influence moisture-change-induced volume changes, namely, dryingshrinkage and swelling of concrete, and quantifiable relationshipsand ways to minimize the volume changes have been developed.

Compared with the extent of research on the drying shrinkage andswelling of concrete, thermal volume changes in concrete have notreceived much attention, even though their importance has been rec-ognized by researchers and practitioners. As a result, there has been nostandardized testing procedure to evaluate the coefficient of thermalexpansion (CTE) of concrete. At this point, the only test method widelyused for CTE measurement is the provisional AASHTO TP60. Thisprocedure was developed a few years ago and is still undergoingreview and revision. Still, this method presents the most sophisti-cated and advanced test method. With this method, a national efforthas been under way to evaluate the CTEs of concrete with differentcoarse aggregates throughout the country and develop a nationaldatabase (1). In the procedure, the CTE is evaluated while the spec-imen is submerged in water. As a result, the concrete is fully saturatedthroughout the testing.

Since the 1950s, it has been recognized that the CTE of cementpaste varies depending on the internal relative humidity (RH). Effortswere made to identify the mechanisms and quantify the relationshipsbetween the CTE of cement paste and RH. The results show signif-icant effects of RH on the CTE of cement paste, with a maximumCTE value of about 70% RH. However, few efforts were made toevaluate the effects of internal RH on the CTE of concrete, which isthe practical material for infrastructure. Field evaluations of RH inconcrete pavement show substantial variations through the slab depth,especially near the surface of the slab. At the same time, concretetemperature variations, daily and seasonal, are greatest near theconcrete surface. If the CTE of concrete varies with RH and is largerat less than 100% RH as in cement paste, concrete near the surfacewill undergo larger thermal volume changes than the concrete belowthe top surface in the slab. Consequently, the environmental stressanalysis in PCC pavement using a CTE value evaluated in accordancewith the AASHTO TP60 might underestimate the stress near thesurface of the concrete slab and result in erroneous pavement design.To evaluate environmental stresses in PCC pavement more accuratelyand develop more reliable pavement designs, it is necessary to identifythe effects of RH in concrete on the CTE and quantify the relationshipbetween them.

OBJECTIVES

There have been several research studies on the effect of RH on cementpaste. The findings from various studies were consistent: (a) the CTEof cement paste varies depending on its RH level, and the maximum

Effect of Relative Humidity on Coefficientof Thermal Expansion of HardenedCement Paste and Concrete

Jung Heum Yeon, Seongcheol Choi, and Moon C. Won

The coefficient of thermal expansion (CTE) of concrete has substantialeffects on the behavior and performance of portland cement concrete(PCC) pavement. The CTE is one of the input variables with signifi-cant effects on PCC pavement performance in the newly developedMechanistic–Empirical Pavement Design Guide. Currently, the mostadvanced and accepted evaluation method for the CTE is the provisionalAASHTO TP60. In this test method, concrete specimens are saturatedbefore and during the testing. It has been recognized that the CTE ofcement paste is influenced by the relative humidity (RH) within thespecimen. Results from previous research studies were nearly consistent:the maximum CTE value occurs at about 70% RH and its value is almosttwice the value at 100% RH. Laboratory evaluations were conducted toquantify the effects of RH on CTEs in cement paste and concrete. In thetesting program, target RH levels within the specimens were 45%, 60%,70%, 80%, and 100%. RH sensors were installed within the specimensduring their preparation. The specimens were fabricated and curedin 23�C (73�F) and 50% RH conditions for 6 weeks. Subsequently, thespecimens were placed in the environmental chamber until the internalRH values reached the target RH levels. Then CTE testing was conductedby changing temperatures while evaluating displacements with externallymounted vibrating wire gauges. The results showed some effects of RHon the CTE of cement paste and concrete, with maximum values at about70% to 80% RH. The effect was larger for cement paste than for concrete.Considering the small effects of RH on the concrete CTE, AASHTO TP60appears to provide adequate CTE values for PCC pavement analysis forenvironmental stresses.

