This paper demonstrates the difference in the shrinkage behavior ofa sealed concrete that undergoes self-desiccation and an unsealedconcrete that experiences external drying in addition to the self-desiccation. The performance of SRA and LWA depends significantlyon boundary conditions of concrete (i.e., sealed versus unsealed),which must be considered when selecting a shrinkage mitigationstrategy.

This paper has two objectives. One is to provide experimentalmeasurements of the shrinkage performance of a low water-to-cement(w/c) plain mixture, a mixture containing SRA, and a mixture con-taining saturated LWA. These experiments include the measurementof drying shrinkage, weight change, autogenous shrinkage, restrainedshrinkage, and internal relative humidity. The second is to discussthe implications of boundary conditions on shrinkage mitigation strate-gies using experimental measurements and theoretical concepts. Thiswill enable practitioners to determine the most appropriate strategyfor a particular application.

The paper begins with results of experimental measurements. Theyare followed by a theoretical discussion of sealed and unsealed shrink-age behavior and how inclusion of SRA or LWA can influence theshrinkage for each boundary condition.

EXPERIMENTAL MEASUREMENTS FOR SEALEDAND UNSEALED SYSTEMS

Materials

Three mixtures were prepared with a w/c of 0.30: plain mortar(w/c = 0.30); mortar with 5% of the mix water replaced by an SRA[i.e., 2.2 gal SRA/yd3 (w/c = 0.30 + 5% SRA)]; and mortar withapproximately 40% volume of sand replaced by a saturated LWA(w/c = 0.30 + LWA). The cement content was the same for all the mix-tures. In all three mixtures, aggregate content was 55% by volume.Natural river sand with fineness modulus 3.13 was used. The LWAwas rotary kilned expanded shale (manufactured) with a finenessmodulus of 3.10. The 24-h absorption of LWA was measured as10.5% according to ASTM C128.

For all mixtures, ASTM C150 Type I ordinary portland cement wasused with a Blaine fineness of 370 m2/kg and a Bogue phase composi-tion of 56% C3S, 16% C2S, 12% C3A, 7% C4AF, and Na2O equivalentof 0.68%. A high-range water reducer (Glenium 3000 NS) was addedat 6.3 fluid oz per 100 lb of cement for the w/c = 0.30 and w/c = 0.30 +5% SRA mixtures, and at the rate of 9.4 fluid oz per 100 lb of cementfor mortar with lightweight aggregate (w/c = 0.30 + LWA). The

Shrinkage Mitigation Strategies in Cementitious SystemsA Closer Look at Differences in Sealed and Unsealed Behavior

Aleksandra Radlinska, Farshad Rajabipour, Brooks Bucher, Ryan Henkensiefken, Gaurav Sant, and Jason Weiss

59

Shrinkage reducing admixtures (SRAs) and saturated lightweight aggre-gates (LWAs) are increasingly used to reduce shrinkage cracking of con-crete mixtures. While both methods show great potential, to obtain thefull anticipated benefits of either SRA or LWA the boundary conditionsof the concrete element must be carefully considered and understood.Addressed are shrinkage and shrinkage cracking behavior of concretewith sealed and unsealed boundaries. The sealed concrete undergoesself-desiccation, while the unsealed concrete simultaneously experiencesboth self-desiccation and external drying. The research work presentedprovides a theoretical and experimental demonstration of the differencesin the shrinkage behavior of mixtures containing SRA and LWA. Dataare provided from experiments that demonstrate the benefits of SRA andLWA under sealed and unsealed conditions. Theoretical considerationsexplain the influence of boundary conditions on shrinkage and crackingof concrete. This has important implications for selecting an adequateshrinkage mitigation strategy. In addition, it is demonstrated that theexperimental results are consistent with the theoretical predictions.

Shrinkage cracking of concrete has been an increasing concern fortransportation engineers. This has spurred the development of sev-eral strategies to reduce shrinkage in concrete (unpublished report,J. Weiss, Early-Age Cracking: Causes, Measurement, and Mitiga-tion, 2007), including the use of higher aggregate volumes (1), use ofexpansive additives (2), or use of modified cement binders. Recently,two innovative shrinkage mitigation strategies have been developed.One is the use of chemical admixtures [shrinkage reducing admix-tures (SRAs)] that alter the surface tension of concrete’s pore fluid(3, 4). The second is the use of water-saturated porous inclusions[lightweight aggregates (LWAs)] that supply additional water duringhydration and can be used for internal curing (5, 6).

