)(tfε& : Viscous strain rate of the solid

)(tcrε : Basic creep strain

)(tν : Load-bearing volume fraction of the solidified matter

)(tσ : Applied stress

))(( tF σ : A stress factor to reflect nonlinearity of creep rate at high stresses

µτ : Retardation time of the µ th Kelvin unit

µη : Viscosity of the µ th dash-pot in the Kelvin chain

µE : Elastic modulus of the µ th spring in the Kelvin chain

t: Age of concrete

to: Age of concrete at loading

3,,, qmo αλ : Constants