Internal volume changes in concrete due to temperature and moisturevariations (environmental loading) could cause distresses in portlandcement concrete (PCC) pavement such as midslab cracking in jointedconcrete pavement. Volume changes are also responsible for trans-verse and longitudinal cracking in continuously reinforced concretepavement. In recognition of the importance of environmental loadingin the behavior and distress development of PCC pavements, effortshave been made to identify factors involved in volume changes, quan-tify the relationships between those factors and the volume changepotential, and develop ways to minimize the volume change potentialand resulting damage. A number of factors have been identified that

J. H. Yeon and S. Choi, Center for Transportation Research, University of Texasat Austin, Austin, TX 78705. M. C. Won, Department of Civil and EnvironmentalEngineering, Texas Tech University, Lubbock, TX 79409. Corresponding author:S. Choi, chois@mail.utexas.edu.

Transportation Research Record: Journal of the Transportation Research Board,No. 2113, Transportation Research Board of the National Academies, Washington,D.C., 2009, pp. 83–91.DOI: 10.3141/2113-10

83

84 Transportation Research Record 2113

value appears at about 70% RH, and (b) the maximum value is abouttwice as large as the value at 100% RH. However, little informationhas been available regarding the effect of RH on the CTE of concrete.

In this study, a correlation between internal RH and CTE in hard-ened concrete is primarily investigated through laboratory experimentsto ensure advanced practicality and applicability. Along with the test-ing on concrete, parallel testing was conducted on hardened cementpaste with the identical testing scheme.

THEORETICAL BACKGROUND

To discuss how RH could influence the CTE of PCC-based materials,the RH in concrete is discussed first, followed by a description ofthermal volume changes in these materials.

Internal RH is defined as a characteristic value describing themoisture property of the air adjacent to the liquid held in the closedsystem (2). In a closed system, such as pores in concrete, the stateof RH in the pores is primarily dominated by the three independentvariables shown in Equation 1 if all the phases of water in the pores—capillary water, absorbed water, and vapor—are in thermodynamicequilibrium. A relationship among these terms can be expressed bya differential form (3):

where

k = inverse slope of desorption isotherm (∂RH/∂w),w = mass of water (evaporable water plus non-evaporable water),κ = hygrothermic coefficient (∂RH/∂T),T = absolute temperature, and

Hs = drop in RH due to hydration.

The first term on the right side of Equation 1 explains the role ofthe absorption and desorption processes on the RH variation of con-crete. As concrete absorbs water, the available portion of water, whichraises the RH, will increase, whereas the desorption process due toloss of water leads to a decrease in the RH.

The second term, the hygrothermic effect, is concerned with theRH variation due to temperature change. As the temperature varies,the curvature of the meniscus at the interface between the liquidwater and the vapor varies because of the fluid pore pressure change,and this change can lead to a change in the water-molecule-holdingcapacity at the meniscus. This phenomenon can be expressed by acombination of Kelvin’s equation (Equation 2) and Laplace’s equation(Equation 3):

d k dw dT dHsRH = + +κ ( )1

where

γ = surface tension of pore fluid,r = average radius of meniscus curvature,R = universal gas constant,v′ = molar volume of water, andp′ = pore pressure of fluid.

The combined form, the Kelvin–Laplace equation, gives thecorrelation between pore fluid pressure and RH:

The pore fluid pressure is related to the capillary stress, which isconsidered to be one of the primary mechanisms for shrinkage andexpansion of partially saturated porous materials. When negativepressure is developed in the pore fluid because of either temperatureor RH change, the water molecules on the meniscus try to contract.As a counterreaction of this contraction, compression is applied tothe solid particles, which leads to shrinkage in the porous materials.When positive pressure is applied in the pore fluid, the opposite takesplace, resulting in expansion, as shown in Figure 1.

Figure 2 shows the experimental data obtained in this study forthe variation of RH in concrete due to temperature changes. The RHin concrete increases with increased temperature, whereas the reverseRH behavior is obtained in ambient conditions.

The third term in Equation 1 describes the drop in RH due to thehydration of concrete. Because concrete keeps hydrating over time,the water held in the pores is consumed if an external source of wateris no longer available (self-desiccation). This consumption of internalwater generally leads to a decrease in RH.