While both methods show great potential, to obtain the completeanticipated benefit of either SRA or LWA the boundary conditionsof the concrete element must be carefully considered and understood.

A. Radlinska, B. Bucher, R. Henkensiefken, G. Sant, and J. Weiss, School of CivilEngineering, Purdue University, 550 Stadium Mall Drive, West Lafayette, IN47907-2051. F. Rajabipour, Department of Civil and Environmental Engineering,University of Hawaii, 2540 Dole Street, Holmes Hall, 383, Honolulu, HI 96822-2303. Corresponding author: J. Weiss, wjweiss@purdue.edu.

Transportation Research Record: Journal of the Transportation Research Board,No. 2070, Transportation Research Board of the National Academies, Washington,D.C., 2008, pp. 59–67.DOI: 10.3141/2070-08

shrinkage reducing admixture was a liquid admixture (TetraguardAS 20). (Any mention of commercial products in the paper is forinformation only; it does not imply recommendation or endorsement.)

Mixing

A mixing procedure in accordance with ASTM C192 was used. Thenormal weight aggregate (natural sand) was incorporated into themixture after oven drying and subsequent cooling. The LWA was firstoven dried, air cooled, and then submerged in water for 24 ± 1 hbefore mixing. The volume of water used to submerge the LWA wasequal to the sum of the volumes of mixing water and water that wouldbe absorbed by the aggregate. The water level remained above the topsurface of the LWA during submersion; however, before mixing,excess water was decanted and used as the mixing water. As such, allof the mixtures should have a very similar w/c and paste porosity.

Experimental Procedures

Measurements of Volumetric Change During First 24 h

The linear autogenous (i.e., sealed) deformation of all the mortarspecimens was measured during the first 24 h using the corrugatedtube protocol (7, 8). The corrugated tube protocol involves the encap-sulation of the fresh mortar (approximately 30 min after water isadded to the mixture) in a corrugated polyethylene tube. The tubehas a length-to-diameter ratio of 400 mm to 30 mm and a higherstiffness in the radial direction than the longitudinal direction. Thisallows the transformation of volumetric deformations into lineardeformations. Two specimens were prepared for each mixture. Thespecimens were then placed in a dilatometer maintained at 23.0 ±1.0°C. The dilatometer was equipped with linear variable differen-tial transformer displacement transducers, with a measuring accuracyof ±5 µm/m. The transducers were interfaced to a PC through Labviewto record length measurements every 5 min.

Measurements of Unrestrained Volumetric Change After 24 h

Free shrinkage was monitored using 75 × 75 × 285-mm prismsaccording to ASTM C157-04, with a slight modification on the areaexposed to drying. Three samples were prepared from each mixturefor each testing condition. The sealed samples were covered withaluminum tape on all sides. The unsealed samples were exposed toa relative humidity of 50% and had all sides sealed, except for twodiametrically opposed faces (75 × 285 mm). Free shrinkage wasmeasured using a comparator. Measurements were begun at 24 husing the strain measured from corrugated tubes as the initial value.

Restrained Shrinkage Measurements

The cracking potential was measured using the restrained ring test,following ASTM C1581-04. Six samples were prepared and moni-tored simultaneously for each testing condition. Before casting,molds were placed in an environmental chamber and were condi-tioned for at least 4 h at a temperature of 23.0°C ± 1.0°C. Each sam-ple was cast in two layers with each layer being vibrated. After

60 Transportation Research Record 2070

casting, all samples were kept sealed for 24 h at constant tempera-ture of 23.0°C ± 1.0°C before they were demolded. Ring specimensthat were exposed to 50% relative humidity (RH) after demoldingwere sealed on the top surface with aluminum tape to limit moistureloss from the outer circumference only (bottom face was sealed bythe ring’s support). Ring specimens that were sealed after demold-ing were covered on the top and the outer circumference with twolayers of aluminum tape. Restrained shrinkage was acquired usingStrain Smart software, and data were collected at 5-min intervals.

Internal Relative Humidity Measurements

To measure change in the internal RH over time, fresh cement pastewas cast in airtight plastic vials. At an age of 12 h, approximately 10 gof cement paste was crushed and placed in a glass vial (diameter25.4 mm and length 50.8 mm) and sealed to prevent moisture loss.The sealed vial was then kept in an environmental chamber at 23.0°C± 0.1°C to maintain thermal equilibrium. A Digitron 2080R temper-ature and RH meter equipped with a Pt-100 temperature sensor anda capacitive RH sensor was used to record RH and temperature datainside the sealed vial at 2-h intervals for a period of 7 days. Beforeand after the measurement period (i.e., from 12 hours to 7 days), cal-ibration of the sensor was carried out using saturated salt solutions(K2SO4, KNO3, KCl, and NaCl) with a known RH in the range of75% to 100% (ASTM E104-02).

EXPERIMENTAL RESULTS

This section describes the results of the tests for sealed and unsealedsystems. For the sealed system, measurements included the internalRH, unrestrained (i.e., free) autogenous deformation, unrestrainedshrinkage, and cracking potential from the restrained ring test. For theunsealed system, measurements included weight (mass) loss, unre-strained total shrinkage, and cracking potential from the restrainedring test.

Sealed Systems

Figure 1 shows the average behavior of two samples from eachmixture under the sealed condition. Figure 1a shows that the cementpaste containing SRA maintained an internal RH approximately 1%higher than the plain cement paste at 7 days. This is consistent withobservations of Bentz et al. (9) and Sant et al. (10). The cement pastecontaining LWA maintained an internal RH approximately 10%higher than that of the plain paste at 7 days. This is consistent withobservations by Geiker et al. (11).

Figure 1b shows the unrestrained length change of each mixture.The data in Figure 1b were determined by combining the corrugatedtube measurements from the first 24 h with the ASTM C157-04 testresults, so that the total autogenous deformation measured from thetime of set could be presented (Figure 1b). The SRA mixture showsshrinkage that was 150 µ� lower than that of plain mixture at 14 days.The LWA mixtures show lower shrinkage, by more than 300 µ�, thana plain system at 14 days. For all mixtures, weight loss was less than0.06%, which means it is essentially negligible, as one would expectfor the sealed system.

Restrained shrinkage measurements (obtained using the restrainedring test) shown in Figure 1c seem to be consistent with free shrink-age and RH measurements. The mixture with LWA maintains a

higher RH humidity and does not shrink significantly in a sealed con-dition. As such, the rings with the LWA show little strain. This wouldimply a very low cracking potential. Similar observations have beenmade by Jensen and Hansen (12). The addition of 5% SRA maintainsa slightly higher RH, reduces autogenous shrinkage (10), and signif-icantly delays the time of cracking compared with what is seen in theplain mixture. Of note is that in the case of mortar containing 5%SRA, the test was terminated at 22 days and cracking was observedfor only 4 out of 6 rings when the test was stopped.

Unsealed Systems

Results of measurements performed on unsealed systems (total shrink-age consisting of autogenous and drying component) are summarizedin Figure 2. As presented in Figure 2a, weight loss is higher for mor-tar with LWA than for plain and SRA mixtures. This can be explainedby the fact that mortar samples with LWA have higher amounts ofwater that can leave the system. The weight change for SRA mortaris slightly lower at 14 days. It should be noted however, that athigher RH (80%), the SRAs lose more water. Previous research hasshown that the final mass loss of SRA mixture is comparable to thatof the plain mixture at 50% RH, but not at higher RH (3).

Radlinska, Rajabipour, Bucher, Henkensiefken, Sant, and Weiss 61

Shrinkage of mortar prisms exposed to an ambient RH of 50% pre-sents a trend similar to those observed in autogenous deformation:the lowest shrinkage is observed in the case of the LWA mortar, whilethe highest one can be noticed for a plain system (Figure 2b). Of note,however, is that these mixtures are not in equilibrium.

The restrained shrinkage measurements (Figure 2c) show thatcracking is observed at later ages for SRA and LWA mixtures thanfor plain mortar. It can be also noticed that not only the times of crack-ing are different, but the magnitude of strains developed is differentas well. For LWA mortar, cracking is observed at a much lower mag-nitude of strain than for the plain mixture. This is due to the tensilestrain capacity of the LWA mixture. The rate of strain development isreduced in the case of the LWA mixture due to a combination ofreduction in shrinkage and reduction in elastic stiffness.

THEORETICAL CONSIDERATIONS FOR SHRINKAGE IN CONCRETE

It is known that concrete shrinks in response to drying, chemicalreaction, or temperature reduction. Shrinkage that occurs in a sealedsystem is due to internal drying (i.e., self-desiccation) and is referredto as autogenous shrinkage. Shrinkage caused by the loss of water

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

84

86

88

90

92

94

96

98

100

Rel

ativ

e H

um

idit

y (%

)

Sealed 0.3_LWA 0.3_5%SRA 0.3_Plain

-600

-500

-400

-300

-200

-100

0

100

Str

ain

(με

)

Ave

rag

e S

trai

n (

με)