MECHANISM OF THERMAL DILATION IN CEMENT-BASED MATERIALS

There has been general agreement that three major dilation com-ponents are associated with the mechanism for thermal dilation ofcement-based materials: pure thermal dilation, thermal swelling andshrinkage, and hygrothermic dilation (RH change) (4, 5).

′ =− ( )

′p

RT

v

ln( )

RH4

′ =pr

23

γ( )

22

γr

RT

v=

− ( )′

ln( )

RH

Solid Particle Solid ParticleAbsorbedWater

meniscus

Vapor

Lowtemperature

Hightemperature

FIGURE 1 RH variation due to temperature change.

Yeon, Choi, and Won 85

Pure Thermal Dilation

Typical hydrated cement paste is composed of solid particles andabsorbed water on a layer of solid particles. When subjected to atemperature increase, the original mass immediately tries to expandwith different rates, since each of the components has a differentCTE value. Among them, absorbed water expands more than theother components since the CTE of water is significantly higher thanthat of the other components, up to 70 times higher.

Because of the CTE of the basic constituents, the entire mass of thecement paste undergoes an instantaneous thermal dilation, that is,immediate deformation (ID), which lasts for a short period of time.As soon as this immediate thermal dilation ceases, a time-dependentdelayed deformation (DD) appears as the counterreaction of the rapidthermal dilation by squeezing out the absorbed water from the layersto achieve pressure equilibrium. Because this thermal behavior basi-cally has a symmetric characteristic, the opposite behavior can occureven under the sudden temperature drop, that is, a sudden contractionof water followed by a delayed dilation due to absorption of waterinto the layer from external sources. The amount of the recoverydepends on its hygral state (RH), as shown in Figure 3a.

Thermal Swelling and Shrinkage

Thermal swelling and shrinkage are related to the DD of the material.As the temperature goes up, the chemical potential of the existingabsorbed water tries to go down to achieve equilibrium of the phases.Since the thicker layer of water has a higher chemical potential dif-ference than the thinner layer of absorbed water, more shrinkageoccurs in concrete with a thicker water layer, that is, concrete witha higher RH. The typical response of this component is shown inFigure 3b.

Hygrothermic Dilation (RH Change)

Hygrothermic dilation explains the influence of temperature variationson the volume changes of hydrated cement-based materials on the

basis of the thermodynamics of the pore structure. As temperaturechanges, the vapor pressure at the interface between liquid and gasin the pores also tries to change in order to achieve pressure equilib-rium. The vapor pressure generally becomes higher as temperatureincreases because the decreased curvature of the meniscus causeswater molecules to evaporate readily from the meniscus, wheretensional force is basically being applied. This increased vapor pres-sure increases the RH level and depresses the capillary tension in thesystem as well.

The vapor pressure difference induces a change in capillary tensionof the meniscus, which is responsible for the volume changes of aspecimen. It is recognized that the partially saturated sample showsa larger vapor pressure difference than the fully saturated one under thesame temperature variation. The maximum extent of the hygrothermicmovement typically appears around 70% RH, as seen in Figure 3c.

By combining those thermal dilation components just described, thecurves shown in Figure 4 can be obtained. The curves in Figure 4bshow the displacement of cement-based materials at various RHlevels for the temperature history shown in Figure 4a. As explainedpreviously, the maximum strain appears at around 70% RH becauseof the strong effect of the hygrothermic dilation component.

LABORATORY TESTING PROGRAM

A laboratory testing setup was established that provided accuratetesting results on RH and strain measurements in cement paste andconcrete. A testing plan was developed to encompass the inferencespace for RH that takes place in PCC pavement. A total of five RHlevels at which the CTE would be evaluated, from 45% to 100%,were selected for both concrete and cement paste. Target RH levelsof 100%, 80%, 70%, 60%, and 45% were selected because (a) thecapillary tension of water primarily dominates the hygrothermicbehavior of concrete and cement paste when RH ranges from 45%to 100%; (b) different mechanisms (disjoining pressure and Gibb’sfree energy) govern the hygrothermic behavior below 45% RH, wherethe meniscus is unstable (4); and (c) the RH of concrete in PCCpavement is in the range of 40% to 100%.

55

60

65

70

75

80

85

90

0 2 4 6 8 10 12 14 16 18 20

Time [hrs]

Rel

ativ

e h

um

idit

y [%

]

15

20

25

30

35

40

45

50

55

60

Relative humidity [%]

Temperature [°C]

Tem

per

atu

re [

oC

]

FIGURE 2 Typical response of RH in concrete to temperature change.

86 Transportation Research Record 2113

In general, it is desirable to have as many testing specimens asis feasible to provide information on testing variability. In thistesting program, the space needed in the environmental chamberto accomplish various RH levels was a limiting factor. It wasdecided that two specimens at each RH level would be made forconcrete and cement paste. Consequently, a total of 10 specimenswere fabricated for each cement paste and concrete and immedi-ately sealed with RH gauges embedded. In this experiment, pris-matic beams with dimensions of 62.5 mm (2.5 in.) in width by62.5 mm in height by 500 mm (20 in.) in length were used. Theselection of the prismatic beams was based on the assumption thatthe geometry of the specimen does not affect the testing results as long as the specimen is symmetric. The size of the specimenwas determined in consideration of the time required to establishRH equilibrium within the specimen and the length of the strainmeasurement gauges.

Materials

As described earlier, both PCC and cement paste were selected forthis investigation. Mixture proportions and corresponding materialproperties evaluated are shown in Table 1. Type I/II portland cementwas used with water-to-cement ratios of 0.50 and 0.28 for concreteand cement paste, respectively. The cement content in the concreteis equivalent to 5.5-sack concrete, which is comparable with mostof the Class P concretes used in Texas. Recommended dosages ofchemical admixtures were incorporated in the mixture.

In this experiment, river gravel was used as coarse aggregate forthe concrete, with a maximum size of 19 mm (0.75 in.) and a spe-cific gravity of 2.61. Although the nominal maximum size of coarseaggregate used in Class P concrete in Texas is 37.5 mm (1.5 in.),coarse aggregates with a maximum size of 19 mm (0.75 in.) wereselected in consideration of the size of the specimens (62.5-mm by62.5-mm cross section). Fine aggregate used in this testing was riversand with a fineness modulus of 2.58, specific gravity of 2.60, andabsorption capacity of 0.56%.

The slump and air content of the concrete were 10 cm (4 in.) and4.5%, respectively. The 28-day compressive strength was 36 MPa(5,220 psi), which exceeded 28 MPa (4,000 psi), the requirement forClass P concrete.

RH and Displacement Measurement

To measure the internal RH of hardened concrete and cementpaste, an RH measurement and acquisition system developed at theUniversity of Illinois at Urbana–Champaign was used in the exper-iment (6). This system utilizes a capacitive-type RH measurementsensor, the SHT75. Several different types of RH sensors are available,and the SHT75 was selected for this study because of the following

T0

0

0

t

T

t

(a)

ε

ε

STEP INPUT OF TEMPERATURE

0

ε

RH = 100%

RH = 70%

RH = 0%

RH = 100%

(b)

RH = 70%

RH = 0%

RH = 70%

RH = 0% or RH = 100%

RH = 40% or RH = 85%

t

t

(c)

FIGURE 3 Estimated thermal response of components to stepinput of temperature: (a) pure thermal dilation, (b) thermalshrinkage and swelling, and (c) hygrothermic dilation (RH change) (4).

0

T

RH = 70%

RH = 100%

RH = 40%

RH = 0%

ε

0

t

t

(a)

(b)

FIGURE 4 Estimated thermal response of components to varioushygral states (4).

Yeon, Choi, and Won 87

advantages: small size, which allows embedment at various depths;relatively good accuracy; low cost of the gauges; and the researchteam’s familiarity with and experience in the use of this gauge. Therewas no need to install an additional temperature measurement gaugein the specimens because the SHT75 measures temperatures as well.Even though the SHT75 provides these advantages, it is prone tomalfunction if it is in direct contact with water. This issue wasaddressed by using a porous plastic tube as a semipermeable mem-brane that prevents direct water infiltration into the tube but allowsvapor transmission.