Sealed 0.3_LW A 0.3_5%SRA 0.3_Plain

(a)

0 2 4 6 8 10 12 14 Time (Days)

(b)

0 2 4 6 8 10 12 14 16 18 20 22 Age of Specimen (Days)

-80

-60

-40

-20

0

20

0.3_LWA 0.3_5%SRA 0.3_Plain

* Test terminated beforeall the rings cracked

(c)

Sealed

FIGURE 1 Comparison of sealed specimen behavior: (a) relative humidity measurements, (b) free shrinkagemeasurements (zeroed at the time of set), and (c) restrained shrinkage measurements.

to the surrounding environment (i.e., external drying) is consideredas drying shrinkage. It should be noted, however, that the totalshrinkage in unsealed system consists of both external drying andself-desiccation.

Before discussing shrinkage in either sealed or unsealed condi-tion, it should be noted that the shrinkage is a paste property, for themajority of aggregates are essentially volumetrically stable. Pickettdeveloped an equation that relates the shrinkage of concrete (�c)(µm/m) to the shrinkage of cement paste (�p) (µm/m) (13):

where (Vagg) is the volume fraction of aggregates and n is a param-eter that ranges from 1.2 to 1.7, depending on the stiffness of theaggregates and the paste (14, 15). Other equations are also availablethat describe shrinkage of concrete as a function of paste shrinkage(14, 16). The focus of this paper is on shrinkage of cement paste andmortar. As such, strategies used to reduce the shrinkage of the pasteare to result in reduction of concrete shrinkage.

A main driving force behind shrinkage in cement paste is capil-lary tension. Drying (internal or external) causes the formation ofcurved liquid-vapor interfaces (menisci) inside the pores of cement

� �c p V= −( )1 1agg ( )

62 Transportation Research Record 2070

paste. The menisci cause generation of a negative pressure inside thepore fluid (the liquid phase), commonly known as capillary tension(Pcap). Shrinkage of cement paste can be described as a function ofthis capillary tension. An example is illustrated by the Mackenzieequation (17 ), later modified by Bentz et al. (18). Equation 2 showsthe shrinkage of paste (�p) as a function of capillary tension:

where

Pcap = capillary tension in fluid (Pa),S = degree of saturation of cement paste,K = bulk modulus of paste (Pa), andKs = modulus of solid skeleton inside cement paste (Pa).

Internal Drying

Hydration reactions that occur between cement and water result ina reduction in volume of approximately 8% to 9% (19, 20). This

� ps

SP

K K= −⎛

⎝⎜⎞⎠⎟3

1 12cap ( )

0 8 6 4 2 10 12 14 Time (Days)

0 8 6 4 2 10 12 14 Time (Days)

(a) (b)

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

Wei

gh

t C

han

ge

(%)

Unsealed 0.3_LWA 0.3_5%SRA 0.3_Plain

Unsealed 0.3_LWA 0.3_5%SRA 0.3_Plain

Unsealed 0.3_LWA 0.3_5%SRA 0.3_Plain

-600

-500

-400

-300

-200

-100

0

100

Ave

rag

e S

trai

n (

με)

Ave

rag

e S

trai

n (

με)

0 3 2 5 7 9 1 4 6 8 10 11 12 13 14 Age of Specimen (Days)

-80

-60

-40

-20

0

20

(c)

FIGURE 2 Comparison of unsealed specimen behavior (at 50% RH): (a) weight loss, (b) free shrinkagemeasurements (zeroed at the time of set), and (c) restrained shrinkage measurements.

means that the volume of hydration products is smaller than the vol-ume of the reactants. This volume reduction is generally referred toas chemical shrinkage. Chemical shrinkage is of little concern withrespect to cracking before concrete sets, for the fluid nature of thesystem allows the paste to collapse on itself. After setting, however,the structure can no longer collapse completely, resulting in the gen-eration of vapor-filled voids (21). This is shown schematically inFigure 3a.

Formation of this vapor-filled space is referred to as self-desiccation(or internal drying). Self-desiccation occurs in every cement pasteregardless of the w/c ratio. Self-desiccation is particularly problem-atic in the case of low w/c mixtures, especially when finer powdersthat modify porosity (e.g., silica fume) are added. In low w/c mixtures,the size of these vapor-filled voids (i.e., this is equal to the radius ofcurvature of the liquid-vapor interface) would be small, which resultsin a significant shrinkage-inducing capillary tension (Pcap). Later,more details are provided on how the magnitude of capillary tensionthat develops in the pore fluid is inversely proportional to the curvatureradius of the liquid–vapor menisci.