Accurate measurement of specimen displacement during thermalchanges is of the utmost importance because the thermal displace-ments expected in this experiment are quite small. On the basis ofthe review of various displacement gauges and experience, a vibrating-wire strain gauge was selected for this experiment. To install thestrain gauge, 75-mm (3-in.) long rebar-like anchors were vertically

embedded into the fresh concrete during specimen preparation. Afterthe final set of the materials, the strain gauge was mounted to measurethe length change of the specimens.

Experimental Procedures

Molds for the specimens were fabricated in accordance with the designdetails shown in Figure 5. Before the fresh materials were placed intothe molds, all the necessary sensors and accessories (SHT75s andholding anchors) were placed in the molds at the preselected locations.

After the materials were mixed, the fresh materials were pouredinto the molds. Once the finishing was done, the molds were movedto and stored in large airtight plastic containers partially filled withwater, which was to ensure good curing by preventing the loss ofmoisture during the initial curing period. The time of final set was

TABLE 1 Mixture Proportions and Properties of Tested Materials

Concrete Cement PasteMaterial Description (w/c = 0.5) (w/c = 0.28)

Cement (kg/m3) Type I/II 307 1,591

Water (kg/m3) 153.5 445

Coarse aggregate (kg/m3) 19-mm siliceous river gravel 1,096 —

Fine aggregate (kg/m3) River sand 745 —

Chemical admixturesAir-entraining agent (mL/45.36 kg) Daravair AT60 7.4 —Water-reducing admixture (mL/45.36 kg) WRDA 64 89 —

Material propertiesAir (%) 4.5 —Slump (cm) 10 —

NOTE: w/c = water-to-cement ratio, — = not applicable.

Plan view

Cross-sectional view

62.5 mm

62.5 mm

62.5 mm

62.5 mm 312.5 mm

500 mm

50 mm75 mm

SHT75sCrackmeter mounting location

12.5 mm from surface

31.25 mm from surface

FIGURE 5 Design of test specimens.

88 Transportation Research Record 2113

measured to determine when to release the hardened concrete andcement paste specimens from the molds.

As soon as the specimens were released from the molds, they werecompletely sealed with aluminum foil tape without delay to preventdrying and moved to a chamber that maintains 23°C (73°F) and 50%RH. To ensure enough curing time for the specimens before the nextstep, they were stored in the chamber for 6 weeks (Figure 6). Afterthe 6-week curing period, eight specimens were transferred to anenvironmental chamber, where drying of the specimens took place.The other two specimens, whose target RH values were 100%,remained in the chamber for CTE testing later once an equilibriumin RH was achieved.

Because the primary goal of this study was to evaluate the CTEat different RH levels—100%, 80%, 70%, 60%, and 45%—it wasnecessary to dry the specimens to target RH values. Drying of thespecimens to lower RH target levels from 100% could have takensubstantial time if they had been dried in the standard laboratory

environment. To expedite the drying of the specimens, they werestored in an environmental chamber maintaining 32°C (90°F) and20% RH. Since the drying starts from the surface of the specimens,there will be variations in the RH—an RH gradient—within the spec-imens while they undergo continued drying. To evaluate the CTE ata specific RH level, it was important that the RH be uniformly dis-tributed throughout the specimen at the specified value. To examinethe RH variations within the specimens, RH sensors were placed at twodepths, one at 12.5 mm (0.5 in.) and the other at 31.25 mm (1.25 in.)from the surface and continuously monitored. When the average RHvalues at those two depths reached the target values, the specimenswere sealed to achieve the equilibrium of RH within the specimensat 23°C (73°F) and 50% RH environmental conditions. It was con-sidered that the RH equilibrium was achieved when the differencebetween RH values at the two depths was less than 3%.

This RH equilibrium process can be explained by the principle ofmoisture redistribution in the specimen because moisture tends tomove from an area with high moisture content to one with low mois-ture content, which leads to an increase in RH in the drier area (7 ).Figure 7 shows the variations of RH over time at two locations withinthe specimen. The results show that just before the specimen wassealed, there was about 25% difference in RH between the two sensorlocations. After the specimen was sealed, moisture redistribution tookplace, resulting in the overall increase of RH at 12.5 mm (0.5 in.)from the surface and the decrease of RH at 31.25 mm (1.25 in.) fromthe surface (center of the specimen). After 1,200 h of sealing, it appearsthat RH equilibrium was obtained within the specimen. In this testingscheme, because of the way the equilibrium was achieved, the RHvalue at which the CTE was evaluated did not necessarily coincidewith the target values.

Once equilibrium was achieved, the CTE was measured for thetemperature cycle from 23°C (73°F) to 53°C (127°F) in an air circulation environmental chamber (Figure 8). An air circulationchamber was used rather than a water bath as in AASHTO TP60 tominimize the risk of moisture transfer between the specimens andthe surrounding water, which might take place when water is used asthe medium to control the temperature of the specimens as suggested

FIGURE 6 Storage of sealed specimens in chamber.

30

35

40

45

50

55

60

65

70

75

0 200 400 600 800 1000 1200 1400

Time after sealing [hrs]

Rel

ativ

e h

um

idit

y [%

]

RH at 31.25 mm

RH at 12.5 mm

FIGURE 7 Internal RH equilibrium over depth of specimen.

Yeon, Choi, and Won 89

by the current AASHTO TP60, even though they were thoroughlysealed with aluminum foil tape.

RESULTS ANALYSIS AND DISCUSSION

Immediate Deformation Versus Delayed Deformation

Temperature changes cause time-dependent deformations in the massof cement-based materials. This temperature-induced deformationcan be classified into two components: immediate deformation (ID)and delayed deformation (DD). ID can be defined as an instantaneousdeformation of a specimen at the time of a temperature change,whereas DD is a substantial portion of the total deformation thattakes place after the temperature equilibrium throughout a specimenhas been achieved (8).

Because of the complexity of the principles behind thermal dilationcomponents, there has been controversy regarding the definition ofthe CTE of concrete and cement paste. For instance, Sellevold andBjøntegaard (5) suggested that only the ID should be considered inCTE calculation because the DD includes both direct temperaturedeformation and an additional complex time-dependent deformationcaused by moisture diffusion. In order to separate those components,the ID component was separated from the total deformation by usingthe known thermal history and relevant CTE (5). However, Bazant (4)and Grasley et al. (2) suggested that the CTE has to be determined onthe basis of the total deformation components (4, 9).

As can be seen in Figure 9, displacement curves are somewhatdifferent in their basic shapes depending on their hygral state, evenwhen they were tested under the same temperature history. Theremarkable decrease of displacement at 100% RH indicates a sig-nificant effect of pure thermal dilation and thermal shrinkage andswelling components, which coincides with the analytical approachby Bazant (4). In this testing, CTE values were evaluated on thebasis of the full response within a specimen, including both ID andDD, by determining the ultimate displacement after stabilization(as indicated in Figure 9).

Correlation Between Internal RH and CTE

The results of CTE testing on both hardened concrete and cementpaste are shown in Figure 10a and 10b, respectively. CTE values atlower RH levels for cement paste were not obtained as of this writing,since the RH equilibrium was not achieved in those specimens withlower target RH levels. To ensure consistency with the RH valuespresented along the x-axis, the initial RH levels were measured at23°C (73°F).

According to the results, the effect was more pronounced forcement paste than for concrete. Up to 10% to 12% difference in theCTE was observed between maximum and minimum CTE values incement paste, whereas values in concrete were less than 3%. It wasalso observed that the maximum CTE values occurred at around70% to 80% RH. This result is because the maximum capillary pres-

FIGURE 8 CTE testing in environmental chamber.

FIGURE 9 Measured displacement of cement paste at different RH levels.

90 Transportation Research Record 2113

sure is applied at 70% to 80% RH ranges. The difference in the RHeffect on CTEs of cement paste and concrete can be explained bythe insensitive nature of the coarse aggregate CTE to RH variations.

Following the same logic, it is postulated that the sensitivity of themortar CTE to the RH could be between those for cement paste andconcrete. Since mortar has a higher CTE than that of coarse aggre-gate, it could be concluded that internal stresses in concrete dueto temperature variations are much higher at an RH of 70% to 80%.Detailed analysis for microcracking in PCC pavements, such asspalling prediction, might require the inclusion of RH effects onCTEs. However, considering the lesser effect of RH on the CTEof concrete, CTE results from AASHTO TP60 appear to be goodvalues for the macroscopic analysis of PCC pavement behavior,such as curling.