External Drying

For an unsealed specimen that loses moisture externally, liquid–vapormenisci also form; however, in this case, they form at the surface ofconcrete. This is schematically shown in Figure 3b and 3c. Figure 3bshows a hypothetical case in which only external drying occurs (i.e.,internal drying is not considered). Figure 3c shows a more realisticpicture of a cement paste that is unsealed at one surface. In this case,while external drying occurs at the exposed surface, self-desiccationdevelops in the interior of the material. This suggests that while asealed specimen experiences only internal drying (Figure 3a), anunsealed system would simultaneously undergo both internal andexternal drying (Figure 3c).

Formation of liquid–vapor menisci corresponds with a reductionin the internal RH of cement paste. In an unsealed specimen, as mois-ture evaporates from the surface, the radius of the menisci continuesto decrease. This causes the drying front to penetrate into smalleropenings and to gradually recede from the surface toward the inte-rior of the material. The internal RH is proportional to the menisciradius (discussed later in Equation 5) and thus decreases continu-ously as drying progresses. Drying continues until the internal RH ofcement paste reaches equilibrium with the ambient RH.

Radlinska, Rajabipour, Bucher, Henkensiefken, Sant, and Weiss 63

Relationships Between Capillary Pressure, Pore Size, and Relative Humidity

It is well known that formation of the liquid–vapor menisci insidecement paste leads to the generation of a capillary pressure (Pcap)inside the liquid phase of material (i.e., pore solution). The meniscicurvature radius is related to the capillary pressure generatedaccording to the Laplace equation (22):

where

Pcap = capillary pressure,γ = surface tension of pore fluid (N/m),θ = liquid-solid contact angle (rad; assumed to be 0 rad), andr = radius of curvature of the meniscus (m).

The negative sign indicates that the pressure is negative (i.e., liquidis in tension). This capillary tension pulls the pore walls (solid sur-faces) together and causes the volume change observed as shrink-age. At equilibrium, the liquid pressure must be the same throughoutthe system, indicating that the curvature radius of all menisci wouldbe the same.

Capillary pressure can also be related to the RH of cement pasteusing the Kelvin equation (22):

where

R = universal gas constant (8.314 J/mol�K),T = temperature (K),

RH = internal RH, andVm = molar volume of pore solution (≈18 × 10−6 m3/mol).

Equations 3 and 4 can be combined, yielding the Kelvin–Laplaceequation, which correlates the menisci radius and the internal RH:

RH =− ( )⎛

⎝⎜⎞⎠⎟

expcos

( )2

5γ θ

r

V

RTmi

PRT

Vmcap

RH=

( )ln( )4

Prcap = −

( )23

γ θcos( )

liquidsolid vapor

(a) (b) (c)

Drying DryingSealed

FIGURE 3 Illustration of drying mechanisms in sealed and unsealed systems: (a) sealed—onlyinternal drying, (b) only external drying, and (c) unsealed—internal plus external drying.

This equation is graphically illustrated in Figure 4a, which showsthe menisci radius as a function of the internal RH for a fluid in twodifferent cement systems (one that would be similar to a plain pastewith γ = 0.072 N/m and the other similar to a paste containing SRAwith γ = 0.036 N/m). According to Equation 5, an internal RH of100% corresponds with an infinite menisci radius (r = ∞ or flatmenisci). Note that this does not account for the presence of ions inpore solution. The influence of ions can be accounted for usingRaoult’s law (22), but since this is a relatively minor correction, itwill not be done here due to space restriction. As drying progresses,the menisci radius becomes smaller and the internal RH decreasesfrom 100%.

Another important point to note is that the menisci radius is closelyrelated to the size of the water-filled capillary pores that empty (i.e.,dry out). For a liquid–vapor meniscus to penetrate inside (or empty)a water-filled pore, the meniscus radius must be smaller than orequal to the pore radius. This can be seen in Figure 4b, which illus-trates the menisci formation in sealed versus unsealed systems andin materials containing SRA and LWA. In the sealed-plain systemshown in the upper left corner of Figure 4b, the menisci radius is r1,equal to the radius of the largest pore. As such, only the largest pore

64 Transportation Research Record 2070

would empty, while the smaller pores remain saturated. Only afterthe largest pore has emptied and the menisci radius is reduced canthe next largest pore start to become evacuated.