CONCLUSIONS AND RECOMMENDATIONS

The primary objective of this study was to establish a correlationbetween internal RH and CTE in cement paste and hardened con-crete based on laboratory experiments. The results of this study canbe summarized as follows:

1. The CTE of cement paste and concrete depends on the internalRH in those materials. Maximum CTE values are obtained at about70% to 80% RH.

2. For cement paste, maximum CTE values are about 10% to 12%larger than the values at lower RH.

3. There is little difference in the CTEs of concrete at 100% RHand at 70% to 80% (maximum). The difference is about 3%.

(b)

(a)

17.0

17.5

18.0

18.5

19.0

19.5

0 10 20 30 40 50 60 70 80 90 100

Relative humidity [%]

Co

effi

cien

t o

f th

erm

al e

xpan

sio

n [

µε/

°°C]

4.4

4.5

4.6

4.7

4.8

4.9

5.0

5.1

0 10 20 30 40 50 60 70 80 90 100

Relative humidity [%]

Co

effi

cien

t o

f th

erm

al e

xpan

sio

n [

µε/

°°F]

FIGURE 10 Measured CTEs of (a) siliceous river gravel concrete and (b) plain cementpaste at specified RH levels.

2. Grasley, Z. C., D. A. Lange, M. D. D’Ambrosia, and S. Chapa-Villalobos.The Internal Relative Humidity of Concrete: What Does It Mean? ConcreteInternational, 2006, pp. 51–57.

3. Bazant, Z. P., and L. J. Najjar. Nonlinear Water Diffusion in NonsaturatedConcrete. Materials and Structures, Vol. 5, 1972, pp. 3–20.

4. Bazant, Z. P. Delayed Thermal Dilatations of Cement Paste and ConcreteDue to Mass Transport. Nuclear Engineering and Design, Vol. 14, 1970,pp. 308–318.

5. Sellevold, E. J., and Ø. Bjøntegaard. Coefficient of Thermal Expansionof Cement Paste and Concrete: Mechanisms of Moisture Interaction.Materials and Structures, Vol. 39, 2006, pp. 809–815.

6. Grasley, Z. C., and D. A. Lange. A New System for Measuring theInternal Relative Humidity in Concrete. Cementing the Future, Winter2004.

7. Åhs, M. Remote Monitoring and Logging of Relative Humidity in Concrete.Proc., 7th Symposium on Building Physics in Nordic Countries, IcelandicBuilding Research Institute, Reykjavik, 2005, pp. 181–187.

8. Sabri, S., and J. M. Illston. Immediate and Delayed Thermal Expansion ofHardened Cement Paste. Cement and Concrete Research, Vol. 12, 1982,pp. 199–208.

9. Grasley, Z. C., and D. A. Lange. Thermal Dilation and Internal RelativeHumidity of Hardened Cement Paste. Materials and Structures, Vol. 40,2007, pp. 311–317.

The Properties of Concrete Committee sponsored publication of this paper.

Yeon, Choi, and Won 91

4. Detailed analysis for microcracking in PCC pavements, suchas spalling prediction, might require the inclusion of RH effects onCTEs for mortar and concrete.

5. Considering the lesser effect of RH on the CTE of concrete,CTE results from AASHTO TP60 appear to be good values for themacroscopic analysis of PCC pavement behavior, such as curling.

ACKNOWLEDGMENTS

This research study was financially supported by the Texas Depart-ment of Transportation in cooperation with the Federal HighwayAdministration. The authors thank Hua Chen and German Clarosof the Texas Department of Transportation for their support in thisresearch effort.

REFERENCES

1. ARA, Inc., ERES Consultants Division. Guide for Mechanistic–EmpiricalDesign of New and Rehabilitated Pavement Structures. Final report,NCHRP Project 1-37-A. Transportation Research Board of the NationalAcademies, Washington, D.C., 2004. www.trb.org/mepdg/guide.htm.