Equations 2 through 6 are used to describe the shrinkage behaviorof plain, SRA, and LWA systems for both sealed and unsealed bound-ary conditions. However, it is first emphasized that these equationsdescribe the fraction of shrinkage induced by capillary tension alone.While at high RH [approximately above 60% for plain paste and 80%for pastes containing 5% SRA (23)], capillary tension is the maindriving force behind shrinkage (23, 24), at lower humidities, othershrinkage mechanisms such as the surface energy of the solid phase(24) and the movement of interlayer water (25) can become significant.The discussions of this paper, however, are limited to the influence ofcapillary tension.

The fundamental features of the SRA and LWA should be men-tioned. Figure 5a shows the surface tension (γ) of water–SRA solutionas a function of SRA concentration for four commercially availableSRAs (type T1 was used in this work). It can be seen that the SRAdrastically reduces the surface tension of the solution. Figure 5billustrates the most salient feature of LWA, a desorption isotherm.To obtain this plot, the LWA was dried at different RHs until equilib-

(a)(b)

Sealed - SRA

Unsealed - Plain Unsealed - SRA

Sealed - LWA

Unsealed - LWA

Sealed - Plain

r1 r1r2

r3 r3r4

0.1 10.01.0 100.0 1000.0Kelvin Radius (nm)

30

40

50

60

70

80

90

100

Rel

ativ

e H

um

idit

y (%

)

γ = 72 x 10-3 N/m(Plain and LW)γ = 36 x 10-3 N/m

(~5% SRA)

FIGURE 4 Menisci radius: (a) illustration of Kelvin–Laplace equation and (b) conceptual illustration ofmenisci formation in sealed and unsealed specimens made of plain, SRA, or LWA concrete.

0 3 6 9 12 15SRA Concentration (%)

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Su

rfac

e T

ensi

on

(N

/m)

SRA T1SRA E1SRA E2SRA E3

50 60 70 80 90 100

Relative Humidity (%)

(a) (b)

0

20

40

60

80

100

% o

f 24

Ho

urs

Ab

sorb

edM

ois

ture

Rem

ain

ing

FIGURE 5 Features of SRA and LWA: (a) surface tension as a function of SRA concentration (27)and (b) desorption characteristic of LWA.

rium was reached. It can be seen that a majority of water is lost at highRH (RH > 96%), implying that the pores are larger than those in thecement paste. The samples are nearly completely dry by 80% RH.

INTERPRETATION OF EXPERIMENTAL RESULTSBASED ON THEORY

The influence of boundary conditions (sealed or unsealed) is dis-cussed for plain mixtures, mixtures containing SRA, and mixturescontaining saturated LWA. A summary of the theoretical shrinkagepredictions and comparison of the shrinkage behavior of plain, SRA,and LWA concretes are provided in Table 1. The following sectionspertain to sealed (autogenous) shrinkage and unsealed (autogenousplus drying) shrinkage.

Sealed Shrinkage

In a sealed specimen, vapor-filled voids form in the interior of cementpaste due to self-desiccation (Figure 3a). Initially, these vapor-filledvoids occupy the largest spaces available (largest water-filled capillarypores) while smaller pores remain saturated. As hydration continues,water is consumed by chemical reactions and as a result, smaller andsmaller water-filled pores are evacuated. Since the menisci radius isgradually decreasing (remember that menisci radius is equal to theradius of the smallest pore evacuated), the capillary tension (Pcap)and shrinkage strain (�p) are increasing with continuous hydration(Equations 2 and 3). Meanwhile, the internal RH of the paste isexpected to decrease as the paste hydrates (Equation 5). This wasobserved experimentally in Figure 1a. Since water is not lost to thesurroundings, the mass loss would be zero.

Shrinkage-reducing admixtures are known to reduce the surfacetension (γ) of the pore fluid (Figure 5a). In a sealed paste containing

Radlinska, Rajabipour, Bucher, Henkensiefken, Sant, and Weiss 65

SRA, vapor-filled voids form in the interior of the paste in a similarfashion as they form in a plain cement paste. In fact, it can be arguedthat the menisci radius (r) would not be influenced by the presenceof SRA (Figure 4b) since the volume of the generated vapor-filledvoids and their curvature radius are controlled by the hydration reac-tions. That is, they are dependent on the degree of hydration that hasbeen measured to be similar in plain and SRA pastes (10). As the pastehydrates, the capillary tension (Pcap) continues to increase (Equation 3);however, since the surface tension (γ) is reduced by the addition ofSRA, the magnitudes of capillary tension (Pcap) and shrinkage strain(�p) would be smaller in the paste containing SRA than in the plainpaste (Figure 1b). This would also result in a smaller reduction in theinternal RH as the paste containing SRA self-desiccates (Equation 5).This is confirmed by experimental results shown in Figure 1a.

Saturated LWAs also reduce the autogenous shrinkage of cementpaste; however, this occurs for a slightly different reason. LWA con-tains water-filled pores (several µm in size) that are much larger thanthe capillary pores inside cement paste (mostly smaller than 1 µm).When the paste begins to self-desiccate, the largest pores (locatedinside LWA) empty first. Only after all the large pores in LWA haveemptied can the capillary pores inside cement paste start to dry out(Figure 4b). As a result, the inclusion of saturated LWA can effec-tively increase the radius of the liquid-vapor menisci (r2 > r1) as thematerial self-desiccates. Consequently, both the capillary tensionand the shrinkage strain would be reduced significantly in compari-son with plain cement paste. This effect can be seen in Figure 1a forinternal RH and Figure 1b for shrinkage strain.

Unsealed Shrinkage

In an unsealed specimen, in addition to internal drying (self-desiccation), moisture is lost to the environment at the exposed sur-face of the specimen. As a result, liquid-vapor menisci form both inthe interior of the material and at its exposed surface. This can beseen in Figure 3c, in which an unsealed specimen experiences simul-taneously both internal drying (Figure 3a) and external drying (Fig-ure 3b). As a result, the total specimen shrinkage can be consideredthe sum of autogenous and external drying shrinkage.

However, these drying mechanisms (internal versus external dry-ing) are not completely independent and in fact they interact with one another. This can be realized by comparing the RH at the surfacewith the humidity of the internal vapor-filled voids. As the systemapproaches equilibrium, the internal RH in all pores (near the surfaceand at the interior) must equilibrate with surrounding environmentand become equal. Thus, external drying not only causes the menisciformation at the surface of the specimen, but it also controls the humid-ity and curvature of the internal vapor-filled voids. In Figure 3c, expo-sure to external drying causes a reduction in the menisci radii of theinternal vapor-filled voids and causes these voids to grow larger bypenetrating further into the surrounding water-filled openings.

The ultimate shrinkage of the unsealed specimen (�p) is a functionof the developed capillary tension (Pcap) and degree of saturation (S) ofthe cement paste (Equation 2). At equilibrium, the capillary tensioncan be calculated using Equation 4 by considering RH to be equalto the ambient RH. Equation 4 presents an important argument, forit suggests that at equilibrium, the capillary tension in unsealed spec-imens is independent of the surface tension of pore fluid (γ). Thismeans that addition of SRA would not alter the capillary tension(Pcap) that develops in an unsealed concrete. Note that this does notnegate Equation 3; as in the case of an unsealed concrete containing

TABLE 1 Change in Shrinkage Parameters in SRA and LWA inComparison with Plain Concrete

SRAConcrete

LWAConcrete

Autogenous Shrinkage

Drying Shrinkagea

Volume of water consumed by hydration

Menisci radius

Capillary pressure

Internal RH

Free shrinkage of paste

Mass loss (evaporation)

Saturation of paste

Menisci radius

Capillary pressure

Internal RH

Ultimate free shrinkage of paste

Ultimate mass loss (evaporation)

Rate of shrinkage prior to equilibrium

NOTES: ↔ ↔ comparable with plain concrete; lower than plain concrete; higher than plain concrete, aParameters reported for drying shrinkage correspond to the equilibrium state.

↔ ↔↔

0 0

↔

↔↔↔

RHambient RHambient

↔↔

SRA, the menisci radius (r) would decrease proportionally withdecreasing surface tension of pore fluid (γ). This is further discussedin the following paragraph. The net effect on the capillary tension(Pcap) is negligible.

Since the ambient RH is the same for plain and SRA mortars, areduction in surface tension (γ) would result in smaller menisciradius (r) based on the Kelvin–Laplace Equation 5. By rewritingEquation 5 in terms of r, it can be seen that for constant RH, themenisci radius (r) is a linear function of the surface tension of porefluid (γ):

This is graphically shown by Figure 4a, in which at an ambientRH of 75%, the menisci radius decreases from 3.6 nm for the plaincement paste to 1.8 nm for the paste containing SRA (note that 3.6 nm/1.8 nm = 72 × 10−3/36 × 10−3 N/m).

A smaller menisci radius suggests that smaller pores would evac-uate in the paste containing SRA (Figure 4b; r4 < r3). As such, whendried to equilibrium, in comparison with the plain paste, the pastecontaining SRA should exhibit a slightly higher mass loss whenexposed to the same ambient humidity. This was in fact observed inprevious work (23), indicating that a higher mass loss is measuredat equilibrium in paste containing SRA at high ambient humidities.Note that the mass loss data shown in Figure 2b for plain and SRAmortars do not correspond to an equilibrium condition. Previousexperiments show that the mass loss from mixtures with SRA sur-passes the mass loss of the plain mixture at higher RH (∼80%), thoughthe weight loss is similar at lower RH (∼50%) (23, 26).

The shrinkage reduction for the SRA mortar in comparison with theplain mortar (Figure 2b) can be attributed to two factors. First, thepresence of SRA reduces the rate of water evaporation from the mor-tar. This is confirmed by a slower mass loss of the SRA mortar in Fig-ure 2a. As a result of this lower drying, the rate of shrinkage would belower. The second factor in the lower shrinkage of the SRA mortar isthat SRA can reduce the ultimate shrinkage of the material. Accord-ing to Equation 2, although the capillary tension (Pcap) is expectedto be similar in both plain and SRA cement pastes, by reducing thedegree of saturation, SRA can reduce the ultimate shrinkage.

Also, it has been suggested that while capillary tension can causesignificant shrinkage in plain mixtures in the relative humidity range60%∼100%, in the SRA mixtures, curved liquid-vapor menisci can-not form below approximately 80% RH (23). Thus, while the plainmixture continues to shrink at RH below 80%, shrinkage in the SRAmixture would be significantly reduced below 80% RH due to theabsence of the curved menisci (23).

The presence of LWA in an unsealed specimen provides extramoisture that would be available for evaporation. As water evapo-rates from the surface of specimen, the moisture inside the LWAstarts to evaporate, keeping the smaller capillary pores of the cementpaste saturated. As the specimen dries, the internal RH; however, itis expected that the RH inside LWA concrete decreases at a slowerrate, since the LWA pores act as water reservoirs and prevent rapidRH reduction. This means that the rate of shrinkage would be smallerin LWA concrete. In short, it takes longer for LWA concrete to cometo equilibrium with its ambient. This is consistent with the results ofFigure 2b showing less shrinkage of the LWA mortar compared withthat of the plain mixture.

While the specimens presented in Figure 2b have not come to equi-librium with their ambient, the theory suggests that when the equilib-

rV

RTm= − ( ) ( )2 6γ θcos

ln( )i

RH

66 Transportation Research Record 2070

rium is reached, the magnitude of capillary pressure (Pcap) that is afunction of the ambient humidity (Equation 4) is not expected to beinfluenced by the presence of LWA. At equilibrium, the ultimateshrinkage strain of LWA concrete (�c) should be comparable with thatof the plain concrete, excluding the effect of LWA on the concretestiffness.

In summary, for unsealed specimens, inclusion of SRA or LWAcan reduce shrinkage and potential of cracking through two differentmechanisms. While SRA reduces both the ultimate shrinkage (bylimiting menisci formation) and the rate of shrinkage (by reducingevaporation rate), LWA reduces shrinkage rate (by providing inter-nal water reservoirs). However, the ultimate shrinkage is expected tobe comparable with that of plain mixtures.

CONCLUSIONS

This paper presented detailed discussion of the shrinkage of cemen-titious materials in a sealed and an unsealed condition. Two shrink-age mitigation strategies, SRA and LWA, were described and thedifference between their mechanisms underlined. A summary of thetheoretical predictions of the change in shrinkage parameters of SRAand LWA concretes are provided in Figure 6.

It can be seen that in the sealed system, the SRA reduces shrink-age by reducing capillary pressure through surface tension reduction,while the LWA reduces shrinkage through providing reservoirs thatprovide additional water and increase the size of the menisci radius.Both the SRA and LWA mixtures have higher internal RH (1% and10%, respectively).

For the unsealed case, at equilibrium, more water is lost from theSRA system than from the plain system at the same environmentalconditions. At lower RH, less shrinkage is observed in SRA systemssince the capillary stress breaks down at approximately 80% RH.The unsealed LWA system loses a large volume of water, resultingin lower rate of shrinkage, although long-term shrinkage is similar.Both SRA and LWA mixtures show reduction in cracking potential.

ACKNOWLEDGMENTS

The authors gratefully acknowledge support received from the Cen-ter for Advanced Cement Based Materials and BASF the ChemicalCompany, as well as material supplied by North East Solite Corpo-ration. This work was conducted in the Materials Characterizationand Simulation Laboratory at Purdue University; as such, the authorsacknowledge the support that has made this laboratory and itsoperation possible.

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The Durability of Concrete Committee sponsored publication of this paper.